Evaluating Metrics of Drainage Divide Mobility

Watersheds are the fundamental organizing units in landscapes and thus the controls on drainage divide location and mobility are an essential facet of landscape evolution. Additionally, many common topographic analyses fundamentally assume that river network topology and divide locations are largely static, allowing channel profile form to be interpreted in terms of spatio-temporal patterns of rock uplift rate relative to baselevel, climate, or rock properties. Recently however, it has been suggested that drainage divides are more mobile than previously thought and that divide mobility, and resulting changes in drainage area, can potentially induce changes to fluvial topography comparable to spatio-temporal variation in rock uplift, climate, or rock properties. Ultimately, reliable metrics are needed to diagnose the mobility of divides. One such recently proposed metric is cross-divide contrasts in `chi', a measure of the current topology of the drainage network, but cross-divide contrasts in a number of topographic metrics show promise. Here we use a series of landscape evolution modeling scenarios in which we induce divide mobility under different conditions to test the utility of a suite of plausible topographic metrics of divide mobility and compare these to natural examples. Specifically, we test cross-divide contrasts in mean slope, mean local relief, channel bed elevation at a reference drainage area, and chi. Our results highlight that cross-divide contrasts in chi can only be accurately interpreted in terms of divide mobility when uplift, rock erodibility, climate, and base-level are uniform across both river networks on either side of the divide. This is problematic for application of this metric to natural landscapes as (1) uniformity of all of these parameters is exceedingly unlikely and (2) quantifying the spatial patterns of these parameters is difficult. Consequently, as shown here for both simulated and natural landscapes, simple measures of cross-divide contrasts in mean slope, mean local relief, and channel bed elevation at a reference drainage area are more robust metrics of divide mobility, correctly identifying stable or mobile divides independent of cross-divide differences in rock uplift, climate, erodibility or baselevel.