article published yes Luisa Hopp author Simone Fatichi author cf8e546b-a9b0-11f0-a43b-aa89ed1b56d6 Valeriy Y. Ivanov author In hydrological models, variably saturated flow is often described using the Richards equation, either in a fully three-dimensional (3D) implementation or using a quasi-3D framework based on the 1D Richards equation for vertical flow and a flow-approximation for the other two dimensions. However, it is unclear in which configuration or under which boundary conditions these approximations can produce adequate estimates. In this study, two formulations with a quasi-3D approach are benchmarked against a fully 3D model (HYDRUS-3D). The formulations are: the Real-time Integrated Basin Simulator + VEGetation Generator for Interactive Evolution (tRIBS + VEGGIE) model that uses the Dupuit–Forchheimer assumption and the Tethys &amp; Chloris (T&amp;C) model that implements the kinematic approach. Effects of domain slope, hillslope size, event size and initial moisture conditions on simulated runoff and soil moisture dynamics are examined in event-based simulations at the hillslope scale. The Dupuit–Forchheimer assumption (tRIBS-VEGGIE) produces deviations from the HYDRUS-3D solutions only for simulations with initially dry soil. Using the kinematic approach (T&amp;C) results in deviations from the 3D solution primarily for the small hillslope domain in combination with a gentle slope angle. This applies especially to the partition between subsurface and surface runoff production, with T&amp;C being biased towards the latter. For all other cases investigated, the simpler formulations provide reasonable approximations of the 3D model. IWA Publishing2016 eng hillslope hydrologyhydrologic modelingparsimonious approximationsurface-subsurface hydrology 1998-9563 2224-795510.2166/nh.2015.126 472274-290 yes L. Hopp, S. Fatichi, and V. Y. Ivanov, “Simulating water flow in variably saturated soils: A comparison of a 3D model with approximation-based formulations,” <i>Hydrology Research</i>, vol. 47, no. 2. IWA Publishing, pp. 274–290, 2016. Hopp L, Fatichi S, Ivanov VY. 2016. Simulating water flow in variably saturated soils: A comparison of a 3D model with approximation-based formulations. Hydrology Research. 47(2), 274–290. Hopp L, Fatichi S, Ivanov VY. Simulating water flow in variably saturated soils: A comparison of a 3D model with approximation-based formulations. <i>Hydrology Research</i>. 2016;47(2):274-290. doi:<a href="https://doi.org/10.2166/nh.2015.126">10.2166/nh.2015.126</a> Hopp, Luisa, Simone Fatichi, and Valeriy Y. Ivanov. “Simulating Water Flow in Variably Saturated Soils: A Comparison of a 3D Model with Approximation-Based Formulations.” <i>Hydrology Research</i>. IWA Publishing, 2016. <a href="https://doi.org/10.2166/nh.2015.126">https://doi.org/10.2166/nh.2015.126</a>. Hopp, L., Fatichi, S., &#38; Ivanov, V. Y. (2016). Simulating water flow in variably saturated soils: A comparison of a 3D model with approximation-based formulations. <i>Hydrology Research</i>. IWA Publishing. <a href="https://doi.org/10.2166/nh.2015.126">https://doi.org/10.2166/nh.2015.126</a> L. Hopp, S. Fatichi, V.Y. Ivanov, Hydrology Research 47 (2016) 274–290. Hopp, Luisa, et al. “Simulating Water Flow in Variably Saturated Soils: A Comparison of a 3D Model with Approximation-Based Formulations.” <i>Hydrology Research</i>, vol. 47, no. 2, IWA Publishing, 2016, pp. 274–90, doi:<a href="https://doi.org/10.2166/nh.2015.126">10.2166/nh.2015.126</a>. 225232026-07-27T12:30:24Z2026-08-06T08:05:42Z