On minimum relative entropy concepts and prior compatibility issues in vadose zone inverse and forward modeling

Abstract

A comprehensive stochastic approach for forward modeling of the state variables in the vadose zone as well as for inverse modeling of the hydraulic parameters is proposed and applied to a field site in Napa Valley, California. The approach combines the Richards equation and the van Genuchten–Mualem soil models, with initial and boundary conditions provided by geophysical and meteorological measurements, into a Bayesian formalism, which allows integration between different complementary information sources. A major challenge in such studies is the integration between different types of data, of different quality and resolution, and with prior information. Accurate modeling of prior information is challenging because of the need to avoid subjective judgment with regard to the quality of the prior information and its significance. To obtain minimally subjective prior probabilities required for the Bayesian approach, we employ the principle of minimum relative entropy (MRE). It can often be the case that information that is considered a suitable prior may, in fact, become incompatible with field observations as more observations become available. Our study considers this possibility and explores possible indications for prior incompatibility. We test our forward and inverse modeling approaches using field data. The results indicate that our approach is consistent, in the sense that as additional data are introduced, the simulated soil moisture content profile better matches the observed profile and the predictive intervals become much narrower. The narrower intervals of the soil moisture predictions indicate the reduction of uncertainties associated with the model parameters.