Modelling overland flow and its partitioning into sheet and rill domains: An energetic perspective on the dynamics of Hortonian overland flow and erosion processes

Overland flow processes possess key importance for flood generation, erosion and sediment redistribution. Hortonian overland flow occurs often during flash flood events in sub-humid and semi-arid regions in response to high intensity convective rainstorms. The recent increase of these events aggravated by climate change, as well as impervious surface expansion and associated increase in runoff generation, highlights the need for a deeper understanding of the mass, momentum and energy balances of overland flow to predict, prevent and mitigate the response processes such as flooding and erosion.

As erosion is driven by the physical work flowing water performs on the land surface, this study investigates Hortonian overland flow formation from an energetic perspective. Key emphasis is on the partitioning of overland flow and its kinetic energy between sheet and rill domains. Rill formation requires an accumulation of overland flow to provide the necessary shear stress, while rills speed up overland flow velocities due to an enlarged hydraulic radius, which in return increases the shear stress. Due to this positive feedback, we hypothesize that hillslope scale rill networks evolve towards a steady-state configuration, which will result in equal partitioning of the kinetic energy flux into sheet and rill flow. The latter would imply that erosion is neither detachment nor transport limited.

We specifically revisited the hillslope-scale rainfall-runoff experiments of Gerlinger in the Weiherbach catchment located in the Kraichgau region, analyzing in a first step the interplay of surface runoff volume, flow velocity and erosion processes. Secondly, we calibrated the physically based numerical model CATFLOW-SED to reproduce overland flow hydrographs and the observed splitting into sheet and rill flow components using the “open book” approach. In a third step, we determined the spatial distribution of potential and kinetic energy within both domains and their relation to flow accumulation in the rills and surface roughness.

Our findings revealed that overland flow formation correlates positively with antecedent soil water content and negatively with surface roughness. A greater surface roughness promotes increased flow accumulation into the rill domain leading to a reduced particle detachment compared to the sheet domain. The simulation results indicate further that the partitioning of overland flow into both domains was generally well matched.

The analysis of the steady-state spatial energy patterns revealed, furthermore, a local maximum in total potential energy, separating the upslope laminar flow regime from downslope turbulent flow regime, where rills emerge. Moreover, higher roughness values corresponded to a stronger flow accumulation into the more energy efficient rill domain. While sheet domain accounted for the greater portion of potential energy along the hillslope, experiments associated with higher flow accumulation coefficients showed near-equal to equal kinetic energy for both domains at the foot of the hillslope.

To conclude, our study highlights the critical role of soil physical properties and flow characteristics on overland flow formation and erosion processes. The results indicate that emergence of rills suggest a steady-state energy-efficient configuration that balances erosion and transport dynamics.