![]() ![]() ![]() The results suggest that older hillslope forms, where advective soil wash erosion dominates, are less efficient than younger forms which relate to diffusive erosion regimes. In a first part, we simulate three rainfall runoff scenarios by numerically solving the shallow water equations, and we analyze those in terms of relative dissipation. Given the transient and intermittent behavior of rainfall runoff, we explore the transient free energy balance with respect to energy efficiency, comparing typical hillslope forms that represent a sequence of morphological stages and dominant erosion processes. Generally, we find that such a hillslope engine is energetically rather inefficient, although the well-known Carnot limit does not apply here, as surface runoff is not driven by temperature differences. To account for both factors, we introduce the concept of relative dissipation, relating frictional energy dissipation to the energy influx, which essentially characterizes energy efficiency of the hillslope when treated as an open, dissipative power engine. We argue that a release of the frequent assumption of steady states is key, as the maximum work that surface runoff can perform on the sediments relates not only to the surface structure but also to “refueling” of the system with potential energy by rainfall events. Here we start with both laws but expand the related principles to explain the co-evolution of surface runoff and hillslope morphology by using measurable hydraulic and hydrological variables. Most of those point to the first and second law of thermodynamics, which describe conservation and dissipation of free energy through fluxes depleting their driving gradients. Given the complexity and variety of the Earth's runoff processes, those findings have inspired researchers for over a century, and they resulted in many principles and sometimes proclaimed laws to explain the physics that govern the evolution of landforms and river networks. The resulting forms and patterns have been shown to follow distinct rules, which hold throughout almost all terrestrial catchments. Surface runoff over time shapes the morphology of the landscape. ![]()
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