Downscaling Satellite-Based Soil Moisture in Heterogeneous Regions Using High-Resolution Remote Sensing Products and Information Theory: A Synthetic Study

In this study, a novel methodology based upon the information-theoretic measures of entropy and mutual information was implemented to downscale soil moisture (SM) observations from 10 km to 1 km. It included a transformation function that related auxiliary remotely sensed (RS) products at high resolution to in situ SM observations to obtain first estimates of SM at 1 km and merging this estimate with SM at coarse resolutions through Principle of Relevant Information (PRI). The PRI-based estimates were evaluated using synthetic observations in NC Florida for heterogeneous agricultural land covers (LC), with two growing seasons of sweet corn and one of cotton, annually. The cumulative density function showed an overall error in SM of < 0.03 cubic meter/cubic meter in the region, with a confidence interval of 95% during the simulation period. The PRI estimates at 1 km were also compared with those from the method based upon Universal Triangle (UT). The spatially averaged root mean square error (RMSE) aggregated over the vegetative LC were 0.01 cubic meter/cubic meter and 0.15 cubic meter/cubic meter using the PRI and UT methods, respectively. The RMSE for downscaled estimates using the UT method increased to 0.28 cubic meter/cubic meter when Laplacian errors are used, while the corresponding RMSE for the PRI remains the same for both Laplacian or Gaussian errors. The Kullback-Liebler divergence (KLD) for estimates using PRI is about 50% lower than those using the method based upon UT indicating that the probability density function (PDF) of the PRI estimate is closer to PDF of the true SM, than the UT method.