Combined spatial and Kalman filter estimation of optimal soil hydraulic properties

A method for determining optimal parameters for a field-scale hydraulic conductivity function is presented and tested on soil moisture and matric potential data measured at several locations in a field drainage experiment. The change in moisture content over time at the individual locations is modeled using Richards' equation, and an optimization for the hydraulic conductivity parameters is performed using a merit function derived from the Kalman filter, which allows consideration of measurement and process noise. The spatial correlation among the different measurement points is explicitly taken into account using the covariance between points in the calculation of the process noise covariance matrix. It is shown that the standard deviation of the effective hydraulic conductivity function estimated by the Kalman filter method applied to all measurements is significantly less than the standard deviations estimated by simple averaging of the parameters derived using other methods applied to the individual point moisture time series.