Kalman Filter for Subsurface Transport Models with Inaccurate Parameters and Unknown Sources

Abstract

In order to improve the contaminant plume prediction in subsurface transport models, a data assimilation scheme using the Kalman filter (KF) is developed. The data assimilation scheme is designed to reduce uncertainties in model predictions. These uncertainties actually represent all the unpredictable variations due to the unknown or uncertain properties in physical law based models and the incomplete knowledge of stochastic fields. Considering the background of subsurface transport is spatially dependent, simulation of spatially correlated uncertainties are proposed and integrated into a data assimilation scheme. Sequential instances of spatially correlated random fields are simulated in examining the effectiveness of the assimilation system. Results show that this data assimilation scheme reduces the uncertainty of predictions from the deterministic model. By assimilating the observations, the predictive contaminant plumes from the assimilation system can trace the randomized irregular plume shape of the assumed case more closely than a non-assimilation deterministic model. The statistical representation of random noise, such as spatially dependency, is critical in improving effectiveness of the statistical optimization process. In two test cases which simulate the scenarios with unknown hidden sources or inaccurate hydrologic properties, the regional noise KF scheme demonstrates the potentials to solve the inverse problems in environmental transport modeling.

Keywords: subsurface transport, uncertainty, inverse problem, Kalman filter, data assimilation, spatial variation