Wavelet-based regularization of the extracted topographic index from high-resolution topography for hydro-geomorphic applications

High-resolution topography, e.g. 1-m digital elevation model (DEM) from light detection and ranging (LiDAR), offers opportunity for accurate identification of topographic features of relevance for hydrologic and geomorphologic modelling. Yet, the computation of some derived topographic properties, such as the topographic index (TI), is characterized by daunting challenges that hamper the full exploration of topography-based models. Particular problems, for example, arise when a distributed (or semi-distributed) rainfall–runoff model is applied to high-resolution DEMs. Indeed, the characteristic dependency between landscape resolution and the computed TI distribution results in the formation of un-physical, unconnected saturated zones, which in turn cause unrealistic representations of rainfall–runoff dynamics. In this study, we present a methodology based on a multi-resolution wavelet transformation that, by means of a soft-thresholding scheme on the wavelet coefficients, filters the noise of high-resolution topography to construct regularized sets of locally smoother topography on which the TI is computed. While the methodology needs a somewhat arbitrary definition of the wavelet coefficients threshold, our study shows that when the information content (entropy) of the TI distribution is used as a filtering efficiency metric, a critical threshold automatically emerges in the landscape reconstruction. The methodology is demonstrated using 1-m LiDAR data for the Elder Creek River basin in California. While the proposed case study uses a TOPMODEL approach, the methodology can be extended to different topography-based models and is not limited to hydrological applications.