Elevating the possibilities of meshless groundwater flow modeling: a developed approach for parameter estimation and uncertainty quantification

Groundwater modeling is often associated with uncertainties due to incomplete knowledge of the subsurface system or uncertainties arising from variability in model system processes and field conditions. So far, not much research has been conducted to investigate the uncertainty of the groundwater flow model. Studies in this field focus on statistical methods. Due to the need to investigate the uncertainty to obtain reliable results, this study presents an approach to evaluate the uncertainty parameters of the groundwater flow model. In this way, modified GLUE (MGLUE) method as the uncertainty assessment method is linked to the meshless local Petrov–Galerkin (MLPG) as the simulation model. The method (which is called MGLUE-MLPG) is applied to two aquifers. In the first aquifer, three parameters of the meshless flow model (parameters related to the numerical method e.g., sizes of the integration and weight subdomains and the amount of the penalty coefficient) are identified as uncertainty parameters. The results indicate that these three parameters have a high degree of uncertainty, so their coefficients of variation are 72.37, 19.92 and 51.55, respectively. In the second standard aquifer, in addition to the numerical parameters, the transmissivity coefficients (model parameters) in two different directions (horizontal and vertical directions) are taken into account in the uncertainty model. The results show more uncertainty for the numerical parameters and do not show many changes in the transmissivity coefficient parameter. This means that the box diagrams of these parameters are almost the same. After precise values have been reached, groundwater flow was simulated. The obtained results are so accurate as to indicate the importance of using this model for all aquifers. In the first aquifer, the root mean square error (RMSE) values for MGLUE-MLPG and finite element method (FEM) are 0.236 and 0.249 m, respectively. The second aquifer shows higher accuracy than the other numerical method, so the RMSE values for MGLUE-MLPG and PPCM are 0.0060 and 0.0121 m, respectively.