Estimation of Parameters in Groundwater Modeling by Particle Filter linked to the meshless local Petrov-Galerkin Numerical Method

Abstract

The present study employs a mathematical method, i.e., Particle Filter (PF), to accurately estimate the parameters of three standard aquifers. The method is linked to a new developed numerical method, i.e., meshless local Petrov-Galerkin based on the moving kriging method (PF-MLPG-MK), to determine the aquifer parameters such as hydraulic conductivity coefficient, transmissivity coefficient, and storage coefficient or specific yield appropriately. For this purpose, a set of particles scattered in the state space. Each particle has two features: location and weight. Particles with greater weight values have the closer location to the estimation. Weight values which are assigned to each particle is computed based on the maximum likelihood function. This function is calculated in MLPG-MK simulation model. Overall, by linking particle filter model to the accurate simulation model, an efficient estimation method for aquifer parameters is obtained. This model applied to three standard aquifers. In the first standard aquifer, the estimated parameters of hydraulic conductivity and specific yield were 30.21 and 0.143, respectively. However, the exact values are 30 and 0.15. Also, in the second standard aquifer, the predicted transmissivity and storage coefficients were 99.7038 and 0.001057 whereas their true values are 100 and 0.001. In the third aquifer, the exact value of six parameters were achieved. The sensitivity analysis of the number of particles was carried out. Results revealed that with increasing the particles more accuracy will be achieved. 60, 80 and 100 particles were considered in the model. Results for 100 particles showed more accuracy.