A Bayesian machine learning method to explain the error characteristics of global-scale soil moisture products

Estimating accurate surface soil moisture (SM) dynamics from space, and knowing the error characteristics of these estimates, is of great importance for the application of satellite-based SM data throughout many Earth Science/Environmental Engineering disciplines. Here, we introduce the Bayesian inference approach to analyze the error characteristics of widely used passive and active microwave satellite-derived SM data sets, at different overpass times, acquired from the Soil Moisture Active Passive (SMAP), Soil Moisture and Ocean Salinity (SMOS), and Advanced Scatterometer (ASCAT) missions. In particular, we apply Bayesian hierarchical modeling (BHM) and triple collocation analysis (TCA) to investigate the relative importance of different environmental factors and human activities on the accuracy of satellite-based data.To start, we compare the BHM-based sensitivity analysis method to the classic multiple regression models using a frequentist approach, which includes complete pooling and no-pooling models that have been widely used for sensitivity analysis in the field of remote sensing and demonstrate the BHM's adaptability and great potential for providing insight into sensitivity analysis that can be used by various remote sensing research communities.Next, we conduct an uncertainty analysis on BHM's model parameters using a full range of uncertainties to assess the association of various environmental factors with the accuracy of satellite-derived SM data. We focus on investigating human-induced error sources such as disturbed surface soil layers caused by irrigation activities on microwave satellite systems, naturally introduced error sources such as vegetation and soil organic matter, and errors related to the disregard of SM retrieval algorithmic assumptions -such as the thermal equilibrium passive microwave systems. Based on the BHM-based sensitivity analysis, we find that assessments of SM data quality with a single variable should be avoided, since numerous other factors simultaneously influence their quality. As such, this provides a useful framework for applying Bayesian theory to the investigation of the error characteristics of satellite-based SM data and other time-varying geophysical variables.