Visualization of Heterogeneous Forest Structures Following 

Treatment in the Southern Rocky Mountains

Wade T. Tinkham, Yvette Dickinson, Chad M. Hoffman, Mike A. Battaglia, Seth Ex, and Jeffrey Underhill

United States Department of Agriculture

Forest Service Rocky Mountain Research Station General Technical Report RMRS-GTR-365 September 2017

Pre-treatment

Forest Structure

Post-treatment

Forest Structure

Comparison of

Treatment Effects
Tinkham, Wade T.; Dickinson, Yvette; Hoffman, Chad M.; Battaglia, Mike A.; Ex, Seth; Underhill, Jeffrey. 2017. 

Visualization of heterogeneous forest structures following treatment in the southern Rocky Mountains. 

Gen. Tech. Rep. RMRS-GTR-365. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, Rocky 

Mountain Research Station. 72 p.

Abstract

Manipulation of forest spatial patterns has become a common objective in restoration prescriptions throughout 

the central and southern Rocky Mountain dry-mixed conifer forest systems. Pre-Euro-American settlement 

forest reconstructions indicate that frequent-fire regimes developed forests with complex mosaics of individual 

trees, tree clumps of varying size, and openings. While it is broadly agreed upon that restoration to these forest 

conditions will improve ecosystem function, development of treatment prescriptions that can achieve desired 

spatial patterns on the landscape have been met with different levels of success. The central purpose of this 

tool is to link quantitative and visual descriptions of immediate post-treatment spatial forest structure to help 

communicate desired spatial structures at the stand level in dry forest types of the Rocky Mountains. This 

tool was developed by simulating four different treatments across four stands with varying productivity that 

had been identified as candidates for ecological restoration. The simulated treatments included a thin from 

below, random tree selection, moderate clumping, and high clumping prescriptions. Following the simulated 

treatments, we produced a visual representation of the spatial pattern of the residual trees and openings; 

calculated traditional stand-scale metrics; and described the fine-scale forest structure including individual 

trees, clumps of trees, and openings. This tool is intended to help communicate the outcomes of complex 

silvicultural treatments to resource managers, contractors, specialists, and others when attempting to meet 

spatially explicit treatment objectives.

Keywords: spatial heterogeneity, forest restoration, spatial statistics, spatial structure, point pattern analysis, 

structural complexity, variable retention harvesting

All Rocky Mountain Research Station publications are published by U.S. Forest Service employees and are in the 

public domain and available at no cost. Even though U.S. Forest Service publications are not copyrighted, they 

are formatted according to U.S. Department of Agriculture standards and research findings and formatting cannot 

be altered in reprints. Altering content or formatting, including the cover and title page, is strictly prohibited.
Authors

Wade T. Tinkham is an Assistant Professor of Forest Biometry, Chad M. Hoffman is an Associate Professor of 

Wildland Fire Science, and Seth Ex is an Assistant Professor of Silviculture and Vegetation Management in the 

Department of Forest and Rangeland Stewardship, College of Natural Resources, Colorado State University, 

Fort Collins, Colorado.

Yvette Dickinson is an Assistant Professor of Silviculture in the School of Forest Resources and 

Environmental Science, Michigan Technological University, Houghton, Michigan.

Mike A. Battaglia is a Research Forester at the USDA Forest Service, Rocky Mountain Research Station, 

Forest and Woodland Ecosystems, Fort Collins, Colorado.

Jeffrey Underhill is a Forester and Regional Silviculturist for the USDA Forest Service, Region 2, Lakewood, 

Colorado.

Acknowledgments

The authors would like to thank the tireless field crews that worked to collect the datasets used in this work and 

Dr. Theresa Jain, Dr. Derek Churchill, Mr. Matthew Tuten, Dr. Alison Hill, and an anonymous reviewer for their 

insightful and helpful review during the production of this document. This work would not have been possible 

without the funding support provided by the Joint Fire Science Program projects 13-1-04-53 and 14-1-01-18 

and the Rocky Mountain Research Station agreement number 13-JV-11221633-058.
Contents

Introduction......................................................................................................................................1

How to Use This Tool ......................................................................................................................2

Treatment Simulations....................................................................................................................8

Summary and Visualization..........................................................................................................10

Pre-treatment: Low-Moderate Density Single Story Stand...............................................14

Thin From Below to 40 ft2 ac-1 of Basal Area.....................................................................16

Random Thinning to 40 ft2 ac-1 of Basal Area....................................................................18

Moderately Clumped Thinning to 40 ft2 ac-1 of Basal Area ................................................20

Highly Clumped Thinning to 40 ft2 ac-1 of Basal Area ........................................................22

Summary: Low-Moderate Density Single Story Stand .......................................................24

Pre-treatment: Moderate Density Multi-Storied Stand ......................................................28

Thin from Below to 40 ft2 ac-1 of Basal Area ......................................................................30

Random Thinning to 40 ft2 ac-1 of Basal Area....................................................................32

Moderately Clumped Thinning to 40 ft2 ac-1 of Basal Area ................................................34

Highly Clumped Thinning to 40 ft2 ac-1 of Basal Area ........................................................36

Summary: Moderate Density Multi-Storied Stand ..............................................................38

Pre-treatment: Moderate-High Density Multi-Storied Stand .............................................42

Thin From Below to 40 ft2 ac-1 of Basal Area.....................................................................44

Random Thinning to 40 ft2 ac-1 of Basal Area....................................................................46

Moderately Clumped Thinning to 40 ft2 ac-1 of Basal Area ................................................48

Highly Clumped Thinning to 40 ft2 ac-1 of Basal Area ........................................................50

Summary: Moderate-High Density Multi-Storied Stand......................................................52

Pre-treatment: High Density Multi-Storied Stand ..............................................................56

Thin From Below to 40 ft2 ac-1 of Basal Area.....................................................................58

Random Thinning to 40 ft2 ac-1 of Basal Area....................................................................60

Moderately Clumped Thinning to 40 ft2 ac-1 of Basal Area ................................................62

Highly Clumped Thinning to 40 ft2 ac-1 of Basal Area ........................................................64

Summary: High Density Multi-Storied Stand ......................................................................66

References .....................................................................................................................................71
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 1

Introduction

Increased wildfire hazard has prompted a 

targeted effort to reduce fuels in dry-mixed 

conifer forests of the western United States. 

To meet fuel hazard reduction objectives, 

treatments have traditionally emphasized the 

removal of smaller trees (i.e., thin from below) 

within a fixed spacing interval (Schwilk et al. 

2009). Such treatments have been shown to 

meet objectives targeting reduced fuel loading 

and stand density and controlling inter-tree 

competition (Graham et al. 1999; Larson and 

Churchill 2012). However, a side effect of these 

treatments is that resulting forest structure rarely 

mimics the historical spatial heterogeneity of dry 

conifer forests of the western United States. Dry 

conifer forests are characterized as a complex 

matrix of tree clumps interspersed with gaps and 

isolated individuals that are thought to promote 

resilience to disturbance (Allen et al. 2002; 

Fulé 2008; Gunderson 2000; Holling 1973; 

Larson and Churchill 2012). More recently, 

management efforts have emphasized variable 

retention harvesting (VRH) prescriptions to 

promote spatial heterogeneity while meeting 

ecological and fuel hazard reduction objectives 

(fig. 1; Churchill et al. 2013a; Fulé et al. 2001; 

Graham and Jain 2005; Keith 2003; Noss et al. 

2006; Reynolds et al. 2013; Youtz et al. 2008). 

Variable retention harvesting treatments differ 

from traditional fuel hazard reduction treatments 

by explicitly incorporating spatial objectives that 

promote spatial heterogeneity rather than creating simple forest structures consisting of evenly 

spaced trees (Evans et al. 2011; Gustafsson et 

al. 2012; Johnson et al. 2007). This document 

provides visual and quantitative data to assist in 

communicating the outcomes of both VRH and 

traditional treatments on spatial and non-spatial 

forest metrics to resource managers, contractors, 

specialists, and others.

Variable retention harvesting treatments 

may take the role of a regeneration treatment 

Figure 1—Examples of post-treatment stands after (a) 

spacing-based and (b) spatially explicit prescriptions 

(photos: Mike Battaglia, U.S. Forest Service).

Visualization of Heterogeneous Forest 

Structures Following Treatment in the 

Southern Rocky Mountains

Wade T. Tinkham, Yvette Dickinson, Chad M. Hoffman, Mike A. Battaglia, 

Seth Ex, and Jeffrey Underhill
2 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

within a multi-aged silvicultural system, or an 

intermediate tending treatment in an even-aged 

silvicultural system depending on the forest 

management objectives, site conditions, and 

level of growing space released for new regenerating trees following harvest (Mitchell and 

Beese 2002). Several VRH treatment implementation strategies have been developed, including 

the individuals, clumps, and openings (ICO) 

method (Churchill et al. 2013b), the ecosystem 

resiliency framework presented by Reynolds et 

al. (2013), the goshawk habitat management implementation strategy described by Youtz et al. 

(2008), or the free selection approach described 

by Graham et al. (2007). Despite a number of 

VRH implementation strategies, the widespread 

use of these treatments remains limited due to a 

legacy of past timber management and the use 

of non-spatial fuels planning and management 

tools (Graham and Jain 2005). In addition, 

the objectives commonly associated with spatially explicit treatments have met resistance 

because they are counter to many traditional 

forest management objectives such as timber 

production and maximizing growth and yield. 

These less production-focused objectives run 

contrary to current contract design approaches 

like designation by diameter, which has slowed 

their incorporation. Despite these challenges, 

VRH treatments provide considerable flexibility 

in meeting both spatial and non-spatial forest 

objectives and are likely to increase in use in the 

coming decades.

This document is intended to provide a visual 

tool that can assist managers in communicating 

the effects of various treatments on spatial and 

non-spatial stand structure in dry forest types of 

the Rocky Mountains. This tool is meant for use 

after stand management objectives have been 

defined to discuss and communicate how different treatments can be used to achieve fine-scale 

spatial objectives. To assist in visualizing the 

effect of treatments on stand spatial structure, we 

simulated four treatments representing two space 

or size-based and two VRH implementation 

strategies across four sites that are characteristic 

of dry conifer forests of the southern Rocky 

Mountains (fig. 2). These sites were selected because they had been identified as being in need 

of ecological restoration. The simulated treatments were identified as the most commonly 

used silvicultural practices within the southern 

Rocky Mountains (Underhill et al. 2014). The 

sites cover a range of productivity and complexity in ponderosa pine (Pinus ponderosa) forests 

and woodlands at site indexes of 35, 55, 65, 

and 90 ft at base age 100 (low-moderate density 

single story, moderate density multi-storied, 

moderate-high density multi-storied stand, and 

high density multi-storied stand in order of site 

index). Within each site, ponderosa pine is the 

dominant overstory species, with Douglas-fir 

(Pseudotsuga menziesii) and quaking aspen 

(Populus tremuloides) representing minor components of stand structure. A summary of each 

stand’s structure is presented using common 

forest metrics (e.g., basal area, trees per acre, 

and so on), clump size distributions, opening 

area, and spatial statistics (Plotkin et al. 2002; 

Sánchez-Meador et al. 2011; Schneider et al. 

2015). In addition, visualizations are provided to 

assist users in seeing what these spatial and nonspatial metrics look like.

How to Use This Tool

The central purpose of this tool is to link 

quantitative and visual descriptions of immediate post-treatment spatial forest structure 

following space/diameter-based and VRH 

treatments. The visual and quantitative data in 

this tool can be utilized to (1) fine-tune silvicultural targets related to spatial forest structure, 

(2) provide insight on the effect that different 

silvicultural treatments may have on spatial 

forest structure, and (3) facilitate communication among land managers, stakeholders, and 

contractors in regard to desired spatial structures 

at the stand level.

The first step in developing any silvicultural 

treatment for a site is to develop site-specific 

management objectives. Once management 

objectives are well defined, this tool might be 

used to assist with interpreting how the spatial 

patterns created by different treatments could 

achieve management objectives. This could 

include promoting fuel discontinuity that might 

be better evaluated by the size of clumps and 

openings rather than through traditional canopy 

fuel estimates. To fully understand the differences 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

3

Figure 2—Distribution of 11.8 

million acres of ponderosa 

pine woodlands and drymixed conifer forest and 

woodlands within the Rocky 

Mountains of Colorado and 

New Mexico, USA. Inset 

photos depict pre-treatment 

forest structure of example 

stands, in order of structural 

complexity: (a) Heil Valley 

Ranch, (b) Red Feather 

Lakes, (c) Long John, 

and (d) Unc Mesa. In the 

visualization, these stands 

are referred to as LowModerate Density SingleStory Stand, Moderate 

Density Multi-Storied Stand, 

Moderate-High Density 

Multi-Storied Stand, and 

High Density Multi-Storied 

Stand, respectively (photos: 

Emma Vakili, USDA Forest 

Service).

a

b

c

d
4 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

in treatment outcomes, it will be necessary to 

look at the range of forest structures produced by 

treatments.

Although this tool focuses on describing 

stands through the fine-scale structures they are 

composed of, these structures exist across a range 

of spatial scales that influence forest composition, 

structure, function, and processes in spatially and 

temporally dynamic ways. Some of these specific 

structures provide vital functions for habitat and 

other management concerns (Youtz et al. 2008). 

At the fine scale (0.25 acres or 0.1 ha), the key 

compositional and structural elements of interest typically include the distribution, size, and 

characteristics of openings, isolated trees, and 

clumps of trees (see box 1; Larson and Churchill 

2012). Stands are the next scale of interest and 

are commonly considered to be smaller than subwatersheds and larger than the largest tree clumps 

and openings desired for the system (Urban et al. 

1987). Stands can be described as the aggregate 

of fine-scale units (clumps of trees, individual 

trees, and openings). Descriptions at the stand 

scale can include both averaged values across the 

stand (i.e., trees per acre and basal area per acre) 

as well as the variability among the finer scale 

patches, openings, and individual trees that are 

present within the stand (i.e., percentage of isolated trees or mean opening size). Finally, the largest 

scale of interest is referred to as a landscape 

(2,500 and 250,000 acres), where the variability 

is defined by the stands that are encompassed by 

any given landscape (see box 2).

Box 1: Fine-Scale Forest 

Structures 

Fine-scale forest structure describes patterns of 

individual trees at a grain size of approximately 

0.25 acres (0.1 ha), which is slightly larger than 

typical forest inventory plots. These features 

are the fundamental building blocks used 

within this guide to describe stand scale forest 

patterns. Larson and Churchill (2012) provide 

five common features that can be used to 

describe fine-scale structural patterns: openings, 

isolated trees, regeneration patches, clumps 

of overstory trees, and clumps of mixed-sized 

trees (figs. 3 and 4). Understanding the defining 

features of fine-scale structures, and specifically 

clumps, is important for successfully marking 

any spatially explicit treatment. Long-term 

upkeep of these features is likely to require 

repeated disturbances through fire, insects, or 

silvicultural intervention; otherwise, ingrowth will 

slowly increase the density and basal area of these 

stands. 

Following the protocols described by Churchill 

et al. (2013a,b), openings include any space 

within the stand that is greater than 19.7 ft (6 

m) from a tree (fig. 4a). Openings include small 

interstitial spaces among trees, as well as larger 

spaces within the stand that receive direct sunlight 

throughout the day. Throughout this tool, we 

characterize clumps of trees as those that have 

a neighbor within 19.7 ft (6 m), but they can 

be further described using a variety of metrics. 

In many cases the size and shape of clumps 

is described by the area, number of trees per 

clump, or the edge to perimeter ratio. However, 

as suggested by Larson and Churchill (2012), the 

vertical structure of a clump of trees can be broadly 

classified as patches of regeneration or smaller 

trees, patches of overstory trees, or patches of 

mixed sized trees (figs. 4c-e respectively). In 

addition, each of the three types of tree clumps 

(regeneration patch, overstory trees, and mixedsized) could be just a single species (pure) or 

a mixture of species. Altering the combination 

of fine-scale structures can serve to achieve 

a variety of different management objectives 

ranging from promoting understory biodiversity or 

improving wildlife habitat, to restoring ecological 

process like frequent-fire regimes. By varying 

the apportionment of different clump sizes and 

types in different stands, these fine-scale features 

can contribute to creating landscape scale 

heterogeneity. 

Figure 3—Depiction of stand-scale forest pattern, with 

inset of fine-scale structures in a restored ponderosa 

pine forest.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 5

Figure 4—Examples of fine 

scale stand structure 

progressing (a-e) through 

(a) openings, (b) isolated 

trees, (c) regeneration 

clumps, (d) mature clumps, 

and (e) mixed clumps (photos: 

Mike Battaglia, U.S. Forest 

Service).
6 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Although restoration or fuel hazard reduction treatments often consider changes in forest 

structure across all of these scales, this tool 

focuses on describing stand-scale distributions 

of individual trees, tree clumps, and openings 

along with common forest metrics. Tree clumps 

are described across each of the simulated stands 

based on the density of trees in each clump, 

while openings are described in terms of their 

size as measured by the distance to the nearest 

individual tree. While other metrics can be used 

to describe fine-scale structures within clumps 

(i.e., multiage vs. single age clumps) and openings (i.e., shape or edge to area ratios), they are 

not included in this tool but could be important 

considerations depending on specific management objectives.

Some of the difficulties among forest managers in communicating desired heterogeneous 

structures stem from issues with grasping 

and describing structures across these scales. 

Although spatial patterns exist at local tree-totree scales, within stands, across landscapes, 

and regionally, it is important to remember that 

heterogeneity at one scale does not necessarily 

result in heterogeneity at larger scales (Hessberg 

et al. 2015). The ecological impact of forest 

structure is likely to vary across these scales, 

with the influence of heterogeneity at fine scales 

differing from those at coarse scales. Therefore, 

it might be important for forest managers to 

carefully consider the context of their forest, 

including management objectives, forest type, 

Box 2: Landscape-Scale 

Heterogeneity

While forest managers apply silvicultural 

treatments at stand scales, it is important to 

consider the impact of treatments on large 

landscape-scale phenomena. Heterogeneity at 

landscape-scales—defined here as areas between 

2,500 and 250,000 acres—describes the spatial 

patterns of the stands within the landscape. 

Landscape scale heterogeneity is influenced 

by a number of factors, including: variation 

in stand types, topography, site conditions, 

soil, and hydrology. Following Bettinger et al. 

(2009), we suggest defining stand types based 

on a combination of metrics, such as forest 

successional pathways and stages, species 

composition, or site index. From a forest planning 

perspective, these factors, along with others 

such as property ownership boundaries and preexisting roads, and infrastructure will constrain 

the ability for treatments to affect landscape-scale 

heterogeneity. Some common factors to consider 

when assessing landscape scale heterogeneity 

include the arrangement, distribution, and 

variability of stand types, sizes, and shapes along 

with the relative spatial relationship of different 

stands structures to each other. Understanding 

the diversity of stand types and their relationship 

to one another across a landscape will dictate the 

range of management alternatives and how they 

may be placed into the landscape. In landscapes 

with many similar stands in proximity, it may be 

necessary to think about staggering the timing of 

their treatment to prevent creating large blocks of 

homogeneous stand types. 

At the coarsest level of consideration, we 

suggest landscapes that only contain a few 

forest conditions (fig. 5a and c) might have a 

narrower range of possible future conditions than 

a landscape starting from a more diverse position 

(fig. 5b and d). For example, in a landscape 

with only a couple of starting forest conditions, 

the timing of treatments within adjacent stands 

of similar forest conditions will be an important 

component in future landscape heterogeneity. 

The next level of consideration when planning 

treatment placement within a broader landscape 

includes looking at the size and distribution 

of stand sizes across the landscape. Stands 

can be very uniform in their size across a 

landscape (fig. 5a and b) or could vary from large 

homogeneous blocks to small patches of unique 

structures (fig. 5c and d ). The way in which 

stand diversity and sizes vary and intermix must 

be considered when planning the sequence or 

timing of multiple treatments in order to keep from 

producing homogeneity at landscape scales when 

implementing multiple treatments in adjacent 

stands. Similarly, patch size has consequences 

for fragmentation if we attempt to over segment 

a landscape in the hope of creating diversity. 

Patch sizes should be considered in the context 

of reference landscape conditions or desired 

functions (Hessburg et al. 2015). It is important 

to note that landscape planning is a complex 

science and it is not our intention to provide a 

comprehensive framework to guide the landscape 

planning process, nor an exhaustive list of the 

facets that inform landscape-scale planning.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 7

Figure 5—Comparison of how stand type diversity (a 

and c are Low, and b and d are High) and stand size 

variability (a and b are Low, and c and d are High) 

influence the intermixing and number of forest types 

and successional stages on a landscape. Stand 

diversity is often controlled by abiotic environmental 

factors (e.g., climate gradients) and stand size is 

usually an artifact of past management decisions and 

disturbance patterns.
8 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

historical disturbance regime, topography, 

climate, and adjacent structures at each scale, 

before deciding on a desired forest structure for 

their stand.

Once desired fine- and stand-scale structures 

for a project have been identified, the stands 

visualized in this tool could be compared with 

specific project pre-treatment forest structures 

to determine which stands have the greatest 

similarities. As this tool is designed to examine 

spatial structure, it is important when comparing 

the example visualization to consider how the 

mean and distribution of tree sizes and densities, 

as well as current spatial pattern of the trees, 

compare to project specific structures.

After example stand(s) have been identified, 

this tool can be used to compare how treatment 

alternatives might affect the distributions of 

clump sizes and openings. It is unlikely that a 

single simulated post-treatment structure perfectly fits any given project’s specific objectives, 

making it likely that a composite of example 

treatments might be necessary. Furthermore, the 

visualizations within this tool might be a useful 

reference in management planning documents 

and/or help with communication if provided to 

prescription marking teams or contractors.

It is important to remember that the possible stand and landscape structures that can be 

created using silvicultural treatments are constrained by the forest structure currently present. 

Often it is necessary to implement a range of 

silvicultural treatments over a number of years 

to encourage both the regeneration of small trees 

and the growth of larger diameter trees within 

a stand. This consideration will be of particular 

importance when reentering a stand that had previously been treated in the past to create stands 

of evenly spaced or sized trees.

Additionally, in order to modify landscapescale forest structure, a number of treatments 

will probably be needed. This visual tool is a 

simple aid to help communicate desired (or undesired) forest structures and evaluate treatment 

alternatives. The consideration of project-specific context is always important when designing 

silvicultural treatments. Furthermore, this tool 

does not consider many of the commonly important considerations within the prescription 

marking process such as regional practices, like 

preferentially removing Douglas-fir and true 

fir species in favor of aspen, which are often 

implemented to modify species composition 

and diversity. The simulated treatments do not 

consider common tree selection criteria like 

species preference, crown position, crown 

ratio, tree health, or legacy trees, all of which 

will influence the ability of a stand to include 

the full range of fine-scale forest structures. To 

that end, the example simulations represent an 

idealized post-treatment stand that was thinned 

without regard for common considerations like 

pathogens or crown ratio. In the face of real 

world prescription marking constraints, achieving the fine-scale structures seen in the examples 

may require multiple stand entries to increase 

the range of fine-scale structures possible over 

many decades. Finally, our simulated treatments 

only consider the immediate impacts on forest 

structure. During the selection of alternative 

treatments, it can be important to consider any 

potential long-term impacts of modifying forest 

structure on ecosystem processes, the ability to 

maintain these desired structures through additional treatment or prescribed burning, and any 

possible ecological or financial trade-offs.

Treatment Simulations

To derive the initial conditions in the visualization tool, we used stem-mapped data from 

Ziegler et al. (2017). Within each stand, the location, diameter at breast height (d.b.h.), height, 

and canopy base height was recorded for each 

tree (fig. 6). This inventory approach allowed for 

the simulation and evaluation of spatial silvicultural treatments on both spatial and non-spatial 

forest metrics.

The stands each received four simulated treatments resulting in a residual basal area of 40 ft2 

acre-1 including a thinning from below, random 

tree selection, and two spatially VRH protocols 

at a high and moderate clumping intensity 

(Churchill et al. 2013b). These treatments were 

chosen because they are the most commonly 

utilized silvicultural practices within the southern Rocky Mountains (Underhill et al. 2014). 

Simulations do not consider common individual 

tree marking/tree selection criteria, which may 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 9

make it difficult to hit the exact structural category targets presented.

The thin from below implementation was 

performed by ranking the trees in order of individual basal area and removing the smallest trees 

until the target basal area was achieved. Random 

tree selection was simulated by randomly assigning a number to each tree and removing 

trees with the smallest assigned number until the 

target residual basal area was achieved.

To implement the VRH simulations on our 

stands, a Python script was created to run on 

each stand’s stem map shapefile in ArcMap 10.0 

(ESRI 2011). The script was written to mimic 

the actions that an experienced tree marker or 

forester might use in marking which trees to 

keep during a harvest. The process allocates different percentages of the trees in a stand into the 

different fine-scale forest structures, depending 

on the desired output (table 1). The simulations were implemented to represent clumping 

levels seen in a range of forest historical reconstructions, but site-specific values should be 

considered if available when considering this 

distribution of clump sizes. Additionally, the 

process of locating clumps and openings in a 

stand should generally be informed by existing 

gradients of density and productivity (Churchill 

et al., in press). This process operates without regard for common secondary marking criteria like 

crown ratio or diameter, instead purely selecting 

trees to keep based on their spatial proximity to 

other trees. The script followed these steps:

Figure 6—Pre-treatment tree stem map of 9.9 acre example sites, where each dot represents a tree location.
10 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

1. Using the mean tree size within a stand, the 

approximate number of trees that should be left 

after treatment to achieve the target basal area 

is calculated.

2. This target number of trees is proportionally 

allocated to the group sizes (table 1) to 

calculate the target number of trees in each 

group size.

3. The script then starts locating structures 

starting with the largest group size (i.e., groups 

>15 trees first, then 10–15 trees, 5–9 trees, 

2–4 trees, and finally Single trees last).

a. The script finds groups of trees of the 

appropriate size that already exist and keeps 

those groups first (regardless of tree size).

b. If more trees are needed in the target group 

size, the script then finds all trees that are 

in groups larger than the size needed. It 

randomly selects one tree in these groups 

and selects the first x trees around that focal 

tree to create a group.

c. As the script selects groups of trees to keep, 

it removes the trees within a buffer zone 

surrounding those groups.

d. Once the target number of trees for 

that group size has been reached or it is 

no longer possible to make more groups, 

the script moves onto the next smallest 

group size. Step 3 is repeated for each 

group size until all structures have been 

identified.

4. Once the targets have been reached 

or all trees have been assigned (as trees 

to keep or remove), the script outputs 

the post-treatment stand tree list.

It should be noted that for the VRH 

simulations it was not always possible to achieve 

both the target residual basal area and the exact 

group size distribution (i.e., some runs with 

higher residual basal area targets left no trees 

greater than 19.7 ft (6 m) from a neighboring 

tree to create Single trees). The post-treatment 

structure will always be constrained by what 

exists pre-treatment, it is difficult to create some 

forest structures immediately post-treatment, and 

it may take time or repeated entries to achieve 

objectives.

Summary and Visualization

In order to characterize the pre- and posttreatment stand conditions, the mean, minimum, 

maximum, and coefficient of variation of traditional forest inventory metrics were calculated 

by dividing each site into sixty-four 82 x 82 ft 

square plots. Using the 64 plots, we calculated 

the mean and variability in trees acre-1, basal 

area per acre (BA acre-1), and canopy base height 

(CBH). In addition, we estimated the total available canopy fuel load and stand quadratic mean 

diameter (QMD), height, and stand density index 

for each site using the Fire and Fuel Extension 

of the Forest Vegetation Simulator (Dixon 2002; 

Reinhardt and Crookston 2003) and generated 

histograms of 2-inch tree diameter class distributions for each site. Finally, each stand was placed 

into ArcMap, where the trees were buffered and 

merged according to their field measured crown 

radius to estimate the percentage of canopy cover 

pre- and post-treatment.

To assess the spatial variability and allocation 

of fine-scale forest structures, we used ArcMap 

(ESRI 2011) to apply a 19.7 ft buffer to each tree 

that was merged with any neighbors it overlapped 

with in order to assess how many trees it was 

clumped with. The clumping criteria of 19.7 ft 

was reached based on the average overstory tree 

crown radius of 9.85 ft for the trees inventoried 

across the plot, similar to methods applied by 

Abella and Denton (2009). Once trees were 

linked with the neighbors they shared a clump 

with, the distribution of clump sizes and areas and 

apportionment of trees per acre and basal area per 

acre within each clump size was calculated. Each 

stand also underwent point pattern analysis using 

the spatstats package (Baddeley et al. 2015) in the 

R statistics program (R Core Team 2016), where 

methods for the empty space function F (Ripley 

1981) were used to generate a map showing the 

distance from any point in the stand to the nearest 

tree.

Table 1—Specific numbers of trees are proportionally allocated 

into different fine-scale stand structures for the VRH 

treatment simulations. These structural categories are only 

examples and structure classes should be locally developed 

to meet management objectives and forest conditions.

Structure Moderate clumping

(percent)

High clumping

(percent)

Single trees 35 10

2–4 Tree clump 30 30

5–9 Tree clump 20 35

10–15 Tree clump 10 15

>15 Tree clump 5 10
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 11

Within this, all distances greater than 19.7 ft 

from a tree were assumed to be within openings 

and provide an estimate of the openness of the 

stands. Further, stand opening size distribution are 

reported by identifying areas within each stand 

that meet a minimum width of 29.5 ft (9 m). This 

threshold of 29.5 ft should be considered in the 

context of the desired openings function, where 

openings of different sizes may serve different 

purposes ranging from understory plant stimulation to disrupting fire behavior. The location of 

each tree was appended to the map, scaled to 

represent its crown radius, and colored according 

to the clump size it belonged to.

Additionally, the empty space function was 

summarized by plotting a histogram showing the 

shift in opening sizes following treatment (fig. 7). 

Finally, 3-D representations of each simulation 

were created using the Smokeview package of the 

Fire Dynamics Simulator (Forney 2015). Each 

stand was visualized according to its trees’ inventoried d.b.h., height, CBH, crown and radius, and 

trees were colored according to the clump size 

they belonged to (fig. 8). Similar 3-D visualizations can also be accomplished by using the Stand 

Visualization System of stem-mapped trees as 

presented by Graham et al. (2007). However, 

caution should be taken in trying to project future 

stand conditions because the Forest Vegetation 

Simulator is an aspatial growth model and may 

prove inadequate for projecting heterogeneous 

stand structures.

Figure 7—Example (a) stem map and (b) histogram of empty space function, showing the 

distribution of distances from the nearest tree into openings.

Figure 8—Example of Fire Dynamics Simulator visualization, with trees 

scaled to field inventoried values and colored according to the size of 

clump they belong to. Circles at the base of each tree are 19.7 ft in 

radius to help identify individual clumps.

a

b
12 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 13

Stand Visualizations
14 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Pre-treatment: Low-Moderate Density Single Story Stand

This stand was comprised of 98 percent 

ponderosa pine, with small portions of the stand 

occupied by Douglas-fir and quaking aspen. 

The site is typical of many xeric low elevation 

(~7,000 ft above sea level) ponderosa pine 

stands with a site index of 35 ft at a base age of 

100 (fig. 9). Prior to treatment, the stand was 

dominated by trees between 6 and 10 inches 

d.b.h. and had a QMD of 9.6 inches with a 

canopy base height of 12 ft (fig. 10; table 2). 

This stand was at a moderately high density of 

169 trees per acre but with regions of higher 

density (>275 trees per acre) and horizontal 

continuity, with a single clump containing more 

than 1,200 trees (table 3; figs. 11 and 12). Only 

4 percent of the stand was classified as openings 

having a radius greater than 20 ft. The stand underwent the 4 simulated thinnings to a residual 

basal area of 40 ft2 acre-1 (9.2 m2

 ha-1).

Table 2—Pre-treatment stand characteristics for 

the low-moderate density single story stand. 

Stand level mean with min, max, and coefficient 

of variation in parentheses calculated from 64 

plots of 6.5 tenths x 6.5 tenths acre (82 x 82 ft).

Pre-treatment

Trees per acre 169 (26–291; 34%)

BA 83 ft2 (11–131; 32%)

QMD 9.6 in (7.5–12.4; 23%)

Tree height 26 ft (21–32; 10%)

Canopy base height 12 ft (8–15; 13%)

Crown biomass 8.26 tons acre-1

Figure 9—Pre-treatment 

forest structure of a lowmoderate density single 

story stand (photo: Emma 

Vakili, U.S. Forest Service).

Figure 10—Pre-treatment distribution of trees per acre 

by 2-inch size classes for the low-moderate density 

single story stand.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 15

Table 3—Pre-treatment clump size distribution for 

the low-moderate density single story stand.

Cluster size #/Acre % TPA % BA

Single tree 2.9 1.7 2.6

2–4 Trees 2.8 4.3 4.7

5–9 Trees 0.5 1.9 2.2

10–15 Trees 0.3 2.2 1.7

>15 Trees 0.9 89.9 88.8

Figure 11—Visualization of 

the 9.9 acre stand, where 

the tree spatial pattern 

is projected with crown 

radii that represent field 

measured crown diameters. 

Clump sizes are portrayed 

by different dot colors. 

The background coloring 

represents the distance to 

the nearest tree from the 

center of a 3.28 ft (1 m) cell 

grid (or the empty space 

function).

Figure 12—a) Virtual 

rendering of stand 

structure over the 9.9 

acre area, where trees 

are scaled according to 

inventoried height, CBH, 

and crown widths and 

are colored following the 

clustering scheme above 

(fig. 11), b) profile view 

of stand structure before 

treatment.

a

b
16 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Thin From Below to 40 ft2 ac-1 of 

Basal Area

Thin from below approaches tend to homogeneous stand structure and in this case resulted 

in all trees less than 10 inches d.b.h. being 

removed (fig. 13) and an increase in stand level 

QMD from 9.6 to 12.5 inches while reducing the 

local variability of QMD (table 4). Following 

Table 4—Changes in stand characteristics for the lowmoderate density single story stand after a thin from 

below treatment. Stand level mean with min, max, and 

coefficient of variation in parentheses calculated from 

64 plots of 6.5 tenths x 6.5 tenths acre (82 x 82 ft).

Pre Post

Trees per acre 169 

(26–291; 34%)

47 

(7–104; 53%)

BA per acre 83 ft2

(11–131; 32%)

40 ft2

(4–96; 54%)

QMD 9.6 in 

(7.5–12.4; 23%)

12.5 in 

(10.7–17.1; 21%)

Total height 26 ft 

(21–32; 10%)

29 ft 

(17–35; 11%)

CBH 12 ft 

(8–15; 13%)

13 ft 

(9–17; 14%)

Crown biomass 8.26 tons acre-1 4.26 tons acre-1

Table 5—Changes in clump size distribution for the low-moderate density 

single story stand after the thin from below treatment.

Pre Post

Cluster size #/Acre % TPA % BA #/Acre % TPA % BA

Single tree 2.9 1.7 2.6 15.3 32.3 34.0

2–4 Trees 2.8 4.3 4.7 6.8 36.8 35.5

5–9 Trees 0.5 1.9 2.2 1.4 19.5 19.3

10–15 Trees 0.3 2.2 1.7 0.3 6.6 6.6

>15 Trees 0.9 89.9 88.8 0.1 4.7 4.6

Figure 13—Comparison of trees per acre distribution 

within 2-inch size classes for the thin from below 

treatment.

completion of the thinning, the stand’s canopy 

cover shifted from 86 to 57 percent and there 

was a substantial increase in the variability of 

local basal area and trees per acre. While local 

horizontal variability increased, there was no 

change to vertical structure. The horizontal 

continuity of the stand was greatly reduced as a 

result of the thinning.

Single tree and 2–4 Tree clumps went from 

being represented by 6.0 to 69.1 percent of the 

trees in the stand, with the largest clump containing 22 trees (table 5).

The thinning also resulted in an increase in 

the number of and mean size of stand openings, 

with openings now reaching 49 ft in radius 

as can be seen by the darker colors within the 

empty space function (figs. 14 and 15).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 17

Figure 14—Visualization of the 9.9 acre stand, 

where the tree spatial pattern is projected 

with crown radii that represent field measured 

crown diameters. Clump sizes are portrayed by 

different dot colors. The background coloring 

represents the distance to the nearest tree from 

the center of a 3.28 ft (1 m) cell grid (or the 

empty space function).

Figure 15—a) Virtual rendering of 

stand structure over the 9.9 acre 

area, where trees are scaled 

according to inventoried height, 

d.b.h., CBH, and crown widths 

and are colored following the 

clustering scheme above (fig. 14), 

b) profile view of stand structure.

b

a
18 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Random Thinning to 40 ft2 ac-1 of 

Basal Area

Proportional thinning throughout the diameter 

range or random thinning techniques tend to 

preserve the pre-existing stand structure and 

in this case removed about 50 percent of trees 

from each diameter class (fig. 16), with the stand 

level QMD holding at 9.6 inches and increasing 

Figure 16—Comparison of trees per acre distribution 

within 2-inch size classes for the random thinning 

treatment.

Table 6—Changes in stand characteristics for the 

low-moderate density single story stand after a 

random thinning treatment. Stand level mean with 

min, max, and coefficient of variation in parentheses calculated from 64 plots of 6.5 tenths x 6.5 

tenths acre (82 x 82 ft).

Pre Post

Trees per acre 169

(26–291; 34%)

81

(7–136; 38%)

BA per acre 83 ft2

(11–131; 32%)

40 ft2

(3–74; 37%)

QMD 9.6 in

(7.5–12.4; 23%)

9.6 in

(7.8–17.0; 35%)

Total height 26 ft

(21–32; 10%)

26 ft

(20–26; 12%)

CBH 12 ft

(8–15; 13%)

12 ft

(7–16; 16%)

Crown biomass 8.26 tons acre-1 4.00 tons acre-1

Table 7—Changes in clump size distribution for the low-moderate 

density single story stand after the random thinning treatment.

Pre Post

Cluster size #/Acre % TPA % BA #/Acre % TPA % BA

Single tree 2.9 1.7 2.6 10.4 12.7 16.1

2–4 Trees 2.8 4.3 4.7 6.6 21.7 22.7

5–9 Trees 0.5 1.9 2.2 2.9 23.1 22.9

10–15 Trees 0.3 2.2 1.7 1.1 16.6 14.5

>15 Trees 0.9 89.9 88.8 0.8 25.9 23.8

the range of QMDs seen throughout the stand 

(table 6). While the range of trees and basal area 

per acre was lowered, the local variability in 

horizontal forest structure increased. Following 

completion of the thinning, the stand’s canopy 

cover shifted from 86 to 60 percent and there 

were small increases in the local variation in 

vertical forest structure.

The stand went from being dominated by a 

single large clump (>1,200 trees) to having a 

nearly uniform distribution of trees in structures 

from Single trees to 15–20 tree clumps (table 7).

The thinning increased the number of openings and produced a greater range of opening 

sizes with radii ranging from 15–49 ft (figs. 17 

and 18).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 19

Figure 17—Visualization of the 9.9 acre stand, 

where the tree spatial pattern is projected 

with crown radii that represent field measured 

crown diameters. Clump sizes are portrayed by 

different dot colors. The background coloring 

represents the distance to the nearest tree from 

the center of a 3.28 ft (1 m) cell grid (or the 

empty space function).

Figure 18—a) Virtual rendering of stand 

structure over the 9.9 acre area, 

where trees are scaled according to 

inventoried height, d.b.h., CBH, and 

crown widths and are colored following 

the clustering scheme above (fig. 17), 

b) profile view of stand structure.

b

a
20 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Moderately Clumped Thinning to 

40 ft2 ac-1 of Basal Area

A moderate clumping scenario following individual, clump, and opening thinning approach 

attempts to increase the number of small clumps, 

and in this case it resulted in a proportional removal of trees throughout the range of diameters 

(fig. 19) and only a minimal increase to stand 

Figure 19—Comparison of trees per acre distribution 

within 2-inch d.b.h. size classes for the moderately 

clumped thinning treatment.

Table 8—Changes in stand characteristics for the 

low-moderate density single story stand after a 

moderately clumped thinning treatment. Stand level 

mean with min, max, and coefficient of variation in 

parentheses calculated from 64 plots of 6.5 tenths x 

6.5 tenths acre (82 x 82 ft).

Pre Post

Trees per acre 169 

(26–291; 34%)

83 

(13–188; 32%)

BA per acre 83 ft2

(11–131; 32%)

42 ft2

(5–93; 38%)

QMD 9.6 in 

(7.5–12.4; 23%)

9.7 in 

(7.3–12.2; 24%)

Total height 26 ft 

(21–32; 10%)

26 ft 

(21–32; 11%)

CBH 12 ft 

(8–15; 13%)

12 ft 

(8–15; 14%)

Crown biomass 8.26 tons acre-1 4.28 tons acre-1

Table 9—Changes in clump size distribution for the low-moderate 

density single story stand after the random thinning treatment.

Pre Post

Clump size #/Acre % TPA % BA #/Acre % TPA % BA

Single tree 2.9 1.7 2.6 24.9 31.3 33.0

2–4 Trees 2.8 4.3 4.7 8.8 31.1 32.4

5–9 Trees 0.5 1.9 2.2 2.7 22.0 21.0

10–15 Trees 0.3 2.2 1.7 0.6 9.1 6.9

>15 Trees 0.9 89.9 88.8 0.3 6.5 6.7

level QMD from 9.6 to 9.7 inches (table 8). 

Following completion of the thinning, the 

stand’s canopy cover shifted from 86 to 64 percent. There were also decreases in the range of 

horizontal structures and nearly no shift in local 

variability of vertical and horizontal structures, 

generally failing to meet the goals of spatially 

explicit prescriptions.

The stand went from being dominated by 

large clumps to having Single tree and clumps 

from 2–4 trees representing the majority of the 

stand (table 9).

The thinning increased the number and mean 

size of stand openings, ranging from 15–39 

ft. However, it failed to create large openings 

(>1/4 acre) within the stand (figs. 20 and 21).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 21

Figure 21—Virtual rendering of stand 

structure over the 9.9 acre area, 

where trees are scaled according to 

inventoried height, d.b.h., CBH, and 

crown widths and are colored following 

the clustering scheme above (fig. 20), 

b) profile view of stand structure.

Figure 20—Visualization of the 9.9 acre stand, 

where the tree spatial pattern is projected 

with crown radii that represent field measured 

crown diameters, and where clump sizes 

are portrayed by different dot colors. The 

background coloring represents the distance 

to the nearest tree from the center of a 3.28 ft 

(1 m) cell grid (or the empty space function).

b

a
22 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Figure 22—Comparison of trees per acre distribution 

within 2-inch d.b.h. size classes for the highly 

clumped thinning treatment.

Highly Clumped Thinning to 

40 ft2 ac-1 of Basal Area

Under the high clumping scenario following 

individual, clump, and opening thinning, the 

goal was to distribute the stands throughout the 

range of clump sizes. In this case, it resulted in a 

proportional removal of trees through the range 

of diameters (fig. 22), with the stand level QMD 

Table 10—Changes in stand characteristics for the 

low-moderate density single story stand after a highly 

clumped thinning treatment. Stand level mean with 

min, max, and coefficient of variation in parentheses 

calculated from 64 plots of 6.5 tenths x 6.5 tenths 

acre (82 x 82 ft).

Pre Post

Trees per acre 169 

(26–291; 34%)

80 

(26–149; 42%)

BA per acre 83 ft2

(11–131; 32%)

41 ft2

(11–83; 46%)

QMD 9.6 in 

(7.5–12.4; 23%)

9.6 in 

(7.1–12.4; 25%)

Total height 26 ft

(21–32; 10%)

26 ft 

(20–32; 11%)

CBH 12 ft 

(8–15; 13%)

12 ft 

(8–19; 15%)

Crown biomass 8.26 tons acre-1 4.18 tons acre-1

Table 11—Changes in clump size distribution for the low-moderate 

density single story stand after the highly clumped thinning treatment.

Pre Post

Clump size #/Acre % TPA % BA #/Acre % TPA % BA

Single tree 2.9 1.7 2.6 8.2 9.9 12.0

2–4 Trees 2.8 4.3 4.7 8.7 29.7 31.0

5–9 Trees 0.5 1.9 2.2 4.4 36.2 34.3

10–15 Trees 0.3 2.2 1.7 0.9 13.8 12.4

>15 Trees 0.9 89.9 88.8 0.5 10.4 10.4

holding at 9.6 inches and a slight increase to the 

range of local QMDs (table 10). Following completion of the thinning, the stand’s canopy cover 

shifted from 86 to 58 percent. This treatment 

provided the greatest increase in local variability 

in trees and basal area per acre, in line with the 

goals of spatially explicit prescriptions.

• The stand went from being dominated by large 

clumps to having a balanced distribution of 

clump sizes (table 11).

• The thinning also resulted in a significant 

increase in the number and mean size of 

stand openings, with several openings now 

reaching minimum radii of 49 ft, represented 

in openings of approximately 1/6 to 1/3 acre 

(figs. 23 and 24).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 23

Figure 23—Visualization of the 9.9 acre stand, 

where the tree spatial pattern is projected 

with crown radii that represent field measured 

crown diameters, and where clump sizes 

are portrayed by different dot colors. The 

background coloring represents the distance 

to the nearest tree from the center of a 3.28 ft 

(1 m) cell grid (or the empty space function).

Figure 24—a) Virtual rendering of stand 

structure over the 9.9 acre area, 

where trees are scaled according to 

inventoried height, d.b.h., CBH, and 

crown widths and are colored following 

the clumping scheme above (fig. 23) 

b) profile view of stand structure.

b

a
24 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Summary: Low-Moderate Density 

Single Story Stand

Prior to treatment, this stand had regions 

of significant density (>600 trees per acre) 

and horizontal continuity, with a single clump 

containing more than 1,200 trees. The stand was 

dominated by trees 6 to 12 inches at d.b.h. (85 

percent of trees) and had a QMD of 9.6 inches. 

There was also a moderate level of vertical complexity throughout the stand (fig. 25, table 12).

• Following the simulated treatments, mean 

stand density was greatly reduced while 

increasing the relative variability of tree 

density in all but the thin from below 

simulations. This increase in variability is 

an important indicator of meeting horizontal 

heterogeneity treatment objectives.

• The relative level of variability in vertical 

structure also increased under all simulated 

treatments, with the spatially explicit 

simulations providing the greatest increase in 

complexity.

Figure 25—Virtual rendering of stand 

structure over the 9.9 acre area for 

each of the various thinning treatments 

according to inventoried height, d.b.h., 

CBH, and crown widths.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 25

Table 12—Changes in stand characteristics for the low-moderate density single story stand after various thinning treatments. 

Stand level mean with min, max, and coefficient of variation in parentheses calculated from 64 plots of 6.5 tenths x 6.5 

tenths acre (82 x 82 ft).

Pre-treatment Thin from below Random thinning Moderately clumped Highly clumped

Trees per acre 169 (26–291) 47 (7–104) 81 (7–136) 83 (13–188) 80 (26–149)

BA per acre 83 ft2 (11–131) 40 ft2 (4–96) 40 ft2 (3–74) 42 ft2 (5–93) 41 ft2 (11–83)

QMD 9.6 in (7.5–12.4) 12.5 in (10.7–17.1) 9.6 in (7.8–17.0) 9.7 in (7.3–12.2) 9.6 in (7.1–12.4)

Mean tree height 26 ft (21–32) 29 ft (17–35) 26 ft (20–26) 26 ft (21–32) 26 ft (20–32)

Canopy base height 12 ft (8–15) 13 ft (9–17) 12 ft (7–16) 12 ft (8–15) 12 ft (8–19)

Crown biomass 8.26 tons acre-1 4.26 tons acre-1 4.00 tons acre-1 4.28 tons acre-1 4.18 tons acre-1

The pre-treatment stand condition placed 

most of the trees into a single very large and 

continuous clump of trees, containing more than 

85 percent of the stands trees and basal area 

(table 13).

• Both the thin from below and moderate 

clumping simulations shifted most of the 

stand into Single tree or small clumps, while 

Table 13—Changes in clump size distribution for each of the thinning treatments for the low-moderate density single story stand.

Pre-treatment Thin from below Random thinning Moderately clumped Highly clumped

Clump size #/Acre % TPA % BA #/Acre % TPA % BA #/Acre % TPA %BA #/Acre % TPA % BA #/Acre % TPA % BA

Single tree 2.9 1.7 2.6 15.3 32.3 34.0 10.4 12.7 16.1 24.9 31.3 33.0 8.2 9.9 12.0

2–4 Trees 2.8 4.3 4.7 6.8 36.8 35.5 6.6 21.7 22.7 8.8 31.1 32.4 8.7 29.7 31.0

5–9 Trees 0.5 1.9 2.2 1.4 19.5 19.3 2.9 23.1 22.9 2.7 22.0 21.0 4.4 36.2 34.3

10–15 Trees 0.3 2.2 1.7 0.3 6.6 6.6 1.1 16.6 14.5 0.6 9.1 6.9 0.9 13.8 12.4

>15 Trees 0.9 89.9 88.8 0.1 4.7 4.6 0.8 25.9 23.8 0.3 6.5 6.7 0.5 10.4 10.4

the random thinning evenly distributed the 

stand into the different structures.

• The high clumping simulation placed a third 

of the stand in 5–9 tree clumps and then 

evenly distributed the remaining trees to all of 

the other structures. This simulation resulted 

in the greatest diversity in forest structures 

and opening sizes.
26 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Prior to treatment, only 7 percent of the stand 

was within openings (>6 m from a tree) with the 

largest opening being less than 1/10 acre (figs. 26 

and 27; table 14).

• Following treatment, all of the treatments 

experienced a shift toward more and larger 

openings.

• The thin from below created the largest shift in 

mean and max opening size, putting 29 percent 

of the stand into openings, but openings were 

dominated by a single large opening.

Table 14—Changes in clump and opening area for each of the 

thinning treatments for the low-moderate density single story 

stand.

Clump area (acres)

Mean Median Min Max

Pre-treatment 0.147 0.018 0.008 4.878

Below 0.022 0.016 0.008 0.131

Random 0.032 0.020 0.009 0.170

Moderate 0.022 0.017 0.008 0.090

High 0.024 0.020 0.007 0.090

Opening area (acres)

n Mean Median Min Max

Pre-treatment 6 0.047 0.042 0.019 0.078

Below 18 0.198 0.049 0.019 2.258

Random 18 0.092 0.057 0.019 0.432

Moderate 9 0.051 0.047 0.019 0.082

High 20 0.116 0.058 0.019 0.529

• While both the random thinning and moderate 

clumping simulations shifted the stand so that 

approximately 17 percent of the stands were 

within openings, the number of openings and 

range of opening sizes was very different.

• The high clumping simulation resulted in the 

most openings and greatest median opening 

size, while putting 29 percent of the stand 

into openings. This created a balance between 

creating forest structures and establishing 

openings.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 27

Figure 27—Treatment 

effects on the distribution 

of the distance to the 

nearest tree.

Figure 26—Visualization of the 9.9 

acre stand, where the tree spatial 

pattern is projected with crown 

radii that represent field measured 

crown diameters, and where clump 

sizes are portrayed by different dot 

colors. The background coloring 

represents the distance to the 

nearest tree from the center of a 

3.28 ft (1 m) cell grid (or the empty 

space function), in order to portray 

openings. 
28 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

This stand was composed of 95 percent 

ponderosa pine, with small portions of the stand 

occupied by Douglas-fir and quaking aspen. The 

site represents many mid-elevation (about 8,400 

ft above sea level) ponderosa pine stands with a 

site index of 65 ft at a base age of 100 (fig. 28). 

Prior to treatment, the stand was dominated by 

trees less than 10 inches d.b.h. (fig. 29) and had 

the highest starting local variability in horizontal 

and vertical forest structure (table 15) of any 

of the simulated stands. This stand had regions 

of significant density (>600 trees per acre) 

and horizontal continuity, with a single clump 

containing more than 1,100 trees (table 16; 

figs. 30 and 31). Outside of the large pre-existing 

opening, more than 90 percent of the stand was 

within 20 ft of a tree. The stand underwent 4 

simulated thinnings to a residual basal area of 

40 ft2 ac-1 (9.2 m2 ha-1).

Pre-treatment: Moderate Density Multi-Storied Stand

Figure 28—Pre-treatment forest 

structure of a moderate density 

multi-storied stand (photo: 

Emma Vakili, U.S. Forest 

Service).

Figure 29—Pre-treatment distribution of 

trees per acre by 2-inch d.b.h. size 

classes of the moderate density multistoried stand.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 29

Table 15—Pre-treatment stand characteristics 

for the moderate density multi-storied stand. 

Stand level mean with min, max, and coefficient 

of variation in parentheses calculated from 64 

plots of 6.5 tenths x 6.5 tenths acre (82 x 82 ft).

Pre-treatment

Trees per acre 209 (0–667; 70%)

BA 62 ft

2 (0–132; 52%)

QMD 7.6 in (0–12.9; 49%)

Tree height 25 ft (13–52; 26%)

Canopy base height 10 ft (4–36; 41%)

Crown biomass 7.15 tons acre-1

Table 16—Pre-treatment clump size distribution 

for the moderate density multi-storied stand.

Clump size #/Acre % TPA % BA

Single tree 3.9 1.9 4.1

2–4 Trees 1.1 3.2 3.6

5–9 Trees 2.5 3.7 10.1

10–15 Trees 0.5 2.7 5.5

>15 Trees 1.1 88.5 76.6

Figure 30—Visualization of 

the 9.9 acre stand, where 

the tree spatial pattern 

is projected with crown 

radii that represent field 

measured crown diameters, 

and where clump sizes are 

portrayed by different dot 

colors. The background 

coloring represents the 

distance to the nearest tree 

from the center of a 3.28 ft 

(1 m) cell grid (or the empty 

space function).

Figure 31—a) Virtual rendering 

of stand structure over the 

9.9 acre area, where trees are 

scaled according to inventoried 

height, d.b.h., CBH, and crown 

widths and are colored following 

the clustering scheme above 

(fig. 30), b) profile view of stand 

structure.

ba
30 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Thin from Below to 40 ft2 ac-1 of 

Basal Area

Thinning from below tends to homogenize 

stand structure and in this case resulted in all 

trees less than 8 inches d.b.h. being removed 

(fig. 32) and an increase in stand-level QMD 

from 7.6 to 12.2 inches (table 17). Following 

completion of the thinning, the stand’s canopy 

Table 17—Changes in stand characteristics for the 

moderate density multi-storied stand after a thin from 

below treatment. Stand-level mean with min, max, and 

coefficient of variation in parentheses calculated from 

64 plots of 6.5 tenths x 6.5 tenths acre (82 x 82 ft).

Pre Post

Trees per acre 209 

(0–667; 70%)

48 

(0–117; 56%)

BA per acre 62 ft2

(0–132; 52%)

40 ft2

(0–106; 60%)

QMD 7.6 in 

(0–12.9; 49%)

12.2 in 

(0–23.5; 46%)

Total height 25 ft 

(13–52; 26%)

41 ft 

(31–57; 13%)

CBH 10 ft 

(4–36; 41%)

17 ft 

(9–36; 27%)

Crown biomass 7.15 tons acre-1 4.60 tons acre-1

Table 18—Changes in clump size distribution for the moderate density multistoried stand after the thin from below treatment.

Pre Post

Clump size #/Acre % TPA % BA #/Acre % TPA % BA

Single tree 4 1.9 4.1 8.1 16.9 17.7

2–4 Trees 1.1 3.7 3.6 17.1 35.7 35.5

5–9 Trees 2.5 3.2 10.1 13.2 27.6 27.3

10–15 Trees 0.5 2.7 5.5 5.8 12.0 11.8

>15 Trees 1.1 88.5 76.6 3.7 7.8 7.9

Figure 32—Comparison of trees per acre distribution 

within 2-inch d.b.h. size classes for the thin from 

below treatment.

cover shifted from 67 to 52 percent. The local variability of horizontal and vertical forest 

structure was greatly reduced in every category 

except basal area per acre that saw a slight 

increase.

• Single tree and 2–4 Tree clumps went from 

representing 5.6 to 52.6 percent of the trees in 

the stand (table 18).

• The thinning also resulted in an increase to 

the number of and the mean size of stand 

opening, with many openings now reaching 

more than 60 ft in radius or openings greater 

than 1/4 acre (figs. 33 and 34).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 31

Figure 33—Visualization of the 9.9 acre 

stand, where the tree spatial pattern is 

projected with crown radii that represent 

field measured crown diameters, and where 

clump sizes are portrayed by different dot 

colors. The background coloring represents 

the distance to the nearest tree from the 

center of a 3.28 ft (1 m) cell grid (or the 

empty space function).

Figure 34—a) Virtual rendering of stand 

structure over the 9.9 acre area, where 

trees are scaled according to inventoried 

height, d.b.h., CBH, and crown widths 

and are colored following the clustering 

scheme above (fig. 33), b) profile view 

of stand structure.

a

b
32 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Random Thinning to 40 ft2 ac-1 of 

Basal Area

Proportional thinning throughout the diameter 

range or random thinning approaches tend to 

preserve the pre-existing stand structure and 

in this case removed about 35 percent of trees 

from each diameter class (fig. 35), causing only 

Table 19—Changes in stand characteristics for the 

moderate density multi-storied stand after a random 

thinning treatment. Stand level mean with min, max, 

and coefficient of variation in parentheses calculated 

from 64 plots of 6.5 tenths x 6.5 tenths acre (82 x 82 ft).

Pre Post

Trees per acre 209 

(0–667; 70%)

137 

(0–395; 68%)

BA per acre 62 ft2

(0–132; 52%)

40 ft2

(0–107; 54%)

QMD 7.6 in 

(0–12.9; 49%)

7.3 in 

(0–12.3; 53%)

Total height 25 ft 

(13–52; 26%)

25 ft 

(7–52; 26%)

CBH 10 ft 

(4–36; 41%)

10 ft 

(1–36; 43%)

Crown biomass 7.15 tons acre-1 4.61 tons acre-1

Table 20—Changes in clump size distribution for the moderate density 

multi-storied stand after the random thinning treatment.

Pre Post

Clump size #/Acre %TPA %BA #/Acre %TPA %BA

Single tree 4 1.9 4.1 5.7 4.1 6.7

2–4 Trees 1.1 3.7 3.6 4.0 8.3 13.6

5–9 Trees 2.5 3.2 10.1 1.7 8.2 10.6

10–15 Trees 0.5 2.7 5.5 0.6 5.2 7.9

>15 Trees 1.1 88.5 76.6 1.4 74.3 61.3

Figure 35—Comparison of trees per acre distribution 

within 2-inch d.b.h. size classes for the random 

thinning.

a small shift in stand level QMD from 7.6 to 

7.3 inches and a slight lowering in local QMD 

variability (table 19). Following completion of 

the thinning, the stand’s canopy cover shifted 

from 67 to 53 percent, with very little change in 

the variability of horizontal and vertical forest 

structures.

• The stand shifted slightly from its pretreatment condition with many clumps of 

200+ trees to having a greater number of 

clumps containing 25–50 trees, but still with 

a clump of 500+ trees and more than 15 tree 

clumps dominating forest structure (table 20).

• The thinning extended the pre-existing 

opening and created several small gaps with 

radii reaching 30 ft (figs. 36 and 37).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 33

Figure 36—Visualization of the 9.9 

acre stand, where the tree spatial 

pattern is projected with crown radii 

that represent field measured crown 

diameters, and where clump sizes are 

portrayed by different dot colors. The 

background coloring represents the 

distance to the nearest tree from the 

center of a 3.28 ft (1 m) cell grid (or the 

empty space function).

Figure 37—a) Virtual rendering of stand 

structure over the 9.9 acre area, 

where trees are scaled according to 

inventoried height, d.b.h., CBH, and 

crown widths and are colored following 

the clustering scheme above (fig. 36), 

b) profile view of stand structure.

b

a
34 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Moderately Clumped Thinning to 

40 ft2 ac-1 of Basal Area

A moderate clumping scenario following 

individual, clump, and opening thinning approach attempts to increase the number of 

small clumps, and in this case it resulted in a 

removal of trees throughout the diameter trees 

(fig. 38) and no change in stand level QMD 

Figure 38—Comparison of trees per acre distribution 

within 2-inch d.b.h. size classes for the moderately 

clumped thinning treatment.

Table 21—Changes in stand characteristics for 

the moderate density multi-storied stand after a 

moderately clumped thinning treatment. Stand level 

mean with min, max, and coefficient of variation in 

parentheses calculated from 64 plots of 6.5 tenths x 

6.5 tenths acre (82 x 82 ft).

Pre Post

Trees per acre 209 

(0–667; 70%)

115 

(0–227; 44%)

BA per acre 62 ft2

(0–132; 52%)

36 ft2

(0–96; 53%)

QMD 7.6 in 

(0–12.9; 49%)

7.6 in 

(0–12.9; 50%)

Total height 25 ft 

(13–52; 26%)

25 ft 

(13–52; 27%)

CBH 10 ft 

(4–36; 41%)

10 ft 

(3–36; 43%)

Crown biomass 7.15 tons 

acre-1 4.27 tons acre-1

Table 22—Changes in clump size distribution for the moderate density 

multi-storied stand after the moderately clumped thinning treatment.

Pre Post

Clump size #/Acre % TPA % BA #/Acre % TPA % BA

Single tree 4 1.9 4.1 7.0 6.1 10.7

2–4 Trees 1.1 3.7 3.6 7.0 17.7 20.8

5–9 Trees 2.5 3.2 10.1 7.5 45.7 45.5

10–15 Trees 0.5 2.7 5.5 1.8 19.0 15.4

>15 Trees 1.1 88.5 76.6 0.7 11.5 7.6

(table 21). Following completion of the thinning, 

the stand’s canopy cover shifted from 67 to 53 

percent, with no changes in local horizontal 

and vertical structure variability except for the 

decrease in trees per acre.

• The stand went from being dominated by large 

clumps to having a balanced distribution of 

clump sizes (table 22).

• Due to the existing pockets of very high 

density, the thinning struggled to achieve its 

intended goal of placing a higher proportion 

of trees into Single tree and 2-4 tree clumps 

(table 22; figs. 39 and 40).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 35

Figure 39—Visualization of the 9.9 acre stand, where 

the tree spatial pattern is projected with crown radii 

that represent field measured crown diameters, 

and where clump sizes are portrayed by different 

dot colors. The background coloring represents the 

distance to the nearest tree from the center of a 

3.28 ft (1 m) cell grid (or the empty space function).

Figure 40—a) Virtual rendering of stand 

structure over the 9.9 acre area, where 

trees are scaled according to inventoried 

height, d.b.h., CBH, and crown widths 

and are colored following the clustering 

scheme above (fig. 39), b) profile view of 

stand structure.

b

a
36 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Highly Clumped Thinning to 

40 ft2 ac-1 of Basal Area

Under the high clumping scenario following 

individual, clump, and opening thinning, the goal 

was to distribute the stand’s structure throughout the 

range of clump sizes, and in this case it resulted in a 

proportional removal of trees throughout the range 

of diameters (fig. 41) and a negligible increase in 

stand level QMD from 7.6 to 7.7 inches (table 23). 

Following completion of the thinning, the stand’s 

canopy cover shifted from 67 to 54 percent, with 

no changes in local horizontal and vertical structure 

variability except for the decrease in trees per acre.

Table 23—Changes in stand characteristics for the 

moderate density multi-storied stand after a highly 

clumped thinning treatment. Stand level mean with 

min, max, and coefficient of variation in parentheses 

calculated from 64 plots of 6.5 tenths x 6.5 tenths 

acre (82 x 82 ft).

Pre Post

Trees per acre 209 

(0–667; 70%)

121 

(0–278; 47%)

BA per acre 62 ft2

(0–132; 52%)

39 ft2

(0–89; 48%)

QMD 7.6 in 

(0–12.9; 49%)

7.7 in 

(0–12.9; 47%)

Total height 25 ft 

(13–52; 26%)

25 ft 

(13–52; 26%)

CBH 10 ft 

(4–36; 41%)

10 ft 

(4–36; 42%)

Crown biomass 7.15 tons acre-1 4.53 tons acre-1

Table 24—Changes in clump size distribution for the moderate 

density multi-storied stand after the highly clumped thinning 

treatment.

Pre Post

Clump size #/Acre % TPA % BA #/Acre % TPA % BA

Single tree 4 1.9 4.1 6.7 5.5 7.9

2–4 Trees 1.1 3.7 3.6 6.1 13.5 14.7

5–9 Trees 2.5 3.2 10.1 5.5 31.8 33.9

10–15 Trees 0.5 2.7 5.5 2.7 27.2 26.1

>15 Trees 1.1 88.5 76.6 1.4 22.0 17.3

Figure 41—Comparison of trees per acre distribution 

within 2-inch d.b.h. size classes for the highly 

clumped thinning treatment.

• The stand went from being dominated by large 

clumps to meeting its intended condition with a 

balanced distribution of clump sizes (table 24).

• The thinning also doubled the number of 

openings within the stand, while maintaining a 

wide range of opening sizes (figs. 42 and 43).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 37

Figure 42—Visualization of the 9.9 acre stand, where 

the tree spatial pattern is projected with crown radii 

that represent field measured crown diameters, 

and where clump sizes are portrayed by different 

dot colors. The background coloring represents the 

distance to the nearest tree from the center of a 

3.28 ft (1 m) cell grid (or the empty space function).

Figure 43—a) Virtual rendering of stand 

structure over the 9.9 acre area, where 

trees are scaled according to inventoried 

height, d.b.h., CBH, and crown widths 

and are colored following the clumping 

scheme above (fig. 42), b) profile view of 

stand structure..

b

a
38 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Summary: Moderate Density 

Multi-Storied Stand

Prior to treatment, this stand had regions of 

significant density (>600 trees per acre) and 

horizontal continuity, with a single cluster 

containing more than 1,100 trees. The stand 

was dominated by trees less than 10 inches 

d.b.h. (85 percent of trees) and had a QMD of 

7.6 inches with a canopy base height of only 10 

ft (table 25). Outside of the large pre-existing 

opening, most canopy openings were less than 

26 ft in radius (figs. 44–46).

• Following the simulated treatments, mean 

stand density was greatly reduced while 

increasing the relative variability of tree 

density in all but the thin from below 

simulations (table 25; figs. 44 and 45). 

This increase in variability is an important 

indicator of meeting horizontal heterogeneity 

treatment objectives.

The pre-treatment stand condition placed 

most of the trees into a single very large and 

continuous clump of trees, containing more than 

80 percent of the stand’s trees and basal area 

(table 26).

• The thin from below simulations shifted most 

of the stand into Single tree or small clumps, 

while the random thinning left a large portion 

of the stand (>60 percent) still in clumps of 

more than 15 trees.

Table 25—Changes in stand characteristics for the moderate density multi-storied stand after various thinning treatments. Stand 

level mean with min, max, and coefficient of variation in parentheses calculated from 64 plots of 6.5 tenths x 6.5 tenths acre (82 

x 82 ft).

Pre-treatment Thin from below Random thinning Moderately clumped Highly clumped

Trees per acre 209 (0–667) 48 (0–117) 137 (0–395) 115 (0–227) 121 (0–278)

BA per acre 62 ft2 (0–132) 40 ft2 (0–106) 40 ft2 (0–107) 36 ft2 (0–96) 39 ft2 (0–89)

QMD 7.6 in (0–12.9) 12.2 in (0–23.5) 7.3 in (0–12.3) 7.6 in (0–12.9) 7.7 in (0–12.9)

Mean tree height 25 ft (13–52) 41 ft (31–57) 25 ft (7–52) 25 ft (13–52) 25 ft (13–52)

Canopy base height 10 ft (4–36) 17 ft (9–36) 10 ft (1–36) 10 ft (3–36) 10 ft (4–36)

Crown biomass 7.15 tons acre-1 4.60 tons acre-1 4.61 tons acre-1 4.27 tons acre-1 4.53 tons acre-1

Table 26—Changes in clump size distribution for each of the thinning treatments for the moderate density multi-storied stand.

Pre-treatment Thin from below Random thinning Moderately clumped Highly clumped

Clump size #/Acre % TPA % BA #/Acre % TPA % BA #/Acre % TPA % BA #/Acre % TPA % BA #/Acre % TPA % BA

Single tree 4 1.9 4.1 8.1 16.9 17.7 5.7 4.1 6.7 7.0 6.1 10.7 6.7 5.5 7.9

2–4 Trees 1.1 3.7 3.6 17.1 35.7 35.5 4.0 8.3 13.6 7.0 17.7 20.8 6.1 13.5 14.7

5–9 Trees 2.5 3.2 10.1 13.2 27.6 27.3 1.7 8.2 10.6 7.5 45.7 45.5 5.5 31.8 33.9

10–15 Trees 0.5 2.7 5.5 5.8 12.0 11.8 0.6 5.2 7.9 1.8 19.0 15.4 2.7 27.2 26.1

>15 Trees 1.1 88.5 76.6 3.7 7.8 7.9 1.4 74.3 61.3 0.7 11.5 7.6 1.4 22.0 17.3
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 39 • Following the simulated spatially explicit 

treatments (Moderately and Highly 

Clumped), the structures within the stand 

were reallocated throughout all of the tree 

clump sizes, providing a balance of these 

structures to help meet many restoration, 

wildlife, and fuels treatment objectives.

Prior to treatment, only 20 percent of the stand 

was within openings (>6 m from a tree) with a 

single 1.15 acre opening dominating this proportion 

(figs. 45 and 46; table 27). • Following treatment, all of the stands 

approximately doubled the number of openings 

and experienced a shift in the percentage of the 

stand in openings.

• The thin from below simulation created the 

greatest shift in distribution, which is to be 

expected since the stand was thinned to 48 trees 

per acre. This resulted in the greatest mean and 

max opening size.

• The spatially explicit simulations enhanced 

the proportion of small and moderately sized 

stand openings. Now 29 percent of the stand was 

in openings with a slight decrease in the mean 

opening size. This indicates a shift toward 

more openings that were smaller in size

Figure 44—Virtual rendering of stand structure 

over the 9.9 acre area, where trees are scaled 

according to inventoried height, d.b.h., CBH, 

and crown widths.
40 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Figure 46—Treatment effects 

on the distribution of the 

distance to the nearest 

tree.

Figure 45—Visualization of the 9.9 acre stand, where 

the tree spatial pattern is projected with crown radii 

that represent field measured crown diameters, 

and where clump sizes are portrayed by different 

dot colors. The background coloring represents 

the distance to the nearest tree from the center 

of a 3.28 ft (1 m) cell grid (or the empty space 

function), in order to portray openings. 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 41

Table 27—Changes in clump and opening area for each of the 

thinning treatments for the moderate density multi-storied 

stand.

Clump area (acres)

Mean Median Min Max

Pretreatment 0.101 0.022 0.008 2.185

Below 0.023 0.015 0.007 0.093

Random 0.054 0.021 0.007 1.527

Moderate 0.022 0.019 0.007 0.073

High 0.025 0.021 0.007 0.081

Opening area (acres)

n Mean Median Min Max

Pretreatment 11 0.147 0.034 0.013 1.150

Below 24 0.198 0.047 0.014 3.388

Random 19 0.119 0.035 0.013 1.230

Moderate 18 0.106 0.035 0.016 1.151

High 20 0.101 0.038 0.013 1.166
42 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

This stand was composed of 82 percent 

ponderosa pine and 14 percent Douglas-fir, with 

small pockets of quaking aspen and Engelmann 

spruce. The site represents many mid-elevation 

(about 8,000 ft above sea level) ponderosa pine 

stands with a site index of 65 ft at a base age of 

100 (fig. 47). Prior to treatment, the stand was 

largely occupied by trees between 2 and 8 inches 

d.b.h. (fig. 48), with a QMD of 8.6 inches and a 

canopy base height of 14 ft (table 28). This stand 

was high in density at 338 trees per acre but 

with regions of significant density (>600 trees 

per acre) and horizontal continuity, with a single 

clump containing more than 3,200 trees. More 

than 98 percent of the stand was classified within 

20 ft of the nearest tree, meaning there were 

nearly no openings in the stand pre-treatment 

(table 29; figs. 49 and 50). The stand underwent 

4 simulated thinnings to a residual basal area of 

40 ft2 acre-1 (9.2 m2 ha-1).

Pre-treatment: Moderate-High Density Multi-Storied Stand

Figure 48—Pre-treatment distribution of 

trees per acre by 2-inch d.b.h. size 

classes for a moderate-high density multistoried stand.

Figure 47—Pre-treatment 

forest structure of a 

moderate-high density multistoried stand (photo: Emma 

Vakili, U.S. Forest Service).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 43

Table 29—Pre-treatment clump size distribution 

for the moderate-high density multi-storied 

stand.

Clump size #/Acre % TPA % BA

Single tree 0.5 0.1 0.2

2–4 Trees 0.5 0.3 0.9

5–9 Trees 0.1 0.1 0.3

10–15 Trees 0.0 0.0 0.0

>15 Trees 0.2 99.4 98.6

Table 28—Pre-treatment stand characteristics 

for the moderate-high density multi-storied 

stand. Stand level mean with min, max, 

and coefficient of variation in parentheses 

calculated from 64 plots of 6.5 tenths x 6.5 

tenths acre (82 x 82 ft).

Pre-treatment

Trees per acre 338 (123–602; 31%)

BA 130 ft2 (76–326; 28%)

QMD 8.6 in (5.7–17.3; 20%)

Tree height 36 ft (24–54; 16%)

Canopy base height 14 ft (9–21; 18%)

Crown biomass 15.86 tons acre-1

Figure 50—a) Virtual rendering 

of stand structure over the 

9.9 acre area, where trees 

are scaled according to 

inventoried height, d.b.h., 

CBH, and crown widths and 

are colored following the 

clustering scheme above 

(fig. 49), b) profile view of 

stand structure.

Figure 49—Visualization of the 9.9 acre 

stand, where the tree spatial pattern is 

projected with crown radii that represent 

field measured crown diameters, and 

where clump sizes are portrayed by 

different dot colors. The background 

coloring represents the distance to the 

nearest tree from the center of a 3.28 

ft (1 m) cell grid (or the empty space 

function).

b

a
44 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Thin From Below to 40 ft2 ac-1 of 

Basal Area

Traditional thin from below approaches tend 

to homogenize stand structure and in this case 

resulted in all trees less than 14 inches d.b.h. 

being removed (fig. 51), leading to a substantial 

increase to stand level QMD from 8.6 to 16.8 

inches, decreasing the relative variability of 

QMDs seen throughout the stand (table 30). 

Following completion of the thinning, the stand’s 

canopy continuity was greatly reduced in terms of 

cover shifting from 94 to 52 percent. These reductions are consistent with the decreases seen in the 

means and ranges of the stand’s tree density and 

basal area, where the mean and range of trees per 

acre were reduced to roughly one-twelfth of the 

pre-treatment condition (table 30).

Table 30—Changes in stand characteristics for the 

moderate-high density multi-storied stand after a 

thin from below treatment. Stand level mean with 

min, max, and coefficient of variation in parentheses 

calculated from 64 plots of 6.5 tenths x 6.5 tenths 

acre (82 x 82 ft).

Pre Post

Trees per acre 338 

(123–602; 31%)

24

(0–52; 47%)

BA per acre 130 ft2

(76–326; 52%)

40 ft2

(0–259; 83%)

QMD 8.6 in 

(5.7–17.3; 49%)

16.8 in 

(0–32.4; 18%)

Total height 36 ft 

(24–54; 16%)

65 ft 

(48- 104; 9%)

CBH 14 ft 

(9–21; 18%)

24 ft 

(12–41; 25%)

SDI 236 55

Crown biomass 15.86 tons acre-1 4.77 tons acre-1

Figure 51—Comparison of trees per acre distribution 

within 2-inch d.b.h. size classes for the thin from 

below treatment.

Table 31—Changes in clump size distribution for the moderate-high density multistoried stand after the thin from below treatment.

Pre Post

Clump size #/Acre % TPA % BA #/Acre % TPA % BA

Single tree 0.5 0.1 0.2 11.3 47.9 44.0

2–4 Trees 0.5 0.3 0.9 4.6 52.1 56.0

5–9 Trees 0.1 0.1 0.3 0.0 0.0 0.0

10–15 Trees 0.0 0.0 0.0 0.0 0.0 0.0

>15 Trees 0.2 99.4 98.6 0.0 0.0 0.0

• Single tree and 2-4 Tree clumps went from 

being represented by 0.1 to 100 percent of the 

trees in the stand, with the largest clump only 

containing 25 trees (table 31).

• The thinning also resulted in an increase to the 

number of and mean size of stand opening, 

with openings now reaching 75 ft in radius 

(figs. 52 and 53).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 45

Figure 52—Visualization of the 9.9 acre 

stand, where the tree spatial pattern is 

projected with crown radii that represent 

field measured crown diameters, and 

where clump sizes are portrayed by 

different dot colors. The background 

coloring represents the distance to the 

nearest tree from the center of a 3.28 

ft (1 m) cell grid (or the empty space 

function).

Figure 53—a) Virtual rendering of stand 

structure over the 9.9 acre area, 

where trees are scaled according to 

inventoried height, d.b.h., CBH, and 

crown widths and are colored following 

the clustering scheme above (fig. 52), 

b) profile view of stand structure.

b

a
46 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Random Thinning to 40 ft2 ac-1 of 

Basal Area

Proportional thinning throughout the diameter 

range or random thinning approaches tend to 

preserve the pre-existing stand structure and 

in this case removed about 60 percent of trees 

from each diameter class (fig. 54), causing only 

a small shift in stand level QMD from 8.6 to 

8.7 inches, but increasing the range of QMDs 

Figure 54—Comparison of trees per acre distribution 

within 2-inch d.b.h. size classes for the random 

thinning.

Table 32—Changes in stand characteristics for the 

moderate-high density multi-storied stand after 

a random thinning treatment. Stand level mean 

with min, max, and coefficient of variation in 

parentheses calculated from 64 plots of 6.5 tenths 

x 6.5 tenths acre (82 x 82 ft).

Pre Post

Trees per acre 338 

(123–602; 31%)

99

(26–188; 39%)

BA per acre 130 ft2

(76–326; 52%)

40 ft2

(9–149; 39%)

QMD 8.6 in 

(5.7–17.3; 49%)

8.7 in 

(4.7–21.7; 29%)

Total height 36 ft 

(24–54; 16%)

36 ft 

(22– 65; 23%)

CBH 14 ft 

(9–21; 18%)

14 ft 

(7–29; 25%)

SDI 236 71

Crown biomass 15.86 tons acre-1 4.83 tons acre-1

Table 33—Changes in clump size distribution for the moderate-high density multistoried stand after the random thinning treatment.

Pre Post

Clump size #/Acre % TPA % BA #/Acre % TPA % BA

Single tree 0.5 0.1 0.2 7.2 7.2 11.0

2–4 Trees 0.5 0.3 0.9 6.3 17.5 20.8

5–9 Trees 0.1 0.1 0.3 2.7 17.5 19.4

10–15 Trees 0.0 0.0 0.0 0.5 5.6 5.8

>15 Trees 0.2 99.4 98.6 1.4 52.1 43.1

seen throughout the stand (table 32). Following 

completion of the thinning, the stand’s canopy 

cover shifted from 94 to 60 percent and there 

was a substantial increase in the local vertical 

structure variability going from approximately 

17 to 24 percent variation. The horizontal continuity of the stand was reduced as a result of 

the thinning, resembling the range of openings 

created by spatially explicit thinnings.

• The thinning reduced the proportion of trees 

located in more than 15 tree clumps from 99 

to 52 percent, with strong increases in the 

proportion of trees in the smaller clump sizes 

(table 33).

• Following the thinning, about 15 percent of 

the stand would now be classified as being in 

openings, but the mean size of these openings 

was only about 0.04 acres in size (figs. 55 and 

56).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 47

Figure 55—Visualization of the 9.9 acre stand, 

where the tree spatial pattern is projected 

with crown radii that represent field 

measured crown diameters, and where 

clump sizes are portrayed by different dot 

colors. The background coloring represents 

the distance to the nearest tree from the 

center of a 3.28 ft (1 m) cell grid (or the 

empty space function).

Figure 56—a) Virtual rendering of stand 

structure over the 9.9 acre area, where 

trees are scaled according to inventoried 

height, d.b.h., CBH, and crown widths 

and are colored following the clustering 

scheme above (fig. 55), b) profile view of 

stand structure.

b

a
48 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Moderately Clumped Thinning to 

40 ft2 ac-1 of Basal Area

A moderate clumping scenario following 

individual, clump, and opening thinning approach attempts to increase the number of small 

clumps, and in this case resulted in a proportional removal of trees throughout the range of 

diameters (fig. 57) and a small increase in stand 

level QMD from 8.6 to 8.9 inches (table 34). 

Figure 57—Comparison of trees per acre distribution 

within 2-inch d.b.h. size classes for the moderately 

clumped thinning treatment.

Table 34—Changes in stand characteristics for the 

moderate-high density multi-storied stand after a 

moderately clumped thinning treatment. Stand level 

mean with min, max, and coefficient of variation in 

parentheses calculated from 64 plots of 6.5 tenths x 

6.5 tenths acre (82 x 82 ft).

Pre Post

Trees per acre 338 

(123–602; 31%)

96

(39–188; 33%)

BA per acre 130 ft2

(76–326; 52%)

41 ft2

(10–139; 47%)

QMD 8.6 in 

(5.7–17.3; 49%)

8.9 in 

(5.9–18.1; 23%)

Total height 36 ft 

(24–54; 16%)

36 ft 

(24– 54; 19%)

CBH 14 ft 

(9–21; 18%)

14 ft 

(8–21; 22%)

SDI 236 72

Crown biomass 15.86 tons acre-1 5.10 tons acre-1

Following completion of the thinning, the 

stand’s canopy cover shifted from 94 to 60 percent and the variability in local basal area nearly 

doubled from 28 to 47 percent. Local variability 

in both horizontal and vertical tree structures 

saw small increases, which is in line with the 

goals of spatially explicit prescriptions. The 

horizontal continuity of the stand was greatly 

reduced as a result of the thinning.

• The stand went from being dominated by a 

single large clump to having Single tree and 

clumps up to 9 trees occupy 83 percent of the 

trees in the stand (table 35).

• The thinning only resulted in a small shift in 

the proportion of the stand within openings, 

going from approximately 2 to 7 percent 

(figs. 58 and 59).

Table 35—Changes in clump size distribution for the moderate-high density multistoried stand after the moderately clumped thinning treatment.

Pre Post

Clump size #/Acre % TPA % BA #/Acre % TPA % BA

Single tree 0.5 0.1 0.2 27.2 28.5 31.8

2–4 Trees 0.5 0.3 0.9 10.3 32.4 31.2

5–9 Trees 0.1 0.1 0.3 2.9 22.4 22.2

10–15 Trees 0.0 0.0 0.0 0.8 10.9 8.5

>15 Trees 0.2 99.4 98.6 0.3 5.7 6.4
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 49

Figure 59—a) Virtual rendering of stand 

structure over the 9.9 acre area, where 

trees are scaled according to inventoried 

height, d.b.h., CBH, and crown widths 

and are colored following the clustering 

scheme above (fig. 58), b) profile view of 

stand structure.

Figure 58—Visualization of the 9.9 acre 

stand, where the tree spatial pattern is 

projected with crown radii that represent 

field measured crown diameters, and where 

clump sizes are portrayed by different dot 

colors. The background coloring represents 

the distance to the nearest tree from the 

center of a 3.28 ft (1 m) cell grid (or the 

empty space function).

b

a
50 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Highly Clumped Thinning to 

40 ft2 ac-1 of Basal Area

Under the high clumping scenario following 

individual, clump, and opening thinning, the goal 

was to distribute the stand’s structure throughout 

the range of clump sizes. In this case, it resulted 

in a proportional removal of trees throughout 

the range of diameters (fig. 60) and no change in 

stand level QMD, but increased the range of local 

QMDs in the stand (table 36). Following completion of the thinning, the stand’s canopy cover 

shifted from 94 to 54 percent. This treatment 

provided the greatest increase in local variability 

when all horizontal and vertical measures are considered in line with the goals of spatially explicit 

prescriptions.

Figure 60—Comparison of trees per acre distribution 

within 2-inch d.b.h. size classes for the highly 

clumped thinning.

Table 36—Changes in stand characteristics for the 

moderate-high density multi-storied stand after 

a highly clumped thinning treatment. Stand level 

mean with min, max, and coefficient of variation in 

parentheses calculated from 64 plots of 6.5 tenths x 

6.5 tenths acre (82 x 82 ft).

Pre Post

Trees per acre 338 

(123–602; 31%)

106

(39–266; 40%)

BA per acre 130 ft2

(76–326; 52%)

43 ft2

(5.1–140; 58%)

QMD 8.6 in 

(5.7–17.3; 49%)

8.6 in 

(4.3–19.0; 27%)

Total height 36 ft 

(24–54; 16%)

36 ft 

(19– 56; 21%)

CBH 14 ft 

(9–21; 18%)

14 ft 

(7–21; 23%)

SDI 236 77

Crown biomass 15.86 tons acre-1 5.29 tons acre-1

Table 37—Changes in clump size distribution for the moderate-high density 

multi-storied stand after the highly clumped thinning treatment.

Pre Post

Clump size #/Acre % TPA % BA #/Acre % TPA % BA

Single tree 0.5 0.1 0.2 10.4 9.9 10.5

2–4 Trees 0.5 0.3 0.9 8.7 29.2 33.5

5–9 Trees 0.1 0.1 0.3 5.5 34.8 33.4

10–15 Trees 0.0 0.0 0.0 10.6 15.9 13.4

>15 Trees 0.2 99.4 98.6 0.6 10.2 9.1

• The stand went from being dominated by 

a single large clump to having a balanced 

distribution of clump sizes that are well spread 

across the stand (table 37).

• The thinning resulted in the most significant 

increase in number and mean size of 

openings, with several openings reaching 

radii of approximately 45 ft, or openings of 

approximately 1/6 acre (figs. 61 and 62).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 51

Figure 61—Visualization of the 9.9 acre 

stand, where the tree spatial pattern is 

projected with crown radii that represent 

field measured crown diameters, and where 

clump sizes are portrayed by different dot 

colors. The background coloring represents 

the distance to the nearest tree from the 

center of a 3.28 ft (1 m) cell grid (or the 

empty space function).

Figure 62—a) Virtual rendering of stand 

structure over the 9.9 acre area, where 

trees are scaled according to inventoried 

height, d.b.h., CBH, and crown widths 

and are colored following the clumping 

scheme above (fig. 61), b) profile view of 

stand structure.

b

a
52 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Summary: Moderate-High Density 

Multi-Storied Stand

Prior to treatment, this stand had regions of 

significant density (>600 trees per acre) and 

horizontal continuity, with a single cluster 

containing more than 13,200 trees. The stand 

was dominated by trees less than 8 inches 

d.b.h. (64 percent of trees) and had a QMD of 

8.6 inches (table 38). The stand also had only 

Table 38—Changes in stand characteristics for the moderate-high density multi-storied stand after various thinning treatments. Stand level 

mean with min, max, and coefficient of variation in parentheses calculated from 64 plots of 6.5 tenths x 6.5 tenths acre (82 x 82 ft).

Pre-treatment Thin from below Random thinning Moderately clumped Highly clumped

Trees per acre 338 (123–602) 24 (0–52) 99 (26–188) 96 (39–188) 106 (39–266)

BA per acre 130 ft2 (76–326) 40 ft2 (0–259) 40 ft2 (9–149) 41 ft2 (10–139) 43 ft2 (5–140)

QMD 8.6 in (5.7–17.3) 16.8 in (0–32.4) 8.7 in (4.7–21.7) 8.9 in (5.9–18.1) 8.6 in (4.3–19.0)

Mean tree height 36 ft (24–54) 65 ft (48–104) 36 ft (22–65) 36 ft (24–54) 36 ft (19–56)

Canopy base height 14 ft (9–21) 24 ft (12–41) 14 ft (7–29) 14 ft (8–21) 14 ft (7–21)

Crown biomass 15.86 tons acre-1 4.77 tons acre-1 4.83 tons acre-1 5.10 tons acre-1 5.29 tons acre-1

one opening that would meet the 20 ft requirement for stand openings (figs. 63–65).

• Following the simulated treatments, mean 

stand density was greatly reduced while 

increasing the relative variability of tree 

density in all but the thin from below 

simulations. This increase in variability is 

an important indicator of meeting horizontal 

heterogeneity treatment objectives.

• The moderate clumping treatment struggled 

to meet both the basal area prescription and 

the allocation of trees into the prescribed 

clump sizes, potentially indicating that 

multiple entries may be needed to meet stand 

objectives.

Table 39—Changes in clump size distribution for each of the thinning treatments for the moderate-high density multi-storied stand.

Pre-treatment Thin from below Random thinning Moderately clumped Highly clumped

Clump size #/Acre %TPA %BA #/Acre %TPA %BA #/Acre %TPA %BA #/Acre %TPA %BA #/Acre %TPA %BA

Single tree 0.5 0.1 0.2 11.3 47.9 44.0 7.2 7.2 11.0 27.2 28.5 31.8 10.4 9.9 10.5

2–4 Trees 0.5 0.3 0.9 4.6 52.1 56.0 6.3 17.5 20.8 10.3 32.4 31.2 8.7 29.2 33.5

5–9 Trees 0.1 0.1 0.3 0.0 0.0 0.0 2.7 17.5 19.4 2.9 22.4 22.2 5.5 34.8 33.4

10–15 Trees 0.0 0.0 0.0 0.0 0.0 0.0 0.5 5.6 5.8 0.8 10.9 8.5 10.6 15.9 13.4

>15 Trees 0.2 99.4 98.6 0.0 0.0 0.0 1.4 52.1 43.1 0.3 5.7 6.4 0.6 10.2 9.1
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 53

Figure 63—Virtual rendering of stand 

structure over the 9.9 acre area, where 

trees are scaled according to inventoried 

height, d.b.h., CBH, and crown widths.
54 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

The pre-treatment stand condition placed 

most of the trees into a single very large and 

continuous cluster of trees, containing more than 

98 percent of the stand’s trees and basal area 

(table 39).

• The thin from below simulations drastically 

shifted the stand toward Single tree or small 

clumps, while the random thinning left a 

majority of the stand (>50 percent) in clumps 

of more than 15 trees.

• Following the simulated treatments 

(Moderately and Highly Clumped), the 

structures within the stand were reallocated 

throughout all of the tree clump sizes, 

providing a balance of these structures to help 

meet many restoration, wildlife, and fuels 

treatment objectives.

• The two treatments differ in that the moderate 

clumping scenario resulted in less local 

variability in tree density, size, and vertical 

structure than the highly clumped treatment.

Prior to treatment, only 3 percent of the stand 

was classified in openings (>6 m from a tree) with 

the largest opening being approximately 1/50 acre 

(figs. 64 and 65; table 40).

• Thin from below had the greatest shift in 

distribution, putting 54 percent of the stand 

into openings, which was dominated by a 

6.2 acre opening that snakes throughout the 

stand. Additionally, it led to the most simplistic 

vertical structure.

• The moderate clumping treatment resulted in 

the smallest shift in opening distribution with 

only about 13 percent of the stand being in 

openings.

• Both random thinning and high clumping 

resulted in similar distributions of stand 

openings, with about 19 percent of the stand 

being within openings. The differences in these 

treatments is that the random thinning left over 

50 percent of the trees in the stand in clumps 

of more than 15 trees and had a smaller range 

of opening sizes. The high clumping treatment 

distributed the remnant stand structures 

throughout all of the clump sizes and created a 

greater diversity of opening sizes.

Table 40—Changes in clump and opening area for each 

of the thinning treatments for the moderate-high density 

multi-storied stand.

Clump area (acres)

Mean Median Min Max

Pretreatment 0.63 0.01 0.007 7.84

Below 0.015 0.014 0.007 0.026

Random 0.038 0.019 0.007 0.481

Moderate 0.017 0.014 0.007 0.070

High 0.018 0.015 0.007 0.064

Opening area (acres)

n Mean Median Min Max

Pretreatment 2 – – 0.019 0.019

Below 10 0.715 0.086 0.019 6.232

Random 24 0.065 0.058 0.019 0.150

Moderate 10 0.031 0.029 0.012 0.055

High 23 0.083 0.067 0.019 0.230
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 55

Figure 64—Visualization of the 

9.9 acre stand, where the tree 

spatial pattern is projected with 

crown radii that represent field 

measured crown diameters, and 

where clump sizes are portrayed 

by different dot colors. The 

background coloring represents 

the distance to the nearest tree 

from the center of a 3.28 ft (1 m) 

cell grid (or the empty space 

function), in order to portray 

openings. 

Figure 65—Treatment effects 

on the distribution of the 

distance to the nearest 

tree.
56 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

This stand was composed of 87 percent 

ponderosa pine, with small portions of the stand 

occupied by Colorado blue spruce, quaking 

aspen, and Gambel oak. The site is typical of 

many mid-elevation (about 8,400 ft above sea 

level) ponderosa pine stands with a site index 

of 90 ft at a base age of 100 (fig. 66). Prior to 

treatment, the stand was largely occupied by 

trees between 2 and 8 inches d.b.h. (fig. 67) and 

had a QMD of 11.4 inches with a canopy base 

height of 20 ft (table 41). This stand was at a 

moderately high density of 204 trees per acre 

but with regions of significant density (>500 

trees per acre) and horizontal continuity, with 

a single clump containing more than 450 trees 

(table 42). Only 5 percent of the stand would 

be considered in openings with a radius greater 

than 20 ft (figs. 68 and 69). The stand underwent 

4 simulated thinnings to a residual basal area of 

40 ft2 acre-1 (9.18 m2

 ha-1).

Pre-treatment: High Density Multi-Storied Stand

Figure 66 —Pre-treatment 

forest structure of a high 

density multi-storied stand 

(photo: Emma Vakili, U.S. 

Forest Service).

Table 41—Pre-treatment stand characteristics for 

the high density multi-storied stand. Stand level 

mean with min, max, and coefficient of variation in 

parentheses calculated from 64 plots of 6.5 tenths 

x 6.5 tenths acre (82 x 82 ft).

Pre-treatment

Trees per acre 204 (58–537; 48%)

BA 131 ft2 (15–249; 53%)

QMD 11.4 in (5.2–20.1; 53%)

Tree height 40 ft (24–72; 24%)

Canopy base height 20 ft (13–38; 25%)

Crown biomass 15.21 tons acre-1

Figure 67—Pre-treatment distribution of trees per 

acre by 2-inch d.b.h. size classes of a high density 

multi-storied stand.

Table 42—Pre-treatment clump size distribution for 

the high density multi-storied stand.

Clump size #/Acre % TPA % BA

Single tree 3.6 1.8 4.4

2–4 Trees 3.6 4.7 8.9

5–9 Trees 1.1 3.5 3.7

10–15 Trees 0.6 3.7 7.5

>15 Trees 2.1 86.3 75.5
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 57

Figure 68—Visualization of the 9.9 acre 

stand, where the tree spatial pattern is 

projected with crown radii that represent 

field measured crown diameters, and where 

clump sizes are portrayed by different dot 

colors. The background coloring represents 

the distance to the nearest tree from the 

center of a 3.28 ft (1 m) cell grid (or the 

empty space function).

Figure 69—a) Virtual rendering of stand 

structure over the 9.9 acre area, 

where trees are scaled according to 

inventoried height, d.b.h., CBH, and 

crown widths and are colored following 

the clustering scheme above (fig. 68), 

b) profile view of stand structure. b

a
58 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Thin From Below to 40 ft2 ac-1 of 

Basal Area

Thin from below approaches tend to homogenize stand structure and in this case resulted in 

all trees less than 20 inches d.b.h. being removed 

(fig. 70) and an increase in stand level QMD 

from 11.4 to 20.1 inches (table 43), significantly 

reducing the local variation in QMD. Following 

Figure 70—Comparison of trees per acre distribution 

within 2-inch d.b.h. size classes for the thin from 

below treatment.

Table 43—Changes in stand characteristics for the high 

density multi-storied stand after a thin from below 

treatment. Stand level mean with min, max, and 

coefficient of variation in parentheses calculated from 

64 plots of 6.5 tenths x 6.5 tenths acre (82 x 82 ft).

Pre Post

Trees per acre 204 

(58–537; 48%)

11 

(0–45; 63%)

BA per acre 131 ft2

(15–249; 53%)

41 ft2

(0–193; 14%)

QMD 11.4 in 

(5.2–20.1; 53%)

20.1 in 

(0.0–31.9; 14%)

Total height 40 ft 

(24–72; 24%)

102 ft 

(76–129; 12%)

CBH 20 ft 

(13–38; 25%)

55 ft 

(18–76; 28%)

Crown 

biomass 15.21 tons acre-1 4.62 tons acre-1

Table 44—Changes in clump size distribution for the high density 

multi-storied stand after the thin from below treatment.

Pre Post

Clump size #/Acre % TPA % BA #/Acre % TPA % BA

Single tree 3.6 1.8 4.4 7.7 73.8 74.3

2–4 Trees 3.6 4.7 8.9 1.1 26.2 25.7

5–9 Trees 1.1 3.5 3.7 0 0 0

10–15 Trees 0.6 3.7 7.5 0 0 0

>15 Trees 2.1 86.3 75.5 0 0 0

completion of the thinning, the stand’s canopy 

cover shifted from 94 to 49 percent. There was 

also a general reduction in the level of local variation in horizontal and vertical forest structures.

• Single tree and 2–4 Tree clumps went from 

being represented by 6.5 to 100 percent of 

the trees in the stand, with no clumps larger 

than 4 trees remaining after the treatment 

(table 44).

• The thinning also resulted in an increase in the 

number of and mean size of stand openings, 

with openings now reaching more than 100 

ft in radius or an opening of 3/4 of an acre in 

size (figs. 71 and 72).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 59

Figure 71—Visualization of the 9.9 acre 

stand, where the tree spatial pattern is 

projected with crown radii that represent 

field measured crown diameters, and where 

clump sizes are portrayed by different dot 

colors. The background coloring represents 

the distance to the nearest tree from the 

center of a 3.28 ft (1 m) cell grid (or the 

empty space function).

Figure 72—a) Virtual rendering of stand 

structure over the 9.9 acre area, where 

trees are scaled according to inventoried 

height, d.b.h., CBH, and crown widths 

and are colored following the clustering 

scheme above (fig. 71), b) profile view of 

stand structure.

b

a
60 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Random Thinning to 40 ft2 ac-1 of 

Basal Area

Proportional thinning throughout the diameter 

range or random thinning approaches tend to 

preserve the pre-existing stand structure and 

in this case removed about 67 percent of trees 

from each diameter class (fig. 73), slightly 

shifting stand level QMD from 11.4 to 10.9 

inches and a decrease in local variation in QMD 

Figure 73—Comparison of trees per acre distribution 

within 2-inch d.b.h. size classes for the random 

thinning treatment.

Table 45—Changes in stand characteristics for the high 

density multi-storied stand after a random thinning 

treatment. Stand level mean with min, max, and 

coefficient of variation in parentheses calculated from 

64 plots of 6.5 tenths x 6.5 tenths acre (82 x 82 ft).

Pre Post

Trees per acre 204 

(58–537; 48%)

63 

(0–188; 51%)

BA per acre 131 ft2

(15–249; 53%)

40 ft2

(0–124; 77%)

QMD 11.4 in 

(5.2–20.1; 53%)

10.9 in 

(0.0–24.1; 35%)

Total height 40 ft 

(24–72; 24%)

40 ft 

(21–89; 51%)

CBH 20 ft 

(13–38; 25%)

21 ft

(10–46; 34%)

Crown biomass 15.21 tons 

acre-1 4.76 tons acre-1

Table 46—Changes in clump size distribution for the high density 

multi-storied stand after the random thinning treatment.

Pre Post

Clump size #/Acre % TPA % BA #/Acre % TPA % BA

Single tree 3.6 1.8 4.4 10.3 16.3 29.8

2–4 Trees 3.6 4.7 8.9 8.9 37.2 41.1

5–9 Trees 1.1 3.5 3.7 1.1 12.3 10.8

10–15 Trees 0.6 3.7 7.5 0.8 15.0 9.8

>15 Trees 2.1 86.3 75.5 0.4 19.3 8.5

(table 45). Following completion of the thinning, 

the stand’s canopy cover shifted from 94 to 

57 percent, and increases to both local horizontal 

and vertical forest structure variability were 

observed.

• The stand went from being dominated by 

very large clumps (>200 trees) to having a 

wide range of structures from Single trees to 

clumps of more than 15 trees (table 46).

• Half of the post-treatment trees were placed 

into 1–4 tree clumps, yet accounted for more 

than 70 percent of the basal area, indicating 

that smaller trees were allocated to clumps of 

5–20 trees (table 46).

• The thinning increased the number and mean 

size of openings, with openings now reaching 

50 ft in radius or 1/5 of an acre in size 

(figs. 74 and 75).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 61

Figure 74—Visualization of the 9.9 acre 

stand, where the tree spatial pattern is 

projected with crown radii that represent 

field measured crown diameters, and 

where clump sizes are portrayed by 

different dot colors. The background 

coloring represents the distance to the 

nearest tree from the center of a 3.28 ft 

(1 m) cell grid (or the empty space 

function).

Figure 75—a) Virtual rendering of stand 

structure over the 9.9 acre area, 

where trees are scaled according to 

inventoried height, d.b.h., CBH, and 

crown widths and are colored following 

the clustering scheme above (fig. 74), 

b) profile view of stand structure.

b

a
62 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Moderately Clumped Thinning to 

40 ft2 ac-1 of Basal Area

A moderate clumping scenario following 

individual, clump, and opening thinning approach attempts to increase the number of 

small clumps, and in this case it resulted in a 

proportional removal of trees throughout the 

range of diameters (fig. 76) and a small increase 

in stand level QMD from 11.4 to 11.9 inches, 

but it increased the variability in local QMDs 

(table 47). Following completion of the thinning, 

Figure 76—Comparison of trees per acre distribution 

within 2-inch d.b.h. size classes for the moderately 

clumped thinning treatment.

Table 47—Changes in stand characteristics for the 

high density multi-storied stand after a moderately 

clumped thinning treatment. Stand level mean with 

min, max, and coefficient of variation in parentheses 

calculated from 64 plots of 6.5 tenths x 6.5 tenths 

acre (82 x 82 ft).

Pre Post

Trees acre 204 

(58–537; 48%)

51 

(7–142; 60%)

BA per acre 131 ft2

(15–249; 53%)

48 ft2

(0.5–193; 64%)

QMD 11.4 in 

(5.2–20.1; 53%)

11.9 in 

(1.6–20.5; 64%)

Total height 40 ft 

(24–72; 24%)

43 ft 

(14–74; 32%)

CBH 20 ft 

(13–38; 25%)

22 ft 

(9–40; 34%)

Crown biomass 15.21 tons 

acre-1 5.04 tons acre-1

Table 48—Changes in clump size distribution for the high density 

multi-storied stand after the moderately clumped thinning 

treatment.

Pre Post

Clump size #/Acre % TPA % BA #/Acre % TPA % BA

Single tree 3.6 1.8 4.4 16.6 32.6 28.3

2–4 Trees 3.6 4.7 8.9 5.3 28.6 33.8

5–9 Trees 1.1 3.5 3.7 1.5 19.9 16.0

10–15 Trees 0.6 3.7 7.5 0.5 11.7 16.2

>15 Trees 2.1 86.3 75.5 0.2 7.2 5.8

the stand’s canopy cover shifted from 94 to 

54 percent and all measures of local horizontal 

and vertical forest structure increased, which 

is in line with the goals of spatially explicit 

prescriptions.

• The stand went from being dominated by large 

clumps to having Single tree and clumps from 

2–9 trees representing the majority of the 

stand (table 48).

• The thinning also resulted in an increase in 

the number and mean size of stand openings, 

with many long sinuous openings now 

reaching radii of more than 50 ft or openings 

of approximately 1/5 to 1/3 acre in size 

(figs. 77 and 78).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 63

Figure 77—Visualization of the 9.9 acre 

stand, where the tree spatial pattern is 

projected with crown radii that represent 

field measured crown diameters, and where 

clump sizes are portrayed by different dot 

colors. The background coloring represents 

the distance to the nearest tree from the 

center of a 3.28 ft (1 m) cell grid (or the 

empty space function).

Figure 78—a) Virtual rendering of stand 

structure over the 9.9 acre area, 

where trees are scaled according to 

inventoried height, d.b.h., CBH, and 

crown widths and are colored following 

the clustering scheme above (fig. 77), 

b) profile view of stand structure.

b

a
64 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Highly Clumped Thinning to 

40 ft2 ac-1 of Basal Area

Under the high clumping scenario following 

individual, clump, and opening thinning, the goal 

was to distribute the stand’s structure throughout 

the range of clump sizes. In this case, it resulted 

in a proportional removal of trees throughout the 

range of diameters (fig. 79) and a small decrease in 

stand level QMD but provided the greatest increase 

Figure 79—Comparison of trees per acre distribution 

within 2-inch d.b.h. size classes for the highly 

clumped thinning treatment.

Table 49—Changes in stand characteristics for the high 

density multi-storied stand after a highly clumped 

thinning treatment. Stand level mean with min, max, and 

coefficient of variation in parentheses calculated from 64 

plots of 6.5-tenths x 6.5 tenths acre (82 x 82 ft).

Pre Post

Trees per acre 204 

(58–537; 48%)

48 

(0–136; 67%)

BA per acre 131 ft2

(15–249; 53%)

44 ft2

(0–193; 76%)

QMD 11.4 in 

(5.2–20.1; 53%)

10.2 in 

(0.0–26.2; 76%)

Total height 40 ft 

(24–72; 24%)

44 ft 

(24–85; 34%)

CBH 20 ft 

(13–38; 25%)

21 ft 

(3–40; 33%)

Crown biomass 15.21 tons acre-1 4.80 tons acre-1

Table 50—Changes in clump size distribution for the high density multistoried stand after the highly clumped thinning treatment.

Pre Post

Clump size #/Acre % TPA % BA #/Acre % TPA % BA

Single tree 3.6 1.8 4.4 4.6 9.8 15.5

2–4 Trees 3.6 4.7 8.9 5.4 30.6 31.9

5–9 Trees 1.1 3.5 3.7 2.5 36.2 23.8

10–15 Trees 0.6 3.7 7.5 0.6 15.7 22.5

>15 Trees 2.1 86.3 75.5 0.2 7.7 6.3

to local variability of QMDs (table 49). Following 

completion of the thinning, the stand’s canopy 

cover shifted from 94 to 54 percent and resulted 

in the highest level of local variability in trees and 

basal area per acre.

• The stand went from being dominated by large 

clumps to having a balanced distribution of 

clump sizes (table 50).

• The thinning resulted in a significant increase 

in the number and mean size of openings, with 

several reaching radii of more than 80 ft or 

openings of approximately 1/2 to 3/4 acre in size 

(figs. 80 and 81).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 65

Figure 80—Visualization of the 9.9 acre stand, where the tree spatial 

pattern is projected with crown radii that represent field measured 

crown diameters, and where clump sizes are portrayed by different dot 

colors. The background coloring represents the distance to the nearest 

tree from the center of a 3.28 ft (1 m) cell grid (or the empty space 

function).

Figure 81—a) Virtual rendering of 

stand structure over the 9.9 acre 

area, where trees are scaled 

according to inventoried height, 

d.b.h., CBH, and crown widths and 

are colored following the clumping 

scheme above (fig. 80), b) profile 

view of stand structure.

b

a
66 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Summary: High Density 

Multi-Storied Stand

Prior to treatment, this stand had regions of 

significant density (>500 trees per acre) and 

horizontal continuity. The stand was dominated 

by trees less than 8 inches d.b.h. (65 percent of 

trees) and had a QMD of 11.4 inches. Outside 

of a few smaller pre-existing openings, most 

canopy openings were less than 13 ft in radius 

(table 51; fig. 82).

Table 51—Changes in stand characteristics for the high density multi-storied stand after various thinning treatments. Stand level mean 

with min and max in parentheses from 64 plots of 6.5 tenths x 6.5 tenths acre (82 x 82 ft).

Pre-treatment Thin from below Random thinning Moderately clumped Highly clumped

Trees per acre 204 (58–537) 11 (0–45) 63 (0–188) 51 (7–142) 48 (0–136)

BA per acre 131 ft2 (15–249) 41 ft2 (0–193) 40 ft2 (0–124) 48 ft2 (0.5–193) 44 ft2 (0–193)

QMD 11.4 in (5.2–20.1) 20.1 in (0.0–31.9) 10.9 in (0.0–24.1) 11.9 in (1.6–20.5) 10.2 in (0.0–26.2)

Mean tree height 40 ft (24–72) 102 ft (76–129) 40 ft (21–89) 43 ft (14–74) 44 ft (24–85)

Canopy base height 20 ft (13–38) 55 ft (18–76) 21 ft (10–46) 22 ft (9–40) 21 ft (3–40)

Crown biomass 15.21 tons acre-1 4.62 tons acre-1 4.76 tons acre-1 5.04 tons acre-1 4.80 tons acre-1

• Following all of the simulated treatments, 

mean stand density was greatly reduced 

while increasing the relative variability of 

tree density in all but the thin from below 

simulations. This increase in variability is 

an important indicator of meeting horizontal 

heterogeneity treatment objectives.

• Under all of the simulations, except the thin 

from below, we also see significant increases 

in the relative level of vertical heterogeneity 

throughout the stand.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 67

Figure 82—Virtual rendering of stand structure over the 

9.9 acre area, where trees are scaled according to 

inventoried height, d.b.h., CBH, and crown widths.
68 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

The pre-treatment stand condition placed 

most of the trees into a few very large and continuous clump of trees, containing more than 85 

percent of the stands trees and 75 percent of the 

basal area (table 52).

• The thin from below and random thinning 

simulations shifted most of the stand into 

Single tree or small clumps (>70%).

Table 52—Changes in clump size distribution for each of the thinning treatments for the high density multi-storied stand.

Pre-treatment Thin from below Random thinning Moderately clumped Highly clumped

Clump size #/Acre % TPA % BA #/Acre % TPA % BA #/Acre % TPA % BA #/Acre % TPA % BA #/Acre % TPA % BA

Single tree 3.6 1.8 4.4 7.7 73.8 74.3 10.3 16.3 29.8 16.6 32.6 28.3 4.6 9.8 15.5

2–4 Trees 3.6 4.7 8.9 1.1 26.2 25.7 8.9 37.2 41.1 5.3 28.6 33.8 5.4 30.6 31.9

5–9 Trees 1.1 3.5 3.7 0 0 0 1.1 12.3 10.8 1.5 19.9 16.0 2.5 36.2 23.8

10–15 Trees 0.6 3.7 7.5 0 0 0 0.8 15.0 9.8 0.5 11.7 16.2 0.6 15.7 22.5

>15 Trees 2.1 86.3 75.5 0 0 0 0.4 19.3 8.5 0.2 7.2 5.8 0.2 7.7 6.3

• Following the simulated spatially explicit 

treatments (Moderately and Highly Clumped), 

the structures within the stand were 

reallocated throughout all of the tree clump 

sizes, providing a balance of these structures 

to help meet many restoration, wildlife, and 

fuels treatment objectives.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 69

Prior to treatment, only 8 percent of the stand 

was within openings (>6 m from a tree), with the 

largest opening being less than 1/10 acre (Figs. 83 

and 84; table 53).

• Following treatment, all of the stands experienced 

a significant shift toward more open conditions 

and larger opening sizes.

• Thin from below simulation created the greatest 

shift in distribution, so that 76 percent of the 

stand area was considered to be an opening. 

To achieve this opening distribution, it was 

necessary to thin the stand to 11 trees per acre.

Table 53—Changes in clump and opening area for 

each of the thinning treatments for the high density 

multi-storied stand.

Clump area (acres)

Mean Median Min Max

Pretreatment 0.077 0.018 0.008 1.112

Below 0.014 0.013 0.010 0.027

Random 0.022 0.015 0.007 0.175

Moderate 0.018 0.014 0.007 0.068

High 0.019 0.014 0.008 0.068

Opening area (acres)

n Mean Median Min Max

Pretreatment 9 0.048 0.043 0.029 0.089

Below 3 – 0.140 0.024 8.816

Random 28 0.123 0.072 0.019 0.449

Moderate 25 0.200 0.085 0.19 0.790

High 8 0.842 0.123 0.029 5.873

• Both random thinning and moderate clumping 

simulations provided more moderate shifts in 

the distribution of stand openings, with about 27 

percent of the stands being within openings and 

the median opening size doubling.

• The high clumping simulation provided a balance 

between shifting the distribution and creating 

heterogeneous forest structures, with 53 percent 

of the stand being within openings and median 

opening size tripling the pre-treatment condition
70 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017.

Figure 84—Treatment 

effects on the distribution 

of the distance to the 

nearest tree.

Figure 83—Visualization of the 

9.9 acre stand, where the tree 

spatial pattern is projected with 

crown radii that represent field 

measured crown diameters, 

and where clump sizes are 

portrayed by different dot 

colors. The background coloring 

represents the distance to the 

nearest tree from the center of 

a 3.28 ft (1 m) cell grid (or the 

empty space function), in order 

to portray openings. 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-365. 2017. 71

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