Interpreting effective hydrologic depth estimates derived from soil moisture remote sensing: A Bayesian non-linear modeling approach

The water balance equation (WBE) describes how net water inflows into a system relate to storage changes over a time span (dt). This equation is fundamental in hydrologic studies, helping to determine water supply and elucidate the terrestrial water cycle. For land surface, the WBE links water fluxes like precipitation (P), evapotranspiration, drainage and surface runoff to soil moisture (SM) changes within a discrete soil layer (dSM). While traditional focus has been on the precision of the WBE-estimated fluxes, there has been increased recent interest in fitting the WBE using remotely-sensed P and SM data to infer water balance parameters, particularly the ΔZ that associates net fluxes and dSM within dt. However, obtaining physically interpretable WBE parameters like ΔZ is a potentially ill-posed problem due to simplifying assumptions imbedded in a WBE implementation, missing hydrologic constraints, and accuracy and revisit limitations in available remotely-sensed data. In addition, WBE parameters obtained from classical maximum likelihood estimation approaches can vary significantly. Here, using a Bayesian non-linear modeling approach, we demonstrate how these factors can impede the identification of useful ΔZ estimates. Specifically, we find that ΔZ estimates are likely to be spuriously biased due to limitations in the temporal resolution and accuracy of satellite-based dSM estimates - as well as the neglect of other hydrological components in the WBE. Maps showcasing the lower and upper bounds of the 94 % HDI from our Bayesian model further elucidate these biases. Results suggests that estimates of ΔZ are effective in nature and great care should be exercised when attempting to interpret them physically. Instead, they should be defined as effective parameters reflecting the characteristics of their fitted remotely-sensed data sets. Drawing from current progress, accurate ΔZ estimates, informed by more advanced remote sensing techniques and precise WBE, will enhance our understanding of terrestrial water cycle.