• Chen, R., , Jupp D. L. B. , , Woodcock C. E. , , and Strahler A. H. , 1993: Nonlinear estimation of scene parameters from digital images using zero-hit run-length statistics. IEEE Trans. Geosci. Remote Sens., 31 , 735746.

    • Search Google Scholar
    • Export Citation
  • Davis, R. E., , Hardy J. P. , , Ni W. , , Woodcock C. E. , , McKenzie C. , , Jordan R. , , and Li X. , 1997: Variation of snow cover processes in the boreal forest: A parametric study on the effects of conifer canopy. J. Geophys. Res., 102 , D24. 2938929396.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dozier, J., 1989: Spectral signature of alpine snow cover from the Landsat thematic mapper. Remote Sens. Environ., 28 , 922.

  • Dozier, J., , and Painter T. H. , 2004: Multispectral and hyperspectral remote sensing of alpine snow properties. Annu. Rev. Earth Planet. Sci., 32 , 465494.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Franklin, J., , Michaelson J. , , and Strahler A. H. , 1985: Spatial analysis of density dependent pattern in coniferous forest stands. Plant Ecol., 64 , 2936.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Frazer, G. W., , Canham C. D. , , and Lertzman K. P. , 1999: Gap Light Analyzer (GLA) Version 2.0: Imaging software to extract canopy structure and gap light transmission indices from true-color fisheye photographs. Simon Fraser University and the Institute of Ecosystem Studies, 36 pp.

  • Hall, D. K., , Foster J. L. , , Verbyla D. L. , , Klein A. G. , , and Benson C. S. , 1998: Assessment of snow-cover mapping accuracy in a variety of vegetation-cover densities in central Alaska. Remote Sens. Environ., 66 , 129137.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hall, D. K., , Riggs G. A. , , Salomonson V. V. , , DiGirolamo N. E. , , and Bayr K. J. , 2002: MODIS snow-cover products. Remote Sens. Environ., 83 , 181194.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hardy, J. P., , Davis R. E. , , Jordan R. , , Li X. , , Woodcock C. E. , , Ni W. , , and McKenzie J. , 1997: Snow ablation modeling at the stand scale in a boreal jack pine forest. J. Geophys. Res., 102 , D24. 2939729406.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hardy, J. P., , Davis R. E. , , Jordan R. , , Ni W. , , and Woodcock C. E. , 1998: Snow ablation modelling in a mature aspen stand of the boreal forest. Hydrol. Processes, 12 , 17631778.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kaufmann, M. R., , and Troendle C. A. , 1981: The relationship of leaf area and foliage biomass to sapwood conducting area in four subalpine forest tree species. For. Sci., 27 , 477482.

    • Search Google Scholar
    • Export Citation
  • Li, X., , and Strahler A. H. , 1985: Geometeric-optical modeling of a conifer forest canopy. IEEE Trans. Geosci. Remote Sens., 23 , 705721.

    • Search Google Scholar
    • Export Citation
  • Li, X., , and Strahler A. H. , 1992: Geometric-optical bidirectional reflectance modeling of the discrete crown vegetation canopy: Effect of crown shape and mutual shadowing. IEEE Trans. Geosci. Remote Sens., 30 , 276292.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, X., , Strahler A. H. , , and Woodcock C. E. , 1995: A hybrid geometric optical-radiative transfer approach for modeling albedo and directional reflectance of discontinuous canopies. IEEE Trans. Geosci. Remote Sens., 33 , 467480.

    • Search Google Scholar
    • Export Citation
  • Liu, J., , Melloh R. A. , , Woodcock C. E. , , Davis R. E. , , and Ochs E. S. , 2004: The effect of viewing geometry and topography on viewable gap fractions through forest canopies. Hydrol. Processes, 18 , 35953607.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Miller, S. L., cited. 2003: CLPX-Airborne: Infrared orthophotography and LIDAR topographic mapping. National Snow and Ice Data Center. [Available online at http://nsidc.org/data/nsidc-0157.html].

  • Ni, W., , and Woodcock C. E. , 2000: Effect of canopy structure and the presence of snow on the albedo of boreal conifer forests. J. Geophys. Res., 105 , D9. 1187911888.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ni, W., , Li X. , , Woodcock C. E. , , Roujean J. L. , , and Davis R. E. , 1997: Transmission of solar radiation in boreal conifer forests: Measurements and models. J. Geophys. Res., 102 , D24. 2955529566.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Painter, T. H., , Dozier J. , , Roberts D. A. , , Davis R. E. , , and Green R. O. , 2003: Retrieval of subpixel snow-covered area and grain size from imaging spectrometer data. Remote Sens. Environ., 85 , 6477.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rosenthal, W., , and Dozier J. , 1996: Automated mapping of montane snow cover at subpixel resolution from the Landsat Thematic Mapper. Water Resour. Res., 32 , 115130.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Salomonson, V. V., , and Appel I. , 2004: Estimating fractional snow cover from MODIS using the normalized difference snow index. Remote Sens. Environ., 89 , 351360.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Salomonson, V. V., , and Appel I. , 2006: Development of the Aqua MODIS NDSI fractional snow cover algorithm and validation results. IEEE Trans. Geosci. Remote Sens., 44 , 17471756.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schaaf, C. B., , Li X. , , and Strahler A. H. , 1994: Topographic effects on bidirectional and hemispherical reflectances calculated with a geometric-optical canopy model. IEEE Trans. Geosci. Remote Sens., 32 , 11861193.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Simpson, J. J., , Stitt J. R. , , and Sienko M. , 1998: Improved estimates of the areal extent of snow cover from AVHRR data. J. Hydrol., 204 , 123.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yang, R., , and Friedl M. A. , 2003: Determination of roughness lengths for heat and momentum over boreal forests. Bound.-Layer Meteor., 107 , 581603.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yang, R., , Friedl M. A. , , and Ni W. , 2001: Parameterization of shortwave radiation flux for nonuniform vegetation canopies in land surface models. J. Geophys. Res., 106 , D13. 1427514286.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yang, Z. L., and Coauthors, 1999: Simulation of snow mass and extent in general circulation models. Hydrol. Processes, 13 , 20972113.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • View in gallery

    Two-dimensional representation on viewing geometry of forest canopy with snow fully covered underneath (white) from a satellite. The visible snow area is shown as a thickened white line in the top panel.

  • View in gallery

    Fractional snow-covered area results from the MODSCAG model for the CLPX St. Louis Creek ISA in the Fraser Experimental Forest (FEF). The dot and whiskers in the plot are the mean and ±1 std dev about the mean.

  • View in gallery

    Between-crown gaps, P(n = 0), and within-crown gaps, P(n > 0), in the geometric optical–radiative transfer model: R and b are horizontal and vertically crown radii, respectively; h1 and h2 are the lower and upper boundaries of crown centers, respectively; n is the number of tree crowns penetrated by a ray.

  • View in gallery

    Between-crown gap fractions and within-crown gap fractions estimated by the GORT model using tree parameter values measured in the Intermediate Stand in the Fool Creek ISA in the Fraser Experimental Forest.

  • View in gallery

    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 tree photos show examples of (left) Engelmann spruce, (center) subalpine fir, and (right) lodgepole pine.

  • View in gallery

    Measured b/R values for different trees species.

  • View in gallery

    Average 95% confidence intervals as a function of number of sample points when estimating 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.

  • View in gallery

    Zero-hit run-length probability as a function of laser footprint size for all four stands in the Fool Creek ISA. The circled points are zero-hit run-length probability (P0.4) for single pixels with the footprint size for the lidar data (0.4 m); P0 represents the true proportion of ground in the scene. The ratio P0.4/P0 shown in the legend is used to correct for footprint size.

  • View in gallery

    Lidar canopy height histogram for Sparse Stand in the Fool Creek ISA.

  • View in gallery

    Viewable gap fraction estimates for photo images on five occasions with varied illumination for two sample points in the St. Louis Creek stand.

  • View in gallery

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

  • View in gallery

    As in Fig. 11 but for the estimated VGF from the hemispherical photos and from the GORT model.

  • View in gallery

    Estimated VGF from the GO and GORT models using canopy cover values from lidar data.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 91 91 13
PDF Downloads 52 52 5

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

View More View Less
  • 1 Department of Geography and Environment, Boston University, Boston, Massachusetts
  • | 2 Engineer Research and Development Center, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire
  • | 3 Department of Geography, University of Utah, Salt Lake City, Utah
© Get Permissions
Full access

Abstract

Forest canopies influence the proportion of the land surface that is visible from above, or the viewable gap fraction (VGF). The VGF limits the amount of information available in satellite data about the land surface, such as snow cover in forests. Efforts to recover fractional snow cover from the spectral mixture analysis model Moderate Resolution Imaging Spectroradiometer (MODIS) snow-covered area and grain size (MODSCAG) indicate the importance of view angle effects in forested landscapes. The VGF can be estimated using both hemispherical photos and forest canopy models. For a set of stands in the Cold Land Field Processes Experiment (CLPX) sites in the Fraser Experimental Forest in Colorado, the convergence of both measurements and models of the VGF as a function of view angle supports the idea that VGF can be characterized as a function of forest properties. A simple geometric optical (GO) model that includes only 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 hemispherical 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 makes the parameterization of the GORT model possible over a landscape. Better knowledge of the angular distribution of gaps in forest canopies holds promise for improving remote sensing of snow cover fraction.

Corresponding author address: Jicheng Liu, Department of Geography and Environment, Boston University, 675 Commonwealth Ave., Boston, MA 02215. Email: jcliu@bu.edu

This article included in the The Cold Land Processes Experiment (CLPX) special collection.

Abstract

Forest canopies influence the proportion of the land surface that is visible from above, or the viewable gap fraction (VGF). The VGF limits the amount of information available in satellite data about the land surface, such as snow cover in forests. Efforts to recover fractional snow cover from the spectral mixture analysis model Moderate Resolution Imaging Spectroradiometer (MODIS) snow-covered area and grain size (MODSCAG) indicate the importance of view angle effects in forested landscapes. The VGF can be estimated using both hemispherical photos and forest canopy models. For a set of stands in the Cold Land Field Processes Experiment (CLPX) sites in the Fraser Experimental Forest in Colorado, the convergence of both measurements and models of the VGF as a function of view angle supports the idea that VGF can be characterized as a function of forest properties. A simple geometric optical (GO) model that includes only 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 hemispherical 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 makes the parameterization of the GORT model possible over a landscape. Better knowledge of the angular distribution of gaps in forest canopies holds promise for improving remote sensing of snow cover fraction.

Corresponding author address: Jicheng Liu, Department of Geography and Environment, Boston University, 675 Commonwealth Ave., Boston, MA 02215. Email: jcliu@bu.edu

This article included in the The Cold Land Processes Experiment (CLPX) special collection.

1. Introduction

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

Forest canopies influence the fraction of the land surface that is visible from above, or the viewable gap fraction (VGF) (Liu et al. 2004). Hence, the VGF limits the amount of snow on the ground that is visible to remote sensors when the ground is fully covered by snow. Since the VGF is strongly dependent on view zenith angle, the amount of snow visible in forests will vary accordingly (Liu et al. 2004). Figure 1 shows the view zenith angle effect on the amount of snow area that is visible from a satellite sensor when the ground surface is fully covered by snow. The amount of visible snow, or VGF, is largest at nadir, decreasing as the view zenith angle increases, and at a view zenith angle of θ2, the satellite sensor can barely see the snow on the ground.

Knowledge of how the VGF changes as a function of view zenith angle may improve the estimation of fractional snow cover from remote sensing in forested areas. Remote sensing of snow cover has evolved from binary mapping of snow (Dozier 1989; Hall et al. 2002) to subpixel mapping of fractional snow cover with regression tree approaches (Rosenthal and Dozier 1996) with use of the normalized difference snow index (NDSI) (Salomonson and Appel 2004, 2006) and multiple endmember direct spectral mixture analysis (Painter et al. 2003). Figure 2 shows the fractional snow-covered area (SCA) results from the Moderate Resolution Imaging Spectroradiometer (MODIS) snow-covered area and grain size (MODSCAG) model for the Cold Land Processes Field Experiment (CLPX) in the St. Louis Creek intensive study area (ISA) of the Fraser Experimental Forest. MODSCAG combines a radiative transfer model for snow spectral endmembers with a multiple endmember spectral mixture analysis approach in which the number of endmembers as well as the endmembers themselves may vary on a pixel by pixel basis. When applied to imaging spectrometer data, the model had an overall SCA root-mean-square error of less than 4% (Painter et al. 2003). Notice the view angle dependence of the SCA estimates in Fig. 2. Near nadir the estimates are near 30% and decline to approximately 15% at high view angles. Note that this area is relatively homogeneous in terms of forest cover and, thus, the effect of change in MODIS resolution as a function of view zenith angle is minimized. The largest possible MODIS pixel size is ∼1 × 2.5 km2 at the highest zenith angles. However, the increasing rate is not constant; the rate increases as the view zenith angle becomes larger. At the largest view zenith angle the enlarged MODIS pixel includes small amounts of southeast-facing slope on the west edge and northeast-facing slope on the south edge. It would be beneficial to demonstrate this on a boreal forest landscape where slope differences are minor.

It is intuitively apparent that the VGF will vary as a function of view angle as well as canopy structure. As view angles increase away from nadir, less of the ground surface is visible in forested areas. Similarly, as the canopy cover of a forest increases, the VGF will also decrease. A quantitative understanding of these effects requires development of a model for the way the VGF varies as a function of view angle, forest canopy properties, and topography. Prior results indicate a geometric optical (GO) model captures the basic shape of the relationship between the VGF and view angle, but consistently underestimates the VGF when compared with the results from hemispheric photos (Liu et al. 2004). The GO model is limited to the estimation of between-crown gaps, and addition of the effects of within-crown gaps could improve estimation of the VGF, especially for those canopies where tree crowns are sparse.

The primary purpose of this paper is to extend studies of the VGF to include a hybrid geometric optical–radiative transfer (GORT) model that includes the effects of within-crown gaps. This paper also explores the effect of the density of field samples and the ability to use airborne light detection and ranging (lidar) data for parameter estimation for discrete object models like the GO and GORT models.

2. Description of the GORT model

The hybrid geometrical optical–radiative transfer model is a canopy directional reflectance model that evolved from the GO model of Li and Strahler (1992) and includes the effects of within-crown gaps, given the foliage area volume density (FAVD) within tree crowns as one of the input parameters (Li et al. 1995). In this model, the individual tree crowns are no longer assumed opaque, as in the GO model, and the amount of within-crown gap is modeled using the within-crown pathlength at the scale of leaves. This model was validated using photosynthetically active radiation (PAR) and solar radiation transmission measurements at the Boreal Ecosystem–Atmosphere Study (BOREAS) sites (Ni et al. 1997). Use of the GORT model for estimating transmission through forest canopies has improved the simulations of snowmelt in boreal forest stands (Hardy et al. 1997; Davis et al. 1997). The GORT model has also been used for radiation modeling in a deciduous aspen stand in the leaf-off condition (Hardy et al. 1998) and for assessing the effect of canopy structure and the presence of snow on the albedo of boreal conifer forests (Ni and Woodcock 2000). More recently, the GORT model has been used to model the shortwave radiation regime in forest canopies, and the results are further used to parameterize land surface models (Yang et al. 2001; Yang and Friedl 2003).

The full GORT model is described in detail by Li et al. (1995), and only a brief description of how the model estimates the VGF is included here. In the GORT model, vegetation canopies are modeled as assemblages of randomly distributed tree crowns of ellipsoidal shape having horizontal crown radius R and vertical crown radius b. Note that the crown shapes of the dominant tree species in our field sites are mainly cone-shaped conifers. The reason why we continue to use the ellipsoidal shape is that for gap probability calculations in this model, particularly for dense forests, the top layer of the canopy has the major impact. For conifer forests, the b/R ratios of the ellipsoidal shape of the tree crown are usually high (>3), which makes the ellipses rather elongated and a reasonable representation of cone-shaped crowns. Crown centers in this model are assumed to be randomly located, following a uniform distribution between heights h1 and h2, the lower and upper boundaries of the heights of crown centers, respectively (Fig. 3). Within each crown, the foliage and branches are assumed uniformly distributed with a specified foliage area volume density. The effect of topography can be taken into account in the GORT model by using several simple transformations in coordinate space (Schaaf et al. 1994).

The GORT model relies on gap probabilities and pathlength distributions to model the penetration of irradiance from a parallel source and the single and multiple scattering of that irradiance in the direction of an observer. In essence, the VGF is equivalent to the gap probability at the background level, or Pgap, which is defined as the probability that a photon incident upon a vegetation canopy will pass directly through the canopy without being intercepted by a leaf, branch, or stem. In this model, between-crown gap probability is termed P(n = 0), where n is the number of plant crowns penetrated by a ray, is modeled in the same way as in the GO model as a function of crown size, shape, and stand count density. The within-crown gap probability, Pgap(s), is modeled as a function of the within-crown optical pathlength s at the scale of leaves:
i1525-7541-9-5-1005-e1
where τ = kDυ and has units of per meter; k is the attenuation of the radiation by leaf area contained within a unit of canopy depth for the incoming radiation direction and is determined by the leaf angle distribution and the transmissivity of the leaf; Dυ is FAVD, which defines the one-sided leaf area per unit volume and is assumed to be a constant and uniformly distributed within the crowns. The gap probability of the canopy, Pgap, can then be modeled as
i1525-7541-9-5-1005-e2
where p(s) is the distribution of s over a canopy plane. With a first-order approximation, Pgap becomes
i1525-7541-9-5-1005-e3
where p(s|1) is the distribution of s, given that a photon will penetrate an individual canopy. For different tree crown geometries, p(s|1) has different expressions. For a sphere with radius of R,
i1525-7541-9-5-1005-e4
where 0 ≤ s ≤ 2R. The case of ellipsoids can be easily derived from the sphere as the sphere becomes an ellipse through a simple linear transformation of one of its axes.

There are two types of input parameters for the GORT model: species related and stand specific. Among the first type are crown ellipticity (b/R, where b is the vertical crown radius and R is the horizontal crown radius) and FAVD that are assumed constant for a forest species or type. The stand-specific input parameters vary for individual stands and include the mean crown radius, lower and upper crown center boundaries, and stand density (Fig. 3). Crown radius and stand density combine to estimate canopy cover, which is the percent of the crown coverage from nadir viewing (Fig. 1), therefore, the complement of the VGF at nadir viewing (when within-crown gap fraction is not included). Canopy cover is the single most important canopy variable for estimating the VGF as view zenith angle increases (Liu et al. 2004).

As an example of the relative magnitude of between- and within-crown gaps, Fig. 4 shows the modeled viewable gap fractions as a function of view zenith angle using measured stand parameters for the Intermediate (density) Stand (see details in the following section) in the Fool Creek ((ISA in the Fraser Experimental Forest, Colorado (available online at http://www.fs.fed.us/rm/fraser/), for two different values of FAVD. At nadir the within-crown gap fraction is roughly 20% of the total gap fraction. As the view zenith angle increases, the within-crown gap fraction becomes a large proportion of the total gap fraction, and near 45° it becomes larger than the between-crown gap fraction. In the hypothetical case of a lower FAVD (a less dense crown), the within-crown gap fraction is a significant part of viewable gap fraction even at small view zenith angles and dominates the total VGF at high view zenith angles. Therefore, accounting for within-crown gap fraction in the estimation of viewable gap fraction is especially important for canopies with low foliage density.

3. Parameterizing the models using field measurements

Field measurements were collected in the summer of 2003 in the Fool Creek and St. Louis Creek ISAs of the Fraser Mesoscale Study Area (MSA) of the NASA Cold Land Processes Field Experiment (CLPX) to parameterize the GO and GORT models. The Fool Creek ISA is a rugged terrain with a planimetric area of about a 1 km2 and has many distinct patches resulting from different management practices (Fig. 5). Four forest stands were selected for measuring the tree parameters in this ISA, as described in Liu et al. (2004). The St. Louis Creek ISA has a relatively flat terrain and one stand was selected in this ISA. Within each stand a rectangular grid of sample points was established. The size of the grids varied slightly between stands such that there were between 35 and 50 sample points per stand for hemispherical photography (10-m spacing) and at least 12 sample points for the more time-consuming forest mensuration measurements (20-m spacing). All four Fool Creek ISA stands are dominated by Engelmann spruce and subalpine fir and the St. Louis Creek Stand is dominated by lodgepole pine. All of these species have cone-shaped tree crowns.

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

Stand density (λ) was estimated from data for variable radius plots, collected with the help of a Relaskop—an optical instrument based on angular measurements. Trees around an observation point are judged to be “in” or “out” based on the diameter at breast height (DBH) of each tree and its distance to the sample point. Smaller DBH trees have a smaller plot size than larger DBH trees, making the sampling of basal 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 of BA associated with the “in” trees and influences the size of the plot for each size of tree. By measuring the actual BA of that tree, the number of trees with this size per unit area can be estimated. The stand count density of trees for that sample point can then be calculated by summing the values for all of the “in” trees. The overall stand density λ is the average from all the measured points:
i1525-7541-9-5-1005-e5
where N is the number of sample points at one stand, Mi is the number of “in” trees in sample point i, BAF is the basal area factor used for the stand, and BAj is the measured basal area of tree j. As Eq. (5) indicates, smaller “in” trees contribute more to the stand count density. All trees that have a DBH less than 3 cm are ignored in this study as these trees are generally not in the canopy.

Crown radii (R) were measured for two trees (the first tree off north and south in a clockwise direction) at each sample point. Each measured R for a tree, combined with the measured vertical crown radius for the same tree, b, is used to calculate the b/R ratio (a measure of ellipticity) for that tree, and the overall b/R ratio for a species is estimated as the mean of all measured b/R values for that species. In the GORT model, the b/R ratio is assumed to be tree species dependent but tree size independent. To test these assumptions, Fig. 6 shows the measured b/R ratio values for individual trees, the mean value for different stands, and two tree species as a function of tree size. For each species, a simple linear regression between DBH and b/R was performed, and the null hypothesis of a slope value of zero could not be rejected based on p values of 0.1811 for lodgepole pine and 0.1170 for subalpine fir, meaning the b/R value is not tree size dependent. The variance in the mean b/R value from different stands of the same species is relatively small, and the overall difference between b/R ratio values for these two species shows the species dependency of b/R. The lodgepole pine trees tend to have less elongated tree crowns (lower b/R ratio) than the subalpine fir.

To conserve the cover value, the mean stand crown radius R is calculated as the quadratic mean of all measured tree crown radii in a stand weighted by the tree density for that size (Wi):
i1525-7541-9-5-1005-e6
where n is the total number of trees measured at one stand, Ri and Wi are the radius and the weight for tree i, and BAFi and BAi are the basal area factor used to measure tree i and the measured basal area for that tree, respectively.
Crown center lower vertical boundary (h1) and upper boundary (h2) are calculated as
i1525-7541-9-5-1005-e7
where Hbottom is the height of crown bottom and Htop is the height of crown top (Fig. 3), and they are measured in the field.

b. Confidence in stand density measurements

In all efforts to estimate properties of forest stands via sampling, the question arises of whether the sampling density is sufficient to keep uncertainties to reasonable levels. The effect of reducing the number of sample points in each stand on the estimated stand density was tested. Figure 7 shows the average 95% confidence intervals on the mean stand count density as a function of the number of sampled points. The estimated range for the tree density is less than ±5% of the estimated mean when the numbers of sample points are close to the actual numbers of sample points used. This result means the numbers of measured points for these four stands are large enough to estimate the stand density within a relatively small amount of uncertainty (less than 5%). One interesting effect in the data is the different rate of decrease in the confidence intervals for different stands. These reflect the varying degree of heterogeneity within the individual forest stands.

c. FAVD estimation

FAVD values were derived for different tree species using the relationship between the effective projected leaf area (EPLA) and DBH developed by Kaufmann et al. (1981) using field measurements in the same general area as our field measurements (M. R. Kaufmann 2003, personal communication). Their sample size ranged from 12 to 15 trees per species, and tree size ranged from small saplings several meters in height to large, mature trees. Trees were carefully felled to minimize the damage on leaves, and foliage samples were collected. For small trees, all foliage was collected including small branches. For the largest trees, fresh foliage area exceeded 5 m3 in volume, and subsampling was required (Kaufmann and Troendle 1981). The EPLA was calculated by first measuring the actual projected area of horizontal needles, and the ratio of total needle area to actual projected area of horizontal needles was 3.21 for Englemann spruce and subalpine fir, and 3.34 for lodgepole pine. Then, with the assumption of random orientation of foliage, the EPLA was calculated as the actual projected area of horizontal needles times 0.6366, which is obtained by integrating the cosine over the range from −90° to 90°. The needles of these conifer trees are neither planophile nor erectophile, so the error due to the random orientation assumption should be minor. A linear relationship between EPLA and DBH was observed for Englemann spruce, subalpine fir, and lodgepole pine, and Kaufmann’s results for the three species are summarized in (Table 1). To estimate FAVD for every measured tree, the EPLA for that tree was calculated, using the equation in Table 1, and divided by its elliptical crown volume, determined from measured b and R. The FAVD value for a species was then calculated as the mean value from all the FAVD values for trees of that species.

d. Parameter summary

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

e. Canopy cover estimation

The canopy cover value estimated from field measurements is a function of both stand density, λ, and the average crown radius, R, with the assumptions of uniform crown size and random locations of the tree crowns within the stand (Li and Strahler 1985; Franklin et al. 1985):
i1525-7541-9-5-1005-e8

4. Parameterizing the models using lidar data

Aerial lidar data provides an alternate, or additional, method of obtaining data about the canopy for model parameterization. The advantage of using lidar data is that canopy information derived from it can be obtained over a larger area than is practical using in situ measurements. The use of lidar data to derive canopy cover, height, and crown radius information for GORT model parameterization is explored here.

Lidar data for the Fool Creek ISA were collected on 19 September 2003 at approximately 4500 feet elevation, normalized to ground controls and processed to remove noise and redundancies (Miller 2003). The data have approximately 1.5-m horizontal spacing, 0.15-m vertical tolerances, and a maximum laser view angle of 15° from vertical, providing an illuminated footprint at level ground of 0.4 m. The first-return data (representing the vegetation-terrain surface) and the last-return data (representing the ground) were differenced to obtain histograms of vegetation height. The ground surface elevations were generated by creating a natural neighbor grid at 0.5-m spacing and then performing a linear interpolation within grids to the locations of the vegetation–terrain elevations. Lidar canopy height histograms were developed for each forest stand (Fig. 5) using the data within the stand boundaries. The boundaries were determined in the field with a Trimble global positioning system.

The lidar footprint has a certain size, and, thus, the proportion of the pulses that miss trees entirely is not equivalent to the complement of tree cover (1 − cover). For a very small lidar footprint these will be similar but, as the footprint increases, the estimate of visible ground surface based on the lidar height histogram will become smaller than the true value. To incorporate the effect of lidar footprint size on cover estimation, a zero-hit run-length model (Chen et al. 1993) was used to estimate the relationship between the lidar-observed proportion of bare ground and the true tree cover based on tree size and density data. In the zero-hit run-length probability model, probabilities are estimated for the lengths of runs of grids of fixed size that do not hit any part of objects that define a scene (such as trees in a stand) (Chen et al. 1993). The simple scene model uses a plane that is covered by randomly located discs of diameter D1 = 2R and Poisson density λ, which is the same case as the GO and GORT model, where the discs are the tree crowns observed from nadir. The scene is imaged by a sensor with a pixel size, D2, and lidar returns are separated into two classes: those that intersect a disc, or tree, (the “hit” pixels) and those that intersect only the background (the “zero-hit” pixels). According to zero-hit run-length statistics, the probability that a pixel (or measurement) hits zero trees for the simple scene described above is
i1525-7541-9-5-1005-e9

This approach has been successfully used to estimate tree density and size from simulated remote sensing images and proved to be especially valid when the objects of interest (trees) are large relative to the size of the observations (Chen et al. 1993), which is the present case.

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 radii and densities (Table 2) of the five measured stands (Fig. 8). The zero-hit run-length probability goes to zero when the footprint size exceeds 5 m, meaning that there will be no background returns expected when the lidar footprint size is greater than this size. The zero-hit run-length probability is 80% ± 5% of the true proportion of the ground surface for the footprint size of 0.4 m, which is the current case. The true proportion of ground surface for each stand in the Fool Creek ISA is estimated by dividing the percentage of ground returns in the lidar data by 0.8. The percentage of the ground returns is determined from histograms of the lidar data. The histogram of the “Sparse Stand” (Fig. 9) suggests that the 1-m height is a good choice for the boundary between ground returns and the returns from the forest canopy. The threshold height of 1 m was used to separate ground returns for all stands.

5. Hemispherical photographs

Hemispherical photos were taken at each sample point in the grid (20-m spacing) for each stand at 1.25-m height with a Nikon Coolpix 995 digital camera and Nikon fisheye converter (FC-E8) lens. Forty-nine photographs were taken in St. Louis Creek, 32 in Dense1, 40 in “Dense2,” 49 in the “Intermediate Stand,” and 34 in the “Sparse Stand”. The locations of the photo plots are those shown in Fig. 5 for the Fool Creek sites. The St. Louis Creek plot was located at U. S. Geological Survey center coordinates 4419964 N, 425897.3 E. The camera and bubble level were mounted on a tripod with a ball head attachment to permit rapid leveling at each sample point. Photographs were taken at dusk in all stands, except the Intermediate Stand photos were taken on a partly cloudy day. Black and white images were acquired at dusk and color images were acquired during the day. The camera was set for automatic exposure, infinite focus, wide-angle lens, full size (resulting in 1519 pixels hemisphere diameter), high quality (¼ jpeg compression), and matrix light metering.

Camera lenses used for hemispherical photo-image collection project a hemispherical image onto an image plane that is then used in measurement analysis. The variation of the FC-E8 lens projection from a polar projection is slight and was corrected using calibration coefficients (c0 = 0, c1 = 1.066 821, c2 = −0.036 160 7, and c3 = −0.031 261 1), provided for use with the Gap Light Analyzer (GLA) software (Frazer et al. 1999). The viewable gap fraction (VGF) as a function of zenith angle was determined as the fraction of unobstructed sky, using a threshold procedure in the GLA to separate sky and canopy pixels. The blue color band was used to threshold the daytime photographs because it typically provided the best contrast between the canopy and sky. The threshold procedure is a subjective one with few options for systemization; however, we have found consistent results in analyses of photographs taken under different lighting conditions (Fig. 10). Gap fraction versus zenith angle relationships were determined at 10° zenith increments. The 95% confidence interval of the mean stand VGF for any view zenith angle is shown as a shaded area in all subsequent graphs for comparison with model results (such as Figs. 11 and 12). Notice that the uncertainty in the estimates is highest near nadir where there are the fewest observations in the hemispherical photos.

Reduced field of views (FOV) due to rugged topography begin at view zenith angles greater than 80° (75°) for the St. Louis Creek (Fool Creek) site. The reduced FOV will decrease the gap fraction determined by hemispherical photography for these near-ground zenith angles, except in the not uncommon circumstance that the illumination of the nearby ridge (when viewed through the canopy) is higher than the underside of the canopy being photographed.

6. Results and discussion

Comparisons of the VGF as a function of view angle estimated by the hemispherical photos and by the GO and GORT models based on the cover values from the field measurements and the lidar data for the four stands in Fool Creek and the St. Louis Creek Stand are shown in Figs. 11 and 12. The rms error of the VGF is a measure of the discrepancy between the modeled results and the results from the hemispherical photos: However, it is unclear whether the hemispherical photos are more accurate than the model results.

The GO model using cover estimates results and the hemispherical results show that the VGF decreases as view zenith angle increases (Fig. 11). The rate of decrease varies between stands until the view zenith angle is larger than 30°. By a view zenith angle of 30°, the VGF values are less than half of the value from nadir. This indicates that, when the forest is viewed by a satellite sensor with a greater than 30° of view zenith angle, the signal from the understory below forests that reaches the sensor is less than half of when it is viewed from nadir. This result, if accurate, implies that the observable fractional snow cover in forested areas is less than half the true fractional snow cover when view zenith angles exceed 30°. We assume that the ground area below the canopy is fully snow covered, and the fraction of the snow cover on the ground that is visible through the forest canopy from a satellite is the best the satellite data can do at estimating snow cover fraction without view zenith angle correction. We also define the “true” fractional snow cover as the fraction of snow cover viewable from nadir (1 − cover). The fraction of snow on the ground that is viewable by a satellite, which is equal to the viewable gap fraction, usually decreases as the view zenith angles increase. The model estimates using the cover value from the field measurements show better agreement with the hemispherical photos for the two dense stands in Fool Creek than using the cover value from the lidar data due to the lower cover estimates from the field measurements. For St. Louis Creek, the model estimates using cover values from the field measurements and lidar data are almost identical. The GO model underestimates the VGF values compared with the hemispherical photos throughout the range of view zenith angles except near nadir in dense stands. In all cases the GO model underestimates the VGF relative to the hemispherical photos at high view zenith angles. This result was found by Liu et al. (2004) and is an understandable result given the limitation of the model to between-crown gaps.

The GORT model takes into account within-crown gaps and agrees better with the hemispherical photos throughout the view zenith angle range in most cases except for the St. Louis Creek Stand, where the VGF estimates are systematically higher than the hemispherical photos (Fig. 12). For other stands, the estimates from the GORT model do not show the systematic bias relative to the hemispherical photo results.

The rate of decrease in the VGF is higher for the low view zenith angles for the two dense stands and almost a constant for the Intermediate Stand and the Sparse Stand, illustrating the view zenith angle effect is larger for dense forests than for sparse forests. This might result from the different b/R ratio values as the b/R ratios of the two dense stands are larger than those from the other stands.

As expected, estimates of the VGF from the GORT model are higher than those from the GO model for all the view zenith angles for all stands. However, the difference is most pronounced for the Fool Creek Intermediate and Sparse stands and the St. Louis Creek Stand (Fig. 13). All of these stands have lower canopy cover than the two dense stands in Fool Creek. For the sparser stands, the within-crown gap fractions at nadir are around 15% of the total VGF and become increasingly important as view zenith angle increases. This result indicates that within-crown gaps are more important for sparse forests. The number of trees that intercept 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 hemispherical photos estimate a stronger view angle dependence for the VGF than the estimates shown for snow cover fraction in Fig. 2. One problem with a direct comparison of these graphs is that MODIS data were the source of the MODSCAG results and the MODIS observations cover a significantly larger area than the St. Louis Creek Stand. If the forests in the surrounding area have a higher canopy cover, that would explain some of the discrepancy.

7. Conclusions

The convergence of both measurements and models of the VGF as a function of view angle supports the idea that the VGF can be characterized as a function of forest properties. Knowledge of the magnitude of view angle effects in remote sensing imagery over forests should benefit remote sensing of snow cover fraction.

Generally speaking, taking into account the within-crown gap fraction improved the model estimation of the VGF as a function of view zenith angle, especially for Intermediate and Sparse stands. Even though the rms error for the GORT results are not significantly lower than the results for the GO model, they do not exhibit the pattern of systematic underestimation of the GO model. For the Intermediate Stand and Sparse Stand, the within-crown gap fractions are around 15% of the total VGF at nadir and become increasingly more important as the view zenith angle increases.

The similar results to field measurements for forest cover estimates emerging from the lidar data support the effectiveness of using the zero-hit run-length model to take into account the effect of pixel size. Lidar data can be used to map forest cover with high accuracy when the lidar footprint size is smaller than the tree crown size. The canopy heights estimated from the lidar data show general agreement with the height values from the field measurements. The use of airborne lidar data provides a way to parameterize the GORT model over landscapes that is not feasible using field measurements.

Acknowledgments

This research was supported by the U.S. Army. The efforts of the more than 200 people who participated in the planning and execution of CLPX 2002-2003 are very much appreciated. The CLPX was funded through the cooperation of many agencies and organizations including the NASA Earth Science Enterprise, Terrestrial Hydrology Program, Earth Observing System Program, and Airborne Science Program; the National Oceanic and Atmospheric Administration Office of Global Programs; the U.S. Army Corps of Engineers Civil Works Remote Sensing Research Program; the U.S. Army Basic Research Program; the National Space Development Agency of Japan (NASDA); the Japan Science and Technology Corporation; and the National Assembly for Wales, Strategic Research Investment Fund, Cardiff, South Glamorgan, United Kingdom. A portion of this work was conducted at the Jet Propulsion Laboratory at the California Institute of Technology, under contract to the National Aeronautics and Space Administration NASA. We would also like to thank Thomas Berry of ERDC/Vicksburg for collecting GPS locations of our forest stands and Stephen Miller of Johnson, Kunkel and Associates, Inc. for information on the specifications of the lidar. This work was supported by U.S. Army Contract DACA42-03-C-0033.

REFERENCES

  • Chen, R., , Jupp D. L. B. , , Woodcock C. E. , , and Strahler A. H. , 1993: Nonlinear estimation of scene parameters from digital images using zero-hit run-length statistics. IEEE Trans. Geosci. Remote Sens., 31 , 735746.

    • Search Google Scholar
    • Export Citation
  • Davis, R. E., , Hardy J. P. , , Ni W. , , Woodcock C. E. , , McKenzie C. , , Jordan R. , , and Li X. , 1997: Variation of snow cover processes in the boreal forest: A parametric study on the effects of conifer canopy. J. Geophys. Res., 102 , D24. 2938929396.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dozier, J., 1989: Spectral signature of alpine snow cover from the Landsat thematic mapper. Remote Sens. Environ., 28 , 922.

  • Dozier, J., , and Painter T. H. , 2004: Multispectral and hyperspectral remote sensing of alpine snow properties. Annu. Rev. Earth Planet. Sci., 32 , 465494.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Franklin, J., , Michaelson J. , , and Strahler A. H. , 1985: Spatial analysis of density dependent pattern in coniferous forest stands. Plant Ecol., 64 , 2936.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Frazer, G. W., , Canham C. D. , , and Lertzman K. P. , 1999: Gap Light Analyzer (GLA) Version 2.0: Imaging software to extract canopy structure and gap light transmission indices from true-color fisheye photographs. Simon Fraser University and the Institute of Ecosystem Studies, 36 pp.

  • Hall, D. K., , Foster J. L. , , Verbyla D. L. , , Klein A. G. , , and Benson C. S. , 1998: Assessment of snow-cover mapping accuracy in a variety of vegetation-cover densities in central Alaska. Remote Sens. Environ., 66 , 129137.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hall, D. K., , Riggs G. A. , , Salomonson V. V. , , DiGirolamo N. E. , , and Bayr K. J. , 2002: MODIS snow-cover products. Remote Sens. Environ., 83 , 181194.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hardy, J. P., , Davis R. E. , , Jordan R. , , Li X. , , Woodcock C. E. , , Ni W. , , and McKenzie J. , 1997: Snow ablation modeling at the stand scale in a boreal jack pine forest. J. Geophys. Res., 102 , D24. 2939729406.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hardy, J. P., , Davis R. E. , , Jordan R. , , Ni W. , , and Woodcock C. E. , 1998: Snow ablation modelling in a mature aspen stand of the boreal forest. Hydrol. Processes, 12 , 17631778.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kaufmann, M. R., , and Troendle C. A. , 1981: The relationship of leaf area and foliage biomass to sapwood conducting area in four subalpine forest tree species. For. Sci., 27 , 477482.

    • Search Google Scholar
    • Export Citation
  • Li, X., , and Strahler A. H. , 1985: Geometeric-optical modeling of a conifer forest canopy. IEEE Trans. Geosci. Remote Sens., 23 , 705721.

    • Search Google Scholar
    • Export Citation
  • Li, X., , and Strahler A. H. , 1992: Geometric-optical bidirectional reflectance modeling of the discrete crown vegetation canopy: Effect of crown shape and mutual shadowing. IEEE Trans. Geosci. Remote Sens., 30 , 276292.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, X., , Strahler A. H. , , and Woodcock C. E. , 1995: A hybrid geometric optical-radiative transfer approach for modeling albedo and directional reflectance of discontinuous canopies. IEEE Trans. Geosci. Remote Sens., 33 , 467480.

    • Search Google Scholar
    • Export Citation
  • Liu, J., , Melloh R. A. , , Woodcock C. E. , , Davis R. E. , , and Ochs E. S. , 2004: The effect of viewing geometry and topography on viewable gap fractions through forest canopies. Hydrol. Processes, 18 , 35953607.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Miller, S. L., cited. 2003: CLPX-Airborne: Infrared orthophotography and LIDAR topographic mapping. National Snow and Ice Data Center. [Available online at http://nsidc.org/data/nsidc-0157.html].

  • Ni, W., , and Woodcock C. E. , 2000: Effect of canopy structure and the presence of snow on the albedo of boreal conifer forests. J. Geophys. Res., 105 , D9. 1187911888.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ni, W., , Li X. , , Woodcock C. E. , , Roujean J. L. , , and Davis R. E. , 1997: Transmission of solar radiation in boreal conifer forests: Measurements and models. J. Geophys. Res., 102 , D24. 2955529566.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Painter, T. H., , Dozier J. , , Roberts D. A. , , Davis R. E. , , and Green R. O. , 2003: Retrieval of subpixel snow-covered area and grain size from imaging spectrometer data. Remote Sens. Environ., 85 , 6477.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rosenthal, W., , and Dozier J. , 1996: Automated mapping of montane snow cover at subpixel resolution from the Landsat Thematic Mapper. Water Resour. Res., 32 , 115130.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Salomonson, V. V., , and Appel I. , 2004: Estimating fractional snow cover from MODIS using the normalized difference snow index. Remote Sens. Environ., 89 , 351360.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Salomonson, V. V., , and Appel I. , 2006: Development of the Aqua MODIS NDSI fractional snow cover algorithm and validation results. IEEE Trans. Geosci. Remote Sens., 44 , 17471756.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schaaf, C. B., , Li X. , , and Strahler A. H. , 1994: Topographic effects on bidirectional and hemispherical reflectances calculated with a geometric-optical canopy model. IEEE Trans. Geosci. Remote Sens., 32 , 11861193.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Simpson, J. J., , Stitt J. R. , , and Sienko M. , 1998: Improved estimates of the areal extent of snow cover from AVHRR data. J. Hydrol., 204 , 123.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yang, R., , and Friedl M. A. , 2003: Determination of roughness lengths for heat and momentum over boreal forests. Bound.-Layer Meteor., 107 , 581603.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yang, R., , Friedl M. A. , , and Ni W. , 2001: Parameterization of shortwave radiation flux for nonuniform vegetation canopies in land surface models. J. Geophys. Res., 106 , D13. 1427514286.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yang, Z. L., and Coauthors, 1999: Simulation of snow mass and extent in general circulation models. Hydrol. Processes, 13 , 20972113.

    • Crossref
    • Search Google Scholar
    • Export Citation

Fig. 1.
Fig. 1.

Two-dimensional representation on viewing geometry of forest canopy with snow fully covered underneath (white) from a satellite. The visible snow area is shown as a thickened white line in the top panel.

Citation: Journal of Hydrometeorology 9, 5; 10.1175/2008JHM866.1

Fig. 2.
Fig. 2.

Fractional snow-covered area results from the MODSCAG model for the CLPX St. Louis Creek ISA in the Fraser Experimental Forest (FEF). The dot and whiskers in the plot are the mean and ±1 std dev about the mean.

Citation: Journal of Hydrometeorology 9, 5; 10.1175/2008JHM866.1

Fig. 3.
Fig. 3.

Between-crown gaps, P(n = 0), and within-crown gaps, P(n > 0), in the geometric optical–radiative transfer model: R and b are horizontal and vertically crown radii, respectively; h1 and h2 are the lower and upper boundaries of crown centers, respectively; n is the number of tree crowns penetrated by a ray.

Citation: Journal of Hydrometeorology 9, 5; 10.1175/2008JHM866.1

Fig. 4.
Fig. 4.

Between-crown gap fractions and within-crown gap fractions estimated by the GORT model using tree parameter values measured in the Intermediate Stand in the Fool Creek ISA in the Fraser Experimental Forest.

Citation: Journal of Hydrometeorology 9, 5; 10.1175/2008JHM866.1

Fig. 5.
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 tree photos show examples of (left) Engelmann spruce, (center) subalpine fir, and (right) lodgepole pine.

Citation: Journal of Hydrometeorology 9, 5; 10.1175/2008JHM866.1

Fig. 6.
Fig. 6.

Measured b/R values for different trees species.

Citation: Journal of Hydrometeorology 9, 5; 10.1175/2008JHM866.1

Fig. 7.
Fig. 7.

Average 95% confidence intervals as a function of number of sample points when estimating 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.

Citation: Journal of Hydrometeorology 9, 5; 10.1175/2008JHM866.1

Fig. 8.
Fig. 8.

Zero-hit run-length probability as a function of laser footprint size for all four stands in the Fool Creek ISA. The circled points are zero-hit run-length probability (P0.4) for single pixels with the footprint size for the lidar data (0.4 m); P0 represents the true proportion of ground in the scene. The ratio P0.4/P0 shown in the legend is used to correct for footprint size.

Citation: Journal of Hydrometeorology 9, 5; 10.1175/2008JHM866.1

Fig. 9.
Fig. 9.

Lidar canopy height histogram for Sparse Stand in the Fool Creek ISA.

Citation: Journal of Hydrometeorology 9, 5; 10.1175/2008JHM866.1

Fig. 10.
Fig. 10.

Viewable gap fraction estimates for photo images on five occasions with varied illumination for two sample points in the St. Louis Creek stand.

Citation: Journal of Hydrometeorology 9, 5; 10.1175/2008JHM866.1

Fig. 11.
Fig. 11.

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

Citation: Journal of Hydrometeorology 9, 5; 10.1175/2008JHM866.1

Fig. 12.
Fig. 12.

As in Fig. 11 but for the estimated VGF from the hemispherical photos and from the GORT model.

Citation: Journal of Hydrometeorology 9, 5; 10.1175/2008JHM866.1

Fig. 13.
Fig. 13.

Estimated VGF from the GO and GORT models using canopy cover values from lidar data.

Citation: Journal of Hydrometeorology 9, 5; 10.1175/2008JHM866.1

Table 1.

Effective projected leaf area (EPLA) (m2) as a function of diameter at breast height (DBH) (cm).

Table 1.
Table 2.

Measured canopy parameter values for the GORT model input.

Table 2.
Save