These MATLAB scripts calculate hilltop curvature, using both 2D continuous wavelet transforms and 2D polynomial functions, as described in Struble and Roering (2021)(1).
The script entitled HilltopCurvature_LidarSites.m walks you through applying the wavelet transform and polynomial fuction to your topographic data. An example lidar DEM of a portion of the Oregon Coast Range is included. Note that this script is dependent on TopoToolbox (Schwanghart and Sherler, 2014)(2), which can be accessed at topotoolbox.wordpress.com. The wavelet script utilized in HilltopCurvature_LidarSites.m is conv2_mexh_curv.m, which is a derivative of the Landslide Mapping Toolbox from Dr. Adam Booth at Portland State University. The full toolbox can be accessed at http://web.pdx.edu/~boothad/tools.html.
The script entitled Sythetic.m constructs syntehtic hillslopes using the functional form for a soil-mantled hillslope experiencing nonlinear diffusion, as described in Roering et al. (2007)(3). TopoToolbox is not required for this script.
Please acknowledge the use of this software in any publications by citing this paper (Struble and Roering, 2021) and software release.
Notes:
(1) Struble, W.T., Roering, J.J., 2021. Hilltop curvature as a proxy for erosion rate: Wavelets enable rapid computation and reveal systematic underestimation. Physical: Landscape Evolution: modelling and field studies. https://doi.org/10.5194/esurf-2021-40
(2) Schwanghart, W., Scherler, D., 2014. Short Communication: TopoToolbox 2 – MATLAB-based software for topographic analysis and modeling in Earth surface sciences. Earth Surf. Dynam. 2, 1–7. https://doi.org/10.5194/esurf-2-1-2014
(3) Roering, J.J., Perron, J.T., Kirchner, J.W., 2007. Functional relationships between denudation and hillslope form and relief. Earth and Planetary Science Letters 264, 245–258. https://doi.org/10.1016/j.epsl.2007.09.035