Application of 3D VAR Kalman Filter in a Three-Dimensional Subsurface Contaminant Transport Model for a Continuous Pollutant Source

Abstract

Modeling of contaminant transport in a subsurface environment by a deterministic model deviates from the real world environment with time because of the highly heterogeneous nature of the subsurface environment. In this study, an optimized stochastic approach coupled with the deterministic model has been applied to predict the contaminant transport in a subsurface environment. A three-dimensional contaminant transport model for a continuous pollutant source has been developed for this purpose. A forward time center space (FTCS) model has been used as a numerical approach to solve the classical advection dispersion flow equation and the Kalman Filter (KF) coupled with 3D variational analysis has been used for data assimilation purpose. The Kalman Filter is a recursive-based algorithm consists of a set of mathematical equations, which takes a prior estimation and observation measurements into consideration to compute the best prediction for a state variable. The 3D variational analysis uses a cost function to find out an optimal solution for an analysis using the KF simulated state as its background. The analysis for 3D VAR is found iteratively minimizing the cost function. A Root Mean Square (RMSE) and Mean Absolute Error (MAE) profile were used to evaluate the efficiency of the analysis. The investigation shows that state prediction to be good for both the background (KF) and analysis (3D VAR KF) steps compared to the deterministic solution whereas the 3D VAR analysis over the background (KF) found to be effective in reduction of the error significantly. An overall improvement of 15.3 % error reduction on RMSE and 14.6 % reduction on MAE over the background is achieved using this new approach.