Kalman Filtering with Regional Noise to Improve Accuracy of Contaminant Transport Models

Spatially independent Gaussian noise has been widely assumed in examining the Kalman filter (KF) properties in different areas of engineering practice. However, for subsurface modeling, it is more reasonable to consider both data and noise as regional. In this study, regional noises are employed in KF and finite-difference schemes in solving the subsurface transport problem. A KF is constructed as a data assimilation scheme for a subsurface numeric model. Also, a regional random field simulation scheme is proposed and employed to examine the impact on effectiveness of KF correction processes. The results indicate that the prediction error of the KF data assimilation scheme is 30% smaller than the error from the deterministic model. Furthermore, by applying a correct regional noise structure, the KF data assimilation scheme reduces the prediction error from 25 to 10 ppm in our model, indicating an improvement of 60% in prediction accuracy.