Inferring landscape response to climate from the relation between mean hillslope angle and channel steepness

Topographic metrics derived from digital elevation models (DEMs) are widely used to infer tectonic, climatic, and lithological variation in time and space in rugged mountainous settings. Much of our understanding of the controls on these topographic metrics is based upon simple models of landscape evolution and to a lesser degree on field calibration of these models. Two particularly useful topographic metrics are mean hillslope gradient and the channel steepness index because they capture the two sets of processes at work in fluvial landscapes. Mean hillslope gradient has been demonstrated to increase monotonically at low erosion rates up to a maximum threshold slope. In contrast, the channel steepness index has been shown to increase monotonically with erosion rate, though channel steepness may also threshold at very high erosion rates due to debris-flow controlled slopes. Consequently, we find mean hillslope angle generally increases monotonically with channel steepness until the threshold hillslope angle is reached - a pattern seen in every landscape we have analyzed. It can be shown that this kink in the slope-steepness relationship occurs at a critical channel steepness value that is set by the ratio of the efficiency of hillslope transport processes to the efficiency of channel incision processes (the D/K ratio). We pursue this opportunity to investigate how mean annual precipitation influences the D/K ratio, which is also thought to control channel spacing. We have examined the relations between catchment-mean hillslope angle and channel steepness index in a suite of 7 mountainous landscapes (catchments 10-50 km^2) cut in granitic rocks which experience mean annual precipitation ranging from < 0.25 m/yr to > 3.0 m/yr, using both 30 and 90 meter DEMs. We find that between our driest sites and the semi-arid San Gabriel Mountains site, the critical channel steepness index value decreases significantly (by a factor of 2) with mean annual precipitation, implying a decrease in the D/K ratio. A decrease in the D/K ratio with increasing precipitation is intuitively satisfying given the direct control of fluvial discharge on K. However, between our semi-arid sites and very humid sites, we can detect no significant change in either the critical channel steepness index or the D/K ratio. This implies that either the effect of enhanced precipitation is greatly subdued in climates wetter than semi-arid (consistent with some prior work) or that hillslope diffusivity (D) and the coefficient of channel incision (K) are equally influenced by precipitation. Further data collected on the relationships among erosion rate, mean hillslope angle, hillslope length, hilltop curvature, and mean channel steepness index will allow us to definitively determine how both D and K vary across this climate transect.