The Numerical Formulation of Simple Hysteretic Models to Simulate the Large‐Scale Hydrological Impacts of Prairie Depressions

Topographic depressions have large impacts on the hydrology, ecology, and biogeochemistry in prairie environments. Topographic depressions control the hydrological flow regime through their role in storing water from precipitation and snow melt, and the storage dynamics of topographic depressions affect the retention, transformations, and transport of sediment, carbon, and nutrients. The water stored in topographic depressions supports a diversity of animal and plant species. More generally, depressional wetlands are an integral component of global water, energy, and biogeochemical cycles. In this technical note, we present simple models to simulate hysteretic relationships between storage and contributing area. We consider both spatially distributed and spatially integrated models. The spatially distributed models (the ensemble‐depression model) explicitly simulate storage dynamics for a distribution of discrete depressions. In these spatially distributed models, the large‐scale storage‐contributing fraction relationships are an emergent property of the modeled system. The spatially integrated models (the meta‐depression model) parameterize the large‐scale storage‐discharge relationships. The spatially integrated models are formulated in a way to represent hysteretic behavior. We present a suite of numerical experiments and demonstrate that the ensemble‐depression and meta‐depression models have similar large‐scale behavior. The simple hysteretic models defined here are formulated in a way so that they can easily be incorporated in conventional hydrological models.