Modeling the View Angle Dependence of Gap Fractions in Forest Canopies: Implications for Mapping...

Modeling the View Angle Dependence of Gap Fractions in Forest Canopies:Implications for Mapping Fractional Snow Cover Using Optical Remote Sensing

JICHENG LIU,* RAE A. MELLOH,� CURTIS E. WOODCOCK,* ROBERT E. DAVIS,� THOMAS H. PAINTER,#

AND CERETHA MCKENZIE�

*Department of Geography and Environment, Boston University, Boston, Massachusetts�Engineer Research and Development Center, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire

#Department of Geography, University of Utah, Salt Lake City, Utah

(Manuscript received 4 January 2007, in final form 11 September 2007)

ABSTRACT

Forest canopies influence the proportion of the land surface that is visible from above, or the viewablegap fraction (VGF). The VGF limits the amount of information available in satellite data about the landsurface, such as snow cover in forests. Efforts to recover fractional snow cover from the spectral mixtureanalysis model Moderate Resolution Imaging Spectroradiometer (MODIS) snow-covered area and grainsize (MODSCAG) indicate the importance of view angle effects in forested landscapes. The VGF can beestimated using both hemispherical photos and forest canopy models. For a set of stands in the Cold LandField Processes Experiment (CLPX) sites in the Fraser Experimental Forest in Colorado, the convergenceof both measurements and models of the VGF as a function of view angle supports the idea that VGF canbe characterized as a function of forest properties. A simple geometric optical (GO) model that includesonly between-crown gaps can capture the basic shape of the VGF as a function of view zenith angle.However, the GO model tends to underestimate the VGF compared with estimates derived from hemi-spherical photos, particularly at high view angles. The use of a more complicated geometric optical–radiative transfer (GORT) model generally improves estimates of the VGF by taking into account within-crown gaps. Small footprint airborne lidar data are useful for mapping forest cover and height, which makesthe parameterization of the GORT model possible over a landscape. Better knowledge of the angulardistribution of gaps in forest canopies holds promise for improving remote sensing of snow cover fraction.

1. Introduction

Snow, because of its unique properties such as highalbedo and low thermal conductivity, affects land sur-face radiation budgets and water balance (Yang et al.1999). Significant gains have been made in snow covermapping using remotely sensed data in recent decades,but the presence of forests continues to present chal-lenges (Simpson et al. 1998; Hall et al. 1998; Hall et al.2002; Dozier and Painter 2004). An understanding ofthe manner in which forest canopies influence the re-mote sensing of snow is important, given that forestscover much of the seasonally snow-covered portion ofthe world.

Forest canopies influence the fraction of the land sur-face that is visible from above, or the viewable gapfraction (VGF) (Liu et al. 2004). Hence, the VGF limitsthe amount of snow on the ground that is visible toremote sensors when the ground is fully covered bysnow. Since the VGF is strongly dependent on viewzenith angle, the amount of snow visible in forests willvary accordingly (Liu et al. 2004). Figure 1 shows theview zenith angle effect on the amount of snow areathat is visible from a satellite sensor when the groundsurface is fully covered by snow. The amount of visiblesnow, or VGF, is largest at nadir, decreasing as the viewzenith angle increases, and at a view zenith angle of �2,the satellite sensor can barely see the snow on theground.

Knowledge of how the VGF changes as a function ofview zenith angle may improve the estimation of frac-tional snow cover from remote sensing in forested ar-eas. Remote sensing of snow cover has evolved frombinary mapping of snow (Dozier 1989; Hall et al. 2002)

Corresponding author address: Jicheng Liu, Department of Ge-ography and Environment, Boston University, 675 Common-wealth Ave., Boston, MA 02215.E-mail: [email protected]

OCTOBER 2008 L I U E T A L . 1005

DOI: 10.1175/2008JHM866.1

© 2008 American Meteorological Society

JHM866

to subpixel mapping of fractional snow cover with re-gression tree approaches (Rosenthal and Dozier 1996)with use of the normalized difference snow index(NDSI) (Salomonson and Appel 2004, 2006) and mul-tiple endmember direct spectral mixture analysis(Painter et al. 2003). Figure 2 shows the fractionalsnow-covered area (SCA) results from the ModerateResolution Imaging Spectroradiometer (MODIS)snow-covered area and grain size (MODSCAG) modelfor the Cold Land Processes Field Experiment (CLPX)in the St. Louis Creek intensive study area (ISA) of theFraser Experimental Forest. MODSCAG combines aradiative transfer model for snow spectral endmemberswith a multiple endmember spectral mixture analysisapproach in which the number of endmembers as wellas the endmembers themselves may vary on a pixel bypixel basis. When applied to imaging spectrometerdata, the model had an overall SCA root-mean-squareerror of less than 4% (Painter et al. 2003). Notice theview angle dependence of the SCA estimates in Fig. 2.Near nadir the estimates are near 30% and decline toapproximately 15% at high view angles. Note that thisarea is relatively homogeneous in terms of forest coverand, thus, the effect of change in MODIS resolution asa function of view zenith angle is minimized. The larg-est possible MODIS pixel size is �1 � 2.5 km2 at thehighest zenith angles. However, the increasing rate isnot constant; the rate increases as the view zenith angle

becomes larger. At the largest view zenith angle theenlarged MODIS pixel includes small amounts ofsoutheast-facing slope on the west edge and northeast-facing slope on the south edge. It would be beneficial todemonstrate this on a boreal forest landscape whereslope differences are minor.

It is intuitively apparent that the VGF will vary as afunction of view angle as well as canopy structure. Asview angles increase away from nadir, less of theground surface is visible in forested areas. Similarly, asthe canopy cover of a forest increases, the VGF willalso decrease. A quantitative understanding of theseeffects requires development of a model for the way theVGF varies as a function of view angle, forest canopyproperties, and topography. Prior results indicate a geo-metric optical (GO) model captures the basic shape ofthe relationship between the VGF and view angle, butconsistently underestimates the VGF when comparedwith the results from hemispheric photos (Liu et al.2004). The GO model is limited to the estimation ofbetween-crown gaps, and addition of the effects ofwithin-crown gaps could improve estimation of theVGF, especially for those canopies where tree crownsare sparse.

The primary purpose of this paper is to extend stud-ies of the VGF to include a hybrid geometric optical–radiative transfer (GORT) model that includes the ef-fects of within-crown gaps. This paper also explores theeffect of the density of field samples and the ability touse airborne light detection and ranging (lidar) data forparameter estimation for discrete object models likethe GO and GORT models.

FIG. 1. Two-dimensional representation on viewing geometry offorest canopy with snow fully covered underneath (white) from asatellite. The visible snow area is shown as a thickened white linein the top panel.

FIG. 2. Fractional snow-covered area results from the MODSCAGmodel for the CLPX St. Louis Creek ISA in the Fraser Experi-mental Forest (FEF). The dot and whiskers in the plot are themean and �1 std dev about the mean.

1006 J O U R N A L O F H Y D R O M E T E O R O L O G Y VOLUME 9

2. Description of the GORT model

The hybrid geometrical optical–radiative transfermodel is a canopy directional reflectance model thatevolved from the GO model of Li and Strahler (1992)and includes the effects of within-crown gaps, given thefoliage area volume density (FAVD) within treecrowns as one of the input parameters (Li et al. 1995).In this model, the individual tree crowns are no longerassumed opaque, as in the GO model, and the amountof within-crown gap is modeled using the within-crownpathlength at the scale of leaves. This model was vali-dated using photosynthetically active radiation (PAR)and solar radiation transmission measurements at theBoreal Ecosystem–Atmosphere Study (BOREAS)sites (Ni et al. 1997). Use of the GORT model for es-timating transmission through forest canopies has im-proved the simulations of snowmelt in boreal foreststands (Hardy et al. 1997; Davis et al. 1997). The GORTmodel has also been used for radiation modeling in adeciduous aspen stand in the leaf-off condition (Hardyet al. 1998) and for assessing the effect of canopy struc-ture and the presence of snow on the albedo of borealconifer forests (Ni and Woodcock 2000). More recently,the GORT model has been used to model the short-wave radiation regime in forest canopies, and the re-sults are further used to parameterize land surfacemodels (Yang et al. 2001; Yang and Friedl 2003).

The full GORT model is described in detail by Li etal. (1995), and only a brief description of how the modelestimates the VGF is included here. In the GORTmodel, vegetation canopies are modeled as assem-blages of randomly distributed tree crowns of ellipsoi-dal shape having horizontal crown radius R and verticalcrown radius b. Note that the crown shapes of the dom-inant tree species in our field sites are mainly cone-shaped conifers. The reason why we continue to use theellipsoidal shape is that for gap probability calculationsin this model, particularly for dense forests, the toplayer of the canopy has the major impact. For coniferforests, the b/R ratios of the ellipsoidal shape of the treecrown are usually high (�3), which makes the ellipsesrather elongated and a reasonable representation ofcone-shaped crowns. Crown centers in this model areassumed to be randomly located, following a uniformdistribution between heights h1 and h2, the lower andupper boundaries of the heights of crown centers, re-spectively (Fig. 3). Within each crown, the foliage andbranches are assumed uniformly distributed with aspecified foliage area volume density. The effect of to-pography can be taken into account in the GORTmodel by using several simple transformations in coor-dinate space (Schaaf et al. 1994).

The GORT model relies on gap probabilities andpathlength distributions to model the penetration ofirradiance from a parallel source and the single andmultiple scattering of that irradiance in the direction ofan observer. In essence, the VGF is equivalent to thegap probability at the background level, or Pgap, whichis defined as the probability that a photon incidentupon a vegetation canopy will pass directly through thecanopy without being intercepted by a leaf, branch, orstem. In this model, between-crown gap probability istermed P(n � 0), where n is the number of plant crownspenetrated by a ray, is modeled in the same way as inthe GO model as a function of crown size, shape, andstand count density. The within-crown gap probability,Pgap(s), is modeled as a function of the within-crownoptical pathlength s at the scale of leaves:

Pgap�s � exp��s, �1

where � � kD� and has units of per meter; k is theattenuation of the radiation by leaf area containedwithin a unit of canopy depth for the incoming radia-tion direction and is determined by the leaf angle dis-tribution and the transmissivity of the leaf; D� isFAVD, which defines the one-sided leaf area per unitvolume and is assumed to be a constant and uniformlydistributed within the crowns. The gap probability ofthe canopy, Pgap, can then be modeled as

Pgap � �0

�

p�s exp��s ds, �2

where p(s) is the distribution of s over a canopy plane.With a first-order approximation, Pgap becomes

Pgap � P�0 � P�1 �0

�

p�s |1 exp��s ds, �3

FIG. 3. Between-crown gaps, P(n � 0), and within-crown gaps,P(n � 0), in the geometric optical–radiative transfer model: R andb are horizontal and vertically crown radii, respectively; h1 and h2

are the lower and upper boundaries of crown centers, respec-tively; n is the number of tree crowns penetrated by a ray.


where p(s |1) is the distribution of s, given that a photonwill penetrate an individual canopy. For different treecrown geometries, p(s |1) has different expressions. Fora sphere with radius of R,

p�s |1 �s

2R2 , �4

where 0 � s � 2R. The case of ellipsoids can be easilyderived from the sphere as the sphere becomes an el-lipse through a simple linear transformation of one ofits axes.

There are two types of input parameters for theGORT model: species related and stand specific.Among the first type are crown ellipticity (b/R, where bis the vertical crown radius and R is the horizontalcrown radius) and FAVD that are assumed constant fora forest species or type. The stand-specific input param-eters vary for individual stands and include the meancrown radius, lower and upper crown center bound-aries, and stand density (Fig. 3). Crown radius andstand density combine to estimate canopy cover, whichis the percent of the crown coverage from nadir viewing(Fig. 1), therefore, the complement of the VGF at nadirviewing (when within-crown gap fraction is not in-cluded). Canopy cover is the single most importantcanopy variable for estimating the VGF as view zenithangle increases (Liu et al. 2004).

As an example of the relative magnitude of between-and within-crown gaps, Fig. 4 shows the modeled view-able gap fractions as a function of view zenith angleusing measured stand parameters for the Intermediate(density) Stand (see details in the following section) inthe Fool Creek ((ISA in the Fraser Experimental For-est, Colorado (available online at http://www.fs.fed.us/rm/fraser/), for two different values of FAVD. At nadirthe within-crown gap fraction is roughly 20% of thetotal gap fraction. As the view zenith angle increases,the within-crown gap fraction becomes a large propor-tion of the total gap fraction, and near 45° it becomeslarger than the between-crown gap fraction. In the hy-pothetical case of a lower FAVD (a less dense crown),the within-crown gap fraction is a significant part ofviewable gap fraction even at small view zenith anglesand dominates the total VGF at high view zenithangles. Therefore, accounting for within-crown gapfraction in the estimation of viewable gap fraction isespecially important for canopies with low foliage den-sity.

3. Parameterizing the models using fieldmeasurements

Field measurements were collected in the summer of2003 in the Fool Creek and St. Louis Creek ISAs of the

Fraser Mesoscale Study Area (MSA) of the NASACold Land Processes Field Experiment (CLPX) to pa-rameterize the GO and GORT models. The Fool CreekISA is a rugged terrain with a planimetric area of abouta 1 km2 and has many distinct patches resulting fromdifferent management practices (Fig. 5). Four foreststands were selected for measuring the tree parametersin this ISA, as described in Liu et al. (2004). The St.Louis Creek ISA has a relatively flat terrain and onestand was selected in this ISA. Within each stand arectangular grid of sample points was established. Thesize of the grids varied slightly between stands such thatthere were between 35 and 50 sample points per standfor hemispherical photography (10-m spacing) and atleast 12 sample points for the more time-consumingforest mensuration measurements (20-m spacing). Allfour Fool Creek ISA stands are dominated by Engel-mann spruce and subalpine fir and the St. Louis CreekStand is dominated by lodgepole pine. All of these spe-cies have cone-shaped tree crowns.

a. Stand density, b/R ratio, R, h1, and h2

Stand density ( ) was estimated from data for vari-able radius plots, collected with the help of aRelaskop—an optical instrument based on angularmeasurements. Trees around an observation point arejudged to be “in” or “out” based on the diameter at

FIG. 4. Between-crown gap fractions and within-crown gap frac-tions estimated by the GORT model using tree parameter valuesmeasured in the Intermediate Stand in the Fool Creek ISA in theFraser Experimental Forest.


breast height (DBH) of each tree and its distance to thesample point. Smaller DBH trees have a smaller plotsize than larger DBH trees, making the sampling ofbasal area (BA) proportional to tree size. Each “in”tree contributes an equal amount of (BA for the stand.A basal area factor (BAF) determines the amount ofBA associated with the “in” trees and influences the

size of the plot for each size of tree. By measuring theactual BA of that tree, the number of trees with this sizeper unit area can be estimated. The stand count densityof trees for that sample point can then be calculated bysumming the values for all of the “in” trees. The overallstand density is the average from all the measuredpoints:

FIG. 5. Location map and orthophotos showing the location of the four measured stands in the Fool Creek ISA(1: Dense1, 2: Dense2, 3: Intermediate, and 4: Sparse), and 5: the one site in the St. Louis Creek ISA. The treephotos show examples of (left) Engelmann spruce, (center) subalpine fir, and (right) lodgepole pine.


Fig 5 live 4/C

� � �i �1N �

i�1

N

�i �1N �

i�1

N

�j�1

Mi BAFBAj

, �5

where N is the number of sample points at one stand,Mi is the number of “in” trees in sample point i, BAF isthe basal area factor used for the stand, and BAj is themeasured basal area of tree j. As Eq. (5) indicates,smaller “in” trees contribute more to the stand countdensity. All trees that have a DBH less than 3 cm areignored in this study as these trees are generally not inthe canopy.

Crown radii (R) were measured for two trees (thefirst tree off north and south in a clockwise direction) ateach sample point. Each measured R for a tree, com-bined with the measured vertical crown radius for thesame tree, b, is used to calculate the b/R ratio (a mea-sure of ellipticity) for that tree, and the overall b/R ratiofor a species is estimated as the mean of all measuredb/R values for that species. In the GORT model, theb/R ratio is assumed to be tree species dependent buttree size independent. To test these assumptions, Fig. 6shows the measured b/R ratio values for individualtrees, the mean value for different stands, and two treespecies as a function of tree size. For each species, asimple linear regression between DBH and b/R wasperformed, and the null hypothesis of a slope value ofzero could not be rejected based on p values of 0.1811for lodgepole pine and 0.1170 for subalpine fir, meaningthe b/R value is not tree size dependent. The variance in

the mean b/R value from different stands of the samespecies is relatively small, and the overall differencebetween b/R ratio values for these two species showsthe species dependency of b/R. The lodgepole pinetrees tend to have less elongated tree crowns (lower b/Rratio) than the subalpine fir.

To conserve the cover value, the mean stand crownradius R is calculated as the quadratic mean of all mea-sured tree crown radii in a stand weighted by the treedensity for that size (Wi):

R � �1

�i�1

n

Wi

�i�1

n

WiRi2�

1�2

� �1

�i�1

n

BAFi�BAi

�i�1

n BAFi

BAiRi

2�1�2

, �6

where n is the total number of trees measured at onestand, Ri and Wi are the radius and the weight for treei, and BAFi and BAi are the basal area factor used tomeasure tree i and the measured basal area for thattree, respectively.

Crown center lower vertical boundary (h1) and upperboundary (h2) are calculated as

h1 � min�Hbottom � b

h2 � max�Htop b, �7

FIG. 6. Measured b/R values for different trees species.


where Hbottom is the height of crown bottom and Htop isthe height of crown top (Fig. 3), and they are measuredin the field.

b. Confidence in stand density measurements

In all efforts to estimate properties of forest standsvia sampling, the question arises of whether the sam-pling density is sufficient to keep uncertainties to rea-sonable levels. The effect of reducing the number ofsample points in each stand on the estimated stand den-sity was tested. Figure 7 shows the average 95% confi-dence intervals on the mean stand count density as afunction of the number of sampled points. The esti-mated range for the tree density is less than �5% of theestimated mean when the numbers of sample points areclose to the actual numbers of sample points used. Thisresult means the numbers of measured points for these

four stands are large enough to estimate the stand den-sity within a relatively small amount of uncertainty (lessthan 5%). One interesting effect in the data is the dif-ferent rate of decrease in the confidence intervals fordifferent stands. These reflect the varying degree ofheterogeneity within the individual forest stands.

c. FAVD estimation

FAVD values were derived for different tree speciesusing the relationship between the effective projectedleaf area (EPLA) and DBH developed by Kaufmann etal. (1981) using field measurements in the same generalarea as our field measurements (M. R. Kaufmann 2003,personal communication). Their sample size rangedfrom 12 to 15 trees per species, and tree size rangedfrom small saplings several meters in height to large,mature trees. Trees were carefully felled to minimize

FIG. 7. Average 95% confidence intervals as a function of number of sample points when estimat-ing stand density for four stands in the Fool Creek ISA (solid lines) and the mean stand density(dotted line); value is in parentheses in the figure title.


the damage on leaves, and foliage samples were col-lected. For small trees, all foliage was collected includ-ing small branches. For the largest trees, fresh foliagearea exceeded 5 m3 in volume, and subsampling wasrequired (Kaufmann and Troendle 1981). The EPLAwas calculated by first measuring the actual projectedarea of horizontal needles, and the ratio of total needlearea to actual projected area of horizontal needles was3.21 for Englemann spruce and subalpine fir, and 3.34for lodgepole pine. Then, with the assumption of ran-dom orientation of foliage, the EPLA was calculated asthe actual projected area of horizontal needles times0.6366, which is obtained by integrating the cosine overthe range from 90° to 90°. The needles of these coni-fer trees are neither planophile nor erectophile, so theerror due to the random orientation assumption shouldbe minor. A linear relationship between EPLA andDBH was observed for Englemann spruce, subalpinefir, and lodgepole pine, and Kaufmann’s results for thethree species are summarized in (Table 1). To estimateFAVD for every measured tree, the EPLA for that treewas calculated, using the equation in Table 1, and di-vided by its elliptical crown volume, determined frommeasured b and R. The FAVD value for a species wasthen calculated as the mean value from all the FAVDvalues for trees of that species.

d. Parameter summary

Table 2 shows the measured canopy parameter val-ues for the GORT model for five test stands. For cal-culation of species-related parameters (b/R andFAVD) for mixed stands, a “composite” tree with av-erage b/R and FAVD values is used.

e. Canopy cover estimation

The canopy cover value estimated from field mea-surements is a function of both stand density, , and theaverage crown radius, R, with the assumptions of uni-form crown size and random locations of the treecrowns within the stand (Li and Strahler 1985; Franklinet al. 1985):

cover � 1 exp��R2. �8

4. Parameterizing the models using lidar data

Aerial lidar data provides an alternate, or additional,method of obtaining data about the canopy for modelparameterization. The advantage of using lidar data isthat canopy information derived from it can be ob-tained over a larger area than is practical using in situmeasurements. The use of lidar data to derive canopycover, height, and crown radius information for GORTmodel parameterization is explored here.

Lidar data for the Fool Creek ISA were collected on19 September 2003 at approximately 4500 feet eleva-tion, normalized to ground controls and processed toremove noise and redundancies (Miller 2003). The datahave approximately 1.5-m horizontal spacing, 0.15-mvertical tolerances, and a maximum laser view angle of15° from vertical, providing an illuminated footprint atlevel ground of 0.4 m. The first-return data (represent-ing the vegetation-terrain surface) and the last-returndata (representing the ground) were differenced to ob-tain histograms of vegetation height. The ground sur-face elevations were generated by creating a naturalneighbor grid at 0.5-m spacing and then performing alinear interpolation within grids to the locations of thevegetation–terrain elevations. Lidar canopy height his-tograms were developed for each forest stand (Fig. 5)using the data within the stand boundaries. The bound-aries were determined in the field with a Trimble globalpositioning system.

The lidar footprint has a certain size, and, thus, theproportion of the pulses that miss trees entirely is notequivalent to the complement of tree cover (1 cover).

TABLE 2. Measured canopy parameter values for the GORT model input.

Stand Species* h1 (m) h2 (m) (trees/m2) R (m) b/R FAVD (m1)

Dense1 Mostly ES 9.72 21.97 0.086 1.53 3.78 0.578Dense2 Mixed 6.55 22.10 0.119 1.32 4.04 0.446Intermediate Mostly SF 4.22 14.07 0.125 1.13 3.46 0.495Sparse Mixed 3.45 11.49 0.116 0.95 3.31 0.570St. Louis Creek LP 7.75 11.24 0.058 1.72 3.09 0.373

* ES: Engelmann spruce, SF: subalpine fir, LP: lodgepole pine, and Mixed: mixed with ES, SF, and LP.

TABLE 1. Effective projected leaf area (EPLA) (m2) as afunction of diameter at breast height (DBH) (cm).

Species Equation R2 Std dev

Engelmann spruce EPLA � 0.0752 DBH2 0.904 178.33Subalpine fir EPLA � 0.0681 DBH2 0.975 60.30Lodgepole pine EPLA � 0.0261 DBH2 0.930 11.15


For a very small lidar footprint these will be similar but,as the footprint increases, the estimate of visible groundsurface based on the lidar height histogram will becomesmaller than the true value. To incorporate the effect oflidar footprint size on cover estimation, a zero-hit run-length model (Chen et al. 1993) was used to estimatethe relationship between the lidar-observed proportionof bare ground and the true tree cover based on treesize and density data. In the zero-hit run-length prob-ability model, probabilities are estimated for thelengths of runs of grids of fixed size that do not hit anypart of objects that define a scene (such as trees in astand) (Chen et al. 1993). The simple scene model usesa plane that is covered by randomly located discs ofdiameter D1 � 2R and Poisson density , which is thesame case as the GO and GORT model, where the discsare the tree crowns observed from nadir. The scene isimaged by a sensor with a pixel size, D2, and lidar re-turns are separated into two classes: those that intersecta disc, or tree, (the “hit” pixels) and those that intersectonly the background (the “zero-hit” pixels). Accordingto zero-hit run-length statistics, the probability that apixel (or measurement) hits zero trees for the simplescene described above is

P�R, �, D2 � exp��D22 � 4D2R � �R2�. �9

This approach has been successfully used to estimatetree density and size from simulated remote sensingimages and proved to be especially valid when the ob-jects of interest (trees) are large relative to the size ofthe observations (Chen et al. 1993), which is the presentcase.

Evaluated for lidar footprint size, the zero-hit run-length probability decreases as the footprint increases,Eq. (7), and the relationship varies for the crown radiiand densities (Table 2) of the five measured stands (Fig.8). The zero-hit run-length probability goes to zerowhen the footprint size exceeds 5 m, meaning that therewill be no background returns expected when the lidarfootprint size is greater than this size. The zero-hit run-length probability is 80% � 5% of the true proportionof the ground surface for the footprint size of 0.4 m,which is the current case. The true proportion ofground surface for each stand in the Fool Creek ISA isestimated by dividing the percentage of ground returnsin the lidar data by 0.8. The percentage of the groundreturns is determined from histograms of the lidar data.The histogram of the “Sparse Stand” (Fig. 9) suggeststhat the 1-m height is a good choice for the boundarybetween ground returns and the returns from the forestcanopy. The threshold height of 1 m was used to sepa-rate ground returns for all stands.

5. Hemispherical photographs

Hemispherical photos were taken at each samplepoint in the grid (20-m spacing) for each stand at 1.25-m

FIG. 8. Zero-hit run-length probability as a function of laserfootprint size for all four stands in the Fool Creek ISA. Thecircled points are zero-hit run-length probability (P0.4) for singlepixels with the footprint size for the lidar data (0.4 m); P0 repre-sents the true proportion of ground in the scene. The ratio P0.4/P0shown in the legend is used to correct for footprint size.

FIG. 9. Lidar canopy height histogram for Sparse Stand in theFool Creek ISA.


height with a Nikon Coolpix 995 digital camera andNikon fisheye converter (FC-E8) lens. Forty-nine pho-tographs were taken in St. Louis Creek, 32 in Dense1,40 in “Dense2,” 49 in the “Intermediate Stand,” and 34in the “Sparse Stand”. The locations of the photo plotsare those shown in Fig. 5 for the Fool Creek sites. TheSt. Louis Creek plot was located at U. S. GeologicalSurvey center coordinates 4419964 N, 425897.3 E. Thecamera and bubble level were mounted on a tripod witha ball head attachment to permit rapid leveling at eachsample point. Photographs were taken at dusk in allstands, except the Intermediate Stand photos weretaken on a partly cloudy day. Black and white imageswere acquired at dusk and color images were acquiredduring the day. The camera was set for automatic ex-posure, infinite focus, wide-angle lens, full size (result-ing in 1519 pixels hemisphere diameter), high quality(1⁄4 jpeg compression), and matrix light metering.

Camera lenses used for hemispherical photo-imagecollection project a hemispherical image onto an imageplane that is then used in measurement analysis. Thevariation of the FC-E8 lens projection from a polarprojection is slight and was corrected using calibrationcoefficients (c0 � 0, c1 � 1.066 821, c2 � 0.036 160 7,and c3 � 0.031 261 1), provided for use with the GapLight Analyzer (GLA) software (Frazer et al. 1999).The viewable gap fraction (VGF) as a function of ze-nith angle was determined as the fraction of unob-structed sky, using a threshold procedure in the GLA toseparate sky and canopy pixels. The blue color bandwas used to threshold the daytime photographs becauseit typically provided the best contrast between thecanopy and sky. The threshold procedure is a subjectiveone with few options for systemization; however, wehave found consistent results in analyses of photo-graphs taken under different lighting conditions (Fig.10). Gap fraction versus zenith angle relationships weredetermined at 10° zenith increments. The 95% confi-dence interval of the mean stand VGF for any viewzenith angle is shown as a shaded area in all subsequentgraphs for comparison with model results (such as Figs.11 and 12). Notice that the uncertainty in the estimatesis highest near nadir where there are the fewest obser-vations in the hemispherical photos.

Reduced field of views (FOV) due to rugged topog-raphy begin at view zenith angles greater than 80° (75°)for the St. Louis Creek (Fool Creek) site. The reducedFOV will decrease the gap fraction determined byhemispherical photography for these near-ground ze-nith angles, except in the not uncommon circumstancethat the illumination of the nearby ridge (when viewedthrough the canopy) is higher than the underside of thecanopy being photographed.

6. Results and discussion

Comparisons of the VGF as a function of view angleestimated by the hemispherical photos and by the GOand GORT models based on the cover values from thefield measurements and the lidar data for the fourstands in Fool Creek and the St. Louis Creek Stand areshown in Figs. 11 and 12. The rms error of the VGF isa measure of the discrepancy between the modeled re-sults and the results from the hemispherical photos:However, it is unclear whether the hemispherical pho-tos are more accurate than the model results.

The GO model using cover estimates results and thehemispherical results show that the VGF decreases asview zenith angle increases (Fig. 11). The rate of de-

FIG. 10. Viewable gap fraction estimates for photo images onfive occasions with varied illumination for two sample points inthe St. Louis Creek stand.


crease varies between stands until the view zenith angleis larger than 30°. By a view zenith angle of 30°, theVGF values are less than half of the value from nadir.This indicates that, when the forest is viewed by a sat-ellite sensor with a greater than 30° of view zenithangle, the signal from the understory below forests thatreaches the sensor is less than half of when it is viewedfrom nadir. This result, if accurate, implies that the ob-servable fractional snow cover in forested areas is lessthan half the true fractional snow cover when view ze-nith angles exceed 30°. We assume that the ground areabelow the canopy is fully snow covered, and the fractionof the snow cover on the ground that is visible throughthe forest canopy from a satellite is the best the satellite

data can do at estimating snow cover fraction withoutview zenith angle correction. We also define the “true”fractional snow cover as the fraction of snow coverviewable from nadir (1 cover). The fraction of snowon the ground that is viewable by a satellite, which isequal to the viewable gap fraction, usually decreases asthe view zenith angles increase. The model estimatesusing the cover value from the field measurementsshow better agreement with the hemispherical photosfor the two dense stands in Fool Creek than using thecover value from the lidar data due to the lower coverestimates from the field measurements. For St. LouisCreek, the model estimates using cover values from thefield measurements and lidar data are almost identical.

FIG. 11. Estimated VGF from the hemispherical photos and from the GO model using cover valuesfrom two different approaches. Rms errors are calculated between the modeled results and theresults from the hemispherical photos with the first number in the figure showing the value using thecover value from the field measurements and the second from the lidar data.


The GO model underestimates the VGF values com-pared with the hemispherical photos throughout therange of view zenith angles except near nadir in densestands. In all cases the GO model underestimates theVGF relative to the hemispherical photos at high viewzenith angles. This result was found by Liu et al. (2004)and is an understandable result given the limitation ofthe model to between-crown gaps.

The GORT model takes into account within-crowngaps and agrees better with the hemispherical photosthroughout the view zenith angle range in most casesexcept for the St. Louis Creek Stand, where the VGFestimates are systematically higher than the hemi-spherical photos (Fig. 12). For other stands, the esti-mates from the GORT model do not show the system-atic bias relative to the hemispherical photo results.

The rate of decrease in the VGF is higher for the lowview zenith angles for the two dense stands and almosta constant for the Intermediate Stand and the SparseStand, illustrating the view zenith angle effect is largerfor dense forests than for sparse forests. This mightresult from the different b/R ratio values as the b/Rratios of the two dense stands are larger than thosefrom the other stands.

As expected, estimates of the VGF from the GORTmodel are higher than those from the GO model for allthe view zenith angles for all stands. However, the dif-ference is most pronounced for the Fool Creek Inter-mediate and Sparse stands and the St. Louis CreekStand (Fig. 13). All of these stands have lower canopycover than the two dense stands in Fool Creek. For thesparser stands, the within-crown gap fractions at nadir

FIG. 12. As in Fig. 11 but for the estimated VGF from the hemispherical photos and from theGORT model.


are around 15% of the total VGF and become increas-ingly important as view zenith angle increases. This re-sult indicates that within-crown gaps are more impor-tant for sparse forests. The number of trees that inter-cept a line of sight is usually small in sparse stands; thus,more gaps can be seen through tree crowns.

One noteworthy result is that the models and hemi-spherical photos estimate a stronger view angle depen-dence for the VGF than the estimates shown for snowcover fraction in Fig. 2. One problem with a direct com-parison of these graphs is that MODIS data were thesource of the MODSCAG results and the MODIS ob-servations cover a significantly larger area than the St.Louis Creek Stand. If the forests in the surroundingarea have a higher canopy cover, that would explainsome of the discrepancy.

7. Conclusions

The convergence of both measurements and modelsof the VGF as a function of view angle supports theidea that the VGF can be characterized as a function offorest properties. Knowledge of the magnitude of viewangle effects in remote sensing imagery over forestsshould benefit remote sensing of snow cover fraction.

Generally speaking, taking into account the within-crown gap fraction improved the model estimation ofthe VGF as a function of view zenith angle, especiallyfor Intermediate and Sparse stands. Even though therms error for the GORT results are not significantlylower than the results for the GO model, they do notexhibit the pattern of systematic underestimation of theGO model. For the Intermediate Stand and Sparse

FIG. 13. Estimated VGF from the GO and GORT models using canopy cover values from lidardata.


Stand, the within-crown gap fractions are around 15%of the total VGF at nadir and become increasinglymore important as the view zenith angle increases.

The similar results to field measurements for forestcover estimates emerging from the lidar data supportthe effectiveness of using the zero-hit run-length modelto take into account the effect of pixel size. Lidar datacan be used to map forest cover with high accuracywhen the lidar footprint size is smaller than the treecrown size. The canopy heights estimated from the lidardata show general agreement with the height values fromthe field measurements. The use of airborne lidar dataprovides a way to parameterize the GORT model overlandscapes that is not feasible using field measurements.

Acknowledgments. This research was supported bythe U.S. Army. The efforts of the more than 200 peoplewho participated in the planning and execution ofCLPX 2002-2003 are very much appreciated. TheCLPX was funded through the cooperation of manyagencies and organizations including the NASA EarthScience Enterprise, Terrestrial Hydrology Program,Earth Observing System Program, and Airborne Sci-ence Program; the National Oceanic and AtmosphericAdministration Office of Global Programs; the U.S.Army Corps of Engineers Civil Works Remote SensingResearch Program; the U.S. Army Basic Research Pro-gram; the National Space Development Agency of Ja-pan (NASDA); the Japan Science and Technology Cor-poration; and the National Assembly for Wales, Stra-tegic Research Investment Fund, Cardiff, SouthGlamorgan, United Kingdom. A portion of this workwas conducted at the Jet Propulsion Laboratory at theCalifornia Institute of Technology, under contract tothe National Aeronautics and Space AdministrationNASA. We would also like to thank Thomas Berry ofERDC/Vicksburg for collecting GPS locations of ourforest stands and Stephen Miller of Johnson, Kunkeland Associates, Inc. for information on the specifica-tions of the lidar. This work was supported by U.S.Army Contract DACA42-03-C-0033.

REFERENCES

Chen, R., D. L. B. Jupp, C. E. Woodcock, and A. H. Strahler,1993: Nonlinear estimation of scene parameters from digitalimages using zero-hit run-length statistics. IEEE Trans.Geosci. Remote Sens., 31, 735–746.

Davis, R. E., J. P. Hardy, W. Ni, C. E. Woodcock, C. McKenzie,R. Jordan, and X. Li, 1997: Variation of snow cover processesin the boreal forest: A parametric study on the effects ofconifer canopy. J. Geophys. Res., 102 (D24), 29 389–29 396.

Dozier, J., 1989: Spectral signature of alpine snow cover from theLandsat thematic mapper. Remote Sens. Environ., 28, 9–22.

——, and T. H. Painter, 2004: Multispectral and hyperspectralremote sensing of alpine snow properties. Annu. Rev. EarthPlanet. Sci., 32, 465–494.

Franklin, J., J. Michaelson, and A. H. Strahler, 1985: Spatialanalysis of density dependent pattern in coniferous foreststands. Plant Ecol., 64, 29–36.

Frazer, G. W., C. D. Canham, and K. P. Lertzman, 1999: GapLight Analyzer (GLA) Version 2.0: Imaging software to ex-tract canopy structure and gap light transmission indices fromtrue-color fisheye photographs. Simon Fraser University andthe Institute of Ecosystem Studies, 36 pp.

Hall, D. K., J. L. Foster, D. L. Verbyla, A. G. Klein, and C. S.Benson, 1998: Assessment of snow-cover mapping accuracyin a variety of vegetation-cover densities in central Alaska.Remote Sens. Environ., 66, 129–137.

——, G. A. Riggs, V. V. Salomonson, N. E. DiGirolamo, and K. J.Bayr, 2002: MODIS snow-cover products. Remote Sens. En-viron., 83, 181–194.

Hardy, J. P., R. E. Davis, R. Jordan, X. Li, C. E. Woodcock, W.Ni, and J. McKenzie, 1997: Snow ablation modeling at thestand scale in a boreal jack pine forest. J. Geophys. Res., 102(D24), 29 397–29 406.

——, ——, ——, W. Ni, and C. E. Woodcock, 1998: Snow ablationmodelling in a mature aspen stand of the boreal forest. Hy-drol. Processes, 12, 1763–1778.

Kaufmann, M. R., and C. A. Troendle, 1981: The relationship ofleaf area and foliage biomass to sapwood conducting area infour subalpine forest tree species. For. Sci., 27, 477–482.

Li, X., and A. H. Strahler, 1985: Geometeric-optical modeling ofa conifer forest canopy. IEEE Trans. Geosci. Remote Sens.,23, 705–721.

——, and ——, 1992: Geometric-optical bidirectional reflectancemodeling of the discrete crown vegetation canopy: Effect ofcrown shape and mutual shadowing. IEEE Trans. Geosci.Remote Sens., 30, 276–292.

——, ——, and C. E. Woodcock, 1995: A hybrid geometric opti-cal-radiative transfer approach for modeling albedo and di-rectional reflectance of discontinuous canopies. IEEE Trans.Geosci. Remote Sens., 33, 467–480.

Liu, J., R. A. Melloh, C. E. Woodcock, R. E. Davis, and E. S.Ochs, 2004: The effect of viewing geometry and topographyon viewable gap fractions through forest canopies. Hydrol.Processes, 18, 3595–3607.

Miller, S. L., cited 2003: CLPX-Airborne: Infrared orthophotog-raphy and LIDAR topographic mapping. National Snow andIce Data Center. [Available online at http://nsidc.org/data/nsidc-0157.html].

Ni, W., and C. E. Woodcock, 2000: Effect of canopy structure andthe presence of snow on the albedo of boreal conifer forests.J. Geophys. Res., 105 (D9), 11 879–11 888.

——, X. Li, C. E. Woodcock, J. L. Roujean, and R. E. Davis, 1997:Transmission of solar radiation in boreal conifer forests:Measurements and models. J. Geophys. Res., 102 (D24),29 555–29 566.

Painter, T. H., J. Dozier, D. A. Roberts, R. E. Davis, and R. O.Green, 2003: Retrieval of subpixel snow-covered area andgrain size from imaging spectrometer data. Remote Sens. En-viron., 85, 64–77.

Rosenthal, W., and J. Dozier, 1996: Automated mapping of mon-tane snow cover at subpixel resolution from the Landsat The-matic Mapper. Water Resour. Res., 32, 115–130.

Salomonson, V. V., and I. Appel, 2004: Estimating fractional snow


cover from MODIS using the normalized difference snowindex. Remote Sens. Environ., 89, 351–360.

——, and ——, 2006: Development of the Aqua MODIS NDSIfractional snow cover algorithm and validation results. IEEETrans. Geosci. Remote Sens., 44, 1747–1756.

Schaaf, C. B., X. Li, and A. H. Strahler, 1994: Topographic effectson bidirectional and hemispherical reflectances calculatedwith a geometric-optical canopy model. IEEE Trans. Geosci.Remote Sens., 32, 1186–1193.

Simpson, J. J., J. R. Stitt, and M. Sienko, 1998: Improved esti-

mates of the areal extent of snow cover from AVHRR data.J. Hydrol., 204, 1–23.

Yang, R., and M. A. Friedl, 2003: Determination of roughnesslengths for heat and momentum over boreal forests. Bound.-Layer Meteor., 107, 581–603.

——, ——, and W. Ni, 2001: Parameterization of shortwave ra-diation flux for nonuniform vegetation canopies in land sur-face models. J. Geophys. Res., 106 (D13), 14 275–14 286.

Yang, Z. L., and Coauthors, 1999: Simulation of snow mass andextent in general circulation models. Hydrol. Processes, 13,2097–2113.


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