Modeling vegetation cover distribution at different scales based on Bayesian statistical inference

Various remote sensing sensor observe the Earth´s surface from coarse spatial resolution to fine spatial resolution. We may get different results from remote sensing images captured at different resolution due to scale effects. On the other hand, vegetation cover is an important parameter in many environmental models. It often affects the model results greatly. So, it is very important to understand the scaling problem of vegetation in remote sensing. This article presents a method to describe the vegetation cover distributions at different scales based on Bayesian Inference techniques. The histograms of vegetation cover show changing shapes with various spatial resolutions, they are very similar to Beta distributions with different parameters. On the other hand, geography spatial distribution probability can be expressed with binominal distribution or negative binominal distribution. Then, given a binominal or negative binominal distribution as likelihood, Beta distribution as a priori, we can get posterior distribution using conjugate prior theory. Such a posterior distribution can be used to predict the histograms of vegetation cover at different scales. Parameters used by this method can be calculated using mean and variance of vegetation cover at various scales. MODIS, Amtis and TM images are used to validate the method. The result shows that if vegetation is scattered, the binominal distribution may be used as the likelihood, on the contrary, a negative binominal distribution is much better. Because determining the spatial distribution is difficult, we combine the two distributions by adding the weight in this paper, and get better result.