Percent Canopy Cover and Stand Structure Statistics from ...

1 United StatesDepartmentof AgricultureForest ServiceRocky MountainResearch StationGeneral TechnicalReport RMRS-GTR-24 April 1999 Percent Canopy Coverand Stand StructureStatistics from the ForestVegetation SimulatorNicholas L. CrookstonAlbert R. StageYear 2140: old forest, single stratumCanopy Cover 74 percentYear 2000: young forest, multistrataCanopy Cover 35 percentRocky Mountain Research Station324 25th StreetOgden, 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 Ana-lyst, is located at the Rocky Mountain ResearchStation s Forestry Sciences Laboratory, Moscow, has been an active participant in the developmentof the Forest Vegetation Simulator and its extensionssince R.

2 Stage, Principal Mensurationist Emeritus,was a leader in the development of the Forest Vegeta-tion Simulator (also known as the Prognosis Model forStand Development) from the late 1960 s to his retire-ment from the Forest Service in 1996. He is an activeForest Scientist at the Moscow Forestry Sciences _____Crookston, Nicholas L.; Stage, Albert R. 1999. Percent Canopy Cover and Stand Structure Statistics fromthe Forest Vegetation Simulator. Gen. Tech. Rep. RMRS-GTR-24. Ogden, UT: U. S. Department ofAgriculture, Forest Service, Rocky Mountain Research Station. 11 of Percent Canopy Cover generated by the Forest Vegetation Simulator (FVS) are correctedfor crown overlap using an equation presented in this paper. A comparison of the new Cover estimateto some others is provided. The Cover estimate is one of several describing Stand Structure . The structuredescriptors also include major species, ranges of diameters, tree heights, and heights to crown base foras many as three significant height strata.

3 From these data a structural class is assigned to the standusing concepts defined by O Hara and others (1996) with some subsequent enhancements. An FVSkeyword for applying and tuning the classification is documented along with information for FVS EventMonitor users. An illustration of the structural classification is : FVS, Prognosis Model, crown Cover , Stand Structure may order additional copies of this publication by sending your mailing information in label formthrough one of the following media. Please specify the publication title and General Technical Service CenterFort Collins Service CenterTelephone(801) 625-5437(970) 498-1719 FAX(801) 625-5129, Attn: Publications(970) ~ ~rmrsMailing AddressPublications DistributionPublications DistributionRocky Mountain Research StationRocky Mountain Research Station324 25th Street3825 E. Mulberry StreetOgden, UT 84401 Fort Collins, CO 80524 Introduction _____Estimates of Percent Canopy Cover generated by theForest Vegetation Simulator (FVS, also known as thePrognosis Model for Stand Development, Stage 1973;Wykoff and others 1982) are corrected for crown over-lap using an equation presented in this paper.

4 Canopycover Percent has been identified as an indicator ofwildlife habitat for deer and elk (Thomas and others1979) and is an output of the Cover and SHRUBSE xtension to FVS (Moeur 1985). A review of othermethods used to estimate Canopy Cover is presentedwith comparisons to the new method. Appendix Adescribes an algorithmic foundation for the new methodin of Stand Structure have become an in-creasingly important consideration in prescribingmanagement actions to preserve wildlife habitat andwatershed values. Traditional FVS-generated out-puts that describe the distribution of tree crownscomprising a Stand are available to users of the COVERand SHRUBS extension. It reports the horizontal andvertical crown distribution by 10 foot tall slices of thecanopy. A new report has been added to the FVSoutput describing Stand Structure . New computationsare used to search for up to three distinct canopystrata.

5 For each significant stratum, the Canopy Cover ,major species, ranges of diameters, tree heights, andheights to crown base are displayed. From these dataa structural class is assigned to the Stand using con-cepts presented by O Hara and others (1966) withsome subsequent enhancements. The new output re-port is illustrated below with a description of theclassification scheme and an overview of the support-ing methods. Appendix B describes the classificationprocedure in added to FVS that support using these newtools are Canopy Cover _____Stand Percent Canopy Cover is the percentage of theground area that is directly covered with tree , the crown area of a tree is computed usingthe formula for a circle as a function of crown radius is estimated using formulae that aredifferent for each FVS geographic variant. The standpercent crown Cover without accounting for crownoverlap 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 ith sample tree,ai= projected crown area for the ith tree in ft2/acre,andA=ft2/acre (43560).

6 To correct for crown overlap, D. Satterlund (in Moeur1986, p. 344) suggested a computing procedure to esti-mate incremental additions of total Canopy Cover . Moeurreported that Satterlund s method produced estimates13 Percent greater than ground-based , in a program called PERCOVE, (1997a)computes Percent Canopy Cover by first placing thesample trees from an FVS projection onto a two dimen-sional grid. The crown circle of each tree is projected onthe grid and the proportion of the grid cells covered bythe circles of one or more trees is the proportion ofcanopy Cover . PERCOVE is capable of representingseveral spatial distributions of trees, and it allowsusers to specify Canopy strata for which independentestimates are PERCOVE must follow the execution ofFVS, the Cover predictions it generates cannot be usedto guide management within FVS using rules evalu-ated by the FVS Event Monitor (Crookston 1990).

7 Percent Canopy Cover andStand Structure Statisticsfrom the Forest VegetationSimulatorNicholas L. CrookstonAlbert R. Stage1 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-24. 1999 Furthermore, as the density of the dot grid increases(necessary for accurate estimates), the computer timerequired to run the program can become solve these problems, a new method was createdfor use in FVS that is based on established approach is fast, accurate for a large class ofproblems, and is part of FVS, so that the valuescomputed can be easily reported in FVS outputs andmade directly available in the Event Monitor. The newmethod is now used in the Cover and SHRUBSE xtension to FVS (Moeur 1985).The new method starts with the assumption thattrees are randomly located within the Stand . Thisassumption is midway between the extremes of equi-distant spacing that might characterize the early dis-tributions of stems in a plantation and the clumpeddistributions that might characterize the latter stagesof a group-shelterwood applied repeatedly and to oldforests (Moeur 1993).

8 To many observers this randomdistribution of points in space appears clumpy. Alogical next step would be to generate a hypotheticalstem map, assign crowns, and project this map ofcrowns onto a dot grid as done in PERCOVE. AppendixA outlines a simplified stem map approach that doesnot include exact stem placement. The technique hasseveral desirable properties outlined in the 1 displays the results using the simplifiedstem map approach detailed in Appendix A plottedagainst results using the equation that does not ac-count for overlap (equation 1). The data for the com-parison were produced using FVS to generate esti-mates of Cover for 447 plots from the north IdahoForest Inventory Assessment data (Woudenberg andFarrenkopf 1995). These data are a systematic sam-pling of conditions in north Idaho. Two estimates weremade for each plot, one for the inventory year andanother for 80 years later.

9 Because no difference inbehavior between these two estimates was detected,they are not distinguished in the tight fit in figure 1 suggested a search for amathematical basis for the relationship. The analyti-cal solution for the problem is available from thetheory of geometrical probability for randomly locatedfigures on a plane (Mack 1954, cited in Kendall andMoran 1963, section on p. 116). Furthermore, themathematical derivation holds for arbitrary convexfigures as well as for circles. Therefore, equations thatdirectly predict projected crown area regardless ofcrown shape could be used in place of those thatassume the crowns are round. Equation 2 estimatesthe 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, andC = equation same function is known in tree physiologicalliterature as the Beer-Lambert law a commonly usedrelation for calculating the absorption of light byfoliage (see Waring and Schlesinger 1985, p.)

10 12; or seeJones 1992, p. 15). In the Beer-Lambert law, foliage ismeasured by leaf area index which replaces C inequation 2. By introducing a coefficient other thanunity multiplying the argument of the exponential,the Beer-Lambert law generalizes the mathematicalresult to allow for non-random distributions. The abil-ity to represent uniform distributions and some spe-Figure 1 Percent Cover with overlap correction plotted overcover without correction for 447 plots from the north Idaho FIAdata. The formula for the line is y = 100 [ 1 exp( x/100)]; seeequation Forest Service Gen. Tech. Rep. RMRS-GTR-24. 1999cial attraction and repelling of canopies (so as to clumptrees or clump openings, as the case may be) woulddepend on empirical relations not currently experience shows that little accuracy would begained by including more 2 illustrates the relationship between esti-mates made with the new method (equation 2, the x-axis) and those made using PERCOVE (the y-axis).