Quantifying Erodibility in Stream Power Incision Models: Practical Guidance and Model Response Dynamics

Abstract. Bedrock river incision models rely on an erodibility coefficient, K, that aggregates lithology, climate, sediment supply, and channel hydraulics into a single term, yet is typically the least constrained parameter in the stream power incision model and its derivatives. This paper has two aims: to give researchers practical guidance on how to estimate and report K, and to demonstrate quantitatively why residual uncertainty in K matters for the landscape evolution models using it. First, we systematically review 25 studies that estimate bedrock erodibility using geomorphic, geochemical and geophysical, or model-calibration and inverse methods. From this review we synthesise a decision framework that directs a prospective user to a method suited to their scientific objective and available data, five cross-cutting caveats that must be considered regardless of method, and four reporting practices that would improve the comparability and reusability of K estimates. Second, we propagate a tightly constrained, single-lithology erodibility range through detachment-limited and sediment-coupled landscape evolution simulations of a real catchment, to test how much this residual uncertainty changes model predictions. Even within a short modelled timeframe in which no configuration approaches long-term equilibrium, this range produces a real, monotonic, and in places mass-conserved divergence in predicted erosion rate, slope, and eroded volume. Switching model formulation at fixed erodibility shifts the predicted response systematically and in a direction that was not anticipated in advance: the sediment-coupled model erodes less than the detachment-limited model, via transient sediment shielding of the bed. Together, these results give researchers both a practical framework for choosing and reporting an erodibility estimate, and quantitative evidence that the method, exponent convention, and model formulation behind that estimate cannot be separated from the value itself.