Is the Dupuit assumption suitable for predicting the groundwater seepage area in hillslopes?

Many physically based hydrological/hydrogeological models used for predicting groundwater seepage areas, including topography‐based index models such as TOPMODEL, rely on the Dupuit assumption. To ensure the sound use of these simplified models, knowledge of the conditions under which they provide a reasonable approximation is critical. In this study, a Dupuit solution for the seepage length in hillslope cross sections is tested against a full‐depth solution of saturated groundwater flow. In homogeneous hillslopes with horizontal impervious base and constant‐slope topography, the comparison reveals that the validity of the Dupuit solution depends not only on the ratio of depth to hillslope length d / L (as might be expected), but also on the ratio of hydraulic conductivity to recharge K / R and on the topographic slope s . The validity of the Dupuit solution is shown to be in fact a unique function of another ratio, the ratio of depth to seepage length d / L S . For d / L S < 0.2, the relative difference between the two solutions is quite small (<14% for the wide range of parameter values tested), whereas for d / L S > 0.2, it increases dramatically. In practice, this criterion can be used to test the validity of Dupuit solutions. When d / L S increases beyond that cutoff, the ratio of seepage length to hillslope length L S / L given by the full‐depth solution tends toward a nonzero asymptotic value. This asymptotic value is shown to be controlled by (and in many cases equal to) the parameter R /( sK ). Generalization of the findings to cases featuring heterogeneity, nonhorizontal impervious base and variable‐slope topography is discussed.