Iterative approach to modeling subsurface stormflow based on nonlinear, hillslope-scale physics

Abstract. Soil water transport in small, humid, upland catchments is often dominated by subsurface stormflow. Recent studies of this process suggest that at the plot scale, generation of transient saturation may be governed by threshold behavior, and that transient saturation is a prerequisite for lateral flow. The interaction between these plot scale processes yields complex behavior at the hillslope scale. We argue that this complexity should be incorporated into our models. We take an iterative approach to developing our model, starting with a very simple representation of hillslope rainfall-runoff. Next, we design new virtual experiments with which we test our model, while adding more structural complexity. In this study, we present results from three such development cycles, corresponding to three different hillslope-scale, lumped models. Model₁ is a linear tank model, which assumes transient saturation to be homogeneously distributed over the hillslope. Model₂ assumes transient saturation to be heterogeneously distributed over the hillslope, and that the spatial distribution of the saturated zone does not vary with time. Model₃ assumes that transient saturation is heterogeneous both in space and in time. We found that the homogeneity assumption underlying Model₁ resulted in hillslope discharge being too steep during the first part of the rising limb, but not steep enough on the second part. Also, peak height was underestimated. The additional complexity in Model₂ improved the simulations in terms of the fit, but not in terms of the dynamics. The threshold-based Model₃ captured most of the hydrograph dynamics (Nash-Sutcliffe efficiency of 0.98). After having assessed our models in a lumped setup, we then compared Model₁ to Model₃ in a spatially explicit setup, and evaluated what patterns of subsurface flow were possible with model elements of each type. We found that Model₁ tended to generate relatively smooth, steady state-like spatial patterns. Model₃ generated more complex patterns, in which lateral flow could be concurrently increasing and decreasing in different parts of the hillslope. We realize that the concepts proposed in this manuscript do not represent the only way in which nonlinear dynamics may be implemented in a model of subsurface stormflow. However, we believe that development of new model structures and the subsequent confrontation of model results with existing preconceptions will lead to a better understanding of subsurface stormflow and catchment runoff dynamics.