Models for scaling the variance of soil moisture

Using remotely sensed maps of soil moisture, previous researchers have noted the apparent self-similar scaling of the variance of spatial soil moisture as the area represented by a single pixel changes. The most commonly used self-similar distributions in statistical literature are the fractional Brownian distribution and Levy stable distributions. These distributions are not appropriate models for the distribution of soil moisture, however, because they are nonstationary and in general unbounded, while real soil moisture content distributions are bounded by 0 and saturation and are often assumed to be stationary. We explore how the long-memory nature of soil moisture fields can give rise to the self-similarity, and what sort of self-similar distributions could be a possible model for soil moisture.