A morphologic proxy for debris flow erosion with application to the earthquake deformation cycle, Cascadia Subduction Zone, USA

In unglaciated steeplands, valley reaches dominated by debris flow scour and incision set landscape form as they often account for > 80% of valley network length and relief. While hillslope and fluvial process models have frequently been combined with digital topography to develop morphologic proxies for erosion rate and drainage divide migration, debris-flow-dominated networks, despite their ubiquity, have not been exploited for this purpose. Here, we applied an empirical function that describes how slope-area data systematically deviate from so-called fluvial power-law behavior at small drainage areas. Using airborne LiDAR data for 83 small (~ 1 km2) catchments in the western Oregon Coast Range, we quantified variation in model parameters and observed that the curvature of the power-law scaling deviation varies with catchment-averaged erosion rate estimated from cosmogenic nuclides in stream sediments. Given consistent climate and lithology across our study area and assuming steady erosion, we used this calibrated denudation-morphology relationship to map spatial patterns of long-term uplift for our study catchments. By combining our predicted pattern of long-term uplift rate with paleoseismic and geodetic (tide gauge, GPS, and leveling) data, we estimated the spatial distribution of coseismic subsidence experienced during megathrust earthquakes along the Cascadia Subduction Zone. Our estimates of coseismic subsidence near the coast (0.4 to 0.7 m for earthquake recurrence intervals of 300 to 500 years) agree with field measurements from numerous stratigraphic studies. Our results also demonstrate that coseismic subsidence decreases inland to negligible values > 25 km from the coast, reflecting the diminishing influence of the earthquake deformation cycle on vertical changes of the interior coastal ranges. More generally, our results demonstrate that debris flow valley networks serve as highly localized, yet broadly distributed indicators of erosion (and rock uplift), making them invaluable for mapping crustal deformation and landscape adjustment.