Information-based uncertainty decomposition in dual-channel microwave remote sensing of soil moisture

The National Aeronautics and Space Administration (NASA) Soil Moisture Active-Passive (SMAP) mission characterizes global spatiotemporal patterns in surface soil moisture using dual L-band microwave retrievals of horizontal (TBh) and vertical (TBv) polarized microwave brightness temperatures through a modeled mechanistic relationship between vegetation opacity, surface scattering albedo, and soil effective temperature (Teff). Although this model has been validated against in situ soil moisture, there is a lack of systematic characterization of where and why SMAP estimates deviate from the in situ observations. Here, we assess how the information content of in situ soil moisture observations from the US Climate Reference Network contrasts with (1) the information contained within raw SMAP observations (i.e., “informational random uncertainty”) derived from TBh, TBv, and Teff themselves and with (2) the information contained in SMAP's dual-channel algorithm (DCA) soil moisture estimates (i.e., “informational model uncertainty”) derived from the model's inherent structure and parameterizations. The results show that, on average, 80 % of the information in the in situ soil moisture is unexplained by SMAP DCA soil moisture estimates. Loss of information in the DCA modeling process contributes 35 % of the unexplained information, while the remainder is induced by a lack of additional explanatory power within TBh, TBv, and Teff. Overall, retrieval quality of SMAP DCA soil moisture, denoted as the Pearson correlation coefficient between SMAP DCA soil moisture and in situ soil moisture, is negatively correlated with the informational uncertainties, with slight differences across different land covers. The informational model uncertainty (Pearson correlation of −0.59) was found to be more influential than the informational random uncertainty (Pearson correlation of −0.34), suggesting that the poor performance of SMAP DCA at some locations is driven by model parameterization and/or structure and not underlying satellite measurements of TBh and TBv. A decomposition of mutual information between TBh, TBv, and DCA soil moisture shows that on average 58 % of information provided by TBh and TBv to DCA estimates is redundant. The amount of information redundantly and synergistically provided by TBh and TBv was found to be closely related (Pearson correlations of 0.79 and −0.82, respectively) to the retrieval quality of SMAP DCA. TBh and TBv tend to contribute large redundant information to DCA estimates under surfaces or conditions where DCA makes better retrievals. This study provides a baseline approach that can also be applied to evaluate other remote sensing models and understand informational loss as satellite retrievals are translated to end-user products.