Numerical errors in groundwater and overland flow models

Numerical error estimates are useful to evaluate the applicability of overland and groundwater flow models and verify the validity of their results. In this paper, methods of estimating numerical errors are developed and then applied to evaluate the numerical accuracy of the South Florida Water Management Model. Analytical expressions for errors generated during the propagation of disturbances due to well pumping, boundary water level changes, and rainfall are obtained for steady and transient conditions using Fourier analysis of the linearized governing equations. Different situations under which truncation errors are introduced into models and their variation with the spatial and temporal discretization are discussed. Numerical experiments are carried out with the three-dimensional groundwater flow model MODFLOW and a number of implicit and explicit models to verify the results. Dimensionless parameters are used in the expressions so that the results can be used to determine discretization errors in any existing or new finite difference model of regional or local scale.