Evaluating Scaling Frameworks for Multiscale Geomorphometric Analysis

Abstract

Multiscale methods have become progressively valuable in geomorphometric analysis as data have become increasingly detailed. This paper evaluates the theoretical and empirical properties of several common scaling approaches in geomorphometry. Direct interpolation (DI), cubic convolution resampling (RES), mean aggregation (MA), local quadratic regression (LQR), and an efficiency optimized Gaussian scale-space implementation (fGSS) method were tested. The results showed that when manipulating resolution, the choice of interpolator had a negligible impact relative to the effects of manipulating scale. The LQR method was not ideal for rigorous multiscale analyses due to the inherently non-linear processing time of the algorithm and an increasingly poor fit with the surface. The fGSS method combined several desirable properties and was identified as an optimal scaling method for geomorphometric analysis. The results support the efficacy of Gaussian scale-space as a general scaling framework for geomorphometric analyses.