Multiresolution analysis of characteristic length scales with high-resolution topographic data

Characteristic length scales (CLS) define landscape structure and delimit geomorphic processes. Here we use multiresolution analysis (MRA) to estimate such scales from high-resolution topographic data. MRA employs progressive terrain defocusing, via convolution of the terrain data with Gaussian kernels of increasing standard deviation, and calculation at each smoothing resolution of (i) the probability distributions of curvature and topographic index (defined as the ratio of slope to area in log scale) and (ii) characteristic spatial patterns of divergent and convergent topography identified by analyzing the curvature of the terrain. The MRA is first explored using synthetic 1-D and 2-D signals whose CLS are known. It is then validated against a set of MARSSIM (a landscape evolution model) steady state landscapes whose CLS were tuned by varying hillslope diffusivity and simulated noise amplitude. The known CLS match the scales at which the distributions of topographic index and curvature show scaling breaks, indicating that the MRA can identify CLS in landscapes based on the scaling behavior of topographic attributes. Finally, the MRA is deployed to measure the CLS of five natural landscapes using meter resolution digital terrain model data. CLS are inferred from the scaling breaks of the topographic index and curvature distributions and equated with (i) small-scale roughness features and (ii) the hillslope length scale.