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A note on equations for steady‐state optimal landscapes

Abstract

Based on the optimality principle (that the global energy expenditure rate is at its minimum for a given landscape under steady state conditions) and calculus of variations, we have derived new governing equations for describing steady state optimal landscapes. Other than building on the well established Manning’s equation, this work does not rely on any empirical relationships (such as those relating hydraulic parameters to local slopes). Using additional constraints, we also theoretically demonstrate that discharge is a power function of local slope, which is consistent with field data and previous studies.

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