Comparing methods for calculating channel steepness index

Channel steepness index, k(s), is a metric derived from the stream power model that, under certain conditions, scales with relative rock uplift rate. Channel steepness index is a property of rivers, which can be relatively easily extracted from digital elevation models (DEMs). As DEM data sets are widely available for Earth and are becoming more readily available for other planetary bodies, channel steepness index represents a powerful tool for interpreting tectonic processes. However, multiple approaches to calculate channel steepness index exist. From this several important questions arise; does choice of approach change the values of channel steepness index, can values be so different that choice of approach can influence the findings of a study, and are certain approaches better than others? With the aid of a synthetic river profile and a case study from the Sierra Nevada, California, we show that values of channel steepness index vary over orders of magnitude according to the methodology used in the calculation. We explore the limitations, advantages and disadvantages of the key approaches to calculating channel steepness index, and find that choosing an appropriate approach relies on the context of a study. Given these observations, it is important that authors acknowledge the methodology used to calculate channel steepness index, to ensure that results can be contextualised and reproduced.