Non-Linear Hillslopes Produce Apparent Non-Linear River Erosion Models

Non-linear relationships between catchment-wide erosion rate and normalized channel steepness within fluvial basins are commonly interpreted to indicate that river erosion is proportional to river slope raised to a power greater than one. This interpretation has crucial implications for the inferred erosion model and for our ability to extract information about past tectonic history from river topography. Here we show that the apparent non-linearity between catchment-wide average erosion rates and average channel steepness may be due in part to non-linear hillslope and debris-flow processes that bias the calculation of normalized, catchment-averaged channel steepness in some landscapes. More specifically, when non-linear hillslopes dominate the high elevation landscape close to the divide, then the transition to the fluvial domain becomes a function of the rock uplift rate, with faster rock uplift dictating longer hillslopes. If the minimum drainage area used for calculating average steepness is not scaled with the rock uplift rate, hillslopes may be included in the fluvial channel steepness analysis. In such cases, the inferred non-linearity between erosion rate and catchment-averaged steepness may be an artifact of the analysis procedure rather than a signature of the erosion process itself.