United States 

Department of 

Agriculture

Forest Service

Pacific Northwest 

Research Station

General Technical 

Report

PNW-GTR-791

August 2009

Forest Growth and Timber Quality:

Crown Models and Simulation Methods

for Sustainable Forest Management

Proceedings of an International Conference

August 7–10, 2007

Portland, OR
ii

TECHNICAL EDITORS

Dennis P. Dykstra, research forest products technologist, and Robert A. Monserud, 

research forester (retired), U.S. Department of Agriculture, Forest Service, Forestry 

Sciences Laboratory, 620 SW Main St., Suite 400, Portland, OR 97205.

The Forest Service of the U.S. Department of Agriculture is dedicated to the principle of multiple use management of the Nation’s forest resources for sustained yields of wood, water, forage, 

wildlife, and recreation. Through forestry research, cooperation with the States and private forest 

owners, and management of the National Forests and National Grasslands, it strives—as directed 

by Congress—to provide increasingly greater service to a growing Nation. 

The U.S. Department of Agriculture (USDA) prohibits discrimination in all its programs and 

activities on the basis of race, color, national origin, age, disability, and where applicable, sex, 

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who require alternative means for communication of program information (Braille, large print, 

audiotape, etc.) should contact USDA’s TARGET Center at (202) 720-2600 (voice and TDD). To 

file a complaint of discrimination, write USDA, Director, Office of Civil Rights, 1400 Independence Avenue, SW, Washington, DC 20250-9410 or call (800) 795-3272 (voice) or (202) 720-

6382 (TDD). USDA is an equal opportunity provider and employer. 

DISCLAIMERS

Papers and abstracts were provided by the authors in final form and have been edited 

only for grammar and for consistency of form and structure. Authors are solely responsible for the content and accuracy of their papers. Opinions expressed do not necessarily 

reflect the position of the U.S. Department of Agriculture.

The use of trade or firm names is for information only and does not imply endorsement 

by the U.S. Department of Agriculture of any product or service.

CREDITS

Graphic design, typesetting, and layout: Adrianna Sutton, Portland, OR; adrianna_

sutton@yahoo.com

Copy editing and proofreading: Judy Mikowski, PNW Research Station, Portland, OR

Cover design: Dennis P. Dykstra, PNW Research Station, Portland, OR

Cover photos: Clockwise from upper left: Mt. St. Helens volcano, Washington, USA; 

young Douglas-fir plantation, Oregon, USA; upper stem and crown of a Douglas-fir tree, 

Oregon, USA; stem and crown of a large dipterocarp tree, Sabah, Malaysia; harvester 

working in lodgepole pine, Washington, USA; lumber produced at a small-log sawmill, 

Washington, USA. All photos by Dennis P. Dykstra.
iii

Forest Growth and Timber Quality:

Crown Models and Simulation Methods 

for Sustainable Forest Management

Proceedings of an International Conference

Dennis P. Dykstra and Robert A. Monserud, Technical Editors

Portland, OR, USA, August 7–10, 2007

Sponsored by:

USDA Forest Service, Pacific Northwest Research Station, Portland, Oregon

Human and Natural Resource Interactions program

Focused Science Delivery program

International Union of Forest Research Organizations (IUFRO), Vienna, Austria

Research Group 4.01.05—Processed-Based Models for Predicting Forest Growth and Timber Quality

Division 3—Forest Operations

Division 4—Forest Assessment, Modeling, and Management

Division 5—Forest Products

Research Group 5.12.00—Sustainable Utilization of Forest Products

United States Department of Agriculture

Forest Service

Pacific Northwest Research Station

Portland, Oregon

General Technical Report PNW-GTR-791

August 2009
iv

ABSTRACT

Dykstra, Dennis P.; Monserud, Robert A., tech. eds. 2009. Forest growth and timber quality: 

crown models and simulation methods for sustainable forest management. Proceedings of an 

international conference. Gen. Tech. Rep. PNW-GTR-791. Portland, OR: U.S. Department of 

Agriculture, Forest Service, Pacific Northwest Research Station. 267 p.

The purpose of the international conference from which these proceedings are drawn was to 

explore relationships between forest management activities and timber quality. Sessions were 

organized to explore models and simulation methodologies that contribute to an understanding 

of tree development over time and the ways that management and harvesting activities can 

influence the quality of timber products recovered from those trees. Five keynote addresses, 

29 plenary presentations, and 16 poster presentations covered the full breadth of forest growth 

and timber quality issues related to forest management. These proceedings comprise 19 papers 

based on presentations and posters, plus 28 abstracts for presentations whose authors chose 

not to write full papers. In addition, the proceedings include abstracts and slides from the 

presentations prepared by three keynote speakers who elected not to write papers for the proceedings. The conference was attended by 75 participants from 19 countries who represented 

universities, private companies, and government research institutes.

KEYWORDS: forest management, forest operations, process models, hybrid models, 

mechanistic crown models, simulation, sustainable forest management, wood quality

ACKNOWLEDGMENTS

The members of the scientific committee for the international conference from which these 

proceedings are drawn deserve special recognition for their efforts in making the event and this 

publication a success: Annikki Mäkelä, University of Helsinki, Finland; Hubert Hasenauer,

University of Natural Resources and Applied Life Sciences, Vienna, Austria; Douglas Maguire, Oregon State University, Corvallis, Oregon, USA; Tony Zhang, FPInnovations-Forintek, 

Vancouver, BC, Canada; Valerie Lemay, University of British Columbia, Vancouver, BC, 

Canada; Christine Todoroki, Scion Research, Rotorua, New Zealand; Shongming Huang,

Alberta Sustainable Resource Development, Edmonton, AB, Canada; Dennis Dykstra, Robert 

Monserud, and Robert Deal, Forestry Sciences Laboratory, Portland, Oregon, USA.

Richard Zabel, Western Forestry and Conservation Association, Portland, Oregon, USA, 

served as registrar, arranged for the conference hotel and meeting facilities, and facilitated the 

entire conference, including single-handedly providing a buffet luncheon for two busloads of 

participants and their guests during the field excursion to the Mt. St. Helens volcano.

Coffee breaks during the conference were sponsored by Relaskop-Technik gmbH, Salzburg, 

Austria.

Bob Tokarcyzk, retired supervisor of the Gifford Pinchot National Forest, and Jim Rombach, 

retired forest engineer from Weyerhaeuser Company, led a remarkable excursion to Mt. St. 

Helens. They provided their personal insights from the 1980 eruption when they were each 

responsible for large areas of forest in the vicinity of the volcano. Richard Ford, Director 

of Weyerhaeuser’s Forest Learning Center at Mt. St. Helens, also addressed the participants 

during the excursion.

The Discovery Museum of the World Forestry Center in Portland provided a fitting location 

for the conference banquet.
v

CONTENTS

Mechanistic Crown Models

1 Keynote: Why Mechanisms Should Be in the Eye of the Beholder: 

Notes from the Overground 

Douglas A. Maguire

15 Predicting Wood and Branch Properties of Norway Spruce as a Part of 

a Stand Growth Simulation System 

Harri Mäkinen, Annikki Mäkelä, Jari Hynynen

23 Models on Branch Characteristics of Wide-Spaced Douglas-fir

Sebastian Hein, Aaron R. Weiskittel, Ulrich Kohnle

35 Radiata Pine Crown Development: Model, Model Performance, and 

Incorporation into Forest Inventory 

Jennifer C. Grace

37 Modeling Crown Recession in Three Conifer Species of the Northern 

Rocky Mountains 

Sean M. Garber, Robert A. Monserud, Douglas A. Maguire

38 Analysis of Within- and Between-crown Variability for Mechanistic 

Crown Models 

H. Temesgen, A.R. Weiskittel, D.A. Maguire, D.S. Wilson

39 The Effects of Including a Model of Crown Shyness for Lodgepole Pine 

(Pinus contorta var. latifolia [Engl.] Critch.) in a Spatially Explicit Crown Growth Model 

James W. Goudie, Kenneth R. Polsson, Peter K. Ott

Hybrid Modeling Approaches

43 Keynote: Hybrid Models of Forest Stand Growth and Production

Annikki Mäkelä

48 Is There a Niche for Hybrid Models?

Margarida Tomé, José Tomé, Paula Soares

49 Development of a Hybrid Model for Intensively Managed Douglas-fir in the Pacific Northwest

Aaron R. Weiskittel, Douglas A. Maguire, Robert A. Monserud

69 Estimating Natural Regeneration in Stands Following Attack by Mountain Pine Beetle Using a 

Linked-Model Approach

Derek F. Sattler, Valerie LeMay, Peter Marshall
vi

78 Effects of Silvicultural Treatments on Wood and Tracheid Properties, and Economic Returns 

of Norway Spruce

Tianjian Cao, Lauri Valsta, Sanna Härkönen, Annikki Mäkelä

79 Simulating Daily Xylem Development in Eucalypts Using Outputs from the Process-Based 

Model CABALA

David M. Drew, Geoffrey M. Downes, Jenny Read, Michael Battaglia

81 Incorporating an Index of Root Zone Water Balance Into an Existing Growth and Yield Model 

CanSPBL(1.2)

Guy Pinjuv, Euan G. Mason, Michael Watt

99 Increased Self-Shading With Tree Size and Increased Wood Density with Diameter Explain 

Some of the Observed Size-Related Decline in Forest Productivity

Remko A. Duursma and Annikki Mäkelä

Forest Operations and Timber Quality

103 Keynote: Influence of Forest Operations on Timber Quality

Dennis P. Dykstra

109 Predicting Branch Diameter of Thinned and Fertilized Coastal US Douglas-fir Plantations at the 

Mean and Individual Tree Levels

David Briggs, Rapeepan Kantavichai, Eric Turnblom

110 Automatic Timber Quality Determination Using Wood Property Models and Harvester 

Measurements

John D. Arlinger, Lennart Moberg, Johan J. Möller, Lars Wilhelmsson

111 Capturing Additional Value Through In-Forest Measurement of Internal Log Properties

Glen Murphy

112 Using the Results from Thinning and Fertilizer Interaction Models in Combination with WoodQuality Studies to Maximize Commercial Benefit in South Australia Radiata Pine Plantations

Jim O’Hehir and Jan Rombouts

113 Further Progress in the Development of Prediction Models for Growth and Wood Quality of 

Plantation-Grown Pinus patula Sawtimber in South Africa

Heyns Kotze and Francois Malan

125 Developments to the Sylvan Stand Structure Model to Describe Wood-Quality Changes in 

Southern Bottomland Hardwood Forests Because of Forest Management

David R. Larsen and Ian R. Scott
vii

Modeling Wood Quality

135 Keynote: Modeling Wood Quality in the Context of Forest Management

S.Y. (Tony) Zhang

145 Resource Inventory for Conversion Modeling

Graeme Palmer and Jerry Vanclay

151 Maximizing Benefits from Oval Logs Using Geometric Modeling with Finite Precision

Christine L. Todoroki, Robert A. Monserud, Dean L. Parry

157 Predicting Lumber Grade and By-Product Yields for Standing Scots Pine Trees

Henna T. Lyhykäinen, Harri Mäkinen, Annikki Mäkelä, Arto Usenius

167 Integrating a Wood-Quality Module with a Growth Simulator to Quantify Silvicultural Scenarios 

in Jack Pine Plantations (Are We Making the Right Choices?)

Robert Schneider, Frank Berninger, S.Y. (Tony) Zhang, Chhun-Huor Ung

169 Optimizing Wood Quality and Stand Diversity in Uneven-Aged Forest Management

Jingjing Liang, Joseph Buongiorno, Robert A. Monserud

Simulation in Sustainable Forest Management

177 Keynote: Tools for Sustainable Forest Management

Hubert Hasenauer and Stephan A. Pietsch

187 Reconstruction of Stand Structure and Growth Following Partial Cutting of Southeast Alaska 

Forests: Sustainable Forest Management or Highgrading?

Robert L. Deal

195 Combining Tree- and Stand-Level Models: A New Prediction System to Improve Growth Prediction in Norway Spruce (Picea abies) 

C. Yue, U. Kohnle, S. Hein

197 The Use of Airborne LiDAR Data to Estimate the Relationship Between Crown Surface Area and 

Stem Surface Area of Chamaecyparis obtusa Stands

Tohru Nakajima, Yasumasa Hirata, Naoyuki Furuya, Katsutoshi Takezoe, Makoto Suzuki, 

Satoshi Tatsuhara, Norihiko Shiraishi

205 Evaluation of an Ecosystem-Based Approach to Mixed-Wood Modeling

B. Seely, C. Hawkins, J.A. Blanco, C. Welham, J.P. Kimmins

211 Assessing Forest Productivity: Satellite versus Terrestrial Data-Driven Estimates in Austria

Richard Petritsch, Céline Boisvenue, Steve Running, Hubert Hasenauer
viii

Poster Presentations

219 The Simulation of Allelopathy in Ecosystem-Level Forest Models: A Study Case in the Pacific 

Northwest

Juan A. Blanco and J.P. (Hamish) Kimmins

224 Simulation of Density Effects on Tree Growth and Stem Form in Plantation Forests Using 

a Stand Growth Model

Yukihiro Chiba

225 Analyzing High-Resolution Stem Growth Data and Re-Mapping Wood Property Data onto 

Time-Axes Using a Database Management System

David M. Drew, Derek Hohls, Geoffrey M. Downes

226 Crown Shape Dynamics in Managed Stands of Pedunculate Oak (Quercus robur L.) and 

Common Hornbeam (Carpinus betulus L.)

Tomislav Dubravac, Stjepan Dekanic ́, Valentin Roth

227 Growth Performance of a Hill Dipterocarps Forest Five Years after Harvesting at Angsi Forest 

Reserve, Negeri Sembilan, Malaysia

Frisco Nobilly (presented by Kamziah Abd Kudus)

228 Effects of Management on Timber Production and Carbon Stocks in a Boreal Forest Ecosystem 

Under Changing Climate: A Model-Based Approach

Jordi Garcia-Gonzalo

231 A Standardized Measure of Goodness-of-Fit for Forest Projection Models Involving Repeated 

Measurements

Shongming Huang

250 Simulation Model of a Hill Dipterocarps Forest Five Years After Harvesting at Angsi Forest 

Reserve, Negeri Sembilan, Malaysia

Kamziah Abd Kudus and Frisco Nobilly

251 Timber Properties of Norway Spruce Predicted by RetroSTEM

Anu Kantola, Sanna Härkönen, Harri Mäkinen, Annikki Mäkelä

252 Modeling the Distribution of Foliar Biomass for Pinus contorta var. latifolia in Interior 

British Columbia

Roberta Parish, James W. Goudie, Lin Ju

253 Working Plan: A Tool for Forest and Wildlife Management with Special Attention to Impacts on 

Habitat and Timber Quality in the Teak Forests of Central India

Ajit K. Shrivastava
ix

263 Impact of Land Use and Climatic Changes on Pulpwood and Carbon Sequestration Sustainability 

at the Landscape Level

Paula Soares, José Loff, Paulo Borges, Ana Rodrigues, Susete Marques, Luís Fontes, José Guilherme Borges, 

Margarida Tomé

264 Estimating Future Carbon Sequestration at National/Regional Level Using National Forest 

Inventory Data: The Impact of Data Aggregation

Margarida Tomé, Susana Barreiro, Joana A. Paulo, Paula Soares, José Tomé

265 Modeling Branch Growth and Mortality to Silvicultural Treatments in Coastal Douglas-fir 

Plantations: Implications for Predicting Tree Growth

Aaron Weiskittel, Doug Maguire, Robert A. Monserud

266 Urban Tree Crown Condition Training and Evaluation Tools

Matthew F. Winn, Neil A. Clark, Philip A. Araman, Sang-Mook Lee

267 Digital Picture Tree Crown Evaluation Software

Matthew F. Winn, Sang-Mook Lee, Philip A. Araman

Mechanistic 

Crown Models

FOREST GROWTH AND TIMBER QUALITY

1

Mechanistic Crown Models

Keynote Presentation

Why Mechanisms Should Be in the Eye of the Beholder: 

Notes from the Overground

Douglas A. Maguire

ABSTRACT

ECOSYSTEMS CAN BE MODELED AT MANY 

different hierarchical levels. The phenomenon 

being simulated has a context represented by the 

next higher level of ecosystem organization, as well as 

driving mechanisms represented by the next lower level of 

ecosystem organization. In this sense, the level at which 

mechanisms are represented in models of tree crowns 

depends on the crown attributes or processes to be simulated. Crown models are reviewed and classified by their 

attribute resolution and the specific mechanisms driving 

the crown system to future states. Ecophysiological models 

fix carbon through photosynthesis and typically allocate 

this photosynthate to branches and foliage. Allometric 

models grow trees in height, diameter, and often crown 

size, retrieving structural attributes of the crown from 

allometric relationships between bole dimensions, branch 

size and location, and foliage amount. Architectural models 

simulate the two- or three-dimensional structure of the 

crown, sometimes by proliferation of individual modules 

comprising the crown. Intended applications of the model 

dictate the appropriate resolution in time and space and, 

therefore, the most appropriate and efficient mechanisms. 

Difficulties often arise when models are developed to meet 

more than one objective, particularly when the objectives 

entail several levels of organization.

Editors’ note: The author elected not to provide a full paper 

for these proceedings because it was being submitted to a refereed journal. As with all of the keynote addresses, this presentation was designed to provide context for the related presentations that follow. In lieu of the keynote paper, the author’s slides 

from the presentation are reproduced on the following pages to 

introduce the topic for this section of the proceedings. 

Douglas A. Maguire (doug.maguire@oregonstate.edu) is a professor of silviculture, Forest Science Department, Oregon State University, Corvallis, 

OR 97331, USA.

This presentation was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 1–13.
FOREST GROWTH AND TIMBER QUALITY

2

Mechanistic crown models

Objectives:

(1) Provide a setting for the six papers of this 

session by looking somewhat comprehensively 

at d l t th t crown models, or at the crown component f o

forest simulation models

(2) Suggest the aspects of crown models that best Suggest the aspects of crown models that best

address the theme of this meeting

Mechanistic crown models

• The issue of mechanisms

• Model types

• Model objectives and context Model objectives and context

• Crown models for linking environment 

and silviculture to wood quantity and and silviculture to wood quantity and

quality

• Kl d d i Kludges and parsimony

What makes a crown model “mechanistic”?

1) Str ct ral elements Structural elements comprising comprising the cro n? the crown?

Crown length? Crown length and 

crown width crown width?

Forest Growth and Timber Quality: 

Crown Models and Simulation Methods for 

Sustainable Forest Management

Session 1: Mechanistic Crown Models

Why mechanisms should be in the

Session 1: Mechanistic Crown Models

Why mechanisms should be in the

eye of the beholder:

Notes from the overground

Doug g Ma uire

Department of Forest Science 

Oregon State University
FOREST GROWTH AND TIMBER QUALITY



Crown length and 

crown width and

biomass?

First-order

(primar ) (primary)

branches?

Branches of all 

orders ith orders with

detailed spatial 

information?

Spatial structure 

of all branches of all branches

and leaves, or all 

structural

modules?

What makes a crown model “mechanistic”?

1) Structural elements comprising crown? Structural elements comprising crown?

2) Processes creating a given crown structure?

Mechanisms

Processes

Branching rules in architectural models (Fisher and 

Honda 1977)

Branch growth resulting from ecophysiological Branch growth resulting from ecophysiological

processes (Ford et al. 1990)

Crown expansion as a response to aerial growing 

space or light (Mitchell 1975)

Crown expansion to maintain allometric balance 

with a given diameter and heig g ( y ght growth (Wykoff et 

al. 1982; Hann et al. 2003)
FOREST GROWTH AND TIMBER QUALITY

4

Mechanistic crown models

• The issue of mechanisms

• Model types

• Model objectives and context Model objectives and context

• Crown models for linking environment 

and silviculture to wood quantity and and silviculture to wood quantity and

quality

• Kl d d i Kludges and parsimony

Historical models addressing 

crown dynamics at some level crown dynamics at some level

Architectural / morphological models

Ecosystem dynamics models

Ecopy g h siological models (p ) “ rocess”)

Allometric models (empirical, theoretical)

Morphological – architectural models (botanical context)

Tree = Branching structure

Sometimes main stem 

and branches have 

secondary thickening

Mechanisms

Processes

Mechanisms

Processes

Morphology/architecture

New buds, elementary units New buds, elementary units 

Foliage production, senescence 

Ecophysiology

Light interception 

Net photosynthesis 

Transpiration 

Respiration 

Carbon allocation

Allometric

Bole and branch growth

What makes a crown model “mechanistic”?

1) Structural elements comprising crown? Structural elements comprising crown?

2) Processes creating a given crown structure?

3) Processes resulting from crown structure?
FOREST GROWTH AND TIMBER QUALITY

5

Allometric models (timber production context)

Tree = a volume of bolewood

Sometimes the tree has 

annoyg g in appendages

like branches, foliage, 

and even roots

Ecosystem models (production ecology context)

Trees = bins of biomass 1-yr 2-yr 3-yr 4+yr

Foliage

Branchwood

Bolewood

Stem

Bark

Coarse Fine

roots roots

Sometimes trees are Roots Sometimes trees are

broken into components 

at a finer resolution 

Ecophysiological models (environmental effects context)

Tree = physiologically 

meaningful compartments meaningful compartments

1-yr

leaves

2-yr

leaves

3-yr

leaves

4+-yr

leaves

Branch

sapwood

leaves

Branch

heart wood

leaves leaves leaves

Bole

sapwood

Bole

heart wood

C bi Phloem

Coarse Fine

Cambium Phloem

roots roots

Ecophysiological models (environmental effects context)

Tree = physiologically 

meaningful compartments

Leaf area density (m2m-3)

meaningful compartments

1-yr

leaves

2-yr

leaves

3-yr

leaves

4+-yr

leaves

Branch

sapwood

leaves

Branch

heart wood

leaves leaves leaves

Sometimes spatial distribution

Bole

sapwood

Bole

heart wood

C bi Phloem Sometimes spatial distribution

of foliage is represented to 

improve simulation of light 

i t ti

Coarse Fine

Cambium Phloem

roots roots interception

Architectural rules

1-yr 

leaves

2-yr 

leaves

3-yr 

leaves

4+-yr 

leaves

Structuralfunctional models

Branch

sapwood

leaves

Branch

heart wood

Bole

sapwood

Bole 

heart wood

Cambium Phloem

leaves leaves leaves

Physiological functions 

driving crown dynamics 

and/or driven by crown 

Coarse t t roots

Fine

roots structure

“Hybrid” models

Crown allometric 

relationships

?

Foliage

Stem

Foliage and branch 

senescence/turnover

Roots

Allometric models (silvicultural context)
FOREST GROWTH AND TIMBER QUALITY



Architectural model:

The normal growth program that determines the 

successive architectural phases of a plant 

d i d f d di t b d b l derived from a seed, undisturbed by unusual or 

severe extrinsic forces (such as pruning, 

defoliation injury) and excluding reiterations defoliation, injury), and excluding reiterations.

The visible morphological expression of the 

genotype at any one time is the architecture a genotype at any one time is the architecture, a

static concept distinguished from the dynamic 

concept of the architectural model concept of the architectural model

Crown architecture & morphology

White (1979) The plant as a metapopulation White (1979) The plant as a metapopulation.

Review of primarily descriptive studies of plant architecture, but 

includes reference to: includes reference to:

Hallé, Oldeman, Tomlinson. (1978). Tropical trees 

andf t ores s – A hit t l l i An architectural analysis:

24 architectural models defined by:

(1) The life span of meristems (determinate or 

indeterminate) and

(2) The differentiation of meristems (sexual or vegetative; 

giving rise to erect or horizontal axes; functioning 

episodically or continuously). episodically or continuously).

Only primary (extension) growth is considered.

Inherited tree models (Hallé and Oldeman 1970) Crown architecture & morphology on the 

basis of elementary units or modules

• Braun (1853): “Our feelings aroused by the 

sight of the most ramified plant-stocks, 

especially by a tree . . . excite the 

presentiment that this is not one single being .

. . comparable with the animal or human 

individual, but rather a world of united 

individuals which have sprung from each 

other in a succession of generations . . . "

Phytonism and modules

The phyton is "the segment 

of the axis which subtends 

a leaf initial and surrounds 

its leaf trace as it 

develops.”

The conceptualized phyton or unit of 

shoot growth in the grass 

Alstroemeria and their 

arrangement in a stem segment 

(Priestley et al. 1935)

Arber (1930): "the phyton theory 

seems to me to belong gp to that group

of over-ingenious, academic 

conceptions which are difficult to conceptions which are difficult to

discuss because they bear so little 

rel ti t lit ” lation to reality”
FOREST GROWTH AND TIMBER QUALITY

7

If a mathematical process or rule If a mathematical process or rule

set produces the right 

morphology does it matter if the morphology, does it matter if the

process or rules have a physical 

count t? erpart?

branching rule set A

branching rule set B crown shape

real branching pattern

crown shape

White notes that attempts at White notes that attempts at

modeling branching structure have 

yielded unrealistic results, with 

some more promii d s ng and

sophisticated approaches “now” 

being explored by :

Cannell (1974)

Combe et al (1974) Combe et al. (1974)

deReffye (1976)

Fisher and Honda (1977) Fisher and Honda (1977) Fisher (1992)

Approaches:

Architectural – morphological models

(1) Branching rules with respect to number 

of buds,g , g angle of buds, longitudinal

extension of buds (Fisher and Honda 

1977)

(2) L-system or Lindenmayer systems 

(Prusinkiewicz and Lindenmayer 1990)

(3) Fractals based on parameters from real 

trees (Chen et al. 1991)

Architectural – morphological models

First computer simulations were:

(1)Deterministic

(2)Invariant in parameters

(3)Stationary (rules of branching remain 

constant throughout crown)

Kellomäki and Kurttio (1991) A model for the 

structural development of a Scots pine crown structural development of a Scots pine crown

based on modular growth.

In the future development of the structural 

model, the influence of the prevailing model, the influence of the prevailing

conditions should be included in such a 

way that the branching principles 

presented in this study provide the 

framework for the structural process being 

modifi d b th l f dified by the supply of resources

affecting the growth and survival of the 

shoot population shoot population.

Structural-Functional Models

Pursued in recognition of the possible advantages of 

more explicit structural representation of tree crowns in 

ecophysiological models ecophysiological models

or

adding effects of environment on genetically coded adding effects of environment on genetically coded

architectural development

Excellent review papers by: Excellent review papers by:

Kurth (1994) Morphological models of plant growth: 

Possibilities and ecological relevance. Possibilities and ecological relevance.

Sievänen et al. (2000) Components of functionalstructural tree models.
FOREST GROWTH AND TIMBER QUALITY



Sievänen et al. (2000) Components of functional-structural tree models.

Two types: Two types:

(1) Structural model modified to be responsive to 

environmental conditions throug py g h ecophysiological

processes.

Examples include:

context sensitive, parametric, or open L-systems; 

AMAPmod (growth rules) AMAPmod (growth rules) Æ AMAPpara (addition of AMAPpara (addition of

ecophysiological processes) (de Reffye et al. 1997)

( ) 2 Process-based model modified to represent more 

accurately crown structure and, hence, to allow better 

estimation of light interception and other processes 

Examples include:

LIGNUM (Perttunen et al. 1996, 1998)

LIGNUM represents tree structure as a set of 

IEMs (Idealized elementary ) units

Basic physiological 

processes are processes are

represented: gas 

exchange, transpiration, 

nutrient uptake, growth 

(carbon) allocation

Authors underscore:

- the challenge of allocation, or 

distributing growth mechanistically

- the computational burden

Plant Modelling Unit at CIRAD in France

De Reffye Fourcaud Barthélémy Blaise Houllier

Yan et al. (2004) A Dynamic, Architectural 

De Reffye, Fourcaud, Barthélémy, Blaise, Houllier

Plant Model Simulating Resource-dependent 

Growth

GREENLAB

Fourcaud et al. (2003) Numerical modelling of shape regulation 

a d g o t st esses t ees p e e tat o t e nd growth stresses in trees. II. Implementation in the

AMAPpara software and simulation of tree growth

Role of 

mechanical

stressses in stressses in

tree form and 

reaction wood

Architectural rules

Hybrid models

1-yr 

leaves

2-yr 

leaves

3-yr 

leaves

4+-yr 

leaves

Structuralfunctional models

Branch

sapwood

leaves

Branch

heart wood

Bole

sapwood

Bole 

heart wood

Cambium Phloem

leaves leaves leaves

Physiological functions 

driving crown dynamics 

and/or driven by crown 

Coarse t t roots

Fine

roots structure

Allometricfunctional models

Crown allometric 

relationships

?

Foliage

Stem

Foliage and branch 

senescence/turnover

Others?

Roots
FOREST GROWTH AND TIMBER QUALITY

9

Hybrid of allometric-functional models

Baldwin et al. (2001) Linking growth and yield 

and process models to estimate impact of 

environmental change on growth of loblolly pine.

PTAEDA + MAESTRO

More fully integrated “hybrids”

Valentine and Mäkela (2005) Bridging processbased and empirical approaches to modeling tree 

growth.

Weiskittel (2006) Development of a hybrid 

modeling framework fo intensively managed modeling framework fo intensively managed

Douglas-fir plantations in the Pacific Northwest.

Weiskittel (2006) 

Crown structure

Net primary production

Growth allocation

Mäkela and Mäkinen (2003) Generating 3D 

sawlogs with a process sawlogs with a process-based growth model based growth model.

PipeQual

C b b l d lb d i Carbon balance model based on pipe 

model theory to grow trees and simulate 

changes in crown height and surface area changes in crown height and surface area

combined with empirical models of branch 

size

Mechanistic crown models

• The issue of mechanisms

• Model types

• Model objectives and context Model objectives and context

• Crown models for linking environment 

and silviculture to wood quantity and and silviculture to wood quantity and

quality

• Kl d d i Kludges and parsimony

Why mechanisms should be in the eye of 

the beholder:

• Cannot start to construct a model unless we have at 

the very least a fuzzy idea of the objective, i.e., what 

we (or someone el ) i h h d lf lse) might use the model for

• Model development will be infinitely more efficient if 

the objective is very explicit (including minimum the objective is very explicit (including minimum

performance standards; validation criteria)

• There will exist no p ,p , erfect, comprehensive, or 

complete simulation model that can answer all 

questions that forest managers or forest scientists may 

want to ask want to ask

• Model objectives

– Questions/hypotheses

– Required accuracy

– Validation criteria Validation criteria

• Ideally, model should be just adequate

• I lit bj ti In reality, objectives are or will soon 

become multiple!
FOREST GROWTH AND TIMBER QUALITY

10

QUESTION OR

HYPOTHESIS

MODEL CONSTRUCTION MODEL CONSTRUCTION

SIMULATION

Objectives often 

not stated, or 

they are fuzzy or

TENTATIVE

they are fuzzy or

only implied

TENTATIVE

ANSWER

Mechanistic crown models

• The issue of mechanisms

• Model types

• Model objectives and context Model objectives and context

• Crown models for linking environment 

and silviculture to wood quantity and and silviculture to wood quantity and

quality

• Kl d d i Kludges and parsimony

Fundamental questions about plant development 

in architectural models:

What are the genetically imposed

in architectural models:

What are the genetically imposed

branching processes that lead to 

different crown forms?

Can a set of branching r les Can a set of branching rules

specified by a growth grammar 

simulate the structural/morphological 

development of tree crowns?

Fundamental questions about plant development:

B hi ranc ng

rules

Crown

Crown

morphology

Crown

architecture

Accurate representation of 

real branching processes? p gy

Genetic design vs. 

environmental effects?

Leaf primordia Environmental alteration of Leaf primordia ti ll i d

Axillary buds

Bud differentiation 

Bud survival

genetically imposed

branching pattern?

Self-shading

Competition Hydraulic

Alternative processes 

l di t

limitations

leading to same 

morphology

Alternative architecture 

yi ldi e ng same morph l o ogy

but different physiological 

behavior

Relevance of branching processes and resulting crown 

architecture to silviculture and forest management architecture to silviculture and forest management

• Implications for light interception, 

photosynthesis, and growth potential

• Allocation of net production to branches and 

foliage

• Implied number, size, and location of 1st-order

(primary) branches

• Nutrient capital in branches and foliage

Wood Quality

Determinants of log, lumber, veneer, composite, 

eng p qy ineered product quality:

Knot size and number

Density

Micro-anatomical properties: fiber length, density, 

cell wall thickness lumen size microfibril angle cell wall thickness, lumen size, microfibril angle
FOREST GROWTH AND TIMBER QUALITY

11

Microfibril angle

Fiber length

Density

Cambial Age (years)

Gartner et al. 2004

Radial trend in microanatomical properties

0 10 20 30 40 50 60 70

juvenile-mature transition

Still have only 

rudi t men ary

understanding of the 

relationship between 

crown dynamics and 

wood properties

Average stem profiles and 

maps of relative wood maps of relative wood

density for Douglas-fir trees 

at six sites in British 

Columbia Josza et al. 1989

More progress has been made on linking 

branch size, and to some extent branch number 

and location, to silvicultural regime

Garber and Maguire (2005)

Contributions toward integrated systems for 

simulating stand dynamics and wood quality

France: Francis Colin / François Houllier / Jean

simulating stand dynamics and wood quality

France: Francis Colin / François Houllier / Jean

Michel LeBan

Finland: Harri M Harri Mäkinen / Annikki Mäkela / Seppo / Annikki Mäkela / Seppo

Kellomäki

PNW/USA: Dave Briggs / Eric Turnblom / PNW/USA: Dave Briggs / Eric Turnblom / Sean

Garber / Aaron Weiskittel / Temesgen Hailemariam

New Zealand: Jenny Grace / David Pont

Canada: Jim Goudie / Ken Mitchell

Germany: Sebastian Hein Sebastian Hein

Needle primordia within bud of Douglas Needle primordia within bud of Douglasfir, set at end of growing season 

(branches formed from axillary buds, but bud 

primordia not initiated until spring) primordia not initiated until spring)

A - Extended bud 

of Douglas-fir

B Extended bud Developing B - Extended bud

with scales and 

some needles 

d

p g

axillary

bud

remove
FOREST GROWTH AND TIMBER QUALITY

12

Potential for simulating the process by which are 

buds set in a select few leaf axils buds set in a select few leaf axils

ÆBranch position by height and azimuth

Particularly appealing for Pseudotsuga, Abies,

Picea species that have interwhorl branches 

g g radin into whorl branches

Pont (2001) Use of Pont (2001) Use of

phyllotaxis to predict 

arrangement and size of 

branches in branches in Pinus radiata Pinus radiata. buds

It h l n erwhorl

branches

Few interwhorl branches surviving

Simulate branch occurrence as 

i hn omogeneous P i o sson process

Changing Poisson mean, Ȝ

Changing probability of bud Changing probability of bud

set or branch initiation

Poisson regression with log link function

(generalized linear model)

Ș = ln(Ȝ) = ȕ0 + ȕ1X1 + ȕ2X2 + . . . + ȕkXk

where Ȝ = mean of Poisson distribution mean of Poisson distribution

Mean number of branches by relative position

in Douglas-fir main stem segments

0.0

Live crown 0.2

h

crown length = 5 m length

0.4

t0 6

ive depth

segment length

0.5 m

1.0 m 0 Annual .6

0.8

Relat

1.5 m Annual

height

growth

1.0

Long stem

segment -1 0 1 2 3 4

Number of branches (rapid growth)

Mechanistic crown models

• The issue of mechanisms

• Model types

• Model objectives and context Model objectives and context

• Crown models for linking environment 

and silviculture to wood quantity and and silviculture to wood quantity and

quality

• Kl d d i Kludges and parsimony

A kludge (or, alternatively, kluge) is a 

clumsy g or inelegant solution to a 

problem or difficulty. 

In engineering, a kludge is a In engineering, a kludge is a

workaround, typically using unrelated 

parts cobbled together.

Applied by George Furnival to 

forest growth models (1987)
FOREST GROWTH AND TIMBER QUALITY

1

Currently have an unprecedented opportunity to borrow bits 

and pieces of models constructed for widely divergent 

objectives.

Thi b d i b th t d li bilit This abundance is both a asset and liability:

Validation value.

Efficiency of model building.

Specialization.

Often less than perfect fit to another application Æ

danger of creating gg or enabling a “kludge”.

Wh d d l d l When does a model or model system 

become a kludge?

Must consider:

Elegance vs. f ti lit functionality

Parsimony vs. complexity

Basic vs. applied models

Cost vs. efficacy

Why mechanisms should be in the eye of the beholder: 

Notes from the overground

How do we balance efficiency gains from a focus on How do we balance efficiency gains from a focus on

objectives with the potential benefits of:

venture research

free-reigning modelling 

serendipity

?

Comfort or angst from Dostoyevsky?

(Notes from the Underground)

“ . . . intellectual activity is a disease intellectual activity is a disease”

“ . . . men of action, doers, quite genuinely give up when 

faced with a wall; to them a wall is not challenge as it is faced with a wall; to them a wall is not challenge as it is

to us, for example, men who think and therefore don’t 

do anything.”

“ . . . all spontaneous people, men of action, are active 

because they are stupid and limited.”

(Recall Arber’s reference to "over-ingenious, 

academic conceptions which are difficult to discuss 

because they bear so little relation to reality”)

Important confessions to assuage critics

All models are wrong.

There is no perfect model for answering more than 

one type of question.

The imperfect representation of our biological and/or 

operational forestry systems by models does not 

preclude their utility preclude their utility.

If we think too hard about all the weaknesses of 

models and all the situations in which they would not models and all the situations in which they would not

apply, we would never get started.

FOREST GROWTH AND TIMBER QUALITY

15

Predicting wood and branch properties of norway spruce 

as a part of a stand growth simulation system

Harri Mäkinen, Annikki Mäkelä, Jari Hynynen

ABSTRACT

The purpose of our study was to model how stem, branch 

and wood properties of Norway spruce (Picea abies (L.) 

Karst.) are linked to each other, and how they are distributed 

along the stem. The branchiness data were used to develop 

models for the crown ratio, the self-pruning ratio (i.e. height 

of the lowest dead whorl divided by the height of the crown 

base), number of living branches in a whorl, total number 

of branches in a whorl, diameter of the thickest branch in 

a whorl, diameters of smaller branches, and branch angle. 

The material on wood and fiber properties was used to 

develop models for wood density, early-latewood ratio, fiber 

length, fiber width, and cell wall thickness. A multilevel 

modeling approach was used to separate the variation of 

branch, wood and tracheid properties at region, stand and 

tree levels, as well as within a tree. A multivariate approach 

was used to simultaneously estimate the parameters of the 

equations. The independent variables were restricted to 

those collected in forest inventories or for forest management planning purposes. Such data sets are normally not 

very detailed.

The models were connected to the empirical growth 

simulation system MOTTI and to a process-based growth 

model PipeQual. The dynamic growth model provides a 

description of tree growth down to the annual ring level. 

This structure will be used as a skeleton for calculating 

branch and wood properties. The growth model will update the stand and tree attributes from year to year and, 

consequently, change the distribution of the branch and 

wood properties within the stem. The variances of branch 

and wood properties and their covariances estimated 

during model development can be used to produce more 

realistic predictions compared to models, which are fitted 

separately. When used in practice, the predictions of other 

models can be calibrated for a particular stand or tree if 

one dependent variable of the system is measured. The 

combined simulation system can be used for predicting 

the development of stem structure under environments 

controlled by different silvicultural management regimes. 

The results as such will also increase our understanding 

of the development of wood quality as a function of forest 

management, and the quality models are applicable independently of the growth models.

KEYWORDS: branchiness, cell wall thickness, modeling, 

Picea abies, tracheid length, tracheid width, wood density

INTRODUCTION

I

N FINLAND, NORWAY SPRUCE IS ECONOMICALLY 

and ecologically one of the most important tree species. Norway spruce timber has mainly been used for 

mechanical pulping and for sawn goods in structural uses. 

Differences in the unit price of the timber grades for Norway spruce have been rather small. Therefore, controlling 

wood quality has been considered a secondary matter. The 

demand for Norway spruce timber used in high-quality 

products such as panels, furniture, and plywood, has increased in recent years. Accordingly, the price of Norway 

spruce lumber has also increased.

Harri Mäkinen (harri.makinen@metla.fi) is a researcher, Finnish Forest Research Institute, Vantaa Research Unit, P.O. Box 18, 01301 Vantaa, Finland; 

Annikki Mäkelä is professor of silviculture (forest production), Department of Forest Ecology, University of Helsinki, PO Box 27, 00014 Helsinki, 

Finland; Jari Hynynen is a researcher, Finnish Forest Research Institute, Vantaa Research Unit, P.O. Box 18, 01301 Vantaa, Finland.

Harri Mäkinen (harri.makinen@metla.fi) is a researcher, Finnish Forest Research Institute, Vantaa Research Unit, P.O. Box 18, 01301 Vantaa, Finland; 

Annikki Mäkelä is professor of silviculture (forest production), Department of Forest Ecology, University of Helsinki, PO Box 27, 00014 Helsinki, 

Finland; Jari Hynynen is a researcher, Finnish Forest Research Institute, Vantaa Research Unit, P.O. Box 18, 01301 Vantaa, Finland.

This paper was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 15–21.
FOREST GROWTH AND TIMBER QUALITY

1

The number and size of branches are major determinants 

of log grading in Norway spruce. For the reasons given 

above, detailed studies on the branch characteristics of 

Norway spruce and the factors controlling them are scarce 

in the Nordic countries. Characteristics of fibers largely 

determine the suitability of wood for further processing 

in the pulp and paper industry as well as in the sawmilling industry. Fiber morphology and cell wall structure 

directly influence fiber flexibility, plasticity and resistance to 

processing and, therefore, influence the strength and other 

physical and optical properties of the end products. Wood 

density is also an important characteristic that is related to 

the yield and quality of pulp and sawn products.

How the stem grows and acquires its structure—or 

how silvicultural management controls the development 

of stem structure—is one of the key considerations in the 

integrated optimization of the wood production and conversion chain. Models have conventionally treated stem 

properties separately from tree growth. A more general and 

flexible model can be constructed if quality characteristics 

are included in a growth model, allowing us to predict 

stem structure at each moment of time (e.g., Houllier et al. 

1995). Such a model would automatically portray the effects 

of silvicultural treatments on stem properties, because the 

primary effect of the environment on tree growth would 

be interpreted in terms of changes in ring width, branchiness, etc.—characteristics which have been demonstrated 

to depend largely on stem growth.

Models describing 

the branch characteristics of Scots pine (Pinus 

sylvestris (L.) and silver 

birch (Betula pendula

Roth.) have been developed in the Nordic 

countries (Mäkinen and 

Colin 1998, 1999, Moberg 1999, Mäkinen et 

al. 2003a). The models 

of Mäkinen and Colin 

(1998, 1999) were connected to the empirical 

growth simulation system MOTTI (Hynynen 

et al. 2005, Salminen 

et al. 2005), and to the 

process-based growth 

model PipeQual (Mäkelä 1997, Mäkelä and Mäkinen 2003, 

Mäkinen and Mäkelä 2003). These tools can be used to 

assess the development of wood quality and to assess the 

possibilities of using silvicultural treatments to control 

timber properties (Mäkinen et al. 1999, 2004, Mäkelä et al.

2000). However, the models developed thus far have been 

concerned with Scots pine and silver birch, as well as the 

properties of logs utilized by sawmilling industries.

Our goal was to extend the previous modeling approach 

to branch, wood and tracheid properties of Norway spruce. 

The purpose was to model how stem, branch, wood and 

tracheid properties are linked with each other and how they 

are distributed along the stem from stem base to apex and 

from pith to bark. The models had to be applicable as a part 

of a stand growth simulation system that is based on growth 

models for individual trees. Although a large number of 

stand and tree characteristics would certainly improve the 

accuracy of the models, the information collected in forest 

inventories or for forest management planning purposes 

is not normally very detailed. Thus, the variables used in 

the models had to be restricted to those found in the data 

sets to which the models are applied.

MATERIAL AND METHODS

Data on the wood and tracheid properties

The material used for modeling the wood and tracheid 

properties consisted of five separate data sets: (1) two thinTable 1— Characteristics of the experiments sampled for modeling wood and tracheid properties.

Data set Location Number of 

sample trees

Age DBH

(cm)

Hdoma

(m)

H100

b

(m)

Thinning Heinola 12 7 29.4 0. 32.4

Punkaharju 12 7 2. 27.2 .0

Thinning+ Parikkala 45 64 24.9 22.7 28.5

fertilization Suonenjoki 40 77 27. 2.1 2.

Fertilization Heinola 10 54 24.5 2. 2.

Kemijärvi 10 65 14.6 11. 1.

Nutrient- Flakaliden 27 40 12.1 . 1.

optimization Asa 1 1 17.2 15.0 1.2

Clones Nurmijärvi  20 . n.a.c 34.0

Ruotsinkylä 4 1 27.0 n.a.c 24.0

a

 Dominant height, height of 100 thickest trees ha-1

b Site index, dominant height at age 100 years

c

 not available
FOREST GROWTH AND TIMBER QUALITY

17

ning experiments in southern and central Finland, (2) two 

thinning-fertilization experiments in central Finland, (3) 

two fertilization experiments in southern and northern 

Finland, (4) two nutrient optimization experiments in 

southern and northern Sweden, and (5) fast-grown clones 

and their reference trees in southern Finland (Table 1). 

The data sets were originally sampled for different purposes 

and studies (Mäkinen et al. 2002a,b, Jaakkola et al. 2005a,b, 

2006, 2007). In all the data sets, however, the measurements 

were carried out according to the same methods. The study 

material included 181 sample trees (Table 1).

Sample trees were felled and stem discs were sawn out at 

different heights on the stem avoiding whorls. Ring width 

and wood density of all annual rings were measured along 

the south radius of each disc. Tracheid lengths of every fifth 

annual ring were measured from bark to pith. In addition, 

lumen diameter and cell wall thickness were measured 

from selected annual rings at regular intervals from pith 

to bark. The sampling and measurements are described in 

detail in Mäkinen et al. (2007).

Branchiness data

The material used for branchiness models consisted of 

five separate data sets: (1) commercial forests in southern 

and central Finland, (2) thinning experiments in southern 

Finland, (3) a young naturally regenerated stand in southern 

Finland, (4) a nutrient optimization experiment in northern 

Sweden, and (5) pruning experiments in southern Finland. 

The data were collected from 677 trees of different age and 

canopy position growing on mineral soils and peatlands 

of different fertility (Table 2). The data sets were originally 

sampled for different purposes and studies. In all the data 

sets, however, the measurements were carried out according to the same methods.

Stem diameter at breast height, tree height, crown length, 

and height to the lowest dead whorl were measured on each 

sample tree. The sample trees were felled and the distance of 

whorls from the stem apex, the horizontal diameter of each 

branch above the butt swell, and the status of each branch 

(living or dead) were measured. The sampling and measurements are explained in detail in Mäkinen et al. (2003b).

Model development

Our goal was to develop generally applicable models. All 

of the models were based on statistical fitting of equations 

to the measured data. When selecting curve forms and 

variables for the models, we considered the potential biological significance of the selected variables to the branch, 

wood and tracheid properties based on the relationships 

presented in the literature.

Multivariate multilevel models were used because, by 

simultaneously estimating the parameters of the equations, they provide techniques to produce consistent and 

asymptotically efficient estimates for regression equation 

systems. Variance components were used to separate random 

variation at different levels, e.g., between regions, stands, 

plots, trees, whorls, branches or stem heights and annual 

rings, depending on the model in question.

For example, the multivariate multilevel model structure 

for two dependent variables (a and b) measured at whorl 

level could be as follows:

a aaaa αμ ),()( ++++= wtpsxfg (1.1)

b bbbb βμ ),()( ++++= wtpsxfg (1.2)

where g(m) is an appropriate 

link function, x matrix of the 

independent variables, ß vectors of fixed parameters, and 

s, p, t and w random variables 

at stand, plot, tree and whorl 

levels. The models can be used 

to decompose the raw variances 

and covariances into parts at 

the four levels. The betweenand within-group covariance 

matrices can then be estimated:

Table 2—Characteristics of the experiments sampled for modeling branch properties.

Data set Location Number of

sample trees

Age DBH

(cm)

Hdom

(m)

H100

(m)

Commercial forests Southern Finland 240 2 2. 22. 24.2

Thinning Punkaharju 12 85 2. 1.0 .

Heinola 12 7 29.4 26.4 33.5

Sapling Lapinjärvi 5 22 .1 4.4 24.5

Nutrient optimization Flakaliden 24 7 12.1 . 1.

Pruning Southern Finland 384 2 12. 12.2 .
FOREST GROWTH AND TIMBER QUALITY

1

cov (sa, sb)=Cs, cov (pa, pb)=Cp, cov (t

a

, tb)=Ct, cov (wa, wb)=Cw

RESULTS

Models for wood and tracheid properties

The data on wood and tracheid properties were used to 

develop models for (1) proportion of latewood in individual 

annual rings, (2) average wood density of individual annual 

rings, (3) tracheid length, (4) tracheid width, and (5) cell 

wall thickness. The wood and tracheid properties were 

mainly related to cambial age of an annual ring and radial 

increment rate. Site index was also a significant variable in 

most of the models. The magnitude of changes associated 

with increasing increment rate differed depending on the 

properties of wood density and tracheid length, as demonstrated in Figure 1. However, increasing increment rate 

caused by thinning or fertilisation resulted in similar kinds 

of changes in wood and tracheid properties, irrespective of 

the factor promoting radial increment. 

The variation that accounted for the fixed part of the 

models was: tracheid length 82.8 percent, tracheid width 

64.9 percent, cell wall percentage 48.0 percent, latewood 

proportion 24.8 percent, and wood density 21.1 percent. 

The behaviour of the models for a randomly selected tree 

Figure 2—Measured (dots) and predicted (line) proportion of latewood (A), wood density (B), tracheid length (C), tracheid width (D) 

and proportion of cell wall (E) of individual annual rings at breast height plotted against ring number counted from the pith outwards 

for a randomly selected tree (age=77 y, dbh=27.3 cm, h=23.7 m).

Figure 1—Predicted profiles of wood density and tracheid length 

for a slow and fast growing tree (radial increment 0.5 and 1.0 

mm y-1, respectively) plotted against ring number counted from 

the pith outwards. The other independent variables were the 

same for both trees.
FOREST GROWTH AND TIMBER QUALITY

1

is demonstrated in Figure 2. The equations and parameters 

of the models are given in Mäkinen et al. (2007).

Models for branch properties

The branchiness data were used to develop models for (1) 

crown ratio, (2) self-pruning ratio, i.e., height of the lowest dead whorl divided by the height of the crown base, 

(3) number of living branches in a whorl, (4) total number 

of branches in a whorl, (5) diameter of the thickest living 

branch in a whorl, (6) diameters of smaller branches, and (7) 

branch angle. The equations and parameters of the models 

are given in Mäkinen et al. (2003b). The behaviour of the 

models for the number of living branches and branch diameter is demonstrated in Figures 3 and 4, respectively.

Application

The above models do not describe dynamic development 

of branch, wood, and tracheid properties. The models can 

be combined with a dynamic growth model that provides 

a detailed description of tree growth down to the annual 

ring width level. This structure will be used as a skeleton 

when predicting branch, wood and tracheid properties 

during stand development. During simulation, information 

on branch, wood, and tracheid properties of each sample 

tree are updated annually together with the other tree and 

stand characteristics. Predicted variation of the latewood 

proportion, wood density, tracheid length, and tracheid 

width within a stem using PipeQual simulation system is 

demonstrated in Figure 5.

DISCUSSION

An integrated system of models was developed for prediction 

of 3D stem structure of different branch and wood properties 

using a wide range of stand and tree data. The main purpose 

Figure 3—Predicted probabilities for 1, 2, 4, and 6 living branches in a 

whorl within the living crown.

Figure 4—Predicted profiles of branch diameter for the thickest, 

third, and fifth thickest branch in a whorl counted from the stem apex 

downwards within the living crown.

Figure 5—Predicted latewood proportion, wood density, tracheid length, 

and tracheid width within a stem. The figures were produced by the PuMe 

software (Vanninen et al. 2006).
FOREST GROWTH AND TIMBER QUALITY

20

was to develop simple and logical models based on routine 

stand and tree measurements. Adding stand level variables 

as independent variables to the models slightly improved 

the model performance, but stem properties were often 

sufficient to reliably predict branch and wood properties.

The branchiness models represent a prediction system 

for the primary branching structure of Norway spruce. The 

models predict the crown ratio and self-pruning ratio, as 

well as the trend in individual branch characteristics along 

the stem. The models must be linked with each other when 

recursively predicting branch characteristics.

Wood and tracheid properties were modeled as a function 

of the position in the stem, growth in this position, and 

the growth conditions of the tree. Most previous models 

for Norway spruce found in the literature describe wood 

and tracheid properties by means of the average value of a 

stem disc taken at a given stem height. In contrast, all the 

annual rings were used as individual observations in this 

study. This approach makes it possible to describe radial 

variations of wood and tracheid properties within the stem. 

In addition, the effects of silvicultural treatments can be 

predicted at the level of individual annual rings.

Even though we found bias in predicting some wood 

and tracheid properties, as well as wide variation of the 

residuals, the behaviour of the models was reasonably 

good. They reproduced the profiles of properties along the 

stem that were similar to those reported in several studies on wood and tracheid properties. The models predict 

the properties within the stem, but they do not describe 

functional relationships between wood formation and tree 

physiology. Annual ring width was closely related to wood 

and tracheid properties, but cannot be regarded as a causal 

driving variable.

Our main goal was to develop models that can be applied 

as part of a growth simulation system. The system consists 

of models for property distributions, which are functions of 

stand and tree characteristics. In application, the models can 

be used stochastically by generating random variation in the 

predictions. The variances and their covariances estimated 

during the simultaneous model development can be used 

to produce more realistic predictions compared to models 

fitted separately. The predictions of other models can be 

calibrated for a particular stand or tree if one dependent 

variable of the system is measured.

The results will increase our understanding of the development of wood quality as a function of forest management. 

They are also applicable independent of the growth models. 

Incorporating wood and tracheid properties into forest 

management planning enables estimates for conversion of 

different silvicultural regimes into internal stem structure 

and wood quality. 

LITERATURE CITED

Houllier, F.; Leban, J.M.; Colin, F. 1995. Linking 

growth modeling to timber quality assessment for 

Norway spruce. Forest Ecology and Management 74: 

91-102.

Hynynen, J.; Ahtikoski, A.; Siitonen, J. [et al.]. 2005. 

Applying the MOTTI simulator to analyse the effects 

of alternative management schedules on timber 

and non-timber production. Forest Ecology and 

Management 207: 5-18.

Jaakkola, T.; Mäkinen, H.; Saranpää, P. 2005a. Wood 

density in Norway spruce: changes with thinning 

intensity and tree age. Canadian Journal of Forest 

Research 35: 1767-1778.

Jaakkola, T.; Mäkinen, H.; Saranpää, P. 2006. Wood 

density of Norway spruce: Responses to timing and 

intensity of first commercial thinning and fertilisation. 

Forest Ecology and Management 237: 513-521.

Jaakkola, T.; Mäkinen, H.; Saranpää, P. 2007. Effects of 

thinning and fertilisation on tracheid dimensions and 

lignin content of Norway spruce. Holzforschung 61: 

301-310.

Jaakkola, T.; Mäkinen, H.; Sarén, M.P.; Saranpää, P. 

2005b. Does thinning intensity affect the tracheid 

dimensions of Norway spruce? Canadian Journal of 

Forest Research 35: 2685-2697.

Mäkelä, A. 1997. A carbon balance model of growth and 

self-pruning in trees based on structural relationships. 

Forest Science 43: 7-23.

Mäkelä, A.; Mäkinen, H. 2003. Generating 3D sawlogs 

with a process-based growth model. Forest Ecology 

and Management 184: 337-354.

Mäkelä, A.; Mäkinen, H.; Vanninen, P. [et al.]. 2000. 

Predicting yield and quality of Scots pine stands. 
FOREST GROWTH AND TIMBER QUALITY

21

Finnish Forest Research Institute, Research Papers

794. 89 p. (in Finnish with English summary)

Mäkinen, H.; Colin, F. 1998. Predicting branch angle 

and branch diameter of Scots pine from usual tree 

measurements and stand structural information. 

Canadian Journal of Forest Research 28: 1686-1696.

Mäkinen, H.; Colin, F. 1999. Predicting the number, 

death, and self-pruning of branches in Scots pine. 

Canadian Journal of Forest Research 29: 1225-1236.

Mäkinen, H.; Hynynen, J.; Colin, F.; Mäkelä, A. 1999. 

Predicting branch characteristics of Scots pine from 

usual tree measurements and stand information. In: 

Nepveu, G., ed. Connection between Silviculture 

and Wood Quality through Modeling Approaches 

and Simulation Software. Proceedings of the Third 

Workshop IUFRO WP S5.01.04, La Londe-LesMaures, France. September 5-12, 1999, pp. 42-49.

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P. 2007. Predicting wood and tracheid properties of 

Norway spruce. Forest Ecology and Management 241: 

175-188.

Mäkinen, H.; Mäkelä, A. 2003. Predicting basal area of 

Scots pine branches. Forest Ecology and Management 

179: 351-362.

Mäkinen, H.; Ojansuu, R.; Hynynen, J.; Niemistö, P. 

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(Betula pendula Roth.) from simple stand and tree 

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Forest Resources and Wood Quality: Modelling 

Approaches and Simulation Software. Proceedings of 

the Fourth Workshop IUFRO WP S5.01.04, Harrison 

Hot Springs, British Columbia, Canada, September 

8-15, 2002, pp. 265-273.

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Predicting branch characteristics of planted silver 

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stand and tree measurements. Forest Science 49: 301-

317.

Mäkinen, H.; Ojansuu, R.; Sairanen, P.; Yli-Kojola, H. 

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tree measurements. Forestry 76: 525-546.

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growth rate on fibre characteristics in Norway spruce 

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nutrient optimization and fibre dimensions. Canadian 

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employing the PipeQual model for forest growth and 

wood quality. New Zealand Journal of Forest Science 

36: 280-292.

2

Models on Branch Characteristics of 

Wide-Spaced Douglas-fir

Sebastian Hein, Aaron R. Weiskittel, Ulrich Kohnle

ABSTRACT

Models of Douglas-fir branch and whorl characteristics 

were developed from contrasting spacing experiments 

in southwest Germany. The dataset was based on 100 

unpruned and partially pruned trees from a 1200, 200, 

and 100 stems ha-1 spacing experiment on 24–42 year 

old Douglas-fir. The material was used to predict (1) the 

number of branches whorl-1, (2) the branch angle, (3) 

the status (living/dead) of the branches within the living 

crown, (4) the maximum branch diameter whorl-1, and 

(5) the diameter of smaller branches whorl-1. For each of 

these models, linear generalized hierarchical mixed effects 

equations were developed. Overall, individual branch and 

tree properties were sufficient to give logical and precise 

predictions of the branch characteristics for the models. 

The models performed well across a range of stand conditions and will be further integrated into an individual tree 

growth and yield simulations system.

KEYWORDS: branchiness, Douglas-fir, generalized linear 

mixed models, timber quality, wide spacing

INTRODUCTION

ATTRIBUTES OF INDIVIDUAL BR ANCHES 

define crown structure and have important implications at multiple levels in a forest stand. For 

example, crown development and structure has been 

related to stem growth, wood quality attributes, wildlife 

habitat, and key physiological processes such as interception of radiation and precipitation. Crown structure is quite 

sensitive to stand conditions imposed by silviculture, but 

these changes are generally predictable from concurrent 

modifications in tree and crown size. 

Models of individual branch attributes exist for several 

commercially important species including: silver birch 

[Betula pendula Roth.] (Mäkinen et al. 2003), Scots pine 

[Pinus sylvestris L.] (Mäkinen and Colin 1999), Norway 

spruce [Picea abies (L.) Karst.] (Hein et al. 2007), radiata 

pine [Pinus radiata D. Don.] (Grace et al. 1999), Douglas-fir 

[Pseudotsuga menziesii var. Menziesii (Mirb.) Franco] (Maguire et al. 1994), and Sitka spruce [Picea sitchensis (Bong.) 

Carr.] (Achim and Gardiner 2006). These models have been 

combined with individual tree growth and yield computer 

simulators and have been found useful for understanding 

the effects of silviculture on wood quality across a wide 

range of stand conditions. Despite the wide array of research 

that has been done on individual branches, little work has 

been done comparing the performance of models based 

on datasets from contrasting thinning regimes (i.e. close 

spacing vs. wide spacing).

An important distinction between branch modeling done 

in Europe and the United States is model form. Hierarchical 

linear models have generally been used in Europe, while 

nonlinear forms have been preferred in the United States. In 

addition, overall modeling approaches have been different. 

For example, Hein et al. (2007) used a generalized mixed 

effects Poisson distribution probability approach to predict 

the number of branches per annual whorl and Maguire et 

al. (1994) used a nonlinear model based on the normal distribution. Further, the degree and impact of autocorrelation 

Sebastian Hein (hein@hs-rottenburg.de) is professor of silviculture at the University of Applied Forest Sciences, 72108 Rottenburg, Germany and Ulrich 

Kohnle is at the Forest Research Institute of Baden, Wonnhaldestrasse 4, Freiburg i Br, Baden-Wurttemberg 7900, Germany. Aaron R. Weiskittel is a 

forest modeling assistant professor, University of Maine, Orono, ME 04471, USA.

This paper was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 23–33.
FOREST GROWTH AND TIMBER QUALITY

24

on branch-level models has not been assessed. Weiskittel et 

al. (2007) found a significant degree of autocorrelation in 

several branch-level models, but Garber and Maguire (2005) 

detected no significant autocorrelation between maximum 

branch diameters throughout an individual crown. In this 

study we apply generalized linear mixed effects models. 

The evaluation of these types of modeling approaches will 

help guide future efforts. 

Douglas-fir is an important species in western Europe 

and specifically in south-western Germany. The development of these branch-level prediction models will further 

our understanding of growth response at the tree-level and 

allow assessment of potential wood product quality in this 

region. This should promote more effective and efficient 

silvicultural practices. The overall goal of this research 

project was to develop branch-level models that can be 

integrated into an individual tree growth and yield simulation system. Specific objectives were to develop models for 

(1) the number of branches per annual whorl, (2) branch 

angle, (3) the probability of a branch being alive or dead, (4) 

branch diameter profiles for the thickest branch per whorl, 

and (5) the subsequent smaller branches. In the process, the 

performance of the models with respect to treatments effects 

and different modeling assumptions will be tested.

MATERIAL AND METHODS

Experiments and Measurements

The material was collected from three spacing experiments 

within the program “Solitary Trees” (“Solitärprogramm”) 

in south-western Germany (Abetz 1987; Abetz and Lässig 

1989). The principal aim of the experiments was to study 

the effects of weather conditions, air pollution, and biotic 

damage on tree growth without confounding effects of 

inter-tree competition. 

The experiments were established in seven approximately 10–25 year-old single-species stands of Douglasfir all located in south-western Germany between 1989 

and 1991. At each location, one to three plots were set up 

including (1) a plot with very wide-spaced density at the 

establishment of the experiment where the saplings were 

thinned to a density of 100 stems ha-1 (4 plots); (2) a plot 

with an initial density of 200 stems ha-1 (8 plots); and (3) 

a plot with an initial density 1200 stems ha-1 (5 plots). The 

latter represents the common number of stems at sapling 

phase in Germany and is also close to recommendations 

for planting Douglas-fir in neighboring countries. In total, 

data from 17 plots from 7 locations were available. The 

site index defined as the dominant height at the age of 

100 years ranged between 49.9 and 56.5 m with no large 

differences between the three treatments. All symbols for 

plot, tree, whorl and branch attributes used in the analysis 

are explained in Table 1.

In total, 100 trees were sampled from the 17 plots with 

23 trees from the lowest density, 40 from the intermediate 

density, and 37 trees from the highest density. The sampling 

was targeted to dominant trees that were randomly selected 

under the condition of having no visible signs of damage. 

The trees used in this study were harvested 15 - 17 years 

after the beginning of the experiments. No thinnings have 

been carried out since the establishment of the experiments. 

Summary statistics of tree attributes are listed in Table 2. 

The whole dataset covers 

a range of tree diameter 

between 24.1 and 54.2cm 

and a height of 18.0 to 

30.0m measured at the 

time of felling.

For each plot tree, 

height; stem diameter 

at breast height; height 

of the crown base (defined as the height of the 

lowest living primary 

branch); and tree age 

were measured. After 

felling the sample trees, 

the distance of whorls 

Table 1—Explaination of Symbols

Variable Definition

brd branch diameter, excluding the thickest branch of a whorl [mm]

brdmax maximum branch diameter in a whorl [mm]

brs branch status [living = 1, dead = 0]

dbh diameter at breast height [cm]

dist distance between the whorl and stem apex [m]

dist1 dist/(h – hcb) [-]

dist2 ln(1.1 – dist/(h – hcb) [-]

dist ln(dist1 + 0.1) [-]

wh whorl height above ground

h tree height [m]

hcb height of the crown base (lowest living branch), measured from stem base [m]

hd h [m]/ diameter at breast height [cm]*100 [-]

ih annual height increment [m]

r rank of the branch, ordered from largest to smallest diameter [-]

nbrt total number of branches in a whorl (living and dead combined) [-]

α, β, γ, δ, ε variance components of the models 4 to 8, respectively

E, |E|, E2 mean error, mean absolute error, mean squared error, respectively l, p, t, w, b, D subscripts for location, plot, tree, whorl, branch, treatment (i.e. initial density), respectively
FOREST GROWTH AND TIMBER QUALITY

25

from the stem apex; branch status (living or dead); the 

branch angle (in steps of 5 degrees); and horizontal and 

vertical diameter (on branch base after base swell) of all 

branches above 1.3m height were measured. The average 

branch diameter was calculated as an arithmetic mean of 

the horizontal and vertical diameters. Cross-sections were 

taken at 0.3 and 1.3m heights, then every 5.0m thereafter 

beginning from 5.0m height upwards. The number of annual rings was counted and compared with the number 

of whorls above the cross-section in order to assure the 

correct numbering of the whorls. In total, 12,855 branches 

from 2226 whorls were measured. The summary branch 

and whorl statistics (Table 3) cover similar ranges for the 

three treatments with the maximum branch diameter per 

whorl as an exception. 

Due to our modeling approach, the number of records differs by the model. Only one observation per whorl was used 

in the model for the maximum branch diameter per whorl. 

For the model on the relative branch diameter of smaller 

branches in a whorl, all branches excluding the maximum 

branch were taken. Furthermore, modeling logic requires 

excluding all green pruned trees (N=57) from the model 

on branch status, as we intended 

to model the branch status within 

the living crown undisturbed by 

artificial pruning. In addition, no 

branch angle was recorded on 15 

trees. We thus record the number 

of observations available for each 

model separately. Lastly, since 

branch angle is a potential predictor 

for branch diameter, we excluded 

trees with no branches recorded 

from the two models on branch 

diameter.

Statistical Analysis

Our dataset contains discrete (e.g. 

counts of branches per whorl) as 

well as continuous data (e.g. maximum branch diameter per whorl). 

In addition, our dataset has a hierarchical structure with branches 

nested within whorls that are 

themselves clustered within trees 

and then in plots. Thus, mutual 

dependence of the measurements should be considered in 

the statistical analysis. An appropriate statistical analysis 

of such data should combine the concept of generalized 

linear or nonlinear models (Agresti 2002, Littell et al. 2006) 

together with the multilevel and mixed model approach 

(Snijders and Bosker 2003). 

We therefore modeled the data using “generalized linear 

mixed models” (GLMM) in which the data may display any 

distribution of the exponential family. In addition, GLMM 

consists of a non-linear link function that describes how 

the response variable is related to the linear predictor. The 

link function creates linearized pseudo-data on the link 

scale, based on the original values (the data scale). We 

considered the hierarchical structure of the data and the 

mutual dependence of the measurements in the statistical 

analysis by applying the mixed model approach including 

random experiment, plot, tree, whorl and branch effects, 

varying around the fixed population mean. Our measurements of the branch and whorl characteristics can be 

thought of as repeated measures along the stem or along 

a gradient within the whorl. Since our data indicated a 

significant longitudinal error for the model on maximum 

Table 2—Plot and tree sample description (Nt=100) by experiment with the initial densities of 100, 

200 and 1200 trees ha-1, abbreviations: see Table 1.

100 200 1200

min.– max. x

– min.– max. x– min.– max. x–

age 24 – 42 0.1 24 – 30 2. 24 – 31 0.0

dbh 35.9 – 54.2 44.8 29.1 – 46.7 40.6 24.1 – 40.3 .1

h 1.0 – 0.0 2.1 20.2 – 26.5 2.1 19.4 – 27.8 23.5

hd 40.8 – 61.8 51.8 48.9 – 76.3 57.3 56.6 – 88.3 71.

hcb .7 – .7 .0 .6 – 9.5 4.9 1. – 12. 7.

si 49.9 – 55.0 51.9 53.8 – 56.5 55.3 53.3 – 56.0 54.0

Table 3— Whorl and branch sample description (Nb=12855) by experiment with the initial densities of 

100, 200 and 1200 trees ha-1, abbreviations: see Table 1.

100 200 1200

min.– max. x

– min.– max. x– min.– max. x–

bra 10 – 10 7.7 10 – 10 .7 10 – 150 .

brdmax . – . 5.0 .7 – 9.4 4.2 . – . 3.4

brdlptwb/ 

brdmaxlptw

.1 – 1.0 .7 . – 1.0 . .1 – 1.0 .7

dist1 .0 – 1.0 .5 .0 – 1.0 .5 .0 – 1.0 .5

dist2 -2.3 – .1 -.7 -2.3 – .1 -.7 -2.3 – .1 -.7

dist -2.2 – .1 -.6 -2.1 – .1 -.6 -2.1– .1 -.6

ih . – 1. . .2 – 1. . .2 – 1.7 .

nbrt 0 – 1 7. 0 – 17 .2 0 – 1 7.1

r 2 – 1 5.3 2 – 1 4.9 2 – 1 5.4
FOREST GROWTH AND TIMBER QUALITY

2

branch diameter in a whorl, we included such an effect 

by choosing a covariance structure for irregularly spaced 

repeated measures (Gregoire et al. 1995).

Models were calculated using the empirical “sandwich” 

estimators to adjust the standard errors and test statistics. 

The sandwich estimators are useful for inferences on fixed 

effects that are not sensitive to the choice of the covariance 

models (SAS 2005). For all our models we used the rootsandwich estimator of Kauermann and Carroll (2001). The 

models on count (number of branches) and binomial data 

(branch status) had an over- or under-dispersion parameter Φ added to the variance function in order to prevent 

misinterpretations from inflated or deflated test statistics. 

The error variance is thus Φ[μ(1-μ)]/n and Φλ for binomial 

and count data, respectively (McCullagh and Nelder 1999), 

where μ and λ are the respective means for binomial and 

count data and n the number of observations. 

In order to examine the residuals of the models at tree, 

whorl, or branch levels, the empirical “best linear unbiased 

predictors” (BLUP) were calculated for each level. The BLUPs 

were calculated from the solution of the random effects 

on the link scale, and then transformed to the data scale. 

All residual graphs display the values in the data scale. It 

should be noticed that by using this procedure, the residuals at the lower levels are conditional to the residuals of the 

higher levels, i.e. the average higher-level residual of each 

sampling unit was removed from the lower-level residuals 

and displayed as the mean residual over the corresponding 

sampling unit. For example, the whorl-level residuals for 

the model of the relative diameter of the smaller branches 

in a whorl are calculated and displayed as whorl-mean 

residuals over the whorl attribute. 

In model-building, independent fixed variables and 

their different combinations describing the properties 

of the plots, trees, whorls, and branches were tested for 

potential relationship to the branch and whorl properties. 

Variables were included into the models at the α=0.05 level 

of significance. 

In order to examine the performance of the fixed part 

of the models, we calculated the following error statistics 

using only the fixed part of the models:

 y(E ˆ n/)y ∑ −= ii

 (1a) mean error 

∑ y||E| −= ˆ n/|yii

(1b) mean absolute error

 ( ˆii /) nyyE2 2

∑ −=

(1c) mean squared error

where yi is the measured observation, yˆi as the predicted 

value, and n the number of observations. For calculating the 

error statistics, all values were used in their data scale. 

In the case of the model on branch status, we also evaluated the goodness of fit by calculating the share of true 

positive events “true positive rate = sensitivity” and the false 

positive rate “1–specificity” for varying cutpoints (event 

= living branch). The cutpoint determines the predicted 

probability where a branch can be considered as living 

for simulations. The optimal cutpoint was taken from the 

probability where the Youden-index reaches its maximum 

value: i.e. sensitivity + 1–specificity – 1 (Youden 1950). As a 

measure of the goodness of fit that is cutpoint independent, 

we constructed the receiver operating characteristic curve 

and calculated the area under curve (AUC).

The applicability of the models to account for the effects 

of stand density on branch properties was tested using the 

marginal residuals. The marginal residuals were calculated 

as a difference between the measured observation and the 

predicted value on the data scale. Depending on the level of 

the measurements (whorl or branch level), the models used 

to test for possibly remaining treatment effects were:

 

lptw lptw lptlplD uuuu lptw ( yy ˆ ) +++++=− τμ (2a)

or

lptwb lptwb lptlplD lptw lptwb ( yy ˆ ) τμ ++++++=− uuuuu

(2b)

where ( ˆ ) lptw lptw − yy are the marginal residuals, μ is the 

overall mean, D the treatment effect, and ul, ulp, ulpt, ulptw

and ulptwb the random effects for location l, plot p, tree t, 

whorl w and branch b. For comparison of the three treatments, a Bonferroni adjustment was used α=0.05. In order 

to analyze the performance of the models for effects of the 

three pruning intensities we applied the same procedure 

as described in the section on stand density. We therefore 

tested the marginal residuals as well for remaining pruning 

effects in a mixed model.

The predictive power r of the models was calculated as 

the squared correlation between the observed response 

and the marginal model predicted value on the data scale 

(Zheng and Agresti 2000):

r 2 = (cor(Y, Yˆ ))2

 (3)
FOREST GROWTH AND TIMBER QUALITY

27

where Y is the observed dependent variable at the data 

scale and ˆY the marginal estimated value of Y given the 

fixed effects predictors. 

The following measures were used to compare the 

goodness of fit of the models: sensitivity to silvicultural 

measures, mean error, mean absolute error, mean squared 

error, the analysis of the marginal residuals for residual 

effects, and the predictive power. As a substitute to the 

predictive power (Model 3) for the model on branch status 

we used the values for sensitivity, 1-specificity (both at a 

predicted probability of 0.5 and at the maximum Youdenindex), and the AUC-value.

All of the linear statistical analyses were carried out by 

SAS software (SAS 2004, 2006). 

RESULTS

Model: Number of Branches Whorl-1

For the construction of the model on number of branches 

whorl-1 the combined number of living and dead branches 

on all the whorls available was used. The dataset contained 2,226 whorls from 100 trees. For the total number 

of branches per whorl (nbrt), a log-link function with the 

Poisson distribution was used: 

( ) lptw lpt lptw lpt lptw ln 10 2ihahdaanbrt αα ++++= 

(4) 

The number of branches per whorl was related to the heightto-diameter ratio (hd-ratio) and annual height increment 

(ih) (Table 4). No other variables were found statistically 

significant. The error statistics (Equation 1a – c) showed no 

large bias (Table 4) and there was no trend in the residuals 

when plotted against the hd-ratio, the height increment, or 

the predicted values of nbrt. The residuals in initial spacings 

of 100, 200 and 1200 trees ha-1 did differ slightly from each 

other (Table 7) with the highest difference (1.4 branches 

whorl-1) occurring between the 100 and the 1200 initial 

spacing plots. The model explained only a low proportion 

from the total variance (6.1 percent).

Model: Branch Angle

For the construction of the model on the branch angle we 

used all observations within the green crown whether from 

pruned or from unpruned trees. The dataset contained a 

total of 11,493 branches from 85 trees. Since branch angle 

(bra) was measured in discrete steps of 5 degrees, a log-link 

function with the Poisson distribution was used:

lpt lptw lptwb

lptwb lpt lptw lptwb brdcdistchdccbra

γγγ +++

10 ++= 2 + 2 )ln( 3

(5) 

The predictors of the branch angle model were the hd-ratio, 

the branch position within the living crown (dist3), and 

the branch diameter (Table 4). No other tree level variables 

were statistically significant. The error statistics (Equation

1a – c) showed no large bias but a large mean squared error 

(Table 4) and there was no trend in the residuals when plotted against the predictors or predicted values (Fig. 2). The 

residuals of the model did not differ significantly between 

the initial spacings (Table 7). The model explained 25.8 

percent of the total variance.

Model: Branch Status (Living or Dead)

The model for the status of individual branches (brs) was 

based on all the branches in the dataset within the living 

crown excluding the trees with pruning to a stem height 

of more than 2.5m (Nb=6879, Nt=43). Status of a branch 

is a binary phenomenon (0, dead; 1, living). Therefore, a 

logit-link function with a binomial distribution was used 

to model the probability (Pr) that a branch is alive:

Table 4—Parameter estimates of the model for the number of branches in a whorl (left, Equation 4, Nt=100, Nw=2226) and of the model 

for branch angle (Equation 6, Nt

=85, Nbranch=11493).

Parameter Estimate se (Sx

_) t-value p > t Estimate se (Sx_) t-value p > t

Fixed parameters

a0 1.711 .1250 13.75 <.0001 c0 4.6698 .01 75.48 <.0001

a1 .0052 .0020 -2.62 .00 c1 -.0038 .000 -4.24 <.0001

a2 .5543 .0558 . <.0001 c2 .2438 .0115 21.14 <.0001

a3 - - - - c3 -.0177 .0034 -5.24 <.0001

Error statistics

E .21 1.3749

|E| 2.50757 8.8577 

E2 10.2 138.3430
FOREST GROWTH AND TIMBER QUALITY

2

Table 6—Parameter estimates of the models for the diameter of thickest branch (left, Equation 7; Nt=85 Nw=1662) and smaller 

branches (right, Equation 7; Nt

=85 Nb=9831) in a whorl.

Parameter Estimate se (Sx

_) t-value p > t Estimate se (Sx_) t-value p > t

Fixed parameters

d0 .2 .072 12.02 <.0001 e0 -3.5258 1.6015 -2.20 .0464

d1 .0152 .0035 4.32 <.0001 e1 .102 .027 3.47 .0005

d2 -.0068 .0022 -3.05 .002 e2 .1480 .002 17.95 <.0001

d3 -2.4167 .112 -21.40 <.0001 e .4000 .0156 -25.60 <.0001

d4 2.112 .0615 34.44 <.0001 - - - -

Error statistics

E .00 .0147 

|E| .5474 .10

E2 .5313 .020

Table 5—Parameter estimates of the linear model for model for branch status (1, living; 0, dead) (Equation 5) 

Nt

=43 Nb=6879.

Parameter Estimate se (Sx

_) t-value p > t

Fixed parameters

b0 7.6453 1.6395 4.66 <.0001

b1 -.0578 .020 -2.22 .022

b2 5.0967 .2 15.77 <.0001

b3 .0985 .002 12.02 <.0001

Error statistics E=-.0190 |E|=.0732 E2=.0495

Cutpoint = .50 predictions “0” predictions “1”

observations “0” 48.4% (ok) 51.6% (wrong)

observations “1” 1.8 % (wrong) 98.2% (ok)

Cutpoint = .76 (max. Youden Index)

observations “0” 88.3% (ok) 11.7% (wrong)

observations “1” 12.4% (wrong) 87.6% (ok)

( )

lpt lptw lptwb

ptw

ptwb

3

2lpt10 lptw

lptwb

lptwb

maxbrd

brd

b

2distbhdbb

)brsPr(1

)brsPr( ln

+ βββ +++

++=

















−

(6) 

The branch status was related to the hd-ratio, the branch 

position within the living crown (dist2), and the relative 

branch diameter within a whorl (Table 5). The other variables were not statistically significant. The error statistics 

(Equation 1a – c) showed no large bias (Table 5) and there 

was no trend in the residuals when plotted against the hdratio, position within the crown, relative branch diameter, 

or predicted values of the branch status. The residuals of 

the model did not differ significantly between the initial 

spacings (Table 7). The area under the ROC-curve was high: 

AUC=0.945. At a cutpoint of 0.5 the true positive rate (living branches) was satisfyingly high (98.2 percent). However 

the false negative rate is also high (51.6 percent) (Table 

5). With the optimal cutpoint at Pr=0.76 the sensitivity is 

still high: 87.6 percent and the 1-specifity is improved to 

11.7 percent.

Model: Maximum Diameter Branch Whorl-1

For building the model on maximum branch diameter, only 

whorls with at least one branch were taken. The parameters of this model were estimated using a dataset of 1,662 

branches from 85 trees. For the model of the maximum 

branch diameter in a whorl (brdmax), a log-link function 

with a normal distribution of the response variable was 

used: 

lptw lpt lptw lptwb + 4 distd 3 δδδ +++

( ) lptw lpt lpt lptw brd maxln +++= distdhddbhddd 1 10 2 3

(7)

The diameter of the thickest branch in a whorl was related 

to the tree’s diameter at breast height (dbh), the hd-ratio, 

and the whorl location within the living crown. The other 

variables were not statistically significant (Table 6). The 

error statistics (Equation 1a – c) show no large bias (Table 

6). In addition, no trend in the residuals was found when 

plotted against the predictors or the predicted variable. 

Furthermore, the residuals did not differ between the initial 

spacings (100, 200, and 1200 trees ha-1, Table 7). The model 

explained 85.3 percent of the total variance.
FOREST GROWTH AND TIMBER QUALITY

2

Table 7—Residual means for the four models tested for differences between the initial densities of 100, 200, and 1200 trees ha-1.

model

100 200 1200

mean se (Sx

_) mean se (Sx_) mean se (Sx_)

Eq.4 -.92a .2958 -.77b .3174 .48ab .5491

Eq.5 2.1a 1.3654 -1.47a 1.1751 1.40a 1.2772

Eq.6 -.02a .0122 -.02a .0143 -.02a .012

Eq.7 .17a .02 -.04a .07 -.02a .072

Eq.8 -.01ab .012 .01ab .0117 -.05ac .0114

The values in the same row marked with a different superscript are significantly different (p>0.05)

Model: Smaller Branches Whorl-1

For the model of the smaller branches’ diameters (omitting 

the thickest branch per whorl) 9,831 branches from 85 trees 

were available. Only whorls with at least 2 branches were 

included in the dataset. The dependent variable was the ratio 

between the diameter of a smaller branch and the thickest 

branch in each whorl, i.e. the values of the dependent variable vary between 0 and 1. If the other branches of a whorl 

had the same diameter as the thickest branch, their diameter 

was reduced by 0.1mm (1/10th of measurement accuracy) 

to avoid non-defined values in the log-transformation. For 

the model of relative branch diameter, a logit-link function 

with a binomial distribution was used: 

lptw lptwb lptlp lptw lptwb + renbrte +++++ εεεε 2 2

lp

ptw

ptwb

ptw

ptwb siee

brd

brd

brd

brd

+=































 − 10 max

1/

max

ln

(8) 

The diameters of the smaller branches were related to 

the site index, the total number of branches whorl-1 and 

their rank within a whorl according to branch diameter 

from rank 2 on (Table 6). The relative diameters of the 

smaller branches were not related to whorl position within 

the living crown. The error statistics (Equation 1a - c) did 

not show a large bias (Table 6) and there was no trend 

in the residuals when plotted against the predictors and 

the dependent variable. Furthermore, the residuals of the 

model did not differ systematically from low to high initial 

density levels (Table 7). The model explains 58.0 percent 

of the total variance.

Simulations

Predictions of the branchiness models as a part of the growth 

and yield simulation system are demonstrated in Figure 1 

and 2. With increasing annual height increment, the number 

of branches in a whorl also increases (Fig. 1A). However, 

trees with higher hd-ratios have fewer branches per whorl. 

With increasing hd-ratio, the branches are more steeply inserted within the crown (Fig. 1B). Along the crown profile all 

branches tend towards a more horizontal insertion. Larger 

branches are more steeply inserted than smaller branches 

(Fig. 1B vs. C). The thickest branch in each whorl has a 

high probability of being alive throughout the living crown 

(Fig. 1D). However, smaller branches tend to die early when 

they are located in the lowest quarter of the living crown. 

With increasing stem diameter and decreasing hd-ratio, the 

diameter of the thickest branch per whorl increases over 

the total length of the living crown (Fig. 2A, B). The size of 

smaller branches within the crown is demonstrated (Fig. 

2C-F) in varying levels and combinations of branch rank, 

diameter at breast height, and hd-ratio.

Figure 1—(A) Predicted number of branches in a whorl for three hd-ratios 

plotted against the annual height increment (Equation 4). (B) Predicted 

branch angle within the living crown for three hd-ratios at a branch 

diameter of 2cm. (C) The same as (B) but branch diameter = 5cm (both 

Equation 5). (D) Predicted probability for a branch being alive within 

the living crown for two hd-ratios combined with two branch relative 

diameters (Equation 6). 0=apex, 1=crown base. The abbreviations refer 

to the explanations given in Table 1.
FOREST GROWTH AND TIMBER QUALITY

0

DISCUSSION

Model: Number of Branches Whorl-1

The hd-ratio can be used as a general indicator for the vigour 

of a tree. In our model the number of branches increased 

with decreasing hd-ratio. According to the previous studies for Scots pine and Norway spruce, the number of new 

branches in a whorl increases with increasing vigour of 

trees (e.g. Kellomäki and Tuimala 1981; Hein et al. 2007). 

The number of branches in a whorl is also related to annual height increment, which is again indicative of tree 

vigour (e.g. Mäkinen and Colin 1999; Hein et al. 2007). 

A possible explanation is that the number of branches 

in a whorl as well as height increment, is controlled by 

the growing conditions during two successive years. For 

Scots pine, Junttila and Heide (1981) and Junttila (1986) 

observed that temperature during bud formation has an 

effect on final shoot length achieved in the following year. 

The influence of tree social position and annual height 

increment on the number of branches per whorl has also 

been observed in Pacific Northwest Douglas-fir (Maguire 

et al. 1994; Weiskittel et al. 2007). 

Annual height increment, which was used as an independent variable in this study, is only occasionally measured. 

However, in growth simulation systems, annual or periodical height increment is often estimated with the help of a 

height increment model. The year-to-year variation in the 

number of branches can then be added according to the 

observed large residual variation. Only a low percentage 

of total variance in the number of branches could be explained. One reason for this could be that the number of 

branches is under moderate genetic control (Velling 1988; 

Liesebach 1994; Vestøl et al. 1999). Another explanation 

may be that our analysis did assess all branches per whorl 

down to the threshold branch diameter for timber grading 

of 5mm. Previous studies on Norway spruce stopped at 

less than the first six branches starting from the thickest 

(Schmidt 2001). However, van Laar (1967), Lewark (1981), 

and Weiskittel et al. (2007) also found a large variability 

in the number of branches per whorl.

Model: Branch Angle

The angle at which branches are attached to the stem has a 

major influence on crown form as well as wood quality. On 

an individual tree, branch angle is largely determined by 

the effects of gravity and light availability. Hence, branch 

diameter and location in the crown were particularly important determinants of branch angle in this study. In addition, tree social position in the stand can be a significant 

factor influencing branch angle. This study supports this 

general observation since branch angles became flatter as 

the tree hd-ratio increased. In the case of Douglas-fir in 

the Pacific Northwest, site index has been found to exert a 

significant influence on branch angle, even after accounting 

for branch size and tree social position (Roeh and Maguire 

1997; Weiskittel et al. 2007). However, site index was not 

found to influence branch angle in German Douglas-fir. 

Model: Branch Status (Living or Dead)

Branch status was modeled within the living crown from 

the stem apex to crown base. The main emphasis was on 

modeling the progress of branch die-off within the living 

crown. It was assumed that branch death at a certain relative distance between the stem apex and crown base is 

independent of the actual length of the living crown. The 

probability of a branch being alive diminished towards 

the base of the living crown in accordance with a reverse 

S form. The shape of the curve was the same regardless of 

Figure 2—(A) Predicted diameter of the thickest branch in a whorl within 

the living crown for two dbhs and hd=40. (B) The same as (A) but hd=80 

(Equation 7). (C) Predicted branch diameters within the living crown 

for three branches of different diameter rank within a whorl (nbrt=4, 

si=60m, dbh=25 cm, hd=40). (D): The same as (C) but hd=40 (Equation 

7). (E) Predicted diameter for branches with rank 5 for two dbhs at a 

hd-ratio of 40 (nbrt=4, si=60m, dbh=25 cm) (Equation 7). (F) The same 

as (E) but hd=80. 0=apex, 1=crown base. The abbreviations refer to the 

explanations given in Table 1.
FOREST GROWTH AND TIMBER QUALITY

1

initial stand density. The model accounted for a sufficient 

proportion of the total variation in branch status. The 

emergence of spike knots results in irregular development 

of branches and may cause additional variation in branch 

mortality.

Stand density is known to be a strong determinant of 

branch mortality and, therefore, it controls branch die-off 

(e.g. Valentine et al., 1994). In our model, increasing competition associated with increasing hd-ratio decreased the 

probability of a branch being alive. Furthermore, the large 

branches in a whorl had a greater probability to remain 

alive than the smaller ones in the same whorl (c.f. on Norway spruce Mäkinen and Colin 1999). Mutual shading by 

branches from upper parts of the crown and neighboring 

trees (Grote and Pretzsch 2002) may give a physiological 

explanation for the statistical model described. The experiments sampled in this study were on rather young trees, 

under 50 years old. Mäkinen et al.(2003) showed that for 

Norway spruce tree age had an effect on the number of 

living branches at a given depth within the crown. Thus, 

it can be expected that the model for the probability of a 

branch being alive must be adapted to older trees.

Models: Branch Diameter

Factors promoting the diameter growth of a tree increase 

branch diameters as well (cf. Kenk 1990). As with branch 

status, branch diameter is closely related to the hd-ratio 

and branch location within the living crown. However, 

differences in branch diameters between trees of different stem diameter (hd and dbh) were larger in the lower 

crown than in the upper crown (Mäkinen 1999). Kantola 

and Mäkelä (2004) also reported for Norway spruce that in 

the first five meters downwards from the tree top, branch 

size did not differ between thinning intensities. Obviously, 

branch growth in the upper crown is not closely related to 

between-tree competition.

Within the living crown, the thickest branches were 

located around 75 percent of the crown length from the 

tree top downwards. Decreasing branch diameters when 

moving downwards near the crown base have also been 

reported by Colin and Houllier (1992) for Norway spruce 

and by Maguire et al. (1994) for Douglas-fir in the Pacific 

Northwest. In a dynamic application, a decreasing branch 

diameter trend near the crown base may cause illogically 

declining branch diameter estimates under some conditions. The mutual dependence between thickest branch and 

smaller branches was taken into account by estimating the 

smaller branches relative to the size of the largest branch 

whorl-1 (see also Hein et al. 2007). 

CONCLUSIONS

Even though the spacing experiments on Douglas-fir were 

originally designed for the development of branchiness 

models, the plots provided interesting information for 

forest management practice. The results demonstrated the 

possibility to predict the effects of a wide range of stand 

densities on branch characteristics with only one model. 

In addition, the behaviour of the models is logical and in 

accordance with the earlier studies. When integrated into 

a stand growth simulator, the models allow simultaneous 

comparison of the effects of different silvicultural treatments 

on tree growth and branchiness. 

Stem and crown properties were sufficient to predict 

reliable branch properties. Thus, branch properties can 

be predicted without detailed knowledge of the past and 

current stand conditions if tree- and crown-level variables 

that synthesize their effects are measured. Even though 

the models were largely unbiased in respect to initial stand 

density, they could not be evaluated in respect to other 

silvicultural treatments. For example, species admixture 

may affect branch profiles in the crown due to changes in 

resource utilization.

LITERATURE CITED

Abetz, P. 1987. Das “Solitärprogramm 1987”. AFJZ 45/ 

1987: 1172. [Original in German]

Abetz, P.; Lässig, R. 1989. Erfreuliches Echo auf das 

“Solitärprogramm 1987”. AFJZ 27/ 1989: 714-716. 

[Original in German]

Achim, A.; Gardiner, B. 2006. Predicting the branching 

properties of Sitka spruce grown in great Britain. New 

Zealand Journal of Forestry Science 36: 246–264.

Agresti, A. 2002. An introduction to categorial data 

analysis. Wiley-Interscience. New York. 710 p.

Colin, F.; Houllier, F. 1992. Branchiness of Norway 

spruce in Northeastern France: Predicting the 

Main Crown Characteristics from Usual Tree 

Measurements. Annals of Forest Science 49: 511-538.
FOREST GROWTH AND TIMBER QUALITY

2

Garber, D.M.; Maguire, D.A. 2005. Vertical trends in 

maximum branch diameter in two mixed-species 

spacing trials in the central Oregon Cascades. 

Canadian Journal of Forest Research. 35: 295-307.

Grace, J.C.; Pont, D.; Goulding, C.J. 1999. Modeling 

branch development for forest management. New 

Zealand Journal of Forest Science 29: 391-408.

Gregoire, T.G.; Schabenberger, O.; Barret, J.B. 

1995. Linear Modelling of Irregularly Spaced, 

Unbalanced, Longitudinal Data from Permanent-Plot 

Measurements. Canadian Journal of Forest Research

25: 137–156.

Grote, R.; Pretzsch, H. 2002. A model for individual 

tree development based on physiological processes. 

Plant Biology 4: 167-180.

Hein, S.; Mäkinen, H.; Yue, C.; Kohnle, U. 2007. 

Modelling branch characteristics of Norway spruce 

from wide spacings in Germany. Forest Ecology and 

Management 242: 155-164.

Junttila, O. 1986. Effects of temperature on shoot 

growth in northern Provenances of Pinus sylvestris L. 

Tree Physiology 1: 185-192.

Junttila, O.; Heide, O.M. 1981. Shoot and needle growth 

in Pinus sylvestris as related to temperature in northern 

Fennoscandia. Forest Science 27: 423-430.

Kantola, A.; Mäkelä, A. 2004. Crown Development in 

Norway Spruce (Picea abies (L.) Karst.). Trees 18: 408-

421.

Kauermann, G.; Carroll, R.J. 2001. A Note on the 

Efficiency of Sandwich Covariance Estimation. 

Journal of the American Statistical Association 96: 

1387-1396.

Kellomäki, S.; Tuimala, A. 1981. Effect of Stand Density 

on Branchiness of Young Scots Pine. Folia Forestalia 

478: 1-27.

Kenk, G. 1990. Fichtenbestände aus Weitverbänden 

—Entwicklung und Folgerungen. Forstwissenschaftliches Centralblatt 109: 86-100.

Lewark, S. 1981. Untersuchungen von Holzmerkmalen 

junger Fichten (Picea abies (L.) Karst.) Jahrringbreite, 

Rohdichte und Ästigkeit von Stecklingsklonen. PhD, 

Universität Göttingen. 193 p. [Original in German 

with English summary]

Liesebach, M. 1994. Untersuchungen an 

ausgewählten Herkünften des internationalen 

Fichtenprovenienzversuchs 1964/68 über den 

Zusammenhang zwischen Isoenzym-Merkmalen 

und morphologischen, phänologischen sowie 

Wachstumsmerkmalen. PhD, Universität Hamburg. 

210 p. [Original in German with English summary]

Littell, R.C.; Milliken, G.A.; Stroup, W.W. [et al.]. 

2006. SAS System for Mixed Models. Cary, North 

Carolina, USA. 814 p.

Maguire, D.A.; Moer, M.; Bennet, W.S. 1994. 

Models for Describing Basal Diameter and Vertical 

Distribution of Primary Branches in Young Douglasfir. Forest Ecology and Management 63: 23-55.

Mäkinen, H. 1999. Growth, suppression, death, and 

self-pruning of branches of Scots pine in southern and 

central Finland. Canadian Journal of Forest Research

29: 585-594.

Mäkinen, H.; Colin, F. 1999. Predicting the Number, 

Death and Self-Pruning of Scots Pine in Finland. 

Canadian Journal of Forest Research 29: 1225-1236.

Mäkinen, H.; Ojansuu, R.; Niemistö, P. 2003.

Predicting external branch characteristics of planted 

silver birch (Betula pendula Roth.) on the basis of 

routine stand and tree measurement. Forest Science 

49: 301-317.

McCullagh, P.; Nelder, J. A. 1999. Generalized Linear 

Models. Chapman & Hall/CRC, Boca Raton. 511 p.

Roeh, R.L.; Maguire, D.A. 1997. Crown profile models 

based on branch attributes in coastal Douglas-fir. 

Forest Ecology and Management 96: 77-100.

SAS. 2004. SAS/STAT 9.1 User’s Guide. SAS Publishing, 

Cary, NC. 5121 p.

SAS. 2006. The GLIMMIX Procedure. SAS Publishing, 

Cary. 256 p.

Schmidt, M. 2001. Prognosemodelle für ausgewählte 

Holzqualitätsmerkmale wichtiger Baumarten. PhD, 
FOREST GROWTH AND TIMBER QUALITY



Universität Göttingen. 302 p. [Original in German 

with English summary]

Snijders, T.A.B.; Bosker, R.J. 1999. Multilevel Analysis. 

SAGE Publications Ltd, London. 266 p.

Valentine, H.T.; Ludlow, A.R.; Furnival, G.M. 

1994. Modeling crown rise in even-aged stands of 

Sitka spruce or loblolly pine. Forest Ecology and 

Management 69: 189-197.

van Laar, A. 1967. Single-Tree Parameters of Norway 

Spruce (Picea abies (L.) Karst.) in Relation to Site 

and Environment. Forstliche Forschungsberichte 

München, Schriftenreihe der Forstwissenschaftlichen 

Fakultät der Universität München und der Bayer. 

Forst-u. Forschungsanstalt, 30. 88 p. [Original in 

German]

Velling, P. 1988. The Relationships between Yield 

Components in the Breeding of Scots Pine. PhD, 

University of Helsinki. 59 p.

Vestøl, G.I.; Colin, F.; Loubère, M. 1999. Influence of 

Progeny and Initial Stand Density on the Relationship 

between Diameter at Breast Height and Knot Diameter 

of Picea abies. Scandinavian Journal of Forest 

Research 14: 470-480.

Weiskittel, A.R.; Maguire, D.A.; Monserud, R.A.; 2007.

Modeling crown structural responses to competing 

vegetation control, thinning, fertilization, and Swiss 

needle cast in coastal Douglas-fir of the Pacific 

Northwest, USA. Forest Ecology and Management 

245, 96-109.

Youden, W. 1950. Index rating for Diagnostic Test. 

Cancer 3: 32-35.

Zheng, B.; Agresti, A. 2000. Summarizing the predictive 

power of a generalized linear model. Statistics in 

Medicine 19: 1771-1781.

FOREST GROWTH AND TIMBER QUALITY

35

Radiata Pine Crown Development: Model, Model 

Performance, and Incorporation into Forest Inventory

Jennifer C. Grace 

Jennifer C. Grace (jenny.grace@ensisjv.com) is a senior scientist at Scion, Private Bag 3020, Rotorua, New Zealand.

EXTENDED ABSTRACT

RADIATA PINE (Pinus radiata D. Don) IS THE MAIN 

commercial forestry species grown in New Zealand, 

covering 1.6 million ha within a land area of 26.9 

million hectares (New Zealand Forest Owners Association, 

2006). New Zealand covers a wide range of environmental 

conditions and early research indicated that there were 

significant differences in the patterns of radiata pine growth 

across the country (Goulding 1994). To account for this 

variation, separate stand and individual tree distance-independent growth models have been developed for different 

regions within New Zealand. 

Radiata pine is also genetically variable. This variability 

has been exploited in a tree-breeding program that has 

been in place since the 1950’s (www.rpbc.co.nz). Different 

“breeds” of radiata pine have been developed, including 

the “Growth and Form (GF) Breed” developed to produce 

trees with fast growth and excellent form and the “Long 

Internode Breed” developed to produce knot-free wood from 

unpruned trees (Jayawickrama and Carson 2000). This later 

breed, in particular, exploits the genetic variability in the 

number of branch clusters formed annually, and has fewer 

clusters in an annual shoot compared to the “Growth and 

Form Breed”. In addition, trees with long internodes tend 

to have larger-diameter branches compared with more 

multinodal trees (www.rpbc.co.nz).

A model predicting crown development in radiata pine 

with a “Growth and Form” rating of GF14 has been developed by destructively sampling 49 trees from eight different 

regions within New Zealand. This has been linked with 

the individual-tree distance-independent growth model 

to create the model “TreeBLOSSIM”. As with the growth 

model, this is a regionally based model. The branching 

component of TreeBLOSSIM is hierarchical in structure. At 

the tree level, it predicts the probability that the tree will 

form stem cones. At the annual shoot level, it predicts the 

number of branch clusters formed and their relative position within the annual shoot. At the cluster level it predicts 

the number of stem cones and branches formed, and their 

angular distribution around the stem. At the branch level, 

it predicts the change in branch diameter through time, the 

age when the branch dies (when the branch knot becomes 

bark encased), and whether there will be bark trapped 

above the live branch (Grace et al. 1998, Grace et al. 1999, 

Grace 2004). 

As with any model, it is important to demonstrate that 

TreeBLOSSIM provides realistic predictions across a wide 

range of sites, silvicultural treatments, and improved seedlots. Model performance in predicting the number of branch 

clusters and the diameter of the largest branch in a cluster 

was examined by comparing model predictions with measurements collected from images using a non-destructive, 

ground-based photogrammetric method, TreeD (Brownlie et 

al. 2007). To date, TreeD data have been collected from 19 

trials. Each trial contains a number of permanent sample 

plots (PSPs), and several were assessed to provide data for 

selected silvicultural treatments and/or seedlots. In total 

measurements are available for:

• 259 trees from 54 PSPs with a GF rating of 14 

• 193 trees from 35 PSPs with a GF rating between 21 

and 25

• 134 trees from 25 PSPs containing long internode seedlots with a long internode rating between 19 and 28 

In terms of “average branch diameter”, TreeBLOSSIM 

This extended abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: 

Crown models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. 

Tech. Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 35–36.
FOREST GROWTH AND TIMBER QUALITY



predictions were good with 85 percent of the GF14 trees falling within the defined acceptable limits. The performance 

was similar for the GF20+ seedlots, but noticeably poorer 

for the long internode seedlots. In terms of “maximum 

branch diameter”, TreeBLOSSIM predictions were good 

for 54 percent of the GF 14 trees. The performance was 

similar for the GF20+ seedlots but noticeably poorer for 

the long internode seedlots. Images were re-examined for 

trees where the “maximum branch diameter” prediction 

was poor. This highlighted that stem damage is a common 

occurrence at some sites and has a major influence on the 

branching characteristics of radiata pine, resulting in larger 

than expected branch diameters. In terms of “number of 

branch clusters”, TreeBLOSSIM predictions were good for 

48 percent of the GF14 trees, but TreeBLOSSIM tended to 

predict more clusters than observed. TreeBLOSSIM predictions were slightly better for the GF20+ seedlots, and indicate 

that the GF20+ seedlots have more branch clusters than 

the GF14 seedlots. TreeBLOSSIM, as expected, predicted 

more branch clusters than observed for the long internode 

seedlots. These results give confidence in the model and 

its use within forest inventory.

During a forest inventory, a tree stem is visually classified into lengths according to a given set of maximum 

branch diameters, i.e. each stem length has an associated 

branch diameter class. Some typical values of maximum 

branch diameters that may be used are 4 cm, 7 cm, 10 cm, 

and 15 cm. These data may be imported into a version of 

TreeBLOSSIM included in Atlas Cruiser (developed by 

Atlas Technology, www.atlastech.co.nz). Rules are in place 

to adjust model predictions to correspond with the inventory data. One positive aspect of inventory data is that it 

will identify the unusually large branches that are often 

underpredicted by TreeBLOSSIM. 

The position of branch clusters is rarely measured in forest inventories. For situations where branch cluster positions 

have not been measured, the possibility of predicting the 

number of branch clusters from environmental variables 

has been investigated using the Land Environments of New 

Zealand (Leathwick et al., 2003). Where a field count of 

branch clusters is available, a method of using these data to 

estimate the number of branch clusters in an annual shoot 

has been developed.

Combining inventory data with TreeBLOSSIM allows 

TreeBLOSSIM to be adapted for specific sites and seedlots, 

and provides a realistic description of the branching pattern of the tree, including the position of unusually large 

branches, which may be grown forward in time to the 

required age to provide estimates of yield by log-types. 

KEYWORDS: Pinus radiata, branching, forest inventory, 

modeling

LITERATURE CITED

Brownlie, R.K.; Carson, W.W.; Firth, J.G.; Goulding, 

C.J. 2007. An image-based dendrometry tool for 

standing trees. New Zealand Journal of Forestry 

Science 37 (2): 153-168.

Goulding, C.J. 1994. Development of growth models 

for Pinus radiata in New Zealand—Experience with 

management and process models. Forest Ecology and 

Management 69: 331-343. 

Grace, J.C. 2004. Links between science and forest 

management: As illustrated by a model of branch 

development. In: Mencuccini, M.; Grace, J.; 

Moncrieff, J.; McNaughton, K.G., eds. Forests at the 

Land—Atmosphere Interface. CABI Publishing pp. 

255-267.

Grace, J.C.; Blundell, W.; Pont, D. 1998. Branch 

development in radiata pine—model outline and data 

collection. New Zealand Journal of Forestry Science

28: 182-194.

Grace, J.C.; Pont, D.; Goulding, C.J.; Rawley, B. 1999.

Modeling branch development for forest management. 

New Zealand Journal of Forestry Science 29: 391-408.

Jayawickrama, K.J.S.; Carson, M.J. 2000. A breeding 

strategy for the New Zealand Radiata Pine Breeding 

cooperative. Silvae Genetica 49 (2): 82-90.

Leathwick, J.; Wilson, G.; Rutledge, D. [et al.]. 2003.

“Land Environments of New Zealand (LENZ)—Nga 

Taiao o Aotearoa”. Ministry for the Environment, 

Wellington. 

New Zealand Forest Owners Association. 2006. New 

Zealand Forest Industry Facts and Figures 2006/7. 

New Zealand Forest Owners Association, Wellington.
FOREST GROWTH AND TIMBER QUALITY

7

Modeling Crown Recession in Three Conifer Species 

of the Northern Rocky Mountains

Sean M. Garber, Robert A. Monserud, Douglas A. Maguire

Sean M. Garber (sean.garber@oregonstate.edu) and Douglas A. Maguire are in the Department of Forest Science, Oregon State 

University, Corvallis, OR 97331, USA. Robert A. Monserud (retired) was a research forester and team leader at the Pacific Northwest 

Research Station, Portland, OR 97205, USA.

ABSTRACT

CROWN LENGTH IS A FUNDAMENTAL TREE

dimension that has important implications for 

growth potential, wildlife habitat, stand aesthetics, and wood quality. The relative rates of height growth 

and crown recession determine the progression of crown 

length over time. We investigated patterns in crown recession of three co-occurring species in the northern Rocky 

Mountains: western white pine (Pinus monticola Dougl. ex 

D. Don), ponderosa pine (Pinus ponderosa Dougl. ex P. & C. 

Laws.), and interior Douglas-fir (Pseudotsuga menziesii (Mirb.) 

Franco var. glauca). Past height, diameter, and crown length 

on 169 forest-grown trees were reconstructed by detailed 

stem analysis. Crown length was estimated for each year of 

the tree’s life by dating the mortality of all whorl branches 

and determining the progression of height to crown base. 

Five-year crown recession was modeled in two parts, the 

first predicting the probability that a crown recedes, and the 

second estimating recession distance conditional on its occurrence. The probability of crown recession increased and 

then decreased with increasing crown ratio for Douglas-fir, 

but increased monotonically with crown ratio in western 

white pine. Both behaviors were observed in ponderosa 

pine, depending on alternative definitions of crown base. 

The conditional distance of recession increased monotonically with crown ratio for Douglas-fir and ponderosa pine, 

but peaked at approximately 0.7 in western white pine. The 

resulting models have applications for simulating stand 

development under various silvicultural alternatives and 

predicting the effect of alternative management regimes 

on the quality of logs and wood products, architectural 

aspects of wildlife habitat, fuel distribution, and crown 

fire hazard.

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 37.
FOREST GROWTH AND TIMBER QUALITY



Analysis of Within- and Between-Crown Variability 

for mechanistic crown models

H. Temesgen, A.R. Weiskittel, D.A. Maguire, D.S. Wilson 

H. Temesgen (hailemariam.temesgen@oregonstate.edu) is an assistant professor, Department of Forest Resources, Oregon State University, 

Corvallis, OR 97331, USA; A.R. Weiskittel is an assistant professor, University of Maine, Orono, ME 04471, USA; D.A. Maguire is a professor 

and D.S. Wilson is a research associate, Department of Forest Sciences, Oregon State University, Corvallis, OR 97331, USA.

ABSTRACT

S

PECIFIC LEAF AREA (SLA) IS AN IMPORTANT 

ecophysiological trait variable, but its variability 

within- and between-crowns has rarely been examined and modeled across multiple species simultaneously. 

Using extensive datasets on SLA for coastal Douglas-fir 

[Pseudotsuga menziesii var. menziesii (Mirb.) Franco], hybrid 

spruce [Picea engelmannii Parry × Picea glauca (Moench) Voss

× Picea sitchensis (Bong.) Carr], and ponderosa pine [Pinus 

ponderosa Dougl. ex P. & C. Laws.], we examined variability 

of SLA within a canopy and its relationship with tree- and 

stand-level covariates. In all species, SLA systematically 

increased from tree tip to crown base and decreased with 

foliage age class. Cardinal direction did not have a highly 

significant influence in either Douglas-fir or hybrid spruce, 

but SLA did significantly decrease from branch tip to bole 

in hybrid spruce. Tree- and stand-level (e.g. age, density, 

site index) factors had relatively little influence on SLA. 

Consequently, a mixed linear model was fitted to estimate 

SLA at various points in the canopy for each species and 

foliage age class using absolute height in the canopy and 

relative vertical height in the tree. 

In this presentation, we also provide a hierarchical model 

that reconstructs within-stand variability of SLA for three 

important Pacific Northwest conifer species. Given that 

SLA is strongly correlated with leaf photosynthetic capacity, 

the model developed in this study can serve as a practical 

tool for assessing tree-level potential primary production 

in mechanistic crown models, can help to understand the 

photosynthetic capacity of the canopy, and refine estimates 

of key environmental conditions such as site water and 

radiation balances in mechanistic crown models.

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 38.
FOREST GROWTH AND TIMBER QUALITY



The Effects of Including a Model of Crown Shyness 

for Lodgepole Pine (Pinus contorta var. latifolia [Engl.] 

Critch.) in a Spatially Explicit Crown Growth Model

James W. Goudie, Kenneth R. Polsson, Peter K. Ott

James W. Goudie (jim.goudie@gov.bc.ca), Kenneth R. Polsson, and Peter K. Ott are scientists in the Research Branch of the BC Ministry of Forests, 

PO Box 9519, Victoria, BC V8W 9C2, Canada.

ABSTRACT

CROWN SHYNESS OR CANOPY DISENGAGEMENT, the phenomenon wherein gaps around 

trees develop from swaying, whipping, and shading, has been identified in the literature since the 1920s. 

Recent results by researchers at the University of Alberta 

have clearly described many of the processes involved for 

lodgepole pine (e.g. Rudnicki et al. 2001, 2003, 2004; Fish 

et al. 2006; Meng et al. 2006). Explicit models of crown 

shyness are in large part lacking in the literature. This 

paper describes the development of empirical models of 

crown shyness in lodgepole pine for British Columbia 

(BC). We measured crown area and neighbor locations on 

60 trees growing in 13 stands in central BC. We estimated 

potential crown area using crown maps, Voronoi polygons, 

and mixed-model frontier functions; and fit several models 

that relate observed crown area to various individual tree 

variables. One of the models was programmed into the Tree 

and Stand Simulator (TASS, Mitchell 1975) to evaluate the 

effect of various management scenarios on crown cover and 

simulated understory light environment. 

LITERATURE CITED

Fish, H.; Lieffers, V.J.; Silins, U.; Hall, R.J. 2006.

Crown shyness in lodgepole pine stands of varying 

stand height, density, and site index in the upper 

foothills of Alberta. Canadian Journal of Forest 

Resources. 9:2104-2111.

Meng, S.X.; Rudnicki, M.; Lieffers, V.J. [et al.]. 2006. 

Preventing crown collisions increases the crown cover 

and leaf area of maturing lodgepole pine. Journal of 

Ecology. 94:681–686.

Mitchell, K.J. 1975. Dynamics and simulated yield of 

Douglas-fir. Forest Science Monographs 17. 

Rudnicki, M.; Lieffers, V.J.; Silins, U. 2003. Stand 

structure governs the crown collisions of lodgepole 

pine. Canadian Journal of Forest Resources. 33:1238-

1244.

Rudnicki, M.; Silins, U.; Lieffers, V.J. 2004. Crown 

cover is correlated with relative density, tree 

slenderness, and tree height in lodgepole pine. Forest 

Science 50:356-363.

Rudnicki, M.; Silins, U.; Lieffers, V.J.; Josi, G. 2001.

Measure of simultaneous tree sways and estimation 

of crown interactions among a group of trees. Trees 

15:83-90.

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 39.

Hybrid Modeling 

Approaches

FOREST GROWTH AND TIMBER QUALITY

43

Hybrid Modeling Approaches

Keynote Presentation

Hybrid Models of Forest Stand Growth and Production

Annikki Mäkelä

ABSTRACT

I

N FOREST GROWTH MODELING, the term “hybrid 

model” is generally used for models that combine 

process-based elements with empirical elements at the 

same hierarchical level. Process models usually focus on 

the physiology of stand production and its dependence on 

the environment at variable time scales, while empirical 

models focus on predictions of the marketable product; 

i.e., the distributions of stems into diameter classes and 

stem attributes relevant for wood quality, over the stand’s 

rotation. Hybrid models hence aim at utilizing relevant 

physiological knowledge while simultaneously incorporating inputs and outputs applicable to forest management. The 

prospect of environmental change has further emphasized 

the importance of the hybrid approach.

Hybrid models defined in this way may be classified 

as follows:

1. Models that utilize process elements as submodels 

to provide additional inputs to empirical growth models. 

The inputs are often expressed as modifiers of the growth 

functions developed statistically, including, e.g., intercepted radiation, gross or net photosynthetic production, 

soil water status, or summary functions derived from full 

process model simulations (e.g., CanSPBL(water), MELAFinnFor).

2. “Genuine hybrid models” that derive potential growth 

from empirical data or functions, modified using a complex 

system of physiologically-based functions or submodels. 

This group includes models of the gap model family, and 

ecosystem models such as FORECAST.

3. Process-driven hybrid models where growth is derived 

explicitly from carbon acquisition and allocation. Empirical 

elements relate, e.g., to the allocation of carbon between 

and within trees, but also to the process of parameterization and calibration of the model as a whole (e.g. 3-PG, 

PipeStem, PipeQual, TRIPLEX).

This paper first presents a brief review of hybrid models, 

their objectives and model building philosophies, and then 

describes the process-driven hybrid approach in more detail 

using the PipeQual model as an example. Carbon acquisition in PipeQual is based on canopy photosynthesis and 

respiration. Size distributions follow from carbon allocation between trees, while the development of tree and stem 

structure is a result of carbon allocation within trees. The 

allocation rules are largely based on empirical relationships. 

The model produces stems with 3D structure as outputs and 

has already been applied to forest management problems. 

Finally, an outlook on the challenges and future prospects 

of developing hybrid models is presented.

KEYWORDS: Growth model, timber products, empirical, 

process-based, forest management, parameter estimation

Editors’ note: The author elected not to provide a full paper 

for these proceedings because it was being submitted to a refereed journal. As with all of the keynote addresses, this presentation was designed to provide context for the related presentations that follow. In lieu of the keynote paper, the author’s slides 

from the presentation are reproduced on the following pages to 

introduce the topic for this section of the proceedings. 

Annikki Mäkelä (annikki.makela@helsinki.fi) is a professor of silviculture (forest production), Department of Forest Ecology, University of Helsinki, 

PO Box 27 (Latokartanonkaari 7), 00014 Helsinki, Finland.

This presentation was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 43–47.
FOREST GROWTH AND TIMBER QUALITY

44

HELSINGIN YLIOPISTO

HELSINGFORS UNIVERSITET

UNIVERSITY OF HELSINKI

Methods for combining empirical and 

theory-based knowledge in growth and 

yield models

Annikki Mäkelä

Department of Forest Ecology

University of Helsinki

7.8.2007 Portland, Oregon

Needs for managment-oriented growth and 

yield models under change

 Value is based on

 wood products

 carbon sequestration

 biodiversity – woody debris

 ...

Model

system

Environment

Initial state

Yield,

Production

Utilisation Value

Management

optimise!

any region 

physiology

environmental drivers

stand level 

short to long time span

productivity

value?

too many inputs

uncertainties

Process models Empirical models

How to combine information / methods from both traditions

to improve growth and yield predictions? 

growth and quality 

rotation length 

explicit size distributions

stand structure 

management

changing site quality? changing site quality?

no extrapolation

Forest growth modelling Hybrid models?

 HYBRID: Thing made by combining two different 

elements. A mixture. (The New Oxford Dictionary of English)

 A HYBRID growth and yield model combines process 

elements and empirical elements

 Process element / Empirical element?

Process element / Empirical element?

Tree tree level

variables

auxiliary variables

integration

synthesis

empirical models

process models

functional organs

tissues

etc

i

i-1

analysis

reduction i i

all data at 

system level

construction data at analysis level,

validation data at system level

Hybrid models

 HYBRID: Thing made by combining two different 

elements. A mixture. (The New Oxford Dictionary of English)

 A HYBRID growth and yield model combines process 

elements and empirical elements

 empirical model with process submodels

 process model with empirical submodels at system level

 One way of combining theory-based and empirical 

knowledge - But many other ways exist! 

Options

 Hybrid models

 Reduced form models

 Environmentally driven empirical models

 Derivation of process parameters from system data

HYBRID models

 Hybridize statistical growth 

and yield models to 

incorporate process-based 

submodels

 Hybridize process-based 

models to incorporate 

statistical submodels 

Model

system

Environment

Initial state

Yield,

Production

Utilisation Value

Management

optimise!

any region
FOREST GROWTH AND TIMBER QUALITY

45

Hybridized statistical growth and yield models:

Examples

 METHOD 1: Additional inputs from a mechanistic submodel 

 CanSPBL(water) (Pinjuv et al. 2006, For Ecol Manage 236:37-46)

 A water balance model was added as a submodel to an empirical growth 

model; parameters were fitted accordingly

Model

Process

Original

inputs

Drivers

Outputs

Process

output

fitted model

Hybridized statistical growth and yield models:

Examples

 METHOD 2: Modifiers of model variables / outputs from a mechanistic 

submodel

 MOTTI with climate change impacts (Matala et al. 2006, Ecol Mod 

199:39-52)

 Relative change in volume growth predicted using FinFor, applied as 

modifier functions

Model

Process

Original

inputs

Drivers

Outputs

Process

output

fitted model

Modified

outputs

Hybridized process-based growth and yield 

models

 Production

 drives growth

 depends on the environment

 is well understood regionally

 Empirical submodels to 

describe allocation of carbon

 between trees

 within trees

Initial state

Production in

year k

New state

of trees Removal

Allocation

to trees

Allocation

in trees

New state

of stand

k=k+1

Plasticity

Rules

Local

environment

Site

Hybridized process-based growth and yield 

models: Examples

 3-PG (Landsberg and Waring 1997)

 Assimilation of carbon from a monthlybased model for NPP

 Mean tree approach

 Allocation within trees: 

- Empirical submodel based on 

allometric relationships

 Allocation between trees (stand 

structure)

- Empirical submodel to account for 

size distributions and their effect 

on mean size of removed trees 

Landsberg et al. Tree Phys 2005

Hybridized process-based growth and yield 

models: Examples

 PipeQual (Mäkelä and Mäkinen 2003, For Ecol Manage)

 Stand production from a summary model 

 Allocation between trees based on shading and photosynthesis

 Competition affects allocation

 Allocation within trees using allometric constraints for structure

 Theoretically-based vs empirical allometries?

Biological constraints or Empirical 

submodels? Examples

 Crown allometry:

WF = [ LC

z

 empirical model: best fit 

parameters

 optimal allocation of wood 

and foliage under shading, 

yields z | 2.5 (Mäkelä & 

Sievänen 1992) 

 fractal allometry of crown, 

yields 2  z  3 (Zeide and 

Pfeifer 1991) 

 volume filling fractal 

allometry, yields z = 3 (West

et al. 1999)

Spruce (Kantola and Mäkelä 2003)

pine

spruce

birch

Hybridized process-based growth and yield 

models: Examples

 PipeQual (Mäkelä and Mäkinen 2003, 

For Ecol Manage)

 Modular from tree to whorl to branch

 Empirical submodels for 

 dividing whorl basal area to individual 

branches

 wood properties in growth rings

(Mäkinen 2007)

Time:

continuous

Time step:

1 year

Structural

parameters

Distribution of

growth by whorls

Initial state

CROBAS WHORL BRANCH

5 biomasses

height

crown base

D13

Number and

Size

 of branches

in each whorl

PipeQual: Results from empirical submodels

 Model yields

 3D stems

 wood properties

 variable environments

 management options

 Cooperation:

 Metla, VTT, STFI-Packforsk, 

INRA, USDA Forest Service

Mäkelä & Mäkinen 2003 For. Ecol.Manage., Mäkelä & Valentine 2006 Ecology; Kantola et al. 2007 For.Ecol.Manage.
FOREST GROWTH AND TIMBER QUALITY

46

PipeQual: Branch Size

ODD

0

1

2

3

4

0 5 10 15 20 25 30

Distance from tree top (m)

W horl-m ean branch 

diam eter (cm )

Predicted

Measured

ODD

0

1

2

3

4

5

6

0 5 10 15 20 25 30

Distance from tree top (m)

Thickest branch in 

whorl (cm )

Predicted

Measured

ODS

0

1

1

2

2

3

0 5 10 15 20

Distance from tree top (m)

Thickest branch in whorl (cm)

Predicted

Measured

ODS

0

1

1

2

2

3

0 5 10 15 20

Distance from tree top (m)

Whorl-mean branch diameter 

(cm)

Predicted

Measured

Reduced form models

 Motivation:

 Process models may have too many inputs for practical use

 Often only few inputs / summarised input combinations 

relevant for system properties at the scale of interest

 A reduced model contains the relevant information but is 

more straight-forward to use and test

 Method:

 Reduce model form => number of parameters & inputs

 computer simulations

 mathematical derivation 

Reduced form models: Examples

 GPP = P0 (1 – exp(-k LAI))

environment •weather

•(light, temp, VPD, rain)

stand structure •grouping into crowns

•clustering

SPP Oker-Blom et al. 1989, 

Mäkelä et al. 2005)

P0

k

-12

-8

-4

0

4

8

12

16

20

0 100 200 300 400

Päivä vuoden alusta 

Keskilämpötila -10

0

10

20

30

40

50

60

70

80

0 100 200 300 400

Päivä vuoden alusta 

PAR (mol m-2 day-1) -2

0

2

4

6

8

10

12

0 100 200 300 400

Päivä vuoden alusta 

GPP (g C m-2 day-1)

T

PAR

GPP

julian day

Duursma and 

Mäkelä 2007

 Example (Mäkelä et al. in press, GCB): Prediction of ecosystem 

GPP on the basis of daily temperature, radiation, air humidity 

and LAI across geographic regions and vegetation zones

Hybridized process-based growth and yield 

models

Reduced form models: Examples

y = 0.4561x + 4.6841

R2

 = 0.9776

0

500

1000

1500

2000

2500

3000

0 2000 4000 6000

E APAR

GPP

Testing an annual level summary model (in prep.)

Eddy sites from Europe, America, Australia

E(N) APARGS

Reduced form models: Examples

 Derivation of diameter and height growth equations from a 

process-based growth model (PipeStem /CROBAS) 

(Valentine and Mäkelä 2005, Tree Phys.)

 Parameters are combinations of metabolic and structural 

parameters

 Model can be identified from parameter definitions but 

also by fitting to data on H, HC and D13

Environmentally driven empirical models

 Empirical growth models for D13, H, etc, with 

environmental factors as explanatory variables, e.g.

'D = 'Dmax f1(T) f2(I)

(JaBoWa)

 Objective: to make models easily applicable to different 

regions and to different local environments

 Often used in individual-based stand models, but

 no mass balance

 construction data and validation data at tree level

 => not process-based / hybrid under present definition

Environmentally sensitive empirical models: 

Example

SORTIE-BC

Pacala, S.W., Canham, C.D., Silander Jr., J.A., 1993. Can. J. For. Res. 23, 1980–1988.
FOREST GROWTH AND TIMBER QUALITY

47

Derivation of process parameters from system 

data

 Fudge factors

 Calibration

 "Inverse problem"

 Bayesian method, Monte Carlo simulation

Model

Prior

Posterior data

parameters prediction

Derivation of process parameters from system 

data: Examples

 FORECAST (Kimmins et al. 1999)

 Objective: Utilise "historical bioassay" in a process model

 "Hybrid approach" (Kimmins 1999) – but not a hybrid model in strict 

sense

 Extreme case of utilising output data for estimating process 

parameters – "Inverse problem" solution part of programme

Model

Prior

Posterior data

parameters prediction

NPP, shading, etc

Derivation of process parameters from system 

data: Examples

 Monte Carlo methods to estimate parameters 

 CROBAS (Mäkelä 1988, Scand. J. For Res.)

 Bayesian synthesis to estimate parameters and their 

uncertainty for process-based models

 PipeStem (Green et al. 1999. Forest Science 45:528-538)

 Four forest growth models (Van Oijen et al. Tree Phys 25:915–927)

Summary 1/2

 Growth and yield models need 

 environmental inputs

 outputs relevant for management decisions

 Hybridized empirical models

 fitted submodels: elaborate transformation of variables

 modifiers: requires confidence in reference PBM => the same 

problems as with PBMs in general

 Hybridized process models

 Carbon balance with constrained allocation a robust alternative

 Reduced form models

 allow us to utilise process understanding in more easily quantifiable 

models, more direct link to measurements

Summary 2/2

 Environmentally driven empirical models

 seems to require more work than (1) conventional empirical or (2) 

process-based models, but some results may be promising esp. for 

modelling competition

 Use of system-level data for parameterisation

 making this procedure systematic is a key to combining empirical

data sets with process models for applications

 could potentially unify modelling and join forces between 

statisticians and process modellers

 Whatever the strategy, modelling alone will not solve the 

problems of predicting into an uncertain future – biological 

experimentation is crucial
FOREST GROWTH AND TIMBER QUALITY

48

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 48.

Is There a Niche for Hybrid Models?

Margarida Tomé, José Tomé, Paula Soares

Margarida Tomé (magatome@isa.utl.pt), José Tomé, and Paula Soares are at the Universidade Técnica de Lisboa, Instituto Superior de Agronomia, 

Centro de Estudos Florestais, Tapada da Ajuda, 1349-017 Lisboa, Portugal.

ABSTRACT

THE TERM “HYBRID MODEL” HAS BEEN USED 

for models developed through a combination of 

process-based and an empirical models. Hybrid 

models offer practitioners advantages from both model 

types, including 1) the ability to simulate the effect of intensive silvicultural practices such as irrigation and/or fertilization, 2) sensitivity to climate change (as process-based 

models), 3) detailed output on stand structure attributes 

such as diameter distribution or merchantable volume to a 

given top diameter (as growth and yield models). The use 

of stand variables as link functions between the two types 

of models has been proposed by the authors in a previous 

study. (Tomé et al.2004). In this study, the methodology 

is further developed and tested with long-term data from 

permanent plots. Our goal was to combine the whole stand 

process-based model 3PG with the whole stand model 

GLOBULUS. One of the objectives of the hybridization 

process was to guarantee total compatibility between the 

outputs of the two models. For most sub-models compatibility was achieved through the fitting of new equations. 

During this hybridization procedure it was found that, in 

the end, not much was left from the original GLOBULUS 

model. The result of the hybridization process was actually 

an improved version of the 3PG model, complemented by 

new sub-models which guarantee simulations with the 

type of detailed output traditionally offered by growth 

and yield models.
FOREST GROWTH AND TIMBER QUALITY

49

ABSTRACT

Hybrid models offer the opportunity to improve 

future growth projections by combining advantages of both empirical and process-based modeling approaches. Hybrid models have been constructed in 

several regions and their performance, relative to a purely 

empirical approach, has varied. A hybrid model was constructed for intensively managed Douglas-fir plantations 

in the Pacific Northwest by embedding a hierarchy of 

components representing fundamental processes (e.g. light 

interception, photosynthesis, carbon allocation) into a spatially implicit individual-tree model. Simulated processes 

operated at a variety of scales from individual branches to 

trees and stands. The resulting hybrid model improved 

predictions of stand-level leaf area index (10–55 percent 

mean square error (MSE) reduction) and periodic annual 

increment (28–49 percent MSE reduction), and reduced 

the bias of individual-tree growth predictions (3–11 percent MSE reduction) when compared to existing models. 

These improvements were attributed to a finer resolution of 

crown structure and dynamics, simple yet mechanistically 

sound representation of key physiological processes at an 

appropriate spatial and temporal scale for simulating tree 

growth, and empirical growth equations that were modified 

by simulated physiological responses to annual climatic 

variation and site edaphic characteristics. The probability 

of individual-tree mortality was predicted equally well as a 

function of either growth efficiency (stemwood increment 

per unit leaf area) or conventional tree dimensions and 

stand density. Overall, the hybrid modeling framework 

showed significant potential for predicting growth of trees 

and stands from fundamental processes mediating tree 

responses to silvicultural treatments.

KEYWORDS: Douglas-fir, hybrid model, plantations growth 

and yield, intensive management

INTRODUCTION

THE LONG-TERM EFFECTS OF INTENSIVE MANAGEMENT on tree growth and stand yield are difficult to 

quantify empirically because natural variability necessitates 

extensive replication. In addition, a thorough understanding of long-term responses to complex treatment regimes 

requires continuous monitoring over a long period of time 

and over an entire region (Monserud 2002). Other difficulties are the constant change of intensive silvicultural 

practices and the relatively high degree of variability in local 

site conditions (e.g. soil, climate, aspect). Empirical growth 

and yield models can predict changes in productivity for 

management regimes represented in the modeling data, but 

their performance outside the range of data carries varying 

degrees of uncertainty. Even in regions with adequate data, 

predicted responses to management can vary dramatically 

due to choices made about the form of equations, predictor 

variables to include, and the manner in which equations 

are assembled into a growth simulator. Johnson (2005) 

recently found a very wide range (1.3–2.3 fold difference) 

of predicted responses to standard regimes of thinning, 

This paper was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 49–67.

Development of a Hybrid Model for Intensively 

Managed Douglas-fir in the Pacific Northwest

Aaron R. Weiskittel, Douglas A. Maguire, Robert A. Monserud 

Aaron R. Weiskittel (aaron.weiskittel@umit.maine.edu) is a forest modeling assistant professor, University of Maine, Orono, ME 04471, USA; Douglas 

A. Maguire is a professor of silviculture, Oregon State University, College of Forestry, Corvallis, OR 97331, USA; Robert A. Monserud (retired) was a 

research forester and team leader, USDA Forest Service PNW Research Station, Portland, OR 97208, USA.
FOREST GROWTH AND TIMBER QUALITY

50

fertilization, and the combination of these treatments among 

six empirical growth models that are widely available for 

species in the Pacific Northwest (PNW), USA.

Process-based models have recently found increasing application for decision-making in intensively managed forests 

(Mäkelä et al. 2000). These models offer the advantage of 

simulating growth responses to silvicultural treatments by 

representing some of the key ecophysiological mechanisms 

driving growth. As a result, they have a much greater capacity for predicting responses to natural and anthropogenic 

changes in environmental conditions, for example, annual 

weather fluctuations, changes in nutrient availability, and 

stand structural influences on environmental conditions. 

However, a strong theoretical basis does not currently exist 

for predicting all aspects of tree growth and morphology 

from fundamental physiology, and the number of parameters that must estimated can sometimes greatly exceed the 

number allowed in empirical models. The hybridization of 

empirical and process-based models has been proposed to 

retain the desirable attributes of both modeling approaches 

(Landsberg 2003a), while keeping parameter requirements 

to a minimum. Hybrid models have been successful at improving stand-level growth predictions (Pinjuv et al. 2006, 

Snowdon 2001, Woollons et al. 1997), but their performance 

in predicting individual-tree growth has been more varied. 

Baldwin et al. (2001) found that an individual-tree hybrid 

model was significantly superior to a purely empirical 

model for predicting growth of Pinus taeda trees in the 

southeastern USA. In contrast, Henning and Burk (2004) 

achieved only a moderate improvement in short-term predictions for mixed conifer and deciduous stands in north 

central USA. This type of modeling approach may be best 

suited for pure even-aged stands of a fast-growing species 

(Henning and Burk 2004), but this hypothesis has not been 

tested. However, it should be pointed out that these specific 

improvements should be expected as it is not surprising 

that residual variation around an empirical model can be 

explained by the use of actual weather information. 

The goal of this research project was to compare the 

performance of existing hybrid models and a newly developed model across a series of several silvicultural trials 

throughout the PNW. The specific objectives of this study 

were to (1) develop a hybrid model for intensively managed 

Douglas-fir stands, (2) compare a variety of approaches 

for mechanistically simulating individual-tree growth and 

mortality, and (3) test performance of the model relative 

to 3-PG and a purely empirical model across a wide range 

of intensively managed plantations. Recommendations for 

future work in refining hybrid models are discussed in the 

context of simulating Douglas-fir responses to silvicultural 

treatments and annual weather variation in the PNW. 

METHODS 

Model development

The modeling approach emphasized a hierarchical treatment 

of multiscale processes (Mäkelä 2003), with predictions 

made at the individual branch-, tree-, and stand-levels. 

The desired features of the model included (1) prediction 

of annual growth in diameter, height, and crown size of 

individual trees; (2) characterization of knot size, knot location, crown wood core, and sapwood width as determinants 

of wood quality; (3) sensitivity to annual climatic variables; 

(4) representation of soil water availability and its effect on 

tree growth; (5) representation of nutrient availability and 

its effect on tree growth; (6) simulation of light interception 

as influenced by solar geometry and stand density; and (7) 

prediction of responses to silvicultural regimes through 

treatment effects on basic ecophysiological processes controlling water and nutrient uptake, carbon assimilation, and 

carbon allocation. This approach ensured that the model 

was capable of answering the questions that motivated the 

modeling effort, i.e., the effect of silvicultural treatments, 

site conditions, and annual weather on wood yield, wood 

quality, and tree and stand structure. Likewise, the hybrid 

structure needed to take advantage of the current state of 

knowledge at the appropriate scale and offer the flexibility 

to accommodate future modifications due to improved 

data availability or physiological modeling. The model is 

comprised of three primary components: characterization of 

crown structure (BCACS), estimation of annual net primary 

production (NPP), and allocation of carbon and growth to 

different parts of the tree (ALOGRO) (Figure 1). The model 

is available online at: http://holoros.com/DF.HGS.htm. 

Branch, Crown, and Canopy Simulator (BCACS)—

The number, size, and location of branches, as well as the 

implied size and position of the live crown, determine 

stem, log, and product quality through their effects on 

micro-anatomical properties and knottiness of the wood 

(Bowyer et al. 2002). Branches are also an appropriate level 

to sample when estimating foliage amount (e.g. Kershaw 

and Maguire 1995), facilitating estimation of vertical foliage 

distribution, particularly in coniferous and other species 
FOREST GROWTH AND TIMBER QUALITY

51

with excurrent form (Garber and Maguire 2005, Maguire 

and Bennett 1996, Weiskittel et al. 2006). BCACS contains a 

set of empirical equations that predict the location, diameter, 

and biomass of every branch on each tree on the sample plot 

being simulated. The input is a tree list containing diameter 

at breast height (DBH), height (HT), height to crown base 

(HCB; lowest live branch), and expansion factor (EXPF, in 

trees per ha) as well as estimates of total age and site index 

(base age 50 years). Past height growth is reconstructed from 

the dominant height curves developed by Bruce (1981) to 

determine the location of annual whorls of branches. Branch 

diameter, length, and angle were predicted following the 

approach outlined by Maguire et al. (1994), but with the 

equations developed by Weiskittel et al. (in review). Branch 

Figure 1. Components of the modeling framework used in this study.
FOREST GROWTH AND TIMBER QUALITY

52

location was assumed to follow the empirical distribution 

in Maguire et al. (1994). Woody biomass, woody surface 

area, foliage biomass, and foliage area of all branches were 

predicted from basal diameter and relative height in the 

crown (Weiskittel and Maguire 2006, Weiskittel et al. 2006). 

These attributes were then summed to estimate biomass 

and surface area at the tree- and stand-levels. 

Total stem and sapwood volume were estimated at the 

tree-level from existing stem volume and sapwood taper 

equations (Maguire and Batista 1996, Walters et al. 1985). 

Volumes were converted to biomass by applying regional 

values for total and sapwood density (500 and 455 kg m-3, 

respectively). Belowground biomass at the stand level was 

estimated from total aboveground biomass assuming the 

relationship presented by Ranger and Gelhaye (2001). 

Crown projection areas were calculated from estimated 

crown widths of individual trees and these areas were then 

summed to determine percent canopy cover (Crookston 

and Stage 1999). 

Net Primary Production (NPP)—

Previous reviews of process-based models and their components (Grant et al. 2006, Landsberg 2003b, Medlyn et al.

2003, Schwalm and Ek 2001, Wang 2003) have suggested 

a common list of attributes that future models should 

possess to accurately capture the effects of silvicultural 

treatments, climate, and their interaction on NPP. These 

attributes include (1) daily time-step; (2) separation of direct and diffuse radiation; (3) light extinction coefficients 

dependent on solar geometry, canopy structure, and type 

of radiation; (4) separation of sunlit and shaded leaf area; 

(5) photosynthesis estimates based on the Farquhar et al.

(1980) biochemical equation, (6) site slope and aspect effects 

on diurnal distribution of radiation and fraction of sunlit 

leaf area (particularly in areas with complex terrain); (7) 

estimates of stomatal conductance as a function of vapor 

pressure deficit and soil water availability; and (8) canopy gas 

exchange linked to soil water and nutrition availability. 

All of these desired attributes were incorporated into 

the NPP submodel, as described below. Inputs were kept 

as simple as possible to capture the fundamental processes 

and included (1) daily climate obtained from DAYMET 

(http://www.daymet.org), (2) site physiographic features 

(elevation, slope, aspect), (3) stand structural attributes 

from BCACS (leaf area index (LAI), biomass, canopy cover, 

etc.), (4) basic soils information (rooting depth, texture, 

rock content), (5) foliar nitrogen concentration, and (6) 

physiological parameters obtained from the literature (Appendix 1). The model runs on daily time-step and estimates 

gross primary production (GPP) five times daily based on 

Gaussian integration (e.g. Leuning et al. 1995). The development of the current-year foliage was assumed to occur 

linearly for 30 days following bud burst, with date of bud 

burst predicted from a model developed by Thomson and 

Moncrieff (1982). Annual foliage litterfall and its seasonal 

distribution were predicted from an empirical equation 

(Weiskittel and Maguire 2007).

Light interception—

Although highly detailed light interception models exist (e.g. 

Brunner 1998), they still remain quite computer intensive 

and too complex for application in management-oriented 

hybrid models. Further, estimating light interception for 

an individual-tree crown based on canopy-level principles 

(e.g. Schwalm and Ek 2004) does not fully account for the 

competitive position of the tree. Light interception was, 

therefore, estimated by applying the Beer-Lambert law after 

accounting for the effects of incomplete canopy closure on 

the sunlit and shaded portions of the canopy. Mean daily 

radiation was separated into direct and diffuse components 

following the approach outlined by Bristow and Campbell (1985), which is based on the ratio of total incoming 

shortwave radiation to potential shortwave radiation. The 

amount of direct and diffuse radiation at a given time of 

the day was estimated from cosine-diurnal distribution 

following the procedure outlined by Wang et al. (2002), 

in contrast to the more common approach of assuming a 

sinusoidal pattern to diurnal radiation. Light extinction 

coefficients for direct and diffuse radiation were based on 

the relationships described by Smith (1993) and Campbell 

and Norman (1998), respectively. The direct radiation extinction coefficient was a function of solar zenith angle, LAI, 

and stand relative density (Curtis 1982), while the diffuse 

radiation extinction coefficient was simply a linear function of LAI. Clumpiness was accounted for by an equation 

presented in Campbell and Norman (1998) that included 

the ratio of stand mean crown depth to diameter and the 

solar zenith angle. A penumbra effect was not simulated 

because any resulting bias from ignoring this effect was 

expected to be relatively small when the diffuse fraction is 

high (e.g. Bernier et al. 2001), as is typical in forest canopies 

of this region.

Photosynthesis—

Net photosynthetic rates were estimated with the Farquhar 

et al. (1980) model for both sunlit and shaded current-year 
FOREST GROWTH AND TIMBER QUALITY

53

foliage. Maximum Rubisco activity (Vcmax), electron transport capacity (Jmax), and dark respiration rate (Rdark) were 

estimated from their relationship to mean canopy concentrations of foliar nitrogen (Manter et al. 2005, Ripullone

et al. 2003). These rates were assumed to be the same for 

both sunlit and shaded foliage. An alternative approach was 

found to perform better. First, Vcmax, Jmax, and Rdark were 

estimated at an optimum foliar nitrogen concentration from 

the equations of Manter et al. (2005), net photosynthesis was 

estimated, and then this rate was multiplied by a modifier 

that ranged from 0 to 1 and was a nonlinear function of actual foliar nitrogen concentration (Brix 1993). Temperature 

modifiers for Vcmax and Jmax were obtained from Manter et 

al. (2003). Other Farquhar et al. (1980) parameters such as 

CO2 compensation point in the absence of mitochondrial 

respiration and the Michaelis-Menten constant of Rubisco 

were estimated from standard equations. To account for 

the effects of complex terrain on canopy photosynthesis, 

sunlit and shaded leaf area were calculated with equation 

[11] presented by Wang et al. (2002). Foliage age structure 

is known to influence total photosynthesis in conifer canopies (e.g. Bernier et al. 2001), but actual Vcmax, Jmax, and 

Rdark measurements for age classes older than the current 

year were not available. Therefore, the net photosynthetic 

rates for the 1-, 2-, 3-, and ≥4-year-old foliage age classes 

were assumed to be 75, 50, 30, and 10 percent of the net 

photosynthetic rates of current year foliage calculated from 

the Farquhar et al. (1980) equation based on information 

available in the literature (Ethier et al. 2006, Manter et al.

2003, Woodman 1971). 

Water stress effects on canopy photosynthesis are particularly important in the PNW because of high evaporative demand during the warm, dry summer (Waring and 

Franklin 1979). In a recent review of models for simulating 

the effect of water stress on canopy photosynthesis, Grant 

et al. (2006) found approaches ranging from simple scaling 

factors (Garcia-Quijano and Barros 2005, Kirschbaum 1999) 

to complex iterative solutions (Williams et al. 1996). Although the impact of stomatal conductance on CO2 fixation 

is poorly understood, proper behavior requires interactive 

effects of soil and atmospheric water deficits on CO2 fixation 

(Grant et al. 2006). The simplest approach was to predict 

stomatal conductance from both soil and atmospheric 

water deficits. However, the equation developed by Bond 

and Kavanagh (1999) predicts only mean daily values of 

stomatal conductance. To estimate conductance throughout 

the day, the mean daily values were modified by the amount 

of intercepted radiation and time since sunrise (Livingston 

and Black 1987). Intercellular CO2 concentration was then 

estimated from a theoretical relationship to CO2 compensation point, atmospheric CO2 concentration, and root water 

potential (Katul et al. 2003). One limitation of this approach 

is the assumption that water deficit effects on CO2 fixation 

are entirely stomatal, which is not entirely true (Warren

et al. 2004). A better understanding of the relationship 

between stomatal conductance and leaf internal transfer 

conductance, and the response of both to environmental 

conditions, is required before they can be better integrated 

into models (Warren and Adams 2006). 

Respiration—

One key simplification in 3-PG is the assumption that NPP 

is a constant fraction of GPP (~0.5). This assumption has 

generated considerable debate in the literature (Lai et al.

2002, Mäkelä and Valentine 2000), but results of several 

studies have supported the generality of this NPP/GPP 

fraction across a wide range of forest types (Gifford 2003, 

Siqueira et al. 2006). Three alternatives to this simplification 

were tested, including (1) daily respiration as a function 

of biomass and temperature (Schwalm and Ek 2004), (2) 

daily respiration as a function of nitrogen content and both 

a short- and long-term response to temperature (Kirschbaum 1999), and (3) annual respiration as a function of 

nitrogen content and temperature (Battaglia et al. 2004). 

Preliminary analysis indicated that estimating NPP as a 

constant fraction of GPP yielded the strongest correlation 

with observed stem volume growth. 

Soil water and nutrients—

Daily soil water balance was calculated in a manner similar 

to Schwalm and Ek (2004). Soil water-holding capacity was 

estimated from rooting depth, texture, and rock content 

using standard equations (Cosby et al. 1984, Rawls et al.

1992). Daily canopy transpiration and soil evaporation 

were simulated with modified Penman-Monteith equations as presented in Waring and Schlesinger (1985) and 

Kirschbaum (1999), respectively. In the canopy transpiration 

equation, mean daily stomatal conductance was estimated 

from leaf and soil water potential, leaf to air vapor pressure 

gradient, and leaf specific conductance (Bond and Kavanagh 1999). Based on the data presented by Tan and Black 

(1976), canopy conductance was estimated by reducing 

this mean daily stomatal conductance by 88 percent. In a 

manner similar to Schwalm and Ek (2004), daily soil water 

balance was determined by subtracting canopy transpira-
FOREST GROWTH AND TIMBER QUALITY

54

tion and soil evaporation from soil water, and adding daily 

net precipitation after subtracting interception by canopy 

leaf and branch surface area. The amount of intercepted 

precipitation was based on empirical rainfall attenuation 

in Douglas-fir stands (Keim 2004). 

For simplicity, daily nitrogen mineralization was the 

only aspect of nutrient availability that was simulated in 

the model. Driving variables included temperature, water 

content, texture, bulk density, and water-holding capacity of 

the soil, as well as daily air temperature, rainfall, and solar 

radiation (Paul et al. 2002). In addition, the mass and height 

of the litter layer must be known or estimated, as well as 

the leaf area index and slope. Simulation of daily nitrogen 

mineralization was achieved by considering the influence 

of all these factors on the optimum nitrogen mineralization 

rate estimated from published data (Chappell et al. 1999). 

Daily soil temperature was calculated from air temperature 

as modified by the effects of the tree canopy, understory 

vegetation, litter mass, and depth of the soil layer (Paul et 

al. 2004). Daily nitrogen uptake was estimated as a function 

of root nitrogen concentration, soil temperature, and the 

amount of available soil nitrogen (Thornley 1991).

Allocation and Growth (ALOGRO)

Allocation—

Several reviews on carbon allocation have outlined the myriad of approaches to quantifying the sources of its variability; 

however, no single solution is yet widely accepted (Barton 

2001, Lacointe 2000, Litton et al. 2007). The 3-PG approach 

of maintaining a fixed NPP/GPP ratio and assuming empirical allometric ratios (Lansberg and Waring, 1997) is robust 

and provides realistic values; however, the ratio of NPP to 

GPP is obviously very influential on estimated dry matter 

productivity, and the allometric ratios available for many, 

if not most, species are based on empirical relationships in 

unmanaged stands. Similarly, Mäkelä (1997) maintained 

a constant ratio of foliage to fine root biomass to reflect an 

expected functional balance between the two, regardless of 

growing conditions. Carbon allocation, however, is highly 

sensitive to intensive management, as well as to inherent site 

resource availability, particularly belowground (e.g. Keyes 

and Grier 1981). Allocation conditional on site resource 

availability was, therefore, initially built into the model. A 

variety of approaches were examined, including those of 

Running and Gower (1991), Johnson and Thornely (1987), 

Kirschbaum (1999), and Landsberg and Waring (1997). 

Preliminary analysis, however, suggested that a modified 

3-PG approach resulted in the highest correlation between 

simulated above-ground NPP and observed stem volume 

growth. The modifications to the 3-PG allocation approach 

involved estimation of the site fertility rating from canopy N 

percentage (Swenson et al. 2005) and applying Duursma’s 

and Robinson’s (2003) correction for inherent bias when 

estimating stand-level biomass (or its allocation in this case) 

from stand-level mean tree size. The site fertility rating 

estimated the amount of belowground allocation and was 

predicted with equation [2] of Swenson et al (2005).

Disaggregating stand growth to individual trees—

Disaggregating stand-level projections of growth to individual trees has been widely debated in the empirical 

growth and yield model literature (e.g. Qin and Cao 2006). 

Process-based models have generally concentrated at the 

whole-stand level, so little work has been done on mechanistically disaggregating stand NPP to individual trees. 

Models such as BALANCE (Grote and Pretzsch 2002) and 

MAESTRO (Wang 1990) make highly detailed physiological calculations at the individual-tree level, but a simpler 

approach was desired for this model. Confronted with the 

same dilemma, Korol et al. (1995) developed an algorithm 

to disaggregate stand NPP and allocate it to individual 

trees. Their approach was to divide the canopy into layers 

of equal leaf area index. Within each layer, individual-tree 

radiation absorbance was estimated as a function of tree leaf 

area (Korol et al. 1995). Allocation to each tree was based 

on the amount of radiation absorbed by that particular tree 

as well as an adjustment for hydraulic architecture (Korol

et al. 1995). Brunner and Nigh (2003) ran extensive simulations with a highly detailed light interception model to 

simulate individual-tree growth. A regression model was 

fitted to the data presented in Brunner and Nigh (2003). 

The final model predicted the mean proportion of incoming light absorbed by an individual crown as a function 

of its size, relative social position, and stand density. This 

proportion was then multiplied by the tree leaf area, similar 

to the weighted leaf areas estimated by Brunner and Nigh 

(2003). Finally, whole-stand NPP was allocated to each 

tree based on its proportion of the total stand weighted 

leaf area. For comparison, disaggregation rules based on 

each tree’s unweighted proportion of stand leaf area and 

on the purely empirical approach of Zhang et al. (1993) 

were also tested. 
FOREST GROWTH AND TIMBER QUALITY

55

Individual tree dimensions—

Several methods were used to estimate individual tree 

diameter and height growth based on the portion of net 

primary production allocated to a tree. These methods 

included differentiated allometric equations (Kirschbaum 

1999, Korol et al. 1996, Zhang and Deying 2003), pipemodel theory (Valentine and Mäkelä 2005), and a transport 

resistance model (Thornley 1999). Vertical distribution of 

annual increment along the bole of an individual tree was 

predicted with an empirical equation similar in form to 

Ikonen et al. (2006) but re-parameterized for Douglas-fir. 

For comparison, predictions were also made with purely 

empirical equations (Weiskittel et al. 2007a) and the following hybridized form of these equations:

[1] 

ΔYadj = ΔYEMP * (βij + βij * NPP + βij*ln(NPP)) + εi 

where ΔYadj is the adjusted growth rate (diameter or height), 

ΔYEMP is the predicted growth from the empirical equation, 

the βij’s are annualized parameters to be estimated from 

an independent dataset for the jth equation (diameter vs. 

height). The modifier was not constrained between 0 and 

1 because the original empirical equations of Weiskittel

et al. (2007a) were developed for plantations that had not 

received any thinning or fertilization treatments. In this 

study, they were being applied to plots with a variety of 

intensive management activities. The modifier was, therefore, expected to be above one for several plots. While Henning and Burk (2004) found no difference in predictions 

made by an additive versus a multiplicative equation form 

in their hybrid model, the multiplicative form performed 

better for Douglas-fir. Presumably this modifier represents 

the environmental effects and fundamental processes that 

impact site quality not captured in site index. In addition, 

it is a more parsimonious approach because predicting 

site index as a function of NPP (e.g. Baldwin et al. 2001) 

required adjustments for stand density and age to ensure 

proper behavior. 

Previous hybrid models have estimated crown recession 

as a function of crown coverage (e.g. Mäkelä 1997), light 

availability (Nikinmaa and Hari 1990), or a combination of 

the two (Valentine and Mäkelä 2005). In this model, crown 

recession was predicted as the consequence of simulated 

individual branch dynamics (Weiskittel et al. in review). 

This approach was shown to perform better than a static 

height to crown base equation. 

Table 1. Physiographic and soils features of the nine Stand Management Cooperative installations yielding verification data for the 

Douglas-fir hybrid model.

Stand

Elevation

(m) % Slope Aspect

Rootable soil 

depth (m) % silt in soil % clay in soil

% rock content 

in soil

704 12. 20 270 0.7 35 35 25

705 250.8 0 10 0.7 25 10 0

70 00 5 0 0.64 25 10 35

71 73.4 5 10 0.7 40 20 50

71 102.1 10 10 1.01 55 35 10

722 204.2 10 270 0. 40 20 20

725 50.9 0 10 0.64 25 10 0

72 27. 10 225 0. 55 20 0

7 54.8 40 270 0.1 40 20 35

Figure 2. Location of Stand Management Cooperative installations in 

Oregon and Washington used for model verification.
FOREST GROWTH AND TIMBER QUALITY

56

Mortality—

The literature review by Hawkes (2000) underscored the 

wide variety of approaches to simulating individual tree 

mortality. Mortality in ALOGRO was assumed to occur 

when individual tree growth efficiency (stem biomass increment/tree leaf area) fell below 0.10 kg m-2 yr-1. Performance 

of this approach was compared to that of an empirical 

model for estimating annual probability of individual tree 

mortality (Flewelling and Monserud 2002).

Model verification

Study area—

Data from nine Stand Management Cooperative (SMC; 

University of Washington) installations in Oregon and 

Washington, USA, comprised the verification and testing 

dataset (Figure 2). These installations covered a wide range 

of growing conditions that are typical for the region (Table 

1). The overall climate is humid oceanic, with a distinct 

dry summer and a cool, wet winter. Twenty-year mean 

annual rainfall for these locations ranged from 150 to 315 

cm and January mean minimum temperature and July 

mean maximum temperature ranged from -2.2 to 3.5°C 

and 21.3 to 26.3°C, respectively. Variation in precipitation 

and temperature were strongly related to elevation and 

distance from the coast. Elevation ranged from 25 to 300 

m above sea level and all aspects were represented. Soils 

varied from a moderately deep sandy loam to a very deep 

clay loam. The plantations were established between 1971 

and 1982 at varying densities (905–1,575 stems per ha) 

and levels of vegetation control. 

Silvicultural regimes—

Several sets of 0.2-ha permanent plots were established 

by the SMC at each installation between 1986 and 1992. 

Since establishment, the 56 plots have received a variety 

of silvicultural regimes that have involved thinning, pruning, and nitrogen fertilization. Canopy mean plot foliage N 

concentration ranged from 1.26 to 2.98. 

Plot measurements—

All trees on each plot were remeasured for DBH every 

4 years. At each remeasurement, a subsample of at least 

40 Douglas-fir trees was also measured for total height 

and height to crown base. Four to eight years after plot 

establishment, current-year foliage was sampled from the 

upper crown of 12 trees in each plot, and analyzed for 

nutrient content. 

Model simulations—

The model assembled from BCACS, NPP, and ALOGRO was 

evaluated by simulating one-sided LAI and growth on each 

of the 56 SMC plots and comparing the predicted stem volume growth to observed periodic annual increment (PAI; m3

ha-1 yr-1). Since observed LAI was not available, initial LAI of 

the plots was derived from BCACS and the three following 

approaches examined by Turner et al. (2000): (1) allometric 

function of DBH; (2) ratio of leaf area to sapwood area at 

breast height; and (3) ratio of leaf area to sapwood area at 

crown base. Although this assumes that PAI is a good proxy 

of LAI, this is a valid assumption in Douglas-fir as a previous analysis has found a highly linear relationship between 

LAI and PAI across a range of LAI values (Schroeder et al. 

1982). Given the uncertainty in carbon allocation patterns, 

the correlation between predicted NPP and PAI was also 

examined to indicate the relative magnitude of estimation 

error that may be attributable to inaccuracy in estimating 

NPP vs. allocation of NPP to stemwood production. The 

same plots were also simulated in 3-PG (Landsberg and 

Waring 1997) and SECRETS-3PG (Sampson et al. 2006) 

Table 2. Mean bias, mean square error (MSE), and r-square (r2) for observed and predicted stand-level periodic annual increment (PAI; m3 ha-1) on 

67 intensively managed Douglas-fir Stand Management Cooperative plots in Oregon and Washington. Predicted PAI was obtained using 4 foliage 

biomass imputation methods and 3 net primary production models (NPP). 

NPP Model

Method used for estimating foliage biomass

Gholz et al. (1979) BHSAP1 CBSAP2 BCACS3

Mean 

Bias MSE R2

Mean 

Bias MSE R2

Mean 

Bias MSE R2

Mean 

Bias MSE R2

This study 6.2544 6.5197 0.0 3.4189 4.5839 0.50 1.7941 .270 0.7 0.07 2.9405 0.7

3-PG4 .10 4.2468 0.70 2.4066 4.0809 0.71 1.8146 4.1833 0. -1.5117 4.1166 0.24

SECRETS 3-PG5 - - - - - - - - - 1.03475 5.7273 0.2

1. constant amount of leaf area per unit of predicted sapwood area at breast height (Turner et al., 2000)

2. constant amount of leaf area per unit of predicted sapwood area at crown base (Turner et al., 2000)

3. Branch, Crown, And Canopy Simulator (this study)

4. Landsberg and Waring (1997)

5. Sampson et al. (2006)
FOREST GROWTH AND TIMBER QUALITY

57

after parameterizing for Douglas-fir with information presented by Waring and McDowell (2002). To estimate soil 

fertility index for 3-PG and SECRETS-3PG, the measured 

soil nitrogen percentage was converted to nitrogen content 

based on soil depth and estimated bulk density (Kaur et 

al. 2002). This value for total nitrogen was then converted 

to the soil fertility index with the equation developed by 

Swenson et al. (2005). Climate information for the growth 

periods represented on the SMC plots was obtained from 

DAYMET (http://www.daymet.org). 

RESULTS

Stand-level growth—

All four methods for estimating LAI led to simulated stem 

volume increments that were significantly correlated with 

observed PAI (p<0.0001). The relative strengths of these 

correlations, in descending order, were associated with LAI 

from the following (1) sapwood area at crown base (r=0.81; 

CBSAP), (2) regional allometric equation based on diameter 

at breast height (r=0.79, Gholz et al. 1979), (3) sapwood area 

at breast height (r=0.78; BHSAP), and (4) summed branch 

predictions from BCACS (r=0.75).

Comparison of observed PAI and simulated stem volume increments indicated that LAI predicted from BCACS 

resulted in the lowest mean bias and lowest mean square 

error, followed closely by CBSAP (Table 2). The NPP algorithm described in this study performed significantly better 

than 3-PG when LAI was estimated by BCACS and CBSAP, 

but the reverse was true when LAI was estimated by either 

BHSAP or the regional allometric equation (Figure 3). 

Across the silvicultural treatments, the hybrid model 

developed in this study improved predictions of volume 

growth in the control and thinned stands, but led to poorer 

predictions in both the fertilized and the fertilized and 

thinned stands (Figure 4). The predictions were significantly 

better than those obtained using 3-PG and SECRETS-3PG 

across all treatments. 

Tree-level growth—

Observed volume growth was significantly correlated with 

predicted volume growth under all four disaggregation 

methods. The relative strengths of these correlations, in 

descending order, were associated with disaggregation by 

(1) weighted tree leaf area (p<0.0001; r=0.73), (2) tree leaf 

area (p<0.0001; r=0.62), (3) competition index (Korol et 

al. 1995) (p<0.0001; r=0.49), and (4) empirical allocation 

(Zhang et al. 1993) (p<0.0001; r=0.46). The level of bias 

from predicting diameter and height growth by the first 

three approaches was higher than that from a purely empirical approach. However, the hybrid approach developed 

in this study produced a level of bias comparable to the 

empirical approach, in large part due to its empirical basis 

(Table 3). The hybrid model predictions modified empirical 

estimates as follows:

[2] 

ΔDBHadj = ΔDBHEMP * (0.4078 + 0.1846*ln(NPP))

Figure 3. Plot of model bias (observed – predicted) over observed periodic 

annual increment.

Figure 4. Mean square error of predicted 4-year volume growth (m3

 ha 

yr-1) by silvicultural treatment. The four models used were an empirical 

one (Weiskittel et al., 2007), the hybrid model developed in this study, 

3-PG (Landsberg and Waring, 1997), and SECRETS-3PG (Sampson 

et al., 2006). 
FOREST GROWTH AND TIMBER QUALITY

58

[3] 

ΔHTadj = ΔHTEMP * (0.5192 + 0.2133*NPP

– 0.0200*ln(NPP))

where ΔDBHEMP and ΔHTEMP are predicted diameter 

and height growth using the equations of Weiskittel et al. 

(2007a). The equations suggest that the diameter growth 

modifier linearly increased with NPP and ranged from 

0.41 to 1.05. The height growth modifier linearly increased up to a NPP of 10 t ha-1

and then slowly decreased. These 

modifiers decreased the mean 

square error of diameter and 

height growth prediction by 3 

and 12 percent, respectively. Tree 

mortality, imposed when growth 

efficiency fell below the threshold, 

produced final stand basal areas 

that were comparable to predictions produced with an empirical 

mortality equation (Figure 5). 

However, both approaches underpredicted mortality in stands with 

higher densities. 

DISCUSSION

The goal of this project was to develop the framework for a hybrid 

model by incorporating features 

from both empirical and processbased models. These features were 

selected based on their potential to 

enhance the capacity of the model to simulate responses 

to both intensive silvicultural treatments and variations 

in environmental conditions. Most of the parameters 

were gleaned from the literature, and the framework was 

intended to be useful to both researchers and forest managers. The framework also needed to be flexible enough to 

accommodate improvements in modeling techniques and 

the increasing availability of physiological data. Although 

3-PG is a simple and very effective model for simulating 

Table 3. Mean bias, mean square error (MSE), and percent (%) bias for individual tree predictions of diameter and height growth 

on 56 Stand Management Cooperative plots with varying levels of silvicultural treatments located throughout the Pacific 

Northwest, USA.

Approach

DBH

(n = 8860)

HT

(n = 2805)

Mean bias MSE % bias Mean bias MSE % bias

1. Empirical

(Weiskittel et al., 2007) -0.01 1.22 -0.61 -0.56 0. -3.76

2. Allometric

(Kirschbaum, 1999) 1.24 1. 4.97 -0.42 1.0 -3.87

3. Pipe-model

(Valentine and Mäkelä, 2005) .07 3.25 13.04 -2.52 3.43 -19.78

4. Thornley (1999) -3.75 .1 -20.63 -0.06 1.2 -1.41

5. Hybrid 0.53 1.1 1. 0.15 0.85 1.04

Figure 5. Bias (observed – predicted) in stand basal area (m2 ha-1) on 56 Stand Management Cooperative 

plots with varying levels of silvicultural treatments located throughout the Pacific Northwest, USA after 4 

years of simulation using an empirical mortality equation and the growth efficiency concept.
FOREST GROWTH AND TIMBER QUALITY

59

stand-level growth (e.g. Pinjuv et al. 2006), its reliance on 

the radiation-use efficiency concept and environmental 

0-1 modifiers limit the model’s capacity to clarify the role 

of important processes (e.g. nutrient uptake, interaction 

of water availability and photosynthesis). A more explicit 

treatment of those processes facilitates future refinements 

and assessment. The framework developed here for Douglasfir resembles many first-generation process-based models 

(reviewed by Ryan et al. 1996), but with some important 

refinements, including (1) hierarchical treatment of growth 

at branch, tree and stand levels, (2) explicit representation 

of crown structure and function to drive growth processes, 

(3) incorporation of slope and aspect effects on canopy 

processes, (4) clear connection between water stress and 

reductions in photosynthesis, (5) patterns in light extinction that depend on stand structure, (6) net photosynthesis 

rates specific to foliage age classes, (7) prediction of tree 

mortality based on a threshold of growth efficiency, and 

(8) initiation from readily available information rather than 

from subjective but very influential parameters or detailed 

and expensive physiological measurements. 

The simulation results from the Douglas-fir hybrid model 

illustrated three important points regarding mechanistic 

hybrid models, namely (1) their performance is sensitive and 

quite dependent on initial LAI estimates, (2) models with 

more detail and finer resolution can significantly increase 

the precision of growth predictions, and (3) a generic modeling approach that works in a variety of geographic regions 

is difficult to develop satisfactorily. Process-based models 

usually require information on tree and stand biomass 

components other than the main stem, but estimating these 

components is usually not straightforward. Different methods for estimating LAI in Douglas-fir stands gave generally 

similar results for younger stands, but differed significantly 

in the older stands (Turner et al. 2000). However, neither 

actual LAI nor the effects of intensive management were 

known or considered in the analysis of these methods. Allometric equations based only on DBH were significantly 

biased in young fertilized Douglas-fir plantations (Grier et 

al. 1984). Actual LAI was unknown in our study also, but 

the degree of bias in the growth projections suggested that 

LAI estimated from crown size and location was superior 

to LAI estimated solely from DBH. This conclusion was not 

surprising given that most silvicultural treatments directly 

affect crown attributes (Weiskittel et al. 2007b). 

With accurate estimates of LAI, the NPP model used in 

the Douglas-fir hybrid model had a much lower level of bias 

in its growth predictions than 3-PG and SECRETS-3PG. 

Given the range of stand structures and silvicultural treatments simulated in this study, 3-PG performed remarkably 

well, although it was slightly biased. Since the carbon allocation algorithms were quite similar in both models, the 

differences appear to be driven by the estimates of NPP. 

The Douglas-fir hybrid model of this study also benefited 

from the mean tree correction factor developed by Duursma 

and Robinson (2003). NPP predicted with 3-PG covered 

a very narrow range compared to the hybrid Douglas-fir 

model. When LAI is relatively high (greater than 5) nearly 

95 percent of all incoming radiation is intercepted and the 

radiation use efficiency (RUE) concept becomes harder 

to apply. Moreover, the relationship between intercepted 

radiation and NPP becomes less clear when stands have 

significant water stress (e.g. Raison and Myers 1992), a 

condition routinely experienced by most Pacific Northwest 

plantations during the summer months. This prevalence of 

water limitation underscores the need to properly simulate 

the effects of soil and atmospheric water deficits on CO2

fixation. Scalars that vary from zero to one in 3-PG and 

SECRETS-3PG are insufficiently flexible to capture net 

effect of daily water relations (Grant et al. 2006). Finally, 

RUE treats direct and diffuse radiation in the same way, 

despite the fact that canopy processes behave differently 

under direct versus diffuse conditions. Schwalm et al. (2006) 

suggested that the ratio of diffuse to total photosynthetically 

active radiation (PAR) was a key predictor of the daily RUE 

across a variety of climate zones and vegetation types. 

Unfortunately, many of the shortcomings of this Douglasfir hybrid model are similar to those found by Ryan et al. 

(1996) in his assessment of several first-generation processbased models. Missing or poorly represented components 

include long-term controls on nitrogen mineralization, the 

uptake and allocation of nitrogen by plants, and the response 

of belowground allocation and respiration to changes in 

resource availability. Both CenW (Kirschbaum 1999) and 

C&N-CLASS (Arain et al. 2006) address many of the difficulties in modeling soil nutrient dynamics, but the level 

of input on soil nitrogen and carbon stores required by 

these models significantly limits their wide application by 

forest managers. Predictions of nitrogen mineralization and 

uptake in the hybrid model were simple and mechanistically 

sound, but its performance against observed responses could 

not be tested. Future refinements to this nutrient availability component and better representation of belowground 

processes in general will be needed in order to develop a 
FOREST GROWTH AND TIMBER QUALITY

0

hybrid model capable of simulating responses to intensive 

nutrient management.

Adding detail and complexity to improve accuracy when 

modeling key physiological processes is not always a justified solution. Respiration calculated under the Waring et 

al. (1998) assumption that NPP is a constant fraction of 

GPP produced the strongest correlation between NPP and 

observed stem volume growth. This simplification remains 

controversial (e.g. Litton et al. in review, e.g. Mäkelä and 

Valentine 2000). However, it is difficult to separate the effect of NPP/GPP assumptions from their interaction with 

the many other model components. Another important 

simplification in this hybrid model was estimation of the 

soil water balance, which was simulated with a single-layer 

tipping bucket approach (Schwalm and Ek 2004). More 

complex approaches have been developed (Kirschbaum 

1999, Paul et al. 2003) but their performance compared to 

simpler approaches has rarely been assessed. A relatively 

simple soil water balance model developed by Rötzer (2004) 

was compared to the performance of a more complex model 

presented by Grote and Pretzsch (2002), and the simpler 

model was found to be equally effective at predicting observed daily soil water balance (T. Rötzer, per. comm.). 

This result suggests that the simpler approach is adequate 

for most practical applications, particularly when detailed 

information on soil water dynamics is not needed. A major 

function of future hybrid modeling efforts will be to find 

the right balance between complexity and simplicity that 

meets the objectives of the simulation model.

Current understanding of the key factors driving carbon 

allocation, dynamics of tree morphology, and mortality of 

individual trees is lacking. The carbon allocation approaches 

of many process-based models are built on the assumption that priorities exist for the products of photosynthesis 

(Kirschbaum 1999, McMurtrie and Landsberg 1992, Running and Gower 1991). However, recent empirical evidence 

does not support the existence of such priorities (Litton

et al. in review). Further, it is commonly assumed that 

allocation to fine roots is driven by resource availability 

(Keyes and Grier 1981). However, several studies have 

concluded that site fertility and fertilization have no effect 

on carbon allocation to fine roots (e.g. Carter et al. 2004), 

and sometimes even the opposite effect of what is generally 

reported; namely, greater allocation under conditions of 

lower fertility (Majdi and Andersson 2005). Dean (2001) 

suggested that stand structure and its apparent influence 

on stem bending stress may drive belowground allocation 

processes, but the data to test this in Douglas-fir do not 

exist. New non-destructive research techniques may allow 

belowground allocation processes to be better quantified 

in the future (e.g. Johnsen et al. 2007). 

Very few studies have linked the dynamics of tree 

morphology with individual tree net primary production. 

In this study, diameter growth was much more difficult to 

accurately predict than height growth. The increment in 

cross-sectional area of the tree bole has commonly been 

assumed to be proportional to the leaf area above a given 

height, implying that increment is constant below crown 

base (Mäkelä 2002). However, empirical evidence has 

suggested a much more complex pattern along the bole 

(e.g. Kershaw and Maguire 2000). Thornley (1999) linked 

diameter and height growth to carbon and nitrogen fluxes 

based on theoretical principles, but this approach performed 

poorly when predicting diameter growth for Douglas-fir. 

However, the relatively simple treatment of carbon and 

nitrogen dynamics in the model of this study may have 

been inadequate to accommodate Thornley’s (1999) approach. The Douglas-fir hybrid model circumvents this 

with empirically derived modifier functions that may not 

extrapolate well to new conditions. This approach does, 

however, increase the flexibility of the empirical equations 

by allowing them to be modified by factors such as climate, 

soil, and edaphic characteristics, which all directly influence 

NPP. The modifiers suggest that individual tree diameter 

growth logarithmically increases with NPP, while height 

growth peaks at a relatively low NPP and then decreases. 

This pattern is consistent with the general observations that 

diameter growth allocation is increased when conditions 

are favorable (e.g. fertilization, thinning) and height growth 

allocation is increased when conditions are less favorable 

(e.g. high competition). The decrease in the height growth 

modifier is unexpected, but may suggest that the empirical 

equation overestimates growth at more productive sites. 

The performance of hybrid models relative to purely 

empirical models has varied. Pinjuv et al. (2006), moving 

to a hybrid model, reduced mean square error of predicting 

stand basal area by approximately 4 percent. Dzierzon and 

Mason (2006), using hybrid models, achieved reductions 

of 14 and 8 percent, respectively, for stand basal area and 

top height growth across Pinus radiata plantations in New 

Zealand. At the individual tree level, using a hybrid model, 

Schwalm and Ek (2004) had a level of bias comparable to 

an empirical model when predicting diameter growth over 

a 25-yr. However, the hybrid model significantly improved 
FOREST GROWTH AND TIMBER QUALITY

1

mean prediction error for height growth. Henning and Burk 

(2004) showed that a hybrid model did not improve mean 

square error of predicted diameter growth when compared 

to an empirical model, but it did significantly decrease the 

mean bias by nearly 50 percent. Although they did not compare performance directly to an empirical model, Rötzer et 

al. (2005) simulated diameter growth with the hybrid model 

BALANCE and obtained discrepancies of 1 to 23 percent 

from actual diameters after 7–8 years of simulation. The 

Douglas-fir hybrid model gave results similar to Schwalm 

and Ek (2004), with a level of bias in diameter growth 

comparable to the empirical model, but with significantly 

improved height growth predictions. Again, it is important 

to mention that these reported improvements with the use 

of hybrid models should be expected given that they utilized 

information (i.e. observed weather records) not used by 

their empirical counterparts. A real test of a hybrid model 

should be how well it performs over key variables such as 

precipitation, soil properties, and foliar N levels. 

Neither empirical nor process-based models have found 

a totally satisfying approach to predicting individual tree 

mortality with the desired level of accuracy (Hawkes 2000). 

In hybrid models, mortality has been predicted using (1) a 

minimum crown ratio (Valentine and Mäkelä 2005), (2) an 

increasing function of crown coverage (Mäkelä 1997), (3) 

empirical functions of tree size (Schwalm and Ek 2004), and 

(4) carbon-based algorithms. Despite their appealing mechanistic basis, carbon-based algorithms have not performed 

well (Hawkes 2000). Mäkelä and Hari (1986) found that 

their mechanistic approach to mortality generated a decline 

in accuracy when compared to empirical approaches. Running (1994) indicated that FOREST-BGC should not be run 

longer than 100 years because mortality predictions became 

too unrealistic. The major obstacles to a carbon balance 

approach are probably the difficulty in accurately estimating respiration and uncertainty about the tree’s ability to 

store reserves. In the Douglas-fir hybrid model, a growth 

efficiency threshold performed comparably to an empirical 

model for predicting probability of mortality, at least in the 

short-term. The growth efficiency threshold has several advantages: (1) thresholds may be less site- or species-specific 

than other approaches, (2) low growth efficiency is a sign 

of a stressed tree, (3) growth efficiency inherently reflects 

climatic variation, and (4) growth efficiency declines with 

age so size and age do not have to be explicitly included as 

predictors (Hawkes 2000). The growth efficiency approach 

showed promise in the Douglas-fir hybrid model, but as 

with the empirical equation, it underpredicted mortality 

at the higher stand densities. The increased availability of 

intensively managed Douglas-fir plantation growth and 

yield data with estimates of individual tree leaf area from 

Light Detection and Ranging (LiDAR) in the upcoming 

years will allow further assessment of this approach for 

predicting long-term trends in mortality. 

Although growth projections are similar to those of a 

purely empirical model, the hybrid model developed in this 

study provides information on stand attributes beyond just 

growth and mortality. For example, the major aspects of 

wood quality such as branch number, size, and location 

as well as bole sapwood and heartwood content are readily available. Future improvements for this model at the 

individual tree level will be the result of (1) developing 

growth modifiers from annual growth measurements on 

destructively sampled stems rather than by annualizing 

growth from periodic plot remeasurements; (2) better 

representing the effects of climate and site edaphic characteristics on tree ring characteristics (e.g. Deckmyn et al.

2006), particularly density, thereby refining the conversion 

of stem biomass increment to volume increment; and (3) 

further quantifying the relationship between tree growth 

efficiency and its probability of mortality. 

CONCLUSIONS

 Hybrid models, which combine the features of empirical 

and process-based models, have been suggested as the next 

step forward for improving growth projections for managed stands (e.g. Landsberg 2003b). The hybrid modeling 

framework combines the strengths of both empirical and 

process-based models. The hybrid model constructed here 

for intensively managed Douglas-fir plantations in the Pacific Northwest significantly improved predictions of LAI 

and PAI compared to other modeling approaches. At the 

individual tree-level, disaggregation of NPP and prediction 

of stem diameter and height growth were improved. In addition, imposing mortality when growth efficiency fell below 

a threshold value predicted mortality at a level of accuracy 

comparable to empirical approaches. These improvements 

resulted directly from (1) more detailed representation of 

crown structure and dynamics, (2) inclusion of key physiological mechanisms at an appropriate spatial and temporal resolution, and (3) application of empirical equations 

modified by simulated NPP to predict diameter and height 

growth of individual trees rather than relying on allometric 

or theoretical equations. Areas of future improvement for 
FOREST GROWTH AND TIMBER QUALITY

2

these types of models include (1) components that simulate the effects of soil water and nutrients on physiological 

processes, particularly respiration and carbon allocation, 

in a simple yet mechanistic manner; (2) components that 

account for the effects of silvicultural treatment and environmental conditions on foliage age class dynamics, so that 

seasonal variation in LAI and net photosynthesis can be 

simulated more accurately; and (3) rigorous assessment of 

the relationship between growth efficiency and probability 

of individual tree mortality. 

ACKNOWLEDGEMENTS

Data were generously made available by Andreas Brunner, 

Hiroshii Ishii, Nathan McDowell, Cindy Prescott, Lars 

Vesterdal, and the Stand Management Cooperative. Thanks 

to David Sampson for simulating these stands in SECRETS3PG. This project was funded by the USDA Forest Service 

PNW Research Station.

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FOREST GROWTH AND TIMBER QUALITY



ABSTRACT

A LINKED-MODELING APPROACH, USING 

PrognosisBC and SORTIE-ND, was tested for 

predicting natural regeneration and forecasting 

future stand conditions in stands attacked by mountain 

pine beetle (Dendroctonus ponderosae Hopkins-MPB). The 

models used data collected from the Interior Douglas-fir 

(IDF), Sub-Boreal Pine Spruce (SBPS), Sub-Boreal Spruce 

(SBS) and Montane Spruce (MS) biogeoclimatic zones of 

central and southeastern British Columbia. PrognosisBC is 

a growth model calibrated for use in complex stands and is 

capable of providing accurate estimates of small and large 

tree growth when used over projection periods of less than 

50 years. The lack of an effective sub-model capable of predicting the abundance and species composition of natural 

regeneration for MPB-attacked stands is a major limitation 

of PrognosisBC. Obtaining regeneration estimates from the 

light mediated growth model SORTIE-ND, was identified 

as a possible alternative to the Most Similar Neighbor regeneration imputation techniques used by PrognosisBC. A 

method to link estimated tree-lists for trees less than 7.5 

cm dbh from SORTIE-ND to PrognosisBC was developed. 

Using a 25-year projection period, the timing of the tree-list 

hand-off from SORTIE to Prognosis was tested at five and 

ten years post-MPB attack and compared to simulations 

using PrognosisBC only and SORTIE-ND only for the entire 

projection period. For spruce and aspen trees less than 

Estimating Natural Regeneration in Stands 

Following Attack by Mountain Pine Beetle 

Using a Linked-Model Approach

Derek F. Sattler, Valerie LeMay, Peter Marshall

Derek F. Sattler (dsattler@ualberta.ca) is a doctoral student, University of Alberta, Department of Renewable Resources, 751 General Services 

Building, Edmonton, AB, T6G 2H1, Canada. When this paper was written he was a graduate student at the University of British Columbia. Valerie 

LeMay is a professor, Forest Resource Management Department, Faculty of Forestry, University of British Columbia, 2424 Main Mall, Vancouver, BC, 

V6T IZ4, Canada; Peter Marshall, is a professor and associate dean, Faculty of Forestry, University of British Columbia, 2424 Main Mall, Vancouver, 

BC, V6T IZ4, Canada.

7.5 cm dbh, the 10-year hand-off simulation provided the 

best estimate of trees per hectare when compared to actual 

observations. For lodgepole pine trees less than 7.5 cm dbh, 

the 5-year hand-off simulation provided the best results. 

Although use of the linked-model approach provided slight 

improvements over using PrognosisBC only or SORTIE-ND 

only, overall results were generally poor. In particular, 

densities of lodgepole pine were largely underestimated 

for smaller trees. Further testing using an extensive dataset 

and further parameterization of the SORTIE-ND model is 

likely required if improvements are to be seen.

KEYWORDS: natural regeneration, individual tree growth 

model, PrognosisBC and SORTIE-ND, mountain pine 

beetle

INTRODUCTION

Accurate growth and yield estimates are an important 

component in the development and implementation of 

sustainable forest management practices (Boisvenue et al. 

2004). Mid- to long-term timber supply estimates rely heavily on growth and yield models (Hyytiainen et al. 2006). In 

the absence of reliable growth estimates, current allowable 

annual cut volumes could be inadvertently set too high or 

too low (Pedersen 2003). In complex forest systems, where 

This paper was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 69–77.
FOREST GROWTH AND TIMBER QUALITY

70

multi-species and multi-cohort stands form a mosaic pattern across the landscape, model projections of growth and 

yield for periods greater 50 years can become increasingly 

unreliable (Zumrawi et al. 2005a). This may, in large part, 

be attributed to the high variability in stand structure and 

species composition, which is a result of frequent small 

scale gap disturbances and less frequent but more extensive 

disturbances such as fires and insect outbreaks (Oliver and 

Larson 1996). Added to the mix are the various silvicultural 

practices (e.g., partial cutting and variable retention) that 

are currently being employed in these complex stands. 

Given these conditions few, if any, growth and yield models 

have been able to excel in both managed and unmanaged 

stands (Robinson and Monserud 2003). Finding the best 

management strategies for complex stands continues to be 

an evolving process (Coates et al. 2004). 

Given this complexity, it is not surprising that the 

province of British Columbia (BC) currently supports 

eight growth and yield models. This allows foresters to 

match their specific requirements to an appropriate growth 

model. One such growth model that is currently being 

used in complex stands of central and southeastern BC is 

PrognosisBC (Snowdon 1997, Zumrawi et al. 2002, Hassani 

et al. 2004). Adapted from the U.S. Forest Service Forest 

Vegetation Simulator (FVS) that was originally developed 

by Stage (1973), PrognosisBC is best suited for projecting 

existing stands and can simulate a wide range of silvicultural treatments. Although the small tree and large tree 

growth components of PrognosisBC were calibrated to the 

Interior Douglas-fir (IDF) and Interior Cedar Hemlock (ICH) 

biogeoclimatic zones, efforts to calibrate the regeneration 

sub-model did not fare well (Boisvenue 1999, Zumrawi 

et al. 2005a). Nevertheless, PrognosisBC has been able to 

provide reliable landscape-level estimates of growth for 

projection periods of 50 years or less; a result of the many 

permanent sample plots (PSP) that were used to calibrate 

the model. 

In place of the regeneration sub-model, model users 

currently have two options: 1) specify the amount and 

composition of natural and/or planted regeneration, or 

2) use the most similar neighbour (MSN) regeneration 

sub-component. The former option limits the use of PrognosisBC to short-term projections unless new regeneration 

lists are added at the end of each growth cycle. The latter 

approach was designed to impute natural regeneration by 

predicting several regeneration variables at once (Hassani 

et al. 2004). To be successful, the MSN approach requires 

a large amount of data collected from stands with natural 

regeneration and which have developed under a wide range 

of ecological conditions (LeMay et al. 2006). Its ability to 

accurately predict regeneration in under-represented ecological conditions is therefore limited (Moeur and Stage 

1995, Hassani et al. 2004). The prevailing ecological conditions of lodgepole pine dominated stands, which have been 

(and are being) created in BC’s interior in the wake of the 

current outbreak of mountain pine beetle (Dendroctonus 

ponderosae Hopkins-MPB), give one example of where the 

applicability of the MSN approach is currently limited. The 

immense magnitude of the current outbreak has created 

ecological conditions that, until now, were less common 

and therefore under-represented in most PSP datasets 

(Hawkes et al. 2004). 

Our search for an alternative means of estimating natural 

regeneration post-MPB attack led us to an existing forest 

simulation model, SORTIE-ND (Kobe and Coates 1997). 

This model is an adaptation of the original SORTIE model 

(Pacala et al. 1993) developed for use in the deciduous forests of northeastern United States (Canham and Burbank

1994). The current SORTIE-ND model (Version 6.07) has 

been calibrated for use in BC’s ICH and Sub-boreal Spruce 

(SBS) forests using long-term PSP data (Kobe and Coates 

1997, Astrup et al. 2007). More recently, efforts to calibrate 

SORTIE-ND using data from managed stands have made 

it useful for application in silvicultural planning (Coates et 

al. 2004). However, our use of SORTIE-ND for this study is 

motivated by the need for a method to accurately estimate a 

tree-list comprised of new seedling recruits and advanced 

regeneration that can be transferred into PrognosisBC. 

In our search for alternative methods we had two main 

criteria, namely that the method be able to predict multiple 

dependent variables and be feasible given the plot data available and the data requirements of PrognosisBC. SORTIE-ND 

satisfied both of these conditions (LeMay et al. 2006). A 

method was then developed to link regeneration estimates 

from SORTIE-ND to PrognosisBC. It was envisaged that 

using these two models as a linked set would allow us to 

take advantage of the strengths of each model. In the case of 

SORTIE-ND, the advantage was related to the model’s flexibility and the ability to adjust model parameters related to 

regeneration establishment, while in the case of PrognosisBC

we could make use of the well developed, empirically-based 

small and large tree growth models. 

In this paper, we describe the model flow of the linkedmodel approach and present the results of an initial test 
FOREST GROWTH AND TIMBER QUALITY

71

using tree measurements collected from stands that experienced a MPB attack roughly 25 years ago.

METHODS

Study Area

Potential stands for sampling were selected from an area 

attacked by MPB between the late 1970s and the late 1990s, 

within approximately 200 km of Williams Lake, BC. Many 

of the sampled stands were located on the Fraser Plateau, 

within the former Cariboo Forest Region. This area contains gentle slopes and has an elevation between 900 and 

1500 m. There are four major biogeoclimatic ecosystem 

classification zones in this area: Sub-Boreal Pine-Spruce 

(SBPS), Sub-Boreal Spruce (SBS), Interior Douglas-fir (IDF), 

and Mountain Spruce (MS). 

Plots were located mainly in stands dominated by 

lodgepole pine (Pinus contorta Dougl. ex Loud. var. latifolia 

Engelm). Overall, species composition in selected stands 

included lodgepole pine (about 80 percent), Douglas-fir 

(Pseudotsuga menziesii var. glauca (Beissn.) Franco) (7 percent), and hybrid spruce (Picea engelmannii x glauca (Moench) 

Voss) (5 percent). Trembling aspen (Populus tremuloides 

Michx.) and subalpine-fir (Abies lasiocarpa (Hook.) Nutt.) 

were present, but in small numbers overall. 

Historically, outbreaks of MPB have been common within 

the study area and have served to shape the forested landscape (Aukema et al. 2006). In the absence of stand-replacing 

fires, regional outbreaks of MPB have served to create gaps 

in the forest canopy. Depending on stocking levels and the 

composition of the understory, previous MPB attacks have 

resulted in either the release of an existing understory or 

the recruitment of new seedlings (Campbell et al. 2007). 

In either situation, such events resulted in the creation of 

uneven-aged, mixed-species stands (Hawkes et al. 2004). 

Field Sampling and Data Collection

Candidate stands for sampling were selected following 

reconnaissance of stands selected from forest inventory 

maps and anecdotal information provided by local foresters 

and researchers. Two to six plots were established in each 

selected stand, depending on the size. Systematic sampling 

with a random start was used. The distance between each 

plot center ranged between 50 m and 150 m, with a minimum distance of 50 m from a road or any other significant 

opening. The plot edges were at least 20 m from any logging 

areas or skid trails.

A total of 175 plots from 55 stands were sampled. Each 

plot consisted of seven circular sub-plots: one for large trees 

(11.28 m radius), another for small trees (5.64 m radius), 

and five for regeneration (2.07 m radius). In the large tree 

plot (overstory trees), all trees greater than or equal to 7.5 

cm diameter at breast height (dbh) were measured. Each 

dead standing or downed tree was assigned a decay class 

based on a nine class scale, created by combining class one 

to four from the wildlife tree classification (Backhouse and 

Lousier 1991) and class five to nine from the coarse woody 

debris classification for downed trees (Stevens 1997). Height 

to live crown (m) was measured for all live trees. Species, 

dbh (cm), and height (m) of each standing tree, live or dead, 

were recorded. For downed trees in decay class seven or 

greater, species, dbh, and height were recorded. For trees 

with broken tops, the height to the broken top (m) was 

measured, and the total height of the tree was estimated. 

Crown width was measured along two axes at right angles 

for two trees selected randomly for each species. In the 

small tree plot, all trees from 2.0 cm to less than 7.5 cm 

dbh were included and species, dbh, status (live or dead), 

visual estimate of live crown ratio (live only), and height 

were recorded for each tree. In the regeneration subplots, 

the number of live seedlings less than 2.0 cm dbh and over 

15 cm in height were recorded by species into four height 

classes: 1) >0.15 to ≤ 0.50 m; 2) >0.50 to ≤1.0 m; 3) >1.0 

to ≤1.5 m; and 4) >1.5 m in height and < 2.0 cm dbh. 

Data Preparation

The overstory conditions at each plot shortly after the time 

of attack were reconstructed using the measures of live and 

dead trees in the large tree plot. Two time of MPB-attack 

cohorts were present in the collected data: (1) attack approximately 25 years ago and (2) attack approximately eight years 

ago. Each live tree was grown back in time by subtracting the 

estimated 10-year diameter growth (DG), using functions 

previously fitted by Zumrawi et al. (2005b). For plots that 

were 25 years post-MPB attack, this process was repeated 

for three intervals, with the third period prorated at half of 

the estimated growth rate. Since measures of competition 

are used in the DG functions, these were summarized for 

each 10-year interval and used in estimating the DG. For 

plots that were eight years post-MPB attack, the 10-year 

DG was prorated for eight years. Once dbh shortly after 

the attack was estimated for each live tree, heights were 

estimated from dbh using existing regression equations 

developed in the process of calibrating PrognosisBC. These 
FOREST GROWTH AND TIMBER QUALITY

72

were localized for each tree by multiplying by the ratio of 

measured height to estimated height for the 2006 measures. 

For standing dead or fallen trees, the decay class was used 

to decide whether the tree was live or dead shortly after 

attack. For all trees that were alive at some point after the 

MPB attack, the crown ratio was estimated using crown 

ratio functions developed for this area. Ten-year DG was 

then estimated using the estimated crown ratio. The same 

process was followed for trees that were alive at the time 

of sampling. Following these approaches, an estimated 

tree-list of all live and dead trees greater than or equal to 

7.5 cm dbh was obtained for each plot shortly after attack. 

The tree-list was coupled with the regeneration (less than 

7.5 cm dbh) measured in 2006, either eight or 25 years 

following MPB attack. 

Linked Model Approach

The process of linking SORTIE-ND and PrognosisBC began 

by importing tree-lists representing individual stands into 

each model. The tree-lists imported into the models were 

from the reconstructed dataset and thus represented stand 

conditions for the years immediately following MPB attack. 

Since each model has its own data input specifications, some 

additional data preparation was required. In the case of 

SORTIE-ND, for example, imported tree-lists must contain 

spatial coordinates for each tree. As this type of information 

was not collected during field sampling, a random number 

generator algorithm was used to assign coordinates to each 

tree within a simulated 9 ha plot. Additionally, SORTIEND requires the user to provide parameter estimates for 

the specific model behaviours that have been selected. For 

this study, we used the collected data to obtain parameter 

estimates for allometric relationships, including height-diameter relationships and crown dimension relationships. 

Parameter estimates were also obtained for the SORTIE-ND 

snag fall-down model, which is used to define the rate at 

which dead standing trees become downed trees. Lastly, the 

fraction of the forest floor occupied by different substrates 

was defined. All other parameters within SORTIE-ND, 

including light and growth parameters, were obtained 

from Astrup et al. (2007). PrognosisBC did not require any 

parameterization as it has been calibrated to the study area 

using permanent sample plots. 

For the analyses presented in this report, we restricted 

our list of potential stands to those stands that were attacked 25 years ago. Thus, the total length of each model 

projection period was 25 years. Once loaded, the stand-level 

tree-lists were projected forward in time in each model. 

For SORTIE-ND, each growth cycle was defined as a single 

year; while in PrognosisBC, the initial growth cycle was 

five years with subsequent cycles operating on a ten year 

basis. The transfer of tree-list projections from SORTIE-ND 

to PrognosisBC was restricted to five years and ten years 

following MPB attack, referred to as the five-year handoff simulation and ten-year hand-off simulation. For the 

five-year off simulation, a list of trees less than 7.5 cm dbh 

was obtained from SORTIE at the end of the fifth growth 

cycle. Since this list represented the number of trees over a 

simulated 9 ha plot, a value of 0.11 stems per hectare was 

given to each tree in this list so that it would be compatible with the tree-list requirements of PrognosisBC. Trees 

selected from SORTIE-ND were appended to the tree-list 

from PrognosisBC following the initial five-year growth cycle, 

replacing any trees less than 7.5 cm dbh that were in the 

PrognosisBC tree-list but retaining all trees greater than 7.5 

cm dbh. The new composite tree-list was then projected 

forward for 20 years using PrognosisBC. A similar approach 

was used for the ten-year hand-off simulation, except that 

tree-lists following the tenth growth cycle were joined and 

projected forward in PrognosisBC for 15 years.

The results of the five and ten year hand-off simulations 

were compared to actual values as well as estimated values 

obtained by using PrognosisBC and SORTIE-ND separately 

over the 25 year projection period. To evaluate the four 

model simulations, we compared the estimated number 

of trees per hectare (tph) across the six stands that were 

tested. Bias, defined here as predicted value minus observed 

value, was calculated by species group (Pine, Spruce-Aspen) and by dbh size class. Two individual stands, one a 

low density stand (425 tph) at the time of MPB attack and 

the other a high density stand (1184 tph), were examined 

to gauge the effectiveness of the models under different 

stand densities. 

Results

Plot data were summarized to provide initial stand conditions following reconstruction (1981 data), as well as 

observed 2006 conditions (Table 1). All stands, with the 

exception of stand 25, had at least a minor component of 

spruce and/or aspen in the understory. All stands were 

dominated by lodgepole pine in the overstory. Understory 

densities at the time immediately following attack ranged 

from 92 tph to 183 tph, while overstory densities ranged 

from 267 tph to 883 tph. Compared with recorded obser-
FOREST GROWTH AND TIMBER QUALITY

7

Table 1—Reconstructed (1981) and recorded (2006) stand level densities (tph=trees per hectare) by species group and 

dbh size class for the six tested stands

Year Stand

No. of 

plots

Pine < 7.5cm 

dbh

Pine > 7.5cm 

dbh

Spruce and 

Aspen < 7.5cm 

dbh

Spruce and 

Aspen > 7.5cm 

dbh Total

(tph) (tph) (tph) (tph) (tph)

11

4  58 0 100  550

15  150 242  25 425

1  50 742 150 141 1084

24  1 384 2 17 734

25  17 350 0  00

2  7 751 25 42 884

200

4  567 225 467 158 1416

15  217 284 7  2550

1  2 17 2 22 1075

24  100 1 433 259 2675

25  750 17 0 58 1125

2  400 409 100 58 7

Figure 1—Average biases (predictedobserved) of estimating the number 

of trees per ha of lodgepole pine 

across all dbh classes for the four 

different simulations following a 

25-year projection.

Figure 2—Average biases (predictedobserved) of estimating the number 

of trees per ha for spruce-aspen across 

all dbh classes for the four different 

simulations following a 25-year 

projection.
FOREST GROWTH AND TIMBER QUALITY

74

vations from 2006, all stands with the exception of stand 

18, showed an increase in the total tph following MPB 

attack. Understory densities in 2006 ranged from 433 tph 

to 2234 tph, while overstory densities ranged from 375 

tph to 609 tph.

Bias values related to tph across all six stands were much 

larger for lodgepole pine than for spruce-aspen. The density 

of lodgepole pine less than 7.5 cm dbh was underestimated in 

all four simulations, with the 2.5 to 5.0 cm dbh class showing 

the poorest results for all simulations (Figure 1). For lodgepole pine trees with a dbh greater than 7.5 cm, the 10-year 

hand-off simulation had the best results, although all four 

simulations had similar results and provided reasonably 

good estimates of tph. Overall, estimates of tph for spruce 

and aspen were much lower than actual values (Figure 2). 

Estimates for the spruce-aspen species group were poorest 

in the 2.5 to 5.0 cm dbh class, with densities being under 

estimated by as much as 850 tph in the 10-year hand-off 

simulation. The lone exception was in the simulation that 

used SORTIE-ND for the entire 25 year projection period. 

Here, the 7.5 to 15 cm dbh class had the poorest results, 

under-estimating densities by 870 tph. The best approximation of stand-level densities for spruce and aspen trees 

larger than 7.5 cm dbh was provided by the simulation that 

used PrognosisBC only. 

In order to gain some insight into how each simulation 

performed given a different stand density immediately 

following MPB attack, we compared the results of two 

stands. The first stand we looked at had a total density 

of 425 tph in 1981, while the second stand had a density 

of 1184 tph in 1981. The stand with the lower density in 

1981 showed poor results for all tree species less than 7.5 

cm dbh in both of the hand-off simulations (Figure 3). 

This is not surprising given the tendency for all simulations to drastically underestimate densities of small trees 

and the fact that this stand turned out to have one of the 

highest densities of small trees 25 years after MPB attack. 

For the stand with the higher density in 1981, the 10-year 

hand-off simulation provided the best estimate of tph for 

trees less than 7.5 cm dbh (Figure 3). In fact, this simulation actually overestimated tree densities in the 0 to 2.5 

cm dbh class. However, it is important to note that actual 

small tree densities recorded in 2006 were low relative to 

the other six stands, although stand densities were high 

in 1981. It appears that the general tendency of the four 

simulations was to dramatically underestimate tph. However, the magnitude of this discrepancy may be lower in 

stands where low tph values for trees less than 7.5 cm dbh 

were recorded in 2006. 

DISCUSSION

Both the 5-year hand-off and 10-year hand-off simulations 

for stands following MPB attack produced minor improvements in density projections for trees less than 7.5 cm dbh 

over the simulation that used PrognosisBC or SORTIE-ND 

only. The most noticeable improvement, although still 

minor, was in the 10-year hand-off simulation when estimating densities for spruce and aspen. This may be due 

in part to low densities of spruce and aspen trees less than 

7.5 cm dbh relative to the densities of small lodgepole pine 

trees. Testing the simulations on stands where the densities of small spruce and aspen trees are on the same order 

as lodgepole pine might reveal different results among the 

Figure 3—Estimated and actual 

trees per ha from a low density and 

a high density stand for all trees less 

than 7.5 cm dbh following a 25 year 

projection using the handoff at year 

5 simulation and the handoff at year 

10 simulation.
FOREST GROWTH AND TIMBER QUALITY

75

different simulations. The tendency for all simulations to 

underestimate densities of large spruce and aspen trees, 

although not as pronounced as was the case with smaller 

trees, was somewhat discouraging. Likewise, the tendency 

for all simulations to overestimate overstory densities of 

lodgepole pine seems to indicate that conditions in MPB-affected stands may have been under-represented in the PSPs 

used in the calibration of PrognosisBC and SORTIE-ND. 

Poor estimates of stand densities following MPB attack 

for trees less than 7.5 cm dbh in the two simulations that 

used the linked-model approach and the simulation that 

used SORTIE-ND only may be indicative of several factors. First, the results presented here are based on results 

obtained from only six stands. These stands were chosen 

for the initial tests of the linked-model approach because 

they were representative of the diverse range of stand conditions observed during sampling. However, increasing the 

number of stands tested may improve the overall results 

of the hand-off simulations. The results obtained from the 

low density stand and the high density stand would suggest 

that averaging the results over more stands may reduce the 

biases of estimating densities.

Second, while the data collected in 2006 was used to 

provide parameter estimates for allometric relationships, 

substrate composition, and snag fall down rates in SORTIEND, other parameters used by the model may not reflect 

the exact conditions of the stands used in the simulations. 

For example, the growth parameters provided to SORTIE 

from Astrup et al. (2007) were for the SBS biogeoclimatic 

ecological classification zone. Although some of our plots 

were collected within this zone, the majority of our plots 

were collected from the SBPS and IDF zones where annual 

rainfall levels are considerably lower and tree growth is 

generally slower (Mah and Nigh 2003). Using growth parameters that overestimate tree growth can cause SORTIEND to increase competition-induced mortality rates, thus 

killing off more understory trees than would be expected. 

Since measurements collected for this study do not allow 

us to directly estimate many of the parameters used by 

SORTIE-ND, additional data may be required to improve 

the overall performance of SORTIE-ND. 

Lastly, it is possible that the poor results obtained from 

the simulations are in large part due to the high variability 

of regeneration densities following MPB attack. This condition is cited as a likely culprit for the poor results obtained 

when using the MSN approach to estimate natural regeneration following partial cutting (Hassani et al. 2004). Since 

one of the sampling objectives was to collect data from a 

wide range of stand types affected by MPB, increasing the 

number of stands used in the simulations may improve the 

results since there would be a better representation of the 

variability in overstory and understory densities.

CONCLUSION

In addition to an overstory tree-list, PrognosisBC requires 

the input of a natural regeneration tree-list to provide accurate mid- to long-term estimates of growth and yield in 

unmanaged complex stands. Our goal in linking regeneration tree-lists estimated by SORTIE-ND to PrognosisBC

was to improve upon the MSN approach of estimating 

natural regeneration following MPB attack. Compared to 

the MSN approach, using SORTIE-ND to estimate natural 

regeneration, including species composition and density, 

allows for greater flexibility since the SORTIE-ND model 

parameters can be easily adjusted to fit a specific dataset. 

This method is potentially advantageous when estimates of 

natural regeneration are required for stands that are unusual 

or under-represented, as is the case for stands affected by 

MPB in central and southeastern BC.

Between the two different hand-off times studied, the 

hand-off of the SORTIE-ND regeneration tree list to PrognosisBC after 10 years showed the best results for small spruce 

and aspen trees when compared to the results obtained when 

using SORTIE-ND or PrognosisBC alone. Only marginal 

improvements in the estimates of small lodgepole pine 

were noted for both the five-year hand-off and the ten-year 

hand-off simulations. The overall poor results obtained by 

using the linked-model approach would likely be improved 

with further parameterization of SORTIE-ND behaviors. 

Also, using a more extensive dataset with measurements 

collected from a larger number of stands should bring the 

estimates of small tree densities closer in-line with actual 

observations. 

LITERATURE CITED

Astrup, R.; Coates, K.D; Hall, E.; Trowbridge, A. 2007.

Documentation for the SORTIE-ND SAS Research 

Parameter File Version 1.0. February, 2007, Smithers, 

British Columbia, Canada: Bulkley Valley Centre. 

50 p.

Aukema, B.H.; Carroll, A.L.; Zhu, J. [et al.]. 2006.

Landscape level analysis of mountain pine beetle 
FOREST GROWTH AND TIMBER QUALITY

7

in British Columbia, Canada: spatiotemporal 

development and spatial synchrony within the present 

outbreak. Ecography 29: 427-441

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Forests, Nelson, B.C. Research Summary RS-003.

Boisvenue, C. 1999. Early height growth and 

regeneration: Applicability of Prognosis components 

to the Southern Interior of British Columbia. M.Sc. 

Thesis, Univ. of B.C., Vancouver, BC. 193 p.

Boisvenue, C; Temesgen, H; Marshall, P.M. 2004. 

Selecting a small tree height growth model for mixedspecies stands in the southern interior of British 

Columbia, Canada. Forest Ecology and Management 

202: 301-312.

Campbell, E.M.; Alfaro, R.I.; Hawkes, B. 2007. Spatial 

distribution of mountain pine beetle outbreaks 

in relation to climate and stand characteristics: a 

dendroecological analysis. Journal of Integrative Plant 

Biology 49: 168-178

Canham, C. D.; Burbank D.H. 1994. Causes and 

consequences of resource heterogeneity in forests—

interspecific variation in light transmission by canopy 

trees. Canadian Journal of Forest Research 24: 337-

349.

Coates, D.K.; Canham, C.D.; Beaudet, M. [et al.]. 

2004. Use of a spatially explicit individual-tree model 

(SORTIE/BC) to explore the implications of patchiness 

in structurally complex forests. Forest Ecology and 

Management 186: 297-310.

Hassani, B.; LeMay, V.M.; Marshall, P.L. [et al.]. 2004.

Regeneration imputation models for complex stands 

of Southeastern British Columbia. The Forestry 

Chronicle 80:271-278.

Hawkes, B.; Taylor, S.; Stockdale, C. [et al.]. 2004.

Impacts of mountain pine beetle on stand dynamics 

in British Columbia. Pages 175–195. In: T.L. Shore, 

J.E. Brooks, and J.E. Stone, editors. Mountain Pine 

Beetle Symposium: Challenges and Solutions. 

Kelowna, British Columbia October 30-31, 2003, 

Natural Resources Canada, Canadian Forest Service, 

Pacific Forestry Centre, Information Report BC-X-399, 

Victoria, BC. 298p.

Hyytiainen, K.; Ilomaki, S.; Makela, A.; Kinnunen, K.

2006. Economic analysis of stand establishment for 

Scots pine. Canadian Journal of Forest Research 36: 

1179-1189.

Kobe, R.K.; Coates, D. 1997. Models of sapling mortality 

as a function of growth to characterize interspecific 

variation in shade tolerance of eight tree species of 

northwestern British Columbia. Canadian Journal of 

Forest Research 27: 227-236

LeMay, V.M.; Lee, T.; Scott, R.E. [et al.]. 2006. 

Modeling Natural Regeneration Following Mountain 

Pine Beetle Attacks in the Southern and Central 

Interior of British Columbia: Results for Year 1. 

Internal report for Natural Resources Canada, MPB 

Standard Contribution Agreement, PO # 8.35. 70 pp. 

http://www.forestry.ubc.ca/prognosis/extension.html

Mah, S; Nigh G.D. 2003. SIBEC site index estimates in 

support of forest management in British Columbia. 

Research Branch, B.C. Ministry of Forests, Victoria, 

B.C. Technical Report 004. www.for.gov.bc.ca/hfd/

pubs/docs/tr/tr004.htm

Moeur, M. and A.R. Stage. 1995. Most similar 

neighbor: an improved sampling inference procedure 

for natural resource planning. Forest Science 41, 337-

359. 

Oliver, C.D.; Larson, B.C. 1996. Forest Stand Dynamics. 

John Wiley and Sons, Inc., New York, 520 p.

Pacala, S.W.; Canham, C.D.; Silander, J.A. 1993. Forest 

models defined by field measurements: The design of 

a northeastern forest simulator. Canadian Journal of 

Forest Research 23: 1980-1988

Pedersen, L. 2003. Allowable Annual Cuts in British 

Columbia: The Agony and the Ecstasy. UBC Faculty of 

Forestry Special Presentation. Vancouver, BC, Canada: 

Faculty of Forestry, University of British Columbia. 24 

p. http://www.for.gov.bc.ca/hts/pubs/jubilee_ubc.pdf

Robinson, A.P; Monserud, R.A. 2003. Criteria for 

comparing the adaptability of forest growth models. 

Forest Ecology and Management 172: 53-67.

Snowdon, B. 1997. British Columbia’s Forest Vegetation 

Simulator application software. In: Proceedings of 

Forest Vegetation Simulator Conference. Teck, R.; 
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Moeur, M.; Adams, J., technical editors. Feb. 3-7, 

1997, Fort Collins, CO. Gen. Tech. Rep. INT- 373. 

Ogden, UT: U.S. Department of Agriculture, Forest 

Service, Intermountain Forest and Range Experiment 

Station. 

Stage, A.R. 1973. Prognosis model for stand 

development. USDA, Forest Service, Res. Pap. 

Intermountain Forest and Range Exp. Station. INT137. Ogden, UT.

Stevens, V. 1997. The ecological role of coarse woody 

debris: an overview of the ecological importance of 

CWD in B.C forests. Research Branch, B.C. Ministry 

of Forests, Victoria, B.C. Working Paper 30/1997.

Zumrawi, A.; Stage A.; Snowdon, B. 2002. Stand level 

scaling of a single tree distance independent diameter 

growth model: Interim calibration of Prognosis in 

the south-eastern interior of British Columbia. In: 

Proceedings of Second Forest Vegetation Simulator 

(FVS) Conference. Crookston, N.L; Havis, R.N., 

compilers. February 12-14, 2002, Fort Collins, 

CO. RMRS-P-25. Ogden, UT: U.S. Department of 

Agriculture, Forest Service, Rocky Mountain Research 

Station. p. 151-157.

Zumrawi, A.A.; LeMay, V.; Marshall, P.M. [et al.]. 

2005a. Implementing a PrognosisBC Regeneration 

Sub-model for Complex Stands of Southeastern 

and Central British Columbia. Collaborative Project 

between Research Branch, Ministry of Forests; Forest 

Resources Management Department, University 

of British Columbia, and ESSA Technologies, Inc. 

Vancouver, British Columbia, Canada. Report 

submitted to: Forest Science Program, Project No: 

Y051355, 157 p. http://www.for.gov.bc.ca/hre/pubs/

azumrawi.htm

Zumrawi A.A.; Marshall, P.M.; Akindele, S.O. [et al.]. 

2005b. Calibrating PrognosisBC in the Sub-Boreal 

Spruce and the Sub-Boreal Pine-Spruce Biogeoclimatic 

Zones: Development of growth and mortality models 

for major tree species. Internal report for Forest 

Science Program, Project No: Y051356.
FOREST GROWTH AND TIMBER QUALITY

7

ABSTRACT

EFFECTS OF THINNING AND FERTILIZATION 

on wood and tracheid properties, and economic 

returns of Norway spruce (Picea abies (L.) Karst.) 

were investigated in two young stands, in southeastern 

Finland and northern Sweden. Models for predicting wood 

and tracheid properties of Norway spruce were integrated 

into a distance-independent process-based growth model. 

Increasing thinning intensity resulted in lower mean 

wood density, tracheid length, and latewood proportion in 

harvest wood. Pulpwood fiber quality slightly decreased 

when the proportion of sawlog yield over the rotation increased. Thinning regimes with high early growing stock 

and decreasing later growing stock were most profitable. 

Fertilization accelerated volume growth and increased value 

growth. Decreased wood density and tracheid length due to 

fertilization resulted in minor effects on economic returns. 

Increased volume growth more than offset the economic 

influence of fiber quality. 

KEYWORDS: fiber quality, forest fertilization, process-based 

growth model, Norway spruce, thinning intensity

Effects of Silvicultural Treatments on Wood and 

Tracheid Properties, and Economic Returns of 

Norway Spruce

Tianjian Cao, Lauri Valsta, Sanna Härkönen, Annikki Mäkelä

Tianjian Cao (tianjian.cao@helsinki.fi) is a doctoral student and Lauri Valsta is a professor, Department of Forest Economics, P.O. Box 27, 

FIN-00014 University of Helsinki, Finland; Sanna Härkönen is at the Faculty of Forestry, P.O. Box 111, FIN-80101 University of Joensuu, Finland;

Annikki Mäkelä is a professor, Department of Forest Ecology, P.O. Box 27, FIN-00014 University of Helsinki, Finland.

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 78.
FOREST GROWTH AND TIMBER QUALITY

7

ABSTRACT

THE NEED FOR ACCURATE WOOD QUALITY 

prediction in hardwoods has increased with the 

growing importance of these species to the global 

forest industry, in particular Eucalyptus species. Several 

process-based models of xylem development have been 

produced (Wilson 1964; Deleuze and Houlier 1998; Fritts et 

al. 2005) but have considered woody tissue development in 

softwoods only. The situation is more complex in hardwoods, 

which produce a greater variety of cell types in the xylem. 

The model described here, which we have called “CAMBIUM”, simulates the growth and development of a hypothetical, simulated population of cells in variable numbered 

cell files, bounded within sets of rays. Although models 

for softwood xylem effectively work in a single dimension (modeling a single radial file of cells), it is necessary 

to consider hardwood xylem in at least two dimensions 

in the transverse plane (modeling multiple, neighboring 

files of cells) because of the highly significant interactions 

between cell types and the importance of their spatial arrangement. These interactions are constantly invoked in 

the hypothetical cell population during the model run to 

modify environmentally determined “potential” cell growth 

and development.

The model predicts cell fate, cell division and production, cell growth, and cell secondary wall development in 

individual cells in the simulated population. It uses outputs 

of whole-tree physiological parameters generated on a daily 

time-step from the CABALA process-based model (Battaglia 

et al. 2004) which has been widely tested and validated for 

various Eucalyptus spp. Outputs of particular importance 

Simulating Daily Xylem Development in Eucalypts Using 

Outputs from the Process-Based Model CABALA

David M. Drew, Geoffrey M. Downes, Jenny Read, Michael Battaglia

David M. Drew (david.drew@sci.monash.edu.au) is at the School of Biological Sciences, Building 18, Monash University, Victoria 3800 and CSIRO 

Ensis, Private Bag 12, Hobart 7001, Tasmania, Australia; Jenny Read is at the School of Biological Sciences, Building 18, Monash University, Victoria 

3800, Australia; Geoffrey M. Downes and Michael Battaglia are at CSIRO Ensis, Private Bag 12, Hobart 7001, Tasmania, Australia.

from CABALA are daily derived estimates of pre-dawn 

and midday water potential, stem and foliage allocation, 

minimum and maximum temperature, and vapour pressure deficit. 

CAMBIUM relies heavily on conceptual morphogenic 

fields of growth-regulating substances, particularly auxin, 

which have been found to affect cambial activity and cytodifferentiation in the cambial zone and developing xylem. 

The model considers different approaches to determining 

cell fate as either a function of cell position with these 

morphogenic fields or as a function of the flow of chemical 

signals, or as a function of both. It currently determines 

between fibers or vessels in the developing xylem from a 

homogenous population of cambial initials. The model also 

provides more than one approach to calculating the potential 

daily growth of developing cells. Following the additional 

consideration of cell-cell interactions, the model is thus 

capable of generating high-resolution estimates of fiber and 

vessel transverse dimensions. The process of secondary wall 

thickening is currently very simple, similar to that proposed 

by Deleuze and Houllier (1998) and generates estimates of 

fiber and vessel wall thickness. Wood density is derived 

empirically from cell transverse and wall dimensions as 

well as potentially from vessel frequencies.

Model parameterization and validation is currently underway using data from four Eucalyptus species from three 

separate research trials in South Africa and Australia. Early 

results indicate that the model is able to accurately detect 

changes in wood properties in a radial profile in response 

to changing environmental conditions in a forest stand.

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 79.

FOREST GROWTH AND TIMBER QUALITY

1

ABSTRACT

The hybrid model, CanSPBL(water) was developed 

to predict the growth of plantation grown Pinus 

radiata in New Zealand’s Canterbury Region. The 

hybrid model is an updated version of an existing model 

CanSPBL(1.2) (Pinjuv 2006), and includes an index of 

water balance over the simulation period. Water balance 

estimates were made using a sub-model for root zone water 

balance included in the hybrid physiological model 3-PG 

(Landsberg and Waring 1997). The hybrid was validated 

with an independent data set of growth measurements 

used for model fitting and was compared to the statistical 

version, CanSPBL(1.2) (Pinjuv 2006). The validation was 

run using both monthly inputs of climate (that displayed 

yearly variation) and monthly inputs of climate (that were 

ten-year averages). Using climatic inputs that included 

yearly variation, the hybrid model showed an increase in 

precision of 1–4 percent over the statistical version of the 

model at a stand level (with the exception of the model for 

maximum diameter, which showed a decrease in precision of 0.78 percent). However, using ten-year averages of 

monthly climatic inputs, the hybrid model showed increases 

of precision from 0.5 to 8 percent (with the exception of 

maximum diameter again, showing a decrease in precision 

of 0.13 percent). The components of the stand model also 

included mean top height, basal area per hectare, stems 

per hectare, and diameter distribution. 

KEYWORDS: Forest growth model, hybrid model, water 

balance, forest productivity, model validation

Incorporating an Index of Root Zone Water Balance 

Into an Existing Growth and Yield Model CanSPBL(1.2)

Guy Pinjuv, Euan G. Mason, Michael Watt

Guy L. Pinjuv (guy.pinjuv@gmail.com) is a doctoral student and Euan G. Mason is an associate professor of forestry at the University of Canterbury, 

Private Bag 4800, Christchurch, New Zealand; Michael Watt is a research scientist at ENSIS (formerly New Zealand Forest Research), P.O. Box 29237, 

Christchurch, New Zealand.

INTRODUCTION

WATER BALANCE IS A WELL-ESTABLISHED INDICATOR 

of growing potential and has been found to be a main constraint for tree development on dry forested sites. Reduction 

in the availability of water decreases stem growth by restricting physiological processes such as leaf area development, 

photosynthesis, and stomatal conductance (Boomsma and 

Hunter 1990). An index for water stress (the water stress 

integral) has been shown by Myers (1998) to account for 

almost all of the variation in basal area increment of Pinus 

radiata subjected to a range of irrigation and fertilization 

treatments. Given the importance of water availability in 

regulating productivity and basal area growth on dry sites, 

a model of root zone water balance may provide a useful 

process-based approach that can be incorporated into a 

classical growth and yield model.

Incorporating a model of root zone water balance into 

a classical growth and yield model may increase accuracy 

of tree growth prediction, and make the model more robust 

under changing climatic conditions. This paper will discuss 

a root zone water balance model that was used to estimate 

water balance for all forests in the Selwyn Plantation Board 

Estate located in New Zealand’s Canterbury Region. An 

index for available water at the each site will be used as a 

variable to predict future forest growth. This index was 

incorporated into the equations that comprise the existing 

growth model CanSPBL(1.2) described in detail by Pinjuv 

(2006). This paper will first examine the modeling strategy used to predict root zone water balance, discuss the 

input data for the model, parameterization of the model, 

This paper was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 81–98.
FOREST GROWTH AND TIMBER QUALITY

2

validation of the model used to predict root zone water 

balance, and then the results of incorporating that index 

into CanSPBL(1.2). 

WATER BALANCE MODELING

3PG Water Balance Model Adapted from 

(Landsberg and Waring 1997) and (Sands 

and Landsberg 2002)

The water balance model used to calculate an index of 

water use over the measurement interval was the model 

sub-model for water balance used in 3-PG (Landsberg and 

Waring 1997). This model is a single layer soil-water-balance model that operates on a monthly time step. Monthly 

rainfall (plus irrigation) is balanced against monthly 

evapotranspiration computed using the Penman-Monteith 

equation (Landsberg and Gower 1997, p. 76.) The general 

equation can be written as:

θT = θT-1 + P - I - E - D (1)

Where: θT is the root zone water balance at time T (mm), 

θT-1 is the root zone water balance at time (T-1) in the previous month (mm), P is precipitation (mm), I is the canopy 

interception (mm), E is evapotranspiration (calculated using 

the Penman-Monteith equation,) and D is the drainage of 

water from the soil (mm).

The model is initialized with soil water content 

= maximum available water in the rooting zone 

(θmm). This is dependent on the water-holding characteristics of the soil and the rooting depth of the trees (see 

Landsberg and Gower 1997). Available water is set to appropriate starting values for each site. The moisture ratio 

(rθ) for the stand is calculated as:

 rθ = Current soil water content + water balance (2)

Available Water

The moisture ratio rθ is used in the calculation of a soil 

water modifier (f

sw), which is used to modify estimates of 

canopy conductance (gc) that will be discussed later. The 

water balance in any month will be reduced if transpiration exceeds precipitation, and vice versa. If the numerator of the expression for rθ exceeds θ, the excess water is 

assumed to have run off or drained out of the system. If it 

is negative rθ = 0.

Canopy interception is a fixed percentage of rainfall 

when the canopy exceeds a threshold leaf area index (LAI) 

in the 3-PG model. When P > 2mm, and LAI ≥ 3, then I 

= 0.15*P. If P< 2 mm, then I = P. And if P > 2mm and 0 < 

LAI < 3, then I = 0.05*LAI*P.

 Vapor pressure deficit, available soil water and stand 

age are assumed to affect stomatal conductance. Canopy 

conductance (gc

 (m s-1)) is determined from a nominal 

stomatal conductance scaled by f

age and by the lesser of 

the environmental modifiers f

sw and fVPD, and increases 

with increasing canopy LAI up to a maximum canopy 

conductance (gc

max (m s-1)). 

The equation for canopy conductance is given by:

gc = gcmax ⋅ e

(-k⋅VPD) (3)

where k is a factor based on the relationship between stomatal conductance and vapor pressure deficit = 2.5 (value 

taken from Landsberg and Waring 1997) and VPD is the 

saturation vapor pressure (kPa).

The age modifier f

age, is calculated from:

nage

a

age

F

f





 



 +

=

95.0 1

1 

(4)

where Fa is the relative age of a forest or plantation denoted 

by the ratio of actual age (in years) to the maximum age 

likely to be attained, nage is a parameter to control the rate 

of change of the function and the default value from the 

3-PG model is nage=4.

The vapor pressure deficit modifier, f

VPD is calculated 

from:

f

VPD = e

(-k⋅VPD) (5)

where k is a factor based on the relationship between stomatal conductance and vapor pressure deficit = 2.5 (value 

taken from Landsberg and Waring 1997) and VPD is the 

saturation vapor pressure (kPa).

The soil water modifier, f

sw is calculated from:

( )

θ

θ

sw n

c

r

f



 

 − +

= 1 1

1

θ (6)

where cθ and the power nθ take different values for different soil types Landsberg and Waring (1997) suggest 
FOREST GROWTH AND TIMBER QUALITY



cθ =0.7, 0.6, 0.5, and 0.4 for sand, sandy-loam, clay-loam, 

and clay soils, respectively, and nθ =9, 7, 5, and 3 for the 

same soil types.

WATER BALANCE VALIDATION

The 3PG, and sub-model for water balance was tested against 

a validation dataset that contained measurements taken 

within the study area. The validation dataset came from a 

study done by Arneth et al., (1998), which contained 49 

measurements of volumetric root-zone water content taken 

at Balmoral Forest, located 100-km Northwest of Christchurch New Zealand, (42°52’S, 172°45’E at an elevation 

198 m above sea level) between 1994 and 1996. A residual 

analysis of the model was run across the validation dataset. 

This residual analysis was conducted on an accumulated 

deficit basis over a given measurement interval. This was 

done to mirror the model’s final use in a growth and yield 

modeling context where the accumulated water deficit over 

a measurement interval is expected to describe variations 

in stand growth and diameter distribution. Table 1 shows 

the actual and estimated accumulated water deficit for the 

3PG and sub-model for water balance. An analysis of mean 

square error (MSE Eq. 7) was used as the final selecting 

criterion to determine the water balance model used in 

further analysis.

∑ ( ) = −= n

n i

MSE YY

1

2 1 '

(7)

where Y is the measured accumulated root zone water 

deficit (mm), and Y′ is the modeled accumulated root zone 

water deficit.

METHODS

Climatic Inputs for Water Balance 

Modeling

The climatic inputs of solar radiation, minimum air temperature, maximum air temperature, and rainfall were 

estimated for each site using the method of correcting 

10-year average values for each site by local met station 

measurements. Actual water balance climate inputs are 

based on a system of corrected estimates from BIOCLIM 

(Leathwick and Stevens 1998) climate surfaces. BIOCLIM 

is a set of surface equations for New Zealand that estimate 

climatic variables on a 10-year average based on interpolation between climate station measurements (Leathwick 

and Stevens 1998). BIOCLIM outputs monthly averages of 

temperature, wind, rainfall, radiation, and average humidity 

extremes across New Zealand based on location. To simulate 

the monthly variation in actual climate readings, as opposed 

to mean monthly values over a 10-year period, the longterm mean monthly climate values derived from BIOCLIM 

were rescaled using monthly climate measurements from 

a nearby weather station. These estimates were corrected 

by reference point measurements made at Christchurch 

Airport (S43.5°, E172.55°, elevation 37m). Differences between climatic estimates from BIOCLIM and measurements 

at Christchurch Airport were calculated for each month 

included in the study from 1984–2004. Corrections were 

added to long term monthly estimates at each permanent 

sample plot. So instead of using the same monthly averages every year, a new value was calculated every month 

based on actual climate at Christchurch Airport to reflect 

years of extreme climatic events such as droughts. Similar 

approaches to correcting long term averages with local 

measurements have been used by Tickle et al. (2001), and 

Snowdon et al. (1999).

Growth and Yield Fitting and 

Validation Data 

The model fitting and validation dataset comprised 4416 

growth observations taken within 1020 unique permanent 

sample plots. All measurements were recorded between 

December 1982 and January of 2004 on the Selwyn Plantation Board Estate located in the Canterbury region of southeastern New Zealand. Sites on the Selwyn estate vary with 

elevation covering the three forest types of plains, hills, and 

coastal sands with elevations ranging from 2–600 

metres above sea level. Distinctions between 

these forest types are due to both elevation and 

soil type. With increasing distance from the sea, 

soils underlying forests in Canterbury change 

from coastal sands, shallow and dry floodplains 

soils, to deep wet loess hill soils (Barringer et al. 

1998). Average temperatures are 10.9 °C for plains 

Table 1—Measured and estimated accumulated water deficit (mm) from 3PG and 

water balance models. 

Interval (month/year)

Measured accumulated 

water deficit (mm) 3PG estimate (mm)

10/1987–5/1988 273.51 273.57

6/1988–5/1989 417.11 379.52

/1–/10 164.72 12.7
FOREST GROWTH AND TIMBER QUALITY

84

and coastal forests, and 11.6 °C for forests growing on the 

hills. Annual rainfall increases from 600 to 1100 mm for 

coastal-plains and hills forest, respectively (Leathwick and 

Stephens 1998). The mean re-measurement interval is 6.6 

years for all measurements, while the mean re-measurement interval per plot was 5.7 years. All validation data 

were independent of any information used for fitting or 

calibrating any of the included models in this study. The 

database was partitioned for model building and model 

validation. In all, there were 4416 plot measurements in 

the entire data set: 3667 were randomly chosen for model 

building, while 969 plot measurements were randomly 

set aside for model validation. A detailed summary of plot 

variable estimates with a breakdown for plains and foothills 

plots is listed in Pinjuv (2006).

Growth Modeling: Incorporating and 

Index of Root Zone Water Balance Into 

the Existing Model CanSPBL(1.2)

Equations used to model growth in CanSPBL(1.2) were 

updated to incorporate an index of root zone water balance. The water balance index used described the average 

available soil water deficit over the simulation period, as 

calculated with the model for water balance used in 3PG 

(Landsberg and Waring 1997). The water balance model 

was represented in the Java programming language by Dr 

E.G. Mason, and the Java program accessed weather data 

for each plot within a Microsoft Access database table and 

arranged for output to be placed alongside growth and yield 

data in a separate Access table. Table 2 shows the descriptive statistics of average monthly available soil water deficit 

(ASW) values for the model fitting data set. 

The method used for incorporating the effect of average 

ASW deficit into the equations used in CanSBPL(1.2) was 

to plot the residuals of the models against ASW deficit and 

observe the pattern of residual bias. This bias was then accounted for by adding curvilinear forms of ASW deficit to the 

models. An example of this is shown in Figure 1 where the 

bias of mean top height residuals plotted against ASW deficit 

can be corrected in part by a curvilinear model including 

a form of ASW deficit and ASW deficit squared.

Residuals of all of the models in CanSPBL(1.2) were 

first plotted against average ASW deficit. All of these plots 

indicated the bias could be corrected for by adding ASW 

deficit and ASW deficit squared to each model. The 4 best 

initial fit sigmoid growth equations where the effects of 

elevation were initially tested in Pinjuv (2006) were fitted 

again with ASW deficit and ASW deficit squared added to 

them. These final models were then tested further to see 

if different forms of elevation and ASW deficit could be 

added to them in a way that would minimize error and 

simplify the final model.

To fit equations, methods used by Zhao (1999), and 

Pinjuv (2006), of non-linear least-square procedures with 

SAS software (SAS Institute Inc., 2001) were employed. 

The Mean Square Error (MSE) and graphical residual patterns were used as the selection criteria to judge model 

performance. Skewness and kurtosis were often checked 

for final models to determine the magnitude of residual 

distributions of normality. Plots of residuals versus predictions and all possible explanatory variables were inspected 

to check for trends but only the five most important graphs 

are displayed in this study for each selected equation. The 

five graphs are residuals versus prediction, age, elevation, 

time increment, and ASW deficit. 

No statistical tests are given in this analysis because 

repeated measurements have been taken from the basic 

experimental units (PSP). The consequences of this are 

(1) estimators of the regression coefficients may no longer 

have minimum variance but will still be unbiased and consistent, (2) standard errors of coefficients in the regression 

will be underestimated, and (3) any significance tests or 

confidence limits constructed using t or F distributions are 

likely to be wrong since assumed independence of errors is 

Table 2: Descriptive statistics of the average ASW deficit in 

modeling data set.

3PG Average Water Deficit

Mean (mm) 32.21

Minimum (mm) 0.00

Maximum (mm) 142.38

Standard Deviation (mm) 24.95

Count 0.00

Table 3—Basal area model fitting results, after the effect of 

average water deficit and elevation are included in the asymptotic 

parameter.

Equation with elevation and 

average 3PG water deficit in 

asymptote Basal Area MSE

Polymorphic Weibull I failed to converge

Polymorphic Gompertz II 16.49

Polymorphic Weibull II failed to converge

Polymorphic Schumacher II 1.1
FOREST GROWTH AND TIMBER QUALITY

85

violated (West et al. 1984). The MSE for the regression is 

also likely to be underestimated if the correlation is positive 

and inflated if the correlations are negative (Snowdon et 

al. 1999). Some statistically valid tests are provided in this 

analysis as a check of the final results by preparing an auto 

correlation free data set. An auto correlation free data set 

was used to test the significance of explanatory variables 

being different from zero for all models and to check the 

normality of residuals with the Kolmogorov-Smirnov test. 

The Kolmogorov-Smirnov test was chosen to test normality 

because of the large size of the data set. 

To validate the newly established model and test its 

performance at a plot level, a validation data set was prepared. The main model components of MTH, basal area 

per hectare, stems per hectare, maximum diameter, and 

standard deviation of diameter were examined using data 

at a plot level. One source of data was selected consisting 

of independent plot measurements chosen randomly before 

model fitting. The average model bias (AMB), efficiency 

factor (EF), skewness and kurtosis were calculated for 

each model component. Graphs of residual patterns were 

examined to detect bias. Normality of residual plots was 

also tested using the Kolmogorov-Smirnov test.

RESULTS

Basal Area

The four models with the best initial fit for basal area in 

chapter 4 were of Pinjuv (2006); Polymorphic Gompertz II, 

Polymorphic Schumacher II, Polymorphic Weibull I, and 

Polymorphic Weibull II. The effects of water balance deficit 

and elevation were added into these models by altering the 

asymptotic parameter for each equation. These equations 

were initially fitted with the form of elevation that was used 

for the final model of basal area in CanSPBL(1.2) and the 

effects of water deficit added in as a linear and curvilinear 

term. The results of initial model fits in terms of MSE are 

shown in Table 3. 

The model with the lowest MSE after the addition of 

the effect of average water deficit and elevation was altered 

further to see if different correction forms for these effects 

would improve model fits. These included a linear correction 

for elevation for PSP’s above 250 m, as was used by Zhao 

(1999), elevation, the square of elevation, a probit correction 

for the effect of elevation, ASW deficit, ASW deficit squared, 

and the interaction of elevation and ASW deficit.

The best model fit was found by adjusting the asymptotic 

parameter of the Polymorphic Gompertz II equation using 

Figure 1: Residuals of mean top height vs. average 3PG available soil water deficit. 
FOREST GROWTH AND TIMBER QUALITY



elevation squared, a dummy variable for elevations above 

450m, mean ASW deficit, and mean ASW deficit squared. 

The final model for basal area has a MSE of 16.53, which 

is slightly higher than the initial fitting of the Polymorphic Gompertz II model listed in Table 3. The reason for 

this result is that this final model does not have the term 

of elevation alone in the asymptotic parameter as it was 

insignificant. The final model was fitted without this term 

and is written as:

( )



























− 



 



 



 



 −⋅+−⋅− 2

1 2212 1 TTTT

e β γ

( ) ( )









 + ⋅ 



 



 



 



 −⋅+−⋅−

=

2

1 2212

1 ln

2

TTTT

eG

eG

β γ

( ( )( ) )

⋅ ⋅+⋅+⋅−⋅+⋅+ 2 2 3 4 2 10

10000

elev ααα 450 Xelev ASW αα ASW

(8)

where G2 is the future basal area (m2 / ha), G1 is the initial 

basal area (m2 / ha), T1 is the initial stand age (years), T2 is 

the final stand age (years), elev is the stand elevation (m), 

X is a binary indicator variable, X = 0 if elevation < 450, 

and X = 1 if elevation ≥ 450, ASW is the average water 

deficit over the simulation period calculated with the 3PG 

water balance model (mm), and β, γ, α0, α1, α2, α3, α4 are 

parameters whose values are listed 

in Table 7.

The parameter estimates of the 

final model of basal area are listed 

in Table 4. The model showed no 

signs of bias for basal area / ha 

when plotted against prediction, 

age, elevation, and time increment 

(Figure 2). 

Mean Top Height

The four models with the best 

initial fit for mean top height 

(Pinjuv 2006) were Polymorphic Gompertz II, Polymorphic Von BertalanffyRichards II, Polymorphic Schumacher II, and the Polymorphic Hossfeld. The effects of water balance deficit and 

elevation was added into these models by altering the asymptotic parameter for each equation. These equations were 

initially fitted with the form of elevation that was used for 

the final model of mean top height in CanSPBL(1.2) and the 

effects of water deficit added in as a linear and curvilinear 

term. The results of initial model fits in terms of MSE are 

shown in Table 5.

The model with the lowest MSE after the addition of 

the effect of average water deficit and elevation was altered 

further to see if different correction forms for these effects 

would improve model fits. These included a linear correction 

for elevation for PSP’s above 250 m, as was used by Zhao 

(1999), elevation, the square of elevation, a probit correction 

for the effect of elevation, ASW deficit, ASW deficit squared, 

and the interaction of elevation and ASW deficit.

The best model fit was found by adjusting the asymptotic 

parameter of the Polymorphic Schumacher II equation using 

elevation squared, a dummy variable for elevations above 

450m, mean ASW deficit, and mean ASW deficit squared. 

The final model for mean top height had a MSE of 0.97 

and is written as:

































+

+ −

β

γ

γ

2

1 1

T

T

( ( ) ) ⋅ ααα αα ⋅+⋅+⋅−⋅+⋅+ 2 2 3 4 2 10

10000

elev 450 ASWXelev ASW

( ) + 















+

+ ⋅

=

β

γ

γ

2

1 1 ln

2 T

T MTH eMTH

(9)

where MTH2 is the future mean top height (m), MTH1 is the 

initial mean top height (m), T1 is the initial stand age (years), 

Table 4—Parameters for basal area model (Equation 8), standard errors, and approximate 

95-percent confidence limits calculated with 3,659 degrees of freedom.

Parameter Estimate Std. Error Approximate 95% Confidence Limits

β 0.153 0.0021 0.1487 0.1573

γ 0.00249 0.0000 0.00242 0.00257

α0 44311.5000 22.0 43862.6 44760.4

α1 0.0358 0.00070 0.0344 0.072

α2 -31.7278 2.172 -35.9881 -27.4675

α 35.2148 4.363 26.6604 43.7691

α4 -0.3759 0.0 -0.4481 -0.3038

Table 5—Mean top height model fitting results, including the 

effect of average water deficit and elevation in the asymptotic 

parameter.

Equation with elevation and 

average 3PG water deficit in 

asymptote Mean Top Height MSE

Polymorphic Gompertz II 1.01

Polymorphic Von BertalanffyRichards II 1.02

Polymorphic Schumachar II 0.7

Polymorphic Hossfeld 1.0
FOREST GROWTH AND TIMBER QUALITY

7

T2 is the final stand age (years), elev

is the stand elevation (m), X is a 

binary indicator variable, where X

= 0 if elevation < 450, and X = 1 if 

elevation ≥ 450, ASW is the average 

water deficit over the simulation period calculated with the 3PG water 

balance model (mm), and β, γ, α0, 

α1, α2, α3, α4 are parameters whose 

values are listed in Table 6.

The parameter estimates of the 

final model of mean top height 

Figure 2: Fitting residual patterns of the final model for basal area: (a) residuals versus predicted, (b) residuals versus stand age, (c) residuals versus 

elevation, (d) residuals versus time increment, and (e) residuals versus ASW deficit.

Table 6: Parameters for mean top height model (Equation 9), standard errors, and approximate 

95-percent confidence limits calculated with 3,659 degrees of freedom.

Parameter Estimate Std. Error Approximate 95% Confidence Limits

β 0.2 0.0425 0.5998 0.7

γ 4.1388 0.4782 .2012 5.0764

α0 44652.2 642.1 43393.3 45911.2

α1 0.02 0.00010 0.021 0.0258

α2 -32.8019 2.5632 -37.8276 -27.7763

α 40.0566 4.1723 1.71 48.2371

α4 -0.4519 0.0 -0.5285 -0.3754
FOREST GROWTH AND TIMBER QUALITY



are listed in Table 9. The model showed no signs of bias 

for mean top height when plotted against prediction, age, 

elevation, and time increment (Figure 3). 

Maximum Diameter and Standard 

Deviation of Diameter

Models for maximum diameter and standard deviation of 

diameter were fitted by selecting the 4 model forms that 

had the best initial fit for basal area. These forms were also 

fitted to the data, incorporating the effects of average water 

deficit and altitude within the asymptotic parameter where 

appropriate. Results for the initial fitting of these models 

for maximum diameter and standard deviation of diameter 

are shown in Table 7.

The best model fit for maximum diameter was found 

by adjusting the asymptotic parameter of the Polymorphic 

Weibull I equation using elevation squared, a dummy variable for elevations above 450m, the inverse of initial stocking, and ASW deficit squared (Eq. 10). The best model fit 

for the standard deviation of diameter was similarly found 

by adjusting the asymptotic parameter for the Polymorphic 

Gompertz II equation using elevation squared, a dummy 

Figure 3: Fitting residuals patterns of final model for mean top height: (a) residuals versus predicted, (b) residuals versus stand age, (c) residuals versus 

elevation, and (d) residuals versus time increment, and (e) residuals versus ASW deficit.
FOREST GROWTH AND TIMBER QUALITY



variable for elevations above 450m, ASW deficit, and ASW 

deficit squared (Eq. 11). The final models for maximum 

diameter and standard deviation of diameter had MSE values 

of 4.59 and 0.38, respectively, and are written as:

( )( ) ( )γγ β 12 1 TT e −⋅− −

αα α ( ) αα ⋅ 1 450 2

4

1

2 3

2

10 ASW

N

elev elev X 















+⋅+⋅−⋅+⋅+ ⋅

( )( )γγ β 12

2 1

TT DMAX eDMAX −⋅− ⋅= +

(10)

( )

























− 



 



 



 



 −⋅+−⋅− 2

1 2 12 2 1 TTTT

e β γ

( ) ( )

















⋅ 



 



 



 



 −⋅+−⋅−

= ⋅

2

1 2 12 2

1 ln

2

TTTT

eDSTD

eDSTD

β γ

( ( ) )









⋅ ⋅+⋅+⋅−⋅++ 2 2 3 4 2 10

10000

elev elev 450 ASWX ASW

e

ααα αα

where DMAX2 is the future maximum diameter 

(m), DMAX1 is the initial maximum diameter (m), 

DSTD2 is the future standard deviation of diameter 

(m), DSTD1 is the initial standard 

deviation of diameter (m), T1 is the 

initial stand age (years), T2 is the 

final stand age (years), elev is the 

stand elevation (m), X is a binary 

indicator variable, X = 0 if elevation < 450, and X = 1 if elevation 

≥ 450, ASW is the average water 

deficit over the simulation period 

calculated with the 3PG water balance model (mm), N1 is the initial 

stocking (stems / ha), and β, γ, α0, 

α1, α2, α3, α4, and α5 are parameters 

whose values are listed in Table 8 

(for maximum diameter eq. 10) and 

Table 9 (for standard deviation of 

diameter eq. 11).

Tables 8 and 9 show parameter 

estimates. Figures 4 and 5 show 

residual patterns with little apparent bias against main modeling 

variables. For projection lengths 

of up to 20 years 95 percent of 

residuals for maximum diameter 

projections were within ± 4.3 cm, 

while 95 percent of the residuals 

for standard deviation of diameter 

were within ± 1.2 cm.

Mortality

A set of six equations, which are variants of those, listed by 

Clutter et al. (1983), those used by Zhao (1999), and those 

used to fit CanSPBL(1.2) were used as the basic equation 

forms for projecting stocking (Pinjuv 2006). These equations were initially fitted using a modeling data set filtered 

in the same way as that used to fit CanSPBL(1.2) (Pinjuv 

2006). A mortality severity index based on the -3/2 power 

law was used as a basis to filter the modeling data set for 

Table 7—Mean square error for initial models of maximum diameter and 

standard deviation of diameter including the effect of average water 

deficit and elevation.

Equation with elevation 

and average 3PG water 

deficit in asymptote

Maximum 

Diameter

Standard 

Deviation of 

Diameter

Polymorphic Weibull I 4.89 0.

Polymorphic Gompertz II 5.09 0.

Polymorphic Weibull II failed to converge failed to converge

Polymorphic Schumacher II 5.06 0.43

Table 8— Parameter values for maximum diameter model (Equation 10). Also shown are 

standard errors, and approximate 95-percent confidence limits for each parameter. Statistical 

values are calculated with 3,659 degrees of freedom. 

Parameter Estimate Std. Error Approximate 95% Confidence Limits

β 0.3657 0.0421 0.22 0.4483

γ 0.7 0.0 0.2 0.4626

α0 64.8266 3.1145 58.7203 70.

α1 0.000159 0.00001 0.0001 0.00017

α2 -0.1755 0.017 -0.21 -0.141

α 772.2 72.1 7. 10207.

α4 0.000463 0.00001 0.00284 0.000642

Table 9— Parameter values for standard deviation of diameter model (Equation 11). Also 

shown are standard errors, and approximate 95-percent confidence limits for each parameter. 

Statistical values are calculated with 3,659 degrees of freedom.

Parameter Estimate Std. Error Approximate 95% Confidence Limits

β 0.0715 0.0012 0.0 0.0751

γ 0.000443 0.00001 0.0002 0.000562

α0 24777.1 358.5 24074.2 25480.0

α1 0.021 0.0010 0.012 0.0235

α2 -39.633 3.5957 -46.6829 -32.5831

α -20.4624 6.0352 -32.2953 -8.6296

α4 0.0935 0.0463 0.0027 0.1843

(11)
FOREST GROWTH AND TIMBER QUALITY

0

mortality and a final model was built with 80 percent of 

the original mortality records under the recommendation 

of managers at SPBL. Equations were fitted incorporating 

the effects of ASW deficit and ASW deficit squared and the 

results of the initial fitting are listed in Table 13. As equation 3 (Table 10) had the smallest MSE it was chosen as 

the basic form of difference equation for further analysis. 

This model was altered further to see if different correction 

forms for these effects would improve model fits. These 

included a linear correction for elevation for PSP’s above 

250 m, as was used by Zhao (1999), elevation, the square 

of elevation, a probit correction for the effect of elevation, 

ASW deficit, ASW deficit squared, and the interaction of 

elevation and ASW deficit.

The final model selected (Eq. 12) was fitted using Equation 3 (Table 13) and produced a MSE of 3282. Parameters 

for the final mortality model (Eq. 12) are listed in Table 

11. Little bias was apparent in residual patterns shown 

in Figure 6. Ninety-five percent (greater than 2.5 percent 

and less than 97.5 percent) of residuals were within ± 116 

stems / ha for projection lengths of up to 21 years. 

Figure 4: Residual patterns of final model for maximum diameter: (a) residuals versus predicted, (b) residuals versus stand age, (c) residuals versus 

elevation, (d) residuals versus time increment, and (e) residuals versus ASW Deficit.
FOREST GROWTH AND TIMBER QUALITY

1

( )

2 2

1

2

2

2

10 2

1

2

100 100

1

−































 



 



  −  





⋅+⋅++= ⋅

TT

ASW ASW

N

N αα α

(12)

where N2 is the future stocking (stems / ha), N1 is the initial 

stocking (stems / ha), T1 is the initial stand age (years), T2 is 

the final stand age (years), ASW is the average water deficit 

over the simulation period calculated with the 3PG water 

balance model (mm), and α0, α1, α2 are parameters whose 

values are listed in Table 11 (for stocking Eq. 12).

Testing Model Parameters

Final model parameters were tested against an autocorrelation-free dataset to see if they were significantly different 

from zero. An autocorrelation-free dataset was prepared 

from the original modeling data by randomly selecting one 

observation from each of the 746 plots. Parameters for the 

models of mean top height, basal area, maximum diameter, 

standard deviation of diameter, and stocking were all found 

to be significant at the 95-percent confidence level (Tables 

Figure 5: Residuals patterns of final model for standard deviation of diameter: (a) residuals versus predicted, (b) residuals versus stand age, (c) residuals 

versus elevation, (d) residuals versus time increment, and (e) residuals versus ASW deficit.
FOREST GROWTH AND TIMBER QUALITY

2

12, 13, 14, 15, and 16). 

Model Validation and Comparison with 

CanSPBL(1.2)

Validation of CanSPBL(water) and CanSPBL(1.2) with a 

subset of the validation data set presented in chapter 4 of 

Pinjuv (2006), produced model fitting statistics and residual 

distribution statistics listed in Tables (17) and Table (18), 

respectively. CanSPBL(water) showed improvements for 

most model components of 1.07 percent to 3.77 percent 

after being updated with an index of root zone water balance. However, CanSPBL(water) showed a -0.78 percent 

decrease in precision for the component of maximum 

diameter. CanSPBL(water) also showed less bias in prediction of stocking, and basal area (Table 17). Residual distributions for CanSPBL(water) showed a worse fit overall for 

skewness and kurtosis, while the 

hypothesis of normality of residuals 

was not rejected for both models 

with the Kolmogorov-Smirnov test 

(Table 18).

A separate validation was also 

completed with the same models 

using long term average climate as 

inputs into the water balance model. This was done to test 

how model accuracy might be affected if managers were to 

estimate future climate using average values. This separate 

validation of CanSPBL(1.2), and CanSPBL(water_using 

average climate) produced model fitting statistics and 

residual distribution statistics listed in Tables (19 and 

20), respectively. CanSPBL(water_using average climate) 

showed improvements for most model components of 

0.47 percent to 7.81 percent after being updated with an 

index of root zone water balance that uses average climate 

inputs. However, CanSPBL(water_using average climate) 

showed a -0.13 decrease in precision for the component 

of maximum diameter. These results indicate that model 

accuracy for the prediction of stocking, basal area, and 

maximum diameter would actually increase precision using 

Table 10—Difference equation forms for projection of stocking. Initial fitted models including ASW deficit and ASW deficit squared in 

asymptotic parameter. Original equation forms are listed in Pinjuv (2006).

Difference Equation Forms

Parameter

Estimates MSE Model

1. ( ) ( ) c c bb TT ASWaASWaa NN

1

6 12

2

10 2

2 1 10 













 −⋅ ⋅+⋅+

+=

a0

a1

a2

b

c

.222

-0.0488

0.00002

1.

-0.5192

3285

2.

 

( )

2

8 12

2

10 2

1

2 10

1 −















 −⋅ ⋅+⋅+

+= bb TT ASWaASWaa

N

N

a0

a1

a2

b

652.7

-5.6079

0.0844

1.1

2

.

 

( )

2 2

1

2

2 2

10 2

1

2 100 100

1 −































 



 



  − 

 



 ⋅⋅+⋅++=

TT ASWaASWaa

N

N

.

a0

a1

a2

0.0462

-0.00035

5.828*10-6

22

4. 

( )( )12 2 10 2

12

TTASWaASWaa eNN −⋅⋅+⋅+ = ⋅ a0

a1

a2

-868.5

10.4256

-0.2191

3488

5.

 

( )

( ) 12

2 10 2

1

2

12

TTb

ASWaASWaa

e

T

T NN −⋅

⋅+⋅+

⋅ 















⋅=

a0

a1

a2

b

0.177

0.002

-0.00004

-0.0217

2

. ( ) ( ) bb TTASWaASWaa eNN 12 2 10 2

12

−⋅⋅+⋅+ ⋅=

a0

a1

a2

b

-18.2851

0.12

-0.00310

2.02

1

Table 11—Stocking model parameters for equation 12, standard errors, and approximate 

95-percent confidence limits calculated with 2,226 degrees of freedom.

Parameter Estimate Std. Error Approximate 95% Confidence Limits

α0 0.0462 0.001 0.0401 0.0524

α1 -0.00035 0.00011 -0.00058 -0.00012

α2 5.83E-06 8.13E-07 4.23E-06 7.42E-06
FOREST GROWTH AND TIMBER QUALITY



average climate inputs as opposed to those that describe 

yearly variations. CanSPBL(water_using average climate) 

showed less bias in prediction of stocking, basal area, and 

maximum diameter than did CanSPBL(water) (Table 17 and 

Table 19). Residual distributions for CanSPBL(water_using 

average climate) showed a worse fit overall for skewness and 

kurtosis in comparison to CanSPBL(1.2), with the exceptions of skewness for basal area and mean top height. The 

hypothesis of normality of residuals was not rejected for 

CanSPBL(water_using average climate) with the Kolmogorov-Smirnov test (Table 20). Although the distributions of 

residuals for CanSPBL(water_using average climate) are 

better on average than CanSPBL(water).

DISCUSSION

Incorporating ASW deficit into equations that predict basal 

area, mean top height, standard deviation of diameter, and 

stocking in the growth and yield model CanSPBL(1.2) 

showed a small, improvement in model accuracy (Table 

17). There was somewhat of an increased precision for 

Figure 6: Residuals patterns of final model for stocking: (a) residuals versus predicted, (b) residuals versus stand age, (c) residuals versus elevation, (d) 

residuals versus time increment, and (e) residuals versus ASW deficit.
FOREST GROWTH AND TIMBER QUALITY

94

longer intervals shown in residual plots (Figures 2, 3, 4, 

and particularly Figure 6). This effect may have been due 

to the leveling of the water balance models’ precision, increasing with time of simulation. If initial water balance 

estimates are different from measurements, they become 

more precise over time for months following initialization, 

and this may affect growth and yield model precision for 

shorter measurement intervals. The results of this study 

show a relatively small improvement in model accuracy 

and growth pattern including ASW deficit into the models. 

This result was surprising in the 

context of varying climate over the 

study area. With yield modeling the 

results could have been markedly 

more significant, as the growing 

condition of the site is not implicit 

in initial stem size (as is used in the 

difference approach). This result 

highlights the power of the different modeling approaches within 

and between regions with varying 

climatic and site conditions. 

Validation with average climatic 

inputs surprisingly increased precision of the models that predict 

stocking, basal area, and maximum diameter. Predicted stocking 

showed the largest reduction of 

residual mean square error, at 7.81 

percent using average climate. This 

result is positive for forest managers 

who may only have average climate 

available to run such models. As 

regions vary in climate, taking this 

into account can result in small 

gains in accuracy. 

The updated version of the 

model included both ASW deficit 

and a simplified form of elevation. 

This result indicates that the effect of elevation in the Canterbury 

region describes more than water 

relations on the site and may be 

a proxy for other site factors such 

as nutrient availability, or possibly 

average temperature. 

The data required to run the 

water balance model are monthly values of maximum 

temperature, minimum temperature, solar radiation, vapor 

pressure deficit, leaf area index, rainfall, soil type, initial 

estimates of available soil water, maximum available soil 

water, and minimum available soil water. Obtaining these 

inputs for a given forest can be time-consuming and expensive and may not warrant the 1 –8 percent improvement 

in accuracy that these models offer. There is also the issue 

of even lower precision for the models of mean top height 

and standard deviation of diameter using average values of 

Table 12— Basal area model parameters for equation 8, standard errors, and approximate 

95-percent confidence limits tested with an autocorrelation-free dataset with 745 degrees 

of freedom.

Parameter Estimate Std. Error Approximate 95% Confidence Limits

β 0.153 0.00419 0.1448 0.112

γ 0.00241 0.0000 0.0022 0.00257

α0 43663.9 451.9 42776.7 44551.0

α1 0.0355 0.00147 0.02 0.0

α2 -36.2397 4.3294 -44.7393 -27.7401

α 56.5576 10.2484 36.4378 76.6774

α4 -0.5827 0.001 -0.7596 -0.4058

Table 13—Mean top height model parameters for equation 9, standard errors, and approximate 

95-percent confidence limits tested with an autocorrelation-free dataset with 745 degrees of 

freedom.

Parameter Estimate Std. Error Approximate 95% Confidence Limits

β 8.1675 1.6642 4.9002 11.4347

γ 1.0427 0.1488 0.7506 1.3349

α0 4181.0 965.0 39586.6 43375.4

α1 0.0214 0.00177 0.01 0.0249

α2 -39.6227 4.5143 -48.4852 -30.7601

α 22.0 8.0674 .22 38.4989

α4 -0.2664 0.072 -0.4083 -0.1246

Table 14—Maximum diameter model parameters for equation 10, standard errors, and 

approximate 95-percent confidence limits tested with an autocorrelation-free dataset with 745 

degrees of freedom.

Parameter Estimate Std. Error Approximate 95% Confidence Limits

β 0.7474 0.2499 0.2568 1.21

γ 0.21 0.071 0.117 0.4175

α0 77.1 9.9047 57.7539 96.644

α1 0.00012 0.00001 0.0001 0.000253

α2 -0.2677 0.0515 -0.3688 -0.1665

α 0.00127 0.000349 0.000587 0.001
FOREST GROWTH AND TIMBER QUALITY

95

climatic inputs to describe future conditions where monthly 

and yearly variation may not be available. The increase in 

model accuracy for the models of mean top height and 

standard deviation of diameter using inputs that including 

monthly and yearly variation are 2.95 percent and 1.07 

percent, respectively. There is a decrease in precision for 

the models of mean top height and standard deviation of 

diameter to 2.57 percent and 0.47 percent, respectively, 

using average monthly climatic inputs. These results suggest model accuracy may be maximized by using average 

monthly inputs for some models and including monthly 

and yearly variation for the inputs of the models of mean 

top height and standard deviation of diameter. Model precision could be increased further by considering the effect 

of drought only in months where growth is likely to occur. 

Drought in the winter months may not have the same effect 

on growth as drought that occurred during the growing 

season. Future research in this area could focus on trying 

to add a weight to ASW deficits according to the month in 

which they occur.

CONCLUSIONS

Model components of mean top height, basal area per 

hectare, stems per hectare, and diameter distribution were 

developed by using non linear least squares regression 

techniques to select appropriate 

equation forms. Explanatory variables to improve model prediction 

were tested and incorporated into 

models where appropriate. The effect of elevation, and ASW deficit 

was added to models of mean top 

height, basal area, and diameter 

distribution, only the effect of ASW 

deficit was added to the model of 

mortality. A polymorphic Gompertz 

equation displayed the best fit for 

basal area, while a polymorphic 

Schumacher equation displayed 

the best fit for mean top height. 

The diameter distribution model of 

maximum diameter displayed the 

best fit with a polymorphic Weibull 

equation, while the standard deviation of diameter model fit best with a 

polymorphic Gompertz equation.

A mortality severity index based 

on the -3/2 power law was used as a basis to filter the 

modeling data set for mortality and a final model was built 

with 80 percent of the original mortality records under 

the recommendation of managers at SPBL. Residual mean 

square error for the model of stocking was decreased by 

2.84 percent by incorporating ASW deficit calculated by 

the equation (13). Residual mean square error was reduced 

further by 7.8 percent by using average climatic inputs. 

Ninety-five percent (greater than 2.5 percent and less than 

97.5 percent) of residuals were within ± 116 stems / ha for 

projection lengths of up to 21 years using monthly climatic 

inputs that show yearly variation, and within ± 92 stems 

/ ha using average climatic inputs. Future stocking is dependent on the current stocking (stems / ha), initial stand 

age (years), final stand age (years), elevation squared (m2

), 

ASW deficit (mm), and ASW deficit squared (mm2). 

( )

2 2

1

2

2

2

10 2

1

2

100 100

1

−































 



 



  −  





⋅+⋅++= ⋅

TT

ASW ASW

N

N αα α

(13)

All model parameters were tested against an autocorrelation free dataset for significance. Tests showed that all 

parameters were significant at a 95-percent confidence level. 

The entire updated version of the model CanSPBL(water) 

Table 15—Standard deviation of diameter model parameters for equation 11, standard errors, 

and approximate 95-percent confidence limits tested with an autocorrelation-free dataset with 

745 degrees of freedom.

Parameter Estimate Std. Error Approximate 95% Confidence Limits

β 0.0649 0.0072 0.0576 0.0722

γ 0.0002 0.000122 0.000143 0.00022

α0 217. . 24232.3 28115.2

α1 0.022 0.00247 0.01 0.02

α2 -59.269 8.4106 -75.7807 -42.7573

α -40.3089 15.4589 -70.6581 -9.9598

α4 0.21 0.112 0.0402 0.4823

Table 16—Mortality model parameters for equation 12, standard errors, and approximate 

95-percent confidence limits tested with an autocorrelation-free dataset with 745 degrees of 

freedom.

Parameter Estimate Std. Error Approximate 95% Confidence Limits

α0 0.047 0.00567 0.0359 0.0582

α1 -0.00048 0.000214 -0.0009 -0.00006

α2 9.87E-06 1.58E-06 6.77E-06 1.30E-05
FOREST GROWTH AND TIMBER QUALITY



was validated against an independent data set and compared 

to the original CanSPBL(1.2). CanSPBL(water) showed 

improvements in MSE of 1 percent to 3 percent after the 

effects of ASW deficit were incorporated into the model, 

however the model of maximum diameter 

showed a worse fit by 0.78 percent. 

Residual distributions for CanSPBL(water) showed a worse fit overall for 

skewness and kurtosis. The hypothesis of 

normality was not rejected for both models 

using the Kolmogorov-Smirnov test.

Residual mean square error for the 

model of basal area was reduced by 3.77 

percent by incorporating ASW deficit calculated by the equation (14). Ninety-five 

percent (greater than 2.5 percent and less 

than 97.5 percent) of residuals were within 

± 8.7 m2

 / ha for projection lengths of up 

to 21 years using monthly climatic inputs 

that show yearly variation, and within ± 

8.8 m2

 / ha using average climatic inputs.

Future basal area is dependent on the 

current stand basal area (m2 / ha), initial 

stand age (years), final stand age (years), 

elevation squared (m2), a binary indicator variable X (X = 

0 if elevation < 450, and X = 1 if elevation ≥ 450), ASW 

deficit (mm), and ASW deficit squared (mm2).

( ) ( )

( ( )( ) )

( )





































−

⋅ ⋅+⋅+⋅−⋅+⋅+

⋅ +





 



 



 



 −⋅+−⋅−





 



 



 



 −⋅+−⋅−

=

2

1 2212

2 2 3 4 2 10

2

1 2212

1

1

10000

450

ln

2

TTTT

TTTT

e

elev Xelev ASW ASW

eG

eG

β γ

β γ

ααα αα

(14)

Residual mean square error for the model of mean top 

height was reduced by 2.95 percent by incorporating ASW 

deficit calculated by the equation (15). Ninety-five percent 

(greater than 2.5 percent and less than 97.5 percent) of 

residuals were within ± 2.1 m for projection lengths of up 

to 21 years using monthly climatic inputs that show yearly 

variation, and within ± 2.2 m using average climatic inputs. Future mean top height is dependent on the current 

mean top height (m), initial stand age (years), final stand 

age (years), elevation (m), elevation squared (m2

), a binary 

indicator variable X (X = 0 if elevation < 450, and X = 1 

if elevation ≥ 450), ASW deficit (mm), and ASW deficit 

squared (mm2

).

Table 17— Comparison of model statistics between CanSPBL(1.2), and 

CanSPBL2(water). Statistics shown include Mean Square Error (MSE), Average Model 

Bias (AMB), Model Efficiency Factor (EF), and percent difference of MSE (% Difference 

of MSE) n = 967.

Model

Model Fitting Statistics

MSE AMB EF MSE % 

Difference

CanSPBL(1.2) Stocking 2154.92 6.51 0.95 2.84

Basal Area 17. 0.55 0.. .77

Mean Top Height 1.10 0.0 0. 2.95

Maximum Diameter 5.60 0.27 0.. -0.78

Standard Deviation 

of Diameter 0.53 0.04 0. 1.07

CanSPBL2 

(water)

Stocking 2094.63 1. 0. -2.84

Basal Area 17.27 0.45 0. -3.77

Mean Top Height 1.07 0.05 0. -2.95

Maximum Diameter 5.64 0.27 0. 0.7

Standard Deviation 

of Diameter 0.52 0.04 0. -1.07

Table 18—Model normality distribution statistics for 

CanSPBL(1.2), and CanSPBL2(water) in terms of skewness, 

kurtosis, and p-value from the Kolmogorov-Smirnov test for 

normality n = 967.

Model

Residual Distribution 

Statistics

SkewnessKurtosisPvalue

CanSPBL(1.2) Stocking -1.01 11.05 0.01

Basal Area 0.42 3.74 0.01

Mean Top 

Height 0.1 0. 0.01

Maximum 

Diameter 1.15 4.73 0.01

Standard 

Deviation of 

Diameter

1.22 7. 0.01

CanSPBL2 

(water)

Stocking -2.80 14.02 0.01

Basal Area 0.22 4.05 0.01

Mean Top 

Height -0.02 1.10 0.01

Maximum 

Diameter 1.1 4.84 0.01

Standard 

Deviation of 

Diameter

1.20 7.35 0.01
FOREST GROWTH AND TIMBER QUALITY

7

( )

( ( ) )

































+

+ −

⋅ ⋅+⋅+⋅−⋅+⋅+

+ 















+

+ ⋅

=

β

β

γ

γ

ααα αα

γ

γ

2

1

2 2 3 4 2 10

2

1 1

1

10000

450

ln

2

T

T

elev elev ASWX ASW

T

T MTH

eMTH

(15)

Residual mean square error for the model of maximum 

diameter was increased by 0.78 percent by incorporating 

ASW deficit calculated by the 

equation (16). Ninety-five percent 

(greater than 2.5 percent and less 

than 97.5 percent) of residuals 

were within ± 5 cm for projection 

lengths of up to 21 years using 

monthly climatic inputs that 

show yearly variation, and within 

± 5 cm using average climatic 

inputs. Future maximum diameter is dependent on the current 

maximum diameter (cm), initial 

stand age (years), final stand age 

(years), elevation squared (m2

), 

a binary indicator variable X (X

= 0 if elevation < 450, and X = 1 

if elevation ≥ 450), the inverse of 

initial stocking (ha / stems), and 

ASW deficit squared (mm2

).

( )( ) ( ) γγ β 12 1 TT e −⋅− −

αα

1 2

4

1

3 ASW

N

X ⋅ 







⋅+⋅+

αα α ( ) 450 2

2

10 elev elev 







⋅−⋅+⋅+

( )( ) γγ β 12

2 1

TT DMAX eDMAX −⋅− ⋅= +

(16)

Residual mean square error for the model of standard 

deviation of diameter was decreased by 1.07 percent by 

incorporating ASW deficit calculated by the equation 

(17). Ninety-five percent (greater than 2.5 percent and 

less than 97.5 percent) of residuals were within ± 1.5 cm 

for projection lengths of up to 21 years using monthly 

climatic inputs that show yearly variation, and within ± 

1.5 cm using average climatic inputs. Future standard 

deviation of diameter is dependent on the current standard deviation of diameter (cm), initial stand age (years), 

final stand age (years), elevation squared (m2

), a binary 

indicator variable X (X = 0 if elevation < 450, and X = 1 

if elevation ≥ 450), ASW deficit (mm), and ASW deficit 

squared (mm2).

( ) ( )

















⋅ 



 



 



 



 −⋅+−⋅−

= ⋅

2

1 2 12 2

1 ln

2

TTTT

eDSTD

eDSTD

( )

























− 



 



 



 



 −⋅+−⋅− 2

1 2 12 2 1 TTTT

e β γ

β γ

( ( ) )









⋅ ++ ⋅ ⋅+⋅+⋅− 2 2 3 4 2 10

10000

elev elev 450 ASWX ASW

e

⋅ ααα αα

(17)

Table 19—Comparison of model statistics between CanSPBL(1.2), and CanSPBL2(water) (using 

average climate inputs). Statistics shown include Mean Square Error (MSE), Average Model Bias 

(AMB), Model Efficiency Factor (EF), and percent difference of MSE (% Difference of MSE) n = 967.

Model

Model Fitting Statistics

MSE AMB EF MSE % Difference

CanSPBL(1.2) Stocking 2154.92 6.51 0.95 7.1

Basal Area 17. 0.55 0.. .2

Mean Top Height 1.10 0.0 0. 2.57

Maximum Diameter 5.60 0.27 0.. -0.13

Standard Deviation 

of Diameter 0.53 0.04 0. 0.47

CanSPBL2 

(water)

using average 

climate inputs

Stocking 12.7 .11 0. -7.81

Basal Area 17.2 0.51 0. -3.82

Mean Top Height 1.07 0.0 0. -2.57

Maximum Diameter 5.60 0.24 0. 0.1

Standard Deviation 

of Diameter 0.52 0.05 0. -0.47

Table 20—Normality distribution statistics for CanSPBL(1.2) and 

CanSPBL2 (water; average climate inputs): skewness, kurtosis, and 

p-value from the Kolmogorov-Smirnov test for normality n = 967.

Model

Residual Distribution Statistics

Skewness Kurtosis P-value

CanSPBL 

(1.2) 

Stocking -1.01 11.05 0.01

Basal Area 0.42 3.74 0.01

Mean Top Height 0.1 0. 0.01

Maximum Diameter 1.15 4.73 0.01

Standard Deviation 

of Diameter 1.22 7. 0.01

CanSPBL2 

(water)

using 

average 

climate 

inputs

Stocking -2.57 12.53 0.01

Basal Area 0.27 4.12 0.01

Mean Top Height 0.02 1.04 0.01

Maximum Diameter 1.1 4.73 0.01

Standard Deviation 

of Diameter 1.25 7.2 0.01
FOREST GROWTH AND TIMBER QUALITY



LITERATURE CITED

Arneth, A.; Kelliher, F.M.; McSeveny, T.M.; Byers, J.N. 

1998. Carbon and water fluxes in a Pinus radiata forest 

subject to soil water deficit. Australian Journal of Plant 

Physiology 25: 557-570.

Barringer, J.; Wilde, H.; Willoughby, J.; [et al.].1998. 

Restructuring the New Zealand land resource 

inventory to meet the changing needs for spatial 

information in environmental research and 

management. Presented at the 10’th colloquium of 

the spatial information research centre, University of 

Otago, New Zealand. 16 – 19 November, 1998.

Boomsma, D.B.; Hunter, I.R. 1990. Effects of water, 

nutrients and their interactions on tree growth, and 

plantation forest management practices in Australasia: 

a review. Forest Ecology and Management 3: 455–476.

Clutter, J.L.; Fortson, J.C.; Pienaar, L.V.; [et al.]. 1983. 

Timber management: a quantitative approach, New 

York, John Wiley and Sons. 333 pages.

Landsberg, J.J.; Gower, S.T. 1997. Applications of 

physiological ecology to forest management. Academic 

Press, San Diego, CA. p. 354.

Landsberg, J.J.; Waring, R.H. 1997. A generalized 

model of forest productivity using simplified concepts 

of radiation use efficiency, carbon balance and 

partitioning. Forest Ecology and Management 95: 

209–228.

Leathwick, J.R; Stephens, R.T.T. 1998. Climate surfaces 

for New Zealand. Landcare Res. Contract Report 

LC9798/126. Landcare Research, Lincoln, New 

Zealand. 19pp.

Pinjuv, G.L. 2006. Hybrid forest modelling of Pinus 

radiata D. Don in Canterbury, New Zealand. Forestry 

thesis for Ph.D. School of Forestry, University of 

Canterbury, 198 pp.

Sands, P.J.; Landsberg, J.J. 2002. Parameterisation of 

3-PG or plantation-grown Eucalyptus globulus. Forest 

Ecology and Management 163: 273–292.

SAS Institute Inc., 2001, SAS/STAT user’s guide, version 

8, Cary, NC.

Snowdon, P.; Jovanovic, T.; Booth, T.H. 1999. 

Incorporation of indices of annual climatic variation 

into growth models for Pinus radiata. Forest Ecology 

and Management 117: 187-197.

Tickle, P.K.; Coops, N.C.; Hafner, S,D. 2001. 

Comparison of a forest process model (3-PG) with 

growth and yield models to predict productivity at 

Bago State Forest, NSW. Australian Forestry 64(2): 

111-122.

West, P.W.; Ratkowsky, D.A.; Davis, A.W. 1984.

Problems of hypothesis testing of regressions with 

multiple measurements from individual sampling 

units. Forest Ecology and Management 7(3): 207-224.

Zhao, W. 1999. Growth and yield modelling of Pinus 

radiata in Canterbury. New Zealand. Forestry thesis 

for PhD, School of Forestry, University of Canterbury. 

192 pages.
FOREST GROWTH AND TIMBER QUALITY



Increased Self-Shading with Tree Size and Increased 

Wood Density with Diameter Explain Some of the 

Observed Size-Related Decline in Forest Productivity

Remko A. Duursma and Annikki Mäkelä

Remko Duursma (remkoduursma@gmail.com) was a postdoctoral research fellow and Annikki Mäkelä is professor of silviculture (forest 

production) in the Department of Forest Ecology, University of Helsinki, PO Box 27 (Latokartanonkaari 7), 00014 Helsinki, Finland.

ABSTRACT

THE DECLINE IN NET PRIMARY PRODUCTION 

(NPP) of forests with stand age is a ubiquitous 

phenomenon, and many hypotheses have been 

set out to explain this decline. The most popular hypotheses; increased fraction of respiration with tree size, and 

increased hydraulic constraints on stomatal conductance; 

have been shown to explain a varying portion, but usually 

not all of this decline. Here, we quantify the contributions 

of two additional hypotheses: 1) self-shading of foliage in 

tree crowns increases with the size of tree crowns and 2) 

increased wood density with increasing diameter increases 

the apparent decline in productivity.

Based on simulation experiments (Duursma and Mäkelä 

2007), our previous work has shown that the ratio of tree 

leaf area to the surface of the crown envelope (LA/SA) determines self-shading and efficiency of foliage. Higher values 

of the LA/SA ratio mean more densely packed crowns, with 

a decreasing average light intensity on leaves and therefore 

lower photosynthetic production. Total leaf area and crown 

surface area are interrelated as LA ∝ SAz/2, where z is the 

fractal dimension of leaf area, and z is larger than 2 for a 

wide range of forest tree species, leading to a gradually 

increasing LA/SA with tree development. 

In conifers, wood basic density typically increases with 

increasing distance from the pith. If this pattern is not 

accounted for, apparent decline in productivity based on 

measurements of wood volume would be exaggerated. For 

Scots pine and Norway spruce in Finland, these relationships are well established.

We incorporate both these relationships in a forest 

growth model (CROBAS, Mäkelä 1997) and quantify the 

decline in NPP and wood volume growth as a result of 

increased self-shading over stand development, and increased wood density. The results indicate that this decline 

is significant, but does not by itself explain the commonly 

observed decline in NPP.

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 99.

Forest Operations 

and Timber Quality

FOREST GROWTH AND TIMBER QUALITY

10

Forest Operations and Timber Quality

Keynote Presentation

Influence of Forest Operations on Timber Quality

Dennis P. Dykstra

Dennis P. Dykstra (ddykstra@fs.fed.us) is a research forest products technologist, Pacific Northwest Research Station, P.O. Box 3890, Portland, OR 

97208-3890, USA.

ABSTRACT

The emphasis in many forested regions has shifted 

from large, older trees to young trees that are not 

only smaller but also much different in character. 

Both mills and forest operations have had to adjust to this 

shift. This adjustment has perhaps been more effective in the 

mills, where conditions can be controlled and it is possible 

to take full advantage of new developments in computer 

and scanner technologies. Increased mechanization has also 

occurred in forest operations, although the evolution has 

been less dramatic due to limitations imposed by the many 

timber and terrain conditions operators must accommodate. 

In the context of thinning operations, timber quality issues 

of particular importance include damage to the logs being 

harvested and damage to the residual trees that will make 

up the stand being managed as a future timber crop. Both 

of these issues are influenced by the equipment and logging 

methods used and by a range of other factors that are only 

partly under the operator’s control.

KEYWORDS: Small logs, mechanized harvesting, logging 

damage, thinning operations

INTRODUCTION

OVER THE PAST SEVERAL DECADES, UTILIZATION 

of timber in many parts of the world has shifted from an 

emphasis on large, older trees to much younger, quickly 

grown trees. The trees now being harvested are often grown 

from planted stock rather than from natural regeneration. In 

order to increase the growth rates of selected trees, thinnings 

are often conducted at various stages during the development of the stand. In drier forest areas, such as the inland 

regions of the western United States, wildfire hazard has 

become a major issue as human populations living in and 

near forests have increased. In these forests, small-diameter 

trees are often removed in an effort to reduce fire hazard, 

particularly around populated areas. To the extent possible, it is desirable to utilize some of the wood from trees 

harvested during thinnings in order to offset some of the 

costs of the thinning operations. This is true regardless of 

whether the purpose of the thinning is to increase growth 

rates on residual trees or to reduce fire hazard. In either 

case, the immature trees being removed pose significant 

problems for handling and utilization.

The timber industry has quickly adapted to reduced log 

sizes in spite of the fact that small logs create substantial 

problems for handling and transport as well as for conversion into solid-wood products such as lumber. Highly 

automated sawmills introduced within the past few years 

are capable of rapidly processing small-diameter logs into 

lumber and other products. Sawing machinery is able to 

compensate for sweep by sawing along the curve and by 

turning the log to best advantage. Sensors read the diameter 

and a variety of other measurements along the length of 

This paper was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 103–108.
FOREST GROWTH AND TIMBER QUALITY

104

the log as it enters the saw box, while computers determine 

the best orientation of the log and the best settings for the 

multiple saws and chipping heads that convert the log into 

lumber and pulp chips. These settings can be adjusted as 

market conditions change in order to maximize the potential 

revenue from each log.

Harvesting equipment and methodologies have also 

changed in order to accommodate smaller logs, although 

the problems encountered in harvesting are somewhat more 

difficult than those in a mill because of remote location, 

variable topography and timber conditions, and factors such 

as weather that cannot be controlled. Harvesting systems 

are increasingly becoming mechanized in order to deal with 

the large number of small logs that must be handled and 

processed. Where terrain permits, mechanized harvesters 

that fell and delimb trees and cut the stems into logs are 

commonly used. The processor head on the harvesting 

machine is able to measure the length and diameter of the 

stem at any point, and computers are used to help determine the log lengths that will meet mill requirements or 

maximize revenues to the landowner. On steeper terrain, 

cable or helicopter yarding systems are typically required 

but these can be coupled with harvesting machines (Drews 

et al. 2001) or with processors stationed at the landing 

to process the stems into logs. Like the saw settings in a 

mill, the logic related to bucking decisions on harvesting 

machines and processors can be adjusted to accommodate 

changing market conditions so that each log provides the 

maximum revenue to the landowner and the harvesting 

operator.

Two timber-quality issues related to small logs are 

particularly important from the perspective of forest operations. First, small logs tend to break or suffer significant 

damage more easily than larger logs. Second, thinning 

operations may result in damage to residual trees caused 

by the harvesting equipment or by contact between harvested stems and residual trees. Each of these issues has 

implications for forest operations and for utilization of the 

harvested timber.

DAMAGE TO LOGS

Although small logs are generally more flexible than large 

logs, they are also more easily broken by heavy equipment 

or improper handling during harvesting and transport 

operations or at the mill. In the forest, broken logs may 

simply have to be left behind because their reduced value 

will not justify the cost of removing them from the site. 

If a broken log is long enough it may be possible to buck 

it into shorter pieces while removing the broken section. 

This may reduce the value because each log then has a 

suboptimal length, and will result in handling two logs 

rather than one so the handling and transportation costs 

will increase. It also adds the cost of an additional bucking 

operation, which often must be done manually.

When logs are broken at the mill, some value can usually 

be recovered by whole-log chipping if the broken pieces 

are shorter than the mill’s minimum processing length. 

However, chip prices are often far below lumber prices so 

the value of the chipped log may be less than the harvesting 

and transportation costs that have already been incurred. 

In addition, some species have dark heartwood that is 

undesirable for pulp, so chip buyers may reject whole-log 

chips from those species or restrict them to a percentage 

of the total chip volume (Zhu et al. 2007).

Surprisingly, even though virtually all logging operations 

involve some breakage or damage to logs (Figure 1), very 

few studies have quantified these effects. Surveys done over 

large areas, such as the Forest Service’s periodic Resource 

Planning Act assessment reports (e.g., Smith et al. 2004), 

often provide regional-level estimates of logging residues. 

However, this information is seldom disaggregated into the 

Figure 1. A Bolivian forester inspects a mahogany tree (Swietenia 

macrophylla) that was destroyed by improper felling. In spite of the fact 

that mahogany wood is exceptionally valuable as a source of appearancegrade lumber and veneer, after being split during felling this tree did not 

retain sufficient value to justify taking it out of the forest.
FOREST GROWTH AND TIMBER QUALITY

105

component parts so it is not possible to determine what 

portion may be due to breakage or log damage.

One of the few studies to have quantified damage to 

logs during logging operations is Wang et al. (2004), which 

assessed log damage associated with four hardwood logging operations in north-central West Virginia. About 6 

percent of logs were reportedly damaged on the operations. 

Types of damage included gouging, splitting, slabbing, and 

abrasion (scraping) as well as breakage. Crushing caused 

by grapples or chain chokers was also observed, although 

it was relatively minor. Altogether, the volume loss from 

log damage was four times greater on the two operations 

utilizing chainsaw felling and skidders than on the other 

two operations utilizing felling machines and skidders. For 

the chainsaw operations the greatest share of the damage 

occurred during felling, with smaller amounts recorded 

during skidding, decking, and loading operations. On the 

felling-machine operations the damage was split more evenly 

among felling, skidding, decking, and loading. Both felling 

machines were fitted with saw heads rather than shears, 

which is probably significant. Other studies (e.g., Greene 

and McNeel 1989) have shown that felling damage associated with the use of shears can result in substantial losses 

when the butt log is later sawn into lumber.

Some of the log damage in the study by Wang et al. 

(2004) was species-related, with more brittle species 

tending to exhibit larger volume losses. There were also 

significant differences among log size classes, with smaller 

logs suffering much higher volume losses than large logs. 

This is due to the fact that a split or gouge of a fixed size 

represents a larger portion of a small log than it would on 

a large log. Small logs are also more likely to be crushed if 

run over by heavy machinery.

DAMAGE TO RESIDUAL TREES

Another important timber-quality issue related to forest 

operations is damage to residual trees caused by harvesting equipment or by contact between harvested stems 

and residual trees. In contrast to the scarcity of published 

information on damage to logs during logging operations, 

a great many studies have quantified logging damage to 

residual trees. This is because such damage can influence 

the quality of timber in the final crop trees and also can 

impact resources other than timber. In this paper the focus is on damage to residual trees resulting from thinning 

operations.

Types of damage to residual trees that are typically 

identified in logging studies include bark damage, deep 

bole wounds, crown damage, stem breakage, and root 

damage. In some hardwood species, abrasion of bark when 

a felled tree rubs along the bole of a residual tree may lead 

to widespread epicormic branching and consequently to a 

proliferation of pinhole knots (Meadows and Skojac 2006). 

This can significantly devalue appearance-grade lumber 

or veneer.

Bark damage (Figure 2) is often a relatively minor type 

of injury unless the wound is large, but even small injuries 

can permit the introduction of insects or decay fungi (Aho 

et al. 1983). Thin-barked or loose-barked species are particularly prone to bark injuries and non-resinous species 

are especially susceptible to infection by fungi. Depending 

on the length of time that elapses from when the damage 

occurs until the residual tree is harvested, volume and value 

losses due to discoloration or decay may occur when the 

tree is converted into lumber or veneer.

Deep bole wounds are usually regarded as more serious 

than bark damage because they are often associated with 

permanent scarring, gouging, or other defects that will 

Figure 2. Bark damage on a young Douglas-fir (Pseudotsuga 

menziesii). If the tree survives it is likely to sustain a substantial volume 

or value loss in the butt log due to discoloration, pitch seams, and decay.
FOREST GROWTH AND TIMBER QUALITY

10

degrade lumber or have to be trimmed out entirely. They 

are also more likely to permit the introduction of decay 

fungi and insects, followed by loss of vigor or even the 

death of the tree.

Trees can usually survive crown damage except in extreme cases. However, significant crown damage may lead 

to loss of vigor and thus prevent the tree from achieving 

the desired growth rate after thinning.

Stem breakage usually results in the death of the tree 

or deforms it so that it is no longer useful as a crop tree. 

In hardwood species stem breakage may induce sprouting, 

and this can be regarded as either good or bad depending 

on the type of thinning and the management objectives 

for the stand.

Root damage may structurally weaken the tree so that 

it is more susceptible to windthrow, and damaged roots 

are likely to serve as conduits for the introduction of root 

rot. This type of damage is almost always caused by heavy 

machinery, especially when crawler tractors are used for 

skidding.

Stage when Damage Occurs

Damage to residual trees can occur at any stage of a logging operation. Unfortunately, studies in temperate forests 

typically report only overall results without disaggregating 

them to the stage when damage occurred. This is regrettable because research in tropical forests strongly suggests 

that, in those forests, by far the most severe damage occurs 

during felling (e.g., see Pinard and Putz 1996). This is probably because tropical tree crowns are large and frequently 

interwoven with vines that connect them to adjacent trees. 

The situation in temperate forests is usually different but 

even so, observation suggests that felling damage can be 

substantial. Unfortunately, where felling damage has been 

studied separately (for instance, Sirén 2001), the studies do 

not report yarding or forwarding damage so comparisons 

are not possible.

Avoiding Damage during Felling 

Operations

Felling damage is caused by contact between the crown 

or stem of the tree being felled and the crowns or stems of 

nearby residual trees. Comparisons between manual and 

mechanized felling (e.g., see Spinelli 2004) suggest that 

mechanized felling is far more effective at avoiding damage because felling machines have better control over the 

direction a tree falls, even if chainsaw operators use the 

best directional felling techniques. Mechanized felling is 

not always feasible, however, when trees are large or the 

operation is located in steep terrain. Felling also influences 

subsequent yarding damage because proper alignment of 

felled trees with respect to the extraction route can reduce 

damage to trees near the extraction corridor. Postponing 

operations during bad weather and during periods when 

sap is flowing heavily can often reduce felling damage.

Damage in Cut-to-Length Harvesting

Cut-to-length harvesting typically involves two machines 

working together in a coordinated operation. A harvesting 

machine fells the trees, delimbs the stems, processes them 

into accurately measured logs, and bunches them at the 

stump. Then a forwarder collects the logs and transports 

them to a landing where they are decked and loaded onto 

trucks for delivery to the mill (Figure 3). Forwarders are 

Figure 3. Left image: Harvesting machine processing a tree into logs in a thinning operation. Right image: Forwarder at the landing with a load of logs.
FOREST GROWTH AND TIMBER QUALITY

107

built like off-road trucks onto which the logs are loaded by 

a crane mounted on the forwarder itself. Skidders, unlike 

forwarders, drag the logs along the ground behind them. 

Forwarders are limited in that they can only be used with 

shortwood systems; skidders are required when whole trees 

or full stems are being yarded. Studies of cut-to-length harvesting suggest that the frequency of damage to residual trees 

is relatively high, with up to half the residual trees being 

injured, but that the damage is generally limited to minor 

bark injuries (Han and Kellogg 2000, Sirén 2001, Drews 

et al. 2001). Other studies have found that fewer than15 

percent of residual trees are damaged in cut-to-length 

operations (e.g., Sauter and Gengle 1995). The difference 

in these findings may be explained by the way damage is 

assessed, coupled with differences in the level of operator skill as well as local timber and terrain conditions. In 

any case, most of the damage in cut-to-length harvesting 

probably occurs during the felling and processing phase, 

although few studies disaggregate overall damage so it is not 

possible to know for certain. Sirén (2001) reported that 90 

percent of the damage associated with cut-to-length harvesting occurred while felled stems were being delimbed and 

processed into logs and only 10 percent occurred during 

felling itself. His study did not include damage associated 

with the forwarding phase of the operation.

Avoiding Extraction Damage

In addition to the forwarders used with cut-to-length harvesting, common yarding systems include skidders (both 

rubber-tired, articulated skidders and crawler tractors), 

which drag logs behind them, and cable yarding systems 

that utilize suspended cables to convey logs from the felling 

site to a landing. Helicopter yarding is less commonly used 

in thinnings but is an additional possibility where special 

considerations require the use of a yarding system that 

must fly over obstacles or produce essentially no ground 

disturbance.

Comparative studies suggest that, other things being 

equal, ground-skidding systems can be expected to produce 

more damage to residual trees than skyline or helicopter 

systems (e.g., Han and Kellogg 2000). The damage is also 

generally lower on the bole and includes a higher incidence 

of root damage. Damage to residual trees on cable yarding 

operations tends to be concentrated along cableways, and 

some trees adjacent to the corridor may suffer severe gouging due to multiple incidents of contact with stems being 

removed. Fan-shaped cable settings typically result in a 

higher degree of damage to trees located near the landing 

as compared to settings where the cableways are laid out 

in parallel strips. Cable yarding is more likely to produce 

crown damage than ground-based yarding. Helicopter 

yarding generally results in very little damage to residual 

trees, although some crown and bark damage (primarily 

to the upper bole) have been reported.

The following guidelines have been suggested for avoiding damage to residual trees during extraction:

• Emphasize the importance of minimizing damage 

to residual trees to loggers. Otherwise, they may not 

realize that this is an important consideration.

• Do not allow logging during periods of the year when 

sap is flowing and bark is loose. At these times trees 

are easier to wound and injuries tend to be larger.

• Mark residual trees where feasible so that the logging 

crews can easily see them.

• Clearly flag skidtrails, forwarder routes, and skyline 

corridors in advance of felling so that the felling crew 

can directionally fall trees toward the extraction 

routes. Reflagging may be required after the trees have 

been felled so that the extraction routes are clearly visible to the yarding crew.

• Ensure that no crop trees are left inside extraction 

routes.

• Cut stumps low to the ground in order to prevent 

hang-ups in cable yarding or damage to nearby trees 

in ground skidding as the skidder drives over the 

stump. Contact with a high stump may cause the 

skidder to lurch sideways into a crop tree.

• Minimize blading of skidtrails in order to avoid root 

damage.

• Space skidtrails or harvester trails close enough that it 

is feasible for the machines to stay on the trail.

• In cable yarding, use parallel rather than fan-shaped 

settings where possible.

• Keep skidtrails as straight as possible and avoid sharp 

turns.

• In situations where damage to a crop tree seems 

almost inevitable (for instance, near a skidtrail), leave 

several nearby trees standing as protection. These buffer trees can be cut and removed as a last step.

• In ground-based yarding operations, short-log removal will almost always reduce damage to residual 

trees compared to whole-tree or tree-length removal. 

Timber purchasers may prefer longer pieces so that 

bucking decisions can be made in the mill rather than 
FOREST GROWTH AND TIMBER QUALITY

10

in the woods. There is thus a tension between what is 

best for the forest and what might be best for the mill.

CONCLUDING REMARKS

Few thinning operations are totally free of damage to the 

logs being removed or to the future crop trees left standing. Yet this should be the goal. High-quality timber can 

maximize revenues to landowners and provide optimal 

resources to the timber industry.

Published research on damage to logs removed from 

thinnings is very limited. This is information that should 

be useful to both landowners and mill operators. Although 

considerable research on damage to residual trees has been 

published, very few studies segregate felling damage from 

yarding damage. Additional work in this area would provide 

information on the relative contributions of each phase of 

the operation and help identify priorities in the effort to 

limit damage from thinning operations.

LITERATURE CITED

Aho, P.E.; Fiddler, G.; Srago, M. 1983. Logging damage 

in thinned, young-growth true fir stands in California 

and recommendations for prevention. Research 

Paper PNW-RP-304. Portland, OR: U.S. Department 

of Agriculture, Forest Service, Pacific Northwest 

Research Station. 12 p.

Drews, E.S.; Hartsough, B.R.; Doyal, J.A.; Kellogg, 

L.D. 2001. Harvester-forwarder and harvester-yarder 

systems for fuel reduction treatments. Journal of 

Forest Engineering 12(1): 81-91.

Greene, W.D.; McNeel, J.F. 1989. Potential costs of 

shear damage in a southern pine chip-n-saw mill. 

Forest Products Journal 39(5): 12-18.

Han, H-S; Kellogg, L.D. 2000. Damage characteristics in 

young Douglas-fir stands from commercial thinning 

with four timber harvesting systems. Western Journal 

of Applied Forestry 15(1): 27-33

Meadows, J.S.; Skojac, D.A., Jr. 2006. Third-year 

growth and bole-quality responses to thinning in a 

late-rotation red oak-sweetgum stand in East Texas. 

In: Connor, Kristina F., ed. 2006. Proceedings of 

the 13th biennial southern silvicultural research 

conference. General Technical Report SRS-GTR-92. 

Asheville, NC: U.S. Department of Agriculture, Forest 

Service, Southern Research Station. 640 p.

Pinard, M.A.; Putz, F.E. 1996. Retaining forest biomass 

by reducing logging damage. Biotropica 28(3): 278-

295.

Sauter, U.H.; Gengle, C. 1995. Felling and logging 

damages by highly mechanized and short timber 

harvest in conifer stands. Poster presented at the XX 

World Congress of the International Union of Forestry 

Research Organizations, Aug. 6-12, 1995, Tampere, 

Finland. http://www.metla.fi/iufro/iufro95abs/

d3pos32.htm (accessed Aug. 1, 2007).

Sirén, M. 2001. Tree damage in single-grip harvester 

thinning operations. Journal of Forest Engineering 

12(1): 29-38.

Smith, W. B.; Miles, P.D.; Vissage, J.S.; Pugh, S.A. 

2004. Forest Resources of the United States, 2002. 

General Technical Report NC-GTR-241. St. Paul, 

MN: U.S. Dept. of Agriculture, Forest Service, North 

Central Research Station. 137 p.

Spinelli, R. 2004. Harvesting of thinnings. In: Burley, 

J.; Evans, J.; Youngquist, J.A. (eds.) Encyclopedia of 

Forest Sciences. Elsevier Academic Press, Oxford, 

U.K. Volume 1, p. 252-259.

Wang, J.; LeDoux, C.B.; Vanderberg, M.; McNeel. 

J. 2004. Log damage and value loss associated 

with two ground-based harvesting systems in 

Central Appalachia. International Journal of Forest 

Engineering 15(1): 61-69.

Zhu, J.Y.; Scott, C.T.; Gleisner, R. [et al.]. 2007.

Mill demonstration of TMP production from forest 

thinnings: Pulp quality, refining energy, and 

handsheet properties. BioResources 2(4): 544-559.
FOREST GROWTH AND TIMBER QUALITY

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Predicting Branch Diameter of Thinned and 

Fertilized Coastal US Douglas-fir Plantations at the 

Mean and Individual Tree Levels

David Briggs, Rapeepan Kantavichai, Eric Turnblom

David Briggs (dbriggs@u.washington.edu) is professor and director, Rapeepan Kantavichai is a doctoral Student, and Eric Turnblom is 

associate professor and silviculture project leader, Stand Management Cooperative, College of Forest Resources, Box 352100, University of 

Washington, Seattle, WA 98195, USA.

ABSTRACT

TREE BRANCHES BECOME VALUE-REDUCING 

knots in wood products and since branch size can 

be affected by the silvicultural regimes employed 

in growing stands, improved understanding of the linkage 

between silviculture, branch size, and knots in products 

is needed. The Stand Management Cooperative routinely 

measures the diameter of the largest limb in the breast height 

(LLBH) region of trees on its field installations. This paper 

focuses on nine Douglas-fir (Pseudostsuga menziesii [Mirb.] 

Franco) installations in which plots were established at ages 

6–13 years with 100 percent, 50 percent, and 25 percent 

of the initial planting density; each of these stocking conditions has a plot that was unfertilized as well as one that 

was fertilized at establishment and every four years since 

with 224kg ha-1 of N as urea. The data set, consisting of 6 

plots from 9 installations (54 plots and 2257 trees total), was 

analyzed when the installations ranged in age from 22–32 

years old. The paper presents models for predicting LLBH 

at two levels. First, we present models predicting the mean 

LLBH of trees in a stand using treatments, site index, stand 

density, and mean tree descriptors as predictive variables. 

Second, we present models predicting individual tree LLBH 

using treatments, site index, stand density, and individual 

tree descriptors as predictive variables. Of special interest 

is the question of whether or not prediction of LLBH is 

improved when treatment and stand variables are used in 

addition to tree variables. 

KEYWORDS: Thinning, fertilization, branch size, knot 

diameter, wood quality, stem quality

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 109.
FOREST GROWTH AND TIMBER QUALITY

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Automatic Timber Quality Determination Using

Wood Property Models and Harvester Measurements

John D. Arlinger, Lennart Moberg, Johan J. Möller, Lars Wilhelmsson

John D. Arlinger, Lennart Moberg (presenter; lennart.mobert@skogforsk.se), Johan J. Möller, and Lars Wilhelmsson are researchers at Skogforsk, 

the Forestry Research Institute of Sweden, Uppsala Science Park, SE-751 83 Uppsala, Sweden.

ABSTRACT

I

N ORDER TO CREATE A SYSTEM FOR AUTOMATIC 

determination of sawlog quality, a study was carried out 

using the measurements from cut-to-length harvesters 

to feed wood property models. The primary goal was to 

establish a basis for payment to forest owners which not 

only was related to species and harvested volume, but also 

to wood quality equivalent to standard national grading 

rules. If successful, other applications could also include 

automatic bucking, allocation of timber to mills with specific 

requirements, or early detection of deviations in log deliveries. Norm values, representing a quality-index value of 100, 

were obtained for maximum knot size per whorl and basic 

density in two different regions, for Norway spruce and Scots 

pine, respectively. Deviations from these norms were given 

weights in accordance with their effect on graded sawlog 

quality. Data was collected in Sweden from 96 harvesting 

sites and 15 different harvesters. This data was accumulated 

in the on-board computers of the harvesters, and used to 

simulate wood properties. By using the calculated property 

values for each harvested stem, comparing these to the 

norm, and weighing the deviations accordingly, a relative 

quality-index was determined. The wood from each site 

was then sent to impartial grading stations at sawmills, and 

the species, volume, grade and value was determined for 

each log (as is customary in Sweden). Finally, the volume 

and value of the wood from each site, as obtained through 

the harvester and grading station measurements, could 

be compared. The standard deviations in value were 2–3 

percent for both species in the two regions—down from 

about 3–4 percent without corrections; reductions were 

most evident at sites with extreme values. Basic density 

was the dominant quality-determining factor for spruce, 

whereas knot size had most influence for pine.

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 110.
FOREST GROWTH AND TIMBER QUALITY

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Capturing Additional Value Through In-Forest 

Measurement of Internal Log Properties 

Glen Murphy

Glen Murphy (glen.murphy@oregonstate.edu) is a professor in the Department of Forest Engineering, Oregon State University, Corvallis, OR 97331, 

USA.

ABSTRACT

I

N SOME PARTS OF THE WORLD, LOG BUYERS 

are now considering wood properties such as stiffness 

and density. Assessing these properties in-forest and 

in real-time will be a challenge for log supply managers. 

The utility of two sensor technologies for sorting based on 

internal quality characteristics were examined in Douglasfir; near infrared (NIR) for measuring wood density, and 

acoustic velocity for measuring stiffness. Wood samples 

and measurements were collected from more than 1500 

stems located at 24 sites around Oregon. 

To evaluate NIR technology, spectra were first gathered 

from saw chip samples produced by a saw chain of a pitch 

similar to that used on mechanized harvesters/processors. 

Multivariate techniques were then used to correlate wood 

density with the NIR spectra. The research showed that 

NIR could be used to predict density with a reasonable 

degree of accuracy and should allow logs to be segregated 

into several density classes.

To evaluate acoustic velocity technology, velocity measurements were gathered at four points along the supply 

chain: in standing trees, in felled stems gripped by a processor, in logs on the ground, and in green veneer. Velocity 

measurements were correlated with log and veneer stiffness 

and product yields. Preliminary results will be presented 

for this work.

The research provides insight into how these technologies could be incorporated into the design of mechanized 

harvesters and processors to enhance bucking and sorting 

for optimal matching of wood properties to markets.

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 111.
FOREST GROWTH AND TIMBER QUALITY

112

Using the Results from Thinning and Fertilizer 

Interaction Models In Combination with Wood-Quality 

Studies To Maximize Commercial Benefit in South Australia Radiata Pine Plantations

Jim O’Hehir and Jan Rombouts

Jim O’Hehir (ohehir.jim@forestrysa.sa.gov.au) and Jan Rombouts are at ForestrySA, the South Australian Forestry Corporation, at PO Box 162, Mount 

Gambier, SA 5290, Australia.

ABSTRACT

THE SOUTH AUSTRALIAN RADIATA PINE 

estate produces approximately 2.5 million m3 of 

wood products annually. South Australian radiata 

pine plantations typically undergo multiple thinnings and 

the practice of post-thinning fertilizer application is becoming increasingly widespread.

Two decades ago, a series of trials designated EP190 

were established. The data from these trials allowed the 

development of models used to predict the volume growth 

response of radiata pine plantations to the interaction of 

two silvicultural tools, thinning and post-thinning fertilizer. The experimental plan also prescribed the collection 

of wood property and stem shape data. These data were 

used to investigate the effect of thinning and post-thinning 

fertilizer on wood quality as a by-product of changes in tree 

growth rate. The availability of SILVISCAN® meant that a 

range of important wood properties could be assessed at the 

resolution of individual growth rings at different heights 

in the stem profile, and at an acceptable cost.

Based on EP190 mensurational data a system of models 

was developed to predict annual volume growth responses 

as a function of natural site productivity, thinning intensity, 

and nitrogen fertilizer dosage, at stand and sub-stand level 

(next thinning crop versus final crop). These models were 

incorporated into the ForestrySA yield regulation system 

enabling prediction of the financial, economic, and logavailability effects of implementing alternative thinning and 

fertilizer practices at a stand and estate level. Coupled with 

wood property information gained from the SILVISCAN 

data it was possible to recommend changes to thinning 

regimes (intensity and frequency) and fertilizer practice 

(timing and dosage) which could be demonstrated—to 

executive decision makers and customers alike—to produce 

an acceptable level of wood quality. The recommended 

changes to management practices resulted in a 3.5 percent 

increase in log product sales, generating additional log-sale 

revenue for the forest owner of some A$1.5M/year.

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 112.
FOREST GROWTH AND TIMBER QUALITY

11

Further Progress in the Development of Prediction 

Models for Growth and Wood Quality of PlantationGrown Pinus Patula Sawtimber in South Africa

Heyns Kotze and Francois Malan

Heyns Kotze (hkotze@klf.co.za) is in the Research Division, Komatiland Forests, Private Bag X11201, Nelspruit, 1200, South Africa and Francois 

Malan is in the Research Division, Komatiland Forests, P.O. Box 574, Sabie, 1260, South Africa.

ABSTRACT

THE OBJECTIVE OF THIS PAPER IS TO FURTHER 

discuss and demonstrate the progress made (after 

an initial report by Kotze and Malan 2005), in the 

understanding, modeling, and simulation of tree growth and 

wood quality of South African-grown Pinus patula sawtimber 

as it responds to the effects of site quality, planting density, 

thinning and pruning. Research to date has focused on the 

development of stand-level growth and yield models. Model 

components for dominant height, survival, and basal area 

are used to estimate growth of unthinned stands in relation to planting density. A basal area/thinning ratio model 

estimates the ratio of basal area removed in a thinning in 

relation to the ratio of stems removed. Thinnings are done 

selectively from below. A basal area thinning response model 

estimates basal area growth after a thinning. At any point in 

time, the diameter distribution can be recovered by using a 

Weibull distribution and a method of moments approach. 

Height-by-diameter and live crown height models estimate 

tree height and live crown height for each dbh class in the 

distribution. Taper models were developed for the estimation of product volumes. Data for the growth and yield 

models were gleaned from long-term spacing trials, thinning 

response trials, permanent sample plots, thinning control 

inventories, and destructive sampling. Current research focuses on the development of models to estimate within-tree 

basic wood density and branch characteristics determining 

the knottiness of lumber such as number of branch clusters 

per annual shoot, maximum branch diameter, distribution 

of branch diameters within a branch cluster, branch angle, 

and branch development over time. Data for the wood quality 

models were gleaned from trees destructively sampled over 

the site-quality range. The inclusion of prediction models 

for tracheid length, spiral grain, and microfibril angle is 

envisaged at a later stage. To demonstrate our progress, 

the growth and wood quality models were combined in a 

simulation program, the Forestry Scenario Analysis Tool. 

This program quantifies the effect of site quality and silviculture (planting density, thinning, pruning, and rotation) 

on stand growth, tree dimensions, log product yields, and 

economics. It also includes a bucking algorithm capable of 

bucking each tree in the stand table to provide an estimate of 

the total log harvest and their qualities in terms of position 

in the tree, log length, and thin-end diameter. Algorithms 

determine the effect of pruning on the defect core size and 

quantify the effect of the live crown height on the live knot 

stem section. A sawmill conversion simulator predicts lumber 

yield and size distribution, using a preset sawing pattern 

for each log type and diameter class. Currently, the output 

also contains information on the expected wood density and 

absence or presence of knots (clear, semi-clear, or knotty). 

This enables the system to provide an estimate of the value 

of each individual lumber piece produced in terms of current lumber prices. Finally, the cash-flow for the whole 

stand is generated, economics criteria are applied and the 

influence of forest practices on wood quality evaluated in 

forest economic terms on a stand-level basis. 

KEYWORDS: Pinus patula, growth and yield, pruning, 

thinning, wood density, branching

This paper was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 113–123.
FOREST GROWTH AND TIMBER QUALITY

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INTRODUCTION

Pinus patula Schiede ex Schlect. & Cham. occurs naturally 

in Mexico where it extends from Tamaulipas right down to 

the mountains of north-eastern and north-western Oaxaca, 

and from there as far west as Guerrero. It is commonly 

known as Weeping Mexican pine.

Poynton (1979) notes that P. patula was first introduced 

to South Africa in 1907, which started the wide scale use 

of this species in South Africa. Today, plantation forestry 

in South Africa occupies 1.33 million ha, predominantly 

in the summer rainfall region along the eastern coastal 

areas and interior. Pine plantations occupy 707 205 ha of 

this area, approximately 48 percent of which is planted 

with P. patula. It is mostly planted in the cooler, mist-belt 

regions of eastern and south-eastern Mpumalanga province. It is also planted in the KwaZulu-Natal midlands, 

southern KwaZulu-Natal, Eastern Cape, and Northern 

Limpopo provinces. Komatiland Forests (Pty) Ltd (KLF) 

has a total forest area of 125 000 ha of which 48 percent 

is planted with P. patula. In KLF, P. patula is established 

in the elevation range between 700 and 2100 m above sea 

level, at mean annual temperature of between 14 and 20 ̊C, 

and a mean annual precipitation of between 850 and 1500 

mm. KLF is predominantly a pine sawtimber grower in 

the Mpumalanga and Limpopo provinces and is situated 

between the 30th and 34th laterals and predominantly in 

the 31st longitude band. 

The genetic improvement of P. patula started in the early 

seventies, with the main focus on improved growth rate, 

adaptability, good branching and stem characteristics. Today KLF manages a total of 20 first- and second-generation 

seed orchards (165 ha in total) of pines and eucalypts for 

the production of improved seed. The P. patula seed are 

harvested from the top ten families in the second-generation 

seed orchards. These are used to establish hedge plants for 

production of commercial cuttings, and seedlings for field 

planting. The majority of seed used for local afforestation 

with P. patula are produced by the company’s own seed 

orchards.

South African forestry scientists are continually trying 

to improve the productivity and economic out-turn of the 

country’s commercial forests. This includes choosing the 

right species and seed source, improving site conditions 

through cultivation, drainage and fertilizer application, and 

manipulating the crop through genetics and silvicultural 

practices. Increased site productivity is one of the primary 

objectives of forestry research, in order to promote forest 

sustainability. However, it is increasingly recognized that 

the ultimate success of the forest industry is strongly linked 

to the quality of the wood produced and the industry’s 

ability to maximise effective and wise utilisation of the 

resource. This is of increasing importance since a synergy 

must be found between the economic reality of harvesting 

at a younger age without sacrificing on volume production 

per unit area (fast growth makes this possible), and a wood 

product market that is becoming increasingly sophisticated 

and demanding in terms of end-product performance. It 

has therefore become of utmost importance to understand 

the timber resource and its changing qualities, to develop 

mechanisms capable of accurately predicting its wood and 

fiber quality, and to transfer this knowledge into industrial 

business processes.

Existing growth and yield prediction models serve as 

valuable tools to planners and harvesting managers, as 

they provide useful information on the likely production 

of a forest in terms of volume and raw material product 

outputs. Until now, the development of models and procedures capable of predicting wood quality in terms of 

species, genotype, silviculture, age, and site have not been 

attempted at a significant scale for the South African timber resource. This is considered a serious shortcoming, as 

improved predictability is becoming increasingly important 

to ensure the sustainable utilization of a variable forest 

resource such as ours, and to effectively accommodate 

changes in resource characteristics due to the impacts of 

improved silviculture, tree breeding, and the introduction 

of hybrids and new species.

This paper describes the initial phases of a project 

launched by KLF designed to eventually model a number 

of wood quality factors for P. patula, as well as the expected 

product output of a sawmill in terms of sawn volume and 

lumber quality, using the existing growth and yield models 

as a framework.

SITE TYPE AND SITE QUALITY

In KLF a detailed 1:10 000 site classification was conducted 

based on soil type, soil depth, depth of limiting material, 

mean annual temperature, mean annual precipitation and 

geology. Each stand has a dominant site type, which is used 

to recommend a preferred (most suitable) species for each 

stand. Site quality is expressed in terms of site index at age 

20 years (denoted as SI20), which is the average height of the 

20 percent largest-diameter trees in a stand (Bredenkamp 
FOREST GROWTH AND TIMBER QUALITY

115

1993). For each site type/species combination, an 

average SI20 value can be estimated. Depending on 

the site type, P. patula achieves SI20-values between 

15 m and 35 m in KLF with an average of 25 m. SI20

is used to quantify site quality effects on tree and 

stand growth and subsequently on wood quality. 

The effect of site quality on utilizable mean annual 

increment at age 20 years (UMAI20) can be seen 

in Figure 1. 

SILVICULTURE

Stands are mostly established with seedlings placed 

into manually prepared planting pits. Pine stands 

are thinned and pruned intensively to improve 

quality and value. In KLF the planned rotation age 

is 30 years and the goal is to produce a target stand 

with an average diameter at breast height (dbh) of 

42 cm over-bark pruned to 9.5 m.

Results from numerous spacing trials in South Africa 

have proven that planting density has a pronounced influence on basal area development of a stand, but a very 

small effect on dominant height. Therefore, stand density 

management is required to enable stands to achieve the 

dimensions of the target tree. Current practice within the 

company is a standard planting density of 1111 stems per 

hectare (3 m x 3 m). With this planting density, canopy 

closure occurs at approximately three years. It allows for 

11 percent mortality during establishment and provides 

sufficient room for selection at first thinning. Thinnings 

are mostly done selectively from below. On flat terrain, a 

7th row thinning is sometimes conducted in combination 

with selective thinning. 

The purpose of thinning is to boost diameter growth, 

to encourage uniform annual incremental growth, to keep 

the stand in a stable and healthy growing condition and to 

provide room for selection at thinning so that a good final 

crop is ensured while providing for an interim income at 

the same time. Table 1 shows how the current thinning 

regimes are applied over the site quality range.

The purpose of live crown pruning is to confine the 

defect core to a cylinder smaller than 20 cm in diameter, 

ensuring that the knots in the defect core cylinder are 

tight and defect free, and that all wood formed outside 

this cylinder is knot free and of good quality until the final 

harvest. Pruning is conducted in such a manner that live 

crown always constitutes at least one third of the tree height. 

This ensures that growth loss due to pruning is minimized. 

To achieve this, pruning schedules were designed for the 

range of SI20-classes. 

GROWTH AND YIELD RESEARCH

Data

Structured growth and yield research started in 1936 when 

O’Connor established the first series of four spacing and 

thinning response trials for P. patula, the so-called Correlated Curve Trend trials (CCT) (O’Connor 1935, O’Connor 

1960). Following through with the CCT trials, Craib (1939, 

1947), Marsh (1957, 1978), Burgers (1976) and Marsh and 

Burgers (1973) continued with the pioneering work in stand 

density management. Bredenkamp (1984) summarized 

Figure 1: The relationship between site quality and mean annual volume their work extensively and designed a new series of more increment of P. patula.

Table 1: Thinning regimes currently applied for P. patula in Komatiland Forest.

TPH 

remaining

after 

thinning

Age of thinning (years)

SI20 class (m)

<21 21-23 23-25 25-27 27-29 >29

500 10 10    

00 15 14 1 12 12

Abbreviations: SI20 = Site Index at the reference age of 20 years

 TPH = Trees per hectare

Table 2: Pruning regimes currently applied for P. patula in Komatiland Forest.

Pruning

lift (m)

Age of pruning (years)

SI20 class (m)

<21 21-23 23-25 25-27 27-29 >29

2.0 4.5 4.0 . . .7 3.5

4.0 .2 5.4 5.0 4.7 4.6 4.4

.0 .0 .7 .1 5.7 5.5 5.3

7.5 . 7.4 . . .

8.5 8.5 7. 7.4 7.0

9.5 9.4 .7 . 7.
FOREST GROWTH AND TIMBER QUALITY

11

cost effective spacing trials in terms of area requirements 

(Bredenkamp 1990), the so-called Standardized Sample 

Size spacing trials (SSS-CCT). With this he addressed the 

shortcomings of the first series of trials and provided a 

base data set for the next generation of growing stock. To 

date three of these SSS-CCTs have been established for 

P. patula by KLF. Over time, data from other sources, like 

thinning control inventories, management inventories, 

Permanent Sample Plots (PSPs), and destructive sampling 

were collected so that the full range of model components 

required in a growth and yield simulator could be developed and tested. 

Results from the Spacing and Thinning 

Research

Results from the spacing and thinning trials on P. patula

indicate that dominant height is not affected significantly 

by planting density and thinning from below, within the 

commercial range of planting densities. Mortality occurs 

at a faster pace when the density is higher. After a thinning 

from below, mortality in a thinned stand is lower than in 

an unthinned stand of the same density. Tree diameter or 

basal area per hectare is greatly affected by planting density. 

Basal area growth in a thinned stand can be expressed with 

a response function to an unthinned counterpart.

Models for Simulating Growth and Yield

Pienaar (1964) and Pienaar et al. (1985, 1988) interpreted 

the data from the CCT trials and developed modeling approaches to describe unthinned stand growth and stand 

growth in response to thinning. The modeling strategy 

currently employed for P. patula was presented by Kotze 

(2003) and is summarized below. 

KLF adopted a stand-level modeling approach because 

all our forests are planted, even-aged, and single-species 

stands. Stand-level growth is defined by three variables, 

namely dominant height, basal area, and stems per hectare. 

Dominant height is modeled by a Chapman-Richards-type 

function (Kotze 1999). Unthinned basal area is also modeled 

with a Chapman-Richards-type function and its parameters 

are dependent on planting density (Kotze 1999). Survival 

is modeled with the Clutter-Jones survival function (Clutter 

and Jones 1980). 

When a thinning is applied to a stand, a number of 

changes occur. It is assumed that dominant height growth 

is not affected by thinning, only the mean height is affected. The thinning regime dictates the number of stems 

per hectare to remain after the thinning. It is assumed that 

no mortality occurs after the first thinning, because of the 

intensive thinning regime. Basal area removed in a thinning 

is estimated with Field’s thinning ratio function (Field et 

al. 1978). Basal area responds to thinning and the response 

is modeled with the index of suppression methodology, as 

proposed by Pienaar and Shiver (1984).

Whole-stand volume is estimated by constructing a stock 

table, where the tree volumes are estimated for each dbh 

class. The stand structure, i.e., a stand table is independent 

of the growth model. The dbh distribution is reconstructed 

by using the Weibull function with Kassier’s implementation method (Kassier 1993). Garcia’s method of moment’s 

technique is used to recover the Weibull parameters (Garcia 

1981). Consistency between distributions before and after 

thinning is obtained with the methodology developed by 

Murray and von Gadow (1991). Pienaar’s average height 

by dbh function (Pienaar et al. 1988) is used to estimate 

the average height for each dbh class. Dyer and Burkhart’s 

(1987) live crown height model is used to predict the 

progression of live crown height over time. This model 

is useful in estimating the development of the dead-knot 

zone above the pruned section of the bole. Product volumes 

are estimated by applying a greedy bucking algorithm to 

each dbh-class in the stand table (Vonck 1997). The Max 

and Burkhart taper function is used to estimate product 

volumes (Max and Burkhart 1976).

Stand growth and yield is normally projected from a 

calibration point where inventory data provide the calibration age (Age1), dominant height (Hd1), basal area per 

hectare (BA1), and stems per hectare (TPH1). If such inventory data do not exist, then a calibration point is created 

before the first thinning age. Each stand has an allocated 

SI20-value and this is used to estimate height at Age1. TPH1

is estimated by multiplying planting density (TPH0) with a 

default survival percentage (Surv%). BA1 is estimated with 

a stand-level basal area yield prediction function from Age1, 

TPH1, and Hd1. 

WOOD QUALITY RESEARCH

Impacts of Site and Silviculture on Wood 

Density

Wood density is the property most commonly considered 

in wood quality studies as it has a strong bearing on lumber 

strength, machining, drying rate, pulp and paper proper-
FOREST GROWTH AND TIMBER QUALITY

117

ties, and permeability. Wood density is extremely variable 

and the variation patterns are very important. Among- and 

within-tree differences within a stand are mostly caused 

by genetic influences and relate strongly to the size of the 

juvenile wood zone and its variability (Zobel 1997, Zobel 

and Jett 1995). However, site factors especially those influenced by elevation, latitude, and soil fertility may also 

affect this property (Cown 1999, Malan 2001). 

The basic density of the wood produced by South African 

P. patula increases from approximately 375 to 400 kg/m3

near the pith to approximately 525 to 575 kg/m3 in the 

mature wood zone. The period of increase normally lasts 

for approximately 20 years before leveling-off starts to occur. The height effect is relatively small as density normally 

decreases only by 40-50 kg/m3 from breast height to 20 m 

from the ground for the same growth ring from the pith. 

Studies by Boden (1982) and Malan (2001) indicated 

that density of the wood produced by P. elliottii, P. taeda, 

P. patula, and P. radiata decreases with elevation and latitude. P. patula seemed to be less affected by these variables, 

however. The interaction terms (elevation x latitude) were 

statistically significant for all species, suggesting that the 

effects of latitude and elevation are complex and should not 

be considered separately. Compared to results of findings 

in Columbia at high elevations, findings in Swaziland suggested that the relationship with elevation at lower elevations might be much weaker. In Zimbabwe little genotype 

x environment interaction was found for density (several 

papers as reported by Dvorak et al. 2000). Clarke et al. 

(2003) found almost no difference in density in P. patula

trees grown at elevations of 1200 and 1450 m above sea 

level at Usutu (Swaziland), but at 800 m elevation the wood 

was only about 15 kg/m3

 denser on average. 

As early as 1939 Craib concluded that rate of growth 

did not affect timber strength in P. patula. This was later 

confirmed by Banks and Schwegmann (ca.1957) who 

found no significant effect of differences in growth rate on 

moisture content, green and dry density, or shrinkage. The 

radial increases in density were largely similar irrespective of growth rate, except that the fast-growers produced 

wood slightly less dense over comparable years of growth. 

However, the weighted mean density of the fast-grown trees 

was the same and sometimes even higher than that of the 

slow-grown trees due to the greater percentage of denser 

wood in the outer layers of the stem. 

Results obtained from a CCT spacing trial at Weza 

(Malan et al. 1997) revealed that slow-grown trees exhibited higher density than fast-grown trees when comparing 

wood formed at the same 

age. The wood formed 

by slow-grown trees also 

seemed to have reached 

maturity at an earlier age. 

However, the differences 

observed were only applicable to extreme differences in growth rate 

(Figure 2). Within the 

range of normal spacing applied in practice, 

it was obvious that the 

effect of growth rate differences due to spacing 

differences on wood density and pulp and paper 

properties was negligible. 

Since this study also revealed that thinning had 

no recognizable effect 

on wood density, it was 

concluded that thinning 

Figure 2: Differences in the radial patterns of variation in wood density at breast height in P. patula trees as affected by 

age and planting density treatments.
FOREST GROWTH AND TIMBER QUALITY

11

could be used to successfully control any effect different 

spacings might have on wood density and related properties, by carefully controlling competition. 

It was clear from this study that the enhancement of 

growth rate of this species by the manipulation of the 

growing space or thinning had no adverse effect on wood 

density, and by implication, on any of the factors related to 

this property. In fact, the advantages of fast growth by far 

outweigh the “advantage” of higher density produced by 

slower growing trees (Figure 3). It implies not only higher 

volume production, but goes hand-in-hand with improved 

uniformity across the radius as well, without compromising the suitability of the wood for structural purposes to 

any serious level. 

More recently, a study was conducted by Kotze and Malan (2005) to establish variation patterns in wood density 

within trees of this species and how it is affected by elevation. Approximately 90 trees were sampled over three sites 

at elevations of 1000, 1300, and 1700 m above sea level, 

respectively. This study showed that the effect of elevation 

on wood density is not clearly defined. Ring number from 

the pith and height above ground level accounted for 63 

percent and 10 percent of the total variability, respectively. 

This study provided a suitable dataset for the development 

of a within-tree wood density model. The within-tree wood 

basic density model as proposed by Tian et al. (1995) was 

selected for parametrization 

with the P. patula data. 

Stem Form 

and Branching 

Characteristics

The combined effects of tree 

breeding towards improvement of branching characteristics and stem form and the 

development of thinning and 

pruning regimes were without 

doubt highly successful in 

promoting the quality of the 

wood produced by the current 

forest resource. As a result, 

problems associated with 

irregular growth; reaction 

wood; eccentricity; wandering pith; localized excessive 

grain deviation; and knots that exceed the limits for size, 

soundness, and clustering have been minimized. In the 

pruned sections of the stems of properly managed trees 

the knots and associated defects are restricted to a core of 

pre-planned diameter, while the proportion of clear wood 

in the outer more mature part of the stem is maximized. 

However, there is a definite need to develop models to 

predict branch characteristics as a function of site quality 

and silviculture. 

Currently, Kotze (2007) is busy with a pilot study on 

branch modeling of P. patula sawtimber in KLF. The purpose 

of the study is to develop a set of models to describe the 

development of branchiness within a tree over time. The 

methodology described by Grace et al. (1999) was used as 

a starting point to define the branch modeling strategy. To 

reconstruct the branch growth in a single tree, the dbh and 

height growth will be reconstructed with the growth model. 

Therefore, the annual shoot lengths and stem profiles, both 

over-bark and inside-bark, will be available. There is of 

course a nodal swelling which is additional to the overbark 

stem profile. Once a branch is formed, it will maintain its 

position and azimuth for its entire life. Within each annual 

shoot, the number of branch clusters and their relative positions within the shoot are predicted. Within each cluster, 

the number of branches is allocated as a random value from 

Figure 3: Differences in the radial patterns of variation in wood density at breast height in P. patula trees with 

linear distance from the pith as affected by planting density treatments. 
FOREST GROWTH AND TIMBER QUALITY

11

an observed distribution. The azimuth of the first branch 

is set as a random value from a circular distribution. The 

azimuth of the second branch is allocated by advancing the 

azimuth clockwise by 137.5 degrees. This sequence simply 

continues to the next cluster. Branch size increases from 

the first to the last branch in each cluster. The last branch 

is considered to be the branch with maximum diameter 

in that cluster. The size of the other branches is allocated 

as a function of maximum branch diameter and branch 

order in the cluster. Each branch is grown over time, with 

the associated branch angle reconstructed. Each branch is 

grown until it dies, thereafter the diameter remains constant 

and the dead branch is encased. 

Potential for Modeling Other Wood 

Quality Factors

A number of other properties that are known to have a 

strong impact on some end-uses will have to be dealt with 

systematically in the future and ultimately be included in 

existing software packages to improve predictability.

Juvenile wood is particularly marked in South Africangrown soft- and hardwoods and is an important quality 

factor since its inherent properties are considerably more 

variable and different than those of mature wood. As 

increased volume growth is continuously and vigorously 

pursued to improve plantation productivity, if rotation ages 

are reduced to reap the benefits of fast growth and result in 

increased proportions of juvenile wood in the final harvest, 

the effect on the quality mix of the wood produced in the 

future could be quite significant.

Fortunately, wood densities, as well as the properties 

discussed below, are all important production variables of 

which age is by far the main controlling factor, especially in 

the juvenile wood zone where rapid changes with age prevail. 

There can thus be little doubt that the age effect will feature 

strongly in models designed to predict these properties and 

the quality of the juvenile zone in particular. 

Microfibrillar Angle

Wood density and microfibril angle are considered to be the 

most important wood properties controlling the technical 

performance of wood. The latter is of particular importance 

because of its marked role in determining the strength, 

stiffness, shrinkage, and stability of wood, especially in 

juvenile wood, where it varies considerably across the radius, with the largest angles near the pith. There can be no 

doubt that modeling the variation of this feature for South 

African commercial species will make a major contribution 

towards predicting the behavioural properties of the wood 

produced, assisting in its effective utilization, and increasing options for wood quality improvement. 

Tracheid Length

Information on the patterns and sources of variation of 

this feature is extremely limited for South African pines. 

Average breast height tracheid length of P. patula increases 

rapidly from about 2 mm at ring 2 to 5 mm at ring 20, 

where after it remains relatively constant (Kromhout 

1962). This means that this species produces 0.5 to 1 mm 

longer tracheids across the entire radius than other local 

commercial pines. Turner et al. (2000) found that the cell 

diameter, lumen diameter, and length of P. patula tracheids 

increase with site quality (growth rate) increases but wall 

thickness is not affected. As a result, collapsibility, which 

is a ratio involving cell diameter and wall thickness and 

which determines the ability of the fiber to defibrillate and 

flatten during sheet formation, improves with site quality. 

Thus the wood from better sites yields pulp fibers that have 

better fiber-to-fiber bonding.

Spiral Grain 

In South African pines, spiral grain is foremost a problem 

of juvenile wood. Grain angles are greatest near the pith 

but normally drop rapidly over approximately the first ten 

annual rings, reaching more acceptable values as more 

mature wood is formed. The patterns of variation in spiral 

grain are not very consistent, neither between trees nor 

within trees (Banks 1969, Gerischer and Kromhout 1964). 

P. patula tends to be more spiral-grained than both P. elliottii 

and P. taeda, averaging from approximately 3.5 degrees near 

the pith to approximately 2.5 degrees at the 30th year of 

growth. Contrary to the other two pines, there is a definite 

tendency toward left-hand spiral grain in P. patula. In the 

latter species the average angle of spiral grain often tends 

to remain larger than in other pines for longer distances 

across the radius, with the result that its influence sometimes extends to lumber cut at quite some distance from 

the pith. P. patula growing in the cooler temperate regions 

tend to be less spiral-grained than those growing in the 

warmer areas (Kromhout and Toon 1977). Otherwise, 

little is known about the variation patterns in spiral grain 

in South African pines, and in P. patula in particular, and 

how it is affected by environmental factors.
FOREST GROWTH AND TIMBER QUALITY

120

The Forestry Scenario Analysis Tool 

(FORSAT)

FORSAT is a stand-alone simulation program operating on 

a stand-level basis (Kotze 2006). This program quantifies 

the effect of silviculture (planting density, thinning, pruning, and rotation) on stand growth, tree dimensions, log 

product yields, and economics. 

The stand-level growth model estimates values for dominant height, stems per hectare, and basal area over time. 

At each thinning event it quantifies the number of stems 

removed and estimates the basal area removed. For any 

age, the diameter distribution is generated and a stand table 

is constructed. For each dbh class midpoint, the number 

of stems per hectare, an average tree height, and the live 

crown height are estimated. A bucking algorithm is then 

employed to buck each tree in the stand table according to 

a log specification and to provide an estimate of the total 

log harvest and their qualities in terms of position in the 

tree, log length and thin-end diameter, whether it is pruned 

or not, the clear-wood radius or the live knot radius, the 

density profile, and the associated log value. Finally, the 

cash flow for the whole stand is generated and economics 

criteria are estimated. Typical economic criteria like Land 

Expectation Value (LEV), Net Present Value (NPV), Equivalent Annual Income (EAI), Internal Rate of Return (IRR), 

Standing Value (SV), and Cost Value (CV) are estimated. In 

this way, the influence of silviculture can be evaluated in 

forest economic terms on a stand-level basis. This is useful 

from the forester’s point of view.

FORSAT represents a useful framework to include 

models predicting wood property variation in terms of 

site, silviculture, and age. The within-tree wood density 

model described above, and models predicting growth 

and tree stem composition with regard to the size of the 

defect core, clear-wood zone, and juvenile wood (in terms 

of density), were included. The models describing branch 

characteristics have not been incorporated yet. 

FORSAT also includes a sawmill processing simulator 

which estimates the potential yield of lumber products and 

their value from a specific stand. The software predicts 

lumber yield and size distribution, using a preset sawing 

pattern specification for each log type and diameter class. 

It also classifies each lumber piece produced into an expected product type (structural and/or any of the industrial 

grades) as dictated by its air-dry dimensions and expected 

spatial position within the stem. The latter enables the 

program to estimate the quality of each piece in terms of 

its expected mean density and status regarding the absence 

or presence of knots. With this information available, the 

system can classify the pieces into products and grades 

and estimate the value of each individual lumber piece in 

terms of current lumber prices as well as the sawn output 

of a stand as a whole.

CONCLUSIONS AND 

RECOMMENDATIONS 

FOR FUTURE RESEARCH

Progress to date has proven that the quality of the wood 

produced by P. patula can be modeled and effectively incorporated into existing growth and yield software and used 

on a stand-level basis. It has been shown that a considerable amount of information can be generated regarding the 

quality of the wood of round timber, as well as the quality 

of sawn products, by utilizing existing wood quality information on the species as basis for prediction. Although the 

latter is limited (in scope as well as in accuracy) it comprises 

three of the most important factors controlling the quality 

of the wood: degree of wood density variation, defect core 

size in the pruned section, and known patterns of branch 

dieback beyond the final pruning height.

While pruning has proven to be one of the most powerful 

techniques to improve the quality of the wood produced 

in the pruned section of the stem (and the predictability 

thereof), results of spacing and thinning trials have shown 

that tree volume growth can be maximized without any 

detriment to the wood produced. In fact, accelerated incremental growth results in increased volume of wood of 

improved uniformity across the radius, without compromising wood strength to any great extent. 

Although studies conducted to date indicated clear site 

differences in within-tree wood density variation patterns, 

the exact site factors controlling these patterns could not yet 

be determined. Thus, there is a strong need for more studies 

to better understand the effects of site conditions on tree 

growth and its wood properties and their variation patterns. 

This will also indicate to what extent the predictive power 

of existing models would improve by incorporating some 

form of model calibration on an individual stand basis. 

There is a need to improve the components and coefficient sets of the stand-level modeling approach as new data 

becomes available. The stand-level modeling approach is 
FOREST GROWTH AND TIMBER QUALITY

121

not the most suitable approach for tracking wood properties in final crop trees and it is possible that individual tree 

models would be more appropriate. 

Finally, there is a need to study the variation patterns 

of a number of quality factors that are of technological 

importance and the factors controlling them in order to 

expand the versatility and accuracy of current software. 

These include the whole branch model component, and 

models to describe spiral grain, tracheid length, and microfibril angle.

ACKNOWLEDGMENTS

The authors acknowledge KLF for initiating and supporting 

this study. FORSAT is being programmed by Brandt van 

der Merwe and his contribution for designing the visualization algorithms is gratefully acknowledged. The field crew 

working at the Sabie Research Centre is thanked for their 

meticulous work in the sampling processes.

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quality of South African timber. Forestry in South 

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density of the three major pine species in the Natal 

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1: 313-332.

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Forestry and the Eucalyptus grandis Research Network, 

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Bredenkamp, B.V. 1993. Top height: A definition for use in 

South Africa. Southern African Forestry Journal 167: 55.

Burgers, T.F. 1976. Management graphs derived from 

the correlated curve trend (CCT) projects. Bulletin 54. 

Department of Forestry, Pretoria. 58 p.

Clarke, C.R.E.; Morris, A.R.; Palmer, E.R. [et al.]. 

2003. Effect of environment on wood density and 

pulp quality of five pine species grown in Southern 

Africa. Tropical Forestry Papers 43. OFI, Department 

of Plant Sciences, University of Oxford, UK. 162 p.

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Department of Agriculture, Forest Service Research 

Paper SE-217. pp: 1-8.

Cown, D.J. 1999. New Zealand pine and Douglas-fir. 

Suitability for processing. Forest Research Bulletin 

216. 72 p.

Craib, I.J. 1939. Thinning, pruning and management 

studies on the main exotic conifers grown in 

South Africa. Science Bulletin 169, Department of 

Agriculture and Forestry, South Africa. 179 p.

Craib, I.J. 1947. The silviculture of exotic conifers in 

South Africa. Journal of the South African Forestry 

Association 15: 11-45.

Dvorak, W.S.; Hodge, G.R.; Kietzka, J. E. [et al.]. 2000. 

Pinus patula. In: Conservation and testing of tropical 

and subtropical forest tree species by the CAMCORE 

cooperative, College of Natural Resources, NCSU, 

Raleigh, NC, USA. pp. 140-173.

Dyer, M.E.; Burkhart, H.E. 1987. Compatible crown 

ratio and crown height models. Canadian Journal of 

Forestry Research 17: 572-574.

Field, R.C.; Clutter, J.L.; Jones, E.P. (JR). 1978. 

Predicting thinning volumes for pine plantations. 

Southern Journal of Applied Forestry 2(2): 59-61.

Garcia, O. 1981. Simplified method-of-moments 

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Gerischer, G.F.R.; Kromhout, C.P. 1964. Notes on 

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Modelling branch development for forest management. 

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height distributions in even-aged pine plantations. 

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167 p.

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A.; Reed, D. and Soares, P. Modelling Forest Systems. 

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sawtimber in Komatiland Forests. Preliminary results 

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Forests. 12 p.

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between Forest Resources and Wood Quality: 

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Pinus patula, Pinus taeda and Pinus elliottii. Forestry in 

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Kromhout, C.P. and Toon, R.E. 1977. Variation in 

wood properties of some tropical species grown in 

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experiments on thinnings and espacements and 

their practical significance. Commonwealth Forestry 

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56, Department of Forestry, Pretoria. 140 p.

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between the diameter distributions before and after 

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reference to planting distances and thinning. British 

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South African Forestry Association: 66-88.

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176 p.

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models of basal area growth in 45-year-old unthinned 

and thinned slash pine plantation plots. Forest Science 

30(4): 933-942.

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Predicting basal area growth in thinned slash pine 

plantations. Forest Science 31(3): 731-741.

Pienaar, L.V.; Harrison, W.M.; Bredenkamp, B.V. 1988. 

Yield prediction methodology for E.grandis based on 
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Langepan CCT data. Unpublished Report, University 

of Georgia. 36 p.

Poynton, R.J. 1979. Tree planting in Southern Africa. 

Vol. 1. The Pines. Report to SARCCUS, Department of 

Forestry, Pretoria. 576 p.

Tian, X.; Cown, D.J.; MCConchie, D.L. 1995. Modelling 

of Pinus radiata wood properties. Part 2: Basic density. 

New Zealand Journal of Forestry Science 25(2): 214-

230. 

Turner, P.; Megown, K.A.; Grzeskowiak, V. [et al.].

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system for P. patula. Proceedings: “Forest genetics for 

the next millennium”, IUFRO working party 2.08.01, 

Durban, South Africa. pp. 228-235.

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Unpublished report, South African Forestry Company 

Ltd. 6 p.

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Proceedings: ‘Timber Management toward Wood 

Quality and End-product Value’, CTIA/IUFRO 

International Wood Quality Workshop, Québec City, 

Canada. Vol. IV: 3-9.

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Production. Springer-Verlag, Berlin. 337 p. 

FOREST GROWTH AND TIMBER QUALITY

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Developments to the Sylvan Stand Structure Model to 

Describe Wood-Quality Changes in Southern Bottomland Hardwood Forests Because of Forest Management

David R. Larsen and Ian R. Scott

David R. Larsen (larsendr@missouri.edu) is a professor of quantitative silviculture and chair of the Department of Forestry-203 ABNR, The School 

of Natural Resources, University of Missouri-Columbia, Columbia, MO 65211, USA and Ian R. Scott is a software engineer at Silicon Navigator, 10050 

N. Wolfe Rd Suite SW2-260, Cupertino, CA 95014, USA.

ABSTRACT

GROWTH MODELS CAN PRODUCE A WEALTH 

of detailed information that is often very difficult 

to perceive because it is frequently presented 

either as summary tables, stand view or landscape view 

visualizations. We have developed new tools for use with 

the Sylvan model (Larsen 1994) that allow the analysis of 

wood-quality changes as a consequence of forest management. Sylview is a new computer program that allows users to visualize wood-quality characteristics of stands and 

individual trees within a stand. These include the effects 

of spacing and thinning on taper, branch size, and clear 

wood production. 

KEYWORDS: Stand structure model, crown change, wood 

quality, silviculture

INTRODUCTION 

The Sylvan Stand Structure model (Larsen 1991a, 1991b, 

1994) was developed to allow foresters to study the development of specific stands of various species mixes based on 

empirical data from a subject stand and from forest stand 

dynamics principles. This model was developed after watching foresters try to make empirical forest-growth models 

fit a subject stand with species not included in the growth 

model or fit densities and forest structures not included in 

original data upon which the models were built. These foresters would try to force the model to work by substituting 

species or simply extrapolating the results. In Sylvan, two 

design criteria were adapted; first, basic stand dynamics 

principles guide the general function of all trees; and second, 

to make effective forest management decisions, the relative 

dynamics and the range of outcomes were more important 

than estimated volume or size. With these ideas in mind, 

Sylvan uses a 3-dimensional spatial pattern defined by 

stem maps and tree heights plus the crown size, defined 

by crown length and crown width, to provide the basis for 

predicting future stand structure.

THE SYLVAN S-PLUS/R DISPLAY

The programming for the original model was written in C 

programming language with a simple tree-list-in and treelist-out approach. In the early 1990’s a series of functions 

in S-plus language were used to provide graphical output. 

While these were just fine for research and publication, 

they were not very convenient for foresters to use.

SYLVAN DISPLAY PROGRAM

One early attempt to build a program to display the model 

output of the Sylvan Stand Structure model is the Sylvan 

Display program (Davison 1995). This program was written by a computer science masters student and had several 

design criteria, two of which were 1) the program should 

be cross platform (Unix, Window, Mac), and 2) it should 

have 2-dimensional and 3-dimenstional views, graphs, and 

tables of the model output. The student was successful in 

satisfying both of these criteria. One major limitation was 

the maturity of the windowing library used at the time.

This paper was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 125–131.
FOREST GROWTH AND TIMBER QUALITY

12

Figure 1— Typical output for a 

single tree from the Sylvan Stand 

Structure model using the Sylvan 

S-plus/R visualization tools. 

Figure 1a is an illustration of the 

tree profile at each time step of 

the model simulation. Figure 1b 

is a cross-section of the stem at 

breast height (1.37 m) rings are 

5-year increments. Images from 

Larsen (1991a) are Douglas-fir 

(Pseudotsuga menziesii (Mirbel) 

Franco) from western Washington 

A B USA.

A B

Figure 2— Typical output for a 

single tree from the Sylvan Stand 

Structure model using the Sylvan Splus/R visualization tools. Figure 2a 

is a stand crown map at time step 9. 

Figure 2b is a stand profile at time 

step 9. Images from Larsen (1991) 

are Douglas-fir (Pseudotsuga 

menziesii (Mirbel) Franco) from 

western Washington USA.

A B

Figure 3— Density management 

diagram and mean annual 

increment (MAI) over periodic 

annual increment (PAI) curve for 

the modeled stand. Volumes are 

in cubic feet and quadratic mean 

diameters in inches. Images from 

Larsen (1991) are Douglas-fir 

(Pseudotsuga menziesii (Mirbel) 

Franco) from western Washington 

USA.
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127

STAND VISUALIZATION SYSTEM (SVS)

The Stand Visualization System (SVS) (McGaughey 1997) 

is a good stand-level visualization tool for the Windows 

operating system. In the initial phase of the recent Sylvan 

Stand Structure model development, SVS was considered 

our primary visualization tool. The Sylvan Stand Structure model has modules that produce SVS-ready files for 

visualization. 

However, after using the program for some time, we recognized several areas for improvement in the SVS interface. 

While the 3-dimensional interface (see Figure 7) looks nice, 

we found it difficult to determine specific information about 

individual trees. A model output visualization tool should 

Figure 5— An example of the Sylvan Display program (Davison 1995). 

This view displays the diameter distribution and the height distribution. 

The stand illustrated is European beech (Fagus sylvatica L.) in Central 

Italy.

Figure 4 — An example of the 

Sylvan Display program (Davison 

1995). The stand illustrated is 

European beech (Fagus sylvatica L.) 

in Central Italy.

Figure 6— An example of the Sylvan Display program (Davison 1995). 

Trees selected for cutting are highlighted in black in both the stand map 

and the histograms of the size distributions, whereas residual trees are in 

light gray. The stand illustrated is European beech (Fagus sylvatica L.) 

in Central Italy.
FOREST GROWTH AND TIMBER QUALITY

12

be designed to convey information about the changes in tree 

dimensions and the interactions of neighboring trees.

Many components, while present in SVS, were not always 

in the most logical location for the user to access. For example, to change the display interface one must select “SVS 

Options”, then “Screen Layout”, then the desired screen configuration. This requires accessing a third-level menu item 

to accomplish a very common task (see Figure 8). Changing 

the perspective of the 3-dimensional view also required a 

pop-up window to set the viewing parameters requiring 

a multi-step process to change this view. Individual tree 

data is available in the interface, but requires entering the 

tree-marking interface and then selecting individual trees. 

All of these items are workable but not very convenient for 

the user to master.

We realized that there is a lot of information available in 

the Sylvan tree list that is not utilized by the SVS program. 

Additionally, the Sylvan Stand Structure model’s main 

development platform is Linux and some team members 

were also using MacOS. We decided to create a new visualization tool, Sylview. The design criteria for this program 

are detailed in the following section. 

SYLVIEW

The Sylview program was designed to be a stand-level visualization tool used to examine the output of the Sylvan 

Stand Structure model and allow the user to grasp the 

stand dynamics principles that are built into the Model. It 

was designed so that the viewer could fully utilize available information within the tree list, information which 

illustrates tree interactions likely to occur during stand 

development. The following design criteria for the Sylview 

software were established: 

Practical Considerations

• It should present a plot of trees in map and profile 

views

• It should be very easy to see tree growth through 

time, both individually and collectively

Figure 7— An example of the Stand Visualization System (SVS) program 

(McGaughey 1997). The stand illustrated is Douglas-fir (Pseudotsuga 

menziesii (Mirbel) Franco) from western Washington USA

Figure 9—An example of the Stand Visualization System (SVS) 

program (McGaughey 1997). This screen allows the user to change the 

3-dimensional perspective for the 3-dimensional view seen under the popup window. The stand illustrated is Douglas-fir (Pseudotsuga menziesii 

(Mirbel) Franco) from western Washington USA

Figure 8— An example of the Stand Visualization System (SVS) 

program (McGaughey 1997). This image illustrates the multiple menus 

used to change the screen layout. The stand illustrated is Douglas-fir 

(Pseudotsuga menziesii (Mirbel) Franco) from western Washington 

USA.
FOREST GROWTH AND TIMBER QUALITY

12

• The user should be able to inspect the internal wood 

character of each tree

Technical Considerations

• It should work on multiple platforms (Linux, Windows, MacOS)

• It should relay 2-dimensional vector graphics for easyto-understand views with smooth screen and print 

display

In Practice

• It is written in C++ language with the Qt cross-platform application framework

• It uses the Sylvan C++ libraries to allow common file 

format and access to the Sylvan functions

We Also Followed the Following Principles: 

• Principle of least surprise—the user should not be 

surprised by the results of his or her actions. For 

example, if a user points to a tree object, then the user 

should get more information about that object. 

• Intuitively obvious—the function of an object should 

be what the user expects. 

Because we were calculating the internal character of 

the wood we used profile or taper equations to predict the 

diameter of the stem at any given height. These taper equations must be sensitive to crown dimensions to appropriately 

illustrate change in the internal structure of the stem as it 

is influenced by stand density and crown competition. All 

depictions of a tree’s vertical profile in Sylview are drawn 

with correctly scaled taper equations. The equations in the 

current version are based on the method of Walters and 

Hann (1986). The predicted wood-quality zones are based 

on the relationship of the wood to the crown at the time 

of wood formation. 

In the Sylvan Stand Structure model we want users to be 

able to learn about the relationship of tree competition (in 

both species and density) and crown size to the resultant 

wood formed in the tree. Additionally, we would like this 

model to be easily adapted to different tree species in different places in the world. To accomplish this, the model 

can be parameterized using data collected in the plot to 

be simulated.

Currently, there is a set of R functions that are used to 

accomplish this task. They are cumbersome and require a 

large number of steps to confirm that the parameters are 

appropriate and reasonable. We are in the early stages of 

developing an additional module that will process users’ 

plot data and produce a valid parameter file with statistical 

feedback on the nature of the selected parameters. 

We feel that the Sylview program allows a user to examine 

model output at a level of interactivity that was difficult until 

now. The design of Sylview was also focused on visualizing 

data in a manner that provides users with clear information 

about the stand they are studying. We opted for graphical 

forms that convey information versus images that present 

Figure 11— An example of the Sylview Program (Scott 2006). The 

stand illustrated is cherrybark oak (Quercus pagoda Raf.)-sycamore 

(Platanus occidentalis L.) from Arkansas, USA. This is a one-acre plot 

natural stand. The profile view displays the trees in the grey horizontal 

box in the map view. The highlighted tree in black at left is also displayed 

at right showing internal wood structure, individual tree crown over time, 

and the stem cross-section. The screen was running on the MacOS.

Figure 10— An example of the Sylview Program (Scott 2006). The 

stand illustrated is cherrybark oak (Quercus pagoda Raf.)-sweetgum 

(Liquidambar styraciflua L.) from Mississippi, USA. This is a one-acre 

plot plantation with alternating species in both directions. The profile 

view displays the trees in the grey horizontal box in the map view. The 

highlighted tree in black at left is also displayed at right showing internal 

wood structure, individual tree crown over time, and the stem crosssection. Also note that the tree-list data are displayed in the status bar at 

the bottom of the screen. This screen was captured under the Windows XP 

operating system.
FOREST GROWTH AND TIMBER QUALITY

10

confusing visuals. We tried to make the software intuitive 

and easy to use, with a lot information available and few 

hidden menus to navigate. The submenus are typically 

software-preference dialogs and are seldom changed. 

In our attempts to covey information we have provided 

model results using both traditional and innovative methods. Some of our traditional outputs include stand tables 

(stand statistics by diameter class), stock tables (stand 

statistics by species), and changes in the spatial statistics/

density management diagrams (both Reineke and Gingrich). 

Figures 8 and 9 illustrate this type of output. Please note 

that the stand and stock tables also report the volume in 

clear wood, mixed knot wood, and green wood. These 

zones are specified by the relationship of the ring of wood 

to the tree’s crown at the time of wood formation. 

CONCLUSIONS

The Sylview program is one program in the set of programs called the Sylvan Stand Structure model. It is a vital 

component allowing users to fully appreciate the complex 

stand-development simulation data generated by the other 

programs. It allows users to comprehend the relationship 

of crown size and stand density to wood quality and stem 

shape. We have several new components planned for Sylview 

including the addition of branch size and number predictions based of the work of Oswalt (2007). We also plan 

to develop a log-sort table that will break the trees in the 

stand into logs of various wood characteristics. The current 

version of Sylview also includes a method to conduct stand 

treatments in the user interface. However, this component 

was not implemented at the time of the meeting.

ACKNOWLEDGEMENTS

The Sylvan Stand Structure model is being calibrated to 

Southern Bottomland Hardwood through collaboration 

Figure 12— An example of the Sylview Program (Scott 2006). The 

stand illustrated is cherrybark oak (Quercus pagoda Raf.)-sweetgum 

(Liquidambar styraciflua L.) from Mississippi, USA. This is a one-acre 

plot plantation with alternating species in both directions. The profile 

view displays the trees in the grey horizontal box in the map view. The 

highlighted tree in black at left is also displayed at right showing vertical 

cumulative leaf area index from the top of the stand to the neighbor trees 

of the selected tree. This information is used in the crown base change 

function.

Figure 14— An example of the Sylview Program (Scott 2006). The 

stand illustrated is cherrybark oak (Quercus pagoda Raf.)-sweetgum 

(Liquidambar styraciflua L.) from Mississippi, USA. This is a standard 

density-management diagram of the model’s data from this plot.

Figure 13— An example of the Sylview Program (Scott 2006). The 

stand illustrated is cherrybark oak (Quercus pagoda Raf. )-sweetgum 

(Liquidambar styraciflua L.) from Mississippi, USA. This window is a 

standard stand table (average statistics by diameter class). Units are Dq in 

inches, BA in square feet per acre, and volume in cubic feet per acre. This 

table also provides the volume of clear wood, mixed knot wood, and green 

knot wood.
FOREST GROWTH AND TIMBER QUALITY

11

with the USDA Forest Service, Southern Research Station, 

Southern Hardwoods Laboratory, Stoneville, MS and the 

US Forest Service, Forest Inventory and Analysis, Southern 

Research Station, Knoxville, TN.

LITERATURE CITED

Assmann, E. 1970. Principle of Forest Yield. Study. 

In: The Constitution and Development of Stands. 

Pergamon Press: 88.

Davison, M. 1995. The Sylvan display program. Master’s 

thesis. University of Missouri-Columbia.

Gingrich, S. F. 1967. Measuring and evaluating stocking 

and stand density in Upland Hardwood forests in the 

Central States. Forest Science 13:38-53.

Larsen, D. 1991a. Projecting forest stand structures 

using stand dynamics principles: an adaptive 

approach. PhD thesis. University of Washington.

Larsen, D. 1991b. Silvicultural planning using a 

Bayesian framework. In: Buford, M., ed. 1991. 

Symposium on Systems Analysis in Forest Resources. 

United States Department of Agriculture: 262–267.

Larsen, D. 1994. Adaptable stand dynamics model 

integrating site-specific growth for innovative 

silvicultural prescriptions. Forest Ecology and 

Management 69: 245–257.

McGaughey, R. J. 1997. Visualizing forest stand 

dynamics using the stand visualization system. In: 

Proceedings of the 1997 Meeting of the American 

Society of Photogrammetry and Remote Sensing, vol. 

4: 248–257.

Oswalt, C. M. 2007. Development of a Simulation 

System for Testing Hardwood Plantation Silviculture. 

Unpublished Dissertation. University of Tennessee. 

Wayne Clatterbuck, Advisor.

Reineke, L. H. 1933. Perfecting a stand density index 

for even-aged forests. Journal of Agricultural Research 

46:627-638.

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Management. Unpublished Masters Thesis. University 

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Advisor.

Walters, D. K.; and Hann, D. W. 1986. Taper equations 

for six conifer species in southwest Oregon. Forest 

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Modeling 

Wood Quality

FOREST GROWTH AND TIMBER QUALITY

135

Modeling Wood Quality

Keynote Presentation

Modeling Wood Quality In the 

Context of Forest Management

S.Y. (Tony) Zhang

S.Y. (Tony) Zhang (tony.zhang@van.forintek.ca) is a senior scientist at FPInnovations—Forintek Division, 2665 East Mall, Vancouver, BC V6T 1W5, 

Canada.

ABSTRACT

AS THE FOREST INDUSTRY IN CANADA IS 

shifting toward intensive forest management and 

value-added wood manufacturing, it is becoming 

increasingly important to take an integrated approach along 

the forest-wood value chain in order to produce quality wood 

and wood products and maximize the value of the forest 

resource. As a result, Forintek has undertaken a series of 

studies in recent years to examine the impact of intensive 

forest management on wood and lumber properties and on 

product recovery in major commercial species in eastern 

Canada. Through these studies, tree-level models have 

been developed to describe key stem, wood, and lumber 

properties as well as product recovery in relation to tree 

and stand variables. Based on these studies, this paper 

reviews wood-quality modeling in the context of forest 

management. Following a review of important wood-quality 

attributes and their evaluation methods, this paper highlights wood-quality variation and manipulation through 

forest management and compares different approaches to 

wood-quality modeling. 

Editors’ note: The author elected not to provide a full paper 

for these proceedings because it was being submitted to a refereed journal. As with all of the keynote addresses, this presentation was designed to provide context for the related presentations that follow. In lieu of the keynote paper, the author’s slides 

from the presentation are reproduced on the following pages to 

introduce the topic for this section of the proceedings. 

This presentation was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. pp. 

135–143.
FOREST GROWTH AND TIMBER QUALITY

1

www.fpinnovations.ca

Modelling Wood Quality

in the Context of Forest 

Management

Tony Zhang, PhD

Senior Scientist and Group Leader

• What are important wood quality attributes

• Wood quality evaluation

• Wood quality variation and manipulation

• Wood quality modelling

Contents

What is wood quality?

• Foresters: mainly refer to external external stem

characteristics

• Manufacturers: attributes affecting wood

processing (e.g. sawing, drying, machining)

• End users:

1) structural 1) structural products (e.g. mechanical mechanical)

2) appearance-based products (e.g. surface) (e.g. surface)

What are important wood quality attributes?

S-950E

Any characteristics which affect the affect the wood

value chain are considered as wood quality

attributes

•Wood structure

• Juvenile wood

• Chemical composition

•Wood density

• Fibre morphology

• Branch growth

• Knottiness

• Visual aspect

Lumber volume/

dimension recovery

• Appearance

• Stability

•Machinability

• Durability

Lumber value Secondary products value

Pulp/paper

value

Strength/stiffness

stability

Lumber quality

• Tree taper

Silviculture Site GENETICS

Crown Structure / Development

• Tree diameter/ 

volume

SDM/Rotation Age Height Growth

What are important wood quality attributes?

S-950E

• Wood quality attributes include a number of

stem and stem and wood characteristics (both external external

and internal internal stem characteristics)

• Wood quality attributes vary with end uses
FOREST GROWTH AND TIMBER QUALITY

17

• Large diameter diameter: low conversion cost, high recovery

• Straight stem: high recovery, large , large dimension,high quality

• Small taper Small taper: high recovery

• Clear log/small knots: high quality

• No decay: low conversion cost, high quality and high recovery

• High wood density: high strength/stiffness

• Low juvenile wood%: stability, strength/stiffness

• No grain No grain deviationt deviationt/reaction wood: stability

Important wood quality attributes for structural lumber

• Long & thin-walled fibres: fibres: form dense sheets with smooth

surface, surface, high tensile strength

• Transverse dimension of fibres: Transverse dimension of fibres: paper properties

• Uniformity in fibre in fibre morphology: paper properties

• Low lignin % & high cellulose %: cellulose %: high yield, low cost

• High wood density: high yield

• Low extractives % & light extractives % & light colour: low cost

• Minimum defect: high yield, low cost

S-950E

Important wood quality attributes for pulp/paper

• Large and straight logs: high recovery

• Minimum taper: high recovery

• Attractive wood appearance: high quality

• No drastic difference between earlywood & latewood:

peeling, surface peeling, surface quality

• Moderate wood density:: easy peeling, peeling, processing

• Clear logs/minimum knots: high quality, low cost, high

recovery

• Minimum decay/other defects: low cost, high recovery

S-950E

Important wood quality attributes for panels

• Attractive appearance (colour, figure, surface , figure, surface 

roughness): quality

• Excellent Excellent dimensional dimensional stability: quality

• Defect-free: quality

• Good machinability: easy processing

• Durability: quality

• Uniformity: quality

S-950E

Important wood quality attributes

for secondary products

• For structural For structural lumber, piece size and size and wood strength should

be a priority priority

• For secondary secondary products products, piece size, appearance & stability stability

should be the focus the focus

• For fibre-based products products, fibre , fibre quality quality and wood density density

are important are important

Key quality attributes for major end uses

Aim at end-product product quality attributes rather

than intermediate wood attributes (e.g., wood

density for lumber)

Important quality attributes for major end uses
FOREST GROWTH AND TIMBER QUALITY

1

• What are important wood quality attributes

• Wood quality evaluation

Contents Ideal tools for wood quality evaluation

– Nondestructive

– Reliable

– Affordable

– Not time-consuming

– Ideally portable

Advanced methods for evaluating wood quality

– Ray-based methods

– Stress wave methods

– Ultrasonic methods

– Vibration methods

– Advanced microscopes

– Others (e.g., mechanical mechanical)

• Microscopes/image systems: microscopic, ultrastructural ultrastructural

features

• Fibre quality analyzer/Kajaani /Kajaani: fibre length & coarseness

• Fiber strucutre analyzer: fibre shape/cross sectional sectional

analysis

• CT Scanner/Micro CT: NDT systems for macro- and

microscopic features

• Silviscan: MFA, cell size

Methods for evaluating wood anatomical/chemical attributes

• Windendro/WinCell WinCell: ring/cell characteristics

• NIR spectrometry: chemical chemical composition, MFA, fibre & composition, MFA, fibre & 

wood mechanical mechanical properties

• X-ray diffractometry: MFA, ultrastructure

• Others

Methods for evaluating wood anatomical/chemical

attributes

• X-ray densitometry: wood density/ring characteristics

• Stress wave: wood stiffness

• Ultrasonic: physico-mechanical mechanical properties

• Vibration: physico-mechanical mechanical properties

Methods for evaluating physical/mechanical attributes
FOREST GROWTH AND TIMBER QUALITY

1

• NIR: wood density, strength/stiffness

• Silviscan: wood density, stiffness

• Computer Computer tomography (CT scanner CT scanner): macro

characteristics of wood/internal internal log

Methods for evaluating physical/mechanical attributes

S-1046

• Pilodyne: wood density of the rings of the rings nearby bark

• SilvaTest SilvaTest: MOE

• Resistograph: wood density

• Fibergene: MOE

• Etc.

Techniques for the NDT of standing trees

Real challenge is to develop more reliable, portable 

and cost-effective tools for the nondestructive

evaluation of standing trees!

• What are important wood quality attributes 

• Wood quality evaluation

• Wood quality variation and manipulation

Contents

• Silviculture

• Genetics

• Environment/site

• Processing

Sources of variation in wood quality

Clear log length

Knottiness

Stem taper

Sapwood%

Juvenile wood%

Bending properties

Ring characteristics and wood uniformity

Wood density

Sources of variation: silviculture
FOREST GROWTH AND TIMBER QUALITY

140

Chemical composition (e.g. lignin%)

Fibre length and MFA

Decay resistance

Wood density

Juvenile wood transition

Branchiness

Stem straightness

Sources of variation: Genetics

Occurrence of defects (decay, wetwood)

Wood color

Ring characteristics and wood uniformity

Sapwood%

Juvenile wood transition

Wood density

Sources of variation: Site

Wane

Grain deviation

Wood texture and figure 

Surface roughness

Dimensional stability

Sources of variation: processing

– Tree breeding

– Forest genomics

– Species selection

– Site selection

– Initial Initial spacing

– Thinning

– Pruning

– Fertilization

– Rotation age

Major management tools for wood quality

manipulation

• Focus on Focus on major heritable, internal internal quality traits: fibre

morphology, chemical chemical composition, composition, microfibril microfibril angle, decay

resistance, wood density, juvenile wood%, etc. %, etc.

• Pay attention to attention to external external quality traits: straightness and

branch characteristics

Wood quality manipulation by genetics

S-950E

Wood quality improvement by silviculture

Focus on Focus on external external quality attributes: Piece

size, clear log length,

branchiness/knottiness

Pay attention to attention to selected internal internal quality

attributes: sapwood%, juvenile wood%, ring 

characteristics, bending properties, wood density, 
FOREST GROWTH AND TIMBER QUALITY

141

It is important important that wood quality improvement improvement

target at end-product product quality attributes rather

than intermediate wood attributes (e.g., wood

density for lumber)

Wood quality improvement Comparing veneer density and MOE between two sites 

Veneer density distribution

0

20

40

60

80

100

120

140

160

180

0.250

0.270

0.290

0.310

0.330

0.350

0.370

0.390

0.410

0.430

0.450

0.470

0.490

More

Veneer density (g/cm3)

Frequency

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

CDF (% )

Valcartier (G)

St-Ignace (B)

Valcartier (G)

St-Ignace (B)

Veneer MOE distribution

0

10

20

30

40

50

60

70

80

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

More

Veneer MOE (million psi)

Frequency

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

C DF (% )

St-Ignace (B)

Valcartier (G)

St-Ignace (B)

Valcartier (G)

Source: Knudson et al. 2006

Comparing genetically improved white spruce veneer to 

those of other Species 

Veneer density

0

0.1

0.2

0.3

0.4

0.5

0.6

Aspen BC spruce Douglas fir White spruce

(Quebec)

Density (g/cm3

)

Veneer MOE

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

Aspen BC spruce Douglas fir White spruce

(Quebec)

Veneer M OE (M M psi)

Source: Knudson et al. 2006

• What are important wood quality attributes 

• Wood quality evaluation

• Wood quality variation and manipulation

• Wood quality modelling

Contents

• Empirical modelling

• Physics-based approach

• Process-based approach

Modelling Approaches to wood quality attributes

• Used to model most wood quality attributes 

such as

1) Wood density & other physical properties

2) Mechanical properties

3) Fibre properties

4) others

• But, most wood quaity attributes are stand typedependent, age-dependent, site-dependent.

1. Empirical Modelling Approach
FOREST GROWTH AND TIMBER QUALITY

142

black spruce lumber stiffness between plantations 

and natural stands

74% 74% 75%

of natural stands 

0

2000

4000

6000

8000

10000

12000

14000

Natural Stands

MOE (MPa)

S-1019

Plantations - Initial Spacing (m)

2.2 2.0 1.8

Source: Zhang et al. 2002

• Models for lumber properties of natural stands (Liu et al. 2007)

MOE = f (DBH, crown length, stem taper)

MOR = f (DBH)

• Models for plantation-grown lumber properties (Lei & Zhang 2005)

MOE = f (DBH, Crown length, stem taper)

MOR = f (DBH, crown length, crown width)

1. Empirical Modelling Approach

• Most wood quaity attributes are age-dependent.

While age can be taken into consideration for some 

attributes (e.g., wood density), it is difficult to 

incorporate age into the prediction models for some 

attributes (e.g. dimensional stability, bending 

properties)

• WD = f (cambial age, ring width, tree height)

1. Empirical Modelling Approach

• Some wood quaity attributes are also sitedependent. And we can not measure wood samples 

from various sites

1. Empirical Modelling Approach

• Relatively easy to develop and has some practical 

applications

• Difficult to integrate the empirical models into growth 

models

• Difficult to serve for forest management purposes

1. Empirical Modelling Approach Variation of selected wood characteristics due to site, 

diameter class and age in balsam poplar

14.3

0.0

12.1

73.6

11.5

0.0

9.8

59.5

370

75

135

59

2

4

4

59

Site

Diameter

Age 

Error

Decay (%)

13.5

0.0

31.6

54.9

171458

0

400954

695738

11779761

1527873

5717434

695738

2

4

4

59

Site

Diameter

Age 

Error

MOE (MPa)

42.6

11.5

11.6

34.3

0.933

0.253

0.255

0.751

22.84

4.56

2.72

0.75

2

4

4

59

Site

Diameter

Age 

Error

Sapwood 

thickness (cm)

48.9

0.0

2.8

48.3

262.5

0.0

15.2

260.4

6120

240

378

260

2

4

4

59

Site

Diameter

Age 

Error

Initial moisture

Content (%)

25.6

0.0

14.4

60.0

173

0

97

406

4776

489

1158

406

2

4

4

59

Site

Diameter

Age 

Error

Wood density

(kg/m3)

Variance V. C. (%)

components

Degree of Mean squares

freedom

Source of 

variation

Characteristics

Source: Zhang and Chauret 1999
FOREST GROWTH AND TIMBER QUALITY

143

• Used to model selected wood quaity attributes 

such as

1) Wood shrinkage and dimensional stability

2) Mechanical properties

2. Physics-based approach

• Physics-based modelling approaches 

essentially link the properties of the 

individual elements (e.g. cells, microfibrils) 

to the properties of a lumber piece using 

finite element analysis and other analytical 

methods

2. Physics-based approach

• Development of such physics-based 

models for physical and mechanical 

properties is technically complex and 

require micro/anatomical information

• Once developed and validated, they could 

be generalized with relative ease over a 

broad range of stands

2. Physics-based approach

• Used to model those wood quaity attributes 

related to crown structure and development 

such as:

1) sapwood content

2) knottiness

3) juvenile wood

3. Process-based Approach

• Applied to stands of different sites and ages

• Require more input variables which are more 

difficult to measure

3. Process-based Approach Development of integrated decision-support 

systems

Stands

Growth

models

DBH

distribution

models

Tree-level

parameter

models

Geometry

-based

modeling

Ecophysiologybased modeling

Qualitative

parameters

Quantitative

parameters

Product

recovery

Further research is needed

Silviculture

FOREST GROWTH AND TIMBER QUALITY

145

Resource Inventory for Conversion Modeling

Graeme Palmer and Jerry Vanclay

Graeme Palmer (woody@biltechnologies.net.au) is a doctoral student and Jerry Vanclay is professor and head, School of Environmental Science and 

Management, Southern Cross University, PO Box 157, Lismore, NSW 2480, Australia.

ABSTRACT

FOR ESTER S ROUTINELY ESTIM ATE THE 

economic potential of a standing forest resource as 

lumber. It is usual to consider the straightness and 

size of a tree to estimate gross recovery and the range of 

lumber products that might be produced. However, such estimates are usually subjective and depend on the knowledge 

and experience of the assessor. Several conversion modeling 

packages are available to assist with such appraisals, but these 

require an established library of log data, or require detailed 

and expensive log measurements. Fortunately, many tree 

attributes that influence lumber out-turn can be easily and 

objectively appraised, and these easy-to-measure attributes 

can be used to infer a larger suite of log characteristics.

This paper briefly describes a computer-based conversion 

modelling system that emulates components of a woodprocessing system and enables users to create a custom 

wood-processing facility producing lumber, veneer, or other 

products. It examines the attributes of trees that need to 

be quantified for such simulation to proceed, describes 

how routine timber cruising can record these details, and 

discusses how a user may modify these attributes to reflect 

different silvicultural regimes. It also describes the accounting module which enables detailed financial analysis 

of conversion strategies, and of the whole value chain. The 

system challenges forest managers to examine silvicultural 

options in a broader context, focusing not on a “better log”, 

but on creating more value in the lumber marketplace.

INTRODUCTION

Wood production in Australasia has undergone considerable 

change over the last 30 years as the wood-using industries 

convert from native forest to plantation-grown wood. 

Change continues with pace now as hardwood plantation 

production emerges and native forests are conserved free 

of harvesting.

Sawmills are the primary wood users and are becoming 

more exposed to global markets; they are, consequently, 

reducing margins. The importance of management has 

never been so critical, nor the impact of wood quality more 

important to achieving commercial goals.

It is the goal of both producer and processors to optimize 

the profitability of the industry. Therefore, management is 

mainly about manipulating the character of wood, the design 

of processes, and as far as possible the price of products.

 The problem that faces most managers is: How can resource quality be evaluated inexpensively so that different 

management scenarios can be compared? 

The parameters contributing to this analysis are:

• Available processing options 

• Market for products

• Average properties of clear wood and variation

• The presence and impact of defects

The important message from this discussion is that 

value, and therefore quality, is a “local” variable. That is, 

the resource produced in say Southeast Queensland needs 

to be different from wood grown in the Northwest of the 

United States.

This paper was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 145–150.
FOREST GROWTH AND TIMBER QUALITY

146

For sawn-wood processing, the primary process-efficiency parameters are the scope and variation of wood properties 

and defect distribution. The average values contribute most 

substantially to product price. Simulation is ideal for this 

kind of problem because the variety in the character of a 

wood resource can be accommodated sensibly.

Industrial optimization, in the context discussed here, 

requires a resource simulator and a process simulator. That 

is, a component that can create virtual stems and a component to convert these stems into virtual products.

The resource description component is the most difficult 

because of the level of detail required by product grading 

systems, and the apparently wide variation in the relevant 

quality parameters. Both these features need to be accommodated if simulation is to incorporate both finished-product value estimates as well as process-cost estimates.

Models and simulators of various types span the range 

of application from standing stems to finished product. 

For example: 

• Yield models are used extensively to program wood 

flows

• MARVL (NZFRI 1987) is an example of a system that 

provides yield by log quality classes

• CAPSIS and WinEPFN (Meredieu et al. 1999) are 

examples of simulators that combine yield or growth 

models with conversion simulators to provide estimates of processed product yield by value

• AUTOSAW (Todoroki 1990) is an example of a complex conversion simulator enabling optimization of 

saw pattern and grade recoveries using virtual logs 

that include knot defect information. This system has 

also been combined with production models to provide stand management optimization like WinEPFN

• GRASP (Occena and Schmoldt 1996) is a sawing 

simulator developed in the USA that uses sophisticated 3D solid-log representations with shape and defect 

derived from CT (computer tomography)

• SATECH (Saatech Systems Pty Ltd.) is a very simple 

saw pattern simulator that uses log sizes and minor 

variations in shape to optimize recovery

• WOODEYS SIM (Innovative Vision) is a docking 

simulator that can provide product yields by quality 

class from board character inputs collected by a scanner/docker system

In the view of the author, if these systems are considered 

in the context described above, potential problems exist 

that include:

• The localized nature of detailed resource character 

and process design inputs

• Limited breadth of resource characters that are supported by simple systems

• The high cost of detailed data such as provided by 

computer-aided tomography 

Additionally, for many potential users, data and or models that describe stem features may not be available, e.g., 

growth and taper functions, knot models, density models, 

etc. For these users, inventory and general and known 

statements of correlation between stem characters are the 

only sources of input data.

In Queensland, the public wood producer has attempted 

to solve these problems by adapting WinEPFN to local 

parameters. This required a significant rebuild of the 

system to incorporate local models and grade rules which 

are “hard coded”.

What is needed is a broadly applicable software system 

that can be used to define or describe detailed stem characteristics for a virtual resource using whatever input data 

that can be assembled easily and/or cheaply. In particular, 

the use of standing resource inventory data offers the best 

opportunity to capture local resource character. 

A software system such as this could be applied to a 

variety of problems; for example, resource valuation, strategic planning of merchandising processes, and process 

design optimization to name a few. The application of such 

a system may also be widened if data can be manipulated 

by “skilled” users to reflect novel stands that may be the 

objective of breeding or silviculture.

INVENTORY DATA

For the purpose of developing and now demonstrating the 

operation of the system, the following inventory data were 

gathered to describe stems.

• Diameter at breast height and total tree height

• Taper formed from height and diameter

• Stem form assessed by measuring the height of each 

bend in the measured stems, the direction of the bend 

measured by compass, and the deviation of the bend 

from straight estimated as a proportion of stem diameter at the bend node

• Crown assessed by locating points in the stem that 

correspond to the bottom of the growing crown 

(identified by the lowest dead branch) and the bottom 
FOREST GROWTH AND TIMBER QUALITY

147

of the live crown (identified as the branch node above 

the lowest dead branch)

o At each point on the stem, a collection of local 

branch nodes assessed—the number of branches, 

along with the size and the direction of each 

branch was recorded (branch size estimated by eye 

as a proportion or percent of stem diameter at the 

point of branch location)

While this format was implemented here, the system 

was designed to accommodate any format adopted by the 

user.

The important point to be made is that the nature of 

the inventory is not limited and, in practice, more detailed 

and expensive data collection can be accommodated with 

the obvious advantages of accuracy and detail that can be 

achieved through a more complex inventory.

A Resource Maker

The system described here attempts to meet the goal of 

generic application.

The system includes:

• An abstract data structure that describes a stem including all the characteristics that a user 

or application demands

• Tools to read data of various types 

• Tools to display and manipulate data

• Tools to make new simulated data

• A tool to display the stems

An important concession is made in the 

design of the system in order to maintain 

reasonable cost and accessibility. A virtual 

stem of sufficient complexity to represent the 

characteristics that define product value is 

assumed to be resolved by a collection of 3D 

forms located in Cartesian space. These forms, 

in turn, are described by simple mathematical 

expressions.

The principle reason for making this concession is that any stem may be stored more 

efficiently within a computer as a collection 

of expressions rather than as a 3D-matrix or 

raster of point data values. The latter requiring large amounts of computer memory, e.g., 

1m3 resolved to 1mm3 units equals 109 bytes 

potentially.

Finally, a sawmill simulator is also under 

development that will convert virtual stems 

to product grade by recovery data. It is the resource maker 

that is the focus of this document.

The Data Type “Stem”

At the center of the system is the abstract stem data type. 

This data type must be designed to accommodate all of the 

usual features of a stem that might impact either conversion 

cost or product grade and recovery. The design also needs 

to accommodate expansion so that other features may be 

accommodated as a given simulation context requires.

The user can define any additional variables to add to the 

data structure, and this feature is used to accommodate any 

wood-quality variable the user wishes to add. For example, 

microfibril angle or heart/sap wood.

The data structure includes the following types:

• values—single value data

• functions—a mathematical expression that solves to 

produce value of y for all x

• sequences—a sequence is a series of values or sequence members that describe characteristics that 

may be correlated between members; for example, the 

distances between branch nodes will be correlated to 

Table 1—The stem data structure.

Attribute or Sub-attribute Type of Entry

Age single value

BHt single value

DBH single value

THt single value

Growth = Function of age

GHt [f (GAge)] expression

GDia [f (GAge)) expression

GAge single value

Form = Sequence of Bends

 Bend = BndHt

 BndDir

BndDev

BndFrm

single value

single value

single value

expression

HForm = Function of Direction

Radius expression

Taper = Function of height

TprDia [f (TprHt)] expression

TprHt single value

Bark = Function of height and direction

BrkHt single value

BrkThk [f (BrkHt)] expression

Crown = Probable sequence of Branch Nodes

 Branch Node = Node Ht, Array of Branches

 Branch = BrDia

 BrDir

 BrAng

 BrGnl

 BrDdl

 BrFrm

single value

single value

single value

single value

single value

expression

Wood Properties = Array of Wood Property

 Wood Property = f (Age) expression
FOREST GROWTH AND TIMBER QUALITY

148

the distance between previous branch nodes

• probable sequences—similar to a sequence except that 

the input data relating to a sequence is a census for 

any single tree while data for a probable sequence are 

in samples; these types vary the manner in which the 

system treats them during resource design

During run time, two data structures are formed and 

utilized by the system. One structure is formed for input, 

and a second is formed as the simulated stems. In practice, 

the user enters data via the input structure, and then uses 

tools to create the simulated structure.

Data Input Tools

Data that can be utilized by the system include both numeric values and expressions. To accommodate the input 

of numeric data, the system includes an input file format 

designer, and a reader. The capacity to design input files 

enables the reading of any data file for any feature of the 

stem.

Input is assumed to be hierarchical. For example, for 

the following data structure,

VarA, ArrayA

ArrayA = VarB, ArrayB

 ArrayB = VarC, VarD

the input file will be arranged as a series of values as 

follows: 

VarA1.

 VarB11

 VarC111, VarD111

 VarC112, VarD112

 VarC113, VarD113;

 VarB12

 VarC121, VarD121

 VarC122, VarD122

 VarC123, VarD123;;

VarA2.

 VarB21

 VarC211, VarD211

 VarC212, VarD212

 VarC213, VarD213;

 VarB12

 VarC221, VarD221

 VarC222, VarD222

 VarC223, VarD223;;;

The system interface is shown in the following figures. 

The upper dialog window in Figure 1 shows the data form 

through which the user defines DBH and total height, then 

opens a new form (lower dialog window) to enter data for 

the bend height, bend size, and bend direction of each 

bend within the stem.

The Function Design Tool

To accommodate input of functions, an interpreter is included within the system that can read and interpret functions (input as typed text) that may then be attached to data 

items. An analogy may be drawn with “macros” used in 

numerical analysis software such as spreadsheets. Figure 2 

shows the function panel and an example expression defining growth in diameter at breast height as a function of age. 

This function has been formed by fitting a curve provided 

by the system of input data, by least squares. This approach 

or an external user-defined function may be used.

The Chart Tool

A data-charting module provides the user with data display 

capacity to view the manner in which variables are related. 

The chart tool also provides the interface for the “make” 

tools mentioned below.

Figure 1: The input format definition panel. At level 1 (upper dialog 

window), diameter at breast height (DBH) and total height (THt) are 

defined. Then, the user accesses level 2 by clicking the “Form” button. This 

opens the lower dialog window through which the stem form is defined 

by entering, for each bend in the stem, the bend height (BndHt), bend 

deviation (BndDe), and bend direction (BndDir).
FOREST GROWTH AND TIMBER QUALITY

149

“Make” Tools

At the core of the system is a set of tools that are designed 

to “make” data values or functions for simulated stems 

from input data or functions generated from real stems. 

The make tools include:

• Making single values 

• Making functions

• Making sequences and 

• Making probable sequences

Each uses the same general approach which is:

• Input data values are used to determine variability 

around an average value.

• This variation is used to select a simulated value either 

at random or biased to reflect a normal distribution 

in the input data. A further bias is applied to cause 

the make process to tend toward producing the same 

variability in the simulated data as is displayed by 

input data, i.e., the next value made will be selected to 

maintain the variance described by the input.

• Sequences are made from individual member data sets 

in sequence.

• Probable sequences use the average and variance of 

samples taken from the range of an independent variable to make simulated values.

Figures 4 and 5 illustrate the use of the “make” tools. 

Figure 4 shows the process through which one of the tools 

is used to define growth curves that display the development of simulated tree stems over time. Figure 5 illustrates 

the result of the “make” process for a specific example. The 

input values are shown by curves connecting light-colored 

points and the simulated growth curves are those connecting the black points.

The Display

Finally, a display tool is provided within the resource maker 

to visualise virtual stems. In Figure 6, profiles are displayed 

of a simulated stem showing the stem surface (upper image) 

and a cross section of wood density (lower image). Note that 

Figure 2. The function input panel.

Figure 3: The data-charting panel showing input and simulated data 

values for inter-bend distance versus height in the stem.

Figure 5: A display of input (curves connecting the light-colored points) 

and simulated (curves connecting the black points) growth curves for the 

first five stems of the input and simulated data sets.

Figure 4. Using the “make” tools to form growth curves for simulated 

stems.
FOREST GROWTH AND TIMBER QUALITY

150

in the stem-surface image, darker shading denotes bending 

into the image, giving information in the third dimension. 

For the wood-density image a simple relationship with 

diameter is displayed in only two dimensions.

Concluding Remarks

This discussion and demonstration have shown how the 

system may be applied to almost any application context 

that might arise. The system offers capacity for any user to 

exploit any form of input to create virtual 3D representations of tree stems that can be manipulated in Cartesian 

space by a conversion simulator.

While the system is fundamentally complete, minor 

developments continue to build a more robust system. In 

the next stages, the distribution of knots will be added to 

the system and display.

The system remains untested in any practical sense, 

however, and this is the subject of work that will go on over 

the next 3 years, using eucalypt hardwood plantations as 

the test environment.

The sawing simulator that is required to partner with 

the resource maker is also under development. The design 

of this system is similar to the resource maker in that it 

attempts to provide a design platform which would enable 

the user to design both saw patterns and the sequence of 

process stations that comprise process design. In this way, 

the system will attempt both to define product-grade volumes that form output and to estimate material flow rates 

and machine productivity.

Figure 6: The display tool showing stem surface over bark (upper image) 

and cross-sectional variation in wood density (lower image).

LITERATURE CITED

Occena, L.; Schmoldt, D. 1996. Grasp: A prototype 

interactive graphic sawing program. Forest Products 

Journal 46(11/12):40-42.

Meredieu C.; Dreyfus P.; Saint-André L. ; Leban 

J.M. 1999. A chain of models from tree growth to 

properties of boards for Pinus nigra ssp. laricio Arn.: 

Simulation using CAPSIS and WinEpifn. In : Nepveu, 

G., ed. Workshop on Connection between Silviculture 

and Wood Quality through Modelling Approaches 

and Simulation Software, Proceedings of the IUFRO 

5.01.04 workshop held at La Londe-Les Maures, 

France, 5-12 Sep 1999. Nancy, France: INRA: 505-

513.

NZ Forest Research Institute. 1987. Stand assessment 

by log grades using MARVL. FRI Bulletin 132. 

Rotorua, New Zealand.

Todoroki, C.L. 1990. Autosaw system for sawing 

simulation. New Zealand Journal of Forestry Science

20(3):332-348.
FOREST GROWTH AND TIMBER QUALITY

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Maximizing Benefits from Oval Logs Using 

Geometric Modeling with Finite Precision

Christine L. Todoroki, Robert A. Monserud, Dean L. Parry

Christine L. Todoroki (Christine.Todoroki@scionresearch.com) is a senior scientist, New Zealand Forest Research Institute Limited, Private Bag 3020, 

Rotorua, New Zealand; Robert A. Monserud (retired) was a research forester and team leader and Dean L. Parry (retired) was a research forester, USDA 

Forest Service, Pacific Northwest Research Station, PO Box 3890, Portland, OR 97208, USA.

ABSTRACT

OVER THE YEARS SAWMILLERS HAVE BY

 by trial and error determined the most advantageous way to improve recovery from their logs. 

For elliptical shapes, primary sawing along the longer axis 

has generally been accepted as the “correct” method. To 

verify this, we applied a series of sawing simulations to 

five replicate groups of oval logs, modeled from measurements of 52 western hemlock logs. Ovality of each group 

was controlled through transformations that progressively 

altered cross-sectional shape while maintaining constant 

log volume. The log models were sawn in a series of simulations with AUTOSAW that altered log orientation, elliptical 

representations, and error bounds. Log orientation was 

altered by 5-degree increments. At the 0-degree orientation 

(and at 180 degrees) logs were sawn with the primary saw 

parallel to the shorter axis, and at 90 degrees (and 270 degrees) were sawn “correctly” along the longer axis. Angular 

orientations yielding the maximum percentage of lumber 

volume to log volume were recorded. Maxima, rather than 

averages were of primary interest due to the closer alignment with sawmillers’ requirements. Contrary to common 

belief, oval logs tended to produce more lumber than round 

logs—when rotated to their optimal orientation. Moreover, 

maximum responses tended to increase with increasing 

ovality. Maxima occurred more frequently at 90 degrees and 

270 degrees. Because of the finite precision implementation, 

round-off errors were prevalent within proven geometric 

algorithms. Increasing the number of co-ordinates in the 

elliptical representations and increasing the error bound 

on numerical comparisons did not eliminate, but shifted 

the problem. Our ability to isolate round-off errors through 

visualization of the various stages, track back to individual 

boards, and add seemingly insignificant amounts of wane 

(0.004 inch) enabled us to overcome limitations due to 

finite precision arithmetic. 

KEYWORDS: Log eccentricity, sawing simulation, conversion, yield, geometric algorithms, computational precision

INTRODUCTION 

In spite of the myth that logs are round, oval logs are more 

common than truly circular shapes (Matérn 1956). Ovality 

tends to be greater for larger logs and for those logs from 

the lower parts of the stem (Asikainen and Panhelainen 

1970, Williamson 1975, Singleton et al. 2003). If ovality is 

described by an ellipticity ratio, defined as the inverse ratio 

of the largest diameter to that perpendicular to it (Figure 1), 

then truly circular logs would have the maximum possible 

ellipticity ratio of 1.0 and oval logs would have an ellipticity 

ratio of less than 1.0. 

The ellipticity ratio of log cross-sections typically lies 

between 0.80 and 1.00. Williamson’s (1975) mean and 

standard deviation for Douglas-fir out-of-roundness corresponds to our ratios of 0.83 and 0.97, and Monserud’s 

(1979) to 0.945 with a standard deviation of 0.04. Kellogg 

This paper was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 151–155.
FOREST GROWTH AND TIMBER QUALITY

152

and Barber (1981) found that the mean ratio (albeit not 

perpendicular) for western hemlock was 0.92, ranging from 

0.85 to 0.96. Biging and Wensel (1988) reported an overall 

mean of 0.94, from which a sub-sample of 45 disks had a 

mean of 0.91 and range of 0.77 to 0.98. Ellipticity ratios 

between 0.82 and 0.94 were found for lodgepole pine (Koch 

et al.1990), and for Norway spruce Saint-André and Leban 

(2000) recorded a mean of 0.94 with the most extreme ellipticity ratio being 0.72. 

Ovality is often perceived as being detrimental to sawn 

lumber recovery. Skatter and Høibø (1998) state that “any 

deviation in shape from circularity will normally reduce the 

yield” while Saint-André and Leban (2000) state concern 

“about the loss in yield due to the non-circular external 

log’s shape” in citing Skatter and Høibø (1998). Skatter and 

Høibø’s findings are, however, based on “mean simulated 

main yield” where “main yield” refers to yield from a central 

block within the log and ignores the contribution of side 

boards. In considering yield from both side boards and cant 

boards Asikainen and Panhelainen (1970) found that yield 

from oval logs depended on how the log was oriented relative 

to the saws. They found that when the log was sawn in its 

“correct” position, with the smaller radius perpendicular to 

the primary saws (equivalent to the longer axis being parallel to the primary saws), and with its volume determined 

on the basis of the minimum diameter, that “the sawing 

yield of an oval log is better than that of a round log of the 

same size”. Furthermore “when sawing is carried out in the 

wrong position, the opposite applies”.

The effect on value recovery, due to ovality, has been 

investigated by Maness and Donald (1994). They found 

that although ovality caused significant reductions in value, 

significant benefits were gained with the optimal rotation of 

logs. They also found the benefits were more highly related 

to cross-sectional eccentricity than to log sweep.

We test the assumption that ovality is detrimental to 

lumber yield, and test the hypothesis that the best sawing 

position is as described by Asikainen and Panhelainen 

(1970). Our primary interest is with maximum responses 

with respect to log rotation because they correspond to 

logs rotated for optimal lumber yield. Our secondary interest is with finite precision arithmetic, data representation 

and error bounds, and the contribution of these factors to 

solution accuracy.

METHOD

The assumption and hypothesis are tested using sawing 

simulation with AUTOSAW (Todoroki 1990, 1997). The 

sawing simulator is based on geometric algorithms and, 

due to computer implementation, finite precision arithmetic 

(Higham 2002). Given that “a finite precision implementation of a proven geometric algorithm is not necessarily correct; 

because of round-off error” (Milenkovic 1988) we test three 

methods for improving accuracy by 1) increasing the 

number of discrete data representing cross-sectional shape, 

2) increasing the error bound in numerical comparisons, 

and 3) increasing the error bound on isolated numerical 

comparisons with known round-off errors. 

Log Models

Five groups of 52 digitized logs ranging from circular 

cross-sections (control) to those with ovality of 0.80 (in 

decrements in the ellipticity ratio of 0.05) were modeled 

from a sample of 52 measured western hemlock logs. The 

52 logs comprised a range of small-end diameters, tapers, 

and volumes. Logs within the control group were modeled 

with circular cross-sections; the other four groups had 

progressively more elliptical cross-sections. Each oval log 

replicate had a cross-sectional area and volume identical to 

the corresponding circular log. The format of the log models 

was compatible with AUTOSAW log model input format, 

Figure 1— Definition of the ellipticity ratio as the inverse ratio of the 

largest diameter to that perpendicular to it.
FOREST GROWTH AND TIMBER QUALITY

153

thus cross-sections were represented using ordinates (xc

, 

yc, zc) to represent the geometric center, and polar notation 

(r1, r2, θ) to represent the semi-major and semi-minor axes, 

r

1 and r2, and the angle of the ellipse to the horizontal, θ.

Sawing Simulation

The log models were processed in the AUTOSAW sawing 

simulator using a cant sawing pattern, cutting lumber that 

was primarily of 2-inch nominal thickness, between 4 and 

12 inches wide, and tallied in 1-ft increments. The primary 

saw had a 0.14 inch kerf while that at the edger was 0.18 

inch. A secondary thickness of 1 inch was also allowed. 

Lumber was edged and trimmed to remove wane. Thus the 

full extent of the effect of ovality on yield, defined as the 

percentage of lumber to log volume and known alternatively 

as “conversion”, could be examined.

The sawpattern described above was repeatedly applied 

in a series of simulations that altered log orientation, elliptical representations, and error bounds. At the initial 

orientation of 0 degrees, the primary saw was parallel to 

the minor axis of the elliptical cross-sections and the cant 

processed in a perpendicular direction (Figure 2) while at 

90 degrees (and 270 degrees) logs were sawn “correctly” 

along the longer axis. Logs were rotated and sawn in 5-degree increments allowing conversions to be tracked across 

rotations. Thus rotations at which maximum conversion 

occurred could be identified.

Elliptical representations of cross-sectional shape, used 

within geometric algorithms in AUTOSAW, were modeled 

by a number of discrete (x, y) co-ordinates. In the first series 

of simulations the number of co-ordinates was set to 30, 

and in a second series the number was increased to 72. In 

both of these simulation series an error bound, ε, equal to 

the available computational precision, 10-12, was used in 

numerical calculations. The following simple numerical 

procedure that repeatedly divides a variable, u, by 2, starting from 1 until no difference is encountered, was used to 

calculate the error bound on computational precision, ε:

 u = 1

 while 1 + u > 1

 ε = u; u = u/2

 end;

In a third series of simulations the error bound was 

increased to 10-3 (while maintaining the number of coordinate pairs per ellipse at 72), effectively allowing an 

additional 0.001mm on measurement calculations. Within 

each series a total of 18,720 automated simulations were 

performed: 72 rotations x 52 logs x 5 ovality groups. 

In a final set of sawing simulations AUTOSAW was invoked interactively, rather than in an automated fashion as 

in the previous simulations. Only those boards with known 

floating point errors, detected through analyzing the results 

for disparities, were re-sawn. For the circular logs, in the 

absence of floating point errors, log to lumber conversions 

were expected to be identical for all rotations. For elliptical logs, conversions across the range of orientations were 

expected to display symmetry, due to the symmetry of 

the log shape and consistency of all sawing factors. Logs 

with conversions that deviated from these expectations 

were identified and the rotational setting of the disparity 

recorded. The disparity was then tracked back to the individual board by re-invoked AUTOSAW with the sawing 

simulation history (binary) file. The board was then un-cut 

(a feature of AUTOSAW that enables cuts to be un-sawn), 

the wane tolerance changed from 0.0 to 0.1mm (0.004 inch), 

and then re-cut, invoking the same cutting algorithms as 

called for in the automated simulations. 

Analysis

Simulated board dimensions were summarized by log, 

orientation, and ovality and combined into datasets that 

also incorporated log volume and diameter information. 

Microsoft Excel® was used to calculate conversions. Normalized responses were calculated by dividing through 

by the corresponding circular log’s response at the initial 

orientation. In this way any effects due to differing log sizes, 

shapes, and branching configurations were eliminated. 

SAS® (1999) was used to analyze the data, calculate confidence intervals (CI), and test for significant differences 

between means using 95 percent confidence levels. Floating 

point errors were detected through comparison of converFigure 2— Initial (0-degree) and 45-degree orientations, with 

conversions, of a log with an ellipticity ratio of 0.80.
FOREST GROWTH AND TIMBER QUALITY

154

sions. For circular logs, conversions at 

adjacent angles were compared, while 

for elliptical logs conversions that had 

been generated with equivalent planes 

of symmetry were compared, e.g., all 

conversions at 5 degrees from horizontal 

(5 degrees, 175 degrees, 185 degrees, 

and 355 degrees).

RESULTS

Floating point errors were detected amongst some of the 

simulated boards. In the initial scenario with ε = 10-12 and 

30 co-ordinates per cross-section, about 60 of the 22,000 

simulated boards per ovality group were sawn incorrectly 

due to floating point error. Neither increasing the number 

of points on the elliptical cross-sections nor increasing the 

error bound from 10-12 to 10-3 eliminated the problem. There 

was, however, a reduction in the number of affected boards 

(to about 50 per 22,000 per ovality group), and a shift to 

different boards. It was only through manual intervention, 

through changing the wane tolerance, that the remaining 

floating point errors were corrected. After correcting the 

floating point errors the following results were obtained.

Orientation for Maximum Log to Lumber 

Conversion

Overall, the 90-degree and 270-degree rotations provided 

the best orientations for placing oval logs (Figure 3) with 

about 60 percent of logs recording maximum conversions 

at those angles. At 0 degrees and at 180 degrees, nearly 

40 percent of those logs with ellipticity ratio 0.80 also recorded a maximum. For circular logs, conversion remained 

constant over all angles. 

Effect of Increasing Ovality on Conversion

Normalized maximum conversions due to oval logs were 

greater than those due to circular logs (Table 1). For the 

least oval set with an ellipticity ratio of 0.95, maximum 

conversion was greater than the circular set by an average 

of 2.1 percent (95-percent CI: 1.4–2.9 percent). For the 

most oval set with an ellipticity ratio of 0.80, conversion 

exceeded that of their circular counterparts by an average 

of 3.2 percent (95-percent CI: 1.1–5.3 percent). 

Increased conversions at the optimal orientation with 

greater ovality can be seen through the logarithmic regression trends with log small-end diameter (Figure 4).

SUMMARY

Floating point errors were detected through observing 

small deviations from the expected flat response across 

rotations for circular logs, and through observing small 

deviations from the expected symmetry for oval logs. The 

occasional small differences of the order of 10-5 were caused 

through finite precision arithmetic and discrete, rather 

than continuous, data representations. These seemingly 

insignificant differences, arising from proven algorithms 

for determining the intersection between the plane of the 

Figure 3— Frequency distributions by ellipticity ratio showing percentage 

of logs attaining maximum conversion at each orientation.

Figure 4— Logarithmic regressions demonstrating the relationship 

between maximum conversion and log small-end diameter by ellipticity 

ratio.

Table 1—Mean, standard deviation, and 95% confidence intervals for the normalized 

maximum conversions by ellipticity ratio. Comparisons are between the oval (ratio < 1.00) 

and circular (ratio = 1.00) log sets.

Ellipticity ratio Sample mean Standard deviation Confidence interval

0.0 1.02 0.07 .011 – .053

0.85 1.01 0.0 .014 – .048

0.0 1.034 0.057 .01 – .049

0.95 1.021 0.02 .014 – .02

1.00 1.000 0.000
FOREST GROWTH AND TIMBER QUALITY

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saw and the log cross-section, resulted in a differing board 

width being fitted to the piece. In an attempt to eliminate 

the differences, simulations were rerun with error bounds 

increased from the bound for computational precision, 10-

12 to 10-3, and the number of points generated per ellipse 

increased from 30 to 72. This did not completely eliminate 

the problem although there was a small reduction in the 

number of affected pieces and a shift in affected pieces. 

Thus those affected pieces (about 50 amongst the 22,000 

simulated for each log ovality group) were manually corrected by re-edging with a small allowance for wane (0.1 

mm or equivalently 0.004 inch).

Floating point errors are likely to be inherent in any 

application that performs calculations and numerical comparisons. Because these seemingly insignificant errors can 

affect results, thorough validation procedures are needed 

to detect, isolate, and correct any anomalies. 

Ovality was found to be beneficial to lumber yield, when 

the log was rotated to its optimal position. The increase 

was of the order of 2–3 percent. As a rule of thumb, the 

best rotation is as described by Asikainen and Panhelainen 

(1970), with the primary saw parallel to the major axis 

of the elliptical cross-section and the cant processed in a 

perpendicular direction.

LITERATURE CITED

Asikainen, K.; Panhelainen, A. 1970. Tukin soikeuden 

vaikutus sahaustulokseen. (The effect of the ovalness 

of the log on the sawing yield). (in Finnish with 

English summary). Papper och Trä 6: 395-402.

Biging, G.S.; Wensel, L.C. 1988. The effect of 

eccentricity on the estimation of basal area and basal 

area increment of coniferous trees. Forest Science 34: 

621-633.

Higham, N.J. 2002. Accuracy and stability of numerical 

algorithms. Second edition. Society for Industrial and 

Applied Mathematics, Philadelphia. 710 p.

Kellogg, R.M.; Barber, F.J. 1981. Stem eccentricity in 

coastal western hemlock. Canadian Journal of Forest 

Research 11: 714-718.

Koch, P.; Côté W.A. Jr.; Schlieter, J.; Day, A.C. 1990. 

Incidence of compression wood and stem eccentricity 

in Lodgepole Pine of North America. Res. Pap. INT420. Ogden, UT: U.S. Department of Agriculture 

Forest Service, Intermountain Research Station. 42 p.

Maness, T.C.; Donald, W.S. 1994. The effect of log 

rotation on value recovery in chip and saw sawmills. 

Wood and Fiber Science 26(4): 546-555.

Matérn, B. 1956. On the geometry of the cross-section of 

a stem. Meddelanden Från Statens Skogforsk 46(11), 

28p.

Milenkovic, V.J. 1988. Verifiable implementations of 

geometric algorithms using finite precision arithmetic. 

Artifiical Intelligence 37: 377-401.

Monserud, R.A. 1979. Relations between inside and 

outside bark diameter at breast height for Douglasfir in northern Idaho and northwestern Montana. 

Res. Note. INT-266. Ogden, UT: U.S. Department of 

Agriculture Forest Service, Intermountain Research 

Station. 8 p.

SAS Institute Inc. 1999. SAS Institute Inc. 1999. SAS 

OnlineDoc®, Version 8, Cary, NC: SAS Institute Inc., 

USA.

Saint-André, L. ; Leban, J.-M. 2000. An elliptical model 

for tree ring shape in transverse section. Methodology 

and case study on Norway spruce. Holz als Roh- und 

Werkstoff 58: 368-374.

Singleton, R.; Debell, D.S.; Marshall, D.D.; Gartner, 

B.L. 2003. Eccentricity and fluting in young-growth 

Western Hemlock in Oregon. Western Journal of 

Applied Forestry 18(4):221-228.

Skatter, S.; Høibø, O.A. 1998. Cross-sectional shape 

models of Scots pine (Pinus silvestris) and Norway 

Spruce (Picea abies). Holz als Roh- und Werkstoff 56: 

187-191.

Todoroki, C.L. 1990. AUTOSAW system for sawing 

simulation. New Zealand Journal of Forestry Science 

20(3):332-348.

Todoroki, C.L. 1997. Developments of the sawing 

simulation software, AUTOSAW: Linking wood 

properties, sawing, and lumber end-use. In: 

Proceedings of the Second Workshop “Connection 

between Silviculture and Wood Quality through 

Modelling Approaches and Simulation Softwares”. 

Ed. G Nepveu, INRA-Nancy, France IUFRO S5.01-04, 

South Africa, August 26-31, 1996: 241-247.

Williamson, R.L. 1975. Out-of-roundness in Douglas-fir 

stems. Forest Science 21(4): 365-370.

FOREST GROWTH AND TIMBER QUALITY

157

Predicting Lumber Grade and By-Product Yields 

for Standing Scots Pine Trees

Henna T. Lyhykäinen, Harri Mäkinen, Annikki Mäkelä, Arto Usenius

Henna T. Lyhykäinen (henna.lyhykainen@helsinki.fi) is a doctoral student in the Department of Forest Economics, P.O. Box 27, FI-00014 University of 

Helsinki, Finland; Harri Mäkinen is a researcher at the Vantaa Research Centre, Finnish Forest Research Institute, P.O. Box 18, FI-01301 Vantaa, Finland; Annikki Mäkelä is a professor of silviculture (forest production) in the Department of Forest Ecology, P.O. Box 27, FI-00014 University of Helsinki, 

Finland; Arto Usenius is a research professor at the VTT Technical Research Center of Finland, P.O. Box 1806, FIN-02044 VTT, Finland.

ABSTRACT

THE PURPOSE OF THIS STUDY WAS TO 

develop models for estimating yields and grades 

of lumber, as well as by-products, of individual 

Scots pine (Pinus sylvestris L.) stems using stem and crown 

dimensions as explanatory variables. The process-based 

growth model, PipeQual, which provides information about 

stem form and branch properties, was used to generate the 

material for analysis. The model was used to predict the 3D 

structure of Scots pine stems in thinning regimes of varying 

intensity and rotation periods. The generated stems were 

sawn using the WoodCim sawing simulator and the yields 

and grades of the individual sawn pieces, as well as by-products, were recorded. The sawn timber was classified on A, 

B, C and D-grades for side and center boards separately (in 

accordance with Finnish export rules). By-products were 

pulpwood, sawmill chips, sawdust, and bark.

The response variables were formulated as cumulative 

proportions of the total volume of each stem. Logistic 

regression models were fitted to the data, and the best 

combination of the explanatory variables was found to be 

living crown height and the natural logarithm of diameter 

at breast height. The models were tested against simulated 

sawing of actual measured Scots pine stems and predictions 

for larger stems were found to be more biased than those 

used in model building.

The developed approach integrates wood production 

and the conversion chain. The models can be used in 

stand management optimization for comparing different 

management options, e.g., on a value-added basis from the 

sawmill’s point of view.

KEYWORDS: Pinus sylvestris, timber products, product 

recovery, process-based growth model, sawing simulations 

INTRODUCTION 

Scots pine (Pinus sylvestris L.) timber is essential raw material for the Finnish mechanical wood industry; two-thirds 

of the forested area of Finland is pine-dominated, and pine 

sawn-goods alone represent one percent of the value of the 

total export in goods (Finnish Statistical 2006). During the 

last few decades the share of pine stands has increased, and 

there has been much public debate regarding whether or 

not wood quality has deteriorated in the end-users’ point 

of view. 

The number, type and size of branches are important 

determinants of grading of Scots pine logs (Heiskanen 1965, 

Uusvaara 1985, Uusitalo 1997). Both statistical (Colin and 

Houllier 1992, Roeh and Maguire 1997, Mäkinen et al. 

2003) and mechanistic models (Mäkelä 2002) have been 

developed to predict branch dimensions along the stem. 

The branch models, with the growth model, have enabled 

predictions of the 3D structure of trees and logs. Since the 

structure can be described in detail, stems can be viewed 

and processed virtually. However, detailed 3D information 

on tree and log properties is often unnecessarily detailed 

for economical analysis based on timber utilization. Prediction of wood-quality distribution of raw material, without 

detailed 3D description and conversion simulations, would 

provide an adequate tool for understanding the connecThis paper was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 157–166.
FOREST GROWTH AND TIMBER QUALITY

158

tion between wood quality and tree growth in different 

management regimes. Therefore, more robust models can 

be used for assessing the potential product recovery from 

different stands and selecting the appropriate raw material 

for each end use. 

The earlier models for predicting lumber grade yields 

of standing trees were based on regression analysis with 

continuous dependent variables (Stayton et al. 1971, Yaussy 

1986, 1989). Howard and Gasson (1989) used a truncated 

normal distribution with a lower bound set to zero. Later, 

Prestemon (1998), Lynch and Clutter (1999), Gobakken 

(2000), and Prestemon and Buongiorno (2000) used discrete multinomial logit or tobit models for predicting the 

probability of a stem, or log, to belong to a certain quality 

class. These models assume that the whole stem or log 

belongs to the same class. Thus, the models predict how 

stems are, on average, distributed to sawn wood grades. The 

models can be used for comparing different silvicultural 

strategies or valuing stands, but not for predicting quality 

grade distributions of individual stems. 

In Finland, Uusitalo (1997) developed multinomial logistic models for predicting average lumber-grade distribution 

of Scots pine logs from final fellings. Separate models of 

battens, outer, and inner boards were estimated for butt, 

second, and third log, and dependent variables were defined as polytomous responses so that a certain number of 

battens, inner boards, and outer boards represent certain 

grades. The results showed that timber grade distribution 

of logs was mainly related to dbh, height of the lowest dead 

branch, and the height of the tree. 

The aim of this study was to develop models for predicting the lumber grade and by-product yield of individual 

Scots pine stems using simple stand and stem properties 

as explanatory variables. We used a process-based growth 

model, PipeQual (Mäkelä 1997, Mäkelä and Mäkinen 2003), 

for assessing the development of wood properties along tree 

growth and the effects of different silvicultural treatments 

on wood properties. In the PipeQual model, tree growth 

is derived from carbon acquisition and allocation, with a 

detailed description of branch structure. This allows the 

model to be applied to predictions of wood quality in individual stems. The model dynamically predicts the growth 

of individual trees at different dominance positions, from 

which the stand level is composed. The stems created by 

the PipeQual model were used as an input to the integrated 

wood conversion simulation system, WoodCim (Usenius 

2002). The WoodCim was developed by the Technical 

Research Centre of Finland for sawmilling companies. It 

enables the virtual sawing of individual logs, as well as 

predictions of grade distribution of sawn timber and byproduct yields at tree level. 

MATERIAL AND METHODS

Material

Stand developments according to several silvicultural strategies of varying intensity were simulated by the PipeQual 

simulator (Mäkelä 1997, 2002, Mäkelä and Mäkinen 2003). 

The model combines stem properties with carbon metabolism by means of a modular structure that consists of stand, 

whole tree, whorl, and branch modules interconnected 

through parametric inputs and outputs at a time resolution 

of one year. The stand level consists of ten size classes of 

trees, each size class is described by a mean tree. At the 

tree level, annual growth is calculated from tree-level photosynthesis (affected by shading from neighboring trees) and 

maintenance respiration. The annual growth is allocated to 

foliage, fine roots, and woody structures (stem, branches, 

and coarse roots). The tree module is connected to a whorl 

module, which contains models for the vertical structure 

of stem and branches. The branch module calculates the 

annual dynamics of individual branches and their properties in each whorl (Mäkinen and Mäkelä 2003).

The PipeQual requires initial values for stem height, 

dbh, crown length, and age for ten size classes of trees, as 

well as the initial number of trees per hectare in each size 

class. The initial size classes were defined in terms of initial 

seedling height with even class intervals, and assumed an 

exponential frequency or normal distribution of seedling 

height depending on the management strategy. In the simulations, site fertility of the stands was matched with Myrtillus

site type (H100 = 28 m) (Cajander 1949) corresponding to 

sites of medium fertility in Southern Finland.

Different silvicultural schedules were formed in order 

to produce as much variation in stand development and 

growth rate of trees as possible. The different silvicultural 

strategies were divided into four main groups based on 

management intensity, named as open-grown, high, normal 

and low intensity (Table 1). Four planting densities (2000, 

3000, 5000, and 10000 stems ha-1) were simulated in all 

the strategies, except in the low intensity strategy where the 

sparsest planting density was excluded. In sapling stands 

at a dominant height of 6.6–6.8 m, tending treatment was 

carried out, i.e., the number of remaining stems was reduced 
FOREST GROWTH AND TIMBER QUALITY

159

to 400, 1200, 1900, or 3000 in the strategies of open-grown, 

high, normal, and low intensity, respectively. In the normal 

and low intensity strategies, the first commercial thinning 

was carried out at dominant height of 14 m. In the opengrown and high intensity strategies, the stand density coincided with or was lower than the density recommended 

for forestry practice (Tapio 2006) and, therefore, no actual 

first thinning was carried out. The later thinnings were 

carried out according to the recommendations for forestry 

practice, expressed as the minimum stand basal area to 

be retained after thinning (Tapio 2006). The final felling 

was carried out when the mean dbh of the stand exceeded 

30 cm or the stand age was 85 years. If there was longer 

than a four-year difference between these two criteria of 

final felling, both alternatives were simulated. Altogether, 

different combinations of the planting densities, tending 

and thinning intensities, and final felling ages resulted in 

48 different treatment schedules.

These mean trees of each diameter-class formed the data 

set of this study. The initial analysis of the data showed, 

that stem dimensions and wood quality of the stands in 

the open growth strategy with 85 year rotation differed 

completely from the other data set. The attempts to force 

the equations through these diverging stems resulted in 

large biases in the other observations. For that reason, 20 

stems from these strategies (Table 1, in parenthesis) were 

omitted. In addition, because some of the size classes were 

completely removed in treatments during the stand rotaFigure 1. The average product distribution of the stems in the data set.

Table 1— Treatment strategies of the PipeQual simulations.

Strategy Planting density Tending of 

sapling stand

First commercial 

thinning

Number of 

later thinnings 

Final felling age

Stems ha-1 Stems ha-1 Stems ha-1 Years

Open-grown 2000 400 - - 48 or (85 )

000 400 - - 49 or (85 )

5000 400 - - 51 or (85 )

10000 400 - - 52 or (85 )

High 2000 1200 - 1 or 2 80 or 85

000 1200 - 1 or 2 84

5000 1200 - 1 or 2 85

10000 1200 - 1 or 2 85

Normal 2000 100 1200/ 600/ 400 0, 1 or 2 69, 79 or 85

000 100 1200/ 600/ 400 0, 1 or 2 68, 81, 85, 89 or 98

5000 100 1200/ 600/ 400 0, 1 or 2 69, 83, 85, 98

10000 100 1200/ 600/ 400 0, 1 or 2 73 or 85

Low

000 000 1200/ 600/ 400 0 or 1 72 or 85

5000 000 1200/ 600/ 400 0 or 1 74 or 85

10000 000 1200/ 600/ 400 0 or 1 76 or 85

Table 2—Properties of the simulated stem data

Minimum Maximum Mean Std. Deviation

Height, m 11.70 2.70 21.2 .

dbh, cm 14.80 .0 27. 5.28

Hdb, m 0.00 7.0 1.1 1.50

Hlc,m 6.40 1.0 11. 2.50

Age, years .00 .00 70.0 1.2

Abbreviations: Hdb = Dead branch height, distance from ground to first dead branch greater than 15 mm.

 Hlc = Living crown height, m.
FOREST GROWTH AND TIMBER QUALITY

10

tion or provided no sawn-timber, the final data set consisted 

of 395 trees. Properties of the data are shown in Table 2.

The generated stems were used as an input for the WoodCim sawing simulations. In the simulations, two typical 

sets of sawn-timber dimensions and sawing set-ups were 

used (Appendix 1). The arithmetic means of the results 

from these two sawing set-ups were used for each stem 

in the modeling. The sawing method was the traditional 

Scandinavian pith-centred cant sawing, in which the first 

machine cuts side boards and a block, and the second 

machine cuts the block into center boards and side boards. 

The center and side boards were classified as A, B, C and 

D-grades according to Nordic Timber grading rules (Pohjoismainen sahatavara, 1994). Center boards were defined 

as sawn pieces from the center of the stem (32–75 mm 

thick, Appendix 1). By-products were pulpwood, sawmill 

chips, sawdust, and bark. The minimum lengths applied 

for logs and pulpwood boles were 3.1 m and 2.0 m and 

the minimum top diameters without bark were 6.5 m and 

16.0 cm, respectively. The average product distribution of 

the data set is shown in Figure 1. On average, the proportion of sawn timber from the total stem volume with bark 

was 43.2 percent. 

Methods

The volume of each quality class of side and center boards 

and by-products was related to the total volume of the stem 

with bark. Then, cumulative relative volumes of the quality 

classes and by-products for each stem were calculated as 

shown in Table 3. The share of pulp wood bole from the top 

can be calculated by subtracting Y11 (the total proportion of 

all lumber grades plus chips, sawdust and bark) from 1.

The models describing the cumulative relative volumes of 

the quality classes of center and side boards and by-products 

were developed using the logistic regression approach:

2211 1

1

i

ε i Y

) iyXiy ...β i Xi β i Xi (α β e

= + −− + (1)

The logistic multivariate models were fitted using SPSS, 

Inc. software. Parameters of the models were estimated 

by iterative linearization method in which linearization is 

done around the set of initial values of coefficients. Iteration is repeated until a convergence of parameters values is 

obtained. Standard statistical tests used to the evaluation 

of fit of the final linearized equations were also calculated 

(Pinduct and Rubinfeld 1998, pp. 266–268). 

Different combinations of independent variables describing dimensions of the stems, crowns, and the growth 

rate (width of the annual rings around the pith), as well as 

their transformations, were tested until the models were 

finally accepted. The independent variables were restricted 

to conventional stand and tree measurements routinely 

collected in forest inventories or for forest management 

planning purposes. The average width of the annual rings 

around the pith was also tested as an independent variable because ring width near the pith and quality of Scots 

pine logs have been closely related (e.g. Heiskanen 1965, 

Kärkkäinen 2003). In addition, highly correlated independent variables were avoided. A correlation matrix was used 

for the preliminary analysis on the relationship between 

the dependent and independent variables. 

In order to examine the performance of the models, the 

product distributions were predicted in two independent 

data sets of the Stem Data Bank collected by the Technical 

Research Centre of Finland (VTT). In the Stem Data Bank, 

the 3D structure of real 

stems, including the 

description of external 

shape, internal knot 

structure, other possible 

defects, and heartwood 

core, is mathematically 

reconstructed into virtual stems, based on 

image analysis of flitch 

surfaces (Usenius 2002, 

Pinto et al. 2003). The 

first data set consisted 

of 38 stems thinned 

Table 3. Explanations of the symbols 

Variable Definition

Hlc Height to the living crown base from the stem base (m)

Ln(Dbh) Natural logarithm of stem diameter at breast height (cm) 

Y1 The proportion of A-grade side boards of the total volume of stem

Y2 Y1

+ the proportion of B-grade side boards of the total volume of stem

Y Y2+ the proportion of C-grade side boards of the total volume of stem

Y4 Y+ the proportion of D-grade side boards of the total volume of stem

Y5 Y4+ the proportion of A-grade center boards of the total volume of stem

Y Y5+ the proportion of B-grade center boards of the total volume of stem

Y7 Y+ the proportion of C-grade center boards of the total volume of stem

Y Y7

+ the proportion of D-grade center boards of the total volume of stem

Y Y+ the proportion of chips of the total volume of stem

Y10 Y+ the proportion of bark of the total volume of stem

Y11 Y10+ the proportion of sawdust of the total volume of stem

S2 Residual variance
FOREST GROWTH AND TIMBER QUALITY

11

from 24 stands in Southern Finland. It is noteworthy that 

the stands were not a random sample from Finnish forests. 

Instead, they represented regularly managed stands of better-than-average wood quality. The data is described in detail 

in Wall et al. (2005). The second data set consisted of 191 

stems from eight final fellings. The data set is described in 

detail in Mäkinen and Song 2002. Properties of the Stem 

Bank Data are shown in Table 4. The sawing of the stems in 

both data sets was simulated using the WoodCim simulator 

with the same parameters as the stems generated by the 

PipeQual model. 

Table 4—Properties of the Stem Bank Data.

Minimum Maximum Mean Std. Deviation

Height, m 12.0 2.0 22.22 4.72

dbh, cm 1.20 49.50 0.1 .7

Hdb, m 0.00 17.00 .21 .0

Hlc,m 3.65 23.50 12.41 .1

Age, years 0.00 194.00 127.64 1.72

Abbreviations: Hdb = Dead branch height, distance from ground to first dead branch greater than 15 mm. 

 Hlc = Living crown height.

Table 5—Variables and parameters of models Y1–Y11.

Dependent variable Independent variable Coefficient S.E 95 % Confidence Interval

Lower Upper

Y1 Constant 11,5729 0.5502 10.4913 12.6547

Adjusted R2 =0.7, s2

<0.001 Hlc 2.1 0.1625 1.8742 2.5131

Ln(DBH) 0.1115 0.0114 0.01 0.1

 Y2 Constant 10.7 0.2657 10.1643 11.201

Adjusted R2 =0.7, s2

<0.001 Hlc 2.3895 0.0804 2.2314 2.5475

Ln(DBH) 0.07 0.0053 0.0584 0.071

 Y Constant 11.0040 0.2035 10.0 11.4042

Adjusted R2 =0.2, s2

<0.001 Hlc 2.5820 0.01 2.4608 2.702

Ln(DBH) 0.0524 0.00 0.0447 0.001

 Y4 Constant 10.01 0.177 .7 10.4325

Adjusted R2 =0., s2

<0.001 Hlc 2.3185 0.0544 2.211 2.4254

Ln(DBH) 0.0531 0.00 0.0460 0.001

 Y5 Constant 9.4063 0.3142 .7 10.0241

Adjusted R2 =0.2, s2

=0.003 Hlc 2.2175 0.00 2.0248 2.4102

Ln(DBH) 0.02 0.00 0.070 0.101

 Y Constant 11.4282 0.1685 11.0 11.7595

Adjusted R2 =0., s2

=0.001 Hlc 3.0140 0.0525 2.10 .1172

Ln(DBH) 0.072 0.0035 0.0714 0.0851

 Y7 Constant 12.1566 0.11 11.8950 12.4182

Adjusted R2 =0., s2

=0.001 Hlc 3.2550 0.0413 .17 .2

Ln(DBH) 0.0757 0.0027 0.0704 0.00

 Y Constant 12.170 0.11 11.077 12.4263

Adjusted R2 =0., s2

=0.001 Hlc 3.2581 0.0409 .1777 3.3385

Ln(DBH) 0.0757 0.0027 0.0705 0.00

 Y Constant 7. 0.0754 7.7414 .07

Adjusted R2 =0., s2

<0.001 Hlc 2.4820 0.02 2.4291 2.5349

Ln(DBH) 0.0439 0.002 0.0395 0.0484

 Y10 Constant .2 0.1055 8.7850 .17

Adjusted R2 =0.7, s2

=0.001 Hlc 2.9965 0.0395 2.17 3.0742

Ln(DBH) 0.0491 0.0035 0.0423 0.0560

 Y11 Constant 1.00 0.12 15.6815 16.4401

Adjusted R2 =0., s2

<0.001 Hlc 5.6700 0.07 5.5248 5.8151

Ln(DBH) 0.02 0.0057 0.0270 0.0493

Explanations of the symbols are given in Table 3. All the parameter values are significant (p<0.001).
FOREST GROWTH AND TIMBER QUALITY

12

RESULTS

The logistic function (Equation 1) was used to model the 

cumulative relative proportions of the quality classes and 

by-products. All the models had the same independent variables and a constant. Using living crown height and natural 

logarithm of stem diameter at breast height as explanatory 

variables, the best model fit was achieved. The models 

and independent variables were significant at a risk lever 

smaller than 0.001, also 95-percent confidence intervals 

are shown in Table 5. The parameters of the models and 

their standard errors, as well as the R2 values and variances 

of the residuals, are shown in Table 5. Explanations of the 

symbols are shown in Table 3.

The smallest adjusted R2 value was 0.67 (Y5) and the 

highest 0.98 (Y7–Y9, Y11). For models in which the proportion of A-grade was added, Y1 and Y5, had the lowest 

R2 values. Thus, for the proportion of the highest quality 

grades, both center and outer boards had the highest random variation. It is noteworthy that the adjusted R2

-value 

of the model Y8, which includes all sawn wood grades, was 

very high, 0.98.

The residuals of the models versus natural logarithm of 

dbh are shown in Figure 2. The variation of the residuals 

is relatively small, but notably related to logarithm of dbh. 

However, the models were not biased in relation to the 

height of the living crown. Variances of the errors of Y1

increase when diameter increases with respect to increasing 

values of Y1, which illustrates the proportion of A-grade 

outer boards. Correspondingly, errors of Y11 decrease 

when diameter increases because the relative amount of 

pulp wood (defined as [1 - Y11]) becomes smaller when 

diameter increases. 

Testing the Models

The real test of the prediction system is whether it accurately 

predicts yield for trees other than those used to develop the 

equations. In this study we used measured stems and results 

from the simulated sawing process for the testing purpose. 

Figure 2. Residuals of the model Y1–Y11 plotted against the logarithm 

of dbh.

Figure 3. Errors of the predictions of the models Y1–Y11 plotted against 

the logarithm of dbh of stems (cm) in the Data Base Stems. 
FOREST GROWTH AND TIMBER QUALITY

1

As can be seen in Figure 3, extrapolation of models does 

not work in testing data for larger stems than those used in 

model building (dbh greater than 37 cm) and the models 

were clearly biased. In larger diameters than those in the 

data, overestimations of the models increase when diameter 

increases. In diameters smaller than 37 cm, models behaved 

relatively well based on the preliminary examination. 

Models Y5–Y8, in which the proportion of center boards is 

added to the cumulative variable, give underestimations in 

the smallest stems which are all from thinnings. Additionally, in small stems symmetrical and wide variation can be 

seen in models Y9 and Y10. Finally, overestimations occur 

in model Y11, which includes all products.

In model Y11, bias decreases when diameter increases, 

because the share of pulp wood becomes smaller when stem 

volume increases. The average tree age in the Stem Data 

Bank was 143 years, i.e., the stems were, on average, much 

older and their diameters much larger than in the stems 

used for model building. Stems with large diameters and 

high quality (high living branch height) had systematic error 

in predictions, and because the proportions are calculated 

as the differences between two cumulative variables error 

causes dislocation to the quality classes. The dbh affects the 

quality distribution in two ways. First, the larger the sawn 

piece is the thicker the permitted knots are, and secondly, 

large amounts of best-quality boards can be sawn just from 

large butt logs (Uusitalo 1997). Based on the testing data, 

however, the effect is overestimated.

DISCUSSION

Earlier studies on modeling the quality of Scots pine have 

shown that the height of the lowest dead branch is an important quality indicator, because thick branches self-prune 

slowly (e.g. Kärkkäinen 1980, Uusitalo 1997). In this study, 

we found that the height of the living crown was a better 

quality indicator. Data of earlier studies have consisted of 

only stems from final fellings. In this study, the stems were 

from different stages of the rotation. In young stems, the 

height of the lowest dead branch is usually very low and, 

therefore, it doesn’t account for the differences in sawn 

timber grades. The size of the sound knot may, however, 

determine the quality class of the board. In the smallest 

typical size class of boards (19*100 mm), on the flat side of 

the board a sound knot with diameter of 20mm or smaller 

is allowed in the pine A-grade, 35 mm or smaller in B-grade, 

and 50 mm or smaller in C-grade (Pohjoismainen sahatavara 

1994). When using models for predicting the product distribution of stands, living crown height can be considered 

an accurate quantifier, both if stems are genuine and stem 

characteristics are measured, or if stems are generated by 

empirical or process-based stand simulators.

The PipeQual model probably overestimates the overall 

quality of stems because other defects than branches are 

not considered. The simulated stems are straight without 

warp, twist, forks and out-of-roundness in cross-section 

and defects like decay or splits do not appear. In Scots pine, 

knots are, however, the most important individual factor 

affecting quality grading. Therefore, the simulated stems 

were supposed to indicate stem quality well enough. The 

data set used for independent testing, however, consisted of 

only stems of good quality and systematic overestimations 

of the models need to be more closely dissected.

Stand development was simulated using a submesic site 

type (MT-type in Cajander’s classification 1949) located in 

Southern Finland. These assumptions could restrict the applicability of the models for other site types or geographical 

locations, but more testing with suitable data is required.

Future Perspectives and Applications 

of the Models

The multiproduct predicting system presented in this paper 

has many application possibilities for optimization of forest 

management at the stand level with different objective functions. By combining models for a simulation-optimization 

system we are able to study the value of end products and 

simultaneously take other aims into account, for example 

carbon sequestration of different end and by-products. 

Carbon sequestration can be taken into account via life 

cycle analysis of different construction wood products, 

furniture products, and short cycle products, i.e., packaging and paper goods. 

In earlier case studies, which have examined the value 

growth and optimal rotation age of pine stands, when the 

quality of timber was taken into account via different quality-pricing methods, improvements in quality (that is, in 

value of logs) didn’t extend optimal rotation length (Pastila 

2003, Makkonen 2006). These case studies examined value 

growth until age 100 years and, in this study, final felling 

criteria was either a diameter of 30 cm or an age of 85 years. 

Because the treatment history of the Stem Data Bank stem is 

well recorded, it is possible to study value growth of these 

stands by connecting the product recovery predictions of 

models (from earlier stages of experimental stands) and 
FOREST GROWTH AND TIMBER QUALITY

164

recorded information of simulation sawings (final fellings) 

with the average costs of treatments, producers’ prices of 

lumber and by-products, and appropriate interest rates. By 

examining net present values and value growths of stands 

we could study whether longer rotation would improve 

grade distribution remarkably enough that the investment 

in standing stock would be profitable. 

The purpose of this study was to build a simple prediction 

system for standing pine stems for evaluation of the effects 

of different stand management regimes on the product 

distribution of stems. Outside of the stem diameter range 

of the data set used for model building, the models were 

clearly biased. We will continue to improve the preliminary 

models in the future. The next step is to develop multilevel 

multivariate models, because stems in same stands are not 

independent of each other and equation systems in which 

parameters have been estimated simultaneously may produce more consistent and efficient estimates than models 

constructed separately. Also, the structure of dependent 

variables, in which responses are volumes instead of properties, and sum of volumes is restricted to total volume of 

stem, will be applied to diminish bias of the models.

CONCLUSIONS

This paper has presented the current state of development 

of the model system. It was possible to develop models for 

predicting the quality distribution and yield of by-products of individual Scots pine stems using the simple stand 

and stem properties as explanatory variables. The models 

presented are, however, preliminary and not yet applicable 

for general use. In the near future, model development will 

be continued, more thorough tests of the models will be 

reported, and based on the test results, the models will 

be modified.

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FOREST GROWTH AND TIMBER QUALITY

1

Appendix 1

Setting series 1

Diameter Class Centre Boards Side Board Models

Dmin, 

mm

Dmax, 

mm

thickness, 

mm

width, 

mm

1. machine, 

mm

2. machine 

innermost board

2. machine 

outermost board

1 120 157  100 1

2 158 12  115 25

 1 174 50 100 1 1

4 175 12 50 125 25

5 1 17  115 25 25

 1 207 50 150 25

7 20 217 2 125 25 1

 21 222  150 25 25

 22 21  125 25 1

10 22 27 75 150 25 25

11 2 242  175 1 1 1

12 243 250  150 25 25

1 251 256 50 175 25 25

14 257 22  200 1 25 1

15 2 271 2 200 1 25 1

1 272 22 75 200 25 25 1

17 2 21  200 25 1 1

1 22 01 75 225 1 25 25

1 02 314 50 225 25 25 25

20 315 325 50 200 25 25

21 2 334 50 200 25 25

22 335 351 50 225 25 25 1

2 352 555 50 225 25 25 25

Setting series 2

24 120 144  100 1

25 145 150 2 100 1

2 151 156 44 100 1 1

27 157 1 2 125 25

2 1 175 50 115 1 25

2 17 12 50 125 25

0 1 1  100 25

1 194 202 50 150 25

2 20 212 75 100 25 1

 21 215 50 150 1 1 1

34 21 221 44 175 25 1

35 222 225 75 125 25 25

 22 2 75 150 25 25

7 240 252 50 200 25 25

 253 21  150 25 25

 22 2  200 1 25 25

40 2 22 75 200 25 25 1

41 2 20  225 1 25 25

42 21 2 50 225 25 25 25

43 00 1 50 225 25 25 25

44 20 555 50 200 25 25
FOREST GROWTH AND TIMBER QUALITY

17

Integrating a Wood-Quality Module with a Growth 

Simulator to Quantify Silvicultural Scenarios in Jack 

Pine Plantations (Are We Making the Right Choices?)

Robert Schneider, Frank Berninger, S.Y. (Tony) Zhang, Chhun-Huor Ung

Robert Schneider (robert.schneider.1@ulaval.ca) and Frank Berninger are in the Département des sciences biologiques, Université du Québec à 

Montréal, c.p. 8888 succ. C.V., Montréal, Québéc H3C 3P8, Canada; S.Y. (Tony) Zhang is a senior scientist at FPInnovations—Forintek Division, 2665 

East Mall, Vancouver, BC V6T 1W5, Canada; Chhun-Huor Ung is at the Laurentian Forestry Centre, Canadian Forest Service, P.O. Box 10380, Stn. 

Sainte-Foy, Québec, Quebec, G1V 4C7 Canada.

ABSTRACT

I

NITIAL PLANTING DENSITY HAS A CRITICAL

effect on establishment costs, growth and yield, product 

quality, and value recovery. Initial planting density for 

major softwoods in Quebec was lowered in the early 1990’s 

in order to increase the success of future thinnings and to 

reduce plantation establishment costs. While these reasons 

might seem sound, we still do not fully understand the impact of this decision on growth, yield, and wood quality of 

these plantations. Furthermore, not enough is known about 

the interaction between thinnings, initial stand density, and 

site fertility or the effects of these interactions on the growth, 

yield, and wood quality. To address some of these questions 

before experimental plots become mature enough to provide 

empirical evidence, a process-based growth simulator is being developed for jack pine plantations based on the CroBas 

model. The simulator has a wood-quality module that yields 

estimates of branch diameter and insertion angle as well as 

wood density and bending properties. Emphasis is placed on 

this module to quantify the impact of silvicultural regimes 

on wood quality and compare the simulated results with 

field data from several plantations sampled across Eastern 

Canada. Preliminary results indicate that total branch basal 

area of the stem decreases exponentially with increasing 

initial stand density, and this trend holds true over time. In 

addition, initial validation shows very little bias in height 

growth predictions in young plantations.

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 167.

FOREST GROWTH AND TIMBER QUALITY

1

Optimizing Wood Quality and Stand Diversity 

in Uneven-Aged Forest Management1

Jingjing Liang, Joseph Buongiorno, Robert A. Monserud

Jingjing Liang (j.liang@uaf.edu) is an assistant professor, Department of Forest Sciences, University of Alaska, P.O.Box 757200, Fairbanks, AK 99775, USA; Joseph 

Buongiorno is a professor, Department of Forest Ecology and Management, University of Wisconsin-Madison, 1630 Linden Drive, Madison, WI 53706, USA; Robert 

A. Monserud (retired) was a research forester and team leader, USDA Forest Service, Pacific Northwest Research Station, PO Box 3890, Portland, OR 97208, USA.

1. This is an abbreviated and fully rewritten paper based on an analysis published in Forest Science 52(5):579–594.

ABSTRACT

WE DEFINED UNEVEN-AGED MANAGEMENT 

alternatives for Douglas-fir (Pseudotsuga menziesii)/western hemlock (Tsuga heterophylla) 

stands by the cutting cycle, C, the residual stand basal area, 

B, and the q ratio. Bootstrap simulation was used to predict 

the effects of B, q, and C on percentage of peeler logs, tree 

species diversity, and tree size diversity. Response surface 

analysis showed that adjusting B, q, and C could control for 

most of the variability in the percentage of peeler logs, tree 

species diversity, and tree size diversity. Other things being 

equal, a higher q ratio increased the percentage of peeler 

logs, tree species diversity and tree size diversity. The same 

combination of B, q, and C, maximized the percentage of 

peeler logs, stand species diversity, and tree size diversity. 

Thus, there was no apparent conflict between wood quality 

and stand diversity. 

KEYWORDS: stand growth, bootstrap, response surface, 

stochastic, Douglas-fir, western hemlock 

INTRODUCTION

One interesting issue concerning all-aged management is 

its effect on wood quality. Research on the relation between 

wood quality and product values has lagged behind research 

on growth and yield, stocking control, and fertilization 

(Briggs and Fight 1992). We still lack information linking 

tree growth to wood quality and product value. In most 

economic analyses, log values are functions only of tree size. 

However, trees of a given size may vary highly in grades, 

due in part to stand characteristics such as density. 

Biological diversity is a necessary condition of ecosystem 

resilience. Stands with greater tree size and species diversity 

provide better habitat for wildlife. They also tend to be more 

aesthetically pleasing (Guldin 1996). 

Forest managers encounter risk in many diverse forms. 

Although research has begun to combine biological and 

economic risk in optimization, it remains difficult to optimize systems with risk in many variables. The method 

used in this study was bootstrap simulation, coupled with 

response surface analysis (Myers and Montgomery 2002). 

The aim was to obtain optimal management regimes, defined 

by a specific target distribution and cutting cycle, while 

recognizing stochastic forest growth, prices, and interest 

rates. In the process, we show the sensitivity to selected 

management regimes of financial returns, stand diversity, 

stand density, and wood quality in Douglas-fir/western 

hemlock stands.

STAND GROWTH MODEL

The stochastic stand growth model we used was an extension of the deterministic growth model for Douglas-fir/western hemlock stands developed by Liang et al. (2005). This 

model predicts the number and volume of trees for four 

species groups (Douglas-fir, other shade-intolerant species, western hemlock, and other shade-tolerant species) in 

nineteen 5.1-cm-wide diameter classes. The elements of the 

This paper was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. pp. 

169–173.
FOREST GROWTH AND TIMBER QUALITY

170

matrix model were obtained with equations of individual 

tree growth, mortality, and stand recruitment, functions 

of tree and stand characteristics. These include species 

diversity, size diversity, stand basal area, and tree size. 

Diversity was measured with Shannon’s index (Magurran 

1988). The equations were estimated with individual tree 

and stand data from 2,706 permanent plots in western 

Washington and Oregon. 

The deterministic model was made stochastic by adding a vector of random shocks. The vector was based on 

observations on the 2,706 sample plots used to calibrate the 

stand growth model. For each plot, the vector of stochastic 

shocks was the difference between the state predicted by 

the deterministic model, and the observed state.

In the simulations, the stochastic shock was obtained 

by bootstrapping (Diebold et al. 1998). At each time step a 

shock vector was drawn randomly, with replacement, from 

the sample of 2,706 vectors of errors. The advantage of bootstrapping is that it leaves the data as is, without imposing 

a particular distribution on the shocks, as when truncated 

multivariate normal distributions are used instead. 

This stochastic stand growth model gave predictions 

of expected basal areas that were similar to those of the 

deterministic model (Liang et al. 2005) for Douglas-fir and 

other shade-intolerant species. The stochastic predictions 

were higher for western hemlock and other shade-tolerant 

species, suggesting that random shocks help the regeneration of shade-tolerant species. 

WOOD QUALITY MODEL

The model-predicted log grade as a proxy for wood quality 

was based on the USFS Product Recovery Database (Stevens 

and Barbour 2000), which had data on 3,378 logs. The logs 

are classified into five grade categories, according to their 

diameter, branch size, growth rate, and minimum length. 

The grade codes are: I for peeler, II for #1 Sawmill, III for 

#2 Sawmill, IV for #3 Sawmill, and V for all other grades. 

For this study, the logs were divided into the four species 

groups used in the growth model. 

The log grade was predicted by species group with a 

logistic regression and a nominal response variable. The 

parameters, estimated by iterative-reweighed least squares 

(McCullagh and Nelder 1992) are in Table 1. For both 

species, log grade was higher for larger trees on the lower 

sites. The positive correlation between tree size and log 

grade is consistent with the definition of log grade by the 

Northwest Log Rules Advisory Group (1998). A possible 

explanation of the negative correlation between log grade 

and site is that lower site reduces growth rate (Liang et 

al. 2005), and consequently increases wood quality with 

smaller annual rings (Barnett and Jeronimidis 2003). The 

other variables (basal area, elevation, aspect, and slope) did 

not have a significant effect on log grade, at the α=5 percent 

level, and were removed from the model.

For other shade-tolerant and shade-intolerant species, 

the observed percentage of total volume by log grade for 

each diameter class was assumed to be constant. 

MANAGEMENT SIMULATIONS

A management regime was defined by the cutting cycle, and 

the target residual stand state. The harvest took the trees 

that exceeded the target residual stand. The simulations 

were for 50 years. The target residual stand was defined 

by basal area, diameter of largest tree, and q ratio, where 

q is the ratio of the number of trees in adjacent diameter 

classes. This BDq method is commonly used to define the 

target diameter distribution in uneven-aged stands. Along 

with the basal area and the diameter of the largest tree, q

defines the distribution of the residual stand (Buongiorno 

and Gilless 2003, p. 291–293). 

By assigning different values to basal area, maximum 

diameter, and the q ratio, the BDq rule defines a wide range of 

Table 1. Estimation results of the equations of log grade

Dependent 

variable

Independent 

variable Coefficient Significance

Douglas-fir

π1 / π4 Constant 2.1 *

D 0.04 **

S -0.10 **

π3 / π4 Constant 1.

D 0.04 **

S -0.10 *

Western Hemlock

π1 / π4 Constant -8.94 *

D 0.41 **

S -0.40 *

π2 / π4 Constant -8.37 *

D 0.35 **

S -0.30 *

π3 / π4 Constant -5.90 **

D 0.2 **

S -0.13 **

πi = probability of log grade i (no Douglas-fir log was of grade 2).

D = tree diameter.

S = site index.

P = level at which the effect of the independent variable would 

be just significant: * = P less than 0.05; ** = P less than 0.01 for 

test of significance.
FOREST GROWTH AND TIMBER QUALITY

171

residuals stands. For a given basal area, increasing the value 

of q would progressively increase the number of trees in the 

small diameter classes relative to the number of trees in the 

large diameter classes. For a given q ratio, increasing the 

target basal area would increase the stand density without 

changing the distribution of trees by diameter class. 

In the following simulations, the maximum diameter 

was set at 102 cm, the largest diameter recognized by the 

growth model. The cutting cycles were 10, 15, 20, 25, or 

30 years. The target basal areas were 14, 23, 32, 41, or 51 

m2

ha-1; and the alternative q ratios used were 1.2, 1.4, 1.6, 

or 1.8. The target basal area by species group was kept at 

the average level observed on all the plots. All combination 

of these values gave 100 possible management regimes. 

As the initial state for each management regime, 500 

plots were randomly selected by bootstrapping, with replacement, from the 2,706 permanent plots used to calibrate the 

growth model. 500 replications were sufficient to obtain 

stable simulation results.

The following criteria were established to measure the 

performance of different management regimes:

• Percentage of peeler logs in total volume

• Tree species diversity

• Tree size diversity

Tree species diversity and tree size diversity were measured with Shannon’s index, based on the basal area by 

size and species class. 

RESPONSE SURFACE ANALYSIS

For each combination, k=1,...,100, of control variables 

(cutting cycle, Ck, target basal area, Bk, and q ratio, qk) the 

simulations gave 500 observations for each management criterion. The response surface analysis determined the effect 

of each control variable on the expected value of a management criterion, with other control variables held constant 

at their mean. This was done by regression analysis of the 

simulated mean responses obtained with a combination of 

control variables. For example, in the case of the percentage 

of peeler logs, the following quadratic response surface was 

fitted by ordinary least squares (OLS): 

 (1)

where Pk was the mean percentage of peeler logs over the 

500 replications for the kth combination of control variables, 

the ω’s were parameters, and vk was the residual error.

We then assessed the sensitivity of the expected response 

to a particular control variable by testing the joint significance of all terms containing a particular variable, and by 

calculating the effect of a variable on the response while 

other variables were held constant at their mean.

The results of estimation of the response surfaces for the 

different management criteria are in Table 2. The control 

variables explained 97–99 percent of the variation in the 

percentage of peeler logs and stand diversity. 

As shown in Figure 1, the cutting cycle had a biologically significant effect only on the species diversity, which 

decreased slightly with longer cutting cycles. 

Increasing the target basal area from 14 to 50 m2

ha-1, 

other things being equal, decreased species diversity by 5 

percent. Meanwhile, the percentage of peeler logs decreased 

only slightly, and the tree size diversity was unchanged.

The q ratio had a significant effect on all three criteria. 

Increasing the q ratio from 1.2 to 1.8, other things being 

equal, decreased percentage of peeler logs, species diversity, 

and size diversity.

When the results of all the management alternatives were 

pooled together, we found that the percentage of peeler 

logs was positively correlated to tree species diversity and 

to tree size diversity (Figure 2). The positive relationship 

between percentage of peeler logs and species diversity was 

statistically the most significant. 

OPTIMIZATION

The last part of the analysis sought the combined values of 

the control variables that optimized a particular management criterion. For example, the maximum percentage of 

peeler logs was found by finding the values of C, B, and q

such that:

 (2)

where the ωˆ ’s were the estimated values of the parameters 
FOREST GROWTH AND TIMBER QUALITY

172

Table 2. Values of management criteria as functions of the control variables. 

Equation R2

P=71.20** -1.61**C +0.21B -26.63**q +0.02C2 -2.10B2 +5.62**q2 -

0.2CB -2.08Bq +1.09**Cq

0.7

Hs=1.35** +0.012C -0.15**B -0.05q +0.0005C2

 +0.11**B2 +0.02q2 -

0.005CB -0.09**Bq -0.02**Cq

0.

Hd=3.24** -0.12**C -0.09B -0.23**q -0.005C2

 -0.03B2 -0.16**q2 -0.01CB

+0.07Bq +0.11**Cq

0.

P = percentage of peeler logs.

Hs= species diversity.

Hd= size diversity.

BA= basal area.

C= length of cutting cycle (10y).

B= target basal area (102

m2ha-1).

q= q ratio of target tree distribution.

*, P less than 0.05; **, P less than 0.01 for test of significance.

Figure 1— Effects of control variables on the expected value of management criteria, with other control variables 

being held constant at their mean

Figure 2— Relationship between wood quality and 

tree diversity
FOREST GROWTH AND TIMBER QUALITY

17

of the response surface for percentage of peeler logs, P. The 

constraints defined the range of the control variables, C, B, 

and q, in the simulations. 

The optimization results showed that a 10-year cutting 

cycle, a target basal area of 14 m2

 ha-1, and a q ratio of 1.2 

led to the highest percentage of peeler logs, the highest tree 

species diversity, and the highest tree size diversity.

SUMMARY AND CONCLUSION

The q ratio had more influence on the management criteria 

than the residual basal area or the cutting cycle. Having a 

higher q ratio, which means more trees in the smaller size 

classes, reduced tree-species diversity, tree-size diversity, 

and the percentage of peeler logs. 

Over all the simulated management regimes, there was 

a positive correlation between the percentage of peeler logs 

and species diversity, and between the percentage of peeler 

logs and tree-size diversity. 

The combination of cutting cycle (10 years), target basal 

area (14 m2

 ha-1), and q ratio (1.2), that maximized percentage of peeler logs also maximized tree-size diversity, and 

tree-species diversity. 

Thus, there was no apparent conflict between the goal 

of stand diversity and the goal of wood quality. Stands 

with a higher diversity of structure (tree size) and a higher 

diversity of species also contained a higher percentage of 

high-grade logs. 

LITERATURE CITED

Barnett, J.R.; Jeronimidis, G. 2003. Wood Quality and 

its biological basis. Blackwell Publishing, Oxford, UK. 

226 p.

Briggs, D.G.; Fight, R.D. 1992. Assessing the effects of 

silvicultural practices on product quality and value of 

coast Douglas-fir trees. Forest Products Journal 42(1): 

40-46.

Buongiorno, J.; Gilless, J.K. 2003. Decision methods 

for forest resource management. Academic Press, San 

Diego. 439 p.

Diebold, F.X.; Ohanian, L.E.; Bekowitz, J. 1998.

Dynamic equilibrium economies: a framework for 

comparison models and data. Review of Economic 

Studies 65: 433–451. 

Guldin, J.M., 1996. The role of uneven-aged silviculture 

in the context of ecosystem management. Western 

Journal of Applied Forestry 11(1): 4–12.

Liang, J.; Buongiorno, J.; Monserud, R.A. 2005.

Growth and yield of all-aged Douglas-fir/western 

hemlock forest stands: a matrix model with stand 

diversity effects. Canadian Journal of Forest Resources 

35: 2369-2382.

Magurran, A.E. 1988. Ecological diversity and its 

measurement. Princeton University Press, Princeton. 

179 p.

McCullagh, P.; Nelder, J.A. 1992. Generalized Linear 

Models. Chapman & Hall, London. 532 p.

Myers, R.H.; Montgomery, D.C. 2002. Response surface 

methodology, 2nd ed. John Wiley & Sons, New York. 

798p. 

Northwest Log Rules Advisory Group. 1998. Official log 

scaling and grading rules. 8th ed. Eugene, Oregon. 48 p.

Stevens, J.A.; Barbour, R.J. 2000. Managing the 

stands of the future based on the lessons of the past: 

estimating western timber species product recovery by 

using historical data. USDA, Forest Service, Res. Note 

PNW-RN-528. 9 p.

Simulation in Sustainable 

Forest Management

Simulation in Sustainable Forest Management

Keynote Presentation

Tools for Sustainable Forest Management

Hubert Hasenauer and Stephan A. Pietsch

Hubert Hasenauer (hubert.hasenauer@boku.ac.at) is a professor and head of institute and Stephan A. Pietsch is an assistant in the Institute of Silviculture, BOKU University of Natural Resources and Applied Life Sciences, Peter Jordan Str. 82, A-1190 Vienna, Austria.

ABSTRACT

WITHIN THE PAST TWO DECADES, AND 

particularly since the “Brundtland Report”, 

sustainability has become a key term in emphasizing the relationship between economic progress and 

nature conservation issues. One option for assessing and 

understanding these changes are forest ecosystem models, 

which are designed to reproduce, quantify, and describe 

forest ecosystem processes. Three major modeling concepts 

have been evolved and successfully applied within forest 

ecosystem modeling: (1) Management models, (2) Succession models, and (3) Biogeochemical-mechanistic models 

(BGC-Models). In this paper the different concepts including 

the main components, their advantages and disadvantages 

in assessing specific end-user needs are discussed. Three 

application examples are presented as well.

KEYWORDS: Ecosystem research, modeling, system analyses, sustainability

INTRODUCTION

Forest management within the context of economic progress 

is an essential issue when considering sustainability. Forests 

have been severely modified by humans. The results are 

a reduction in forest-covered land area (in Europe from a 

potential coverage of 80 percent to 40 percent), a change 

in tree-species distribution, and intensive management to 

enhance timber production. One tool used to assess and 

FOREST GROWTH AND TIMBER QUALITY

177

understand these changes is forest ecosystem modeling. 

Conflicting interests such as simplicity, observability and 

biological realism must be addressed to ensure a well balanced modeling approach. Because field observations are 

usually only available for short time periods or for a limited 

number of locations, models are an important tool used to 

extrapolate in space and time (Pacala et al. 1996).

An important constraint in our modeling efforts is that, 

in some research fields, the scientific knowledge has room 

for improvement. In such situations, models help to detect 

research needs and to inform the design of field studies. 

Simple input/output approaches can be used until a comprehensive understanding of missing research information 

is available.

Within science, the term model is defined as a simplified 

reproduction of a much more complex reality (Shugart 1998). 

Consequently, models will always include a certain level 

of abstraction by creating a system, which is less complex 

than reality, but still describes the pattern and behavior of a 

real-world scenario. Models are available in a wide variety of 

forms ranging from conceptual models to graphical models 

to computer simulation tools (Kimmins 1987).

Building models requires a system analytical approach 

(see Figure 1). First a problem must be formulated. Objectives need to be defined according to the criteria of simplicity, observability, and biological realism. While defining 

objectives, the framework of the model’s function in terms 

of its application and expected model output is defined. 

This paper was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 177–185.
FOREST GROWTH AND TIMBER QUALITY

17

Next, resource planning is important because data collection is expensive and time consuming. Thus, a lot of our 

modeling efforts are limited by data constraints. This limits the scaling in space and time. If models are to be applied 

on a larger scale or to a longer time period the data structure used for calibration and model initialization has a 

major impact on the reliability of the expected output.

All modeling work must include validation and/or evaluation of the model. This is a continuous process because 

each model is based on the latest available knowledge to 

ensure reliability. Data not used for calibration are used for 

assessing the expected error range of key output variables. 

One important objective in modeling is to mimic nature 

as well as possible, to achieve biological realism in the 

model output. This may require procedures or experiences 

which are not always rigorously tested in typical statistical 

validation.

When using ecosystem models it is important to understand how a model responds to undisturbed “regular” 

conditions as well as to different scenarios (assumed disturbances). Such scenario simulations are important for 

sensitivity analysis. Thus, they are a major step in evaluating 

and testing the reliability of expected model output even if 

no adequate test data sets are available. 

Ecosystem processes act at different levels, which may 

require different procedures for data collection and integration. Some processes may be on a leaf- or tree-level (such 

as photosynthesis) other processes may act at a regional or 

even global scale (such as expected change in climate). The 

same holds true for time; some processes operate within 

seconds or less (such as gas exchange within the stomata), 

while others take years or centuries to have an impact on 

a forest ecosystem (such as soil processes). If we wish to 

combine different processes, accommodating these differences in scale is critical. At this point, issues of formal 

conceptual implementation center around the three major 

modeling criteria: simplicity, observability, and biological 

realism. These criteria are essential for ensuring a “well 

balanced” model approach.

 The term “well balanced” refers to the fact that it makes 

no sense to give one model driver a very careful and detailed 

description while others are less rigorously implemented 

or even inconsistant. An imbalanced approach such as this 

may lead to misleading and ill-defined modeling results 

since biological realism is not correctly addressed. From a 

statistical point of view, random variation may be removed. 

Such models pretend to produce accuracies in their predictions, which do not exist. Each model needs a “unit”. While 

this is easy to achieve for typical production models (such 

as volume increment) achieving this may become complex 

within biogeochemical-mechanistic modeling, since these 

models integrate different ecosystem processes at various 

spatial and temporal scales. 

Models are developed to combine existing knowledge, 

describe interactions between key ecophysiological processes, formulate hypotheses, identify gaps in our knowledge, and to perform scenario analysis to support decisions. 

With the development of the computer industry and the 

improvement in our ecological understanding, a wide variety of models have been developed. Nevertheless, from a 

Figure 1. System analytical approach in the design of ecosystem models 

(Hasenauer et al. 2000).

Figure 2: The three most common forest ecosystem modeling concepts 

according to implementation principles (see Hasenauer et al. 2000).
FOREST GROWTH AND TIMBER QUALITY

17

conceptual point of view, we may distinguish between the 

three following forest ecosystem model concepts (see also 

Hasenauer et al. 2000).

MODELING CONCEPTS

Management Models

Forest conditions are assessed by periodical forest inventories. However, for forest planning, models are needed to 

predict forest growth. Forest inventories combined with 

model-driven forest growth predictions provide the basic 

information from which to derive sustainable cutting plans 

at the company, regional, or national level. Traditionally, 

forest management has relied on yield tables (Weisee 1880). 

The main assumptions concerning yield tables are that the 

forest stands are pure, even-aged and undergo only one stand 

treatment, if any. Based on a given site quality (such as site 

index) the mean stand development over time—one rotation 

period—is described. This model type has existed for more 

than 100 years. It is important to note that the main interest 

in growth and yield models was always the prediction of 

future stand development in order to avoid over-cutting and 

exploitation of forest resources. These are the key features 

for developing sustainable management plans.

With the movement of forest management towards uneven-aged forests, existing yield tables have been improved 

and/or partly replaced by tree growth models. The idea is 

driven by the fact that uneven-aged mixed species stands 

may increase or at least maintain soil fertility, increase 

biodiversity, and improve stand resilience. As a result, tree 

growth models have been developed which operate at the 

individual tree level. Examples of these models in North 

America include Stage 1973, Wykoff et al. 1982, and Monserud 1975; and in Europe: Pretzsch 1992, Hasenauer 1994, 

Sterba et al. 1995, and Nagel 1999. The main advantage of 

tree models is that they are independent from any specific 

mixture, age, and stand treatment, because the growth and 

mortality of each tree within a stand is described.

From a conceptual point of view, we may distinguish 

between tree models which predict the periodical 5-year 

growth rates (diameter and height increment) based on a 

given potential (Hasenauer 1997) which is then reduced 

to the actual growth of a tree (see also the concept of gap 

models) versus those which predict periodical tree growth 

directly. Tree mortality is determined by a survival probability within a given period. Such models have been 

developed mainly to provide an alternative tool (replacing 

yield tables) within uneven-aged mixed-species stands 

and to ensure sustainable forest management. For further 

details related to this topic see Hasenauer (2005) and the 

ITM homepage: http://www.boku.ac.at/itm.

Succession Models

Succession, Gap, or Patch models describe the reproduction 

growth and mortality of trees (Botkin 1993). Old trees die, 

resulting in forest gaps or patches into which new trees will 

grow (Shugart 1998). The first and most famous succession model was JABOWA I (Botkin et al. 1972) developed 

for describing the stand dynamics of the Hubbard Brook 

experimental forest in the Northeastern United States. Since 

then, numerous applications have been developed (Shugart 

1998, Pacala et al. 1996, Lexer and Höninger 2001).

In a succession model, predefined species-specific growth 

potential (considered as the maximum growth) is calculated in a way similar to the site-specific “growth potential” 

calculation of management models. Next, reduction factors 

for assessing the competition for light, temperature, water, 

and nutrients (nitrogen) are derived as so-called response 

functions. These response functions can be thought of as 

multipliers between 0 and 1, which reduce the speciesspecific growth potential to actual values according to site 

variation and the competitive status of the trees. Thus, succession models explicitly assess the impact of temperature, 

water, and nutrients on tree growth by applying multipliers 

while management models use individual tree competition 

measures to predict the 5-year growth rates of trees.

Although tree growth is simulated, the main goal of 

succession models is to describe vegetation patterns over 

time. The original aim of gap models was to understand 

and reproduce existing vegetation patterns that have developed since the last glacier periods. The stand dynamic 

as it has evolved during centuries was and still is one of 

the main features. The regeneration, growth, and death of 

individual trees and the interaction between different tree 

species are key features. Management impacts are usually 

not assessed, because a constant height-to-diameter ratio 

and a fixed mortality percentage are implemented. Interactions between the main driving forces of growth (energy, 

temperature, water, nutrients) are the main research areas 

used to enhance the functioning of this model type. Today, 

such models are used for assessing the potential vegetation 

pattern and potential changes in vegetation distribution 

under expected climate change. 
FOREST GROWTH AND TIMBER QUALITY

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Biogeochemical-mechanistic Models

Mechanistic models describe the circulation, transformation, and accumulation of energy within and through a 

forest ecosystem. The main goal is to assess the interaction between plants and their surrounding environment. 

BGC-Models are considered diagnostic tools to understand 

ecosystem behavior. Thus, they are often called process or 

biogeochemical models (BC-Models). In contrast to tree 

population models, such as management or succession 

models, BGC models incorporate a mechanistic description of the interaction between plants and the surrounding 

environmental conditions (Waring and Running 1998). 

Consequently, they are designed to be responsive to changes 

in environmental conditions.

BGC models operate on a monthly to daily time resolution to simulate the cycles of carbon, water, and nitrogen 

for generalized biome types (Thornton 1998) or species 

(Pietsch et al. 2005). Leaf area index (LAI, m2

 leaf area 

per m2 ground area) controls canopy radiation absorption, 

water interception, photosynthesis, and litter inputs to 

detritus pools. BGC models operate on a stand level and 

simulate net primary production (NPP) calculated from 

a photosynthesis routine (Farquhar et al. 1980) minus 

autotrophic respiration. Autotrophic respiration comprises 

maintenance respiration, calculated as a function of tissue 

nitrogen concentration and growth respiration and a function of the amount of carbon allocated to the different plant 

components (leaf, root, and stem).

NPP is partitioned into the leaves, roots, and stems as a 

function of dynamic allocation patterns, with consideration 

for limitations due to availability of and competition for 

nitrogen. BGC models require meteorological input data, 

such as daily minimum and maximum temperature, incident 

solar radiation, vapor pressure deficit, and precipitation, 

which may be derived for any location within the area of 

interest using interpolation algorithms (see Hasenauer et 

al. 2003).

BGC models have been applied for large as well as smallscale applications. The specific strength of these models is 

the description of the carbon cycle as it can be used for 

assessing growth responses to environmental impacts (see 

Hasenauer et al. 1999). The daily time resolution adequately 

addresses the annual patterns of weather events. Other applications are the description of the water cycle (Running 

and Coughlan 1988, Pietsch et al. 2003) and the nutrient 

cycle as it may depend on the tree population. Major goals for 

improving mechanistic modeling techniques are enhancement of the species representation (Pietsch and Hasenauer 

2001, Pietsch et al. 2005) and inclusion of management 

scenarios (Merganicova et al. 2005). 

APPLICATION EXAMPLES

In this chapter a typical example for forest management 

and two mechanistic modeling examples are presented. In 

the first example, the distance tree growth model MOSES 

modeling stand response (Hasenauer 1994) is applied for 

uneven-aged mixed-species stands in Switzerland. The 

second and third examples demonstrate the application of 

our species-specific version of BIOME-BGC (Thornton 1998, 

Pietsch et al. 2005) to assess historic land use impacts and 

the carbon flux within old growth forests in Austria. 

Modeling Uneven-aged Forests 

in Switzerland

The purpose of this study was to apply the tree growth model 

Table 1: Differences in diameter increment (predicted-observed) for spruce, fir, and beech and three 5-year growth periods; n is 

the number of observations, idobs is the mean of the observed increment, Di

 is the mean of the differences between predicted 

and observed values, SD the standard deviation of the differences and PI and TI are the prediction and tolerance intervals of the 

error (Reynolds 1984).

Species Period n idobs[cm] Di[cm] SD[cm] PI [cm] TI [cm]

 Spruce 1

2



27

3421

11

0.20

0.21

0.1

-0.08

-0.06

-0.21

0.2

0.24

0.7

-0.59 to 0.43 

-0.53 to 0.41 

-1.50 to 1.92 

-0.59 to 0.42 

-0.54 to 0.42

-1.93 to 1.50 

 Fir 1

2



2017

1849

1595

0.42

0.35

0.

-0.22

-0.20

-0.38

0.22

0.45

1.07

-0.65 to 0.21

-1.08 to 0.68

-2.48 to 1.72

-0.65 to 0.20

-1.09 to 0.69

-2.49 to 1.74

Beech 1

2



18114

1272

10385

0.22

0.21

0.20

-0.08

-0.08

-0.11

0.1

0.21

0.45

-0.45 to 0.29

-0.49 to 0.33

-0.99 to 0.77

-0.45 to 0.29

-0.49 to 0.33

-0.99 to 0.77
FOREST GROWTH AND TIMBER QUALITY

11

MOSES (Hasenauer 1994) to uneven-aged mixed-species 

forests (Schultz 1997). This model predicts the growth of 

each individual tree within a given forest. MOSES follows a 

potential growth concept where the actual increment results 

from different reduction factors. These reduction factors, 

according to Eke and Monserud (1974), are derived from 

two main competition factors: crown ratio and individual 

tree competition.

Data not used for calibration were obtained for this 

study. They consisted of 16.398 growth periods for Norway 

spruce (Picea abies L. Karst), 2.495 for silver fir (Abies alba

Mill.), and 19.292 for Common beech (Fagus sylvatica L.). 

MOSES uses a distance dependent competition measure 

(Ek and Monserud 1974). Thus, it includes an algorithm 

for generating tree distributions (STAND-GEN) allowing 

the analysis of structural and textural effects (Kittenberger 

2003). With these data, a comparison was done between 

predictions and observation. The results suggest no trends 

(see Table 1) and consistent prediction results for unevenaged conditions. The range in the error limits are calculated 

according to Reynolds (1984) and can be interpreted as follows: The prediction interval (PI) gives—within 95 percent 

probability—the range where 95 percent of errors will be 

for any other plots not included in the validation data set. 

The tolerance interval (TI) shows—within 95 percent probability—the range of errors to be expected upon repeated 

model applications. 

For spruce we can be confident that, with a probability 

of 95 percent, no bias for the prediction of the increment 

exists. For single future model applications (95 percent 

probability) the bias will be between -0.59 and 0.43 cm in 

period 1. When applying model simulations repeatedly there 

is a 95 percent probability that 95 percent of the errors will 

be between -0.59 and 0.42 cm in the first period.

In Figure 3, a long-term simulation of the diameter at 

breast height between 1950 and 2004 for two different plots 

is given. The upper plot is a 150-year-old selection forest 

composed of spruce, fir, and beech located 861 m above 

sea level. The lower plot is a 116-year-old even-aged forest 

that has been regularly thinned, located 570 m above sea 

level. In both plots, every treatment was simulated over 50 

years. No trend or bias is evident.

Modeling Forest Ecosystem Restoration

For centuries, European forests have been influenced by 

humans resulting in a reduction of forest-covered land area, 

changes in forest species-distribution, and changes in soil 

conditions. Fast-growing tree species such as Norway spruce 

(Picea abies L. Karst) and Scots pine (Pinus sylvestris L.) were 

promoted in large areas typically covered with broadleaf 

or mixed-species stands in order to increase commercial 

timber growth. 

One method to assess the effects of species composition 

is the use of mechanistic models because they integrate the 

main biogeochemical and physiological processes based 

on the current understanding of key ecophysiological 

Figure 3. Development of mean diameter at breast height (DBH) for two 

plots between 1950 and 2004 (mean ± standard deviation). For both the 

selection forest and the uneven-aged forest, differences between observed 

values (represented by solid lines connecting diamond points) and 

predicted values (represented by dashed lines connecting square points) 

were not significant.

Figure 4. Predicted vs. observed tree volume including regression lines 

developed by using independent validation data
FOREST GROWTH AND TIMBER QUALITY

12

mechanisms (Waring and Running 1998). The purpose of 

this study was to investigate potential degradation effects 

in the soil carbon content according to species change. The 

hypothesis was that historic land use change may affect the 

soil and that it might be possible to mimic theses changes 

with a biogeochemical model. 

Data available for this study were from comparable sites 

with different management strategies: a typical broadleafdominated forest versus a secondary coniferous forest next to 

the broadleaf forest. With these data the water-, carbon- and 

nitrogen- cycle where assessed. For this study, the speciesspecific calibration described by Pietsch et al. (2005) was 

used. For model validation and testing, the 26 spruce and 

18 beech plots established within the Forest Ecosystem 

Restoration research program (Sterba and Hasenauer 2000) 

were used. These plots varied in site index, stand density, 

and stand age and represented an excellent data source for 

studying land-use impacts on the flux dynamics of forest 

ecosystems. On each plot, soil nitrogen, soil carbon, and 

tree volume per hectare were available. 

The main results (see Figure 4) clearly indicate that landuse impacts are essential to the flux dynamics and that soil 

is the key compontent. Ignoring such effects will lead to 

an overestimation in the soil carbon content and thus to 

biased assessments (Pietsch and Hasenauer 2001).

Figure 5. Two full carbon 

cycles within the old-growth 

forest, Rothwald, in Austria 

based on data. NPP is Net 

Primary Production and NEE 

is Net Ecosystem Exchange, 

indicating the source and sink 

potential of unmanaged forests.
FOREST GROWTH AND TIMBER QUALITY

1

The Sink and Source Potential of Forests

An excellent test case for modeling the sink and source 

behavior of undisturbed forests is the flux dynamics of 

old growth or virgin forests. A very good example and application case is provided by the Central European virgin 

forest reserve Rothwald in Austria. Rothwald is located in 

the northern limestone Alps at 15°05’E and 47°46’N at an 

elevation between 950 and 1300 m above sea level. The parent rock is composed of limestone and dolomite. Soil types 

range from lithic and rendzic leptosols to chronic cambisols. 

Mean annual temperature is about 7°C and mean annual 

precipitation 1300mm. Living biomass is comprised of 68 

percent Common beech (Fagus sylvatica L.), and admixture 

of Norway spruce (Picea abies L./Karst.) and silver fir (Abies 

alba Mill.). The documented history of the forest reserve 

starts in 1330, when Albrecht II Habsburg founded the 

charterhouse, Gaming, and endowed the area of Rothwald 

to the contemplative fraternity of the Carthusians. In 1782, 

Joseph II Habsburg eliminated the charterhouse. After 

this, the forest changed owners until it became part of the 

Rothschild estate in 1875. Today, Rothwald is a preserve 

area and was declared a wilderness area (IUCN category 

I) in 2001 (Splechtna and Gratzer 2005). 

For our study we obtained 18 plots covering different 

successional stages within the Rothwald wilderness area. 

On each of the 18 plots, six sub-plots were randomly 

chosen from which we obtained soil and humus samples 

as well as the above-ground tree population conditions. 

The variables available for model testing are volume, dead 

wood volume, nitrogen and carbon within the humus 

and for three different soil layers. These data were used 

to validate the biogeochemical model for old growth forest conditions and to assess the carbon dynamics of such 

forests (see Figure 5).

The results show the sink and source potential of forest. 

During the optimum phase the ecosystem exhibits a net 

carbon sink (optimum phase), stationary phases with no 

net carbon exchange (old growth, juvenescence), and time 

periods where it constitutes a carbon source (breakdown, 

regeneration). Such source-sink transitions are part of natural ecosystem dynamics (Pietsch and Hasenauer 2006). 

DISCUSSION AND CONCLUSION

Forest ecosystem models assess forest ecosystem processes. 

They are designed to detect, quantify, and reproduce the 

dynamics within our forests. These models are important 

tools used to extrapolate forest ecosystem processes at different spatial and temporal scales such as from the point 

to the landscape level (bottom-up approach), or from the 

landscape to the plot level (top-down approach). Accommodation of these scales is important to ensure a successful application. According to the background of the model 

developer, the main subjects of interest and the three basic 

principles for building models are simplicity, observability, 

and biological realism. Three main modeling concepts may 

be distinguished (see Figure 2).

Management models are considered the classical approach developed within growth and yield sciences. They 

are designed to provide information for forest management 

purposes. Their main goal is to forecast timber to ensure 

sustainable harvesting and income. Succession models assess vegetation patterns. They are developed and used to 

understand the tree population dynamic as it has evolved 

over centuries. One main area of application for succession models is the assessment of potential forest-vegetation 

patterns. Mechanistic models are explicitly designed to 

understand the complex interaction between energy, water, and nutrient cycles within forest ecosystems. They are 

used for assessing the interactions and flows within forest 

ecosystems and the surrounding environment and may be 

thought of as classical carbon-cycle models.

In this study, two different modeling concepts were applied. The management-oriented tree growth model MOSES 

(Hasenauer 1994) was used to analyze the growth within 

an uneven-aged mixed-species forest in Switzerland. The 

main results of this modeling exercise suggest no bias and 

that tree growth modeling is an appropriate tool to use 

in meeting the increased silvicultural demand to manage 

structurally diverse forests. 

Our second applied model—the species-specific version 

of the biogeochemical model BIOME-BGC (see Pietsch et 

al. 2005)—demonstrated that the flux dynamics of managed and unmanaged forest ecosystems can be addressed. 

This proves that BGC-Models are an appropriate tool for 

assessing land use changes as well as the sink and source 

potential of forests. The correct formal implementation of 

key ecosystem processes is essential to studying climatechange impacts and degradation effects, which are used in 

sustainable impact-assessment studies. 

It is shown that both mechanistic as well as management-oriented modeling can be applied successfully for 

scenario calculations. Note that the level of detail and, thus, 

the complexity of the different approaches, though different, each adequately addressed the objectives and expected 
FOREST GROWTH AND TIMBER QUALITY

184

needs. Choosing the correct level of model complexity is 

an important step within the modeling process because 

it ensures an efficient use of available resources, and the 

reliability of the model output. 

ACKNOWLEDGMENTS

This research was funded by the Austrian Ministry of 

Forestry and Agriculture as well as the Austrian Ministry 

Water and Environment. It is part of an effort to investigate 

tools to be used in managing the protective function of 

mountainous forests in Austria. We thank Bob Monserud 

and Dennis Dykstra for organizing a great meeting in 

Portland, Oregon. Special thanks to Bob for his support 

and friendship over the last 15 years. 

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FOREST GROWTH AND TIMBER QUALITY

17

Reconstruction of Stand Structure and Growth 

Following Partial Cutting of Southeast Alaska Forests: 

Sustainable Forest Management or Highgrading?

Robert L. Deal

Robert L. Deal (rdeal@fs.fed.us) is a research forester, U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station, 620 SW 

Main Street, Suite 400, Portland, OR 97205.

ABSTRACT

THE EFFECTS OF PARTIAL CUTTING ON STAND 

structure, growth, mortality, and species composition were evaluated on 73 plots in eighteen stands 

that were harvested 12–96 years ago in southeast Alaska. 

Stands were reconstructed using historical records and tree 

increment cores from 986 western hemlock, Sitka spruce, 

western red-cedar, and yellow-cedar trees. Site-specific 

regression equations were developed to predict diameter at 

breast height (DBH) at time of cutting for all trees, relating 

former DBH with current DBH, basal area, species, and 

plot cutting intensity. These equations explained 77–99 

percent of the variation in DBH at the time of cutting. 

Stand mortality was estimated using snag class and snag 

age. Results were used to test assumptions that partial cutting of older forests results in reduced stand growth and 

vigor, increased wounding and mortality, and changes in 

tree species composition. The current stand basal area, 

tree species composition, and stand growth for all cutting 

intensities was strongly related to trees left after harvest. 

Residual trees, including larger remnant trees and small 

advance regeneration, grew rapidly after partial cutting 

and became a significant and dominant component of the 

current stand. The net basal-area growth was greater in 

the partially cut plots than in the uncut plots, and stand 

basal-area growth generally increased with increasing cutting intensity. Mortality, however, was not significantly 

different between cut and uncut plots. Concerns about 

greatly reduced stand growth and vigor, lack of spruce 

17

regeneration, and increased stand mortality were largely 

unsubstantiated. Sustainable forest management using 

silvicultural systems based on partial cutting could provide 

a sustainable timber resource while maintaining complex 

stand structures similar to old-growth stands. 

KEYWORDS: Partial cutting, stand reconstruction, Sitka 

spruce, southeast Alaska, stand structure, western hemlock

INTRODUCTION

Southeast Alaska is a coastal temperate rainforest region 

with large areas of old-growth forests that are renowned 

for their scenic quality, fish and wildlife habitat and timber 

resources. Forest managers in the region have been working 

to develop management strategies that will provide wood 

resources to the local economy without compromising 

scenic quality, or aquatic and wildlife habitat. Managers are 

interested in developing silvicultural solutions to enhance 

options for multiple-resource management.

The coastal rain forests of southeast Alaska have simple 

tree composition but complex forest age and tree-size 

structure. The two predominant tree species, Sitka spruce 

(Picea sitchensis (Bong.) Carr.) and western hemlock (Tsuga 

heterophylla (Raf.) Sarg.), contain more than 90 percent 

of the total forest volume (Hutchison 1967). The forests 

are generally multi-aged, and stands developed following 

high frequency, small-scale natural disturbances such as 

This paper was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 187–194.
FOREST GROWTH AND TIMBER QUALITY

1

windthrow, landslides, and endemic tree disease (Deal et 

al. 1991, Kramer et al. 2001, Hennon and McClellan 2003). 

These multi-aged stands contain complex forest structures 

with many forest canopy layers, abundant understory 

vegetation, large trees and snags, heartrot cavities in live 

trees, large woody debris, and other important ecological 

characteristics of old-growth forests (Franklin et al. 1981, 

Alaback and Juday 1989, Franklin and Spies 1991). 

Since the 1950s, clearcutting has been the dominant 

timber management practice in southeast Alaska forests 

(Harris and Farr 1974). Forest development following 

stand-replacing disturbances such as clearcutting is different than typical forest development following natural 

small-scale disturbances. Post-harvest conifer regeneration 

is frequently abundant (greater than 10,000 trees ha-1) 

with the development of a dense new cohort of western 

hemlock and Sitka spruce trees. The forest canopy closes in 

20–30 years followed by a dense, long-lasting stage of stem 

exclusion (Alaback 1982, Deal et al. 1991). Canopy closure 

eliminates most herbs and shrubs (Alaback 1982) and attempts to re-establish understory plants by thinning dense 

young-growth stands has led mostly to conifer regeneration 

(Deal and Farr 1994) with little success in herbaceous plant 

colonization (Tappeiner and Alaback 1989). These dense 

young-growth stands have relatively uniform tree height 

and diameter distributions, and notably lack the multilayered, diverse forest structures and shrub/herb layers 

found in old-growth or multi-aged stands (Alaback 1984, 

Deal 2001, Hennon and McClellan 2003). 

Stand development in partially cut stands happens differently than in young-growth stands, which develop after 

clearcutting. In a study that assessed several stands that 

were partially cut between 1900–1950, results indicated 

that stand structural diversity, plant diversity, and plant 

abundance were much greater in these partially cut stands 

than in young-growth stands developing after clearcutting 

(Deal 2001, Deal and Tappeiner 2002). Recent forest-management plans have prescribed forest practices using a variety of silvicultural systems including even-aged, two-aged, 

and uneven-aged management (TLMP 1997), even though 

there is little information available on their silvicultural or 

ecological effects. A large scale alternatives-to-clearcutting 

(ATC) study has been established in the region (McClellan 

et al. 2000) to assess the long-term effects of experimentally manipulated forests but it will be many years before 

results are available. 

There is increasing interest in developing forest-management practices that maintain or enhance biodiversity and 

assure long-term sustainability of forest products, wildlife, 

and aquatic resources. Some major silvicultural concerns 

with the use of partial cutting (and highgrading of forests) 

have been previously reported in southeast Alaska (Harris and Farr 1974). However, most of these concerns are 

speculative or based on research done in other regions. In 

this paper I assess the effects of partial cutting in 18 stands 

throughout southeast Alaska and evaluate the following 

concerns with partial cutting:

• partial cutting will cause changes in tree species composition and loss of Sitka spruce

• trees left after partial cutting will be of low vigor with 

poor growth

• partial cutting will lead to significant increases in tree 

mortality

METHODS

Study Areas and Site Selection 

Eighteen partially-harvested sites were selected to sample 

a range of time-since-cutting and intensity of cutting 

throughout southeast Alaska (Figure 1) using the following 

criteria: a) range of time-since-cutting from 10–100 years 

ago; b) only one partial cutting; c) a wide range of cutting 

intensities at each site, including an uncut area; and d) 

uniform topography, soils, and forest type. At each site 

Figure 1. The 18 study sites in southeast Alaska. See Table 1 for 

definitions of the site codes.
FOREST GROWTH AND TIMBER QUALITY

1

I located an uncut control and generally three partially 

cut areas (light, medium, and heavy) and installed 0.2 ha 

plots in each cutting intensity area with a total of 73 0.2-ha 

overstory plots installed in 18 stands (Table 1).

Stand Structure and Growth

In each plot, tree species, DBH, height, and crown class 

was recorded for all live trees with a DBH greater than 2.5 

cm (1.3 m). Species, DBH, and decay class were recorded 

for each snag to characterize current stand structure. On 

each plot, I reconstructed basal area of cut trees from stump 

diameter and took increment cores from 10–20 trees of 

each tree species and crown class to determine tree age, 

basal area growth, and cutting date for each stand. I reconstructed stand structure, basal area, species composition, 

and cutting intensity for each plot from this information 

(see section below on stand reconstruction methodology and 

Table 1). Differences in tree species composition, tree-age 

cohorts, and stand growth were assessed among cut and 

uncut plots (Deal and Tappeiner 2002). Tree radial growth 

increments were used to investigate the effects of partial 

cutting on the growth of hemlock and spruce trees, and 

the size and growth of new and residual trees (new trees 

include new regeneration and trees shorter than 1.3 m at 

time-of-cutting, and residual trees were at least 1.3 m tall 

at date of cutting). 

Tree Wounding and Tree Mortality

For each dead tree with a DBH greater than 25 cm, DBH, 

species, decay class and status (uprooted, standing dead, 

or broken bole) were recorded. Snag and log decay classes 

and estimated time since death for hemlock and spruce are 

reported elsewhere (Hennon et al. 2002). Only trees that 

were determined to have died after partial cutting were used 

in reconstructing tree mortality. Analysis of variance with 

site as a blocking independent variable was used to test for 

differences in the incidence of tree wounding and mortality 

between uncut and cut plots. Regression analysis tested 

for correlation between these variables and the intensity 

of cutting, (i.e., percent basal area removed). Tests were 

conducted for both understory and overstory trees.

Stand Reconstruction Methodology

Tree increment cores and stem sections were measured in 

the laboratory. Cores were mounted on grooved boards 

with rings vertically aligned to provide the best resolution 

of tree-ring boundaries. Cores and stem sections were 

sanded, and tree rings were measured under a dissection 

Cutting Intensity Current Standa Composition

Research Site

Cutting

Date

Basal Area

Cut Cut Left

Basal

Area

All 

Trees Picea Tsuga Otherb Forest Type

(year) (%) (m2

 ha-1) (m2 ha-1) (m2 ha-1) (trees ha-1) (%) (%) (%)

WC - Weasel Cove 100 17-51 9-23 22-45 53-75 450-1220 0-24 67-100 0-17 Picea sitchensis

GP - Glass Peninsula 111 23-69 15-41 17-47 60-84 147-397 11-34 28-83 0-49 Picea sitchensis

FB - Florence Bay 1914 50-57 33-38 26-38 56-83 120-360 18-75 25-82 0 Picea sitchensis

PB - Portage Bay 11 26-65 7-28 14-25 47-56 459-1202 5-33 67-95 0 Tsuga heterophylla

KL - Kutlaku Lake 120 31-63 17-31 18-37 58-139 305-525 5-49 35-95 0-16 Picea sitchensis

HB - Hanus Bay 122 49-96 24-85 3-25 56-83 413-1180 6-62 38-94 0 Picea sitchensis

SK - Sarkar 1925 27-59 14-28 19-37 57-76 467-1163 0-11 89-100 0 Tsuga heterophylla

EP – Elf Point 127 17-73 12-36 13-57 42-116 453-1443 2-4 72-96 0-24 Tsuga heterophylla

CP - Canoe Passage 127 16-75 9-57 19-46 44-66 815-2452 2-13 74-92 6-19 Tsuga heterophylla

SB - Salt Lake Bay 12 48-55 28-35 29-31 63-87 158-642 17-73 27-83 0 Picea sitchensis

WH - Winter Harbor 12 24-38 19-39 56-70 73-95 785-1311 2-33 67-98 0 Picea sitchensis

FC - Finger Creek 1941 18-41 11-33 44-51 58-75 331-522 5-60 40-95 0 Tsuga heterophylla

RF - Rainbow Falls 1942 34-61 15-25 16-29 44-66 348-1108 0-28 63-100 0-10 Picea sitchensis

MB - Margarita Bay 1958 23-83 9-48 10-30 41-63 694-2695 4-24 76-96 0 Tsuga heterophylla

BB - Big Bear Creek 1958 17-36 9-27 47-63 53-79 270-754 15-47 53-85 0 Picea sitchensis

PV - Pavlof River 177 36-58 21-43 31-47 37-69 288-823 4-29 42-96 0-46 Picea sitchensis

GR -Granite 1 18-86 9-51 9-50 13-70 368-1440 0-7 93-100 0 Tsuga heterophylla

TB - Thomas Bay 1984 20-29 18-19 42-77 49-70 237-766 1-17 83-99 0 Tsuga heterophylla

a Stand data for trees and basal area includes all trees that are at least 2.5 cm DBH

b

 The other minor species include western red-cedar (Thuja plicata Donn ex D. Don), yellow-cedar (Chamaecyparis nootkatensis (D. Don) Spach), red alder (Alnus rubra Bong.), and 

mountain hemlock (Tsuga mertensiana (Bong.) Carr.).

Table 1—Descriptions of research sites listed from the oldest to the most recently cut site. Cutting intensity data show the range for the partially 

cut plots at each site. The current stand data include the range of both uncut and cut plots at each site. The forest type is the major overstory tree 

species at each site.
FOREST GROWTH AND TIMBER QUALITY

10

microscope using the methods of Swetnam et al. (1985). 

Each tree’s radial growth since time-of-cutting was calculated. Tree DBH at time-of-cutting was determined by using 

radial-width adjustment equations for off-center cores and 

species-specific bark thickness equations (Deal 1999).

The date-of-cutting was determined by using tree-radial 

growth analyses (Lutz 1928, Henry and Swan 1974, Oliver 

1982, Lorimer 1985, Bailey and Tappeiner 1998) and verified by historical data if available. Patterns of tree release 

indicating an abrupt and sustained increase in growth for 

at least 10 consecutive years averaging at least 50–100 

percent greater than the previous 10 years (Lorimer et al. 

1988) were used to determine the cutting date. Nine of 

the twelve stands with historical records matched cutting 

dates within ± 1 year of the cutting date determined from 

increase in tree radial growth. 

I developed stem-taper equations to predict tree DBH 

from the stump diameter, by using forward stepwise regression analysis (Snedecor and Cochran 1980). The tree 

DBH and basal area of each stump was used to determine 

the amount of basal area cut for each plot. The diameter 

at time-of-cutting of current live trees was determined by 

using increment cores and stem sections from 986 western 

hemlock, Sitka spruce, western red-cedar (Thuja plicata 

Donn ex D. Don), and yellow-cedar trees (Chamaecyparis nootkatensis (D. Don) Spach). I developed site-specific 

regression equations to predict DBH at time of cutting for 

all trees, relating DBH at time of cutting to current tree 

DBH, basal area, species, and plot cutting intensity (Deal 

and Tappeiner 2002). These equations (p < 0.001) explained 

77–99 percent of the variation in tree DBH at time-ofcutting (Table 2). The basal area of all trees at time-ofcutting was multiplied by the appropriate plot-expansion 

factor to determine stand basal area per hectare for each 

plot at time-of-cutting.

I used snag class and snag age data to determine the 

snag DBH at cutting date, and then estimated stand mortality since cutting. Each snag was assigned a decay class, 

and an average age for each decay class was determined 

(Hennon et al. 1990, 2002, Table 3). The DBH for snags 

at the date-of-cutting were predicted using the live tree 

regression equations and growth calculated for the period 

of time snags were alive. Periodic basal-area mortality per 

hectare was estimated for each plot.

I determined the proportion of stand basal-area cut 

(P%CUT) for each plot from:

P%CUT = [CUTBA/(RESBA + CUTBA + MORTBA)]*100

 (1)

where CUTBA is the stand basal area cut, RESBA is the 

live-tree stand basal area at cutting date, and MORTBA is 

the periodic stand basal-area mortality since the cutting 

date. I then used the proportion of stand basal area cut 

as a continuous variable in regression analyses to analyze 

changes in tree species composition, tree-age cohorts, 

growth of tree-diameter, and stand basal-area growth 

since cutting.

Dependent variable n B0 B1 X1 B2 X2 B X B4 X4 R2 MSE 

Tree DBH (mm) at cutting date

Thomas Bay 39 9.1389 0.8955 DBH -15.9034 TRMT 0.000066 DBH2

 0.9964 26.5359

Granite 31 -25.9198 0.9950 DBH -14.3791 TRMT 0.9904 33.3668

Pavlof River 65 -49.5589 0.9829 DBH 0.9932 30.9784

Big Bear Creek 55 -1.1164 0.8715 DBH -18.5378 TRMT 0.00005 DBH2

 0.9859 46.2153

Margarita Bay 60 87.9575 0.3145 DBH -55.4578 TRMT 0.00051 DBH2

 0.8442 78.2703

Rainbow Falls 42 168.731 0.00044 DBH2 -63.4244 TRMT -96.1845 SPEC 0.3127 DBH 0.9031 100.775

Finger Creek 62 64.5816 0.00034 DBH2 0.4176 DBH -73.4940 SPEC 0.9062 92.4447

Winter Harbor 53 -62.9720 0.8104 DBH 0.000074 DBH2

 0.9667 80.1479

Salt Lake Bay 62 109.198 0.00034 DBH2 -34.7033 TRMT -72.5692 SPEC 0.3798 DBH 0.9111 103.593 

 Canoe Passage 64 14.2886 0.00094 DBH2 -23.6187 TRMT 0.8958 98.6757

Elf Point 61 -276.472 0.00047 DBH2 -60.2159 TRMT 82.3128 ln(DBH) 0.8517 125.299 

Sarkar 45 167.7315 0.8323 DBH -114.774 TRMT -114.499 SPEC 0.8757 133.490

Hanus Bay 49 191.108 0.00056 DBH2 -61.2362 TRMT -94.5875 SPEC 0.8345 145.447

Kutlaku Lake 54 1968.728 1.4432 DBH -69.3543 SPEC -74.1878 TRMT -383.626 ln(DBH) 0.8616 181.251

Portage Bay 64 -93.3010 0.7059 DBH 0.00015 DBH2

 0.9091 96.0436

Florence Bay 60 353.259 0.00055 DBH2 -90.3223 TRMT -136.677 SPEC 0.8173 148.229

Glass Peninsula 54 -85.8333 0.8576 DBH -61.5255 TRMT -43.6595 SPEC 0.8124 187.423

Weasel Cove 63 111.536 0.00070 DBH2 -47.8378 TRMT 0.7733 132.780

Note: n is the number of observations; B0 is the intercept and B1-B4 are slope coefficients of the regression line; R2 is adjusted coefficient of determination; 

MSE is mean square error; P is the probability value; DBH is current tree diameter breast height (1.3 m); SPEC is tree species; and TRMT is intensity of cutting.

Table 2—Regression models with regression R2, MSE, and P for tree DBH at the cutting date for stands at 18 research sites.
FOREST GROWTH AND TIMBER QUALITY

11

RESULTS AND DISCUSSION

Tree Species Composition

Partial cutting had little effect on current tree species composition. We found no significant difference between cut 

and uncut plots in the proportion of either western hemlock 

trees or Sitka spruce trees. The proportion of Sitka spruce 

trees averaged 17.5 percent in the cut plots and 15.2 percent 

in the uncut plots. The proportion of spruce trees and basal 

area increased slightly with increasing cutting intensity, but 

cutting intensity explained only 3–5 percent of the variation in tree-species proportion. We found no significant 

relation between cutting intensity and the proportion of 

either spruce or hemlock trees or the proportion of spruce 

and hemlock basal area. 

The results of this study show that the establishment 

of new regeneration and the growth of large, uncut trees 

of both hemlock and spruce can maintain species composition similar to that of study plots before cutting. New 

regeneration was generally plentiful on cut plots, most new 

trees were hemlock, and cutting more than 50 percent of 

the stand basal area always led to the establishment of new 

regeneration (Deal and Tappeiner 2002). New cohort spruce 

trees were found on 44 percent of the cut plots and on only 

11 percent of the uncut plots. These results indicate that 

partial cutting can generally help establish tree regeneration, and, in contrast to other opinions (Andersen 1955), 

spruce will regenerate after partial cutting. Our results 

indicate that silvicultural systems using partial cutting can 

be successfully applied to maintain spruce in mixed western 

hemlock-Sitka spruce forests in southeast Alaska. 

Stand Structure and Growth

Most trees cut were large-diameter spruce trees, and more 

residual hemlock than residual spruce trees were left in 

almost all plots. However, after cutting, there were usually some large trees left 

in the stand. The number 

of trees left after cutting 

in diameter class L-(>100 

cm), M-(71-100 cm), and 

S-(41-70 cm) averaged 7, 14 

and 43 trees ha-1, respectively (Figure 2). Before 

cutting, an average of 18, 

32 and 64 trees ha-1 were 

in these diameter classes, 

and we found significant 

differences (p < 0.005) 

between stands before 

and after cutting in the 

number of L-,M-, and Sclass trees. After 60 years, 

however, the number of 

trees in these size classes 

was similar to the stands 

before cutting, with an 

average of 16, 29 and 81 

trees ha-1 in the L-, M-, 

and S-classes, respectively 

(Figure 2). The current 

stands had slightly more 

trees in class S (+17 trees 

ha-1) and slightly fewer 

trees in M (-3 trees ha-1) 

Picea sitchensis1 and Thuja plicata2 and

Tsuga heterophylla1 Chamaecyparis nootkatensis2

Class 1 Some twigs retained; most bark intact; Some twigs retained; most bark intact;

logs with little outer decay logs with little outer decay

 Age 10 years (range 0-12) 14 years (range NA)

Class 2 Twigs gone, long primary branches Twigs gone, long primary branches and

and some secondary branches retained; some secondary branches retained;

bark beginning to slough; top usually bark beginning to slough; top usually

broken; sapwood decaying intact; sapwood decaying

 Age 20 years (range 12-33) 26 years (range NA)

Class  Secondary branches gone, but short Primary branches retained; top usually

primaries or stubs present; height Intact; bark mainly gone; sapwood

decreasing; most bark gone; logs decaying, heartwood sound but

decaying but can support themselves beginning to check

 Age 50 years (range 33-63) 51 years (range 27-96)

Class 4 Branch stubs mainly gone; height Primary branches mainly gone; bole

decreasing; most bark gone; usually intact coming to point; surface

considerable decay of heartwood at deeply checked, bark and sapwood

base; logs slumping and colonized mainly gone

by moss or other vegetation

 Age 80 years (range 63-117) 81 years (range 49-128)

Class 5 Broken stumplike appearance; top Bole broken often with jagged top;

portion with branch stubs gone; bark downed portion covered by vegetation

almost completely gone; wood decaying or unrecognizable

and sloughing away; colonized by

vegetation; log cannot support itself,

becoming oval as slumps into forest

 Age 100+ years 100+ years

1

 From Hennon et al. (2002).

2

 From Hennon et al. (1990).

Table 3—Snag decay classes for Sitka spruce (Picea sitchensis (Bong.) Carr.), western hemlock 

(Tsuga heterophylla (Raf.) Sarg.), western red-cedar (Thuja plicata Donn ex D. Don), and yellow-cedar 

(Chamaecyparis nootkatensis (D. Don) Spach).
FOREST GROWTH AND TIMBER QUALITY

12

and L (-3 trees ha-1) classes than the stands before cutting, 

but no significant differences were found in the frequency 

of trees for any diameter class.

Sitka spruce diameter growth was slightly greater than 

western hemlock growth for all tree-diameter classes, but 

growth differences between species were not statistically 

significant (p > 0.05) for any diameter class. Residual trees 

of both species in all size classes increased diameter growth 

after cutting. The current stand basal area, tree species 

composition, and stand growth for all cutting intensities 

was strongly related to trees left after harvest. These results 

are contrary to conventional thinking about partial cutting 

in southeast Alaska where residual trees are assumed to be 

of poor quality and low vigor. In this study, we found that 

these small advance regeneration and larger residual trees 

responded with rapid and sustained growth after overstory 

removal and became a major part of the current stand. 

Tree Wounding and Mortality

Overstory trees had significantly greater incidence of 

wounding (p = 0.04) in cut than uncut plots and wounding increased with intensity of cutting (p = 0.03). Many 

wounds could not be attributed to logging, however, as 

falling trees and porcupine damage were other causal factors on some sites. 

For trees of all sizes, mortality was not significantly 

different between cut or uncut plots. However, estimating mortality over time is the most difficult piece of stand 

reconstruction and the wide ranges in average age of snags 

highlights the difficulty of accurately estimating stand 

mortality (Table 3). The reported average age of snag classes 

includes a considerable amount of variation and these snag 

classes provide only a rough estimate of stand mortality. 

Another concern in partially harvested stands is windthrow 

and the fate of large residual trees is of particular interest. 

In this study, the percentage of dead, large residual trees in 

cut plots (27 percent) was not significantly different than in 

uncut plots (22 percent). Of large residual trees that died, 

an average of 37 percent and 28 percent, respectively, died 

through uprooting in partially cut and uncut plots; the 

remainder died standing or by bole breakage. Windthrow 

did not significantly increase after partial cutting; indeed, 

mortality of residual trees was only marginally higher in partially cut than in uncut stands. For residual trees that died, 

the higher rate of uprooting associated with cutting does 

suggest that wind has an increased role in tree death. Thus, 

our results may underestimate the severity of wind-damage 

risk in some landscape settings. Managers concerned about 

windthrow should consider wind exposure (Kramer et al. 

2001) when designing partial cutting treatments.

CONCLUSION

The stands reported here were cut to provide specific 

wood products and cutting occurred without a planned 

silvicultural system. Little effort was taken to ensure spruce 

regeneration, encourage stand growth, control or reduce tree 

damage agents, or maintain the complex stand structures 

found in old-growth forests. Nevertheless, Sitka spruce 

was maintained in these stands and greatly reduced stand 

growth did not occur. There were not large changes in tree 

species composition, greatly reduced diameter growth and 

vigor, or higher incidence of tree wounding, decay, and 

windthrow-mortality with partial cuts. Stand structural 

diversity and plant diversity and abundance were much 

greater in partially- cut stands than in young-growth stands 

developing after clearcutting. These results indicate that 

new silvicultural systems that use partial cutting could alleviate some of the problems associated with conventional 

Figure 2. The number of trees per hectare by size class in the partially cut 

plots immediately after and before cutting, and in the current stand 60 

years after cutting. Vertical bars indicate standard errors.
FOREST GROWTH AND TIMBER QUALITY

1

clearcutting in southeast Alaska while also providing a 

sustainable timber resource.

LITERATURE CITED

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in Sitka spruce-western hemlock forests of southeast 

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forest structure in the western hemlock-Sitka spruce 

forests of southeast Alaska. In: Fish and Wildlife 

Relationships in Old-Growth Forests. Meehan, W.R., 

Merrell, T.R.J., Hanley, T.A. (Eds.), American Institute 

of Fishery Research Biologists, Morehead City, NC. 

pp. 219-226.

Alaback, P.B.; Juday, G.P. 1989. Structure and 

composition of low elevation old-growth forests in 

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Areas Journal 9: 27-39.

Andersen, H.E. 1955. Clearcutting as a silvicultural 

system in converting old forests to new in southeast 

Alaska. Society of American Foresters Proceedings 

1955: 59-61.

Bailey, J.D.; Tappeiner, J.C. 1998. Effects of thinning 

on structural development in 40- to 100-year-old 

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Structure and Growth, and Forest Plant Communities 

of Western Hemlock-Sitka Spruce Stands in Southeast

Alaska. Ph.D. Thesis. Oregon State University, 

Corvallis, OR. 191 p.

Deal, R.L. 2001. The effects of partial cutting on forest 

plant communities of western hemlock-Sitka spruce 

stands of southeast Alaska. Canadian Journal of Forest 

Resources 31: 2067-2079.

Deal, R.L.; Farr, W.A. 1994. Composition and 

development of conifer regeneration in thinned and 

unthinned natural stands of western hemlock and 

Sitka spruce in southeast Alaska. Canadian Journal of 

Forest Resources 24 (5): 976–984.

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Reconstruction of mixed hemlock-spruce stands in 

coastal southeast Alaska. Canadian Journal of Forest 

Resources 21: 643-654.

Deal, R.L.; Tappeiner, J.C. 2002. The effects of partial 

cutting on stand structure and growth of western 

hemlock-Sitka spruce stands in southeast Alaska. 

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Franklin, J.F.; Cromack, K.J.; Denison, W. [et al.]. 

1981. Ecological characteristics of old-growth 

Douglas-fir forests. Gen. Tech. Rep. PNW-GTR-118. 

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Station, Portland, Oregon. 48 p.

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and structure of old-growth Douglas-fir forests. In:

Ruggiero, L.F., Aubry, K.B., Carey A.B., Huff, M.H., 

eds. Wildlife and vegetation of unmanaged Douglas-fir 

forests. Gen. Tech. Rep. PNW-GTR-421. USDA Forest 

Service, Pacific Northwest Research Station, Portland, 

Oregon. 25p.

Harris, A.S.; Farr, W.A. 1974. The Forest Ecosystem 

of Southeast Alaska, 7: Forest Ecology and Timber 

Management. Gen. Tech. Rep. PNW-GTR-25. USDA 

Forest Service, Pacific Northwest Research Station, 

Portland, Oregon. 109 pp

Hennon, P.E.; Hansen, E.M.; Shaw, C.G. III. 1990.

Causes of basal scars on Chamaecyparis nootkatensis in 

southeast Alaska. Northwest Science 64: 45-54.

Hennon, P.E.; McClellan, M.H. 2003. Tree mortality 

and forest structure in temperate rain forests of 

southeast Alaska. Canadian Journal of Forest 

Resources 33: 1621-1634.

Hennon, P.E.; McClellan, M.H.; Palkovic, P. 2002.

Comparing deterioration and ecosystem function of 

decay-resistant and decay-susceptible species of dead 

trees. Gen. Tech. Rep. PSW-GTR-25. USDA Forest 

Service, Pacific Southwest Research Station, Albany, 

CA. pp. 435-443. 

Henry, J.D.; Swan, J.M.A. 1974. Reconstructing forest 

history from live and dead plant material—an 

approach to the study of forest succession in 

southwest New Hampshire. Ecology 55: 772-783.

Hutchison, O.K. 1967. Alaska’s forest resource. Res. 

Bull. PNW-19. USDA Forest Service, Pacific Northwest 

Research Station, Portland, Oregon. 74pp.
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Succession and Stand Development Research in the 

Northwest: Proceedings of the Symposium. Oregon 

State University, Forestry Research Laboratory, 

Corvallis, OR. pp. 100-112.

Snedecor, G.W.; Cochran, W.G. 1980. Statistical 

Methods, 7th ed. The Iowa State University Press, 

Ames, IA. 507 p.

Swetnam, T.W.; Thompson, M.A.; Sutherland, 

E.K. 1985. Spruce budworms Handbook: Using 

Dendrochronology to Measure Radial Growth of 

Defoliated Trees. Agricultural Handbook 639. USDA 

Forest Service, Cooperative State Research Service, 

Washington, DC. 39 p.

Tappeiner, J.C.; Alaback, P.B. 1989. Early establishment 

and vegetative growth of understory species in the 

western hemlock-Sitka spruce forests in southeast 

Alaska. Canadian Journal of Botany 67: 318-326.

Tongass Land Management Plan (TLMP) Record 

of Decision. 1997. Record of Decision for Tongass 

National Forest Land and Resource Management Plan 

Revision, Alaska. Alaska Region, R10-MB-338a. USDA 

Forest Service, Region 10, Juneau, AK. 44 pp.

Kramer, M.G.; Hansen, A.J.; Taper, M.L.; Kissinger, 

E.J. 2001. Abiotic controls on long-term windthrow 

disturbance and temperate rain forest dynamics in 

southeast Alaska. Ecology 82: 2749-2768.

Lorimer, C.G. 1985. Methodological considerations in 

the analysis of forest disturbance history. Canadian 

Journal of Forest Resources 15: 200-213.

Lorimer, C.G.; Frelich, L.E.; Nordheim, E.V. 1988.

Estimating gap origin probabilities for canopy trees. 

Ecology 69: 778-785.

Lutz, H.J. 1928. Trends and Silvicultural Significance of 

Upland Forest Successions in Southern New England. 

Environmental Studies Bulletin 22. Yale University 

School of Forestry, New Haven, CT. 68 p.

McClellan, M.H.; Swanston, D.N.; Hennon, P.E. [et 

al.]. 2000. Alternatives to clearcutting in the oldgrowth forests of southeast Alaska: study plan and 

establishment report. Gen. Tech. Rep. PNW-GTR494. USDA Forest Service, Pacific Northwest Research 

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FOREST GROWTH AND TIMBER QUALITY

195

Combining Tree- and Stand-Level Models: A New 

Prediction System to Improve Growth Prediction in 

Norway Spruce (Picea abies)

C. Yue, U. Kohnle, S. Hein

C. Yue, U. Kohnle (presenter; ulrich.kohnle@forst.bwl.de) and S. Hein are researchers at the Forest Research Institute of Baden-Wuerttemberg, 

Freiburg, Germany.

ABSTRACT

A NEW PREDICTION SYSTEM IS PRESENTED 

to improve the estimation of single tree diameter 

and stand basal area growth. The prediction system consists of three steps: prediction, combination, and 

modification. The prediction of stand basal area is based on 

a tree-level diameter growth model and a stand-level basal 

area growth model. A cumulative diameter-rate model is 

developed for the tree-level diameter growth model. The two 

models working at different levels are combined based on 

variance and covariance method. The combined estimator 

is further used to modify the two models (the tree-level as 

well as the stand-level model). In contrast to a straightforward linking approach (such as for disaggregation) the new 

prediction system works in a feedback process.

For the estimation of the annual growth model parameters from periodical measurements, a general loss function is introduced to counterbalance possible effects of 

irregular measurement intervals. Based on an independent 

validation data set, projections of stand basal area with the 

combined estimator gain in efficiency from 14–43 percent 

compared to projections with the tree-level model alone, 

and from 4–16 percent compared to projections with the 

stand-level model, depending on the temporal horizon of 

the projection (5–30 years).

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 195.

FOREST GROWTH AND TIMBER QUALITY

17

The Use of Airborne LiDAR Data to Estimate the 

Relationship Between Crown Surface Area and Stem 

Surface Area of chamaecyParis obtusa Stands

Tohru Nakajima, Yasumasa Hirata, Naoyuki Furuya, Katsutoshi Takezoe, 

Makoto Suzuki, Satoshi Tatsuhara, Norihiko Shiraishi

Tohru Nakajima and Katsutoshi Takezoe are graduate students, Satoshi Tatsuhara is an associate professor and Norihiko Shiraishi is a professor 

in the Graduate School of Agricultural and Life Sciences, the University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-8657, Japan; Yasumasa Hirata

is a group leader, Shikoku Research Center, Forestry and Forest Products Research Institute, 2-915 Asakuranishimachi, Kochi 780-8077, Japan; 

Naoyuki Furuya is a researcher, Forestry and Forest Products Research Institute, 1 Matsunosato, Tsukuba, Ibaraki 305-8687, Japan; Makoto Suzuki 

is a lecturer, University Forest in Chiba, Graduate School of Agricultural and Life Sciences, the University of Tokyo, 770 Amatsu, Kamogawa, Chiba 

299-5503, Japan.

ABSTRACT

I

N THIS STUDY, WE CALCULATED the relationship 

between the average crown surface area and the stem 

surface area of dominant trees. The study site was the 

University of Tokyo Forest in Chiba. First, we estimated 

the crown surface area based on a digital surface model 

(DSM) and a digital elevation model (DEM) obtained from 

airborne light detection and ranging (LiDAR) data acquired 

on August 14, 2005. The region of interest (ROI) from which 

the data were extracted was 200 m wide and 1,700 m long. 

The airborne LiDAR data had a footprint diameter of 50 cm, 

a distance between neighboring footprints of 25 cm, and a 

laser pulse rate of 70,000 Hz. Next, we estimated the stem 

surface area based on ground survey data. We established 

seven circular plots in Chamaecyparis obtusa plantations 

and measured the diameter at breast height (DBH), and 

tree height in each plot. We applied a relative-crown curve 

and a relative-taper curve to these data, and estimated the 

average crown surface area and stem surface area of dominant trees. A linear regression between the crown surface 

area and stem surface area was carried out, resulting in a 

coefficient of determination of 0.97. This result showed a 

strong relationship between the average crown surface area 

and the stem surface area estimated from airborne LiDAR 

data and ground survey data. 

KEYWORDS: Airborne LiDAR, Chamaecyparis obtusa, crown 

surface area, stem surface area

INTRODUCTION

A forest grows due to the photosynthesis of its trees. As 

previous studies have shown, the greater the respiration 

volume of trees, the less forest growth (Bosc et al. 2003, 

Arain and Restrepo-Coupe 2005). This suggests that one 

can predict forest growth based on the balance between 

the photosynthesis and respiration of trees. 

The main parts of a tree involved in photosynthesis 

and respiration are the canopy and wood including the 

stems, branches, and roots, respectively. To estimate forest 

resources, one can collect direct, ground-based data on 

woodiness, such as the diameter at breast height (DBH) 

and the stem number. Various growth models have been 

developed based on stem information, including the tree 

height and DBH (Castedo-Dorado et al. 2007, Qin et al. 

2007, Shiraishi 1986). However, it is difficult to measure a 

crown structure that is high and complex. It is even more 

difficult to measure crown information over a wide area. 

Chiba (2005) introduced crown-length information into 

a growth model for estimating the DBH and stem form. 

This paper was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 197–204.
FOREST GROWTH AND TIMBER QUALITY

1

However, no growth models that include crown information have been developed for Japanese mountainous areas 

at the regional scale.

Previous studies have suggested the usefulness of remotely sensed data for measuring forest resources such 

as stand age (Farid et al. 2006), tree height (Hirata 2005, 

Takahashi et al. 2005, Næsset and Bjerknes 2001), and forest 

biomass (Labrecque et al. 2006). In addition, airborne light 

detection and ranging (LiDAR) data enable us to obtain a 

wide range of canopy information, including the leaf area 

(Roberts et al. 2005), canopy fuel (Andersen et al. 2005), 

and canopy structure (Coops et al. 2007) information. For 

a mountainous forest in Japan, where the terrain was very 

complex and steep, Nakajima et al. (2006) reported that the 

average crown length of dominant trees could be estimated 

using airborne LiDAR data.

As mentioned above, it is important to analyze the 

relationship between woody information and canopy information for developing a growth model that considers the 

balance of respiration and photosynthesis. However, few 

previous studies have analyzed the relationship of crown 

information estimated from LiDAR and woody information measured by a ground survey in Japan. The objective 

of our study was to estimate the relationship between the 

average crown surface area and the woody surface area of 

dominant trees using airborne LiDAR data. For calculating the crown surface area and stem surface area, we used 

the relative-crown curve reported by Kajihara (2000) and 

the relative-taper curve reported by Nagumo and Tanaka 

(1981), respectively. We then conducted a linear regression 

between the crown surface area and the stem surface area. 

Considering the balance of tree photosynthesis and respiration for development of the growth model, we discuss 

the relationship between the crown surface area and the 

stem surface area. 

METHODS 

Study Site

The study focused on Chamaecyparis obtusa plantation forests in the University of Tokyo Forest in Chiba, Japan. The 

University Forest in Chiba is located in the southeastern 

Boso Peninsula. The plantation forests are 824 ha in area, 

occupying 37 percent of the total forest area of 2,226 ha. 

Natural forests cover the rest of the forest area. The total 

stem volume of the University Forest is approximately 

500,000 m3

. Of this stem volume, 300,000 m3 is stocked 

in plantation forest and 200,000 m3

 is stocked in natural 

forest. The total annual growth volume is approximately 

8,069 m3, which converts to approximately 3.6 m3 per ha. 

The average yearly temperature in this area is 13.8 degrees 

Celsius. The hottest month is August, with the average 

temperature of 24.2 degrees Celsius. The coldest months 

are January and February, in which the average temperature 

is 4.4 degrees Celsius. The altitude above sea level ranges 

from approximately 50 m to 370 m, and the terrain of the 

area is complex and precipitous for its altitude range.

Figure 1— DSM measured using airborne LiDAR. White circles indicate 

the locations of sample plots used for ground surveys of Chamaecyparis 

obtusa stands.
FOREST GROWTH AND TIMBER QUALITY

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Data Collection

Airborne LiDAR data were acquired on August 14, 2005. 

The region of interest (ROI) from which the data were extracted was 200 m wide and 1,700 m long. The LiDAR data 

specifications were as follows; flying height, 500 m; speed, 

70 km h-1; footprint diameter, 50 cm; distance between 

neighboring footprints, 25 cm; and laser pulse rate, 70,000 

Hz. We used a digital surface model (DSM) (Figure 1) and 

a digital elevation model (DEM) 

derived from the LiDAR data to 

extract information on the crowns 

of standing trees.

In the region covered by the 

LiDAR data, we established seven 

circular sample plots for ground 

surveys. These sample plots were 

approximately 22.6 m in diameter (0.04 ha) and were located in 

Chamaecyparis obtusa plantations of 

various stand densities. At least 450 

stems ha-1 were measured in each 

plot (Table 1). The central coordinates of each plot were found using 

a differential global positioning 

system (DGPS) receiver (ProMark2, 

Ashtech and Pathfinder ProXR, 

Trimble Navigation). The four highest trees in each plot were selected 

as the dominant trees, equivalent to 

100 stems ha-1 selected as dominant 

trees. The DBH of each standing 

tree in each plot was measured. The 

heights of more than 40 percent 

of all trees were measured using a 

Vertex III system (Haglöf), and were 

estimated for other trees using a 

Näslund height-diameter curve. 

Data Analysis

Estimating the crown crosssectional surface from LiDAR 

data— 

The crown cross-sectional surface 

of the dominant trees was estimated 

from LiDAR data with TNTmips ver. 

6.6 (MicroImages 2001). Using the DEM and DSM data, we 

estimated the crown cross-sectional surface of dominant 

trees in each plot. First, we selected four trees (100 stems 

ha-1) as dominant trees. In this case, the dominant trees 

were the highest in each plot. Because the DSM includes the 

height above sea level, it is difficult to calculate the exact 

tree height from DSM data. Accurate tree height can be 

obtained from the digital crown model (DCM) calculated by 

Table 1. Sample plots used for ground surveys of Chamaecyparis obtusa stands.

Plot No. Compartment Subcompartment Stand age Stand density (stems ha-1)

1 11 C1  450

10 20 C1 27 3925

11 20 C1 27 2350

14 4 C1 44 2025

21 11 D2 55 700

22 11 D2 55 700

2 11 D2 55 1475

Figure 2— Enlarged view of airborne LiDAR data of Plot 10.
FOREST GROWTH AND TIMBER QUALITY

200

subtracting the DEM, i.e., the height above sea level, from 

the DSM. The tree height was defined as the height of the 

top of the tree derived from the DCM. Figure 2 shows that 

airborne LiDAR can identify the canopy of each individual 

tree. The four highest trees in each plot were selected as 

the dominant trees from the DCM and overlapped on the 

vector data from the DGPS for the circular plots. 

Second, we estimated the crown cross-sectional surface. 

The crown length of each tree was estimated by subtracting the height to the base of the crown from the total tree 

height. We measured the height to the base of the crown on 

the rebound point obtained from the DSM cross-sectional 

surface, because we considered the far side canopy from 

the rebound point to be the crown of the neighboring tree 

(Figure 3). The direction of the DSM cross-sectional surface 

was estimated from the average slope aspect derived from 

the DEM in each plot, because there is normally more space 

for branch and leaf expansion on the slope side of trees. 

Figure 4 shows an example of a cross-sectional surface of 

a dominant tree. We calculated the crown length, crown 

width, and width at approximately the middle point of the 

crown length for this figure. Nakajima et al. (2006) reported 

that the average crown length of dominant trees could be 

estimated accurately by airborne LiDAR data. Thus, we 

assumed that the crown widths of dominant trees could 

be estimated by LiDAR data without large differences from 

ground-truth measurements. These crown information 

data were used for estimating the crown surface area as 

follows.

Relationship Between the Crown and Stem 

Surface Areas

Finally, we obtained the relationship between the surface 

areas of the crown and stem using data derived from 

airborne LiDAR and the ground survey. In this study, we 

assumed that the stem surface and crown surface would be 

the main sites of respiration and photosynthesis, respecFigure 3— Position at which tree height was measured to determine the 

base of the crown. The base of the crown is indicated by a bold arrow.

Figure 4—Example of the cross-sectional surface of a dominant tree.
FOREST GROWTH AND TIMBER QUALITY

201

tively. This assumption is based on suggestions by previous 

studies that photosynthesis activity is very high on the 

crown surface (Kajihara 2000). Bosc et al. (2003) reported 

that the surface area of wood has a stronger relationship 

with respiration than with woody volume. With this assumption, we calculated the crown surface area and stem 

surface area and estimated the relationship of the size of 

the average photosynthetic organ and woody organ of the 

dominant trees.

Calculation of the crown surface area—

In this procedure, we applied formula (1), the relative 

crown curve reported by Kajihara (2000), to the crown 

profile:

(1)

where x: relative distance from the top of the tree (0 - 

1.0)

y: relative crown width (0 - 0.5)

a, b: parameters

By definition, this curve passes the point (1, 0.5). Therefore, the relationship between parameter a and b is shown 

as formula (2):

(2)

Formula (1) could be transformed into formula (3) 

through formula (2):

(3)

Formula (4) is the actual crown curve based on the relative 

crown curve, formula (3):

(4)

where X: distance from the top of the tree (m)

 Y: width at distance X (m)

 D: crown width (m)

 L: crown length (m)

We estimated parameter a with formula (3), to which we 

assigned the coordinate value exchanged from the crown 

width and the distance from the top of the tree at the middle 

point of the crown derived from LiDAR data on the relative 

crown curve. By assigning parameter a to formula (4), we 

can derive the actual crown curve. The crown surface area 

is estimated with formula (5) showing the surface of the 

solid revolution of formula (4):

(5)

where Sc: crown surface area (m2)

We calculated the crown surface area by integrating formula 

(5) with Romberg quadrature. We applied these calculations 

to the four dominant trees in each plot and estimated the 

average crown surface area of the dominant trees.

Calculation of the stem surface area—

We calculated the stem surface area based on the tree height, 

DBH, observed during the ground survey, and the relative 

taper curve. We applied the relative taper curve estimated 

in the University Forest in Chiba (formula (6) as reported 

by Nagumo and Tanaka (1981)):

(6)

Where ys: relative stem radius (0 - 0.5) 

a, ß,γ: parameters

Formula (7) is the actual taper curve based on the relative taper-curve, formula (6):

(7)

where Ys: stem radius (m) 

 Ds: radius at breast height (1.3m) 

 H: tree height (m) 

The stem surface area is estimated with formula (8) 

showing the surface of the solid revolution of formula (7):

(8)

where Ss: stem surface area (m2)

We calculated the stem surface area by integrating 
FOREST GROWTH AND TIMBER QUALITY

202

formula (8) with Romberg quadrature. The average stem 

surface area is the average value of the stem surface areas 

of the four dominant trees. The stem surface areas based 

on ground survey data were regressed against the crown 

surface areas based on airborne LiDAR data. We then calculated the coefficient of determination. This result and the 

relationship between the average crown surface area and 

average stem surface area are discussed below.

RESULTS AND DISCUSSION 

The relationship between the average stem surface area and 

the crown surface area of the dominant trees can be seen 

in Figure 5. The constant term and slope of the regression 

line were 0.2442 and -3.0999, respectively. As shown in this 

figure, the average stem surface area per tree was smaller 

than the crown surface area per tree. The coefficient of 

determination was 0.97. This result suggests a very strong 

correlation between the average stem surface area and the 

crown surface area of dominant trees. This finding is also 

consistent with those of previous studies, which found that 

in general, the greater the respiration volume, the more 

photosynthesis is required (Arain and Restrepo-Coupe 

2005). In this study, we established sample plots in plantations with various stand densities. Figure 5 shows the 

strong relationship between the crown and stem surface 

area for various stand densities. These plots established in 

Chamaecyparis obtusa stands have been regularly managed 

by staff of the University Forest in 

Chiba in an integrated fashion based 

on standard density control measures 

(Shiraishi 1986). Thus, the relationship between the crown surface 

area and the stem surface area had 

been controlled throughout various 

stand densities at the management 

unit level. This could be one of the 

reasons for the very high coefficient of 

determination even though the plots 

included stands of various densities. 

However, the dominant trees were 

not suppressed by other trees because 

the tops of these trees were relatively 

high. This situation could also account for the very strong relationship 

between the average crown surface 

area and the stem surface area of the 

dominant trees throughout low- and 

high-density stands. This observation will be verified in a 

further case study in another experimental forest belonging 

to the University of Tokyo managed under the standard 

density control.

In our study, we estimated the crown length by the 

DSM obtained from the first pulse. The first pulse reflected 

against the sunlit canopy does not include information on 

the shaded portion of the canopy, where sunlight is blocked 

by other tree branches. In other words, Figure 5 suggests a 

strong relationship between the sunlit crown surface area 

and the stem surface area. This result is also consistent 

with previous reports that the shaded canopy does not 

contribute to tree growth (Kajihara 1985).

Note that we considered only the stem surface area as 

the main contributor to respiration. However, a tree respires 

not only on the surface of its stem but also on the surface 

of its branches and roots. Thus, to obtain an accurate estimation of the relationship between photosynthesis and 

respiration, we should compare the crown surface area with 

the sum of the surface area of stems, branches, and roots. 

If the surface area of the stems, branches, and roots were 

summed up, the graph of the figure would move upward, 

and the regression line would pass closer to the coordinate 

origin. If this were the case, the rate of the crown surface 

area to the total surface area of stems, branches, and roots 

could be more constant.

Another general relationship is that the larger the crown, 

Figure 5—The crown surface area obtained from airborne LiDAR data versus the stem surface area 

estimated by ground survey data.
FOREST GROWTH AND TIMBER QUALITY

20

the larger the branches and roots (Fukuda et al. 2003). If 

the branch and root surface areas are added to the stem 

surface area, the increase in the upper-right side value in 

Figure 5 is larger than that of the lower-left side value. 

Thus, if we plot the total stem, branch, and root surface 

area and the crown surface area on the figure, the slope of 

the regression line would become steeper.

CONCLUSIONS

In this study, we estimated the relationship between the 

average crown surface area and the stem surface area of 

dominant trees in Chamaecyparis obtusa stands. First, we 

estimated the crown surface area based on a DSM and DEM 

obtained from airborne LiDAR data. In this procedure, the 

relative crown curve was applied to these LiDAR-derived 

data. Second, we estimated the stem surface area based on 

ground survey data such as the DBH and tree height. The 

relative taper curve was applied to these ground-survey data 

in this procedure. Finally, a linear regression between the 

crown surface area and the stem surface area was carried 

out, resulting in a coefficient of determination of 0.97. The 

results of our study suggest a strong relationship between 

the average sunlit crown and stem surface area.

The next challenge is estimating the branch and root 

surface area in more plots and developing a growth model 

to consider the relationship between the crown surface area 

and the surface areas of stems, branches, and roots.

ACKNOWLEDGMENTS

We would like to thank the staff of the University Forest in 

Chiba, University of Tokyo, for assistance with field measurements. This research was partly supported by Research 

Fellowships from the Asahi Breweries Foundation.

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LIDAR data. Remote Sensing of Environment 94: 441-

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stock estimates for sugi and hinoki forests in Japan. 

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by using sunny crown-surface area and stem-surface 

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canopy information. Tokyo: Japanese Society of Forest 

Planning Press. 139 p. (in Japanese) 

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2006. A comparison of four methods to map biomass 

from Landsat—TM and inventory data in western 

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MicroImages, Inc. 2001. TNTmips ver.6.6. Lincoln, NE, 

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heights and number of stems in young forest stands 

using airborne laser scanner data. Remote Sensing of 

Environment 78: 328-340.

Nagumo, H.; Tanaka, M. 1981. Construction of a 

volume table with a relative stem-curve. Journal of 

Japanese Forestry Society 63: 278-286. (in Japanese 

with English summary)

Nakajima, T.; Hirata, Y.; Furuya, N. 2006. Developing 

methodology for estimating canopy information by 

LiDAR. Proceedings of the International Conference 

Silvilaser 2006: 249.

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diameter distribution through time. Canadian Journal 

of Forest Research 37:188-194.

Roberts, S.D.; Dean, T.J.; Evans, D.L. [et al.]. 2005.

Estimating individual tree leaf area in loblolly pine 

plantations using LiDAR-derived measurements of 

height and crown dimensions. Forest Ecology and 

Management 213:54-70.

Shiraishi, N. 1986. Study on the growth prediction of 

even-aged stands. Bulletin of the Tokyo University 

Forests 75:199-256.

Takahashi, T.; Yamamoto, K.; Senda, Y.; Tsuzuki, 

M. 2005. Estimating individual tree heights of 

sugi (Cryptomeria japonica D. Don) plantations in 

mountainous areas using small-footprint airborne 

LiDAR. Journal of Forest Research 10:135-142.
FOREST GROWTH AND TIMBER QUALITY

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Evaluation of an Ecosystem-Based Approach 

to Mixedwood Modeling

B. Seely, C. Hawkins, J.A. Blanco, C. Welham, J.P. Kimmins

B. Seely (brad.seely@ubc.ca), J.A. Blanco, C. Welham, and J.P. Kimmins are in the Department of Forest Sciences, University of British Columbia, 2424 

Main Mall, Vancouver, BC, V6T 1Z4, Canada; C. Hawkins is in the Faculty of Natural Resources and Environmental Studies, University of Northern 

British Columbia, 3333 University Way, Prince George, BC V2N 4Z9, Canada.

EXTENDED ABSTRACT

KEYWORDS: FORECAST, mixedwood management, model 

testing, process-based model, resource competition

INTRODUCTION 

MIXED CONIFER-BROADLEAF FORESTS 

(mixedwoods), covering more than a third of the 

productive forest landbase in British Columbia, 

are highly valuable both as sources of fiber and as areas rich 

in biodiversity. Historically, these forest types have been 

managed as single-species stands with herbicide and manual 

brushing treatments employed to promote conifer plantations (Comeau et al. 2000, Harper and Kabzems 2003). More 

recently, the benefits of retaining and managing for intimate 

mixtures of conifers and hardwoods have been recognized 

(Grover and Greenway 1999) and management paradigms 

have transitioned from a focus on promoting conifer plantations in mixedwood areas to the management of intimate 

mixtures. Research with respect to the production ecology 

of mixedwood ecosystems has illustrated that mixtures 

of conifers and broadleaf species can be more productive 

than pure stands (Man and Lieffers 1999) and that reasonably good conifer growth can be maintained in intimate 

mixtures if steps are taken to reduce broadleaf competition 

(Simard and Hannam 2000, Simard et al. 2004, Comeau 

et al. 2000). Explanations for these findings have focused 

on the differential utilization of resources by broadleaves 

and conifers (light, nutrients, and water) (Man and Lieffers 

1999), the positive impacts of broadleaf species on nutrient 

cycling rates (Comeau 1996, Cote et al. 2000) and shared 

mycorrhizal networks (Simard et al. 1997).

The dynamic nature of mixedwood forests presents a 

number of management challenges, not the least of which 

is how best to project their growth and development under 

different management systems. One model that utilizes 

a mechanistic approach for projecting forest growth and 

ecosystem dynamics is FORECAST (Kimmins et al. 1999). 

FORECAST was designed to accommodate a wide variety 

of harvesting and silvicultural systems in order to compare 

and contrast their effect upon forest productivity, stand 

dynamics, and various biophysical and social indicators of 

non-timber values. The model has been applied to a variety 

of mixedwood stand types (Welham et al. 2002, Seely et 

al. 2002, Seely et al. 2004, Sachs 1996), but establishing its 

utility as a decision-support tool for mixedwood management 

still requires evaluations of its performance against longterm, mixedwood forest growth data from well-documented 

field trials. Here we evaluate the ability of a mechanistic 

forest growth model (FORECAST) to project patterns of 

stand growth and dynamics in a spruce-aspen mixedwood 

forest type subjected to different silvicultural treatments. 

Model output is compared against field measurements from 

long-term silviculture trials in the Sub Boreal Spruce (SBS) 

biogeoclimatic zone in British Columbia, Canada. 

METHODS

Model Description

FORECAST is a management-oriented, stand-level forest 

growth and ecosystem dynamics simulator. A detailed deThis extended abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: 

Crown models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. 

Tech. Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 205–210.
FOREST GROWTH AND TIMBER QUALITY

20

scription of the FORECAST model is provided in Kimmins 

et al. (1999) and Seely et al. (In press), only a summary is 

provided here. The model was designed to accommodate a 

wide variety of harvesting and silvicultural systems in order 

to compare and contrast their effect on forest productivity, 

stand dynamics, and a series of biophysical indicators of 

non-timber values. Projection of stand growth and ecosystem dynamics is based upon a representation of the rates of 

key ecological processes regulating the availability of, and 

competition for, light and nutrient resources (a representation of moisture competition is being completed but was 

not included in this study). The rates of these processes are 

calculated from a combination of historical bioassay data 

(biomass accumulation in component pools, stand density, 

etc.) and measures of certain ecosystem variables, (e.g., 

decomposition rates, photosynthetic saturation curves) by 

relating ‘biologically active’ biomass components (foliage 

and small roots) with calculations of nutrient uptake, the 

capture of light energy, and net primary production. Using 

this ‘internal calibration’ or hybrid approach, the model 

generates a suite of growth properties for each tree and 

plant species to be represented. These growth properties 

are subsequently used to model growth as a function of 

resource availability and competition. FORECAST performs 

many of its calculations at the stand level but it includes a 

submodel that disaggregates stand-level productivity into 

the growth of individual stems with user-inputted information on stem size distributions at different stand ages. Top 

height and diameter at breast height (DBH) are calculated 

for each stem and used in a taper function to calculate total 

and individual stem gross and merchantable volumes.

Test Site

Site description—

The study site was located approximately 50 km east of 

Prince George in the SBSwk1 variant (MacKinnon et al. 

1990). The site was established in 1985 in an area that was 

clearcut in 1969, broadcast burned in 1970, and planted in 

1971 with 2+1 bare-root white spruce (Picea glauca) seedlings. Following the burn, the plantations had a vigorous 

regeneration of aspen (Populus tremuloides) such that when 

plots were established in 1985, the aspen canopy was well 

above that of the spruce. A validation data set was derived 

from long-term monitoring plots established as part of a 

study of spruce weevil (Pissodes strobi) attacks on young 

spruce plantations treated to have varying degrees of 

aspen cover (see Taylor and Cozens 1994, for a complete 

description). The study area contained three separate sites 

intended as replicates, but because of differences in species and density among the sites, only one site (Site 2) was 

selected for model evaluation.

Treatments and plot establishment—

Long-term plots were installed to examine the impact of 

two levels of aspen removal on both weevil attack rates 

and spruce growth. The first treatment was the mechanical removal all of the aspen (referred to as ‘brushed’) and 

the second treatment was a partial removal of the aspen 

using strip cuts (partial brushed). A control plot was also 

established in which no aspen were removed. All plots were 

rectangular in shape with dimensions of 50 m x 115 m. In 

the partial brushed plot, 5-meter wide strips with no aspen 

removed were left adjacent to 7-meter wide strips in which 

all the aspen had been removed mechanically. Strips were 

made perpendicular to the long axis of the rectangular plot. 

This treatment resulted in the removal of approximately 60 

percent of the overstory aspen. 

All spruce trees were measured (top height and DBH) in 

each plot in 1986, 1988, 1991 and 2003 (18 years after treatment). Tree mortality was also recorded. Aspen trees were 

measured (top height and DBH) in 2003 only. Estimates of 

total volume and stem biomass were made for both species 

in years where both height and DBH data were available 

using standard species specific volume (BCFS 1976) and 

biomass equations (Standish et al. 1985).

Simulation of Treatments

Prior to the simulation of the specific management treatments an initial site condition was established in the model 

using a procedure described by Seely et al. (In press). 

Simulations were conducted to represent each of the 2 

treatments (brush & partial brush) and the control. In 

each simulation, spruce was planted in year 1 (1971) at 

1500 stems per hectare and aspen regeneration occurred 

in year 1 at 2000 stems per hectare. A small population 

(5 percent cover) of a general (medium height) Vaccinium

sp. shrub was also initiated in year 2. In the case of the 

brushed treatment, 100 percent of the aspen was harvested in year 15 (1985) and regenerated at 5000 stems 

per hectare the following year (to represent suckering). 

In the case of the partial brushed treatment, 60 percent 

of the aspen stems were removed with stems distributed 

evenly across all size classes. Since FORECAST has an 

aspatial representation of tree distribution, the simulation 

was based on the assumption that the removal strips were 
FOREST GROWTH AND TIMBER QUALITY

207

narrow enough (7 m) that the spruce would behave as if 

the residual aspen were distributed evenly throughout the 

treated area, particularly as the residual aspen matured 

and crown expansion occurred. It was assumed that there 

was some regeneration of aspen by suckering (2500 stems 

per hectare) following the thinning treatment. The control 

scenario had no management interventions following the 

initial planting of spruce. 

Evaluation of Model Performance

Model performance was evaluated using graphical comparison to examine treatment response with respect to 

standard growth and yield variables. In addition, overall 

model fit was assessed for each species and variable using 

the modelling efficiency (ME) statistic described in Vanclay 

and Skovsgaard (1997):

This statistic provides a simple index of performance on a 

relative scale, where ME = 1 indicates a perfect fit, ME = 0 

indicates that the model is no better than a simple average, 

while negative values indicate poor model performance.

RESULTS

Evaluation of Model Performance

ME values were greater than 0.9 for all variables tested 

with the exception of total stand spruce stemwood biomass 

(ME=0.88), average DBH for spruce (ME = 0.76) and average 

DBH for aspen (ME =0.77) (Table 1). The model did a better 

job of predicting the diameters of the top 200 spruce trees 

relative to that for all spruce trees in a given simulation 

(Table 1). It also performed well in projecting the treatment 

effects on patterns of total stand wood production for both 

spruce and aspen in both treatments and the control. 

The simulated long-term impacts of the brushing 

treatments on spruce volume, mean annual increment of 

spruce volume, aspen volume, and total stand volume are 

shown in Figure 1. The impact of the treatments on spruce 

growth rates was subtle for more than a decade following 

the treatment but was substantial over a longer time period 

(Fig. 1A, B). Impacts on aspen volume happened quickly 

and were more dramatic (Fig. 1C). The influence of the 

treatments on total stand volume was relatively small (Fig. 

1D) with the control stand producing slightly more (15 

percent) volume than the fully brushed stand at rotation 

age (approximately 75 years). However, the aspen content 

of the total stand volume changed significantly with the 

different treatments. 

Simulated Competitive Interactions

Light competition—

Foliage shading index, an integrated measure of simulated 

competition for available light between species, is shown 

for the spruce-aspen mixedwood stand type in Figure 

2. Specifically, the foliage shading index represents the 

relative decline in foliar N productivity caused by shading 

(including self-shading and shading by other species). The 

index is calculated based on the quantity of light captured 

by the foliage of each tree species summed throughout the 

canopy profile (see Kimmins et al. 1999 for more detail). 

The relative productivity of the foliage (per unit foliar N) 

is determined as a function of the species-specific light 

response curves shown in Figure 2C. 

Table 1—Goodness of fit of model relative to field data as 

measured by modeling efficiency (ME) for the spruce-aspen 

simulations (n: number of data).

Variable Spruce Aspen

ME n ME n

Average top height 0.7 12 0. 

Average stem biomass na na na na

Top 200 top height 0. 12 na 

Average DBH 0.7  0.77 

Top 200 DBH 0.  na 

Stand volume 0.7  0. 

Stand stem biomass 0.  0. 

Figure 1. Simulation results for a 100-year time period for the 

spruce-aspen mixedwood showing A) total Sw Volume, B) Sw 

mean annual increment (MAI), C) total At volume, and D) total 

volume for all species for the two treatments and the control site. 

The treatment occurred in year 15.
FOREST GROWTH AND TIMBER QUALITY

20

Figure 2. Simulated foliageshading index as a measure of light 

competition for A) spruce and B) 

aspen for the two aspen brushing 

treatments and the control in the 

spruce-aspen mixedwood stand 

type. Panel C shows the relative 

photosynthetic rates (per unit foliar 

N) for spruce and aspen as a function 

of light levels calculated throughout 

the canopy profile.

Figure 3. Simulated annual nitrogen 

(N) uptake for A) spruce and B) 

aspen and C) total tree for the two 

aspen brushing treatments and 

the control in the spruce-aspen 

mixedwood stand type.
FOREST GROWTH AND TIMBER QUALITY

20

The foliage shading index of spruce was reduced for 

several decades following both brushing treatments relative 

to the control but gradually returned to levels similar to 

that in the control stand by year 70 (Fig. 2A). In the case 

of aspen, the foliage shading index increased dramatically 

immediately following the full brushing treatment and 

resprouting and remained high relative to the control (Fig. 

2B). In contrast, the foliage shading index for aspen in the 

partial brushing treatment (for both residual and resprouting trees combined) increased only slightly following the 

treatment after which it remained at a level similar to that 

for aspen in the control stand.

Nitrogen competition—

The simulated impact of the aspen brushing treatments on 

N competition, as measured by total tree N uptake, is shown 

for the spruce-aspen mixedwood stand type in Figure 3. 

Total annual N uptake by spruce increased gradually but 

substantially over the long-term with increasing aspen removal relative to the control stand (Fig 3A). Total N uptake 

for the simulated pure spruce reference plantation (Fig. 

3A) provides an indication of total potential N uptake in 

the absence of aspen competition. The simulated N uptake 

pattern for aspen was opposite to that observed for spruce 

(Fig. 3B). Following the brushing treatments, total tree N 

uptake rates were highest in the control stand for the duration of the 100-year simulation period (Fig. 3C).

DISCUSSION

The overall fit of the model to observed values (as measured 

by ME) was good for all the simulated treatments examined. 

Model predictions of DBH, particularly for smaller trees, 

were among the least accurate of all variables examined. 

While comparisons of average measures of individual stems 

are informative and useful, comparisons of stand-level 

summaries of total volume and stem biomass are perhaps 

the best measures of overall model performance as they 

represent an integrated accounting of total production for all 

of the trees (whether measured or simulated) in the stand. 

FORECAST performed well in predicting the effects of the 

different brushing treatments on these stand-level measures 

of production for spruce and aspen. The model was able 

to simulate these effects by representing the impact of the 

silviculture interventions on interspecific competition for 

light and nutrient resources. 

Simulation results indicate that competition for both 

light and nutrients is important in the dynamics of these 

mixedwood forest types although it is difficult to isolate 

specific effects as there are interactions between them. The 

analysis also highlighted the fact that long-term response 

data and modeling are required to adequately assess the 

rotation-length effects of treatments on stand development.

The projected 15 percent higher total stand volume in the 

control treatment relative to the full brushing treatment 

is consistent with field-based estimates made by Man and 

Leiffers (1999). The main effect of the treatments was an 

increase in the relative spruce content of the total stand volume. The brushed and alternative brushed treatments had 

45 percent and 31 percent more spruce volume at rotation 

relative to the control, respectively. Managers evaluating 

these options based on model output may make different 

decisions depending upon which species is favored for 

specific resource values.

As management practices shift increasingly towards the 

management of complex stand types it is critical that we 

develop a range of models with the capability to project 

the short and long-term impacts of alternative stand management systems on both timber and non-timber values. 

Given our general lack of field experience with many of 

the silvicultural systems employed under ecosystem-based 

management and the uncertainty associated with natural 

disturbance agents and changing climate, models which 

incorporate some level of causality and/or understanding 

through the representation of key ecological processes are 

generally better suited for this purpose than models driven 

predominantly by empirical relationships (Korzuhkin et al. 

1996, Johnsen et al. 2001). The analysis described herein 

provides a level of confidence for the use of the model as a 

decision-support tool in these ecosystem types, but more 

validation work should be conducted across a range of different mixedwood forest types and management interventions 

as long-term datasets become available.

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volume equations and tables: centimetre diameter 

class merchantable volume factors. Forest Inventory 

Division, British Columbia Forest Service, Dept. of 

Forests, Victoria, BC. 103 p.

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P.G., Thomas, K.D., eds. Silviculture of temperate and 

boreal broadleaf-conifer mixtures. British Columbia 

Ministry of Forests, Victoria, British Columbia. Land 

Managers Handbook 36:1–7.

Comeau, P.G.; Biring, B.S; Harper, G.J. 2000. Conifer 
FOREST GROWTH AND TIMBER QUALITY

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response to brushing treatments, a summary of B.C. 

data. British Columbia Ministry of Forests, Victoria, 

British Columbia. Ext. Note 41. 12 p.

Cóté, L.; Brown, S.; Paré, D. [et al.] 2000. Dynamics 

of carbon and nitrogen mineralization in relation to 

stand type, stand age and soil texture in the boreal 

mixedwood. Soil Biology and Biogeochemistry 32: 

1079-1090.

Grover, B.E.; Greenway, K.J. 1999. The ecological and 

economic basis for mixedwood management. In: 

Veeman T.S, Smith D.W., Purdy B.G., Salkle F.J., Larkin 

G.A., eds. Proc. 1999 sustainable forest management 

network conference: Science and practice: sustaining 

the boreal forest. February 14–17, 1999. University of 

Alberta, Edmonton, Alberta, Canada. Pp. 419–428.

Harper, G.; R. Kabzems. 2003. Growing-space 

Management in boreal-mixedwood Forests—The 

establishment of EP 1192.02, Fort Nelson River Site. 

British Columbia Ministry of Forests, Victoria, British 

Columbia. Ext. Note 64.

Huang, S.; Titus, S.J. 1994. An age-independent 

individual tree height prediction model for boreal 

spruce-aspen stands in Alberta. Canadian Journal of 

Forest Research 24: 1295-1301.

Johnsen, K.; Samuelson, L.; Teskey, R. [et al.] 2001.

Process models as tools in forestry research and 

management. Forest Science 47: 2-8.

Kimmins, J.P.; Mailly, D.; Seely, B. 1999. Modelling 

forest ecosystem net primary production: the hybrid 

simulation approach used in FORECAST. Ecological 

Modelling 122: 195-224.

Korzukhin, M.D.; Ter-Mikaelian, M.T.; Wagner, R. 

1996. Process versus empirical models: which approach 

for forest management? Canadian Journal of Forest 

Research 26: 879-887.

Mackinnon, A.; DeLong, C.; Meidinger, D. 1990. A 

Field Guide for Identification and Interpretation of 

Ecosystems of the Northwest Portion of the Prince 

George Forest Region. LMH 21. British Columbia 

Ministry of Forests. 

Man, R.; Lieffers, V.J. 1999. Are mixtures of aspen and 

white spruce more productive than single species 

stands? Forestry Chronicle 75: 505-513.

Sachs, D. 1996. Simulation of the growth of mixed stands 

of Douglas-fir and paper birch using the FORECAST 

model. In: Comeau, P.G, Thomas, K.D., eds. Silviculture 

of temperate and boreal broadleaf-conifer mixtures. 

British Columbia Land Management Handbook No. 36: 

152-158.

Seely, B.; Hawkins, C.; Blanco, J.A. [et al.] In Press.

Evaluation of a mechanistic approach to mixedwood 

modelling. The Forestry Chronicle.

Seely, B.; Nelson, J.; Wells, R. [et al.] 2004. The 

application of a hierarchical, decision-support system to 

evaluate multi-objective forest management strategies: A 

case study in north-eastern British Columbia, Canada. 

Forest Ecology and Management 199: 283-305.

Seely, B.; Welham, C.; Kimmins, J.P. 2002. Carbon 

Sequestration in a Boreal Forest Ecosystem: Results 

from the Ecosystem Simulation Model, FORECAST. 

Forest Ecology and Management 169: 123-135.

Simard, S.W.; Hannam, K.D. 2000. Effects of thinning 

overstory paper birch on survival and growth of 

interior spruce in British Columbia: implications for 

reforestation policy and biodiversity. Forest Ecology 

and Management 129: 237-251

Simard, S.W.; Perry, D.A.; Jones, M.D. [et al.] 1997. Net 

transfer of carbon between tree species with shared 

ectomycorrhizal fungi. Nature 388: 579-582. 

Simard, S.W.; Sachs, D.L.; Vyse, A.; L. Blevins. 2004.

Paper birch competitive effects vary with conifer tree 

species and stand age in interior British Columbia 

forests: implications for reforestation policy and 

practice. Forest Ecology and Management 198: 55-74.

Standish, J.T.; Manning, G.H.; Demaershalk, J.P. 1985.

Development of biomass equations for British Columbia 

tree species. Rep. No. BC-X-264. Canadian Forestry 

Service, Pacific Forest Research Centre, Victoria, British 

Columbia. 47 p.

Taylor, S.P.; Cozens, R.D. 1994. Limiting white pine 

weevil attacks by side and overstory shade in the Prince 

George Forest Region. Journal of the Entomological 

Society of British Columbia 91: 37-42.

Vanclay, J.K.; Skovsgaard, J.P. 1997. Evaluating forest 

growth models. Ecological Modelling 98: 1-12.

Welham, C.; Seely, B.; Kimmins, J.P. 2002. The utility of 

the two-pass harvesting system: an analysis using the 

FORECAST ecosystem simulation model. Canadian 

Journal of Forest Research 32: 1071-1079.
FOREST GROWTH AND TIMBER QUALITY

211

Assessing Forest Productivity: Satellite versus 

Terrestrial Data-Driven Estimates in Austria

Richard Petritsch, Céline Boisvenue, Steve Running, Hubert Hasenauer

Richard Petritsch (richard.petritsch@boku.ac.at) and Hubert Hasenauer are in the Department of Forest- and Soil Sciences, 

University of Natural Resources and Applied Life Sciences, Peter-Jordan-Strasse 82, A-1190 Vienna, Austria; Céline Boisvenue and 

Steve Running are in the Numerical Terradynamic Simulation Group, University of Montana, Missoula, Montana, USA.

ABSTRACT

FOREST PRODUCTIVITY HAS ALWAYS BEEN A 

major issue within sustainable forest management. 

While in the past, terrestrial forest inventory data 

have been the major source for assessing forest productivity, recent developments of modeling techniques and 

satellite-derived information have become of increasing 

interest for productivity estimates. Using a mechanistic 

model enables us to analyze the pools and fluxes within a 

forest ecosystem. On the other hand, satellite data as they 

can be derived from, say, the Moderate Resolution Imaging Spectroradiometer (MODIS) Sensor may be used for 

monitoring global and/or regional Net Primary Production 

(NPP). In this study we first present the incorporation of 

management within a mechanistic ecosystem model and 

then use this approach for comparing satellite vs. terrestrial 

driven NPP based on different estimation procedures: (1) 

NPP estimates derived from MODIS satellite, (2) estimates 

from the species specific adaptation of Biome-BGC, and (3) 

NPP estimates derived from inventory data using biomass 

expansion functions (BEF). First results suggest that the 

scaling issue is of major concern since the area covered by 

the satellite images is much larger than the area which is 

commonly assumed to be represented by inventory plots. 

Thus, satellite-based approaches may overlook details which 

are covered by inventory data. After aggregating the available inventory information to ecological growth regions, 

the correlation between satellite vs. terrestrial data-driven 

NPP estimates improved substantially.

KEYWORDS: Forest production, NPP, ecosystem modeling, MODIS

INTRODUCTION

Forests play a large role in the global carbon cycle, and 

they are already responding to global climate and atmospheric changes (Boisvenue and Running 2006). Forest 

NPP, however, cannot be directly measured (Clark et al. 

2001). It must be inferred even for on-site estimates. Reliable and globally available estimates of NPP at a site level 

would support the monitoring of carbon sequestration. NPP 

estimates enter into the global carbon budget (Nemani et al. 

2003) and large-scale patterns of food and fiber production 

(Running et al. 2004). They are essential in understanding 

physiological processes in forests and the effects of climate 

change on individual forests as well as on whole biomes 

(Richardson et al. 2007).

Terrestrial forest inventory data has always been a major 

source for assessing the productivity of forest ecosystems. 

Due to the demanding efforts for large area inventories they 

are usually limited to measuring routine data like diameter 

at breast height of a sample of a forest stand. Biomass of 

the whole stand is then projected using allometric equations (Wirth et al. 2004). As an alternative to the purely 

statistical approach, different types of models have been 

developed. Biogeochemical mechanistic (BGC) models assist in obtaining knowledge on key ecosystem processes 

as they focus on the interaction between soil, plants, and 

This paper was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 211–216.
FOREST GROWTH AND TIMBER QUALITY

212

the atmosphere by assessing the fluxes of energy, water, 

nitrogen, and carbon within a given ecosystem (Waring 

and Running 1998).

An important limitation of BGC models is that they operate on fully stocked even-aged stands since they are not 

explicitly designed to be sensitive to varying stand density. 

It is important to distinguish between historic management 

(Pietsch and Hasenauer 2002) and current management, 

which mainly addresses density changes. As forest management has been, and still is, the main driving impact for 

changes in forest growth in Europe (Kauppi et al. 1992) the 

conceptual integration of thinning is essential.

Recent developments in satellite-derived information 

become of increasing interest, as they are able to provide 

globally available estimates of NPP at a site level. Sensors, 

such as the Moderate Resolution Imaging Spectroradiometer (MODIS) on NASA’s Terra satellite, are being used for 

monitoring global NPP (Running et al. 2004). Comparisons 

of MODIS production estimates, which are globally available, to ground-based estimates have taken place (Turner 

et al. 2006). In these studies, site-level estimates were 

scaled up. In the present study, we compare the unaltered 

smallest common spatial denominator of NPP estimates 

from MODIS, Biome-BGC, and routine inventory data with 

Biomass Expansion Factors (BEFs).

Thus the objectives of this study can be summarized as:

1. Application of the mechanistic ecosystem model Biome-BGC to managed forest stands in Central Europe.

2. Comparison of satellite vs. terrestrial data-driven NPP 

estimates using a set of sample plots across Austria.

INCORPORATING FOREST

MANAGEMENT

We use the mechanistic ecosystem model Biome-BGC Version 4.1.1 (Thornton et al. 2002) with improvements regarding hydrology (Pietsch et al. 2003), species representation 

(Pietsch et al. 2005) and self-initialization (Pietsch and 

Hasenauer 2006). Land-use history for considering potential 

soil degradation from past human impacts is addressed 

(Pietsch and Hasenauer 2002). Applications for managed 

forest stands assumed that thinnings only produced changes 

in the stem, leaf, coarse and fine root pools. Six parameters 

are available to characterize intervention in terms of stem 

removal, stem to coarse woody debris (cwd), leaf removal, 

leaves to litter, coarse roots to cwd, and fine roots to litter. 

These values are given in percent (Merganicová et al. 2005). 

The original model assumes a fully stocked stand but forest 

Figure 1. Five-year total stem volume increment rates in percent of the 

unthinned conditions using Monte-Carlo simulations.

Figure 2. Predicted vs. observed volume increments following thinning 

using the current model setup.

Figure 3. Allocation change after thinning.
FOREST GROWTH AND TIMBER QUALITY

21

management options usually change stand density. Thus, 

we are interested in how the model performs immediately 

after biomass removal.

Model Analysis

For studying management impacts we use the species parameters for Common beech (Fagus sylvatica) and Norway 

spruce (Picea abies) (Pietsch et al. 2005). Within 50 MonteCarlo simulations we applied thinnings where we randomly 

chose time and intensity of the intervention. The reaction 

of the model was evaluated by calculating the volume increment immediately after thinning relative to the volume 

increment of the unthinned forest stand. Since there is no 

explicit stand density within the model, it is determined as 

the remaining stem biomass in percent of the stem biomass 

before thinning (Assmann 1970). This assumption is only 

valid immediately after the intervention.

Although the original model is set up for fully stocked 

stands it was sensitive to management (Figure 1). This 

response is species specific and the more shade-tolerant 

species, beech, is less responsive than spruce. Although this 

is consistent with findings from growth and yield studies 

the response seems to be too optimistic and requires some 

further adjustments. The volume increment after thinning 

increased compared to the unthinned stand with the same 

biomass fraction (1:1 line). This can be attributed to the 

fact that there is more access to resources (water, nitrogen, 

and light) after thinning. With increased thinning intensity 

the simulated growth acceleration of beech was higher 

than that of spruce. Although the situation is consistent 

with findings in growth and yield studies (e.g. Assmann 

1970), the application of the model to managed forest 

stands produced significant under-estimations in volume 

increment (Figure 2).

Allocation Change

Trees change their physiology as a result of reduction in 

competition. This affects the distribution pattern between 

above- and below-ground biomass and between wood and 

leaf biomass as they may change in response to specific 

environmental conditions (Mooney and Winner 1991). 

A management submodel was developed, with changed 

allocation pattern after thinning (Petritsch et al. 2007), 

using 66 sample plots from 12 different regions in Central 

Europe. Model behavior after thinning was investigated 

using 8 sample plots per species. The allocation pattern 

was changed after the intervention to stimulate stem 

growth (Figure 3). The values of the parameters Ddelay, 

Dconst, and the maximum of change in the proportions 

were optimized using the evaluation plots. The duration of 

the effect (Dact) is estimated from the thinning intensity 

while the change decreased linearly until it vanished after 

a maximum duration of 20 years (Figure 3).

Results

Using the remaining sample plots as a validation dataset 

the application of the improved model gave unbiased volume increment (Figure 4) as well as stand volume predictions by species. Although the parameters for spruce were 

established using only sample plots with lowland spruce 

they are also valid for the application to highland spruce. 

A detailed description of the management submodel with 

all results of the model validation can be found in Petritsch 

et al. (2007).

COMPARING NPP ESTIMATES

Satellite NPP

NASA’s Earth Observation System (EOS) satellite carries the 

Moderate Resolution Imaging Spectroradiometer (MODIS). 

Several products are derived from these raw data on a daily 

basis. We use NPP (Heinsch et al. 2003) as it is calculated 

by the Numerical Terradynamic Simulation Group (NTSG) 

at the University of Montana. NPP estimates (MOD17) 

Figure 4. Predicted vs. observed volume increments after thinning for the 

improved (with allocation change) model.
FOREST GROWTH AND TIMBER QUALITY

214

are available as annual values on 1km spatial resolution. 

MOD17 requires meteorological data, and up-stream MODIS 

products such as GPP (MOD17A2), Leaf Area Index (LAI), 

Fraction of Photosynthetically Active Radiation (FPAR; 

MOD15), and MODIS Land Classification (MOD12). The 

meteorological data used for the web-available NPP estimates are retrieved from NASA’s Global Modeling and 

Assimilation Office (GMAO).

Due to georeferencing constraints, and to ensure pixelto-site coherence, satellite estimates were obtained for a 3 

x 3 km area around the site latitude and longitude. Each 

of these nine pixels has an attached land classification 

from an up-stream MODIS product, MOD12. The MODIS 

productivity estimates are highly dependent on the land 

classification of each pixel, because the land classification 

defines which biome and therefore which ecophysiological 

parameter value will be used in the algorithm (see Heinsch 

et al. 2003 for details).

Terrestrial NPP

The first approach uses the mechanistic ecosystem model 

Biome-BGC (Thornton 1998) Version 4.1.1 with extensions (Pietsch et al. 2003, Pietsch et al. 2005, Pietsch and 

Hasenauer 2006) and daily climate data from the Austrian 

version of DAYMET (Hasenauer et al. 2003). In addition 

to daily climate data only generally available site data are 

used as input parameters for the model.

The second procedure is based on allometric equations. 

Total biomass is estimated using Lehtonen et al. (2004) for 

conifers and VandeWalle (2005) for broadleaves, aggregated 

for the whole stand and converted to carbon for each site. 

NPP is assumed to be the annual biomass increment of the 

forest stand. This is a completely statistical approach depending on constant biomass expansion factors (BEFs).

Comparison Dataset

We obtained MODIS data for 624 sites across Austria where 

terrestrial measurements were also available. Some of the 

locations (144 of the 624) were previously used in a validating effort to produce species-specific parameter estimates of 

the ecosystem model (Pietsch et al. 2005). The remaining 

480 sites are from the Austrian National Forest Soil Survey 

(Englisch et al. 1992) and include soils, humus, as well as 

forest growth information.

To assess NPP as the increment in stand biomass it is 

essential to have re-measurements of stand data. Thus only 

166 (Figure 5) plots which have more than one measurement 

could be used in the analysis. These are all forested sites.

Results

We found that NPP estimates using Biomass Expansion 

Factors (BEF) show the largest variation. On the plot level 

only BGC vs. BEF are significantly correlated (r=0.35; t=4.82; 

α=0.05; N=166). The correlation between satellite and terrestrial data-driven estimates were low (r<0.1; t<1.0; α=0.05; 

N=166). As NPP is estimated on different scales, we expected 

low correlation on plot level. Thus, we spatially aggregated 

Figure 5. Location of the 166 sample plots for the comparison of NPP 

estimates.

Figure 6. Growth districts and ecoregions in Austria (Killian, 1994).

Table 1. Correlations of the NPP estimates on different 

aggregation levels.

N BGC vs. 

MODIS

BEF vs. 

MODIS

BGC vs. 

BEF

plots 1 0.0 0.02 0.35 

growth districts 22 0.58 0.2 0.0 

eco-regions  0.54 0.51 0.2 
FOREST GROWTH AND TIMBER QUALITY

215

the estimates to growth districts and ecoregions (Figure 

6) as given in Killian (1994). These aggregated estimates 

improved the correlations and resulted in higher r values 

(r>0.5; t>1.5; α=0.05; N=9) for all combinations (Table 1). 

Correlation between BGC and BEF further improved to 

0.82 (t=3.79; α=0.05; N=9).

Discussion and Conclusion

Since forest NPP cannot be directly measured it must be 

inferred even for on-site estimates. In the present study we 

compared three different methods for estimating forest NPP. 

The mechanistic ecosystem model Biome-BGC provides 

NPP on a daily basis as GPP minus respiration. Since this 

model operates on fully stocked even-aged stands we had to 

adapt it for managed forests in Central Europe. Application 

of the original model gave unbiased results in terms of an 

under-estimation of volume increment after thinning. By 

implementing a management submodel, which changes 

the allocation pattern after thinning, we achieved unbiased 

results for the volume and volume-increment prediction 

(Petritsch, et al. 2007).

Terrestrial forest inventory data from the Austrian National Forest Soil Survey (Englisch et al. 1992) combined 

with allometric equations (BEF, Lehtonen et al. 2004, 

VandeWalle 2005) were used to calculate total biomass 

increment. This number was used as the second estimate. 

The inventory data consist of repeated 5-year measurements. 

Due to the purely statistical properties and the long measurement cycle no climate impact or inter-annual variation 

was expected. Thus the estimates are mainly driven by site 

characteristics.

Satellite NPP estimates come from MODIS and are 

available online as annual averages. For the calculation, 

meteorological data and upstream MODIS products such 

as GPP, LAI, FPAR, and land classification are required. 

MODIS productivity estimates strongly depend on the 

ecophysiological parameters. They are chosen according 

to the land classification (Heinsch et al. 2003).

On plot level BGC and BEF were significantly correlated 

(r=0.35; t=4.82; α=0.05; N=166) but satellite versus terrestrial approaches showed no significant correlation (r<0.1; 

t<1.0; α=0.05; N=166). According to the different scales of 

satellite and terrestrial data this result was expected. Holman 

and Peterson (2006) analyzed growth pattern at multiple 

scales (plot, forest type, watershed, and subregion) and 

found that at larger scales (watershed and subregion), foresttype growth patterns show coherence. Our BGC estimates 

probably capture more of the variation due to larger scale 

factors such as climate, as compared to the BEF estimate. 

The satellite estimates probably capture even more than the 

BGC estimates. Satellite estimates do not capture variability 

due to inter-tree competition but do capture variability due 

to processes of larger-scale influence.

Correlations strongly improved after grouping the results 

to growth districts and ecoregions (Killian 1994). For terrestrial vs. satellite estimates we calculated r>0.5 (t>1.5; α=0.05; 

N=9) and BGC vs. BEF r=0.82 (t=3.79; α=0.05; N=9).

Scaling is obviously very important when comparing satellite vs. terrestrial data. Since MODIS-driven productivity 

estimates are assessed on a 3 x 3 km area the grouping of 

inventory-driven estimates strongly affected the correlation 

between the different methods. Although scaling biases are 

quantifiable, the data required for doing so are beyond the 

scope of this study.

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Poster Presentations

FOREST GROWTH AND TIMBER QUALITY

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The Simulation of Allelopathy in Ecosystem-Level Forest Models: A Study Case in the Pacific Northwest

Juan A. Blanco and J.P. (Hamish) Kimmins

 Juan A. Blanco (juan.blanco@ubc.ca) is a postdoctoral research fellow in forest ecology and J.P. (Hamish) Kimmins is a professor of forest ecology in 

the Department of Forest Sciences, Faculty of Forestry, University of British Columbia. 2424 Main Mall, Vancouver, BC, V6T 1Z4, Canada.

ABSTRACT

ALLELOPATHY IS ONE OF THE FACTORS THAT 

determine interactions among plants. Allelochemicals have been found in many forest ecosystems, 

but the importance of allelopathic interactions depends 

on forest type and environmental conditions. Despite the 

wide presence of this phenomenon, its modelization has 

been little developed, but its inclusion should be carefully 

considered in forest models dealing with environmental 

stress, exotic plant invasions (or introduction) and ecological 

succession. In these situations, multiple factors influence 

allelochemical production or toxicity such as nutrient 

availability, soil moisture and texture, solar radiation, and 

temperature, among others. Ecosystem-level effects of allelopathy are changes in germination rates, inhibition of 

seedling growth, mycorrhizal function, insect and bacterial 

growth, inhibition of nitrification or litterfall decomposition 

and dieback of mature trees. In this work, a comprehensive 

conceptual model on the interactions between different factors suitable to be incorporated in ecosystem-level models 

is presented. In addition, to illustrate the utility of simulating allelopathy, a virtual experiment was carried out with 

the forest ecosystem-level model FORECAST applied in a 

forest of western red-cedar (Thuja plicata) interacting with 

the ericaceous understory shrub salal (Gaultheria shallon) 

in coastal British Columbia, Canada. Our results showed 

different effects of allelopathy on several ecological variables 

depending on the type of allelopathic influence simulated, 

with important reductions in predicted merchantable 

volume when reduction in germination and litterfall decomposition by allelopathy was simulated. Furthermore, 

This paper was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. pp. 

219–223.

a great increase in understory biomass was also predicted 

as consequence of allelopathy. This experiment showed 

the suitability of ecosystem-level models to simulate, if 

not directly allelopathic interactions, at least the ecological 

effects of allelopathy at the ecosystem level. Overall, this 

work pointed out that forest managers and researches should 

think carefully about the inclusion of allelopathy as a way 

of improving the accuracy of forest models. 

KEYWORDS: allelopathy, allelochemicals, phytotoxicity, 

ecosystem-level models, silviculture practices, conceptual 

model, virtual experiment, FORECAST

ALLELOPATHY AND FORESTRY

Historically, the study of allelopathic interactions has been 

focused mainly on relationships between crops and weeds 

(Pellissier and Souto 1999). Studies about allelopathic 

relationships in forest soils are scarce and dispersed. Nevertheless, several studies have identified the importance of 

allelopathy in forest ecosystems. For example, Rietveld et 

al. (1983) have reported premature birch (Betula papyrifera 

Marsh) death in mixed plantations with walnut (Juglans nigra 

L.). Problems of conifer regeneration caused by ericaceous 

understory species have also been described (Mallik 2003). 

These examples show the importance of chemical interactions among plants in forest development and, therefore, 

show the necessity of including these relationships in forest 

models dealing with similar situations. The objective of 

this work is to provide suggestions concerning the most 
FOREST GROWTH AND TIMBER QUALITY

220

important issues that should be taken into account when 

modeling allelochemical relationships in forests, presenting 

an example of ecosystem-level simulation using FORECAST 

to illustrate the use of allelopathy in modeling forests at an 

ecosystem-level. The paper presented here is an extended 

abstract of the work by Blanco (2007).

The presence of allelochemicals able to influence forest growth and development seems to be widespread in 

all ecosystem types (McKey et al. 1978, Williamson et al. 

1992, Mallik 2003). The inclusion of allelopathy in forest 

models would be a good way to analyze the potential role 

of this phenomenon in ecosystem dynamics, and could 

be a useful contribution to the controversial debates over 

the ecological role of allelopathy. Three special cases have 

been mentioned as situations in which allelopathy should 

be analyzed; stress, invasion, and succession (Chuo 1986, 

Calloway 2001). Plants may use a passive interference in 

the development of their competitors by releasing allelochemicals (Reigosa et al. 2002) under nutrient or water stress 

(Koeppe et al. 1976, Kohl 1993), or other stress conditions 

such as UV radiation and physical damage by herbivores 

(Baldwin 1989, Reigosa et al. 1999). Given that natural 

communities have been evolving together for centuries, the 

most important effects of allelochemicals might appear in 

resource competition between species which did not share a 

common environment in the past (Rabotnov 1974). Recent 

studies have pointed out that allelochemical production and 

tolerance could be a key factor in determining success in 

exotic species invasion and in defining the new community 

resulting from the invasion process (Bais et al. 2003, Hierro 

and Callaway 2003). Understanding the role of allelopathy 

in succession following disturbances could be important in 

forest regeneration success (Rizvi et al. 1992). 

Different factors affect allelopathy at various points 

within a tree. Additionally, scale is important in the modeling of allelopathy, and additional factors stand out at the 

stand-level. Plants growing in nutrient-rich environments 

tend to have lower allelochemical production than plants 

growing on nutrient-poor sites (McKey et al. 1978, Tang et al. 

1995). Water stress can increase allelochemical production 

(Melkiana 1992, Reigosa et al. 2002). Water soil potential 

determines the rate of microorganism activity, allelochemical movement, and leaching (An et al. 2002). Differences 

in allelochemical production as a function of altitude and 

latitude have been reported by Anaya et al. (1992). Radiation 

affects donor plants, depending on wavelength, intensity 

and photoperiod (Reigosa et al. 1999). Temperature is another parameter affecting allelopathy (Melkania 1992). In 

addition, other local factors such as edaphic microclimate, 

intensity and duration of rainfall, pH or oxygen concentration may also be important (Weidenhamer et al. 1989, 

Fisher et al. 1994). Plant-related factors such as age or type 

of allelochemical produced are also important. Ecological 

factors include fire or the presence of other organisms able 

to degrade allelochemicals to less toxic forms or to stimulate 

allelochemical production in plants (Williamson and Black 

1981, Melkiana 1992, Reigosa et al. 1999). Nitrification in 

later seral stages may be strongly inhibited for this reason 

(Pellissier et al. 2002) and succession may be directed 

towards the selection of plants that inhibit nitrification of 

other organisms to reduce interspecific competition (Rice 

and Pancholy 1973, Chou 1986). 

Allelopathy effects at the ecosystem level are directly 

related to forestry issues. Phenomena such as the delay 

and reduction of germination by allelochemicals, restricted 

root development, altered water balance, or decrease in 

mycorrhizal formation due to allelopathy have been widely 

reported (Einhellig 1986, Mallik and Pellisier 2000). One of 

the most important effects may be change in site fertility due 

to alteration of humus decomposition (Damman 1971) or 

changes in the influence of the understory on tree regeneration (Mallik 2003). Allelochemical activity can be reduced 

by mechanical elimination of donor plants or by using steam 

to reduce allelochemical activity. Fertilization has also been 

used, with contradictory results (Prescott et al. 1993, Mallik 

1996). In addition, if the number and intensity of wildfires 

are reduced, it is possible that allelochemicals can reach 

levels that cause dieback in established tree species (Ellis 

et al. 1980) or may make tree regeneration after harvesting 

or windthrow almost impossible (Mallik 2003).

AN EXAMPLE OF SIMULATION OF

ECOSYSTEM-LEVEL ALLELOPATHIC

EFFECTS WITH FORECAST

To our knowledge, FORECAST is the only forest ecosystemlevel model specifically designed to allow the simulation 

of allelopathic effects. FORECAST is a stand-level, non 

spatially-explicit, ecosystem model. A complete, detailed 

description of the model can be found in Kimmins et al. 

(1999). The model was calibrated for western red-cedar 

(Thuja plicata Don.) stands in the Coastal Western Hemlock biogeoclimatic zone of the Duncan Forest District 

(Vancouver Forest Region, British Columbia, Canada). Four 
FOREST GROWTH AND TIMBER QUALITY

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Figure 1—Simulated development of Douglas-fir and other plants in a 

red-cedar stand under some effects of allelopathy (decomposition and 

germination rates reduction) in two different scenarios: Non-fertilized 

(left column) and fertilized with 225 kg-1 N ha at years 22 and 40 (right 

column). Arrows indicate fertilization schedule. 

rotation (Figure 1). This situation clearly points out that 

reduction of decomposition had a longer lasting effect on 

stand growth, and probably is one of the most important 

allelopathy effects (Damman 1971). This effect was caused 

because decomposition rates were reduced by the presence 

of salal during the whole rotation length, while germination reduction was important only at the establishment of 

the new stand. For this reason, economic and ecological 

analysis of stand development in situations with potential 

allelopathic inhibition of important species growth should 

consider this natural phenomenon. Finally, it must be emphasized that fertilization had little influence in the severity 

of allelopathic inhibition of growth. 

Our results showed different effects of allelopathy on 

several ecological variables depending on the type of allelopathic influence simulated. In addition, this experiment 

showed the suitability of ecosystem-level models to simulate, 

if not directly allelopathic interactions, at least the ecological 

effects of allelopathy at the ecosystem level. Overall, our 

work points out that forest managers and researches should 

think carefully about the inclusion of allelopathy as a way 

of improving the accuracy of forest models.

different simulations were carried out, all of them with 

the same starting conditions: site index 24 m at 50 years, 

3000 stems ha-1 as initial density, and initial aboveground 

biomass of salal (Gaultheria shallon Pursh) of 35 kg ha-1. The 

rotation length was fixed at 100 years for all simulations. 

The first run did not simulate any allelopathic effect, and 

was considered a reference situation. For subsequent runs, 

we selected the two effects most frequently described and 

analyzed in the literature: a germination decrease of 15 percent for trees (Mallik and Pellissier 2000), and a reduction 

of decomposition rates by 10 percent (Damman 1971), but 

no effects micorrhizal effects were simulated in any run. 

Finally, the fourth run simulated both effects simultaneously. In addition, fertilization was simulated (addition of 

225 kg N ha-1 at years 22 and 40).

The least sensitive variable to allelopathy was dominant 

top height (Figure 1), with changes lower than 3 percent. 

On the other hand, merchantable volume showed a high 

sensitivity to allelopathy. At the end of the rotation, in the 

unfertilized scenario, both decomposition and germination 

decreased and caused a reduction of 7 percent in merchantable volume. When both effects are simulated simultaneously the reduction is close to 11 percent. A similar pattern 

can be observed in the total aboveground biomass of redcedar, although in this case the reduction in biomass started 

more than 10 years sooner than for merchantable; volume. 

Finally, the most sensitive variable was salal aboveground 

biomass. When allelopathy was simulated as a reduction in 

decomposition rates, changes in salal biomass were small, 

but when red-cedar germination was reduced a significant 

relative increase in salal biomass was observed around year 

80 (Figure 1). It also must be pointed out there was very little 

fertilization influence on stand response to allelopathy, with 

results almost identical in the fertilized and non-fertilized 

scenarios. The only important difference between these two 

scenarios was for salal aboveground biomass. Changes in 

germination and decomposition rates had opposite effects 

on stand development. Lower germination reduced nutrient competition between survivor trees, emulating an early 

self-thinning. By contrast, reduction in decomposition rates 

caused a general reduction in stand growth. This reduction 

was due to lower availability of soil nutrients, which were 

sequestered for more time in litterfall than in the simulation without allelopathy. In addition, maximum differences 

caused by decomposition alteration were generally reached 

at the end of the rotation. However, changes in germination 

reduction reached the maximum differences earlier in the 
FOREST GROWTH AND TIMBER QUALITY

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ACKNOWLEDGMENTS

The author was supported by a postdoctoral fellowship 

granted by the Spanish Ministry of Education and a Travel 

Grant by The Green College of The University of British 

Columbia.

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Simulation of Density Effects on Tree Growth 

and Stem Form in Plantation Forests Using a 

Stand Growth Model

Yukihiro Chiba

Yukihiro Chiba (chiro@ffpri.affrc.go.jp) is a researcher at the Forestry and Forest Products Research Institute, Tsukuba, Ibaraki, 305-8687 Japan.

ABSTRACT

I N THIS STUDY, A FOREST GROWTH MODEL WAS 

developed to describe the effect of stand density using 

mathematical models of tree architecture that quantify 

the relationships among tree organs. This stand-growth 

model was developed in conjunction with a mechanistic 

stability model of tree form representing branching structure 

(Chiba 1990, 1991), a stem-form model approximated by 

a hyperbolic function (Chiba 1990), and crown shape of 

forest trees reflecting density effects. 

 Tree growth is dependent on soil condition rather than 

stand density. Thus, the present model is driven by height 

growth of trees that is given by the Mitscherlich growth 

curve with a maximum height specific to forest site. Crown 

form of forest trees changes depending on growing space 

(determined by stand density) therefore, crown length 

also changes. In the model presented, crown length is a 

key parameter to represent crown (leaf and branch mass), 

and thus individual tree growth. Examining the stem-form 

model, it is clear that all the parameters in the stem-form 

model can be determined by tree size (i.e., tree height and 

crown length).

 Applicability of the stand growth model was validated 

using the data on stand growths obtained for various thinning 

regimes. Employing this model, tree growth and biomass 

partitioning were well modeled along stand development 

with various initial tree densities and subsequent thinning 

regimes, showing serrated growth pattern. The growth 

patterns exhibiting a time trajectory between tree weight 

and stand density will be discussed in relation to density 

effects on tree growth in plantation forests.

REFERENCES

Chiba, Y. 1990. Plant form analysis based on the pipe 

model theory. I. A statistical model within the crown. 

Ecological Research 5: 207–220.

Chiba, Y. 1991. Plant form analysis based on the pipe 

model theory. II. Quantitative analysis of ramification 

in morphology. Ecological Research 6: 21–28.the 

ecosystem 

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 224.
FOREST GROWTH AND TIMBER QUALITY

225

Analyzing High-Resolution Stem Growth Data and 

Re-Mapping Wood Property Data onto Time-Axes Using 

a Database Management System

David M. Drew, Derek Hohls, Geoffrey M. Downes

David M. Drew (david.drew@sci.monash.edu.au) is at the School of Biological Sciences, Building 18, Monash University, Victoria 3800 and CSIRO 

Ensis, Private Bag 12, Hobart 7001, Tasmania, Australia; Derek Hohls is at CSIR Environmentek, PO Box 395, Pretoria , Gauteng 0001 South Africa; 

Geoffrey M. Downes are at CSIRO Ensis, Private Bag 12, Hobart 7001, Tasmania, Australia, Private Bag 12, Hobart 7001, Tasmania, Australia.

ABSTRACT

OVER THE LAST 50 YEARS, A LARGE NUMBER 

of researchers have made use of high-resolution 

electronic dendrometer systems to finely measure 

stem growth. More recently, use has been made of this 

kind of data to estimate the dates of formation of woody 

tissue, where the properties of this wood were analyzed 

at high resolution on pith-to-bark profiles. Stem growth 

and time-based wood property variation measured at this 

resolution is critical for developing and testing models that 

can explain short-term responses in the growing tree to 

changing environmental conditions. This kind of data is 

extremely voluminous, however, and its storage and management can be complex. We developed a 3-point integrated 

approach to dealing with all aspects of this kind of data, 

using the MySQL database management system (DBMS) 

in conjunction with custom-designed software and a web 

portal, so that all stakeholders in the research project/s 

could easily access data. This provides a generic means of 

dealing with this kind of data, which means that multiple 

researchers can apply the basic design to their research. 

The internet-based access provides powerful opportunities 

for collaborative work. In addition, we believe this data 

can be easily extracted and compared with predicted data 

from multiple modeling platforms with a small amount of 

customisation, since the data format is standardized.

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 225.
FOREST GROWTH AND TIMBER QUALITY

22

Crown Shape Dynamics in Managed Stands 

of Pedunculate Oak (Quercus robur L.) and 

Common Hornbeam (carPinus betulus L.)

Tomislav Dubravac, Stjepan Dekanic ́, Valentin Roth

Tomislav Dubravac and Valentin Roth are scientists and Stjepan Dekanic (presenter; stjepan.dekanic@zg.t-com.hr) is a research assistant in the 

Department of Ecology and Silviculture, Forest Research Institute Jastrebarsko, Trnjanska 35, HR-10000, Sagreb, Croatia.

ABSTRACT

S

PECIES-SPECIFIC CROWN SHAPE, EXPRESSED 

as a relation of crown diameter and crown length (D l

k

-

1

) changes during the tree lifetime in concordance 

with the ecological constitution of the species, productive 

capacities of the stand, and implemented management activities. In young stands (at the time of maximum current 

annual height increment) the crown is usually elongated, 

and becomes shorter as the stand reaches maturity. This 

is more evident in deciduous tree species. 

We investigated average crown shapes (models) of pedunculate oak and common hornbeam trees, as well as their 

change over time and with respect to diameter at breast 

height (DBH). Results are based on the measurements of 

2,235 trees from 47 permanent experimental plots with a 

total area of 33.45 ha. The plots are situated in two-layered, 

even-aged pedunculate oak and common hornbeam stands 

of different age classes.

Pedunculate oak trees develop crowns with maximum 

width roughly between one half and one third of the upper 

crown length. In more open canopies (as a result of management activities or degraded stand conditions) height of the 

maximum crown width decreases and the relative length of 

the sun-exposed crown increases. Common hornbeam trees 

constitute the lower layer of the canopy with the maximum 

crown width in the lower third of the crown length. Length 

of the sun-exposed crown in common hornbeam trees is 

always greater than half of the total crown length. 

Knowledge about the development of crown shape in oak 

and hornbeam trees across stands of different age classes 

is indispensable for further calculations of crown volume. 

These calculations are widely used in diverse models of 

energy and material exchange within forest ecosystems and 

between forest ecosystems and the larger environment.

KEYWORDS: crown shape, pedunculate oak, common 

hornbeam, managed stands, tree age

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 226.
FOREST GROWTH AND TIMBER QUALITY

227

Growth Performance of a Hill Dipterocarps Forest 

Five Years After Harvesting at Angsi Forest Reserve, 

Negeri Sembilan, Malaysia

Frisco Nobilly (presented by Kamziah Abd Kudus)

Frisco Nobilly (frisco@putra.upm.edu.my) and Kamziah Abd Kudus (kamziah@putra.upm.edu.my) are at the Faculty of Forestry, Universiti Putra 

Malaysia, 43400 UPM Serdang, Selangor, Malaysia.

ABSTRACT

THE FUTURE LONG-TERM TIMBER SUPPLY FROM 

sustainably managed forests in Peninsular Malaysia 

is largely dependant on the availability of timber 

from the productive Permanent Forest Estate, particularly 

from the hill dipterocarps forests. Since little virgin forest 

of this kind remain, much of the future log-production 

will come from the second and successive cuts in regenerated logged-over forest. Therefore, specific information on 

behaviors of particular forest stands pertaining to growth 

performance, mortality, density, structure, and speciescomposition is urgently required to evaluate management 

systems and their suitability in different types of forests. 

The study was conducted in a logged-over hill dipterocarps 

forest in Angsi Forest Reserve, Negeri Sembilan, Malaysia. The data consists of five early measurement periods 

(2000–2005) collected from 4 permanent sample plots. 

The sample plots were 100m x 100m, and designed based 

on the International Tropical Timber Organization (ITTO) 

guidelines. The residual stand showed signs of growth five 

years after logging. Stocking of trees, both over 5 cm diameter at breast height (DBH) and over 30 cm DBH showed an 

increase in DBH over the measurement period. However, 

the overall increment rates of all trees over 30 cm dbh 

were relatively low, when compared to the rates assumed 

under the Selective Management System (SMS). Though 

the mean annual diameter increment of the dipterocarps 

was higher than that of the non-dipterocarps, the overall 

contribution to forest growth was small due to a lower 

stocking of dipterocarps in the residual stand. The overall 

mean annual mortality (3.51 percent) of all trees over 30 cm 

DBH for the 5-year period was higher than that assumed 

under the SMS (0.9 percent). Besides poorer-than-average 

site conditions, the low growth rates could be attributed 

to the lack of post-harvest silvicultural treatment. Based 

on these growth rates, anticipating a second cut in 25–30 

years as stipulated under SMS, would be overly optimistic 

for this area.

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 227.
FOREST GROWTH AND TIMBER QUALITY

22

Effects of Management on Timber Production and 

Carbon Stocks in a Boreal Forest Ecosystem Under 

Changing Climate: A Model-Based Approach

Jordi Garcia-Gonzalo

Jordi Garcia-Gonzalo (jordi.garcia@joensuu.fi) is a doctoral student in forestry at the University of Joensuu, PO Box 111, Joensuu, 

FIN-80101 Finland.

ABSTRACT

A PROCESS-BASED MODEL WAS USED TO

investigate how management, forest structure (in 

terms of age-class distribution), and climate change 

affect the growth, timber yield, and carbon (C) stocks in 

a boreal forest ecosystem, (i.e., forest management unit 

(FMU)). Moreover, an approach to calculate the cost of C 

sequestration was used. In addition, it was demonstrated 

that the combined use of a process-based growth model, a 

wood products model, and a multi-objective optimization 

heuristic in the analysis of optimized management plans 

considering timber production, C sequestration in situ as 

well as in wood products, and biodiversity (in terms of 

deadwood) for the FMU under changing climatic conditions. 

In this context, we also analyzed the potential benefits of 

considering climate change in forest management planning. 

For the optimization, three objective scenarios were analyzed to represent contrasting views on forest management 

objectives within multiple-purpose forestry. 

Simulations covered 100 years using three climate scenarios (current climate, ECHAM4, and HadCM2) and six 

management regimes (also called stand treatment programs 

(STP)) including five thinning regimes and one unthinned 

regime. The management regimes were based on forest 

management recommendations applied until recently in 

Finland and differed from each other in the sense that the 

mean tree stocking varied in the stand over the rotation. 

Simulations were undertaken with ground-truthed stand 

inventory data of a forest management unit (1451 hectares) 

made up of a mosaic of Scots pine- (Pinus sylvestris), Norway spruce- (Picea abies), and silver birch- (Betula pendula) 

dominated stands in central Finland. 

A wood products model (WPM) was used to estimate 

carbon sequestration in products produced from simulated 

harvesting, with the results of the stand simulations being 

used as input. The output data from the WPM was used 

along with the results of forest stand simulations as input 

data for the multi-objective optimization. Thereafter, a 

combined random and direct search optimization heuristic 

was employed to find, for each stand, a STP that optimizes 

an additive utility function consisting of stand-level and 

unit-level components. A total of three management-objective scenarios were analyzed: timber production (maxTP), 

carbon sequestration (maxCS), and multi-objective management (MO: timber production, carbon sequestration, 

and biodiversity). 

Regardless of the climate scenario and initial age-class 

distribution used, stand management had a clear effect on 

the mean C stock in the forest ecosystem. Any management 

regime allowing a higher tree stocking than usual over the 

rotation increased timber production and simultaneously 

maintained or increased the C stock in the forest ecosystem. 

On the other hand, the maximum C stock in the forest and 

the lowest net present value (NPV) were observed when 

no thinning was applied before the final cut. The gradual 

increase in temperature and precipitation with a concurrent elevation in CO2 over the simulation period enhanced 

the timber production and C stocks. When using the same 

management for the entire management unit, the initial 

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 228–229.
FOREST GROWTH AND TIMBER QUALITY

22

age-class distribution had a large influence on the results 

of timber production (up to 20 percent difference) but not 

on C stock in the forest ecosystem (3 percent difference).

As a result of the optimization under changing climatic 

conditions, significant differences were found in the share 

of allocated STPs within the FMU between different management-objective scenarios as well as between climate scenarios within each objective scenario. The relative increase 

in the utility of optimized plans due to climate change 

differed somewhat between the objective scenarios. For 

maxTP, the maximum increase was 16.8 percent (ECHAM4), 

while for maxCS it was 9.9 percent (HadCM2), and for MO 

11.3 percent (ECHAM4). Depending on the management 

objectives and climate scenario, optimization contributed 

between 30 percent and 50 percent of that gain, the rest 

comes from increased production due to climate change. 

In conclusion, the combined use of process models and 

multi-objective optimization appears to be a promising 

approach for multiple-use management planning under 

conditions of climate change.

KEYWORDS: Process-based model, climate change, boreal 

forest, management, timber production, carbon stocks, 

multi-objective optimisation, forest planning, heuristic 

optimisation.

FOREST GROWTH AND TIMBER QUALITY

21

A Standardized Measure of Goodness-of-Fit for Forest 

Projection Models Involving Repeated Measurements

Shongming Huang

Shongming Huang (shongming.huang@gov.ab.ca) is in the Forest Management Branch, Alberta Ministry of Sustainable Resource Development, 

8th Floor, 9920-108 Street, Edmonton, Alberta T5K 2M4, Canada.

ABSTRACT

Forest projection models are commonly used to provide quantitative forward and backward projections of complex stand dynamics over time. In order to 

judge the goodness-of-fit of these models, various statistical measures, and graphic techniques such as residual and 

studentized residual plots have traditionally been used, 

with the most common ones being R2

 (coefficient of determination), root mean square error, and chi-square related 

statistics. Unfortunately, many of these measures usually 

apply only to one-time measurement data. They could 

provide very misleading results when applied to repeatedly 

measured data (RMD). In this study, data structures and 

model types from RMD were discussed. The dangers of using these measures to gauge the goodness-of-fit of a model 

or to discriminate the goodness-of-fit of alternative models 

were illustrated. An alternative measure of goodness-of-fit, 

based on a vector of R2 values each calculated in a way 

similar to the prediction sum of squares (PRESS) concept, 

was proposed. The usefulness and the robustness of this 

alternative measure for differentiating the goodness-of-fit 

of models that would otherwise be undistinguishable, was 

demonstrated based on repeatedly measured height-age, 

mortalitym and basal area increment data from permanent 

sample plots. 

INTRODUCTION

REPEATEDLY MEASURED DATA (RMD) REFERS TO

data sets with multiple measurements of a variable or 

variables on the same experimental unit over a period of 

time (Davidian and Giltinan 1995, Little et al. 2006). In 

forestry, the most common experimental unit (or “subject”) 

is a permanent sample plot (PSP), or a stem analysis tree 

(Gregoire et al. 1995). In a PSP, all trees that meet a minimum threshold, (e.g., 0.3 m or 1.3 m in height) are measured 

repeatedly over time for their heights, diameters, conditions 

and mortality status, etc. When conducting stem analysis 

(tree sectioning) studies, the trajectories of height-age, 

diameter-age, and height-diameter can be re-constructed 

to determine how the heights and diameters of the trees 

change over time. Fig. 1 illustrates some of the most common RMD obtained from PSPs and stem analysis trees.

RMD can also refer to data sets with multiple measureFigure 1. Examples of repeatedly measured data: volume-age (top-left) 

and density-age (top-right) trajectories from permanent sample plots, 

and height-age trajectories (bottom-left) and diameter-relative height 

curves (bottom-right) from stem analysis trees, where h is the height above 

ground corresponding to the point of diameter measurement, and H is 

total tree height.

This paper was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 231–249.
FOREST GROWTH AND TIMBER QUALITY

22

ments over distance or space. A typical example of such 

data is the diameter measurement taken along the stems of 

sectioned trees at intervals of equal or unequal lengths (as 

shown in Fig. 1, bottom-right graph), for developing tree 

volume or taper functions (Gregoire and Schabenberger 

1996, Trincado and Burkhart 2006).

When RMD from different experimental units (plots or 

trees) are pooled together for model development, the pooled 

data are frequently referred to as longitudinal data, crosssectional data, or panel data in different contexts (Judge 

et al. 1985, Diggle et al. 1994, Gregoire et al. 1995, Baltagi 

2005). In practice, these different terms for data sets are 

often used interchangeably, and are commonly referred to 

as RMD in a generic sense.

RMD is the foundation for developing forest growth 

and yield models. There are a number of distinct, yet very 

flexible features about the RMD analysis. Different data 

structures could be formulated from the observed data, 

different modeling approaches could be taken, and different 

goodness-of-fit measures could be reported. Because of its 

flexibility and the lack of a common, intuitive goodness-of-fit 

measure, it can be very difficult to judge the goodness-offit of models developed using RMD. Many of the reported 

goodness-of-fit measures appear to be uninformative, futile, 

misleading, or just plain wrong.

The main objective of this study was to propose and 

evaluate a goodness-of-fit measure for models developed 

using RMD. Data structures and modeling approaches 

associated with RMD were first reviewed, along with an 

assessment of the traditional goodness-of-fit measures. 

A goodness-of-fit index (GOFI) was then proposed and 

evaluated using data obtained from PSPs. The concept was 

first illustrated on a hypothetical data set based on simple 

linear regression.

DATA

Hypothetical Data

Table 1 lists 28 hypothetical data points used for this study, 

where x is the explanatory variable and y is the response 

variable. A scatter plot of the data is shown in Fig. 2(a). 

The same data were also connected in different ways in 

Fig. 2(b)-2(d) to create RMD, emulating data obtained from 

PSPs and stem analyses.

Figure 2. Twenty-right hypothetical data points unconnected (a), 

and connected in different ways (b, c and d). The data points and the 

connected trajectories in (b), (c) and (d) are listed in Table 1. The simple 

linear regression line (y = 31.9217 + 0.35189x) obtained from the 

ordinary least squares fit is overlaid on the data. Note that the same data 

points appear in all four graphs.

Table 1—Twenty-eight hypothetical data points.

Subject Subject

                   x                y  Fig. 2(b) Fig. 2(c) Fig. 2(d) x  y Fig. 2(b) Fig. 2(c) Fig. 2(d)

 45 40 3 1 1 200 80 2 4 4

 56 65 1 1 1 204 130 1 3 4

 80 40 2 2 2 210 115 3 4 4

 84 73 1 1 1 230 105 2 5 3

100 55 2 2 1 240 135 1 4 5

101 90 1 1 2 254 106 2 6 5

120 60 2 2 2 260 131 3 5 5

125 80 3 2 2 278 130 3 6 5

140 85 3 2 2 280 110 2 7 5

154 69 2 3 3 288 152 1 5 6

160 110 1 2 2 300 140 3 6 6

170 90 3 3 3 310 125 2 7 6

180 76 2 4 3 323 142 3 7 6

190 106 3 3 3 335 160 1 7 6

Note: Fig. 2(a) shows a scatter plot of the data points. Subject refers to the trajectories shown in Fig. 2(b), 2(c) and 2(d). For example, the x-y 

values were assigned to 3 subjects (trajectories) in Fig. 2(b). 
FOREST GROWTH AND TIMBER QUALITY

2

RMD from Permanent Sample Plots

Repeatedly measured PSP data collected by the Forestry 

Division of Alberta Ministry of Sustainable Resource Development were used for this study. The PSPs were installed 

across the province. They covered typical ranges of stand 

and site conditions. Details of the data collection procedure 

can be found in the PSP manual (http://srd.alberta.ca/forests/managing/manuals.aspx).

Three data sets from the PSP database were selected for 

use in this study (see Fig. 3): white spruce (Picea glauca (Moench) Voss) top height–age data, aspen (Populus tremuloides

Michx.) density–age data, and black spruce (Picea mariana

(Mill.) B.S.P.) basal area–age data. Two main characteristics 

of these three data sets are 1) the response variable for each 

plot was measured repeatedly over time, and 2) each plot 

was measured at irregular time intervals. As a result, the 

measurements were unequally spaced and the total number 

of measurements per plot were different (e.g., some were 

measured three times, others five and six times following 

different, irregular schedules).

Data Structure from RMD

Different growth intervals can be obtained from RMD and 

arranged into one of the six data structures to estimate model 

parameters (Huang 1997): I (longest forward), II (longest), 

III (non-overlapping forward), IV (non-overlapping), V (all 

possible forward), and VI (all possible combinations). These 

growth intervals and the data structures derived from them 

are summarized in Table 2 and illustrated in Fig. 4, based 

on a trajectory measured four times. For a trajectory that 

is measured k times, the number of growth intervals are 

1, 2, (k-1), 2(k-1), k(k-1)/2, and k(k -1) for data structures 

I, II, III, IV, V, and VI, respectively.

In the past, many models were estimated based on data 

structures arranged in a forward direction. This restriction 

appears unwarranted because there are many cases in which 

an earlier value or an initial condition must be predicted 

from a later value. For instance, tree/plot height at age 50 

(site index) is predicted from the height-site index model, 

based on the observed height at 100 years. The data structures II, IV, and VI shown in Fig. 4 and Table 2 removed 

Figure 3. Repeatedly measured data from permanent sample plots: white spruce top height–age data (left), aspen density–age data (middle), and black 

spruce basal area–age data (right). 

Table 2. Growth intervals and data structures based on a trajectory measured four times.

Structure I Structure II Structure III Structure IV Structure V Structure VI

y1

, x1 - y4, x4 y1, x1 - y4, x4 y1, x1 - y2, x2 y1, x1 - y2, x2 y1, x1 - y2, x2 y1, x1 - y2, x2

 y4, x4 - y1, x1 y2, x2 - y, x y2, x2 - y, x y1, x1 - y, x y1, x1 - y, x

 y, x - y4, x4 y, x - y4, x4 y1, x1 - y4, x4 y1, x1 - y4, x4

 y2, x2 - y1, x1 y2, x2 - y, x y2, x2 - y, x

 y, x - y2, x2 y2, x2 - y4, x4 y2, x2 - y4, x4

 y4, x4 - y, x y, x - y4, x4 y, x - y4, x4

 y2, x2 - y1, x1

 y, x - y1, x1

 y4, x4 - y1, x1

 y, x - y2, x2

 y4, x4 - y2, x2

 y4, x4 - y, x
FOREST GROWTH AND TIMBER QUALITY

234

this restriction. They incorporated the backward growth 

intervals into the estimation process to ensure that the data 

structures to be encountered in model applications were 

fully represented during model estimation. Otherwise, 

the reported goodness-of-fit measures and other fit statistics resulting from the model estimation might not be as 

relevant or compatible.

Common Measures of Goodness-of-fit

Numerous goodness-of-fit measures have been developed 

to judge how well a model fits the data. The most common ones are R2

 (coefficient of determination or fit index), 

adjusted R2, and mean square error (MSE) or root mean 

square error (RMSE):

[1] 2

2

2

)(

( ˆ ) 1

∑

∑ −

− −= yyyy R

i

ii

[2] )1( 1 1 2 2 R

pn

n Radj − 















−

− −=

[3] 

pn

yy

pn

SSE RMSE MSE ii

−

− = − == ∑ 2 ( ˆ )

where yi and yˆ

i are the ith observed and predicted y values, y

_ is the arithmetic mean of yi (i = 1, 2, 3, ...n), SSE

is sum of square errors, and p is the number of model parameters. Eqs. [1]–[3] (plus residual plots) have been used 

ubiquitously as the criteria for gauging the goodness-of-fit 

of a model, and for comparing and discriminating among 

alternative models.

Many other goodness-of-fit measures have also been 

developed, such as Amemiya’s adjusted R2

, Mallow’s Cp, 

random walk R2, Akaike’s information criterion, Schwarz 

Bayesian information criterion, and Amemiya’s prediction criterion (Judge et al. 1985). They are all modified 

or scaled forms of R2, MSE or SSE. For instance, the least 

squares based Akaike’s information criterion (AICLS) and 

the Schwarz Bayesian information criterion (BICLS) take 

the following forms:

[4] AICLS = n ln(MSE) + 2p

[5] BICLS = n ln(MSE) + p ln(n)

Various χ2–based goodness-of-fit statistics can also 

be used (Huber-Carol et al. 2002, Yang et al. 2004). 

Most of them are derived from Pearson’s χ2 test statistic, 

χ2 = Sc

i=1(Oi

 – Ei)

2

 / Ei where Oi is the observed frequency 

and Ei is the expected frequency from a theoretical distribution, and i is the number of classes (i = 1, 2, ..., c). 

For classical ordinary least squares regression where each 

response observation is assumed to come from a normal 

distribution centered vertically at the level implied by the 

fitted model, and where the variance of each normal distribution is assumed to be the same (σ2

, estimated by MSE), 

the χ2 goodness-of-fit statistic can be written as:

[6]

 ∑=

− = n

i

i

ii

y

yy

1

2

2

ˆ

( ˆ ) χ

The χ2 statistic expressed in [6] is asymptotically

χ2

(n–p–1),α distributed with (n – p – 1) degrees of freedom at 

a given α level (α = 0.05 throughout this study). 

Since the size of the RMSE (or MSE), AICLS, BICLS and 

χ2 are dependent on the scale and the type of data involved 

(e.g., an RMSE of 0.1 or an AICLS of 2000 may indicate a 

very good or a really bad model), the most common single 

overall goodness-of-fit measure is R2 (or adjusted R2 when 

comparing competing models). R2 indicates the proportion 

of total variation explained or accounted for by a fitted 

model. In most practical applications, the R2 value for an 

appropriately fitted model is generally between 0 and 1, 

with 0 indicating no relationship and 1 indicating a perfect 

relationship. Poorly fitted models, especially those without 

Figure 4. An illustration of the growth intervals and data structures: I 

(longest forward), II (longest), III (non-overlapping forward), IV (nonoverlapping), V (all possible forward), and VI (all possible combinations).
FOREST GROWTH AND TIMBER QUALITY

235

an intercept term, can have negative R2

 values. 

While R2 has its own limitations (Kvalseth 1985, Anderson-Sprecher 1994), it does give modelers and model users 

an overall indication of the goodness-of-fit of a model, in 

addition to being suitable for comparing competing models. 

For instance, an R2 value of 0.98 represents a good fit, as 98 

percent of the total variations in the data were accounted for 

by the model. An R2 value of 0.10 represents a poor fit, as the 

model only accounted for 10 percent of the total variation 

and the remaining 90 percent was unaccounted for.

Modeling Approaches Based on RMD

To appreciate different modeling approaches that can be 

used for RMD analysis, RMD was first treated as if it were 

one-time, temporary measured data (TMD). 

RMD Treated as TMD

If repeatedly measured data are treated as one-time, 

temporary measured data, the trajectories shown in Fig. 

2(b)–2(d) would be disconnected and all three graphs 

would become scatter plots of 28 data points, as shown in 

Fig. 2(a). The same simple linear regression line would be 

obtained for all four data sets, based on the ordinary least 

squares (LS) method:

[7] y = b0 + b1x (b0 = 31.9217 and b1 = 0.35189)

More detailed fit statistics are listed in Table 3. Residual 

plots from the LS fits treating the data as TMD looked the 

same, as shown in Fig. 5(a). For illustration, the residuals 

were connected in Fig. 5(b)–5(d) to form residual trajectories that correspond to the data trajectories shown in 

Fig. 2(b)–2(d).

Once the parameters were available, the χ2 statistic could 

be calculated using eq. [6] (χ2

 = 66.3673). The calculated 

χ2 statistic is greater than χ2

(n-p-1),α = χ225,0.050 = 37.6525, 

which means that the agreement between observed yi and 

predicted yˆ

i values is poor and there is a lack of fit. This is 

bewildering considering that the regression line fitted the 

data in Fig. 2(a) reasonably well. Yang et al. (2004) observed 

a similar phenomenon in which the χ2 test was found to 

be overly sensitive. Narsky (2003) discussed the problems 

associated with the χ2

 test and presented a new method 

using distance to nearest neighbor. Schunn and Wallach 

(2005) discussed reasons why the use of χ2 test could be 

disastrous for most applications.

When RMD was treated as TMD, the first key point to 

note is that many important fit statistics, such as the R2

and RMSE values, lose their ability to represent and/or differentiate the goodness-of-fit of models. This is illustrated 

in Fig. 2, where a reasonable fit, as in Fig. 2(a), and a poor 

fit, as in Figs. 2(c)–2(d), have the same R2 and RMSE values given in Table 3. It is often futile and sometimes very 

misleading to report the conventional fit statistics when 

RMD was treated as TMD. 

The second key point to note is that any judgement on 

the goodness-of-fit of a model, or the determination of the 

‘best’ model among alternative models, is better handled 

by ocular methods guided by a reasonable understanding 

of the relevant biological theory. For instance, visually inspecting the graphics, such as the plots of the fitted model 

overlaid on the original data (e.g., Fig. 2), or the plots of 

residual trajectories (rather than residual points) against the 

predicted y (e.g., Fig. 5), provides a much more powerful 

tool than many fit statistics for discerning the goodnessof-fit of a model.

The more fundamental question to be addressed is: if 

RMD are recognized as repeatedly measured data (i.e., not 

as one-time TMD), are the conventional fit statistics such 

as R2

 and RMSE appropriate for judging the goodness-offit of a model? 

In order to answer this question, we first need to look 

at the type of models that can be developed based on the 

data structures associated with RMD.

Model Types Based on RMD

Three general approaches can be used to develop three 

types of models based on RMD.

1) Cumulative function—

All cumulative functions can be expressed in a general 

Table 3. Summary statistics from the least squares fit of eq. [7] on data shown in Fig. 2.

Model Type Data structure n Estimate Std. Err. t-value Pr > |t| RMSE R2

 R2

adj.

[7] Cumulative Scatter 28 b0 = 31.9217 7.20586 4.43 0.0002 15.160 0.8031 0.7955

 b1 = 0.35189 0.03418 10.30 <.0001

Note: Cumulative type refers to y = b0 + b1x, which can be expressed as a cumulative function of the general form y = f(x). RMSE, R2 and R2

adj. are defined and 

calculated in [3], [1] and [2], respectively. Std. Err. is standard error of the estimate.
FOREST GROWTH AND TIMBER QUALITY

2

form as:

[8] y = f(x) 

where the response variable y is expressed as a linear or 

nonlinear function of the explanatory variable x (x can be 

a single variable or a multiple variable matrix). Cumulative 

functions are typically developed by treating RMD as TMD, 

as illustrated in the preceding section.

Cumulative functions have been widely used in forest 

growth and yield studies. They are appropriate for many 

purposes, including obtaining averages for RMD. However, 

these functions have a number of serious limitations, the 

most important one being that they generally don’t take 

into account the growth patterns embedded in the observed growth trajectories in RMD. Seemingly reasonable 

cumulative functions as judged by fit statistics could in 

fact be very poor representations of RMD. This was clearly 

evident in Figs. 2(c). and 2(d). In most cases when RMD 

are treated as TMD, ocular methods are the only methods 

that can be used to correctly determine the goodness-of-fit 

of cumulative functions.

2) Difference equation—

Difference equations can be expressed in the following 

general form, where y1 and y2 are the y values at (typically) 

times x1 and x2, respectively: 

[9] y2 = f(y1, x1, x2) 

Difference equation techniques have been widely used 

in growth and yield modeling, particularly in the development of site index models (Clutter at al. 1983). They have 

also been used to develop mortality (density-age) and other 

types of models (Huang et al. 2001). Using the simple linear regression [7] as an example, difference equations can 

be obtained by expressing any two y-x pairs on the same 

growth trajectory as follows:

[10] y1 = b0 + b1x1 y2 = b0 + b1x2

Isolating b0 in [10] and solving for y2 produces:

[11] y2 = y1 + b1(x2 – x1) 

Alternatively, if b1 is isolated in [10], we have:

[12] y2 = b0 + (y1 – b0) x2 / x1

For a function with p parameters, p difference equations 

can be formulated.

There are two different approaches for obtaining the 

parameter estimates for difference equations. The first apFigure 5. Residual plot (a) and residual trajectories (b, c, d) from the 

ordinary least squares fits of the simple linear regression y = b0 + b1x on 

the data shown in Figure 2.

Figure 6. Difference equation growth curves generated from eqs. [11] (left) and [12] (right), based on the estimated coefficients (b0 = 

31.9217, b1 =0.35189) for the cumulative function y = b0 + b1x, and given y1 values of 50, 85 and 120 at a fixed reference x1 value of 150.
FOREST GROWTH AND TIMBER QUALITY

27

proach involves fitting a cumulative function first. After the 

parameters are estimated, the cumulative function with p

parameters could be converted into p difference equations. 

For instance, after the two parameters in y = b0 + b1x are 

estimated, they could be constrained to formulate two difference equations [11] and [12]. Fig. 6 shows two sets of curves 

generated from eqs. [11] and [12], based on the estimated 

coefficients (b0 = 31.9217, b1 = 0.35189) for the cumulative 

function, and given y1 values of 50, 85 and 120 at a fixed 

reference x1 value of 150. Note that, from the same original 

cumulative function y = b0 + b1x, two very different sets of 

difference equation growth curves are obtained.

The first approach applies to other more complex functions. For instance, once the cumulative Chapman-Richards 

function y = a(1-e-bx)

c

 has been estimated, any one of the 

three parameters could be isolated to form three difference 

equations and to generate growth curves (Clutter et al. 1983). 

Depending on which parameter is chosen for isolation, the 

resulting curves would have very different shapes. There 

really is not a way of selecting the best parameter to isolate 

from among all the parameters that could be isolated, even 

though modelers provided all sorts of justifications to contend why a particular parameter related to the asymptote, 

rate or shape should be isolated (the likely truth is that 

the asymptote, rate and shape can all change). Additional 

analyses must be conducted to find out the ‘best’ parameter 

to isolate, and to determine which, if any, set of curves may 

be considered the most reasonable. Such analyses are best 

carried out by ocular methods, guided by the suggestions 

of relevant theory, by a modeler’s knowledge of the data and 

the understanding of the innate relationship to be built, 

and (unfortunately sometimes) by a desire to produce a 

pre-conceived or “wanted” answer for various purposes.

Since the first approach entails the fitting of cumulative 

functions, it does not require RMD. Even if RMD is available, cumulative functions are often developed by treating 

RMD as TMD, which could cause serious problems as 

previously discussed. The most critical problem is that 

the goodness-of-fit measures and the other fit statistics 

obtained in the model estimation process become irrelevant 

when a cumulative function is re-formulated into difference 

equations. The goodness-of-fit of the difference equations 

is unknown and shall not be misinterpreted. 

The second approach involves directly estimating difference equations based on one of the data structures formulated from RMD. Rather than first fitting a cumulative 

function, parameters of a difference equation are directly 

estimated on one of the RMD structures. As an example, for 

the three trajectories shown in Fig. 2(b), six data structures 

as described in Table 2 and Fig. 4 can be formulated, and 

the parameters for the difference equations [11] and [12] 

directly estimated. The estimates obtained in this manner 

(Table 4) are different from those obtained from fitting the 

cumulative function (Table 3).

Compared to the first approach, the goodness-of-fit 

measures (RMSE, R2, R2

adj.) from the second approach 

(as shown in Table 4) differ depending on the model and 

the data structure used, particularly for model [12] where 

the RMSE and R2 vary greatly. For [11], the estimated 

coefficients are identical for data structures I and II, III 

and IV, as well as V and VI. Growth curves (not shown 

here) based on the direct estimates shown in Table 4 were 

different from those shown in Fig. 6. The goodness-of-fit 

measures obtained from the second approach are relevant 

Table 4. Fit statistics for equations [11] and [12] on the data shown in Fig. 2(b)

Model Type Data n Estimate Std. Err. t-value Pr > |t| RMSE R2

 R2

adj.

 structure

[11] Difference I 3 b1 = 0.35770 0.00943 37.92 0.0007 4.302 0.9396 0.9396

equation II 6 b1 = 0.35770 0.00597 59.96 <.0001 3.848 0.9948 0.9948

III 25 b1 = 0.36713 0.03740 9.82 <.0001 6.535 0.9511 0.9511

IV 50 b1 = 0.36713 0.02620 14.03 <.0001 6.468 0.9557 0.9557

 V 118 b1 = 0.35620 0.00538 66.19 <.0001 7.232 0.9214 0.9214

VI 236 b1 = 0.35620 0.00380 93.80 <.0001 7.217 0.9514 0.9514

[12] Difference I 3 b0 = 29.7931 8.8174 3.38 0.0775 74.43 -17.08 -17.08

equation II 6 b0 = 29.7366 5.6029 5.31 0.0032 47.95 0.1952 0.1952

III 25 b0 = 24.2689 4.2158 5.76 <.0001 8.847 0.9104 0.9104

IV 50 b0 = 25.6332 3.3410 7.67 <.0001 7.843 0.9348 0.9348

 V 118 b0 = 28.7940 1.2286 23.44 <.0001 22.305 0.2528 0.2528

VI 236 b0 = 28.9035 0.8913 32.43 <.0001 16.814 0.7360 0.7360

 

Note: RMSE, R2 and Radj.2 are defined in [3], [1] and [2], respectively. Std. Err. is standard error of the estimate. Data structures are illustrated in Table 2 and Fig. 4.
FOREST GROWTH AND TIMBER QUALITY

2

only to the specific difference equation formulation and to 

the data structure used.

The second approach also applies to other more complex 

functions. For instance, parameters a, b and c of the Chapman-Richards function y = a(1-e-bx)

c

 can be isolated first to 

produce the following difference equations, and then the 

remaining parameters in the difference equations can be 

directly estimated, or related to other variables through the 

parameter prediction method and estimated (Clutter et al. 

1983, Huang 1997):

[13]

( )

)exp(1

)exp(1

111 4 5

113

/

210

1

2

12

xyb b b

c

xybcbybb

bx

bx

yy

= =

















−

− =

[14] ( )

( )

/1)1( 1 4

12

10 13

/1

1

/

2 b b

xx c c

ybcyba

aymmay

==

−= , −=

[15]

( )

)]exp(1ln[

)]exp(1ln[ ,

1 3

10 12

1

1 2

2

b b

m

ybbyba

bx

bx

m

a

y ay

==

−−

−−  = 

 



 =

where the parameter prediction functions are expressed 

in parentheses. Once the parameters of a difference equation are related to other variables through the parameter 

prediction method, the difference equation may not possess the standard difference equation characteristics any 

more (Huang 1997). Typically, the parameters of difference equations are estimated based on one of the six data 

structures presented earlier after the difference equations 

are formulated.

3) Increment (or decrement) function—

An increment (or decrement) function is also referred to 

as a change function. It usually models the change in y as 

a function of initial conditions:

[16] )( 1

12

12 xf

xx

yy

yinc = −

− =

where yinc is the change in y per unit of x (e.g., per year), 

and f (x1) indicates a linear or nonlinear function of the 

initial condition x1. In the simple linear regression case, 

[16] can be expressed more explicitly as:

[17] 1101)( xbbxfyinc +==

Alternatively, the increment yinc can also be expressed 

as periodic increment, where yinc = (y2 – y1). If this is the 

case, the interval length (x2 – x1) must be appropriately 

accounted for on the right-hand side of the equation. There 

are also cases where the increment function [16] might be 

expanded to include other additional variables: 

[18] 

),,( 211

12

12 xxyf

xx

yy

yinc = −

− =

However, since such an expression allows a variable or 

its transformations (e.g., y1 or x1) to appear on both sides of 

an equation, some specialized techniques such as two- or 

three-stage least squares (Judge et al. 1985, LeMay 1990, 

Huang and Titus 1999) may need to be used to obtain the 

most appropriate estimates, and the interpretations must 

be made pertinently and carefully. Otherwise, both the 

fit statistics (usually with an overstated R2 value) and the 

interpretations could be very misleading. In this study the 

more common type [17] was fitted on six data structures 

Table 5. Fit statistics for increment function [17] on the data shown in Fig. 2(b).

Model Type Data n Estimate Std. Err. t-value Pr > |t| RMSE R2

 R2

adj.

 structure

 [17] Increment I 3 b0 = 0.343292 0.05330 6.44 0.0981 0.0217 0.0840 -0.8320

function b1 = 0.000260 0.00086 0.30 0.8128

II 6 b0 = 0.359345 0.01160 31.06 <.0001 0.0161 0.0003 -0.2496

 b1 = -1.85E-6 0.00005 -0.04 0.9721

III 25 b0 = 0.589959 0.12680 4.65 0.0001 0.2460 0.1415 0.1042

 b1 = -0.00128 0.00066 -1.95 0.0638

IV 50 b0 = 0.604899 0.09330 6.49 <.0001 0.2410 0.1398 0.1219

 b1 = -0.00125 0.00045 -2.79 0.0075

 V 118 b0 = 0.462134 0.02910 15.88 <.0001 0.1320 0.1214 0.1139

 b1 = -0.00075 0.00019 -4.00 0.0001

VI 236 b0 = 0.446895 0.02230 20.04 <.0001 0.1347 0.0771 0.0731

 b1 = -0.00047 0.00011 -4.42 <.0001

Note: RMSE, R2 and R2

adj. are defined in [3], [1] and [2], respectively. Std. Err. is standard error of the estimate. Data structures are illustrated in Table 2 and Fig. 4.
FOREST GROWTH AND TIMBER QUALITY

2

formulated from the data shown in Fig. 2(b). Results are 

given in Table 5.

Compared to the difference equation results shown in 

Tables 4, the goodness-of-fit measures from the increment 

model shown in Table 5 also differ depending on the data 

structure used. However, the most striking aspect is that 

the R2

 values from the increment model are much lower 

than those from the difference equations (except for data 

structure I where only three observations were used). Given 

the R2 values from the increment model (in the range of 

0.0003 to 0.1415), one would without hesitation conclude 

that the model gave very poor fits to the data. Later it will 

be shown why such a conclusion could be erroneous.

A fitted cumulative function may sometimes be converted 

into an increment model indirectly by taking the derivative of y with respect to x. For the simple linear regression 

function [7], the increment function (i.e., the rate of change 

per unit of x) is a constant b1:

[19] ∂y / ∂x = b1 

While the concept of taking the derivative of a cumulative function to obtain the increment function is fairly 

straightforward, in practice the execution may not be easy 

because the derivative could be very complex and computationally very expensive to obtain, especially for nonlinear 

models with multiple, interrelated variables. In addition, 

the derivative obtained from a cumulative function is supposed to represent growth rate. Many have suggested taking 

derivatives as one of the methods for developing increment 

models, and some have used derivatives to compute growth 

rates, as illustrated in eq. [19]. However, this approach 

would be valid only if the function and the data follow the 

same trend, as in Fig. 2(b). Otherwise, the growth rate does 

not reflect the true growth rate embedded in RMD at all, 

as in Fig. 2(c)–(d). Although this may be relatively easy to 

understand for a simple linear model, it could be very difficult to comprehend in a multivariate, multi-dimensional 

situation. The deficiencies associated with the fitting of a 

cumulative function by treating RMD as TMD could be 

found in a derivative-based increment model. Furthermore, 

the goodness-of-fit of an increment model obtained in such 

a manner is unknown, as the goodness-of-fit measures obtained for the cumulative function are no longer applicable 

to the derivative-based increment model.

A Goodness-of-Fit Index on RMD

The conventional R2 value on model fitting data indicates 

the proportion of total variation explained by a fitted model. 

It is scale-independent. Given an R2

 of 0.8, we know that 

80 percent of the total variation in the data is accounted 

for by the fitted model. This gives us a direct, intuitive 

indication about the overall goodness-of-fit of the model 

on the data. 

In the analysis of RMD, the reported R2 values vary 

considerably depending on the model type and the data 

structure used. When RMD was treated as TMD and a 

cumulative function estimated, the R2 value (e.g., in Table 

3) ignored repeated measures and pertained only to the 

scattered point data. When RMD was treated as RMD and 

a difference equation or an increment function estimated, 

the R2 values (e.g., in Tables 4 and 5) fluctuated greatly 

(and are typically misleading, as will be shown later), which 

made the choice of a better approach almost impossible. 

This may explain why R2

 has typically not been reported 

in standard RMD analysis (Pinheiro and Bates 2000, Littell 

et al. 2006). 

The reported statistics in RMD analysis are likelihoodbased statistics such as: -2 log-likelihood, Akaike’s information criterion (AIC) and Schwarz Bayesian information 

criterion (BIC):

[20] AIC = –2ln(L) + 2p

[21] BIC = –2ln(L) + p ln(n) 

where L is the likelihood function, p is the number of model 

parameters and n is the sample size (Judge et al. 1985, Littell 

et al. 2006). Note that the likelihood-based AIC and BIC 

are different from the LS-based AICLS and BICLS (eqs. [4] 

and [5]). Both AIC and BIC are used to compare competing 

models. BIC charges a heavier penalty for a large number of 

parameters (similar in concept to adjusted R2

). The model 

with the smaller information criteria is said to be a better 

fit. Both AIC and BIC can also be utilized for choosing 

amongst several covariance structures.

While AIC and BIC have been used extensively in comparing competing models, when all models are poor, the 

model with the smaller information criteria is considered 

relatively better, but it is still a poor model. An AIC (or 

BIC) value of 200 or 1800 does not connote to any direct, 

intuitive, and scale-independent R2

-type indication about 

the overall goodness-of-fit of the model, or about how 

much total variation was explained by the model. In other 

words, an AIC (or a BIC) value of 200 or 1800 could mean 
FOREST GROWTH AND TIMBER QUALITY

240

a superb model, or an abysmal fit.

Without a direct, intuitive, and scale-independent R2

-

type indicator, we really do not have any idea about the 

overall goodness-of-fit of a model, and we do not know how 

much total variation was explained by the model. However, 

if the conventional R2 values were reported (as in Tables 

3, 4 and 5), they could be very misleading. Reporting the 

AIC and BIC values would help to differentiate competing 

models, but they do not indicate the goodness-of-fit of a 

model as is normally understood. This creates a dilemma 

for model developers and model users alike. 

For linear models estimated based on likelihood methods, researchers (mostly economists) have developed 

pseudo-R2s and other types of measures to help in assessing model fit (Hardin and Hilbe 2007, Pan and Lin 2005). 

They include McFadden’s R2 (1 – likelihood (intercept 

only model) / likelihood (full model)), Ben-Akiva and 

Lerman’s R2, maximum likelihood R2, Craig and Uhler’s 

R2, and Makelvey and Zavoina’s R2. However, the pseudoR2s have some serious limitations. Even the software that 

adopted the pseudo-R2s stated that “we do not intend that 

our pseudo R2 should be reported in formal write-ups of 

results” (http://www.stata.com/).

The proposed goodness-of-fit index (GOFI) on RMD 

uses the same basic formula for the standard R2, but it is 

modified as described below and illustrated in Fig. 7, to 

alleviate the problems and to provide a consistent measure 

of goodness-of-fit for RMD analysis.

First, assume that a forward projection from a fitted 

model is made for a trajectory measured three times at 50, 

80, and 120 years (solid lines in Fig. 7). Forward projection 

uses the first data pair at the beginning of the trajectory (at 

time 1) as input into the model to project forward to get 

predicted y values at other times (e.g., times 2 and 3). Once 

the predicted values were obtained, the differences (errors 

or residuals) between the observed and predicted values are 

assessed and a forward coefficient of determination, denote 

as R2

F or R21 in this example, is calculated:

[22]

 

2

1

1

2

2

1

2

)(

( ˆ ) 1

yy

yy RR

i

kn

i

kn

i ii

F

−

− −==

∑

∑ −

=

−

=

where all variables are as defined before, except the summation is over i = 1, 2,...(n - k), and k is the number of 

trajectories. The first pair of each trajectory was excluded 

from the calculation because there was no error for the first 

pair (the model passes through the pair, see Fig. 7).

Similarly, a backward projection that uses the last pair 

(at time 3) as the starting point was made, and a backward 

coefficient of determination, denote as R2

L (or R23 in this 

example), was calculated using the same formula [22], but 

with the last data pair with zero error excluded. For the 

data pair 2 in the middle of the trajectory, bi-directional 

(forward and backward) projections were made, with this 

data pair as the starting point (see Fig. 7). An R2

M (or R22

in this example) was calculated in the same manner, but 

with the data pair 2 excluded. The goodness-of-fit index 

is simply the average of the three R2 values:

[23] GOFI3 = (R2

1 + R22 + R23

) / 3

For a trajectory measured n times, a general expression 

for GOFI is:

[24] GOFIn = (R2

1 + R22 + R23 + ... + R2n

) / n

The interpretation of GOFI is similar to that of the 

model fitting coefficient of determination. It provides an 

Figure 7. An illustration of forward (left), backward (middle), and bi-directional (right) projections for the calculation of the goodness-of-fit index. The solid 

lines represent observed trajectories. The dashed lines represent model projections. The first, third (last), and second (middle) observations are used as the 

starting point in forward, backward, and bi-directional (forward and backward) projections, respectively.
FOREST GROWTH AND TIMBER QUALITY

241

overall performance measure for the developed model on 

model fitting data. 

Since RMD is often unequally spaced and unbalanced, 

a recommended simplified GOFI can be computed using 

only the forward projection from the first data pair and the 

backward projection from the last data pair (see Fig. 8):

[25] 

2

22 RR LF GOFI + =

where R2

F is the forward coefficient of determination based 

on the first pair, and R2

L is the backward coefficient of 

determination based on the last pair. Because the computation of R2

F and R2L involves the longest possible intervals, 

the prediction errors are typically the largest. The GOFI 

calculated in [25] generally represents the worst goodnessof-fit on a given data set—a feature that guards against an 

inflated goodness-of-fit that might otherwise be obtained. 

It is interval length dependent—a feature that echoes a 

general fact that short-term predictions are usually more 

accurate than long-term predictions. This second feature 

should be interpreted carefully, as a high GOFI obtained 

from short intervals may not be pertinent if the desired 

prediction intervals that a model should be assessed against 

need to be longer.

Many other related standard goodness-of-fit measures 

could also be calculated, for example:

[26] 

kn

yy RMSEP

kn

i ii

−

− = ∑ −

=1

2 ( ˆ )

[27] 

kn

yy ME

kn

i ii

−

− = ∑ −

=1 ( ˆ ) or

 

∑ −

= −⋅ − = kni ii yy kn

MAD 1 ˆ 1

[28] ∑ −

= 













 − ⋅ − = kn

i

i

ii

y

yy

kn

MPE 1

100 ˆ

 

or

 

∑ −

=

− ⋅ − = kn

i

i

ii

y

yy

kn

MAPE 1

100 ˆ

where RMSEP is root mean square error of prediction, ME is 

mean error, MAD is mean absolute difference, MPE is mean 

percent error, and MAPE is mean absolute percent error. 

The summation is to (n – k) because there are k trajectories 

and the starting points used in projections have zero errors 

and are removed from the calculations. 

In the cases where a model can only make forward or 

backward projection, [25] reduces to:

[29] GOFI = R2

F

 or GOFI = R2

L 

The GOFI statistic obtained in this manner would be similar 

to the standard R2 statistic, except that it does not use the 

first or the last data pair in its calculation. If RMD is treated 

as TMD and a cumulative function fitted, GOFI would be 

equivalent to the standard R2 statistic.

RESULTS AND DISCUSSION

The coefficients shown in Tables 4 and 5 were used to make 

Figure 8. An illustration of forward (left) and backward (right) projections on unequally spaced, unbalanced repeatedly measured data, for the calculation of 

the goodness-of-fit index. The solid lines represent observed trajectories. The dashed lines represent model projections. 
FOREST GROWTH AND TIMBER QUALITY

242

forward and backward projections on the data shown in 

Fig. 2(b). Prediction errors were obtained. Table 6 lists the 

summary statistics from the projections. Compared to the 

results presented in Tables 4 and 5, the results shown in 

Table 6 are striking on several aspects, as detailed below.

1) If the traditional R2

 fit statistics (as in Table 5) were 

used to judge the goodness-of-fit of the models, the increment function, with R2 ranges from 0.0840 to 0.1415, 

would have been considered very poor. This could have led 

to some erroneous conclusions. The increment function in 

fact provided some of the best fits to the data, especially 

for data structures III, IV, and VI (see Table 6). 

2) Judging from Table 4, the difference equation [12] 

had R2 values exceeding 0.9 (for data structure III and IV). 

This could have meant that the model provided a fairly 

reasonable fit to the data. In truth, however, the estimates 

obtained from [12] would generate growth curves similar to 

those shown in Fig. 6(b), which were poor representations 

of the true trajectories shown in Fig. 2(b). Only the GOFI 

statistics shown in Table 6 adequately reflected the poor 

fits by [12], regardless of the data structure used. The GOFI 

statistics are also more consistent (ranging from 0.1469 to 

0.2093, Table 6) than the R2 values (ranging from -17.08 

to 0.9348, Table 5).

3) The reported R2 values for [11] range from 0.9214 up 

to 0.9948 (Table 4), the latter means an almost perfect fit. 

Four of the reported R2 values for [11] exceed 0.95. The 

GOFI statistics are almost identical (range from 0.9270 to 

0.9279, Table 6), and they are always lower than the R2

values except for the data structure V. The reported R2

values from the difference equation [11] were mostly inflated and unachievable in application, particularly those 

that exceeded 0.95. 

4) The value in reporting R2

 from a difference equation formulation y2 = f (y1,x1,x2) is questionable to say the 

least. The R2 values vary considerably depending on the 

Table 6. Forward and backward projection summary statistics on the data shown in Fig 2(b)

 Prediction error

Model-data Type n – k RMSEP R2

F

 or R2

L

 GOFI

structure Mean SD Min. Max.

[11]-I & II Forward 25 5.9885 5.672 -4.798 15.980 8.1698 0.9239 0.9279

 Backward 25 5.4086 6.221 -5.653 16.859 8.1486 0.9318 

[11]-III & IV Forward 25 4.5857 5.802 -7.429 14.424 7.3042 0.9391 0.9270

 Backward 25 6.7639 6.217 -4.616 18.094 9.1023 0.9150 

[11]-V & VI Forward 25 6.2117 5.660 -4.380 16.227 8.3268 0.9209 0.9275

 Backward 25 5.1931 6.229 -5.818 16.662 8.0136 0.9341

[12]-I Forward 25 13.4598 35.509 -80.406 55.655 37.3045 -0.5874 0.1469

 Backward 25 4.0084 10.192 -14.363 20.950 10.7604 0.8811

[12]-II Forward 25 13.3074 35.510 -80.687 55.493 37.2504 -0.5828 0.1491

 Backward 25 4.0336 10.191 -14.321 20.990 10.7692 0.8809

[12]-III Forward 25 -1.4378 36.773 -107.928 39.773 36.0589 -0.4832 0.1856

 Backward 25 6.4709 10.204 -10.264 24.809 11.9092 0.8544

[12]-IV Forward 25 2.2414 36.240 -101.131 43.695 35.5788 -0.4439 0.2093

 Backward 25 5.8627 10.185 -11.276 23.856 11.5741 0.8625

[12]-V Forward 25 10.7654 35.558 -85.383 52.783 36.4654 -0.5168 0.1804

 Backward 25 - 4.4537 10.181 -13.621 21.648 10.9248 0.8775

[12]-VI Forward 25 11.0607 35.549 -84.838 53.098 36.5449 -0.5234 0.1773

 Backward 25 4.4049 10.182 -13.703 21.572 10.9058 0.8779

[17]-I Forward 25 2.2470 7.199 -14.924 12.909 7.4032 0.9375 0.8711

 Backward 25 11.9747 6.986 -2.396 24.167 13.7931 0.8047

[17]-II Forward 25 5.7857 5.680 -5.157 15.747 8.0279 0.9265 0.9283

 Backward 25 5.5836 6.212 -5.524 17.009 8.2595 0.9300

[17]-III Forward 25 0.4096 4.453 -9.368 6.570 4.3825 0.9781 0.9694

 Backward 25 -3.7304 5.045 -16.079 2.621 6.1924 0.9606

[17]-IV Forward 25 -2.4919 4.255 -11.663 5.140 4.8569 0.9731 0.9729

 Backward 25 -0.5867 5.232 -13.592 7.635 5.1602 0.9727

[17]-V Forward 25 7.4287 5.336 -3.480 16.151 9.0838 0.9059 0.9253

 Backward 25 -4.4958 5.933 -15.244 4.317 7.3487 0.9446

[17]-VI Forward 25 3.3580 4.769 -5.760 11.111 5.7544 0.9622 0.9625

 Backward 25 2.6152 5.541 -9.051 11.919 6.0263 0.9627

 

Note: RMSEP is root mean square error of prediction computed by [26], R2

F

 and R2

L

 are computed by [22], GOFI is the goodness-of-fit index computed by 

[25], and SD is standard deviation.
FOREST GROWTH AND TIMBER QUALITY

243

parameter(s) to be constrained and the data structure used 

(see Table 4). In many cases, a difference equation formulation tends to give unrealistically high R2

 values that look 

‘nice’ but are not relevant in applications when predictions 

are made. This could be a result of the high correlation 

between y2 and y1, or an artefact of this particular type of 

formulation.

5) The GOFI statistic can be used more reliably than 

other statistics for determining the ‘best’ parameter(s) to 

constrain. This is evident in Table 6, where constraining 

parameter a (eq. [11]) is found to be consistently better 

than constraining parameter b (eq. [12]). Using the R2

(and/or RMSE) values to determine the best parameter(s) 

to constrain could sometimes lead to erroneous conclusions 

(see Table 4). More importantly, the R2 values (e.g., 0.9104 

and 0.9348 for [12] on data structures III and IV, Table 

4) are not appropriate for assessing the goodness-of-fit in 

applications where the attainable goodness-of-fits were 

much poorer (e.g., 0.1856 and 0.2093 for [12] on the same 

data structures III and IV, Table 6). Clearly the difference 

equation R2

 values were grossly overstated.

6) Data structures from RMD play an important role in 

parameter estimation and model development. Previous 

studies (e.g., Goelz and Burk 1992, Cao 1993, Huang 1997, 

Wang et al. 2004) showed that the ‘best’ data structure was 

model dependent, but in general, data structures III, IV, 

V, and VI were all reasonable. Those results were further 

confirmed in this study. It was found that data structure 

III was the most efficient and that data structure VI was 

the most consistent and stable. Since the longest growth 

interval data structures I and II ignore the observed information from intermediate measurement(s), their use 

should be limited. Additional studies may be needed to 

evaluate the bias and efficiency of various data structures 

from other repeatedly measured data sets. This is an area 

for further research.

To see if the results obtained from the hypothetical data 

still hold for real RMD from PSPs, three models corresponding to the data sets shown in Fig. 3 were fitted: 

White spruce height-site index model:

[30] 















++++ +

++++ + ×= exp(1 )][ln()1ln( )exp(1 )][ln()1ln( )

4 1

2

21 132

4 1

2

21 131

12

bb totagebHbtotage

bb totagebHbtotage HH

where H2 and H1 are top height (i.e., average height of the 

100 largest DBH trees per ha) at total age 1 and 2 (totage1

and totage2), respectively, and total age refers to the total 

age from the time of germination.

Aspen mortality (density-age) model:

[31] 















++++

++++ ×= 1[log()ln(exp(1 )])1[log()ln(exp(1 )])

2

1

12 cSIba bhage

cSIba bhage NN

 

( ) ]

)ln( [

11

/1

11

1 1

1

1

1

1

12 1

)1(

1 )1ln()1ln(

1000/

1

N

N Nb

Nbb Nbc

bhage bhage N

bhage

N a

+

= +=

+×















−= ++ +

where N2 and N1 are stems/ha (for trees > 1.3 m) at breast 

height age 1 and 2 (bhage1 and bhage2), respectively, and 

SI is site index (m), i.e., top height at 50 years bhage. 

Black spruce basal area increment model: 

[32] 

(

) ( )2

3 3

/)1ln()]11[ln( (1 )

exp( )

1

2

0 1

1

)1(

1 2 1 1

a

aa

N bhage SI BA

bhageaaBAINC bhage SC

++ ++

−= + ×

where BAINC = annual basal area increment (m2/ha/year), 

SC1 = black spruce species composition (BAblack spruce/BAall 

species) at time one, BA1 = black spruce basal area (m2/ha) at 

time one, bhage1 = breast height age (years) at time one, N0

= initial density (stems/ha for trees > 1.3 m) at bhage zero, 

and SI = site index (m), i.e., top height at 50 years bhage.

All three models are parts of the GYPSY model (Growth 

and Yield Projection System) used in Alberta (Huang et al. 

2001). Both [30] and [31] were developed from a combination of the difference equation and the parameter prediction 

formulation of the logistic-type model (Monserud 1984). 

Fit statistics for the models on data structure VI are listed 

in Table 7.

Table 7. Fit statistics for models [30], [31], and [32] on repeatedly measured data from PSPs

Model Type b1 b2 b3 b4 RMSE R2

 R2

adj.

[30] Difference 13.079210 -6.03800 -0.25712 0.178732 1.1675 0.9904 0.9904

[31] Difference 0.738940 6.53357 245.30 0.8584 0.8584

[32] Increment 0.000112 0.05690 0.40459 0.2001 0.2668 0.2653

 Note: RMSE, R2

, and Radj.2 are defined and calculated by [3], [1], and [2], respectively
FOREST GROWTH AND TIMBER QUALITY

244

The R2

 values shown in Table 7 would suggest that, the 

difference equation site index model [30] fitted the data 

extremely well (R2 = 0.9904), with more than 99 percent 

of the total variation accounted for by the model. The 

basal area increment model [32] fitted the data poorly (R2

= 0.2668), with less than 27 percent of the total variation 

accounted for by the model.

The estimated coefficients shown in Table 7 were used 

to make forward and backward projections for the relevant 

data sets shown in Fig. 3. As an example, Fig. 9 shows the 

forward and backward projections and associated error 

trajectories from the white spruce height-site index model 

[30]. Similar graphs from [31] and [32] were also produced 

(available upon request). They displayed similar patterns 

as shown in Fig. 9. Summary statistics from forward and 

backward projections for all three models are listed in 

Table 8.

The results shown in Table 8 confirmed most of the 

Figure 9. Forward (left graphs) and backward (right graphs) projections and associated error trajectories from model [30] on the white spruce top 

height-age data shown in Fig. 3. 

Table 8. Summary statistics from forward and backward projections based on the PSP data.

 Prediction error

Model Type n – k RMSEP R2

F

 or R2

L

 GOFI Mean SD Min. Max.

[30] Forward 1496 -0.1811 1.478 -5.654 5.807 1.48819 0.8748 0.9065

 Backward 1496 0.1102 1.040 -4.531 6.587 1.04526 0.9382

[31] Forward 1054 20.7475 157.699 -1047.11 1019.49 158.984 0.9219 0.8611

 Backward 1054 4.0670 254.241 -2052.97 3192.27 254.153 0.8003

[32] Forward 459 0.8301 3.286 -14.144 14.096 3.3856 0.9361 0.9425

 Backward 406 0.2452 2.980 -14.166 14.122 2.9866 0.9488 

Note: RMSEP is root mean square error of prediction computed by [26], R2

F

 and R2

L

 are computed by [22], GOFI is the goodness-of-fit index computed by 

[25], and SD is standard deviation.
FOREST GROWTH AND TIMBER QUALITY

245

earlier observations. The reported R2

 (0.8584, Table 7) for 

the difference equation [31] was in line with the calculated 

GOFI (0.8611, Table 8). However, the reported R2 (0.9904, 

Table 7) for the difference equation [30] was overstated 

and not achievable in application when predictions were 

made. The GOFI for [30] was 0.9065 (Table 8), an achieved 

number that was lower than the reported R2. 

For the basal area increment model [32], the reported 

R2 (0.2668, Table 7) is much lower than the GOFI (0.9425, 

Table 8) achieved in application. If the R2 statistic was 

used to assess the goodness-of-fit of the basal area increment model, the model would be deemed as a poor model. 

However, as shown in Table 8 (and figures showing the 

forward and backward projections and associated error 

trajectories, available upon request), the increment model 

provided very reasonable fits to the data. When predictions 

were made, the fitted model accounted for about 94 percent 

of the total variation.

While all previous analyses and results were demonstrated on model fitting data, it is worthwhile to note that 

the logic embedded in them is equally applicable to independent model validation data in which the GOFI could 

be more aptly called goodness-of-prediction index (GOPI). 

When the data were split into a model-fitting data set and a 

model-validation data set by two groups of distinct regions 

(i.e., not a random split), the results and subsequent inferences obtained from the validation data set (to be reported 

elsewhere) were very close to those obtained from the modelfitting data set, with the marginal differences likely caused 

by the so-called optimism principle of model validation 

(Picard and Cook 1984, Yang et al. 2004).

All previous analyses and results were based on the 

ordinary least squares method, which assumes that the 

error terms of a model are independently and identically 

distributed (i.i.d.) with mean zero and a constant variance. 

However, for RMD from PSPs (and stem analysis), serial 

correlation (i.e., correlation between the errors within 

the same plot), contemporaneous correlation (i.e., correlation between the errors of different plots), and various 

within- and between-plot heteroskedasticity (unequal error 

variance) might be present. In addition, the correlations 

could be both temporal and spatial. Furthermore, the 

RMD obtained from PSPs and stem analysis is typically 

unequally spaced (i.e., measurements were taken over intervals of varying times or distances) and unbalanced (i.e., 

different number of measurements were made on different 

experimental units). 

Violation of the i.i.d. error assumption may have some 

important statistical consequences for LS regression. It 

invalidates standard regression hypothesis testing and 

interval estimations. The problem may be solved using the 

generalized least squares (GLS) method (Judge et al. 1985, 

LeMay 1990, Baltagi 2005) or the mixed model technique 

(Davidian and Giltinan 1995, Gregoire et al. 1995, Littell 

et al. 2006). The use of GLS and three nonlinear mixed 

model methods (i.e., approximate first-order, second-order, and marginal structures) was demonstrated in Huang 

(1997) on the stem analysis data for the development of 

site index models. To avoid the digression from the main 

purposes of this study, only the results obtained from the 

nonlinear mixed model fittings of [30] from the marginal 

structures method (Method 3) of the nonlinear mixed 

model estimations described in Littell et al. (2006), were 

presented here.

Since the PSP data used in this study are unequally 

spaced, unbalanced RMD, many of the time-series covariance structures such as AR(1), AR(2), MA(1), and ARMA(1,1), 

which all assume that the measurements are made at equally 

spaced time intervals, are inappropriate. Instead, spatial 

covariance structures used in spatial data analyses were 

used (Littell et al. 2006). With spatial covariance structures, 

the covariance is assumed to be a function of the distance 

(e.g., time interval) between two locations:

[33] Cov(ei

, ej) = σ2[f(dij)]

where σ2 is the overall error variance, dij is the distance 

between two measurements at times or distances i and j 

(dij = | ti – tj |), and f (dij) represents a function of dij. Seven 

functions listed in Littell et al. (2006) were examined to 

determine the most appropriate function for the data used 

in this study:

[34a] f(dij) = [1–1.5(dij / ρ) + 0.5(dij / ρ)

3

] × 1{dij < ρ} 

(Spherical)

[34b] f(dij) = exp(–dij / ρ) (Exponential)

[34c] f(dij) = exp(–d2

ij / ρ2

) (Gaussian)

[34d] f(dij) = (1 – ρdij) × 1{ρdij < 1} (Linear)

[34e] f(dij) = [1 – ρ log(dij)] × 1{ρ log(dij) < 1} (Linear Log)
FOREST GROWTH AND TIMBER QUALITY

246

[34f] f(dij) = ρdij (Power)

[34g] f(dij) = (dij / 2v)

v

 2Kv(dij / ρ) / G(v) (Matérn)

where ρ is the correlation parameter (|ρ| < 1). The term 1{dij

< ρ} used in the spherical function is an indicator function 

that equals to 1 when dij < ρ and equals 0 otherwise. Similar 

1{·} terms were used in the linear and linear log functions 

to indicate that they equal 1 when the condition within the 

parentheses holds and equal 0 otherwise. The additional 

parameter ν in Matérn’s function is a smoothness parameter, 

and the Kν(·) is the modified Bessel function. Littell et al. 

(2006) provided more details about these functions. The 

covariance structure associated with the power function 

[34f] for unequally spaced data, Cov(ei, ej) = σ2ρdij = σ2ρ|ti

–tj|

, 

provides a direct generalization of the continuous autoregressive AR(x) structure for equally spaced data (Pinheiro 

and Bates 2000). It has been used in a number of recent 

studies (e.g., Nord-Larsen 2006, Trincado and Burkhart 

2006, Fortin et al. 2007).

The potential problem of heteroskedasticity associated 

with the height-site index model [30] is relatively easier to 

tackle. First, White’s test and the modified Breusch-Pagan 

test were conducted to examine the significance of the 

heteroskedasticity (results showed that it was significant at 

α = 0.05 level). Then, following the procedures described in 

Huang (1997), several assumptions about the nature of the 

heteroskedasticity were proposed and evaluated. The variance of errors was assumed to be (1) a linear or nonlinear 

function of the predicted height, (2) a linear or nonlinear 

function of the independent variables, or (3) a factor of age 

or predicted height (with weight = agek

 or weight = pred.

htk, where k is a constant, e.g., k = -2, -3/2, -1, -1/2, 1/2, 

1, 3/2, 2). Plots of studentized residuals against predicted 

height resulted from various fittings based on different 

weighting factors were examined. It was found that the 

weighting factor w = 1/pred.ht produced the most satisfactory studentized residual plot, an outcome that coincides 

Table 9. Nonlinear mixed model estimation of equation [30] with generalized error structures.

Covariance Estimate Std. Err. t-value Pr > |t| Lower Upper AIC BIC

Spherical b1 = 12.6712 0.1487 85.22 <.0001 12.3795 12.9629 6180.8 6203.7

Exponential b2 = -5.9990 0.1124 -53.37 <.0001 -6.2195 -5.7785

Matérn b = -0.1749 0.01811 -9.66 <.0001 -0.2105 -0.1394

 b4 = 0.1176 0.03002 3.92 <.0001 0.05872 0.1765

Gaussian b1 = 12.6667 0.1494 84.79 <.0001 12.3736 12.9597 6182.8 6210.2

 b2 = -5.9941 0.1138 -52.69 <.0001 -6.2173 -5.7709

 b = -0.1749 0.01815 -9.64 <.0001 -0.2105 -0.1393

 b4 = 0.1171 0.03015 3.88 0.0001 0.05793 0.1762

Linear b1 = 12.6656 0.1495 84.71 <.0001 12.3723 12.9589 6182.7 6210.2

Linear Log b2 = -5.9929 0.1140 -52.57 <.0001 -6.2165 -5.7693

 b = -0.1749 0.01816 -9.63 <.0001 -0.2105 -0.1393

 b4 = 0.1169 0.03017 3.88 0.0001 0.05774 0.1761

Power b1 = 12.6705 0.1488 85.14 <.0001 12.3785 12.9624 6182.8 6210.3

 b2 = -5.9983 0.1127 -53.22 <.0001 -6.2194 -5.7772

 b = -0.1749 0.01811 -9.66 <.0001 -0.2104 -0.1394

 b4 = 0.1175 0.03004 3.91 <.0001 0.05859 0.1765

 

Note: AIC and BIC are Akaike’s information criterion and Schwarz Bayesian information criterion computed by [20] and [21], respectively. A weighting factor 

of one over predicted height (wi = 1/pred.H2) was used.

Table 10. Ordinary nonlinear least squares fit statistics for equation [30]

Parameter Estimate Std. Err. t-value Pr > |t| RMSE R2

 R2

adj.

 b1 13.0021 0.2679 48.54 <.0001 1.3800 0.9851 0.9851

 b2 -6.48752 0.2176 -29.82 <.0001 

 b -0.16233 0.0225 -7.22 <.0001 

 b4 0.163142 0.0367 4.45 <.0001 

Note: RMSE, R2 and R2

adj. are defined in [3], [1] and [2], respectively. Data structure III defined in Fig. 4 was used.
FOREST GROWTH AND TIMBER QUALITY

247

with the results of the site index model derived from stem 

analysis data (Huang 1997). 

Final fittings of [30] under seven covariance structures 

with heteroskedastic errors were implemented using the 

nonlinear mixed model macro NLINMIX (Littell et al. 

2006). Results based on the RMD data structure III (which 

is the most efficient, see Wang et al. 2004), are shown in 

Table 9. The covariance structures that produced identical 

estimates (e.g., spherical, exponential, and Matérn) were 

grouped together. For comparison, results (see Table 10) 

from an ordinary nonlinear least squares fit of [30] without 

accounting for the correlated and heteroskedastic errors were 

also obtained, based on the same RMD data structure III.

The estimated coefficients shown in Tables 9 and 10 

were used to make forward and backward projections. 

Summary statistics about the prediction errors, along 

with the calculated GOFI values and other statistics, are 

presented in Table 11.

The results shown in Table 11 indicate that the GOFI 

values from different fits with and without accounting for 

the heteroskedastic and correlated errors are marginally 

different. The practical benefits of using more complex 

estimation techniques are subtle. The important fact to 

recognize is that they all are lower than the reported, inflated R2

 value shown in Table 10. One might argue that 

this R2 value was specific and unique to the particular data 

and model used, and as such, it could still be interpreted 

meaningfully with regard to the particular data and model. 

Such an argument would have been valid for TMD analysis. 

However, for RMD analysis, the argument becomes less 

relevant, as the R2

 value loses its quality of reflecting and 

representing the goodness-of-fit of a model.

When an R2 value is reported, it is generally assumed that 

when the model is used in application, a similar accuracy 

as represented by the R2 can be expected. Unfortunately, 

this was not the case when a fitted model such as [30] 

was used in a way consistent with how it should be used 

in application. The traditional R2 for difference equations 

expressed by y2 = f (y1,x1,x2) tends to always overstate the 

performance accuracy. Readers should not be deceived by 

the reported high R2 for such equations, as it is very easy 

to obtain. On the other hand, the R2 for increment functions expressed by yinc = f(x1) routinely understates the 

performance accuracy. A low R2 for an increment function 

can in fact mean a good fit to the data and very reasonable 

performance accuracy in application when predictions are 

made. This was clearly evident for the basal area increment 

function [32] (see Tables 7 and 8). In both cases the GOFI 

provided a consistent, reliable, and intuitive alternative to 

the traditional R2

. The GOFI can also be used to reliably 

determine the best parameter to constrain when deriving 

difference equations.

In the cases where the heteroskedastic and correlated 

errors were accounted for by the nonlinear mixed model 

methods (as in Table 9), a reported AIC value such as 6182.8 

for the power function had little relationship to how good 

or bad the height-site index model [30] may be. The only 

conclusion one can arrive at from Table 9 is that, since a 

smaller AIC (or BIC) indicates a better fit, the spherical 

covariance structure is the most reasonable one for model 

Table 11. Summary statistics from forward and backward projections on the top height-age data

 Prediction error

Covariance Type n RMSEP R2

F or R2L GOFI

structure Mean SD Min. Max.

Spherical Forward 1496 0.1684 1.500 -5.122 6.607 1.5092 0.8712 0.9066

 Backward 1496 -0.0115 1.013 -4.504 6.257 1.0126 0.9420

Gaussian Forward 1496 0.1662 1.500 -5.126 6.604 1.5091 0.8712 0.9066

 Backward 1496 -0.01064 1.013 -4.503 6.259 1.0126 0.9420

Linear Forward 1496 0.1668 1.500 -5.126 6.605 1.5091 0.8712 0.9066

 Backward 1496 -0.01079 1.013 -4.503 6.259 1.0126 0.9420

Power Forward 1496 0.1686 1.500 -5.122 6.607 1.5092 0.8712 0.9066

 Backward 1496 -0.01156 1.013 -4.504 6.257 1.0126 0.9420

Ordinary Forward 1496 0.4990 1.489 -4.624 7.053 1.5699 0.8606 0.9007

NLS Backward 1496 -0.13190 1.015 -4.705 5.967 1.0235 0.9408

 

Note: RMSEP is root mean square error of prediction computed by [26], R2

F and R2L are computed by [22], GOFI is the goodness-of-fit index computed by 

[25], and SD is standard deviation. The original data are shown in Fig. 3
FOREST GROWTH AND TIMBER QUALITY

248

[30]. However, if the model itself was a poor one, a smaller 

AIC may mean little, and we still do not have any direct, 

intuitive idea about how much total variation may have 

been explained by the model and how good the model 

fits the data. 

With GOFI, model developers and users attain a direct, 

intuitive, consistent and reliable measure for gauging the 

goodness-of-fit of a model in a more realistic manner (as 

compared to reporting the traditional R2

). In the case of 

model [30], for instance, one can infer that approximately 90 

percent of the total variation in predictions was accounted 

for by the fitted model. Together with plots of residual 

or studentized residual trajectories, this provides model 

developers and model users with an immediate indication 

about the goodness-of-fit of the model. The GOFI can also 

provide a common basis for comparing competing models 

developed using different methodologies, and reported 

with different R2

 values each claimed to be “higher” than 

the others.

CONCLUSIONS

The conventional goodness-of-fit measure represented 

by R2 was found to be inadequate in reflecting the goodness-of-fit of a model when repeatedly measured data were 

involved. The R2 usually overstates the performance accuracy of difference equations and understates the accuracy 

of increment functions. It is often futile and misleading to 

report the R2 for repeatedly measured data when difference 

equations or increment functions are used. The reported 

R2 does not relate to the performance accuracy of a model 

in application. A modified goodness-of-fit measure, termed 

GOFI (goodness-of-fit index), was proposed. It was shown 

that the GOFI provided a direct, intuitive, consistent and 

reliable goodness-of-fit measure for models developed from 

different methodologies, data structures, and estimation 

techniques. It is recommended that the GOFI should be 

reported as a standard goodness-of-fit measure and used 

as a common basis for determining the goodness-of-fit of a 

model, and for comparing alternative models when repeatedly measured data are used in model development. 

ACKNOWLEDGMENTS

I would like to thank Dr. Y. Yang, Mr. D. Morgan, Dr. S.X. 

Meng, Dr. D.W. Dempster, and several companies and 

consultants for reviewing or supporting this project in a 

variety of ways. 

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Simulation Model of a Hill Dipterocarp Forest 

Five Years After Harvesting at Angsi Forest Reserve, 

Negeri Sembilan, Malaysia

 Kamziah Abd Kudus and Frisco Nobilly

Kamziah Abd Kudus (kamziah@putra.upm.edu.my) and Frisco Nobilly are at the Faculty of Forestry, Universiti Putra Malaysia, 43400 UPM Serdang, 

Selangor, Malaysia.

ABSTRACT

DIPTEROCARP FORESTS ARE OF VITAL 

economic and ecological importance in Peninsular 

Malaysia. Despite their economic importance, 

dipterocarp forests have been greatly depleted. The Selective 

Forest Management System (SMS) was introduced in 1978 

and is the current forest-management system practiced. The 

SMS is designed to optimize the management objectives of 

economical and efficient forest harvesting, forest sustainability, and minimum forest development costs. 

This study was conducted at Compartment 19, Angsi 

Forest Reserve, Negeri Sembilan, Malaysia. Compartment 

19 is comprised of 399 hectares of forest from the total 

concession, which covers 12,741 hectares. The Forestry 

Department of Peninsular Malaysia Four established four 

growth and yield study plots in 1999, before logging activities started. The area is classified as a hill dipterocarp 

forest. At the end of 1999, the forest was logged under 

SMS with cutting limits of at least 65 cm diameter at 

breast height (dbh) for Neobalanocarpus species (chengal), 

at least 55 cm dbh for dipterocarp species, and at least 

45cm dbh for non-dipterocarp species. Since the study 

plot establishment, data were collected in 2000, followed 

by annual visits from 2002 to 2005. Stem identity class, 

wood-quality group, species name, status of tree, dbh, and 

commercial bole height were recorded during each visit. 

Stems per hectare, basal area per hectare, gross volume, 

and net volume were calculated. A forest simulation model 

based on an empirical approach was developed for growth 

and yield prediction of the regenerated forest. Ideal cutting 

cycle will be recommended from this study.

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 250.
FOREST GROWTH AND TIMBER QUALITY

251

Timber Properties of Norway Spruce 

Predicted by RetroSTEM

Anu Kantola, Sanna Härkönen, Harri Mäkinen, Annikki Mäkelä

Anu Kantola (anu.kantola@metla.fi) and Harri Mäkinen are researchers at the Vantaa Research Centre, Finnish Forest Research Institute, PO Box 18, 

01301 Vantaa, Finland; Sanna Härkönen is at the Faculty of Forestry, P.O. Box 111, FIN-80101 University of Joensuu, Finland; Annikki Mäkelä is 

professor of silviculture (forest production), Department of Forest Ecology, University of Helsinki, PO Box 27, 00014 Helsinki, Finland.

ABSTRACT

I

N THE SAWMILL INDUSTRY, STEM FORM, 

branchiness, and wood density are the most important 

factors of Norway spruce (Picea abies [L.] Karst.) defining the yield and quality of sawn products. This study tests 

the prediction power of the Retrospective Stand and Tree 

Evaluation Model (RetroSTEM) in terms of timber properties 

(stem taper, branchiness, wood density) of Norway spruce. 

RetroSTEM reconstructs a measured tree from its current 

age and size (h, DBH, crown length), using the pipe model 

and regular crown allometry as constraints, and generates 

3-dimensional objects with growth rings and knots. The 

model employs empirical sub-models for branch population dynamics and wood properties, the latter embedded 

by the visual tool TreeViz. 

Material and Methods

RetroSTEM was tested against the stems from an independent data set, collected in Southern Finland in 1988–90 as 

a sub-sample of the temporary plots of the 8th National 

Forest Inventory in Finland (NFI8). The data consists of 

31 trees from 9 stands, with varying fertility. The age of 

the sample trees varied between 46 and 134, DBH was 

between 11 and 45 cm, and crown ratio was between 0.6 

percent and 1 percent. In the felled trees, maximum branch 

diameters per measured even meter over stem, stem taper, 

and sample disks were measured. Wood properties and 

the accuracy of stem properties were measured in terms 

of estimation bias.

Results

The simulated taper curves, branch sizes, and wood 

densities were compared with those of the sample trees. 

The simulated taper curves showed some overestimation 

of stem diameter (cm) in the mid part of the stem, with 

-0.4 cm bias. The measured and predicted diameters of 

branches (cm) increased at the top third of the crown, then 

stabilized and finally decreased below the living crown, 

showing a bias of 0.3 cm. If the crown ratio of a measured 

tree was high (greater than 90 percent), the largest measured branches occurred at the bottom of the stem, and the 

model prediction at this area was underestimated. TreeViz 

estimation for wood basic density (kg m-3) over stem was 

generally similar in simulated and measured trees as well 

as in measured stem disks.

Conclusions and Further Analysis

The RetroSTEM model provides a feasible tool for describing 

stem characteristics in Norway spruce. However, a further 

evaluation of the crown development in trees of large crown 

ratio and growing space is required. Our future work will 

focus on finding out reasons for the observed bias in the 

distribution of branch and stem diameter over the stem. 

Similarly, the model will be tested against stand-level quality distributions of timber.

KEYWORDS: Branchiness, Norway spruce, process-based 

models, stem taper, wood density

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 251.
FOREST GROWTH AND TIMBER QUALITY

252

Modeling the Distribution of Foliar Biomass for 

Pinus contorta var. latifolia in Interior British Columbia

Roberta Parish, James W. Goudie, Lin Ju

Roberta Parish (roberta.parish@gov.bc.ca), James W. Goudie, and Lin Ju are research scientists in the Research Branch of the BC Ministry of 

Forests, PO Box 9536, Victoria, BC V8N 2S8, Canada.

ABSTRACT

LODGEPOLE PINE (PINUS CONTORTA var. 

Latifolia) is a widespread and valuable commercial 

species in interior British Columbia. The amount 

and vertical distribution of foliar biomass in the crown of 

lodgepole are important characteristics of stand structure, 

which influence many aspects of ecosystem function. We 

developed a mixed effects model based on 60 trees in 

13 stands to predict foliar biomass from branch size and 

location within the crown. We then fitted a mixed-model 

β-function to the internodal foliar biomass data. Positions 

in the crown and growth increment were important predictors of internodal biomass accumulation.

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 252.
FOREST GROWTH AND TIMBER QUALITY

253

Working Plan: A Tool for Forest and Wildlife 

 with Special Attention to Impacts on Habitat and 

Timber Quality in the Teak Forests of Central India

Ajit K. Shrivastava

Ajit K. Shrivastava (ajitshri@gmail.com) is Chief Conservator of Forest Research and Extension, Indian Forest Service, Jabalpur, 

Madhya Pradesh 480 661, India

ABSTRACT

S

INCE THE MID-19TH CENTURY IN INDIA, 

scientific management of forests has been practiced 

in accordance with the prescriptions of a Working 

Plan. The objective of forest management has always been 

sustained yield of timber with less emphasis on wildlife 

habitat. India prepares, and periodically revises, Working 

Plans for management of established forest divisions. About 

72 percent of all India’s forests are managed according 

to the prescription of Working Plans. Nearby 10 million 

hectares of production forests are managed under such 

plans. Several different silviculture systems are followed 

as models in India including a selection system, a shelterwood system, clear cutting, and artificial regeneration with 

valuable species. There are various tropical timber species 

in production and trade such as, Shorea robusta, Eucalyptus, 

Acacia spp., Dalbergia sisoo, and Tectona grandis (teak). Teak 

is a high quality, high-priced timber largely available in 

central India. Timber harvesting cannot be done without 

following the Working Plan prescription, which is prepared 

for a large area of forest.

Forest management under a Working Plan has great 

impact on wildlife habitat, a fact that has been overlooked 

for some time. In Madhya Pradesh, the central state in India, 

11 percent of forested area is protected as wildlife habitat 

under such designations as National Parks and Wildlife 

Sanctuaries. The remaining 89 percent of forested area is 

managed according to Working Plan prescriptions.

Currently, what is needed most for the efficient, systematic, and scientific management of India’s forests is 

the ability to estimate the quality of timber available from 

a teak tree of any given diameter and height class within 

permissible limits. This is not part of the Working Plans 

at present. 

It is common to see a wide variation between estimated 

quality of timber in a stand and actual quality assessed 

after felling. Local volume tables are easily applicable to 

those areas of restricted range of locality, but only with the 

assumption that trees of the same diameter have the same 

height. These tables are based mainly on one parameter, 

i.e., diameter at breast height. The crown size and shape 

is not taken into account. Timber quality is not taken into 

consideration under current forest management plans, even 

though it can be a strong indicator for forest protection and, 

in turn, better conservation efforts for wildlife habitat.

 This paper deals with the effect various silviculture 

systems and treatments have on timber quality and methods of estimating timber volume in teak trees. It assesses 

and evaluates the relationship between timber quality and 

wildlife habitat in the rich teak areas of Mandla, Seoni, and 

Chhindwada in Central India.

Out of the 23.38 percent of forested area in Central 

India, 4.75 percent is under a Protected Area Network and 

is not available for utilization. In such a scenario, there is 

a tremendous amount of pressure on the managed forests. 

If the Protected Areas and wildlife are to survive for long, 

the future of the production forests needs to be secured. It 

needs to be borne in mind that the majority of the wildlife in 

this country occupies the managed forests. Thus, the manThis paper was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

pp. 253–262.
FOREST GROWTH AND TIMBER QUALITY

254

aged forests need more attention so that they can perform 

a production function as well as ensure a better future for 

the Protected Areas by conserving biodiversity.

INTRODUCTION

A Working Plan for a forest area is a management plan, 

which coordinates all planning activities for development 

and growth of the forests. It is an instrument to effectively 

monitor and evaluate forestry operations. The primary objective of the plan is to maximize timber production from the 

forests. It aims at evolving a felling program so that forests 

are harvested within a definite period. Recently, in order 

to achieve sustained timber yields a regeneration strategy 

was included in the Working Plan. The timber projection 

was first done through thumb rules for partial enumeration 

of trees. Recently, detailed inventories of forest resources 

have come into practice. Forest management objectives 

are currently changing. Emphasis is shifting from a purely 

timber-oriented management approach while social and 

conservation issues are gaining more importance. The 

National Working Plan Code (Government of India 2004) 

emphasizes the necessity of writing Working Plans that are 

consistent across the nation with specific prescriptions for 

wildlife management along with forest management. The 

main objectives of the Working Plan Code are: 

• increasing the productivity of forests to meet essential 

national needs 

• preserving the national forests with an emphasis on 

biological diversity and natural resources

• meeting the natural resource requirements of rural and 

tribal populations with a need for fuel-wood, fodder, 

minor forest produce, and small timber.

OBJECTIVES

Forest management for timber production, as wildlife habitat, and for other resources is most efficiently accomplished 

by considering all objectives simultaneously and by: 

• Evaluating the present systems of forest management, 

i.e., silviculture systems 

• Improving co-ordination between managed forests and 

protected areas

• Delineating wildlife habitat and corridors in protected 

areas

• Retaining existing old growth forests

• Retaining snags and hollow trees

• Maintaining grassy openings

• Providing for weed control

• Balancing the removal of exotic shrubs (such as lantana) with the restoration of native shrubs

STUDY AREA

The Satpuda Maikal landscape is about 50,000 km2 in 

area, covering 178 forest ranges and 3,150 beats with an 

abundance of tiger and ungulate. Tigers are present in 290 

beats with 78 having a high, 57 having a medium, and 155 

beats having a low abundance of tiger sign. Ungulates are 

prey to tiger in 1,678 beats (Mathur 2002). The study area 

is a heterogeneous mosaic of large contiguous forest that 

includes the protected areas Kanha and Pench National 

Park along with a few sanctuaries where resource use has 

been stopped or controlled for some time. These areas are 

managed for wildlife and wild plants. The remaining second-category forests are managed for goods and services. 

These are regulated through Working Plan prescriptions. 

The forests are among the most economically valuable of 

the dry deciduous types. Tectona grandis (teak), also known 

as “king of timbers” is the principal timber species. The 

area is home to one of the contiguous populations of critically endangered tiger—estimated as 48 individuals living 

in managed forests. Other endangered species found here 

include mammals, birds, reptiles, amphibians, fishes and 

insects. Tree species found in the area are: Tectona grandis, 

Terminalia Tomentosa (Saja), Adina cordifolia (Haldu), Anogeissus latifalia (Dhawda), Diospyros melanoxylcm (Tendu), 

Ougeinia oogeirsis (Tinsa), Pterocarpus marsupium (Bija). 

Details of the forest area in the three districts considered 

here are shown in Table 1.

Table 1. The total areas and forest cover in the three districts of the study area, in km2.

District Total Area 

Area in Forest Cover Types Percent of 

Very Dense Moderately Dense Open Forest Total Forest Forest Cover 

Mandla 5,800 443 1,0 0 2,72 47.10

Seoni 8,758 2 1,412 1,7 ,0 34.69

Chhindwara 11,815 20 2, 1, 4,409 7.2

Total 2,7 885 5,089 4,205 10,17
FOREST GROWTH AND TIMBER QUALITY

255

SYSTEM OF FOREST MANAGEMENT

IN THE STUDY AREA

The seven Working Plans for the three forest divisions in 

the study area are for East Mandla, West Mandla, North 

Seoni, South Seoni, East Chhindwara, West Chhindwara, 

and South Chhindwara. The different silvicultural systems 

in use here are modified versions of European systems and 

are described below:

Selection System (SCI): 

Involves the removal of mature and over-mature trees singularly over a large area of forested land, on a periodic basis, 

and without creating gaps. This system is mainly used for 

managing teak crop. Trees that are dead, dying, discarded, 

defective, of undesirable species, and of exploitable diameter 

are removed. This is the most flexible system used, and is 

practiced under all the plans. A total of 410,580 hectares 

are managed under the SCI system in the study area. 

Improvement Working Circle (IFS):

This system is used for management of young and middleaged crops, which are mainly pole crop. These areas do not 

produce good quality timber. A total of 54,586 hectares is 

managed under the IFS system in the study area. 

Rehabilitation of Degraded Forest (RDF): 

This management system is practiced in the degraded forest 

areas with very sparse density. These areas contain good 

rootstock and are supplemented by artificial planting. A 

total of 224,961 hectares is managed under the RDF system 

in the study area. 

Modified Clearcut System (Plantation 

Establishment):

This management system is practiced in the areas managed by the forest corporation in Madhya Pradesh. Under 

this system areas of even-aged mature crop are felled. An 

average of 2,100 hectares in two divisions in Seoni and 

Mandla districts are partially clearcut each year for plantation. In each clearcut hectare, 70–80 young to middle-aged 

trees are left with a green belt of 10 m separating adjacent 

20–hectare clearcuts. 

The total area managed under each of these systems 

per year for the three districts and their subdivisions is 

shown in Table 2.

PRINCIPLES OF YIELD REGULATION

IN THE CURRENT WORKING PLANS

Yield regulation is considered an important aspect of 

forest management; and influences forest management 

practices. Productivity of Indian forests is on the decline, 

due to immense biotic pressure. Hence, conservation of 

existing dense forest and restoration of degraded forest is 

of great significance. It is a fact that the primacy of timber 

production over other management objectives has come to 

an end and conservation of forest ecosystems, including 

wildlife, have taken precedence over other objectives. As 

a result, yield regulation is losing its previous importance 

and relevance. In dense forests, suitable methods of yield 

regulation need to be developed while maintaining the 

principles of sustainable forest management. Yield is regulated based on volume and/or increment of growing stock. 

The concept of a “normal forest” is a dream in the mind of 

forest managers. The time has come to give importance to 

Table 2. Annual areas allotted to different forest management systems within the three districts and their subdivisions, 

in hectares.

Management 

System

Mandla Seoni Chhindwara Total for

10 years

Area allotted 

each year East West North South East West South

SCI 37,473 64,606 44,799 80,246 2,2 7,2 74,892 410,580 41,058 

IFS - 24,258 19,885 10,443 - - - 54,586 5,459 

RDF 2,77 26,525 30,744 22,444 65,989 2,1 1,7 224,961 22,496 

Plantation - - ,0 2,17 - ,7 12,248 1,72 ,17 

Total 64,240 115,389 104,058 115,311 95,315 120,527 107,019 721,859 72,186 
FOREST GROWTH AND TIMBER QUALITY

256

the quality instead of the quantity of timber. 

Yield Tables:

• Yield tables are a standard of reference available for 

growth of teak in even-aged plantations

• A rotation of maximum continuous net income is 

considered the most economically rewarding rotation 

on which to grow teak plantations on government 

plantations 

• Yield tables are based on number of trees per unit area 

and average diameter for each quality class (Sharma 

1998)

Local Volume Tables:

These are compiled from the measurements of trees growing 

in a restricted geographical area or locality, based on one 

independent variable, i.e., diameter at breast height (dbh), 

in an area of or more or less uniform crop or site quality. 

(Tiwari 1996)

These are applicable to such restricted areas as coupe/

compartment or to a felling series in a small area, with the 

assumption that trees of the same diameter will have the 

same height and will hold good.

CALCULATION OF YIELD

(SHRIVASTAVA 2006)

1. Von Mantle’s formula:

I = 2 GS/R, where

I = increment, in m3/year

GS= growing stock volume, in m3, 

R= rotation age, in years.

It gives an unrealistic forecast of yield.

2. Brandis’s method: Based on data generated from strip 

enumeration and stump analysis of teak forests. Yield is 

calculated based on average number of trees reaching exploitable size annually plus a fraction of surplus trees in a 

diameter class above the exploitable class or size. 

3. Smethie’s Safeguarding Formula: Yield calculation is 

done on the basis of volume.

Because it is based on the principles of sustained yield, 

Smethie’s method is the most widely used for calculation 

of yield in selection forests in India. 

X = f/t (II - Z% II)

X: No. of trees selected for felling. 

f : Felling cycle in years. 

t: Time taken by class II trees to pass into class I 

Table 3. Estimated yield and actual teak yield in the South Seoni Forest Division for the year 2006.

Division Range Coupe

Trees 

harvested 

(no.)

Estimated Yield Actual Yield

Timber

(m3

)

Poles

(no.)

Fuelwood 

Stacks (no.)

Timber

(m3)

Poles

(no.)

Fuelwood 

Stacks (no.)

South

Seoni

West 

Khawasa

III Bawanthari 40,855 77.70 685 7, 209.943 1,71 2,1 

III Khawasa 8,502 124.020 264 42 85.903 355 27 

III Kohka 4,080 22.705 12 71 28.149 1,22 1

III Kothar 23,835 24.685 20 1,334 31.653 1, 470 

Total 77,272 549.200 1,357 9,788 355.648 16,681 3,215 

Rukhar III Banjari 1,1 230.353 1 17 17. 335 104 

III Karhaiya 1,2 0.70 22 10 528.374 364 487 

III Karmajhira 5,086 72.555 224 1,954 49.469 2,1 270 

III Khapa 1 57.306 52 2 60.356  42 

III Nayegaon ,072 349.555 1 0 27.002 71 200 

III Richhi ,1 405.210 324 , 2. 4,240 459 

III Rukhar 1,642 175.000 17 579 1.20 1,00 12 

Total 21,683 1,670.949 1,477 6,798 1,542.883 9,807 1,724 

West 

Khawasa

IV Bawanthari 27,0 835.085 13,653 77 512.037 12,702 2,70 

IV Khawasa 2 45.800  1 16.053 24 474 

IV Kohka ,12 160.950 904 112 12.2 1,021 450 

IV Kothar 3,957 1.00 1,22 112 74.904 1,7 257 

Total 38,146 1,132.865 15,842 1,313 732.322 15,414 3,551 
FOREST GROWTH AND TIMBER QUALITY

257

category. 

Z : Percentage of class II trees that do not pass into 

class I stage in years on account of mortality or removal 

in thinning etc. 

The estimate for teak timber production is done with 

the help of form factors and yield tables. For teak, current 

form factors give an estimate higher than the actual yield 

due to variation in size and shape of trees and a long gap in 

the revision of the volume tables and form factors. Table 3 

shows differences in estimated yield and actual production 

for several forest areas.

TEAK AREA IN MANDLA, 

CHHINDWARA AND SEONI

Teak, a species of the Tectona genus, is the most important 

tree of India producing timber of worldwide reputation. 

It is a large deciduous tree that is quite variable in size 

depending on climatic conditions and soils. In favorable 

conditions, it has a long, straight, clean bole carrying its 

girth well up the stem. With advanced age, the stem becomes more fluted and buttressed towards the base. The 

sapwood of teak is white to pale yellowish-brown, whereas 

the heartwood is dark golden, turning brown, dark brown, 

and finally darker brown with age. It is a coarse and uneven textured timber without taste. However, it possesses 

a characteristic smell similar to the smell of old leather. In 

the study area, teak trees grow up to 30-meters in height, 

are fluted near the base, have pale brown bark, and gray 

leaves which are opposite, broadly elliptical, rough, 20–50 

cm long, and 15–20 cm wide. The history of the planting 

of teak dates back in central India to 1891. Regular teak 

plantation started in 1928. Teak is found mostly on hilly 

or undulating country up to 900 m elevation with good 

sub-soil drainage. In recent years, some areas have been 

converted to high-tech plantations as high input areas and 

artificial irrigation are provided.

Teak is one of the most widely distributed and one of 

the most economically important timber species in India. 

Owing to the much higher prices of teak timber, it has been 

planted more extensively than any other single species.

Species associated with teak in central India:

• Terminalia tomentosa (Saja)

• Bombax ceiba (Semal)

• Cassia fistula (Amaltas)

• Madhuca indica (Mahua)

• Lagerstroemia parviflora (Lendia)

• Buchanania lanzan (Achar)

Salient features of teak wood:

• Principal timber tree in peninsular (central) India 

• Major timber source for 

buildings, bridges, furniture, 

cabinetwork, wheel spokes, 

and general carpentry

• Termite-, fungus-, and 

weather-resistant while also 

lightweight, strong, attractive, workable, and seasons 

without splitting, cracking, 

warping, or significantly 

altering shape

• Coarse textured, oily, and 

scented when fresh

• Suitable for carpentry, it 

can have a smooth finish and 

fair polish

• Light to moderately heavy, 

moderately hard, somewhat 

brittle, straight or wavy 

grained, coarse and uneven 

textured

• Growth rings are distinct

Table 4. Teak forest area compared to total forest area in the three study divisions.

Divisions Total Forest Area (ha) Teak Area (ha) % of Teak

Mandla East 118,240.880 19,715.150 

West 141,990.000 61,149.180 

Total 260,230.880 80,864.330 31.07%

Seoni North 122,1.20 31,868.570 

South 119,535.799 53,991.390 

Total 241,855.619 85,859.960 35.50%

Chhindwara East 128,713.532 41,444.451 

West 1,111.770 47,493.370 

South ,12.71 77,432.961 

Total 395,954.021 166,370.782 42.02%

Grand Total 898,040.520 333,095.072 37.09%

Table 5. Annual teak production in the study divisions.

Divisions

Teak

Timber (m3) Fuelwood Stacks (count)

Mandla 9,472 3,482

Seoni 10,185 4,162

Chhindwara 12,0 ,21

Total 32,265 1,0
FOREST GROWTH AND TIMBER QUALITY

258

TIMBER QUALITY IN CENTRAL INDIA

To assess timber-quality of teak, logs were obtained from 

working circles and plantations from the Mandla, Seoni 

and Chhindwara districts. For each sample, a teak log 

with a diameter of 60 cm and length of 120-cm was cut 

and converted into a standard size for use in determining 

the compressive strength of the wood, both parallel and 

perpendicular to the grain. 

A total of 38 samples were tested by the timber mechanics 

division of the Forest Research Institute (FRI), Dehradun. 

The test samples are obtained from logs according to the 

standard schedule given in IS:2455-1974. All the samples 

are surfaced to a smooth, finished standard cross-section of 

5 x 5 cm. The mechanical property of compressive strength 

is measured using the procedure described in IS:1708-1969. 

We are awaiting test results from FRI, Dehradun.

The average value of standard teak from Malabar, Nilambur, and Coimbatore in south India are taken as standards 

and used for the purpose of comparing the strength of teak 

under testing.

The number of samples taken was not a sufficient representation of the vast area and locality factor. However, the 

samples clearly show that the compressive strength of teak 

grown here is greater than that found in other plantations 

under other silvicultural treatments. This gives a clear idea 

about variation in compressive strength. In other studies 

of teak wood at the Forest Research Institute, it was found 

that there is variation in wood properties from the pith to 

periphery of the log and that the central portion is often 

weaker, especially in fast-grown woods probably due to the 

presence of a greater proportion of juvenile wood. (Rajpoot 

et al 1983, 1990; Shakula et al 1998, 1991). There may 

be significant variation in wood properties among individual teak trees. This is often a reflection of the different 

silvicultural systems used to grow teak. Previous studies 

have shown that with increases in growth rate, there is an 

increase in wood quality following an initial decrease in 

wood quality. 

This was a unique study with a small number of samples. 

The results need to be further investigated through more 

detailed studies in order to establish a strong relation 

between silvicultural systems, timber quality, and habitat 

health. The results do indicate a direct relationship with 

high timber quality and high standards of forest management that, in turn, benefit wildlife and the conservation 

of wildlife habitat. 

THE EFFECT OF FOREST

MANAGEMENT SYSTEMS UNDER

THE WORKING PLAN ON WILDLIFE

Timber harvesting and road building affect wildlife habitat 

more than any other forest management activity. Every year 

in the Mandla, Seoni, and Chhindwara districts of Central 

Table 6. Notable wildlife occurring within the study area.

Name Species

Mandla Seoni Chhindwara

Total Kanha 

NP (PA)

Pench 

NP (PA) Total Grand 

Total East West North South East West South

Tiger Panthera tigris  2 21 2   5 48 11 - 11 17 

Panther Panthera pordus 7  15 12  1  7 112  151 21 

Deer 

(Cheetal) Cervus axis 774 550 70 1,2 1,053  654 ,027 21,484 14,850 36,334 42,361 

Sambhar Cervus unicolor 43 101 480 17 125 205 12 1,439 3,472 2,835 ,07 7,746 

Barking 

Deer

Muntiacus 

muntjak 405 72 1,00 1,410 2 1,140 77 5,938 1,17 1 1, 7,334 

Blue bull Boselaphus 

traqocamelus - - 1 12 153 211 142 651 104 2,143 2,247 2,

Sloth Bear Melursus ursinus - 5 1 70 95 0 53 2 158 2 184 483 

Wild Boar Sus scrofa 2,7 ,2 5,094 4,300 1,0 ,10 1,0 25,579 8,941 ,2 12,20 7,0 

Indian 

Bison Bos gaurus  - - - - - -  1, 735 2,374 2,407 

The three study districts ( Mandla, Seoni and Chhindwara) are managed forest dominated by teak. Kanha and Pench national parks are protected areas in the 

vicinity of the study area.
FOREST GROWTH AND TIMBER QUALITY

259

India, 72,186 hectares are utilized for timber production 

and management. It recent years, forest managers been 

responsible specifically for the enhancement of wildlife 

habitat in managed forests. It is necessary to develop an 

understanding of wildlife habitat in managed forests, to 

predict the impact of forest management practices on 

wildlife, and to take an interest in how the system can be 

applied for the benefit of wildlife. Current scenarios suggest 

that it is of utmost importance to protect wildlife habitats 

in managed forests.

Opinions regarding wildlife management:

• Good forestry leads to good wildlife management

• Forest managers must learn sound wildlife management principles 

• It is necessary to have proper communication and cooperation when implementing a Working Plan

• There should be an interdisciplinary attitude towards 

the management of natural resources

• In current budgets, insufficient funds are allotted for 

the implementation of wildlife habitat management

• Few studies focused on wildlife management are available

• Loss of species-diversity and extinction of species 

should be of great concern to every forester under 

every system

There is an urgent need for the study of:

• Research on the ecological effects of logging operations

• Distributional ranges, lifecourse, habitat association, 

and diet of wildlife in the Satpuda Maital area of 

central India

• Temporary rises in wildlife population densities immediately after logging

• Reduction of wildlife food supply

• Overpopulation and degraded habitat

• Loss of key microhabitats and changes in microclimate 

and microhabitat

• Juvenile mortality due to increased predation and loss 

of forage 

• Non-resident or invasive-species spreading and increasing competition for reduced resources such as food, 

shelter, and mating grounds

• Increased morbidity due to new diseases and declining 

population health

• Increased hunting pressure

• Mortality and injury to wildlife directly caused by tree 

felling, skidding, and other timber extraction activities

Logging and Wildlife:

• There is an urgent need for research regarding the biological and ecological requirements wildlife.

• Attributes of each species and species group need to 

be investigated from a natural history perspective to 

understand what makes them particularly vulnerable 

to the impacts associated with timber harvesting.

• Existing forest management guidelines need to be 

refined with the goal of enhancing wildlife habitat in 

teak forests.

• While there is much literature available on vertebrates 

in general, more studies need to be done specifically 

on amphibians and fishes, as well as on insects and 

other invertebrates. These species are more sensitive 

to the effects that logging operations play a role in 

healthy ecosystems.

• Although still in the initial phases, flagship species 

studies represent a good starting point for improving 

wildlife habitat in managed forests. 

• Special attention should be paid to the birds most affected by logging such as trogons, woodpeckers, babblers, barbets and flycatchers (the paradise flycatcher 

is the state bird).

Importance of the Working Plan in wildlife management:

• Even-aged crops should be grown under current silvicultural systems with the goal of creating edges and 

edge effects.

• Annual cuts should be no more than 40 hectares in 

size.

• Permanent gaps in the forest are to be avoided.

• During harvesting, intense human disturbance should 

not be permitted in two neighboring drainage areas 

simultaneously. 

• No felling is to be allowed in riparian zones. 

• Felling in areas used by wildlife for mating, nesting, 

calving, and fawning during the season of intensive 

use is to be avoided. Felling of trees and other vegetation bearing nests or surrounding nets, caves, and 

shelters should be prohibited.

• Removal of evergreen trees and shrubs, which remain 

green during summers, should be prohibited.

• Wood should be extracted from the forest in the shortest amount of time possible. 

• Monkeys inhabit large trees and in the process cause a 

large amount of leaf fall which is, in turn, utilized by 

deer. These large trees should not be felled.

• Trees and shrubs bearing edible fruits used by wildlife 
FOREST GROWTH AND TIMBER QUALITY

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should not be felled.

• Bamboo is a very important fodder species and should 

be conserved. Sowing and planting of fruit and fodder 

species like Peepal, Gular, Anjan, Bamboo, and Ber 

should be encouraged.

Some factors that are detrimental to wildlife conservation: 

• Presence of roads—including type of roads, location, 

and degree of use 

• Harvesting operations:

- should be limited to smallest possible area. 

- should be done in shortest possible time. 

- should have a no-activity zone adjoining cuts.

- should be limited to cutting in only one drainage 

area per watershed at a time

• Fire—necessary measures should be taken to prevent 

forest fires

RECOMMENDATIONS

1. Close co-operation is required between forest and wildlife 

managers in the area of study. Forest management is 

the process of manipulating the forest environment to 

produce a mix of products and desired states.

2. It is necessary to practice forest management in such 

a way as to maintain forest tree species as well as soil, 

air, and water resources while providing a habitat for 

wildlife and aquatic life.

3. Wildlife habitat is a by-product of timber management. 

Instead of managing for larger yield in timber management, the focus should shift to managing for high 

quality timber.

4. Care must be taken in selecting and using forest management systems that will promote forest sustainability 

and species-diversity.

5. In a selection system, generally 50 percent of the trees of 

an available selection diameter are removed. The forests 

managed under this system have a high degree of vertical 

diversity. They are irregular in height, with great variation in tree size. There is competition between unequal 

age-classes of trees, with the larger trees suppressing 

the smaller trees.

6. In a selection system, initially there is an observed increase 

in diversity of plants and animals due to a temporary 

increase in shade-intolerant plants and forage plants in 

small openings. 

7. A strong process should be developed to consider the 

impact of timber management on wildlife.

8. More should be done to research and understand wildlife 

requirements in particular areas.

9. Important wildlife areas in managed forest need to be 

given consideration.

10. A system should be developed to predict the affect 

of timber management on wildlife habitat, with the 

recognition that timber management inevitably affects 

wildlife habitat.

11. Alternatives should be investigated before actual cutting 

operations begin.

12. Any change in forest structure or composition will favor 

some wildlife species while adversely affect others. 

13. Such changes can affect the number and type of wildlife 

species and their use of habitat. 

14. The selection system tends, over time, to reduce the 

diversity of plants and animals in the forest. In this 

system there is a gradual reduction of shade-intolerant 

trees and understory plants. This system tends to produce large blocks of continuous forest cover dominated 

by relatively mature trees. Such forests lack the array of 

distinct successional stages that ensure diversity and a 

myriad of habitat niches. 

SUMMARY

The teak forests in Central India are under increasing pressure to prove their economic viability and to offer land use 

options. Optimizing the impact of logging is an essential 

task in the improvement of teak forest management—both 

for timber production and for wildlife conservation. The 

empirical formulas used in the past need to be improved 

to provide realistic estimates of timber production to aid 

in planning production activities. The current Working 

Plans should focus on the quality of timber products and 

modify management prescriptions to protect rich timber 

areas, which will result in an improved wildlife habitat. 

Better harvesting practices with better reinforcement of 

the prescriptions should be the norm when implementing 

Working Plans. 

Long-term sustainability, conservation, restoration of 

biodiversity, and forest productivity will be achieved in 

concert only by ensuring that objectives are consistent 

between forest management and wildlife management. 

There is a need to co-ordinate data, and analyze the technical aspects of resource planning across forest management 

and wildlife management. It will be necessary to redefine or 
FOREST GROWTH AND TIMBER QUALITY

21

modify procedures for thinning and other forest harvesting 

operations to meet broader biodiversity goals.

LITERATURE CITED

Bali, B.I.; Singh, K.R. 1983. A note on the physical and 

mechanical properties of Tectona grandis (Teak) from 

Gorakhpur division, Uttar Pradesh. Timber Mechanics 

Branch, Forest Research Institute and Colleges, 

Dehradun. pp. 25-33.

Dudley, N.; Jeanrenaud, J.P.; Sullivan, F. 1996. Bad 

Harvest?: The Timber Trade and the Degradation of 

the World’s Forests. Earthscan Publications, Ltd., 

London, UK. 224 p.

Forest Survey of India in Collaboration with Food and 

Agriculture Organization (FAO). 2004. Pilot Study 

on Assessment of Status of Sustainability of Forest 

Resources in India. Forest Survey of India, Ministry 

of Environment and Forests, Government of India, 

Dehradun. pp 82-83.

Gopal, R.; Qureshi Q.; Jhala Y.V. 2005. Focus on Tiger 

Conservation. The Indian Forester 131 (10): 1393-

1398.

Government of India. 2004. National Working Plan 

Code. Government of India, Ministry of Environment 

& Forests, New Delhi. 52 p.

Grieser Johns, A. 1997. Timber Production and 

Biodiversity Conservation in Tropical Rain Forests. 

Cambridge Studies in Applied Ecology and 

Resource Management. Cambridge University Press, 

Cambridge, U.K. 248 p.

Kadambi, K. 1993. Silviculture and Management of 

Teak. Natraj Publishers, Dehradun. 137p.

Kimmins, H. 1997. Balancing Act: Environmental Issues 

in Forestry. University of British Columbia Press, 

Vancouver, B.C., Canada. 305 p.

Laurie, M.; Ram, B. 1939. Yield and Stand Tables for 

Teak (Tectona Grandis, Linn. F.) Plantations in India 

and Burma. Indian Forest Record Silviculture 4-A (1). 

Forest Research Institute, Dehra Dun, India.

Mathur, P.K.; Lehmkuhl, J.F.; Sawarkar, V.B. 2002. 

Management of Forests in India for Biological 

Diversity and Forests Productivity, A New 

Perspective—Volume I: Concepts, Approaches 

and Project Overview. WII-USDA Forest Service 

Collaborative Project Report, Wildlife Institute of 

India, Dehra Dun. 70p.

Ministry of Environment and Forests. 2003. State of 

Forest Report. Forest Survey of India, Ministry of 

Environment and Forests, Dehradun. pp. 72-75.

Negi, Y.S.; Jain, J.D. 2001. Physical and mechanical 

properties of plantation grown timbers tested at forest 

research institute. Forest Products Division, Forest 

Research Institute, Dehradun. TDA 47 (3–4): 27–30.

Panayotou, T.; Ashton, P.S. 1992. Not By Timber 

Alone: Economics and Ecology for Sustaining Tropical 

Forests. Island Press, Washington, D.C. 302 p.

Principal Chief Conservator of Forests MP. 2004.

Statistics of Forest wealth in Madhya Pradesh. Madhya 

Pradesh Forest Department. Pp. 25-33.

Rajput, S.S.; Shukla, N.K.; Lal, M. 1991. Some studies 

on the variation of strength properties of Tectona 

grandis from Mizoram. Forest Research Institute 

and Colleges, Dehra Dun. Journal of the Timber 

Development Association 37(2): 33-38.

Sanyal, S.N.; Bali, B.I.; Singh, K.T.; Sharma, B.D. 1987.

A note on the physical and mechanical properties of 

plantation grown Tectona grandis (Teak) from Tanjavur 

district, Tamilnadu. Timber Mechanics Branch, Forest 

Research Institute and Colleges, Dehradun. Journal of 

the Timber Development Association 33(4) 15-22.

Sanyal, S.N.; Saxena, R.D. 1980. Physical and 

Mechanical Properties of Some Maharashtra Timbers. 

N.B.O. Journal 25(2): 1-5.

Sawarkar, V.B. 1995. A Manual for Planning Wildlife 

Management in Protected Areas and Managed Forests. 

Wildlife Institute of India, Dehradun. Director WII 

Dehradun India. pp.48-73.

Shrivastava, A.K. 2006. Working Plan of West Mandla 

Division. Conservator of Forest Working Plan Jabalpur 

MP. pp. 24-148.

Shukla, N.K.; Lal, M. 2004. Physical and mechanical 

properties of plantation grown Tectona Grandis (Teak) 
FOREST GROWTH AND TIMBER QUALITY

22

from Mizoram. Forest Products Division, Forest 

Research Institute, Dehradun. Journal of the Timber 

Development Assocation XL (3): 38-48.

Thomas, J.W. (ed.). 1979. Wildlife Habitats in 

Managed Forests the Blue Mountains of Oregon and 

Washington. Agriculture Handbook No. 553. USDA, 

Forest Service. 512 p.

Tiwari, K.P.; Pandey, R.L. 1996. Local Volume Tables 

for Teak, Sal and Other Species for Central Circle, 

Jabalpur (M.P.). Mensuration Branch. State Forest 

Research Institute, Jabalpur. 

Tiwari, K.P.; Sharma, M.C.; Pandey, R.L. 1998.

Yield and Stand Tables of Teak in Madhya Pradesh. 

Mensuration Branch, State Forest Research Institute, 

Jabalpur. Director State Forest Research Institute 

Jabalpur MP India. pp. 3-11.
FOREST GROWTH AND TIMBER QUALITY

2

Impact of Land Use and Climatic Changes on 

Pulpwood and Carbon Sequestration Sustainability 

at the Landscape Level

Paula Soares, José Loff, Paulo Borges, Ana Rodrigues, Susete Marques, 

Luís Fontes, José Guilherme Borges, Margarida Tomé

Paula Soares (paulasoares@isa.utl.pt), José Loff, Paulo Borges, Ana Rodrigues, Susete Marques, Luís Fontes, José Guilherme Borges and 

Margarida Tomé are at the Universidade Técnica de Lisboa, Instituto Superior Agronomia, Centro de Estudos Florestais, Tapada Ajuda, 1349-017 

Lisboa, Portugal.

ABSTRACT

THE EXPANSION OF TASMANIAN BLUEGUM 

(Eucalyptus globulus Labill.) in Portugal occurred 

in the second half of the twentieth century as a 

consequence of the implementation and development of 

the pulpwood industry in the country. Nowadays, and according to provisory data presented by the national forest 

inventory in July 2006, eucalyptus plantations represent 

22.9 percent of the national forest area, corresponding to 

743, 000 hectares. These plantations produce mainly raw 

material for the pulp industry. The importance assumed by 

the pulp companies in the national economy justifies the 

development of specific applications to simulate the impact 

of land use and climatic changes on the sustainability of 

pulpwood production and carbon sequestration at the landscape level. To achieve this goal, it is essential to develop 

computer-based decision support systems (DSS) adapted 

to the actual reality. To model the pulpwood production 

and carbon sequestration it was necessary (1) to select 

and parameterize a process-based model, (2) to improve a 

growth and yield empirical model specifically developed 

for Portuguese eucalyptus plantations, (3) to develop 

methodologies to link both types of models resulting in a 

hybrid model, and (4) to implement the models at landscape 

level. In general, process-based models are based on the 

knowledge of the physiological processes in the interfaces 

of plant-soil and carbon-nutrients-water. In this work the 

3PG model was selected. This is a stand-level model that 

uses monthly time steps. It requires as inputs initial stand 

data (stem number, stem, foliage, and roots biomasses) and 

soil and weather data. A detailed analysis pointed out some 

weak points: (1) the stand density module is not appropriate for the stand density x rotation ages presently used in 

Portugal, and (2) output is not detailed enough for most 

management decisions. The Globulus model is a stand-level 

growth and yield empirical model. In this work, Globulus 

version 3.0 was used. In order to obtain models that (1) 

can work using regular forest inventory data as input, (2) 

are able to give good predictions under climate change, (3) 

provide information on the effect of different silvicultural 

alternatives, not only on tree growth but also on other forest products and services, (4) provide reliable information 

on stand structure and wood quality, and (5) account for 

the possible occurrence of several damages, a methodology 

was developed to link growth and yield models with process-based models. The result is the GLOB-3PG model that 

uses stand variables as linking functions. All the referred 

models were implemented in a DSS that encompasses the 

simulation of stand-specific management alternatives and 

the evaluation of total wood production and the respective 

net present value for each combination of prescriptions. The 

developed software, GLOBfLOR, is used to show results 

obtained in a case-study area predominantly occupied by 

eucalyptus plantations in central Portugal.

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station.

p. 263.
FOREST GROWTH AND TIMBER QUALITY

264

Estimating Future Carbon Sequestration at the 

National/Regional Level Using National Forest Inventory Data: The Impact of Data Aggregation

Margarida Tomé, Susana Barreiro, Joana A. Paulo, Paula Soares, José Tomé

Margarida Tomé (magatome@isa.utl.pt), Susana Barreiro, Joana A. Paulo, Paula Soares, and José Tomé are at the Universidade Técnica de Lisboa, 

Instituto Superior de Agronomia, Centro de Estudos Florestais, Tapada da Ajuda, 1349-017 Lisboa, Portugal.

ABSTRACT

THE EVALUATION OF THE CONTRIBUTION OF 

forests to climate change mitigation through the 

carbon cycle is of utmost importance due to the 

Kyoto Protocol to the United Nations Framework Convention on Climate Change. The National Forest Inventory 

(NFI) provides information on the current status of the 

forest but there is a need to predict future carbon sequestration under alternative forest management and land-usechange scenarios. Problems such as data aggregation and 

choice of appropriate growth models, among others, are 

important points to be considered for the development of 

national/regional simulators of carbon sequestration. The 

objective of the present presentation is to compare the use 

of alternative simulators, based in different levels of data 

aggregation as input, for the case of the Portuguese forests: 

from intensive plantations (Eucalyptus globulus) to private 

poorly-managed pine plantations (Pinus pinaster) to slowgrowing sparse oak stands (Quercus suber and Quercus ilex

ssp. rotundifolia). There is a lot of variation concerning the 

available data and the existing growth models for each of 

the species and forest types. Therefore, different methodologies had to be adapted for each case, which makes this case 

study an interesting one. Finally, preliminary estimations 

for the period of 1995–2005, obtained with each of the 

proposed methodologies, will be presented.

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 264.
FOREST GROWTH AND TIMBER QUALITY

265

Modeling Branch Growth and Mortality to 

Silvicultural Treatments in Coastal Douglas-fir 

Plantations: Implications for Predicting Tree Growth

Aaron Weiskittel, Doug Maguire, Robert A. Monserud

Aaron R. Weiskittel (aaron.weiskittel@umit.maine.edu) is a forest modeling assistant professor, University of Maine, Orono, ME 04471, USA; Douglas 

A. Maguire is a professor of silviculture, Oregon State University, College of Forestry, Corvallis, OR 97331, USA; Robert A. Monserud (retired) was a 

research forester and team leader, USDA Forest Service PNW Research Station, Portland, OR 97208, USA.

ABSTRACT

S

TATIC MODELS OF INDIVIDUAL TREE CROWN 

attributes such as height to crown base and maximum 

branch diameter profile have been developed for 

several commercially important species. Dynamic models 

of individual branch growth and mortality have received 

less attention, but have generally been developed retrospectively by dissecting felled trees; however, this approach is 

limited by the lack of historic stand data and the difficulty 

in determining the exact timing of branch death. This study 

monitored the development of individual branches on 103 

stems located on a variety of silvicultural trials in the Pacific 

Northwest, USA. The results indicated that branch growth 

and mortality were significantly influenced by precommerical thinning, commercial thinning, fertilization, vegetation 

management, and a foliar disease known as Swiss needle 

cast [Phaeocryptopus gaeumannii (T. Rohde) Petr.]. Models 

developed across these datasets accounted for treatment 

effects through variables such as tree diameter growth and 

the size and location of the crown. Insertion of the branch 

growth and mortality equations into an individual-tree 

modeling framework, significantly improved short-term 

predictions of crown recession on an independent series of 

silvicultural trials, which increased mean accuracy of diameter growth prediction (reduction in mean bias). However, 

the static height to crown base equation resulted in a lower 

mean square error for the growth predictions. Individual 

branches were highly responsive to changes in stand and 

site conditions imposed by silvicultural treatments, and 

therefore represent an important mechanism explaining 

tree and stand growth responses.

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 265.
FOREST GROWTH AND TIMBER QUALITY

2

Urban Tree Crown Condition: 

Training and Evaluation Tools 

Matthew F. Winn, Neil A. Clark, Philip A. Araman, Sang-Mook Lee

Matthew F. Winn is a forestry technician, Neil A. Clark was a research forester, Philip A. Araman (presenter; paraman@fs.fed.us) is a research team 

leader, and Sang-Mook Lee is a postdoctoral fellow at the Southern Research Station, USDA Forest Service, 1650 Ramble Road, Blacksburg, VA 24060, 

USA.

ABSTRACT

The USDA Forest Service Southern Research Station in 

Blacksburg, Virginia is in the process of constructing a website that will provide web-based training 

to FIA crews, urban foresters, university scientists, urban 

and citizen foresters in the area of urban tree monitoring. 

Initially, the website will focus primarily on tree crown 

characteristics but will eventually contain information on 

site and bole characteristics as well. In addition to the training module, the website will also include a testing module 

and crown analysis software. The testing module will be 

used to examine the repeatability of observer estimates of 

crown measurements using controlled tree models. The 

crown analysis software will allow users to assess the health 

of urban trees using digital photographs.

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 266.
FOREST GROWTH AND TIMBER QUALITY

27

Digital Picture Tree Crown Evaluation Software 

Matthew F. Winn, Sang-Mook Lee, Philip A. Araman

Matthew F. Winn is a forestry technician, Sang-Mook Lee is a postdoctoral fellow, and Philip A. Araman (presenter; paraman@fs.fed.us) is a research 

team leader at the Southern Research Station, USDA Forest Service, 1650 Ramble Road, Blacksburg, VA 24060, USA.

ABSTRACT

The USDA Forest Service Southern Research Station 

in Blacksburg, Virginia is developing stand-alone 

software to analyze digital pictures of tree crowns, 

partial tree crowns, or groupings of tree crowns for foliage 

transparency. One program called URBANCROWNS can 

be used to evaluate density and transparency of complete 

or partial trees in an urban setting from digital pictures. 

We are also developing software to determine leaf area 

estimates. The second program called FORESTCROWNS 

can be used to evaluate digital pictures of crowns from 

below in forested settings. Single trees, multiple intersecting 

trees, or canopy areas pictures can be analyzed to determine 

transparency. Examples will be presented. The software 

packages are not complete but they are usable and will be 

made available for trial use.

This abstract was published in: Dykstra, D.P.; Monserud, R.A., tech. eds. 2009. Forest growth and timber quality: Crown 

models and simulation methods for sustainable forest management. Proceedings of an international conference. Gen. Tech. 

Rep. PNW-GTR-791. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

p. 267.

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