Evaluating metrics of local topographic position for multiscale geomorphometric analysis

The field of geomorphometry has increasingly moved towards the use of multiscale analytical techniques, due to the availability of fine-resolution digital elevation models (DEMs) and the inherent scale-dependency of many DEM-derived attributes such as local topographic position (LTP). LTP is useful for landform and soils mapping and numerous other environmental applications. Multiple LTP metrics have been proposed and applied in the literature; however, elevation percentile (EP) is notable for its robustness to elevation error and applicability to non-Gaussian local elevation distributions, both of which are common characteristics of DEM data sets. Multiscale LTP analysis involves the estimation of spatial patterns using a range of neighborhood sizes, traditionally achieved by applying spatial filtering techniques with varying kernel sizes. While EP can be demonstrated to provide accurate estimates of LTP, the computationally intensive method of its calculation makes it unsuited to multiscale LTP analysis, particularly at large neighborhood sizes or with fine-resolution DEMs. This research assessed the suitability of three LTP metrics for multiscale terrain characterization by quantifying their computational efficiency and by comparing their ability to approximate EP spatial patterns under varying topographic conditions. The tested LTP metrics included: deviation from mean elevation (DEV), percent elevation range (PER), and the novel relative topographic position (RTP) index. The results demonstrated that DEV, calculated using the integral image technique, offers fast and scale-invariant computation. DEV spatial patterns were strongly correlated with EP (r2 range of 0.699 to 0.967) under all tested topographic conditions. RTP was also a strong predictor of EP (r2 range of 0.594 to 0.917). PER was the weakest predictor of EP (r2 range of 0.031 to 0.801) without offering a substantial improvement in computational efficiency over RTP. PER was therefore determined to be unsuitable for most multiscale applications. It was concluded that the scale-invariant property offered by the integral image used by the DEV method counters the minor losses in robustness compared to EP, making DEV the optimal LTP metric for multiscale applications.