United States

Department

of Agriculture

Forest Service

Rocky Mountain

Research Station

General Technical

Report RMRS-GTR-24

April 1999

Percent Canopy Cover

and Stand Structure

Statistics from the Forest

Vegetation Simulator

Nicholas L. Crookston

Albert R. Stage

Year 2140: old forest, single stratum

Canopy cover 74 percent

Year 2000: young forest, multistrata

Canopy cover 35 percent
Rocky Mountain Research Station

324 25th Street

Ogden, UT 84401

Contents_______________________

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

Percent Canopy Cover .............................................. 1

Stand Structure ......................................................... 3

FVS User Information ................................................ 7

StrClass Keyword................................................... 7

Event Monitor Use .................................................. 7

References ................................................................ 8

Appendix A: Computing Percent Canopy Cover ........ 9

Appendix B: Structural Classification Logic ............. 10

The Authors ____________________

Nicholas L. Crookston, Operations Research Analyst, is located at the Rocky Mountain Research

Station’s Forestry Sciences Laboratory, Moscow, ID.

He has been an active participant in the development

of the Forest Vegetation Simulator and its extensions

since 1978.

Albert R. Stage, Principal Mensurationist Emeritus,

was a leader in the development of the Forest Vegetation Simulator (also known as the Prognosis Model for

Stand Development) from the late 1960’s to his retirement from the Forest Service in 1996. He is an active

Forest Scientist at the Moscow Forestry Sciences Laboratory.

Abstract ___________________________________________

Crookston, Nicholas L.; Stage, Albert R. 1999. Percent canopy cover and stand structure statistics from

the Forest Vegetation Simulator. Gen. Tech. Rep. RMRS-GTR-24. Ogden, UT: U. S. Department of

Agriculture, Forest Service, Rocky Mountain Research Station. 11 p.

Estimates of percent canopy cover generated by the Forest Vegetation Simulator (FVS) are corrected

for crown overlap using an equation presented in this paper. A comparison of the new cover estimate

to some others is provided. The cover estimate is one of several describing stand structure. The structure

descriptors also include major species, ranges of diameters, tree heights, and heights to crown base for

as many as three significant height strata. From these data a structural class is assigned to the stand

using concepts defined by O’Hara and others (1996) with some subsequent enhancements. An FVS

keyword for applying and tuning the classification is documented along with information for FVS Event

Monitor users. An illustration of the structural classification is presented.

Keywords: FVS, Prognosis Model, crown cover, stand structure classification.

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Rocky Mountain Research Station Rocky Mountain Research Station

324 25th Street 3825 E. Mulberry Street

Ogden, UT 84401 Fort Collins, CO 80524
Introduction ____________________

Estimates of percent canopy cover generated by the

Forest Vegetation Simulator (FVS, also known as the

Prognosis Model for Stand Development, Stage 1973;

Wykoff and others 1982) are corrected for crown overlap using an equation presented in this paper. Canopy

cover percent has been identified as an indicator of

wildlife habitat for deer and elk (Thomas and others

1979) and is an output of the COVER and SHRUBS

Extension to FVS (Moeur 1985). A review of other

methods used to estimate canopy cover is presented

with comparisons to the new method. Appendix A

describes an algorithmic foundation for the new method

in detail.

Descriptors of stand structure have become an increasingly important consideration in prescribing

management actions to preserve wildlife habitat and

watershed values. Traditional FVS-generated outputs that describe the distribution of tree crowns

comprising a stand are available to users of the COVER

and SHRUBS extension. It reports the horizontal and

vertical crown distribution by 10 foot tall slices of the

canopy. A new report has been added to the FVS

output describing stand structure. New computations

are used to search for up to three distinct canopy

strata. For each significant stratum, the canopy cover,

major species, ranges of diameters, tree heights, and

heights to crown base are displayed. From these data

a structural class is assigned to the stand using concepts presented by O’Hara and others (1966) with

some subsequent enhancements. The new output report is illustrated below with a description of the

classification scheme and an overview of the supporting methods. Appendix B describes the classification

procedure in detail.

Features added to FVS that support using these new

tools are documented.

Percent Canopy Cover ___________

Stand percent canopy cover is the percentage of the

ground area that is directly covered with tree crowns.

Generally, the crown area of a tree is computed using

the formula for a circle as a function of crown radius.

Crown radius is estimated using formulae that are

different for each FVS geographic variant. The stand

percent crown cover without accounting for crown

overlap is computed using equation 1:

C ′ = 100( ∑ piai )A–1 (1)

where:

C ′ = percent canopy cover without accounting for

 overlap,

pi = trees per acre for the i

th sample tree,

ai = projected crown area for the i

th tree in ft2

/acre,

and

A = ft2/acre (43560).

To correct for crown overlap, D. Satterlund (in Moeur

1986, p. 344) suggested a computing procedure to estimate incremental additions of total canopy cover. Moeur

reported that Satterlund’s method produced estimates

13 percent greater than ground-based observations.

McGaughey, in a program called PERCOVE, (1997a)

computes percent canopy cover by first placing the

sample trees from an FVS projection onto a two dimensional grid. The crown circle of each tree is projected on

the grid and the proportion of the grid cells covered by

the circles of one or more trees is the proportion of

canopy cover. PERCOVE is capable of representing

several spatial distributions of trees, and it allows

users to specify canopy strata for which independent

estimates are computed.

Because PERCOVE must follow the execution of

FVS, the cover predictions it generates cannot be used

to guide management within FVS using rules evaluated by the FVS Event Monitor (Crookston 1990).

Percent Canopy Cover and

Stand Structure Statistics

from the Forest Vegetation

Simulator

Nicholas L. Crookston

Albert R. Stage

USDA Forest Service Gen. Tech. Rep. RMRS-GTR-24. 1999 1
Furthermore, as the density of the dot grid increases

(necessary for accurate estimates), the computer time

required to run the program can become burdensome.

To solve these problems, a new method was created

for use in FVS that is based on established techniques.

This approach is fast, accurate for a large class of

problems, and is part of FVS, so that the values

computed can be easily reported in FVS outputs and

made directly available in the Event Monitor. The new

method is now used in the COVER and SHRUBS

Extension to FVS (Moeur 1985).

The new method starts with the assumption that

trees are randomly located within the stand. This

assumption is midway between the extremes of equidistant spacing that might characterize the early distributions of stems in a plantation and the clumped

distributions that might characterize the latter stages

of a group-shelterwood applied repeatedly and to old

forests (Moeur 1993). To many observers this random

distribution of points in space appears clumpy. A

logical next step would be to generate a hypothetical

stem map, assign crowns, and project this map of

crowns onto a dot grid as done in PERCOVE. Appendix

A outlines a simplified stem map approach that does

not include exact stem placement. The technique has

several desirable properties outlined in the appendix.

Figure 1 displays the results using the simplified

stem map approach detailed in Appendix A plotted

against results using the equation that does not account for overlap (equation 1). The data for the comparison were produced using FVS to generate estimates of cover for 447 plots from the north Idaho

Forest Inventory Assessment data (Woudenberg and

Farrenkopf 1995). These data are a systematic sampling of conditions in north Idaho. Two estimates were

made for each plot, one for the inventory year and

another for 80 years later. Because no difference in

behavior between these two estimates was detected,

they are not distinguished in the figure.

The tight fit in figure 1 suggested a search for a

mathematical basis for the relationship. The analytical solution for the problem is available from the

theory of geometrical probability for randomly located

figures on a plane (Mack 1954, cited in Kendall and

Moran 1963, section 5.56 on p. 116). Furthermore, the

mathematical derivation holds for arbitrary convex

figures as well as for circles. Therefore, equations that

directly predict projected crown area regardless of

crown shape could be used in place of those that

assume the crowns are round. Equation 2 estimates

the percent canopy cover that accounts for overlap

(illustrated as the solid line in fig. 1).

C = 100 [1 – exp ( – .01 C ′ )] (2)

where:

C = percent canopy cover that accounts for

 overlap,

 and

C ′ = equation 1.

The same function is known in tree physiological

literature as the Beer-Lambert law—a commonly used

relation for calculating the absorption of light by

foliage (see Waring and Schlesinger 1985, p. 12; or see

Jones 1992, p. 15). In the Beer-Lambert law, foliage is

measured by leaf area index which replaces C′ in

equation 2. By introducing a coefficient other than

unity multiplying the argument of the exponential,

the Beer-Lambert law generalizes the mathematical

result to allow for non-random distributions. The ability to represent uniform distributions and some speFigure 1—Percent cover with overlap correction plotted over

cover without correction for 447 plots from the north Idaho FIA

data. The formula for the line is y = 100 [ 1 – exp(–x/100)]; see

equation 2.

2 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-24. 1999
cial attraction and repelling of canopies (so as to clump

trees or clump openings, as the case may be) would

depend on empirical relations not currently available.

Early experience shows that little accuracy would be

gained by including more refinements.

Figure 2 illustrates the relationship between estimates made with the new method (equation 2, the xaxis) and those made using PERCOVE (the y-axis).

The solid lines in the graphs are 1:1 reference lines.

PERCOVE estimates differ from estimates using

equation 2, and the differences are different for the

inventory-time estimates as compared to those made

after 80 years of simulated time. Regression lines

characterize these differences as follows: for the inventory time estimates the formula y = 3.27 + 0.927x

(r2

 = 0.91) is the best fit; for 80 years of simulated time

y = –4.65 + 1.03x (r2 = 0.99) fits best; and for all data

taken together y = 1.56 + 0.94x (r2 = 0.94) fits best.

It is clear that PERCOVE estimates are about 4

percent lower than those generated by our method

after 80 years of simulated time (versions of PERCOVE

prior to April 1998 have slightly higher bias). These

estimates have much lower variance compared to

those made at inventory time indicating that

PERCOVE benefits from increased sample sizes coincident with longer projections in FVS (attributable to

in-growth and the FVS record tripling logic).

Stand Structure _________________

The stand structural classification generated by

FVS is based on concepts described by O’Hara and

others (1996). Stage and others (1995) applied these

rules in analyses using FVS simulations to support the

Columbia River Basin Succession Model (CRBSUM,

Keane and others 1996). Stage (1997) has augmented

the classification rules to accommodate users concerns and experience with several alternative classification rules (Warren and others 1997). The method

presented in this report incorporates further refinements of these rules particularly for cases that arise

from sparse sampling of the stand and for poorly

stocked stands.

Users of structural classifications should be aware

that arbitrary division of essentially continuous variables, such as tree size, into broad classes can introduce undesirable artifacts in any planning process

(Haight and others 1991; Philpot and others 1998). We

recommend that continuous metrics of stand structure, like the number of strata and the size of trees in

the uppermost stratum, be retained along with the

class itself. The interpretation of the structural class

is aided when this additional information is part of the

analysis and is part of the classification output. Tuning the classification rules may be necessary to meet

the needs of a particular application. In general, the

structural classifications are best for interpretive purposes only.

The new Structural Statistics report (fig. 3) lists the

nominal d.b.h. and height, the heights of the tallest

and shortest trees, the crown base height, percent

Figure 2—Percent cover estimates from PERCOVE (McGaughey 1997a) plotted over those

made with equation 2, “A” for inventory time and “B” for 80 years later. PERCOVE estimates

are generally lower and the variance of the estimates made for the inventory year are higher

than the variance made for the stand after 80 years of simulated growth.

USDA Forest Service Gen. Tech. Rep. RMRS-GTR-24. 1999 3
canopy cover, major species, and a code indicating if

the stratum is invalid, valid, or the uppermost valid

stratum. For the stand, the number of valid strata,

percent canopy cover, and structural class are reported. These statistics are output for the stand before

simulated harvests and are repeated for post harvest

conditions when a harvest is simulated. Table 1 provides a summary of the data displayed in the report,

and table 2 defines the structural classes.

The canopy strata are initially defined by naturally

occurring gaps in the distribution of tree heights. The

gaps are found when the heights of two trees in a list

sorted by height differ by more than 30 percent of the

height of the taller and at least 10 feet. The two largest

gaps define three potential strata. If there is only one

gap, two potential strata are defined and if there are no

gaps, one potential stratum is defined. Trees in the

sorted list that have very small sampling probability

are skipped until the sum of the skipped trees’ sampling probability accounts for over two trees per acre.

Initially defined strata must have over 5 percent

canopy cover or they are rejected. Nominal stratum

d.b.h. and height are computed by averaging the nine

sample trees centered on the 70th percentile tree.

Once the strata are defined, the stand is classified as

bare ground, stand initiation, stem exclusion, understory reinitiation, young forest multistrata, old forest

single stratum, or old forest multistrata as a function

of the number of strata, the nominal d.b.h. of trees in

the strata, and stocking (table 2).

Appendix 2 contains a more detailed explanation of

the method used to produce the report. The classification logic can be tuned to achieve specific goals using

an FVS keyword that is described in the next section

titled “FVS User Information.”

Latham and others (1998) have presented a procedure for defining strata based on the crown length of

the single tallest tree in each succesive “stratum.” Our

search for naturally occurring gaps in the height

distribution attempts to focus on the outcome of disturbance-triggered pulses of regeneration—a concept

fundamental to the O’Hara classification.

O’Hara and others (1996) described two stem exclusion classes, open and closed canopy. In the method

presented in this report, this distinction is not made.

To capture O’Hara’s distinction, we classify stands

that meet the d.b.h. criteria for stem exclusion and

have low stocking as stand initiation. Stands with low

stocking are those with a stand density index (Reineke

1933) below 30 percent of the site-specific maximum

for the stand. Site-specific maximum stand density

indices are part of FVS.

Stands that would be old forest single stratum using

Stage and other’s (1995) rules are classified old forest

multistrata when the d.b.h. of the smallest tree in the

stratum is less than 3 inches. This rule is designed to

Figure 3—Example of a Structural Statistics report.

4 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-24. 1999
Table 1—Description of the data displayed in the Structural Statistics report.

Heading Description

Year FVS cycle year. Data reported are for the beginning of each cycle.

Rm Cd 0 = row reports the conditions prior to any simulated tree removals. 1 = row reports the conditions after any

simulated tree removals. If there are no removals in a cycle, then there is no row with a “Rm Cd” of 1.

DBH Nominal d.b.h. attributed to the stratum is computed as follows: a list of trees in the stratum is constructed by

accumulating trees in descending order of height until the sum of the cover is 95 percent (a percentage that does

not account for crown overlap). Percentiles in the distribution of crown areas are computed for all trees in this list

and the 70th percentile tree is found. The four trees larger and the four trees smaller than this 70th percentile tree

are selected. An average d.b.h. is computed for those 9 sample trees, weighting each tree record by the number

of trees per unit area represented by the record. When less than four larger or four smaller trees are found, just

those within the range are included in the average. This rule was devised in an attempt to mimic the selection of

trees seen in an aerial photograph under the assumption that the observers estimates would be more strongly

influenced by the larger trees.

Height, Nom Nominal height of the stratum. It is the weighted average heights of the same trees used to compute nominal d.b.h.

Height, Lg Height of the tallest tree in the stratum.

Height, Sm Height of the shortest tree in the stratum.

Crown Bas Weighted average height to crown base of all trees in the stratum.

Crown Cov Percent canopy cover, accounting for overlap, of trees in the stratum.

Major Sp1 Code for the tree species that accounts for the most crown cover of all trees in the stratum.

Major Sp2 Code for the tree species that accounts for the second most crown cover of all trees in the stratum.

CD Stratum status code, where 0 = the stratum is invalid, 1 = the stratum is valid, and 2 = the stratum is the uppermost

valid stratum.

NS The number of valid strata.

Tot Cov Percent canopy cover, accounting for overlap, of trees in the stand.

Struc Class Stand structural class (table 2).

Table 2—Definition of structural classes for the forest stand or patch (several parameters values can be set by the user, see

the StrClass keyword presented below).

Code Name Description of stand

0 = BG bare ground Less than 5 percent crown cover (StrClass field 2) and fewer than 200 trees per acre

(StrClass field 6).

1 = SI stand initiation Less than 5 percent crown cover (StrClass field 2) and greater than or equal to 200

trees per acre (StrClass field 6), or one stratum with an nominal d.b.h. less than 5 inches

(StrClass field 3; a stratum must have more than 5 percent crown cover to be

considered a valid stratum).

2 = SE stem exclusion One stratum with an nominal d.b.h. between 5 and 25 inches (StrClass fields 3 and 4).

This classification is changed to stand initiation if the stand density index is below 30

percent (StrClass field 7) of the maximum allowed for the stand.

3 = UR understory reinitiation Two strata with the uppermost having a d.b.h. between 5 and 25 inches (StrClass fields

3 and 4).

4 = YM young forest, multistrata Three or more strata with the uppermost having a d.b.h. between 5 and 25 inches

(StrClass fields 3 and 4).

5 = OS old forest, single stratum One stratum, over 25 inches d.b.h. (StrClass field 4), and smallest tree is greater than 3

inches d.b.h.

6 = OM old forest, multistrata Two or more strata, d.b.h. of uppermost stratum is over 25 inches d.b.h.; or one stratum,

over 25 inches d.b.h., and smallest tree is less than or equal to 3 inches d.b.h. (this

could alternatively be called an old forest, continuous stratum stand).

USDA Forest Service Gen. Tech. Rep. RMRS-GTR-24. 1999 5
Figure 4—SVS (McGaughey 1997b) illustration of a young forest, multistrata

stand in year 2000 (top) that is classified as old forest, single stratum by year 2140

(bottom). Note that fewer original large trees exist in the older stand and that the

distinct valid strata that existed earlier in the stand’s life have merged by year 2140.

6 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-24. 1999
better capture the situation where there are no breaks

in the canopy but where a wide range of diameters

indicates substantial continuing regeneration.

Figure 4 portrays a young forest, multistrata stand

using the Stand Visualization System (McGaughey

1997b) for the end of the first simulation cycle (year =

2000). Later, the stand is classified as old forest, single

stratum in the year 2140 because the initially distinct

strata have merged.

A comprehensive analysis of the classification logic

is beyond the scope of this report, but early experience

indicates that the procedure provides an informative

characterization of structural variation in an extensive inventory data set (Stage and others 1995). However, incorrect interpretations can occur if the other

structural statistics are ignored. User’s are encouraged to experiment with the parameters of the rules to

serve their particular needs.

Note that the classification can vary between runs of

FVS with different starting values of the random

number generator. This behavior is inherent in any

classification system based on statistics sensitive to

random variation such as average d.b.h. of a subset of

trees. When the stratum d.b.h. is near the class boundary, the classification of the stand in one class versus

another is sensitive to the interaction between the

arbitrary rules and the variation inherent in the sample

data and in the processes of growth and regeneration.

FVS User Information ____________

StrClass Keyword

Use the StrClass Keyword to cause the table of stand

structural class statistics to be printed, to set some of

the parameters of the structural classification, or

both. This keyword conforms to the standard FVS

usage rules.

StrClass Request calculation of structural classification by FVS and that the results be made

available to the Event Monitor (Crookston

1990).

Field 1: A nonzero entry causes FVS to print the

table of structural statistics; default is 1.

Field 2: The minimum percent cover that must be

exceeded for a potential stratum to qualify

as a valid stratum; default is 5 percent.

Field 3: The d.b.h. boundary separating seedling/

sapling-sized trees from pole-sized trees,

default is 5 inches.

Field 4: The d.b.h. boundary separating pole-sized

trees from large trees that may be considered old, default is 25 inches.

Field 5: The percentage of a tree’s height that is

used to define the minimum gap size, default is 30 percent.

Field 6: Minimum trees per acre that must be exceeded for a stand that has less than 5

percent cover to be classified stand initiation rather than bare ground (default is 200

trees per acre, which implies an average

spacing of about 15 feet).

Field 7: The percentage of the maximum stand density index that must be exceeded for a stand

to be classified stem exclusion rather than

stand initiation, default is 30 percent.

Event Monitor Use

When the StrClass keyword is used, thereby triggering the classification logic, the following Event Monitor variables are automatically defined by FVS:

BSClass The before-thinning structural class code,

see table 1.

ASClass The after-thinning structural class code,

see table 1.

BStrDbh The before-thinning nominal d.b.h. of the

uppermost stratum.

AStrDbh The after-thinning nominal d.b.h. of the

uppermost stratum.

BCanCov The before-thinning percent canopy cover

for the stand.

ACanCov The after-thinning percent canopy cover for

the stand.

The Event Monitor contains an often used function

called SpMcDBH (Crookston 1990, p. 19). Since the

introduction of this function, it has been enhanced to

include more arguments. With the introduction of the

new percent canopy cover, this function has been

enhanced further to compute the cover for any subset

of the trees in the stand, including the subset of all

trees. The subset is defined by the arguments to the

function. The current definition of this function is as

follows:

SpMcDBH (arg1,...,arg8) Returns one of seven attributes for a subset of the trees. The attribute depends on the value of the first argument:

1 = trees per acre

2 = basal area per acre

3 = total cubic volume/acre

4 = total board foot volume/acre

5 = quadratic mean diameter

6 = average height

7 = percent canopy cover

The subset of trees is defined by the remaining seven

arguments:

arg2 = the numeric species code for the trees in the

subset. A zero indicates all species are

included.

USDA Forest Service Gen. Tech. Rep. RMRS-GTR-24. 1999 7
arg3 = the tree-value class for trees included in the

subset. A zero indicates trees of all treevalue classes are included (codes 1, 2, and 3

are defined).

arg4 = to be included in the subset, the tree’s d.b.h.

must be greater than or equal to this value.

arg5 = to be included in the subset, the tree’s d.b.h.

must be less than this value.

arg6 = to be included in the subset, the tree’s height

must be greater than or equal to this value.

arg7 = to be included in the subset, the tree’s height

must be less than this value.

arg8 = code 0 for live trees, code 1 for recent mortality, or code 2 for harvested trees.

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of Agriculture, Forest Service, Intermountain Research Station.

222 p.

Woudenberg, Sharon W.; Farrenkopf, Thomas O. 1995. The Westwide

forest inventory data base: user’s manual. Gen. Tech. Rep. INTGTR-317. Ogden, UT: U.S. Department of Agriculture, Forest

Service, Intermountain Research Station. 67 p.

Wykoff, W. R.; Crookston, N. L.; Stage, A. R. 1982. User’s guide to

the Stand Prognosis Model. Gen. Tech. Rep. INT-133. Ogden, UT:

U.S. Department of Agriculture, Forest Service, Intermountain

Forest and Range Experiment Station. 112 p.

8 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-24. 1999
Appendix A: Computing Percent

Canopy Cover __________________

The simplified grid method used to compute canopy

cover percent while accounting for overlap follows the

procedure outlined here. After running the algorithm,

the fundamental underlying mathematical relationship described in equation 2 was found to represent

the logic of the algorithm. The algorithm is presented

as evidence that the equation is appropriate.

Accept the following definitions:

percentCover is the percent canopy cover,

crareai is crown area per acre of sample tree record i

grid is a vector of 1000 real values indexed with the

letter k,

full is the number of square units of crown area to fill

one member of grid (when the units are feet and

acres, the value of full is 43560/1000 = 43.560 ft2),

ix is a random integer between 1 and 1000.

Follow this procedure.

For each tree i {

remain = crareai / full

while (remain > 0) {

define a new ix

k = ix

if (remain > 1) {

remain = remain – 1

gridk = 1 }

else if (gridk < 1) {

gridk = gridk + (( 1 – gridk ) * remain)

remain = 0}}}

percentCover = 0.1 Σ gridk

Note that grid cells are represented by real numbers

rather than binary bits that have the value 1 when the

cell contains some projected canopy cover and the

value 0 when the cell contains no canopy cover. In this

case, the proportion of a grid cell covered by canopy is

stored. If a sample tree projects less than full cover,

the proportion is accumulated. This is often the case in

FVS when a tree has a very small sampling probability

or after several years of simulated mortality reduced

the sampling probability. In a bit map approach, such

trees are either lost because they project less canopy

than represented by the bit, they are over accounted

for because the bit is turned on regardless of the

amount of cover represented by the bit, or another

random number is needed to see if the bit should be

turned on or not.

Overlap is accounted for by not letting a grid cell

contain more than full units of canopy cover. If a single

grid cell is selected twice, the crowns, or some portion

thereof, are defined to be overlapping. When remain

and gridk are both less than 1, a tree record’s canopy,

or some portion thereof, is not sufficient to fill a cell.

The method used for this case is the same used by

Moeur (1986) except that Sutterland’s rule applied to

the total canopy rather than one thousandth.

The simplified grid method assumes that the distribution of trees in space is random, but only to the

resolution of the grid cell. When two trees are in the

same grid cell, the assumption of some overlap implies

that they must be near each other. The smaller the

trees are, the closer they must be if their crowns

overlap even a fractional amount. However, the actual

spatial arrangement of the trees is never actually

inferred as is the case with a bit map approach,

thereby avoiding complications arising from tree stems

occupying the same point.

The simplified grid method accounts for all the

crown area of each tree in the sample. In a bit map

approach, part of the crown area for a boundary tree

may be lost by extending outside the grid, causing

underestimates of percent canopy cover. Bit map approaches can make up for this lost crown by placing

that portion that falls outside of the map somewhere

inside the map’s edge. Corners of the map present

complications that can lead to inaccurate results if

ignored. Our method avoids this issue and accounts for

the complete crown area.

USDA Forest Service Gen. Tech. Rep. RMRS-GTR-24. 1999 9
Appendix B: Structural

Classification Logic _____________

Five parameters, which can be changed by using the

StrClass keyword in FVS, are used in the classification

rules. They are defined as follows:

Parameter Field on StrClass

name Role of parameter keyword

cmin Minimum percent crown cover 2

that must be exceeded for a

potential stratum to be considered a significant stratum;

default = 5 percent crown cover

dpole Nominal d.b.h. that defines the 3

break point between seedling/

sapling-sized trees and polesized trees; default is 5 inches.

dlarge Nominal d.b.h. that defines the 4

break point between pole- and largesized trees; default is 25 inches.

pht Percentage of a sample tree’s height 5

that defines the minimum size of a

gap between the top of sample tree

and the top of the next shorter

sample tree. That is, a gap must

be equal to or larger than this gap

size to be considered true gap;

default is 30 percent.

tmin Minimum number of trees per acre 6

that must be exceeded for a stand

that has less than cmin cover to be

classified stand initiation rather than

bare ground; default is 200 trees.

pSDImax Percentage of the maximum stand 7

density index that must be exceeded

for a stand to be classified stem exclusion rather than bare ground.

Classification proceeds through the following steps:

1. If there are no sample trees, then the stand is bare

ground.

2. A list of sample tree records, each of which represent over 0.00001 trees per acre, is constructed.

3. If there is only one sample tree record in the list

(a rare event), then the following rules apply:

a) If the sample tree’s canopy covers less than

cmin of the ground, then the stand is classified bare

ground if the sample tree represents less than tmin

trees, and otherwise the stand is classified as stand

initiation.

b) If the sample tree’s canopy covers over cmin of

the ground (this can happen if the sample tree represents many trees per acre, if it is a large tree, or both),

and its diameter is less than dpole, then the stand is

classified stand initiation.

c) If the sample tree’s canopy covers over cmin of

the ground and its diameter is greater than or equal to

dpole and less than dlarge, then the stand is classified

stem exclusion. This classification is changed to stand

initiation if the stand density index is below pSDImax

of the maximum SDI allowed for the stand.

d) If the sample tree’s canopy covers over cmin of

the ground and its diameter is greater than or equal to

dlarge, then the stand is classified old forest single

stratum.

4. Find the two largest gaps in the distribution of

tree heights to define boundaries of potential strata. In

the list of trees sorted by descending order of heights,

the two largest gaps are located using these rules:

a) A gap between a tree and the next smaller tree

must be larger than a minimum gap size. The minimum gap size is a percentage (pht) of the height of the

taller tree or 10 feet, whichever is greater. For example, if pht is 30 percent, and the larger tree is 100

foot tall, then the gap size must be at least 30 feet.

Consider another example where the larger tree is 20

foot tall. Because the 30 percent rule gives 6 feet, the

minimum gap size between a 20 foot tall tree and the

next smaller tree would be set to 10 feet because 10 feet

is greater than 6 feet. The indices of the two largest

gaps are recorded.

b) An additional rule is used during the search for

gaps. If the next smaller sample tree represents less

than two trees per acre, the program skips it and looks

to the tree that is smaller than it, and so on, until the

sum of the number of trees per acre represented by the

smaller sample trees passed over exceeds two trees

per acre. For example, say the larger tree is 100 feet

tall and the next smaller tree is 75 feet tall (the gap is

25 feet, which is less than 30 feet, and therefore does

not qualify). Furthermore, say that the 75 foot tall tree

represents only 0.5 trees per acre and that the next

smaller tree below it is 65 feet tall and represents 1.6

trees per acre. In this case, the 75 foot tree would be

considered an “insignificant ladder” tree, one that

would not be seen as forming a continuous canopy

because it is so rare. But it is not entirely ignored

because it, in combination with the 65 foot tall tree,

represents over two trees per acre. In this case the gap

is defined to be 35 feet (100 foot tall tree minus the 65

foot tree), which is larger than the minimum required

for a valid gap.

c) If no valid gaps are found, the stand is considered to have only one potential stratum. If one valid

gap is found, the stand has two potential strata, and if

two gaps are found, the stand has three potential

strata.

5. Canopy cover is computed for each potential stratum. A stratum is considered valid if the cover exceeds

cmin.

10 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-24. 1999
6. Compute the nominal d.b.h. of the uppermost

stratum by averaging the d.b.h.’s of the nine trees

centered on the 70th percentile sample tree in the

distribution of crown widths. (Fewer than four trees

above or four below may be used if the sample is

sparse).

7. Using the number of valid strata computed in

steps 2 through 5, the nominal d.b.h. of the uppermost

stratum from step 6, the site’s maximum SDI, and the

number of trees (when there is less than 5 percent

crown cover), the structural class for the stand is

assigned using the definitions in table 2.

USDA Forest Service Gen. Tech. Rep. RMRS-GTR-24. 1999 11

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