Error analysis of a multi-cell groundwater model

The basic advantages of the multi-cell groundwater models are the parsimony, speed, and simplicity that make them ideal for hydrological applications, particularly when data are insufficient and/or repeated simulations are needed. However, the multi-cell models, in their basic version, are conceptual models and their parameters do not have physical meaning. This disadvantage may be overcome by the Narasimhan and Witherspoon’s integrated finite difference method, which, however, demands that the cells’ geometry conforms to the equipotential and no-flow lines. This restriction cannot be strictly satisfied in every application. Particularly in transient conditions, a mesh with static geometry cannot conform constantly to the varying flow kinematics. In this study, we analyse the error when this restriction is not strictly satisfied and we identify the contribution of this error to the overall error of a multi-cell model. The study is experimental based on a synthetic aquifer with characteristics carefully selected so as to be representative of real-world situations, but obviously the results of these investigations cannot be generalized to every type of aquifer. Nonetheless these results indicate that the error due to non-conformity to the aforementioned restriction plays a minor role in the overall model error and that the overall error of the multi-cell models with conditionally designed cells is comparable to the error of finite difference models with much denser discretization. Therefore the multi-cell models should be considered as an alternative option, especially in the cases where a discretization with a flexible mesh is indicated or in the cases where repeated model runs are required.