Minimum dissipation of potential energy by groundwater outflow results in a simple linear catchment reservoir

Abstract. Streamflow recessions of catchments during periods of no recharge can often be reproduced by a simple, linear reservoir despite the complexity of the catchments. Here we show that such a simple linear behaviour can result from the assumption that groundwater drains from smaller units within the catchment into the stream in such a way that the potential energy of groundwater of the whole catchment is dissipated at the minimum possible rate. To do so, we consider the mass balances of groundwater of two connected sub-catchments that form a hypothetical catchment and consider the depletion of potential energy as groundwater drains into the channel network. We show analytically that the catchment-level depletion of groundwater potential energy has a minimum with respect to a groundwater flux that connects the sub-catchments. The catchment-level minimisation results in equal groundwater levels in the sub-catchments with respect to their channels, which then results in a simple, linear reservoir model for the whole catchment. We then discuss the requirements for such a minimum dissipation state to exist and propose possible mechanisms by which groundwater flow can organise and evolve to such a state. We conclude that the simple, linear response in streamflow recession can be interpreted as the outcome of groundwater flow within the catchment organised to dissipate potential energy at the minimum possible rate. Hence, it would seem that energetic considerations provide an important, additional constraint in the dynamics of water flow networks within catchments that potentially reduces the problem of equifinality in hydrology.