Date of Award
A three dimensional subsurface contaminant 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), Ensemble Kalman Filter (EnKF) and Ensemble Square Root Kalman Filter (EnSRKF) schemes have been used for data assimilation purpose. EnKF and EnSRKF both use Monte Carlo simulation in Bayesian implementation to propagate state estimation. The key difference between EnKF and EnSRKF is that EnSRKF does not require perturbation of observation during analysis stage. In this study, contaminant concentration is the state that has been propagated by this model. Reference true solution derived from analytical solution with added noise 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, KF and EnKF approaches. For a 10x12x4 space domain (480 nodes) with 10,000mg/L initial concentration, numerical scheme shows an average error of 127.01 mg/L, whereas EnSRKF shows an average error of 5.47 mg/L, indicating an improvement of 95.69%. KF and EnKF schemes show average error of 26.16 and 5.74 mg/L. Therefore, EnSRKF approach reduces mean RMSE by 79% and 4.70% compared to KF and EnKF approach respectively. Although EnSRKF shows marginal improvement compared to EnKF, EnSRKF is computationally cheaper compared to EnKF for larger problems with more nodes. For a 50x60x4 space domain (12,000 nodes) EnSRKF produces similar accuracy of EnKF with much less execution time. For 12,000-nodes domain, it can reduce computational time by 68% compared to EnKF. EnSRKF also shows better performance than EnKF with small ensemble sizes.
Ghoshal, Torupallab, "Efficiency Of Ensemble Square-Root Kalman Filter In 3D Subsurface Contaminant Transport Modeling" (2014). Theses. 351.