Modelling of Space-Time Soil Moisture in Savannas and its Relation to Vegetation Patterns

A physically derived space-time representation of the soil moisture field is presented. It includes the incorporation of a "jitter" process acting over the space-time soil moisture field and accounting for the short distance heterogeneities in topography, soil, and vegetation characteristics. The modelling scheme allows for the representation of spatial random fluctuations of soil moisture at small spatial scales and reproduces quite well the space-time correlation structure of soil moisture from a field study in Oklahoma. It is shown that the islands of soil moisture above different thresholds have sizes which follow power distributions over an extended range of scales. A discussion is provided about the possible links of this feature with the observed power law distributions of the clusters of trees in savannas.