### Abstract

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.

Original language | English |
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Pages (from-to) | 2394-2406 |

Number of pages | 13 |

Journal | Water Resources Research |

Volume | 50 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2014 |

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## Cite this

*Water Resources Research*,

*50*(3), 2394-2406. https://doi.org/10.1002/2013WR014284