Local hilltop and debris-flow morphometrics predict drainage divide migration

In terrestrial landscapes, neighboring catchments that experience contrasting erosion rates can be in disequilibrium such that drainage divides migrate. Cross-divide differences in measured erosion rate can indicate whether a drainage divide is stationary or mobile, and fluvial and hillslope morphologic proxies for erosion rate are often used to infer divide motion. However, these morphometrics do not measure the morphology of the divide itself. Furthermore, these metrics often neglect processes that spatially disconnect the divide from nearby fluvial channels, particularly debris-flow dominated valleys. Here, we test the efficacy of alternate morphometrics that correspond to nonfluvial processes proximal to the divide and compare our results to traditional divide-stability morphometrics (“Gilbert Metrics,” channel steepness, χ). Specifically, our alternate morphometrics are: A_df, a measure of the extent of debris-flow dominated channels, and hilltop curvature, C_HT, within each drainage basin. Finally, we quantify the asymmetry of hilltop curvature of the main drainage divide – termed C_asym – which represents the only morphometric that measures the drainage divide itself. We investigate these descriptors of landscape form in three landscapes that exhibit a range of uplift and erosion rates, as measured with cosmogenic nuclides in river sands: the Oregon Coast Range (OCR) and Ozark Plateau, Arkansas, both humid landscapes with moderate and low erosion rates, respectively, and the San Gabriel Mountains (SGM), California, a semi-arid region with high erosion rates.

We find that across all landscapes, classic morphometrics like channel steepness, χ, and the Gilbert Metrics can generally estimate divide mobility. However, the accuracy of these metrics differs and depends on measurement scale, and they are subject to assumptions regarding spatial variability in lithology, tectonics, and climate, as has been previously noted. Similarly, we find that the ability of A_df and C_HT to predict divide mobility is dependent on the dominant processes within each landscape as well as the magnitude of erosion rate. For example, in landscapes like the SGM where debris flows are common at high erosion rates, A_df accurately predicts divide migration, whereas it struggles to record migration at low erosion rates in the OCR and Ozarks. In contrast, we find that catchment-averaged C_HT is an effective proxy for divide migration in the OCR and Ozarks, but becomes ineffective at the most rapid erosion rates in the SGM, where hillslopes become devoid of soil as erosion rates exceed soil production rates. Notably, in all landscapes, we observe that C_asym accurately predicts divide migration, indicating that asymmetry near the hillcrest can be captured by curvature morphometrics that isolate each side of the mobile divide. Overall, our results encourage an ensemble approach to predict divide migration, with attention paid to whether morphometrics faithfully record dominant surface processes in a landscape.