Crown Area Equations for 13

Species of Trees and Shrubs in

Northern California and

Southwestern Oregon

Fabian C.C. Uzoh Martin W. Ritchie

United States

Department of

Agriculture

Forest Service

Pacific Southwest

Research Station

Research Paper

PSW-RP-227-Web

1996
Abstract:

Uzoh, Fabian C.C.; Ritchie, Martin W. 1996. Crown area equations for 13 species of

trees and shrubs in northern California and southwestern Oregon. Res. Paper

PSW-RP-227-Web. Albany, CA: Pacific Southwest Research Station, Forest

Service, U.S. Department of Agriculture; 13 p.

The equations presented predict crown area for 13 species of trees and shrubs

which may be found growing in competition with commercial conifers during early

stages of stand development. The equations express crown area as a function of basal

area and height. Parameters were estimated for each species individually using

weighted nonlinear least square regression.

Retrieval terms: growth and yield, simulators

Authors

Fabian C.C. Uzoh and Martin W. Ritchie are Research Forester and Research

Statistician, respectively, in the Station’s Conifer Silviculture Research unit, 2400

Washington Avenue, Redding, CA 96001.

Acknowledgments

The data used in this analysis were provided by Dr. Robert J. Laacke of Pacific

Southwest Research Station, 2400 Washington Avenue, Redding, CA 96001.

Publisher:

Albany, California

Mailing address:

PO Box 245, Berkeley CA

94701-0245

510 559-6300

http://www.pswfs.gov

July 1996

Pacific Southwest Research Station

Forest Service

US Department of Agriculture
Crown Area Equations for 13 Species

of Trees and Shrubs in Northern

California and Southwestern Oregon

Fabian C.C. Uzoh Martin W. Ritchie

Contents

In Brief ...................................................................................................................... iii

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

Methods ..................................................................................................................... 2

Measurements ................................................................................................................................ 3

Analysis and Results ................................................................................................. 3

Concluding Discussion ............................................................................................. 4

References ............................................................................................................... 13

Pacific Southwest

Research Station

USDA Forest Service

Research Paper

PSW-RP-227-Web

July 1996
Uzoh, Fabian C.C.; Ritchie,

Martin W. 1996. Crown

area equations for 13 species of trees and shrubs in

northern California and

southwestern Oregon.

Res. Paper PSW-RP-227-

Web. Albany, CA: Pacific

Southwest Research

Station, Forest Service,

U.S. Department of

Agriculture; 13 p.

Retrieval Terms: growth and

yield, simulators

In Brief...

Growth and yield simulators are valuable tools in forest management

decision making. A number of simulators have been developed to meet

current management challenges. However, little attention has been given to

the impact of brush and non-commercial hardwood trees on stand dynamics.

This presents a serious problem when attempting to predict the early stages of

stand development where shrubs and sprouting hardwood trees may have a

significant impact on growth of commercial species. Crown area may be useful

as an index of the competition level. One means of estimating crown area is to

predict it as a function of variables which may be readily available in a

simulator, such as height or diameter. In this paper, we present crown area

equations for 13 species of plants common to southwestern Oregon and northern

California. Crown area is expressed as a function of stem basal area and height

for each plant. Parameters were estimated for each species individually using

weighted nonlinear least square regression. For the purpose of this study,

crown area is defined as the area of a vertical projection of the crown to a

horizontal plane.

In Brief...

USDA Forest Service Res. Paper PSW-RP-227-Web. 1996. iii
USDA Forest Service Res. Paper PSW-RP-227-Web. 1996. 1

Introduction

Growth and yield models are becoming one of the primary tools aiding

forest managers in decision making. Traditionally, modeling efforts have

focused on merchantable species. In the western United States, these are

primarily coniferous trees. As a result, very little modeling work has been done

on hardwood trees or shrubs.

There is increasing interest in simulators which are capable of predicting

growth for early seral stages of stand development. These simulators must

address the influence of shrubs and hardwood trees. One such model is

SYSTUM-1 (Ritchie and Powers 1993). In SYSTUM-1, competing vegetation is

quantified as an aggregate percent cover and height by species on each plot.

However, SYSTUM-1 is not responsive to changes in species composition on

tree growth. Furthermore, growth functions for percent cover and height are

not effective in representing response to release treatments. In order to address

this problem, stem growth models are being developed for shrubs and

hardwood trees in which crown area is expressed as a function of crown

volume. This work is part of a larger effort to develop a suite of functions which

will allow simulators to better respond to questions relating to the impact of

non-commercial species on growth of commercial conifers.

The objective of this study is to develop equations to predict crown

area as a function of plant height and basal diameter. Crown area and crown

cover values have been used in studies of biomass production (Martin and

others 1981; Mitchell and others 1987) as well as in predicting the competitive

effects of shrubs on tree growth (e.g. Dahms 1950; Oliver 1979). A crown area

function may help existing simulators such as SYSTUM-1 provide more reliable

predictions of shrub cover over time. For the purpose of this study, crown area

is defined as the area of a vertical projection of the crown to a horizontal plane.

This paper presents equations that predict crown area for the following

13 species of trees and shrubs: Vine maple (Acer circinatum [Pursh]), Manzanita

(green leaf) (Arctostaphylos patula [Adams]), Golden chinkapin (Castanopsis

chrysophylla [Dougl.] A.DC.), Whitethorn (mountain) (Ceanothus cordulatus),

Deerbrush (Ceanothus integerrimus [Hook. & Arn.]), Snowbrush (Ceanothus

velutinus [Dougl.]), Tanoak (Lithocarpus densiflorus [Hook and Arn.] Rehd.),

Black oak (Quercus kelloggii [Newb.]), Pacific madrone (Arbutus menziesii

[Pursh]), Bitter cherry (Prunus emarginata [Dougl.]), Pacific rhododendron

(Rhododendron macrophyllum [D. DON.]), Huckleberry (bush) (Vaccinium

ovalifolium [Smith]), and Bigleaf maple (Acer macrophyllum [Pursh]).

Introduction
2 USDA Forest Service Res. Paper PSW-RP-227-Web. 1996.

METHODS

The data for this study were collected from temporary plots in 29 plantations in

northern California and southwestern Oregon during the summers of 1987,

1988, and 1989 (fig. 1). The plantations were between 25 and 45 acres in size.

On each plantation, 30 plots (15 non-tree-centered and 15 tree-centered plots)

2.6 meters in radius were established systematically at 40-meter intervals along

a continuous transect that changed direction every 200 meters. The choice of

the initial starting point at each plantation was made by selection from a

random number table. Even digits (0,2,4, etc.) designated a tree-centered plot,

odd digits a vegetation plot.

When a tree-centered plot was chosen, the plot center was moved from

the transect center line to coincide with the location of the nearest seedling.

However, if there were no seedlings within 2.6 meters of the 40-meter mark on

the transect, the plot number was recorded, no other data taken, and the

transect continued. Plot type refers to whether the plot was tree-centered or

not. Data collected from the two types of plots were the same. A plant was

considered to be in the plot if the center of the plant where it emerged from the

ground was within 2.6 meters of plot center. For all plants in the plot, the data

were collected from the entire plant, including those parts that extended outside

the plot. Parts of a plant that did not emerge from the soil surface within the

plot were not measured. The only exception to this rule was during estimation

of percent cover (percent cover is the ocular estimation of percent of grasses and

forbs at each plot). The majority of the plants measured were shrub clumps

often from multi-stemmed individuals.

Figure 1—Location of plantations in

study area (northern California and

southwestern Oregon). Each location

may have more than one plantation.

Methods

0 100 200 300 400 Miles

0 100 200 300 400 Kilometers

35o
USDA Forest Service Res. Paper PSW-RP-227-Web. 1996. 3

Measurements

The following were recorded for each woody plant in a plot:

• Species,

• Distance in decimeters from the plot center to the center of the root

crown ( i.e., center of where the plant originates from the ground for

multi-stemmed individuals),

• Height (HCB) to base of crown (in meters),

• Long width of the crown (CWL) in decimeters,

• Width of the crown perpendicular to long width of the crown (CWS)

in decimeters,

•Diameter (D) of each stem 8 centimeters from the root collar or burl

(nearest cm), and

• Total height (HT) in meters.

Crown area (CA) in square meters is calculated by:

CA CWL CWS =××π /400

Plant basal area (BA) in square centimeters is calculated as:

where:

ns = number of stems per plant.

ANALYSIS AND RESULTS

We assumed that there is no plot effect, and we treated each individual plant as

if it were drawn at random from all possible plants. Two model forms were

considered:

CA a EXP HT b error =× − × + ( ( )) 1 [1]

[2]

where a, b, and c = regression coefficients. Because of the availability of height

measurements, and the difficulty of measuring basal area in shrubs, a model

using only height may be more desirable. Of these two, Eq. [2] had the lower

mean square error across species. Further, unweighted fit R2 values for equation

[1] ranged from .0603 to .6802 while R2

 values for Eq. [2] ranged from .4288 to

.9237. Also, a more generalized method of model comparison (AndersonSprecher 1994) was used to compare the two equations. Their GR2

 parameter is

an index of how much the full model (Eq. #2) improves over the reduced model

(Eq. #1). The values of GR2

 are presented in table 1. Given the values of R2 and

GR2

, Eq. [2] was chosen. The estimate of the coefficient of determination, R2, was

calculated using the formula: R2 = 1 - [SSE/CTSS], where SSE = Sum-of-squares

error about the equation; and CTSS = Corrected total sum of squares. The

estimate of was GR2 calculated using the formula: GR2 = 1 - [RSS(full)/

RSS(reduced)], where RSS(full) = Residual sum of squares about Eq. [2], and

RSS(reduced) = Residual sum of squares about Eq. [1]. This approach provides

a generalized R2

 value which implies a comparison with the reduced model CA

= a + error (Anderson-Sprecher 1994).

Crown area is modeled as a function of stem basal area and height.

Preliminary plotting of crown area against the independent variables revealed

the following:

Analysis and Results

BA D i

ns

i = × =1

4 2 Σ( /) π

CA a BA EXP HT error = × ×− × + b ( ) ( ( )) c 1
4 USDA Forest Service Res. Paper PSW-RP-227-Web. 1996.

• Crown area increased with basal area and height but not in a linear

fashion.

• There was a strong relationship between crown area and basal area.

• There appeared to be increasing variance of crown area over both

basal area and height.

Initially, parameters were estimated for all 13 species using unweighted

nonlinear least squares regression. Plotting of the residuals indicated that the

values of the residuals were increasing over the estimate. To improve parameter

estimates, we employed an iteratively reweighted nonlinear least squares fit.

We tried two weights to homogenize variance. We weighted by 1/exp ( ) ected CA and

1/expected(CA). These two weights correspond to assumptions that variance of

residuals increased with expected(CA) and square of expected(CA) respectively.

Residual plots and Furnival’s (1961) index were used to compare unweighted

regression with each of the weighted regressions to determine which weight

best met the assumptions of homogeneity of variance and normality of the error

term. In all cases, the weighted regressions provided the lowest index of fit. The

weight of 1/expected(CA) provided what appeared to be the best fit for 7 of the 13

species. In most instances, convergence occurred before six iterations. Tables 2

and 3 present the regression coefficients and associated statistics for the

modeling data set for Eq. [2]. Figures 2-14 show resulting functions over basal

area for five levels of height. Comparison of these plots with those from

unweighted fits did not reveal any dramatic statistically significant difference.

The SAS (SAS Institute Inc. 1987) statistical software package was used to

estimate the regression parameters.

CONCLUDING DISCUSSION

These equations are intended primarily for the purpose of predicting missing

data values for data describing the structure of young plantations. Crown area

is a variable which may be useful in describing levels of competition in such

stands (e.g., Tappeiner and others 1984). Since height growth is easily measured

on shrubs and hardwoods in young stands, a crown area using only height as a

predictor is preferable. However, we found substantial improvements using

Concluding Discussion

Table 1—Unweighted models GR2 values for the 13 non-conifer species.

Species GR2

Vine maple (Acer circinatum [Pursh]) 0.727

Manzanita (green leaf) (Arctostaphylos patula [Adams]) 0.373

Golden chinkapin (Castanopsis chrysophylla [Dougl.] A.DC.) 0.549

Whitethorn (mountain) (Ceanothus cordulatus) 0.495

Deerbrush (Ceanothus integerrimus [Hook. & Arn.]) 0.441

Snowbrush (Ceanothus velutinus [Dougl.]) 0.728

Tanoak (Lithocarpus densiflorus [Hook and Arn.] Rehd.) 0.479

Black oak (Quercus kelloggii [Newb.]) 0.705

Pacific madrone (Arbutus menziesii [Pursh]) 0.656

Bitter cherry (Prunus emarginata [Dougl.]) 0.408

Pacific rhododendron (Rhododendron macrophyllum [D. DON.]) 0.877

Huckleberry (bush) (Vaccinium ovalifolium [Smith]) 0.228

Bigleaf maple (Acer macrophyllum [Pursh]) 0.809

 GR2= an index of how much the full model (Eq. #2) improves over the reduced model (Eq. #1).
USDA Forest Service Res. Paper PSW-RP-227-Web. 1996. 5

total basal area and height in the model. We believe the models using height alone

were inadequate for predicting crown area; therefore we did not present the results

of these fits.

In the chosen model, crown area increases monotonically with increasing

basal area and height. This may provide for reasonable behavior beyond the range of

the data in our sample. However, we have no basis for assessing the robustness of

these equations to extrapolation. Although the model chosen contains an asymptote

which is conditional on the value of BA, for most of the species, the sampled data

range is well below any implied asymptote. Therefore no conclusions may be drawn

about maximum crown area from these equations.

The species depicted in figures 2-14 show substantial variability. The

variability between species is to be expected given the wide range in form of these

species. The tanoak and madrone models are very similar within the ranges of data

common to both species. However, the tanoak sampled in this study covered a much

wider range in basal area than was found among the sampled madrone.

 Table 2—Crown area model parameter estimates for the 13 non-conifer species for Eq. [2].

Standard errors appear in parentheses beneath each coefficient.

Parameters estimates

Species Weights Na b c S R2

Vine maple 1/expected(CA) 85 0.040789 0.650943 -2.198338 0.0234 0.788

(0.00476) (0.04801) (0.935723)

Manzanita 1/expected(CA) 1172 0.148292 0.729466 -0.636752 0.0099 0.827

(0.00356) (0.00768) (0.189866)

Chinkapin 1/expected(CA) 22 0.125473 0.450952 -1.668147 0.0527 0.766

(0.04451) (0.08102) (0.175212)

Whitethorn 1/expected(CA) 1179 0.159864 0.739687 -1.608342 0.0273 0.669

(0.00707) (0.00951) (0.368471)

Deerbrush 1/expected(CA) 1957 0.324670 0.666789 -0.416567 0.0201 0.625

(0.00569) (0.00163) (0.002064)

Snowbrush 1/expected(CA) 64 1.053987 0.705213 -0.144486 1.2971 0.825

(0.00163) (0.00427) (0.013631)

Tanoak 1/expected(CA) 1081 1.532414 0.455347 -0.142682 0.0747 0.786

(0.00567) (0.00097) (0.001591)

Black oak 1/expected(CA) 163 1.294278 0.532337 -0.102492 0.0167 0.923

(0.00215) (0.00196) (0.011933)

Madrone 1/expected(CA) 143 0.692053 0.526578 -0.194721 0.0837 0.850

(0.00215) (0.00332) (0.007936)

Bitter cherry 1/expected(CA) 596 0.19766 0.740537 -0.503159 0.0219 0.761

(0.00355) (0.00162) (0.003152)

Rhododendron 1/expected(CA) 53 0.03509 0.904504 -2.011825 0.1475 0.982

(0.01441) (0.00335) (0.009857)

Huckleberry 1/expected(CA) 282 0.18478 0.603152 -0.914294 0.0388 0.750

(0.00881) (0.00132) (0.004025)

Bigleaf maple 1/expected(CA) 108 0.05086 0.566284 -1.989914 0.0432 0.476

(0.00596) (0.00136) (0.002046)

N = number of observations

S = standard deviation of residuals

CA = crown area
6 USDA Forest Service Res. Paper PSW-RP-227-Web. 1996.

The relationship between crown area and height and basal area may be

influenced by origin of the plant. Among these plantations, shrubs and

hardwoods have developed both from seed and sprouts after fire or release

treatment, and we make no effort here to distinguish between the two.

Parameter estimates may be influenced by the particular mix of seed and

sprout origin of individuals in the data set. Model performance may be

enhanced if this factor is explicitly included in the model.

Table 3—Summary statistics for data used in crown area equations

Species Minimum Maximum Mean Std Dev

Vine maple

Height (m) 0.200 3.100 0.969 0.682

Basal area (cm2) 0.785 19.635 3.070 2.966

Crown area (m2

) 0.008 0.236 0.052 0.050

Manzanita

Height (m) 0.100 2.500 0.715 0.414

Basal area (cm2) 0.785 6280 26.859 30.633

Crown area (m2) 0.008 5.655 0.547 0.815

Chinkapin

Height (m) 0.200 1.000 0.582 0.274

Basal area (cm2) 0.7854 66.759 9.948 16.066

Crown area (m2) 0.008 0.707 0.174 0.207

Whitethorn

Height (m) 0.100 1.900 0.921 0.336

Basal area (cm2) 0.785 275.675 31.679 34.524

Crown area (m2) 0.008 12.370 1.148 1.627

Deerbrush

Height (m) 0.100 5.500 1.426 0.906

Basal area (cm2) 0.785 231.692 17.768 23.236

Crown area (m2

) 0.008 12.252 0.984 1.451

Snowbrush

Height (m) 0.030 4.670 2.192 1.389

Basal area (cm2) 0.785 451.607 70.269 93.90

Crown area (m2) 0.00008 47.967 6.159 8.393

Tanoak

Height (m) 0.04 6.060 1.354 1.369

Basal area (cm2) 0.785 633.031 30.485 66.246

Crown area (m2) 0.00008 19.400 1.354 2.452

Black oak

Height (m) 0.100 3.700 0.718 0.795

Basal area (cm2) 0.785 228.551 14.923 20.780

Crown area (m2) 0.008 4.673 0.389 0.779

Madrone

Height (m) 0.050 8.100 1.239 1.477

Basal area (cm2) 0.785 113.097 12.620 22.099

Crown area (m2) 0.00008 5.697 0.582 0.983

Bitter cherry

Height (m) 0.100 4.000 0.866 0.699

Basal area (cm2) 0.785 71.471 6.161 9.396

Crown area (m2) 0.0079 3.793 0.289 0.532

Rhododendron

Height (m) 0.100 2.010 1.165 0.457

Basal area (cm2) 0.785 230.122 36.766 47.401

Crown area (m2) 0.00008 5.091 0.815 1.023

Huckleberry

Height (m) 0.050 2.090 0.918 0.392

Basal area (cm2) 0.785 179.071 23.723 28.213

Crown area (m2) 0.00008 4.823 0.650 0.646

Bigleaf maple

Height (m) 0.200 3.100 0.980 0.905

Basal area (cm2) 0.785 16.493 2.247 3.704

Crown area (m2) 0.008 0.251 0.056 0.259
USDA Forest Service Res. Paper PSW-RP-227-Web. 1996. 7

0.30

0.24

0.18

0.12

0.06

0.00

0.00 5.00 10.00

Basal area (cm2)

HT = 3 m

HT = 0.9 m

HT = 0.5 m

HT = 0.25 m

HT = 0.09 m

Crown area (m2)

15.00 20.00

10.00

8.00

6.00

4.00

2.00

0.00

0.00 100.00 200.00

Basal area (cm2)

HT = 2 m

HT = 1.35 m

HT = 0.8 m

HT = 0.45 m

HT = 0.15 m

Crown area (m2)

300.00 400.00 500.00

Figure 2—Plot of fitted equation for

vine maple—crown area as a function

of height (m) and basal area (cm2).

Figure 3—Plot of fitted equation for

manzanita—crown area as a function

of height (m) and basal area (cm2

).
8 USDA Forest Service Res. Paper PSW-RP-227-Web. 1996.

1.00

0.80

0.60

0.40

0.20

0.00

0.00 10.00 50.00 20.00 30.00 40.00

Basal area (cm2)

HT = 3 m

HT = 0.95 m

HT = 0.55 m

HT = 0.25 m

HT = 0.09 m

Crown area (m2)

60.00 70.00

12.00

10.00

8.00

6.00

4.00

2.00

0.00

0.00 100.00

Basal area (cm2)

HT = 2.5 m

HT = 1 m

HT = 0.55 m

HT = 0.35 m

HT = 0.15 m

Crown area (m2)

200.00 300.00

Figure 4—Plot of fitted equation for

chinkapin—crown area as a function

of height (m) and basal area (cm2).

Figure 5—Plot of fitted equation for

whitethorn—crown area as a function

of height (m) and basal area (cm2).
USDA Forest Service Res. Paper PSW-RP-227-Web. 1996. 9

12.00

10.00

8.00

6.00

4.00

2.00

0.00

0.00 100.00 50.00

Basal area (cm2)

HT = 4 m

HT = 2.5 m

HT = 1.5 m

HT = 0.75 m

HT = 0.25 m

Crown area (m2)

150.00 250.00 200.00

40.00

30.00

20.00

10.00

0.00

0.00 180.00 90.00

Basal area (cm2)

HT = 4 m

HT = 3 m

HT = 2 m

HT = 1 m

HT = 0.5 m

Crown area (m2)

270.00 450.00 360.00

Figure 6—Plot of fitted equation for

deerbrush—crown area as a function

of height (m) and basal area (cm2).

Figure 7—Plot of fitted equation for

snowbrush—crown area as a function

of height (m) and basal area (cm2

).
10 USDA Forest Service Res. Paper PSW-RP-227-Web. 1996.

20.00

15.00

10.00

5.00

0.00

0.00 260.00 130.00

Basal area (cm2)

HT = 6 m

HT = 4 m

HT = 3 m

HT = 2 m

HT = 1 m

Crown area (m2)

390.00 650.00 520.00

6.00

5.00

4.00

3.00

2.00

1.00

0.00

0.00 46.00 92.00

Basasl area (cm2)

HT = 2.5 m

HT = 2 m

HT = 1.5 m

HT = 1 m

HT = 0.5 m

Crown area (m2)

138.00 230.00 184.00

Figure 8—Plot of fitted equation for

tanoak—crown area as a function of

height (m) and basal area (cm2).

Figure 9—Plot of fitted equation for

black oak—crown area as a function

of height (m) and basal area (cm2).
USDA Forest Service Res. Paper PSW-RP-227-Web. 1996. 11

7.00

6.00

5.00

4.00

3.00

2.00

1.00

0.00

0.00 40.00 20.00 60.00

Basal area (cm2)

HT = 8 m

HT = 5 m

HT = 3 m

HT = 2 m

HT = 1 m

Crown area (m2)

80.00 120.00 100.00

5.00

4.00

3.00

2.00

1.00

0.00

0.00 15.00 30.00

Basal area (cm2)

HT = 4 m

HT = 2 m

HT = 1.5 m

HT = 1 m

HT = 0.5 m

Crown area (m2)

45.00 75.00 60.00

Figure 10—Plot of fitted equation for

madrone—crown area as a function of

height (m) and basal area (cm2).

Figure 11—Plot of fitted equation for

bitter cherry—crown area as a function

of height (m) and basal area (cm2).
12 USDA Forest Service Res. Paper PSW-RP-227-Web. 1996.

5.00

4.00

3.00

2.00

1.00

0.00

0.00 60.00 120.00

Basal area (cm2)

HT = 2 m

HT = 0.8 m

HT = 0.4 m

HT = 0.2 m

HT = 0.1 m

Crown area (m2)

180.00 240.00

5.00

4.00

3.00

2.00

1.00

0.00

0.00 50.00 100.00

Basal area (cm2)

HT = 3 m

HT = 1.5 m

HT = 1 m

HT = 0.45 m

HT = 0.15 m

Crown area (m2)

150.00 200.00

Figure 12—Plot of fitted equation

for rhododendron—crown area as a

function of height (m) and basal area

(cm2).

Figure 13—Plot of fitted equation for

huckleberry—crown area as a function

of height (m) and basal area (cm2).
USDA Forest Service Res. Paper PSW-RP-227-Web. 1996. 13

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Martin, Robert E.; Frewing, David W.; McClanahan, James L. 1981. Average biomass of our

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Agriculture; 6 p.

Mitchell, J.E.; Bartling, P.N.S.; O’Brien, R. 1987. Understory cover-biomass relationships in the

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Ritchie, Martin W.; Powers, Robert F. 1993. User’s guide for SYSTUM-1 (Version 2.0): A

simulator of growth trends in young stands under management in California and Oregon.

Gen. Tech. Rep. PSW-GTR-147. Albany, CA: Pacific Southwest Research Station, Forest Service,

U.S. Department of Agriculture; 45 p.

SAS Institute Inc. 1987. Guide for personal computers, version 6 Edition. Cary, NC: SAS Institute

Inc.; 1028 p.

Tappeiner, John C.; Harrington, Timothy B.; Walstad, John D. 1984. Predicting recovery of tanoak

(Lithocarpus desiflorus) and Pacific madrone (Arbutus menziesii) after cutting or burning.

Weed Science 32: 413-417.

References

0.50

0.40

0.30

0.20

0.10

0.00

0.00 5.00 10.00

Basal area (cm2)

HT = 4 m

HT = 0.8 m

HT = 0.5 m

HT = 0.3 m

HT = 0.1 m

Crown area (m2)

15.00 20.00 Figure 14—Plot of fitted equation for

bigleaf maple—crown area as a function

of height (m) and basal area (cm2).
The Forest Service, U.S. Department of Agriculture, is responsible for Federal leadership in forestry.

It carries out this role through four main activities:

• Protection and management of resources on 191 million acres of National Forest System lands

• Cooperation with State and local governments, forest industries, and private landowners to help protect and

manage non-Federal forest and associated range and watershed lands

• Participation with other agencies in human resource and community assistance programs to improve living

conditions in rural areas

• Research on all aspects of forestry, rangeland management, and forest resources utilization.

The Pacific Southwest Research Station

• Represents the research branch of the Forest Service in California, Hawaii, American Samoa, and the

western Pacific.

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national origin, sex, religion, age, disability, political beliefs, and marital or familial status. (Not all prohibited

bases apply to all programs.) Persons with disabilities who require alternative means for communications

of program information (braille, large print, audiotape, etc.) should contact the USDA Office of Communications

at (202) 720-5881 (voice) or (202) 720-7808 (TDD). To file a complaint, write the Secretary of Agriculture,

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USDA is an equal employment opportunity employer.