Search for: All records

Abstract. Estimation of erosion rate is an important component of landscapeevolution studies, particularly in settings where transience or spatialvariability in uplift or erosion generates diverse landform morphologies.While bedrock rivers are often used to constrain the timing and magnitude of changes in baselevel lowering, hilltop curvature (or convexity), CHT, provides an additional opportunity to map variations in erosion rate given that average slope angle becomes insensitive to erosion rate owing to threshold slope processes. CHT measurement techniques applied in prior studies (e.g., polynomial functions), however, tend to be computationallyexpensive when they rely on high-resolution topographic data such as lidar,limiting the spatial extent of hillslope geomorphic studies to small studyregions. Alternative techniques such as spectral tools like continuouswavelet transforms present an opportunity to rapidly document trends inhilltop convexity across expansive areas. Here, we demonstrate howcontinuous wavelet transforms (CWTs) can be used to calculate the Laplacianof elevation, which we utilize to estimate erosion rate in three catchmentsof the Oregon Coast Range that exhibit varying slope angle, slope length,and hilltop convexity, implying differential erosion. We observe thatCHT values calculated with the CWT are similar to those obtained from2D polynomial functions. Consistent with recent studies, we find thaterosion rates estimated with CHT from both CWTs and 2D polynomialfunctions are consistent with erosion rates constrained with cosmogenicradionuclides from stream sediments. Importantly, our CWT approachcalculates curvature at least 103 times more quickly than 2Dpolynomials. This efficiency advantage of the CWT increases with domainsize. As such, continuous wavelet transforms provide a compelling approachto rapidly quantify regional variations in erosion rate as well aslithology, structure, and hillslope sediment transport processes, which areencoded in hillslope morphology. Finally, we test the accuracy of CWT and 2Dpolynomial techniques by constructing a series of synthetic hillslopesgenerated by a theoretical nonlinear transport model that exhibit a range oferosion rates and topographic noise characteristics. Notably, we find thatneither CWTs nor 2D polynomials reproduce the theoretically prescribedCHT value for hillslopes experiencing moderate to fast erosion rates,even when no topographic noise is added. Rather, CHT is systematicallyunderestimated, producing a power law relationship between erosion rate andCHT that can be attributed to the increasing prominence of planarhillslopes that narrow the zone of hilltop convexity as erosion rateincreases. As such, we recommend careful consideration of measurement lengthscale when applying CHT to estimate erosion rate in moderate tofast-eroding landscapes, where curvature measurement techniques may be prone to systematic underestimation.