State and Parameter Estimation with an SIR Particle Filter in a Three-Dimensional Groundwater Pollutant Transport Model

Abstract

Mathematical modeling of the contaminants in the subsurface is important to predict the spread of the plume as well as for risk assessment. A three-dimensional subsurface contaminant transport model with an instantaneous input is developed to represent the high dimensionality of the real field. Because of the inherent randomness, heterogeneity of the transport process, macrodispersion, non-Fickian motion, and ergodicity, general assumptions of linearity and Gaussian distribution do not hold for the real field. Therefore, a state-space transport model for the nonlinear and non-Gaussian system is proposed in this study. In this paper, the state variable (concentration vector) and parameter (first-order decay) are updated with the simulated measurements. A particle filter, which is a sequential Monte Carlo method, provides a rigorous general framework for dynamic state estimation problems in the Bayesian scheme. In this paper, the reactive contaminant transport in the subsurface is treated as a dynamic state and parameter estimation problem. A type of particle filter, commonly called sequential importance resampling (SIR) is used for this subsurface transport problem. The model estimation is compared with a true random field, which acts as a reference. A promising improvement of the estimation accuracy is attained with the SIR particle filter when compared with a traditional deterministic approach. The particle filter data assimilation scheme reduces the prediction error by 48% in estimation accuracy. A standard technique to perform parameter estimation consists of extending the state with the parameter to transform the problem into a suboptimal filtering problem. This approach requires the use of special particle filtering techniques which are affected by several drawbacks. An alternative approach in combining parameter estimation with the particle filter method is considered in this study. The concept of the norm has been introduced to address the sequential weight assignment to the parameter estimation. The estimates of the parameter clearly show the efficacy of this innovative approach in this field.