A multiple scale state-space model for characterizing subgrid scale variability of near-surface soil moisture

This paper addresses the problem of characterizing variability of soil moisture at various scales by combining information, such as measurements and soil hydrologic properties, available at different scales. This problem is motivated by the need to provide a way to predict subgrid/subpixel variability from measurements made at satellite footprint scale. A mean-differenced multiple scale fractal model is developed for soil moisture. The salient features of this model are as follows. 1) Differences in soil moisture in various hydrologic groups are modeled through a difference in mean, while the fluctuations are assumed independent of the mean. 2) Mean soil moisture is linearly related to available water capacity of the soil. 3) Fluctuations are modeled as fractional Gaussian noise. Estimation techniques based on multiresolution trees are implemented to obtain the values at multiple scales. Since estimation is a smoothing process that may not provide a good representation of the variability, particularly in regions where there are no observations, a complementary conditional simulation technique is developed. This allows the authors to construct synthetic fields that are representative of the intrinsic variability of the process. The technique is applied to problems of estimation and conditional simulation for the following scenarios: domain with missing values, sparsely sampled data, in domain outside of where measurements are available, and at scales smaller than at which measurements are available.