The relative performance of an explicit grid cell by grid cell approach and a statistical-dynamical method widely used in Topmodel for modeling topographically driven subsurface flow was evaluated using a series of numerical experiments. Both approaches were compared with analytical solutions to the kinematic wave equation for flow down an inclined plane of constant slope. The hillslope discharge and water table profiles simulated by the explicit method were in good agreement with the analytical solution in all test cases. The statistical-dynamical method converged to the correct steady state solution but failed to reproduce accurately transient conditions. The two algorithms were also compared using topography and observed hourly precipitation for the U.S. Department of Agriculture Mahantango, Pennsylvania, research catchment. The percent root-mean-square-difference in hourly discharge between the two methods for a 1 year simulation ranged from 20% to several hundred percent. The agreement in discharge between the two methods was best for deep soils, high surface conductivity, and large values of the power law exponent describing the decay in vertical hydraulic conductivity with depth. Calibration of the statistical-dynamical model to discharge simulated by the explicit method was most effective for soils with low power law exponents. However, even in the calibrated cases, there were large discrepancies between local water table depths simulated by the two models. ¿ 1999 American Geophysical Union