Privette initially discussed the bidirectional reflectance model and some results from combining vegetation indices with bidirectional reflectance characteristics. Next, he discussed the inversion of a bidirectional reflectance distribution function (BRDF) model. Investigations on the invertibility of the model are followed by results using ground-based reflectance data from the First ISLSCP Field Experiment (FIFE). Privette also discussed results from inversions with satellite reflectance data collected over the FIFE site.

This study was limited to grassland applications. Grasslands cover approximately 16% of Earth's land surface and account for nearly 10% of its net productivity. In addition, some results suggest grasslands are one of the most climatologically sensitive earth covers. Thus, grasslands may be early indicators of a changing climate.

The bidirectional reflectance of a vegetated surface is a function of the irradiance field, the spectral properties of the plant organs and soil particulates, and the structure of the vegetation, litter and soil. Although soil and atmosphere scattering is modeled relatively easily, scattering from vegetation is more difficult due to the finite size scatterers at fixed positions. To make the problem more amenable to mathematical solution, we invoke the turbid medium approximation whereby we consider the leaves ground up into infinitesimal leaflets and redistributed between the atmosphere and soil in the same orientation as the original plant leaves. The DISORD model from Ranga Myneni is perhaps the most accurate vegetation turbid medium model available. It is based on the radiative transfer equation, uses discrete ordinates to solve the multiple scattering problem, and has been validated against a series of canopies. It is a function of leaf area index (LAI), leaf angle distribution, leaf optical properties, soil reflectance (Lambertian or anisotropic), leaf specular reflectance, a hot spot parameter and the ratio of direct-to-total irradiance. This model was used throughout this study.

Vegetation Indices

A grassland reflectance distribution in the red and near-infrared (NIR) bands shows strong anisotropy. Since the NIR angular distribution is not a constant multiple of the red distribution, vegetation indices must depend on the view and solar geometry. To compensate for this, we often attempt to use near-nadir view geometries. While convenient, nadir views may not be best. Indeed, samples at other geometries may be more sensitive to the desired vegetation parameters. For example, many have reported the near-linear relationship between fAPAR and NDVI. To find a geometry where this relationship is most linear, NDVI was modeled for canopies of LAI=1, 3 and 5 and erectophile and planophile leaf distributions for 12 solar zenith angles. All view angles in the upper hemisphere were considered. At 75 degrees forward scattering, the squared linear correlation coefficient for the fAPAR-NDVI relationship was 0.247. However, at other angles, very encouraging results were possible. At 30 degrees backscatter, off the principal plane, r^2=0.928. The sensitivity of NDVI to fAPAR (the slope of the regression line) is also highest at medium backscatter angles. A comparison of NDVI with LAI suggests, however, that this correlation is greatest at higher view zenith angles in the backscatter direction.

The effects of using different angles for red and NIR reflectances in the construction of NDVI were also considered. Using principal plane data, one can see that an index formed with forward scattered red reflectance and near-nadir NIR reflectance has the highest correlation with fAPAR. Sensitivity to fAPAR is greatest with an index formed from red reflectance in the middle backscatter region and NIR reflectance in the middle forward scatter region. Such indices could be formed from a single pass of EOS MISR or multiple passes from AVHRR or EOS MODIS. In conclusion, the knowledgeable combination of BRDF effects and vegetation indices can significantly improve the accuracy of retrieved biophysical parameters from indices.

The inversion problem

As stated above, the angular distribution of radiation scattered by the Earth's surface contains information on the structural and optical properties of the surface. Potentially, this information may be retrieved through the inversion of surface bidirectional reflectance distribution function (BRDF) models. An inversion requires the adjustment of a set of model parameters until the model-predicted reflectance best matches a set of empirical reflectance data. Once this occurs, the set of parameters leading to the best match is considered the best estimate of surface conditions at the time of the data sampling.

Only model parameters most affecting the canopy reflectance can be retrieved. In this study, the sensitivity of a top of canopy (TOC) reflectance was determined for canopies of arbitrary optical depth. In general, the TOC reflectance was primarily sensitive to soil reflectance and LAI for LAI < 1. For canopies of LAI > 1.5, reflectance was primarily sensitive to leaf optical properties.

The invertibility of the discrete ordinates model was shown for typical conditions us ing synthetic, noise-free data. In general, solutions were reasonably accurate except for cases of high LAI, low solar zenith angle (SZA) and incorrect leaf angle distribution (LAD) specification. Even for cases with incorrect inversion solutions, however, estimates of spectral albedo, absorbed radiation and canopy photosynthetic efficiency were accurate. These were determined from forward modeling using the retrieved canopy parameters. Inversions using data collected under satellite sampling schemes (AVHRR and MISR) were reasonably accurate in most cases. The only exception was the case of orthogonal plane samples from MISR. Principal plane samples resulted in the most accurate solutions.

Effects of Gaussian noise in the empirical reflectance data were also tested. Parameters to which reflectance was most sensitive were retrieved with less than 10% relative error for noise of 10% relative variance. Surface state parameters remained accurate for all noise levels. These general experiments suggested the model could be inverted under many conditions. Thus, inversions with empirical reflectance data were tried.

Data from the FIFE experiment were used for the inversions described here. FIFE was a multi-year, international study of a grassland climate and ecosystem. The experiment was conducted on a 15 km x 15 km site near Manhattan, Kansas (39° 0' latitude, 96° 3' longitude). The FIFE site consisted mostly of grazed and burned grassland. To a reasonable degree, the terrain was flat (±50 m elevation), had natural homogeneous vegetative cover, and had strong climatic forcing. FIFE included the coordinated measurement of soil, canopy and atmospheric parameters via ground, aircraft and space-borne detectors. Data was used from a site that underwent a prescribed burning in the spring of 1989 to eliminate dead vegetation from previous years. This resulted in a comparatively dense canopy over the summer months. The predominate vegetation included three C4 grasses: little bluestem (Andropogon scoparius Michx), big bluestem ( Andropogon gerardii Vitmin), and indian grass ( Sorghastrum nutan L. Nash). The site was not grazed or cultivated.

Before inversions were attempted, a decision on the use of a Lambertian or anisotropic soil background was necessary. Simulations with Lambertian and anisotropic backgrounds revealed that soil anisotropy affects TOC reflectance for relatively thick (LAI < 8) canopies. Thus, an anisotropic soil model was deemed necessary for FIFE. Inversions were conducted with FIFE soil data. A relatively invariant solution was determined using data represent ing a wide range of spectral, SZA and soil moisture conditions. In this case, the mean of the absolute values of reflectance errors was 0.006 (3.5%).

Next, inversions were conducted with field measured canopy reflectance data. FIFE data from a ground-based MMR instrument was chosen for model inversions. The MMR had seven bands in the visible and NIR wavelengths. Results were binned according to SZA (above or below 40°). Only LAI results were shown since this is the parameter generally of greatest interest. LAI was most accurately determined at low SZA with NIR data. Shortwave albedo agreed well with pyranometer-measured values, however fAPAR was overestimated in all cases. Nevertheless, there was significant variability in measured fAPAR data. It is expected that results will improve with more accurate validation data.

Finally, inversions with satellite data were attempted. Based on its wide range of sampling geometries, global coverage, and high temporal resolution, AVHRR data was used. Since satellite data has more noise in it than ground radiometer data, the number of model parameters was reduced. The model was configured for inversion by fixing LAD with the site-wide value. Moreover, leaf transmittance was coupled to leaf reflectance using a regression equation determined from empirical spectrometer data. LAI and leaf reflectance/transmittance remained variable.

To improve the accuracy and efficiency of model inversions, a scheme was developed for differentially weighting the empirical data. The scheme is based on the sensitivity of TOC reflectance at a given sun-target-sample geometry to model parameters. For example, the sensitivity to a 10% reduction in LAI is shown in Figure 14.1. Directions for which reflectance is more sensitive to a given parameter have a larger weight than directions for which reflectance is less sensitive. Simulations with synthetic data verified that merit function gradients increased when this weighting scheme was applied (see Figure 14.2). Steeper gradients were found to improve optimization accuracy and efficiency.

To validate the model, mean parameter values were determined over the entire FIFE site via various averaging schemes. Using atmospherically corrected AVHRR data from 1987, model estimates were compared to AVHRR data. Model estimates agreed reasonably well with empirical data from mid-June through mid-August. Errors in data gathered before mid-June and after mid-August were attributed to non-green surface conditions (burned and senescent canopies, respectively).

The weighting scheme was used to select promising 11-day subsets of AVHRR data for inversions. Using the LAI and leaf reflectance/transmittance weighting schemes, site-wide LAI and leaf optical properties were accurately retrieved in one parameter inversions (see Figure 14.3). Solutions from inversions with two adjustable parameters were less accurate, but were acceptable in some cases. Specifically, the accuracy of the retrieved LAI depended on the accuracy of the retrieved leaf optical properties. When one was accurately retrieved, so was the other. Where there were large errors in one, there were large errors in the other.

Conclusions from this study are:

• 2-3 parameters (LAI, leaf optical properties, soil single scattering albedo) could be estimated from AVHRR (MODIS) data collected over grasslands. This requires reasonably accurate estimates of other model parameters, however.

• MISR sampling geometry should allow the accurate retrieval of the same parameters when the ground track is close to the principal plane.

• Retrieval accuracy for LAI depends on the accuracy in leaf optical property estimates, and vice-versa.

• LAI and soil properties can be accurately estimated only for thin canopy (LAI < 3) cases.

• Leaf optical properties can only be estimated accurately for canopies of LAI > 1.

• NIR bands are superior for the determination of spectrally independent parameters of grasslands. At very low LAI (<1), red bands may be superior.

• LAI, soil properties and LAD are most accurately estimated with low SZA and view zenith angle (VZA). SZA should not be less than 10°, however, or azimuthal asymme try is lost.

• Leaf optical properties are most accurately estimated at high SZA and VZA.

• Surface state parameters (fAPAR, albedo, etc.) may be accurately estimated for the time of sampling even if moderate errors occur in the retrieved soil and canopy parameters.

• Surface state parameters can only be accurately estimated at other times if errors are small in the retrieved soil and canopy parameters.

• An anisotropic soil model is required to accurately model relatively thick canopies (LAI < 8), especially if reflectance near the hot spot is estimated. Inversions of the model of Jacquemoud et al. [1992] requires data from multiple spectral bands, at multiple VZA and SZA, and in multiple azimuthal planes to produce invariant es timates of roughness and phase function parameters.

• Optimization routines work best when the merit function surface is steep and does not contain local minima. The slope of the merit function around the minimizer can be steepened via weighting the merit function terms by the partial derivative of directional reflectance with respect to model parameters. This increases the efficiency and accuracy of the inversion.