State and Parameter Estimation in Three-Dimensional Subsurface Contaminant Transport Modeling using Kalman Filter Coupled with Monte Carlo Sampling

Abstract

Accurate contaminant prediction is very important for risk assessment and site remediation. Several predictive tools in the form of mathematical models have been used to model the movement and behavior of contaminants in groundwater. These deterministic models do not account for the heterogeneity and uncertainties in the subsurface environment. Discretization of the models spatially and temporally introduces approximation and truncation errors. In this research, to improve the accuracy of subsurface contaminant prediction in time and space and to assess the impact of first-order decay rate parameter estimation, Kalman filter coupled with Monte Carlo sampling was used in a specified three-dimensional domain space. The filter is perturbed with random Gaussian noise to reflect real life case of contaminant movement. Set of sparse observation points selected at specific locations are used to guide the filter at every time step to improve the accuracy of the prediction. The first-order decay rate parameter is estimated using Monte Carlo sampling method. The algorithms to generate the simulation results were run on Matlab 7.1. The efficacy of the Kalman filter coupled with Monte Carlo sampling, Kalman filter without Parameter Estimation and the numerical method were tested using Mean Absolute Error (MAE) and Maximum Absolute Error (Emax) equations. The results show that the Kalman filter coupled with Monte Carlo sampling performs better than both the Kalman filter without Parameter Estimation and the numerical method. Also, the Kalman filter coupled with Monte Carlo sampling is capable of reducing the error in the numerical solution by approximately 75% when Mean Absolute Error equation is used to estimate the prediction error. The error reduction is due to the adaptive nature of the Kalman filter to the observation data used in the simulation.

Keywords: Kalman filter, parameter estimation, data assimilation, Monte Carlo sampling, groundwater, modeling