Morphological controls on Hortonian surface runoff: An interpretation of steady-state energy patterns, maximum power states and dissipation regimes within a thermodynamic framework.

Recent developments in hydrology have led to a new perspective on runoff processes, extending beyond the classical mass dynamics of water in a catchment. For instance, stream flow has been analysed in a thermodynamic framework, which allows the incorporation of two additional physical laws and enhances our understanding of catchments as open environmental systems. Related investigations suggested that energetic extremal principles might constrain hydrological processes, because the latter are associated with conversions and dissipation of free energy. Here we expand this thermodynamic perspective by exploring how hillslope structures at the macro- and microscale control the free energy balance of Hortonian overland flow. We put special emphasis on the transitions of surface runoff processes at the hillslope scale, as hillslopes energetically behave distinctly different in comparison to fluvial systems. To this end, we develop a general theory of surface runoff and of the related conversion of geopotential energy gradients into other forms of energy, particularly kinetic energy as the driver of erosion and sediment transport. We then use this framework at a macroscopic scale to analyse how combinations of typical hillslopes profiles and width distributions control the spatial patterns of steady-state stream power and energy dissipation along the flow path. At the microscale, we analyse flow concentration in rills and its influence on the distribution of energy and dissipation in space. Therefore, we develop a new numerical method for the Catflow model, which allows a dynamical separation of Hortonian surface runoff between a rill- and a sheet flow domain. We calibrated the new Catflow-Rill model to rainfall simulation experiments and observed overland flow in the Weiherbach catchment and found evidence that flow accumulation in rills serves as a means to redistribute energy gradients in space, therefore minimizing energy expenditure along the flow path, while also maximizing overall power of the system. Our results indicate that laminar sheet flow and turbulent rill flow on hillslopes develop to a dynamic equilibrium that corresponds to a maximum power state, and that the transition of flow from one domain into the other is marked by an energy maximum in space. [ABSTRACT FROM AUTHOR]