A hotspot function in a simple bidirectional reflectance model for satellite applications

The model presented here is an improvement over the semiempirical model of Roujean et al. [1992] for estimating the bidirectional reflectance from vegetation. Roujean's model has been considered for global applications because of its simplicity and the underlying physics. However, the model does not adequately describe the hotspot near the Sun's illumination direction. In this paper, a hotspot kernel based on a canopy gap size distribution theory developed by Chen and Leblanc [1997] is used to modify Roujean's model. The modified model requires two additional coefficients for controlling the hotspot magnitude and width, respectively. It is found that the hotspot magnitude coefficient is only weakly dependent on cover type and can be treated as a constant at a given geographical location. The hotspot width parameter is determined by the ratio of the characteristic foliage clump size and canopy height. The ratio varies in a small range across different cover types because the foliage clump size and canopy height are usually correlated. For example, the ratio of leaf size to crop height is similar to the ratio of crown size to tree height. Because of the small variabilities of these parameters, the modified model can be a substantial improvement over the original model by just using best estimates for the parameters. With this hotspot adjustment the simple form of the semiempirical model is preserved for remote sensing applications without additional input requirements. The performance of the modified model is shown using data from the advanced very high resolution radiometers (AVHRR). The results show that the patterns of reflectance distribution with the view angle are similar among all cover types investigated, suggesting that one simple model may be sufficient for global applications. The modified model based on simplified physics with four adjustable coefficients may be adequate for this purpose. The model can be further improved to consider the noncircular hotspot shape. Formulae for this purpose are suggested.