Simulation error in groundwater models with rectangular and non rectangular discretization

The error of groundwater numerical models depends on the boundary conditions, the hydraulic conditions of the aquifer, the geometry of the flow field, the parameterization used to describe the heterogeneity of hydraulic field, the distribution and quality of the measurements and the discretization resolution. In this study we focus on the dependence of the error to the type and resolution of the spatial discretization. Using a two-dimensional stochastic model with a hypothetical aquifer, we produced a synthetic field of 100x100 hydraulic conductivities and we used a finite differences model (MODFLOW) to obtain synthetic fields of hydraulic head. Hereupon we used 4 grids (100x100, 50x50, 20x20, 12x12) and a simple parameterization (6 zones of homogeneous conductivity), common for all grids, along with a parameter estimation algorithm based on a modified Gauss-Newton method. Moreover we used 3dkflow, a model based on finite volumes method with simplified integration that uses a non rectangular sparse discretization (43 cells) in conjunction with the Shuffled Complex Evolution optimization algorithm. In the latter model every cell had a unique conductivity resulting in 43 conductivity parameters. Finally we compared the accuracy of the simulation of the 4 rectangular grids and the sparse non rectangular discretization to investigate the deviation of estimated parameters from the true conductivities and the deviation of simulated hydraulic head from the true synthetic field. We concluded that to keep the model error low a reliable parameterization along with a rectangular grid of high resolution should be used. Alternatively a sparse non rectangular spatial discretization with a unique parameter for each cell can keep the error small and is more advantageous in the applications that require simulation speed.