Preprints
https://doi.org/10.5194/hess-2021-79
https://doi.org/10.5194/hess-2021-79

  11 Feb 2021

11 Feb 2021

Review status: this discussion paper is a preprint. It has been under review for the journal Hydrology and Earth System Sciences (HESS). The manuscript was not accepted for further review after discussion.

Hortonian Overland Flow, Hillslope Morphology and Stream Power I: Spatial Energy Distributions and Steady-state Power Maxima

Samuel Schroers1, Olivier Eiff1, Axel Kleidon2, Jan Wienhöfer1, and Erwin Zehe1 Samuel Schroers et al.
  • 1Institute of Water Resources and River Basin Management, Karlsruhe Institute of Technology – KIT, Karlsruhe, Germany
  • 2Max-Planck Institute for Biogeochemistry, Hans-Knöll-Str. 10, 07745 Jena, Germany

Abstract. 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 analyzed 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 macro and micro hillslope structures control the free energy balance of Hortonian overland flow. This may ultimately help understanding why these structures have evolved to their present shape. 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 driver of erosion and sediment transport. We then use this framework to analyze 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. Additionally, we provide a first order estimate whether and when rills reduce the overall energy dissipation compared to sheet flow. Finally, we relate accumulated stream power of linear hillslopes to slope angles, closing the loop to Horton's original formulation of erosion force. The analytical analysis of stream power reveals that the common formulation, a function of the depth-discharge product is a reduced version of the more general equations if we neglect changes in velocity and discharge in space. The full equations of stream power result in maximum energy fluxes in space for sinusoidal and exponential hillslope profiles, while linear and negative exponential forms unlimitedly increase these fluxes in the downstream direction. Depending on geometry, rill flow increases or decreases kinetic energy fluxes downslope, effectively counteracting or increasing the dissipation of potential energy. For accumulated power in space for steady state runoff, we find that on linear hillslopes a slope angle of 45° maximizes the conversion of potential energy into dissipation and an angle of 35° maximizes the conversion of potential energy into kinetic energy.

Samuel Schroers et al.

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2021-79', Anonymous Referee #1, 08 Mar 2021
    • AC1: 'Reply on RC1', Samuel Schroers, 09 Mar 2021
    • AC2: 'Reply on RC1', Samuel Schroers, 09 Mar 2021
  • RC2: 'Comment on hess-2021-79', Anonymous Referee #2, 18 Apr 2021
    • AC3: 'Reply on RC2', Samuel Schroers, 23 Apr 2021
  • RC3: 'Comment on hess-2021-79', Hubert H.G. Savenije, 26 May 2021
    • AC4: 'Reply on RC3', Samuel Schroers, 27 May 2021

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2021-79', Anonymous Referee #1, 08 Mar 2021
    • AC1: 'Reply on RC1', Samuel Schroers, 09 Mar 2021
    • AC2: 'Reply on RC1', Samuel Schroers, 09 Mar 2021
  • RC2: 'Comment on hess-2021-79', Anonymous Referee #2, 18 Apr 2021
    • AC3: 'Reply on RC2', Samuel Schroers, 23 Apr 2021
  • RC3: 'Comment on hess-2021-79', Hubert H.G. Savenije, 26 May 2021
    • AC4: 'Reply on RC3', Samuel Schroers, 27 May 2021

Samuel Schroers et al.

Samuel Schroers et al.

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Short summary
In this study we ask the basic question why surface runoff forms drainage networks and confluences at all and how structural macro form and micro topography is a result of thermodynamic laws. We find that on a macro level hillslopes should tend from negative exponential towards exponential forms and that on a micro level the formation of rills goes hand in hand with drainage network formation of river basins. We hypothesize that we can learn more about erosion processes if we extend this theory.