Analyzing Canopy Structure in Pacific Northwest Old-Growth Forests with a Stand-Scale Crown Model

Home , Canopy (biology)

~obertgan Pelt,Bnd Malcolm P. horth, College of Forest Resources, Box 352100, University of Washington. Seattle, Washington 98195

Abstract In forests, the canopy is the locale of critical ecosysteln processes such as photosynthesis and evapotranspirrrtion. and it provides essential habitat for a highly diverse array of animals, plants, and other organisms. Despite its importance, the structure of the canopy as a whole has had little quantitative study because limited access makes quantification difficult and integration of detailed measures of many individual tree crowns is necessary. A model is presented for simulating the crown architecture of individual trees in the Pacific Northwest to analyze their collective influence on canopy structure at the stand scale. The model uses ground-based measurements of tree height, height to crown base, and crown radii. Crown shapes are modeled as solid geometric shapes based on these measures. Two examples are used to illustrate the model's applications: an estimation of the vertical distribution of foliage in an old-growth Douglas-firlwestern hemlock forest; and an estimation of understory light conditions in an experimental gap, made by applying ray tracing technology to a model of the overstory tree crowns. Both examples illustrate how the model can increase detail in the description of canopy structure. Further application and future testing of the model will help refine its precision.

Introduction Spies 1992, Wu and Strahler 1994). Detailed measures of branch patterns and leaf orientation . The forest canopy has been hailed as one of the can be used to assess shade tolerance or branch last biological frontiers and the greatest source architecture (Hutchinson et al. 1986, Canham of species diversity in forests (Erwin 1982, 1988), but these measures are specific to the struc- Schowalter 1988, Lesica and Antibus 1991, ture of individual trees or the canopy process under Terbough 1985, 1992, Wilson 1992). Canopies study (Norman and Campbell 1989). Aerial pho- are critical elements of the forest ecosysteln from tography and satellite imagery are used to exam- numerous viewpoints. They modify both meso- ine changes in canopy cover with succession or and micro-climate, affect regional evaporation, disturbance (Cohen et al. 1990, Nel et al. 1994, cloud condensation, and temperature fluctuations Nilson and Peterson 1994), but they do not pro- (McNaughton 1989, Harr 1982, Chen 199 1). The vide detailed information on the internal struc- canopy is the exchange site for atmospheric gases, ture of the canopy. precipitation, and particulate interception Measures of canopy structure at intermediate (Hutchinson et al. 1986, Campbell and Norman spatial scales are not well developed because stand- 1989, Gao and Li 1993). In old-growth forests of scale analysis requires direct measurement of many the Pacific Northwest, the complex canopy struc- tall, complex tree crowns. h mature and old-growth ture has been recognized as essential for many forests, accessing and measuring a sufficient species of wildlife, arthropods, and epiphytes (sev- sample of tree crowns to describe a stand's canopy eral articles, this issue). Research in forest cano- structure is difficult. In spite of these difficulties, pies has been limited, however, by both the lo- a three-dimensional stand-scale measure of canopy gistical problems of accessing the tall tree crowns, structure is needed for at least three reasons: this and the heterogeneous structure of the canopy scale is necessary to link processes operating across environment. Despite numerous studies of canopy fine (individual tree architecture) and coarse (re- processes and species diversity, the structure of mote measures of large-scale canopy cover) scales the canopy remains poorly understood and has of structure; many arboreal wildlife species may. rarely been quantitatively analyzed. respond to canopy structure at this scale; and land Other studies of canopy structure have exam- management monitoring and planning often oc- ined the fine scale of individual tree crown ar- cur at the stand scale. chitecture (Massman 1982) or large-scale canopy A direct method of modeling the canopy struc- cover for a watershed or landscape (Cohen and ture of old-growth forest stands in the Pacific

Northwest Science, Vol. 70, Special Issue, 1996 15 Northwest is presented in this paper. The model of the foliage distribution in individual old-growth ' is used to quantitatively describe the vertical dis- Douglas-fir trees at the H.I. Andrews Experimental tribution of crown foliage within a stand and as- Forest in central Oregon showed that the crown sociated effects on the amount of light in the un- shape of each tree was unique and irregular (Pike derstory. Estimates of individual crown volumes et al. 1977, Massman 1982). are made from ground-based measures of tree height, height to the live crown, crown shape, and Scale and Access crown diameter. Although these methods were developed in coniferous old-growth forests, the Canopies are studied at many different scales techniques should be applicable to other forest depending on the arboreal species or process. From types, to successional stages where canopy struc- landscapes to stands to individual trees to branches, ture !nay be less complex, or both. As research the scale of interest determines the detail at which activities in forest canopies increase, standard- canopy structure should be measured (Kruijt 1989). ized methods for quantitatively analyzing canopy Researchers interested in fine-scale processes are structure are needed. This model is presented as not concerned with the unique shape of each old- a preliminary approach toward measuring stand- growth tree crown. When canopy-dwelling scale canopy structure while the model's accu- arthropods are being studied, for example, foli- racy is tested further. age distribution on a single branch can be exam- ined for habitat use and availability (Winchester, Approaches to Measuring Canopy this issue). For studies of photosynthesis and par- Structure ticulate interception, canopy structure may require a map of foliage or branch distribution within a Canopy Structure and Tree Age single crown. When working at these scales, direct access to the canopy is possible using tow- Canopy structure refers to the spatial arrangement ers, lifts, or rope techniques developed by urban of tree stems, branches and foliage within a for- arborists. Athough these systems are time con- est. As forest stands develop, the vertical and suming to establish, they afford precise horizontal distribution of the canopy becomes more measurments of crown components. heterogeneous, and its measurement becomes more difficult. In young stands of trees, particularly Landscape ecologists and foresters interested conifers, canopy structure is fairly homogeneous in canopy structure on a watershed or regional and growth patterns are predictable. Models of scale rely on remote imagery from airplanes and individual trees can predict annual branching satellites (Woodcock et al. 1990,Wu and Strahler patterns, branch angles, and leader and branch 1994). Remote methods eliminate access prob- extension lengths with some accuracy for young lems and increase the canopy sample size, but trees (Hamilton 1969, Horn 197 1, Hatch et al. also decrease detail. Digital satellite imagery has 1975, Halle et al. 1978). Growth and yield mod- been used to classify forest stands by age class els, such as OREGANON (Hann et al. 1992), can across landscapes, by using the reflectance sig- provide good estimates of a tree's crown growth, nal of canopies, (Morrison 1989). Digital imag- including responses to thinning mortality. ery or videography from low-flying aircraft can distinguish individual tree crowns, shadows and As trees age, however, they become taller and the openness of a stand (Cohen et a]. 1990). their crowns longer, more complex, and more idiosyncratic. Trees in an old-growth forest are Remote imagery provides valuable large-scale products of hundreds of years of individual re- images of changes in canopy structure with age sponses to disturbance, competition, injury, light or disturbance, but it provides little information availability and quality, and other stochastic events. about the interior canopy environment. In forests For each tree, the sum of these collective differ- with multiple crown layers, high foliage densi- ences creates a unique, complex, crown shape that ties, or irregular crown cover, measures of only is difficult to predict or model (Canham 1988, the outer canopy surface provide little informa- Young and Hubbell 1991). In conifer forests, the tion about canopy structure. Assessing canopy canopy may begin as a fairly uniform band of structure at the stand scale requires integration cone-shaped crowns, and develop into a multi- of numerous measures of individual tree archi- layered array of polymorphous crown shapes. Maps tecture. Measurements must include more than a

1 G Van Pelt and North sample of a few tree crowns, but must provide . To confound matters, the amount of light reach- greater detail than can be obtained from a remote ing the forest floor may not reflect the canopy image of the canopy's upper surface. This com- structure directly overhead. In the Pacific North- promise between sample size and detail, along west (at latitudes from 44 to %"), sun angles are with problems accessing mature forest canopies, oblique during most of the growing season. Analy- has often led to the use of indirect measures of ses of fisheye photos reveal that significant amounts canopy structure, such as light transmission. of light filter through a Pacific Northwest forest The amount of light in a forest is influenced canopy at 45 degrees or more off vertical (Figure by the density and distribution of canopy foliage 1a and 1b) (Easter and Spies 1994). Flat projec- (Anderson 1963, Horn 197 1, Reifsnyder et al. tions of tree crowns used to model canopy effects on understory light may work well in low- 197 1). The percentage of full sunlight that reaches latitude tropical forests or short-stature, broadleaf the forest floor is a broad measure of foliage density. temperate forests (e.g., Runkle but they The most common methods of measuring light 1992), do poorly in the Pacific Northwest. penetration, however, integrate the incoming light over the whole sky (Reifsnyder et al. 197 1, For Pacific Northwest old-growth forests, Hutchinson et al. 1980, Oberbauer et al. 1988, measurement of the location and crown dimen- Chazdon and Pearcy 1991) providing little infor- sions of individual trees can be integrated to pro- mation regarding the distribution of light as a vide a stand-scale description of canopy struc- function of canopy structure. Fisheye photographs ture. Ground-based measurement is a practical can help isolate the direction of incoming light compromise between direct measurements of a (Evans and Coombe 1959, Anderson, 1963, Horn few branches and remote, large-scale sampling 1971, Canham et al. 1990); however, each photo of a forest's outer canopy cover. With ground-based represents only a single location, making stand- measures, an observer can quickly and directly scale analysis difficult. A larger scale measure of measure the individual tree parameters that col- canopy structure that does not use light transmis- lectively describe the density and distribution of sion is leaf area index (LAI), a measure of the a stand's canopy foliage. Treating each tree crown number of foliage layers over a given area of for- as a simple geometric shape is possible, thus est floor, provides a stand-level index of foliage niaking canopies of complex, old-growth stands relatively easy to model in three dimensions. quantities (Waring et al. 1982). A11 of these techniques, however, provide little detailed informa- Although treating crowns as solids may be tion on canopy structure because they do not inappropriate at fine scales, such simplification measure how foliage is spatially distributed (Oker- can provide a three-dimensional map of general- Blom and Kellomaki 1982, Chason et al. 199 1). ized tree crowns that collectively approximate stand-scale structure. For example, this level of structure modeling might help assess foraging Canopy Structure in Pacific Northwest Old- conditions for an owl which flies between rather Growth Forests than through crowns. Although this model is a Pacific Northwest old-growth forests have tall, simplification of a complex canopy environment, multilayered canopies, which are difficult to ac- it is a step toward the three-dimensional analysis cess and structurally complex. Much of the old necessary to understand the influence of canopy growth below 1000 m in elevation is dominated structure on arboreal processes and species di- by Douglas-fir (Pseudotsuga menziesio and west- versity. ern hemlock (Tsuga heterophylla). These forests can be up to 80 m tall, with foliage distributed Measuring Canopy Structure: Crown throughout (Franklin and Waring 1980), so that Model Technique the amount of understory light provides little in- Data for model development were collected in a formation about foliage distribution in the canopy. Douglas-fir / western hemlock old-growth forest The trees may be tall but are generally not very at the Wind River Experimental Forest in the south- wide. Branch lengths seldom exceed 8 m and the ern Washington Cascade Range. The site is a rela- upper canopy tends to have distinct crowns be- tively flat, moderately productive forest that origi- cause of branch abrasion. nated 400-500 years ago (Franklin and DeBell

Stand-Scale Crown Model 17 rlgure la. Hemispherical photogri~ph(lisheyc photo) taken in a closed portion of an old-growth Douglas-fir/ western hemlock forest. The center of the image is directly above the camera, and the white circle Total open space - 2.1 % represents 45 degrees below vertical. Note that significant light penetration occur at angles greater than 45 degrees. 0.25 -a, .-a 1988). The forest stand is near the upper limits of 0.2 - the western hemlock zone (Franklin and Dymess 3 1973), with an understory tree layer dominated 2 by Pacific silver fu (Abies amabilis), Pacific yew 5 0.15 - (Tanrs brevifolia) and western hemlock. No de- 2 tectable major disturbance has occurred since stand n initiation, resulting in a multilayered forest. The 0.1 - largest trees are Douglas-firs up to 60 m tall and from 275-500 years old (Franklin and Waring 0.05 1980), and the western hemlocks occupy all strata - from seedlings to old trees (Figure 2).

All trees taller than 50 cm were mapped for 0 I I use in the spatially explicit model. This height 0 15 30 45 60 75 90 was chosen because small seedlings can be ephem- Zenith angle eral; population numbers do not stabilize until Figure i b. ihe distribution of open space for the image in la. understory trees become well established (Van Maximum light penetration is at 25 degrees.

18 Van Pelt and North Douglas-fir western Pacific Pacific hemlock silver fir Yew Figure 2. 50 x 20 m cross section of the study site at the Wind River Experimental Forest. Note the diversity of tree heights and the vertical distribution of the foliage.

Pelt, unpublished). Each crown was characterized diameter at breast height (dbh) were mapped in a by measuring the tree's height and height to the 20 m wide band centered on the transect line. Each crown base, mapping the crown projection or of these trees was identified to species and also measuring four crown radii, and assigning a crown measured for total tree height, height to crown shape (Figure 3). If a detailed view of the lower base, and crown radii. Trees taller than 50 cm crown is required, height to crown base could be were sampled in a 2 m wide transect centered on replaced by a value for the height to partial crown, the same transect line. Although time permitted the height to full crown, and the compass direc- tree height measurements for only 85%of the trees, tions of the partial crown (North 1993). regressions of dbh by species on the 1429 mea- Two 400 m transects were placed in interior sured trees were used to estimate the remainder portions of the forest. Trees greater than 5 cm in (Table 1).

Stand-Scale Crown Model 19 Concs are perhaps the most commonly used shape for modeling conifers because they are easy to describe mathematically and are conformable to many crown shapes (Figure 4). In addition, most . conifers and many broadleaf trees have conical shapes for the first several decades of their lives, and indeed many retain this shape for several hundred years (Horn 1971). Cylinders are another group of geometric shapes that could be used to simulate certain tree crowns. Tall, closed canopy forest trees often develop deep, narrow crowns best represented by cylindrical shapes. Although young conifers are generally not flat topped, emergent old-growth trees can develop flat tops when they have stopped growing in height. The calculations for cylinders are simple and this shape should not be overlooked for appropriate situations. Paraboloids are versatile shapes that are adapt- able to a wide variety of crowns. These shapes Figure 3. The variables required for the crown model: a, the can be used for trees that have either the deep tree height; b, height to full crown base; c, height crowns of main canopy trees, or the short, wide to partial crown; d, four crown radii. crowns of suppressed understory trees. In either case, the widest part of the crown is at or near the Data were also collected in a 0.2 ha circular bottom of the crown, which makes paraboloids gap in the Experimental Forest. This gap was cut an appropriate choice. as part of a larger study looking at the effects of Ellipsoids (including prolate and oblate sphc- cxpcrirnenlal canopy rcmovill on thc tbrcst un- roids) or truncated ellipsoids arc si~rlilarto pa- derstory (Van Pelt et al. 1992). All trees taller than raboloids in that they also approximate some 50 cm were mapped in a 0.4 ha area centered on old-growth tree crowns. A half-ellipsoid looks the gap, and measurements for each tree followed similar to a paraboloid of equal height and width, the protocol used for the transect samples. yet the paraboloid is narrower at all heights ex- cept for the bottom. Old-growth Douglas-firs of- Crown Shape ten have ellipsoidal crowns, with the widest part - For model construction, the crown of each sample of the crown low but not at the crown base. tree was classed as one of several solid geomet- Geometric shapes for each crown were selected ric shapes. No single shape can be applied to all in the field after viewing crown shape from sev- trees because old-growth crowns are unique and eral angles. All Douglas-fir tree crowns in this irregular. Several simple forms, however, can be study were modeled as truncated ellipsoids, and applied to most tree crowns. all other trees are modeled as paraboloids. To

TABLE 1. Regression equations used to predict height from dbh for the trees used in the crown model; 1429 trees were used to develop the equations.

Species Predicting equation N adj ?

Tsuga iteterophylla ~t = 50.863*(le-( OZZ*DBH~~.S~Z) 693 0.947 Abies cunabilis HI = 45.5g*(l -e4"28*DBHr'.5391 468 0.958 Pseudotsuga mettziesii ~t = 136.389*(1-e-f.OOPDBHN.MS 1 149 0.746

20 Van Pelt and North Figure 4. Potential crown shapes used in the model, from left to right: cone, cylinder, ellipsoid, paraboloid (wider than tall), and another paraboloid (taller than wide). qualitatively assess the fit between actual crown m transects. This estimate is presented only to shape and selected geometric shapes, photographs illustrate the model's capabilities because we do of 13 trees were digitally scanned. Two-dimen- not have an exact measure of the real foliage dis- sional silhouettes of the crowns were compared tribution. The second example is a spatially ex- with the geometric shape selected in the field plicit application that estimates understory light (Figure 5). The geometric shapes exclude irregu- surrounding the experimental canopy gap. In this lar, lower branches and long branch tips, and fill application, a subset of the model's results from in crown gaps where branches are missing. specific locations are compared to fisheye pho- The selected geometric shape, crown length, tographs taken at the same locations. and crown radii were used to model the crown shape and height of each tree at its specific X-Y Application I: Vertical Distribution of location along the transect. The resulting stand Foliage model closely approximates crown locations us- The crowns for all trees along the transect were ing specific height and position measurements, modeled and then horizontally sliced at 5 m height but it simplifies crown shape as a geometric solid. intervals. Crown cross-sectional area and volume were calculated for each tree at each interval. Applications of the Crown Model Frustum volumes were summed by species for The following two examples illustrate how the each 5 m layer to estimate the vertical distribu- model can be used to describe canopy conditions. tion of crown foliage. These data are presented The first estimates the verticaI distribution of fo- in Figure 6 in two ways; graph A shows the total liage based on measurements from the 20 x 400 crown volume /ha at each height for each species;

Stand-Scale Crown Model 21 Western hemlock

Figure 5. Top: Six photographic silhouettes of oid-growth Douglas-fir trees with a truncated ellipsoid overlaid to show the model's approximation of the actual crown shape. Bottom: Seven photographic silhouettes of old-growth western hemlock trees with parabolic shapes overlaid to show the versatility of paraboloids for modeling a diversity of crown structures.

22 Van Pelt and North - is open. Shade-intolerant Douglas-fir extcnds and -Western hemlock dominates the upper canopy environment, pro- Douglas-f'c viding most of the crown volume above 43 m. In e total volume, however, the stand is dominated by Pacifii silver fw western hemlock and in the lower canopy most -C Pacifi yew of the space is occupied by hemlock crowns. In this stand, although large Douglas-fir may punc- tuate the outer canopy, most of the canopy structure is determined by the density and distribution of subdominant, shade-tolerant species.

Application I!: Using the Crown Model to Estimate Light Reaching the Forest Floor 0 - Hemispherical (fisheye) photography can be used 0 5000 10000 15000 20000 25000 A to estimate the amount of light penetrating a canopy. Crown volume (&/ha) Through the use of the crown model and a computer animation technique called ray tracing, a 50 - computerized equivalent of fisheye photos can be generated. From a selected point, the visible hemisphere's tree crowns are drawn by using the 40 - model, and the animation technique presents an overhead view from the ground. This view, similar to a fisheye photo, can be analyzed and the amount of visible open sky can be calculated. The ray tracing program (POV-RAY2.0, 1993) models the light through the canopy by mathematically placing a camera, light source, and objects in three-dirncnsional spacc using ASCII tcxt dcli- nitions. A window of a given resolution is de- fined and the program then calculates the path of light rays from each pixel back to the light source based on the reflective nature of the objects. AI- though ray tracing is commonly used for detailed photorealistic images, its accurate rendering of 0 20 40 60 80 100 objects in three-dimensional space makes it use- Space occupied by crowns (%) ful for scientific illustration. Figure 6. Vertical foliage distribution for the forest at Wind The canopy's effect on understory light was River: A, for each species individually in cubic explored using the ray tracing techniques and crown meters per hectare; and, B, by species (individual shades), or total stand (outer boundary) as a per- models to simulate the canopy. To estimate light cent of total available open space. distribution throughout the 0.4 ha plot contain- ing the experimental gap, ray-traced images were generated for 204 stations placed 4 m apart in graph B is an area graph showing the total three- each gap. A radial grid, like those used in fisheye dimensional space occupied by each species by photo analysis (Rich 1989), was imposed on each height interval. ray-traced image. By using the grid, the total per- The model helps visualize foliage distributions centage of open sky in each image was calcu- that cannot be measured with above-canopy re- lated. Each cell in the grid is analyzed for the mote imagery or understory light conditions. Slic- percentage of the cell blocked by tree crowns, ing the canopy clearly showed that the highest and cell percentages are summed over the im- ' density of foliage was between 20 and 42 m. Yet age. The image for the gap center is shown in even in this vertical zone, 40% of the canopy space Figure 7A. This process is repeated for all images

Stand-Scale Crown Model 23 Figure 7. A, A simulated fisheye image taken from the center of a 0.2 ha opening in the Wind River old-growth forest (1 20 degree aperture); and B, the same image but with transparent textures added to more closely approximate actual conditions. Transparent textures were calibrated with a subset of actual hemispherical photos.

24 Van Pelt and North generated for each location and kriging is used difl'ilsc light condi tiotls in thc understory, which to spatially interpolate the light distribution be- in our example occurs at the center of the open- tween the 204 stations. ing (Figure 8A). A more accurate simulation of the light distri- To investigate the influence of latitude on un- bution can be made by using texturing techniques derstory light distribution, sun-paths throughout within the ray tracing program. Texturing lets the the growing season were modeled. This measure tree crowns transmit light in a more realistic man- provides an idealized value (i-e. no cloud cover) ner. A subset of fisheye photographs taken from of direct light conditions in the gap (Figure 8b). the Experimental Forest were used to calibrate The maximum direct light possible over the en- tree transparency in the model. Figure 7B shows tire year (Direct Site Factor, DSF) is 0.325 and is whcrc this was donc for tlic samc Icxation as Figure shiftcd 17 111 north of thc gap center. Thc 0.325 7A. value means that 32.5 percent of the possible di- To evaluate how well this application of the rect light reaches that spot, given no clouds or crown model simulates light transmission, com- haze. The shift indicates that light filtering through parisons of ray-traced images and fisheye photo- tall Pacific Northwest forests influences under- graphs from the same location were made for 10 story conditions at an oblique angle to the forest stations in two experimental gaps at Wind River. floor. Simple vertical or horizontal measures will The fit between actual and predicted values of not give an accurate assessment of tree reponse open sky were significant when summed either to canopy gaps, because the changes may be com- by zenith angles or by azimuth direction (Table pletely shifted out of the gap. This result is simi- 2). lar to that presented by Canham et al. (1990), who modeled gaps as cylinders at the same latitude. TABLE 2. Regression statistics for comparisoins of actual fisheye photos with simulated fisheye photos. For Discussion the zenith angle regressions, N = 20; for azimuth direction, N = 8. All values are significant. The measure of an ecological model is its ability to accurately illuminate complex processes at the Zenith angle Azimuth direction expense of some simplification. Powerful com- Plot Location ? p value fi p value puters and new statistical techniques have made 17mN three-dimensional modeling of the forest canopy 14mN possible. Yet these models will always be built on some simplified measurments of canopy struc- Center 14mS ture determined by the selection of scale and access method. 28 m S 25 m N Because the model is a simplification of a com- 13MN plex structure, the model is meant for stand-scale Center research, not for detailed analyses. Crown shapes 13mS are treated as solids in this model, yet foliage 25 m S density within a single crown is actually distributed as a foliage shell of variable thickness (Jensen and Long 1982). For young trees and shade-tol- Once the entire array of locations has an im- erant old trees, the inside of the shell is an area of age, surface maps of the distribution of open sky high shade and is thus largely photosynthetically by percentage throughout the gap were generated inactive. Old trees, however, have unique branching using a geographic information system (ARC/ patterns and can develop very open crowns. At INFO, v. 6.1.2,1993). This can be combined with the stand scale this variability is minimized, but a model of the amount of diffuse radiation dis- more detailed models will be needed if a closer tributed across the sky to estimate the total amount examination of forest structure is required. For of diffuse radiation that is penetrating the canopy. old-growth tree crowns, attaining the next higher The ratio of this to the total amount of diffuse level of detail is a major step that will require radiation in an unobscured sky is known as Indi- modeling tree crowns through their individual rect Site Factor (ISF). The ISF is a measure of branches. Such a model would require numerous

Stand-Scale Crown Model 25 Figure 8. A, Results of the diffuse light model. Indirect Site Factor for a 0.4 ha area surrounding the 0.2 ha gap. The outer boundary is the limit of the plot and the irregular white line represents the crown piojections of the remaining canopy trees. The gap center has the highest ISF. B, A direct light model showing the percentage of possible direct sun (Direct Site Factor, DSF) over the course of a growing season. This analysis makes no predictions for clouds or haze. The maximum value is shifted 17 rn north of gap center.

26 Van Pelt and North Stand-Scale Crown Model 27 measurements within individual crowns, rather ture which could further a more analytical explo- than a few easily measured crown dimensions. ration of the canopy environment. The applications presented describe two of the many potential uses of this model to stand-scale Conclusion research. Two applications illustrate how crown Studies of forest structure have often focused on volumes are vertically distributed and how crowns tree stems, and the function and composition of affect light penetration. The next logical step for the immediate environment near the ground. In a this application is to combine the vertical distribution with horizontal spacing of trees to come plant community where the vegetation is 30 to up with a three-dimensional analysis of crown 80 m tall, however, many of the dynamic eco- distribution. A corollary to this approach is an logical processes and biodiversity will occur in analysis in three dimensions of the open space the arboreal environment about which little is within the forest canopy. For arboreal species such known. Before the ecological interactions of spe- as the northern flying squirrel (Glaucomys cies and processes can be linked with their envi- sabrinus) or the northern spotted owl (Strix ronment, a measure of the aggregate crown or occidentalis caurina), the amount and distribu- stand-scale structure is needed. This measure would tion of open space may be important to move- have at least three benefits: until most of the spe- ment or foraging success (Carey 1985, Rosenberg cies and complex interactions of an ecosystem and Anthony 1992). are well studied, measures of structure must often serve as a surrogate measure of function or The computer-generated hemispherical pho- biotic diversity; for experimental design and sarn- tos also have wide applicability. Not only can large pling, researchers need to know how the cano- areas be analyzed once the stand parameters have pies of different stands are distinct and what fac- been mapped, but analysis of canopy openness tors make them so; and most monitoring, planning, at various vertical locations is easily accomplished, an aspect that has limited canopy photography and management of forests are at the stand scale. from the ground. Simulations of proposed har- A measure of canopy structure that uses ground- vesting activities is yet another application of the based methods would provide foresters with a light model. Selective logging, green-tree reten- means of comparing canopy environments between tion, strip cutting, and other forestry practices can different stands. be simulated under current and futirk conditions. In this paper, we present a method for model- At present the accuracy of the model is diffi- ing old-growth forest canopies at the stand scale cult to assess because there is no absolute mea- using ground-based measures. This technique is sure of canopy structure. Unlike ground-level forest based on easily measured crown dimensions and structure, the canopy environment does not readily can aid in three-dimensional analysis of forest imply a standard unit of measure. A stand's basal processes. Two applications of the model were area is easily sampled because tree boles are dis- used to examine the vertical distribution of foli- crete structures. Tree crowns, however, can be age and understory light levels in a Pacific North- considered a fractal shape (Zeide 1993) because west old-growth forest. The model indicates that their dimensions will change depending on the much of the foliage mass in the old-growth sample size of the sample unit. Any model's representa- stands is dominated by shade-tolerant, subcanopy tion of the canopy is relative to the scale it works species, and that light conditions for a point on at and the size of its smallest sample unit. The the forest floor are more influenced by the canopy's crown model presented is for stand-scale assess- structure at an oblique angle than the tree crowns ment of canopy structure using individual tree directly overhead. We believe the model can help crowns which are treated as simple geometric researchers analyze the complex structure of the solids. Given these parameters we believe the overstory environment as they explore the ecol- model can help visualize patterns in canopy struc- ogy of the canopy frontier.

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30 Van PeIt and North