Inverse modeling of large‐scale spatially distributed vadose zone properties using global optimization

Abstract

Computational capabilities have evolved to a point where it is possible to use multidimensional physically based hydrologic models to study spatial and temporal patterns of water flow in the vadose zone. However, models based on multidimensional governing equations have only received limited attention, in particular because of their computational, distributed input, and parameter estimation requirements. The aim of the present paper is to explore the usefulness and applicability of the inverse method to estimate vadose zone properties using the solution of a physically based, distributed three‐dimensional model combined with spatially distributed measured tile drainage data from the 3880‐ha Broadview Water District (BWD) in the San Joaquin Valley of California. The inverse problem is posed within a single‐criterion Bayesian framework and solved by means of the computerized Shuffled Complex Evolution Metropolis global optimization algorithm. To study the benefits of using a spatially distributed three‐dimensional vadose zone model, the results of the 3‐D model were compared with those obtained using a simple storage‐based bucket model and a spatially averaged one‐dimensional unsaturated water flow model for a 2‐year period. District‐wide results demonstrate that measured spatially distributed patterns of drainage data contain only limited information for the identification of vadose zone model parameters and are particularly inadequate to identify the soil hydraulic properties. In contrast, the drain conductance and a soil matrix bypass coefficient were well determined, indicating that the dominant hydrology of the BWD was determined by drain system properties and preferential flow. Despite the significant CPU time needed for model calibration, results suggest that there are advantages in using physically based hydrologic models to study spatial and temporal patterns of water flow at the scale of a watershed. These models not only generate consistent forecasts of spatially distributed drainage data during the calibration and validation period but also possess unbiased predictive capabilities with respect to measured groundwater table depths not included in the calibration.