When Does the Concavity Index Constrain Stream Power Parameters?

By defining the attributes of river networks, we can quantitatively extract records of climatic and tectonic changes from them. The stream power incision model (SPIM) provides a framework within which this can be achieved, as it facilitates the calculation of the relative rock uplift from river characteristics. One parameter that has been widely employed in tectonic and fluvial geomorphology is the channel steepness index, a metric that can represent the normalized rock uplift rate experienced by a river. However, to accurately infer the channel steepness index, we must accurately estimate m/n, the ratio between the two positive exponents of the SPIM. Present methodologies to constrain m/n rely on an assumption that rock uplift and erodibility are spatially invariant. These conditions are rarely present on Earth. In this study, we use a synthetic example and examples from the Siwalik Hills and Olympic Mountains to demonstrate how existing methodologies to constrain m/n produce systematic errors when there is spatial variation, and particularly spatial gradients, in the processes driving landscape evolution. To solve this problem, we present a methodology to estimate m/n based on a large river network inversion that accounts for spatial variation in landscapes. After demonstrating that the methodology can accurately recover m/n in our synthetic landscape, we show that our methodology can reconcile contrasting observations in the Siwaliks, and is critical to inferring accurate values of channel steepness index in the Olympic Mountains. This highlights the utility of large topographic inversions for investigating landscape dynamics.