Application of Ensemble Square Root Kalman Filter in a Three-Dimensional Subsurface Contaminant Transport Model

Abstract

A three-dimensional transport model with advection, dispersion, and reaction has been developed to predict transport of a reactive continuous source pollutant. Numerical Forward-Time-Central-Space (FTCS) scheme has been used to solve the advection-dispersion-reaction transport model and Kalman filter (KF) and Ensemble Square Root Kalman Filter (EnSRKF) have been used for data assimilation purpose. EnSRKF uses Monte Carlo simulation in Bayesian implementation to propagate state ensemble without perturbing observation during assimilation period. In this study, contaminant concentration is the state that has been propagated by this model. Reference true solution derived from analytical solution has been used to compare model results. Root Mean Square Error (RSME) profile shows that the EnSRKF concentration estimate can improve prediction accuracy better compared to numerical and KF approaches. With 10,000 mg/L initial concentration numerical scheme shows an average error of 130.84 mg/L, whereas EnSRKF shows an average error of 10.65 mg/L, indicating an improvement of 91.80 %. Kalman Filter (KF) shows an average error of 31.08 mg/L. Therefore, EnSRKF approach reduces mean RMSE by 65.70 % compared to KF approach.