Application of Kalman Filter with Time-Correlated Measurement Errors in Subsurface Contaminant Transport Modeling

Abstract

Prediction of a conservative solute transport in the subsurface is investigated by applying a Kalman filter (KF) that uses time-correlated-error and a KF that uses Gaussian error. The observation data generated from an analytical solution of a two-dimensional advection-dispersion equation with additive time-correlated random errors were used as the measurement equation for the KF with time-correlated measurement errors and the KF with white Gaussian errors. A measurement-differencing algorithm was adopted in deriving a discrete time varying KF with time-correlated measurement errors for predicting contaminant transport in the subsurface in the case of observations with time-correlated errors. Simulation results indicated an improved root mean square error (RMSE) profile of KF with time-correlated errors over KF with white Gaussian error. The KF with time-correlated-error reduced the error in the prediction by 11.4% when compared to the KF with white Gaussian error. The stability analysis of the two filters indicated that both filters were stable and convergent for the entire simulation duration.