Data Assimilation for Vadose Zone Flow Modeling Using the Ensemble Kalman Filter

Abstract:

The natural system is open and complex and the hydraulic parameters needed for describing flow and transport in the vadose zone are often poorly known, making it prone to multiple interpretations, mathematical descriptions and uncertainty. Quite often a reasonable “handle” on a sites flow characteristics can be gained only through direct observation of the flow processes itself, determination of the spatial- and probability distributions of material properties combined with computationally expensive inversions of the Richards equation. In groundwater systems, the ensemble Kalman filter (EnKF) has proven to be an effective alternative to model inversions by assimilating observations directly into an ensemble of groundwater models from which time and/or space-variable variable probabilistic quantities of the flow process can be derived. Application of EnKF to Richards equation-type unsaturated flow problems, however, is more challenging than in groundwater systems because the relation of state and model parameters is strongly nonlinear. In addition, the type of functional dependence of moisture content and hydraulic conductivity on matric potential leads to high-dimensional (in the parameter space) problems even under conditions where closed-form expressions of these models such as van Genuchten-Mualem formulations are used. In this study, we updated soil water retention parameters and hydraulic conductivity together and used Restart EnKF, which rerun the nonlinear model from the initial time to obtain the updated state variables, in synthetic cases to explore the factors that may influence estimation results, including the initial estimate, the ensemble size, the observation error, and the assimilation interval. We embedded the EnKF into the Bayesian model averaging framework to enhance the model reliability and reduce predictive uncertainties. This approach is evaluated from a 15 m deep semi-arid highly heterogeneous and anisotropic vadose zone site at the University of Arizona Maricopa Agricultural Center, Phoenix, Arizona.