Probabilistic inference of ecohydrological parameters using observations from point to satellite scales

Abstract

Vegetation controls on soil moisture dynamics are challenging to measure and translate into scale- and site-specific ecohydrological parameters for simple soil water balance models. We hypothesize that empirical probability density functions (pdfs) of relative soil moisture or soil saturation encode sufficient information to determine these ecohydrological parameters. Further, these parameters can be estimated through inverse modeling of the analytical equation for soil saturation pdfs, derived from the commonly used stochastic soil water balance framework. We developed a generalizable Bayesian inference framework to estimate ecohydrological parameters consistent with empirical soil saturation pdfs derived from observations at point, footprint, and satellite scales. We applied the inference method to four sites with different land cover and climate assuming (i) an annual rainfall pattern and (ii) a wet season rainfall pattern with a dry season of negligible rainfall. The Nash–Sutcliffe efficiencies of the analytical model's fit to soil observations ranged from 0.89 to 0.99. The coefficient of variation of posterior parameter distributions ranged from < 1 to 15 %. The parameter identifiability was not significantly improved in the more complex seasonal model; however, small differences in parameter values indicate that the annual model may have absorbed dry season dynamics. Parameter estimates were most constrained for scales and locations at which soil water dynamics are more sensitive to the fitted ecohydrological parameters of interest. In these cases, model inversion converged more slowly but ultimately provided better goodness of fit and lower uncertainty. Results were robust using as few as 100 daily observations randomly sampled from the full records, demonstrating the advantage of analyzing soil saturation pdfs instead of time series to estimate ecohydrological parameters from sparse records. Our work combines modeling and empirical approaches in ecohydrology and provides a simple framework to obtain scale- and site-specific analytical descriptions of soil moisture dynamics consistent with soil moisture observations.