Using Unscented Kalman Filter in Subsurface Contaminant Transport Models

Abstract

Using a traditional numerical approach in subsurface contaminant transport models generates unavoidable deviation due to unknown or uncertain sources, inaccurate transport and hydraulic parameters, and numeric scheme errors. As a result, stochastic data assimilation or filtering techniques have been employed in the subsurface simulation processes to improve the accuracy of model results. The Kalman Filter (KF) has been widely used for estimation and tracking of linear systems. In the subsurface transport model, even if the system dynamics are linear, it can become a nonlinear one because of the presence of the unknown parameters. The Unscented Kalman Filter (UKF) is one of the data assimilation filters that offer a potential solution to the problem of model development with noisy and incomplete data when the system is nonlinear. The objective of this study was to apply the UKF in subsurface contaminant transport models and to find the contaminant plume. The performance was then evaluated in comparison with the KF and numerical model. A two dimensional transport model with advection and dispersion was used as the deterministic model of a conservative contaminant transport in the subsurface. Random Gaussian noises were added to the numerical method result to simulate the true solution and the observation data. Then the UKF and KF filtering techniques were applied for the data assimilation. An Error Standard Deviation (ESD) of pollutant concentrations was used to examine the effectiveness. The UKF can reduce 6~75% and 2~52% of prediction errors when compared with the numerical and KF results, respectively.

Keywords: stochastic process, Error Standard Deviation (ESD), Kalman Filter (KF), Unscented Kalman Filter (UKF), contaminant transport