Investigation of a stochastic inverse method to estimate parameters in groundwater models

Natural systems are heterogeneous and they contain noise due to random inputs, irregular varying coefficients and fluctuations in boundary conditions. In this paper, we model the behaviour of natural systems using stochastic differential equations, present a parameter estimation procedure for such models in a general setting, and extend it to simple groundwater models. The applications to groundwater models are within the context of one dimensional solute transport problem to estimate parameters for two governing equations, one consisting of a single parameter and other of two parameters. The results of this inverse methodology are reliable in the presence of noise. However, the investigation of solute transport parameter estimates shows an inverse relationship to the noise level. The main advantage of the estimation methodology presented here is its direct dependence on field observations of state variables of natural systems in the presence of uncertainty