Effect of interpolation methods on quantifying terrain surface roughness under different data densities

Abstract

Terrain surface roughness (TSR) is an important parameter in various geoscience applications. TSR can be easily estimated from digital elevation models (DEMs), which are generally derived from the interpolation of Light Detection and Ranging (LiDAR) point clouds. Thus, the quality of TSR is inevitably influenced by data density and interpolation method. However, to what extent the data density can be reduced and which method is more accurate than the others for quantifying TSR are still ambiguous. Thus, this paper evaluated the performance of five classical interpolation methods (ordinary kriging (OK), thin plate spline (TPS), natural neighbor (NN), Delaunay with linear interpolation (TIN) and inverse distance weighting (IDW)) for quantifying TSR under different airborne LiDAR data densities (90 %, 70 %, 50 %, 30 % and 10 % of the original data) in three study sites (samp1, samp2 and samp3) with different terrain characteristics. Results demonstrate that regardless of data density and study sites, TPS is consistently more accurate than the other methods for DEM production in terms of root mean square error (RMSE) and normalized median absolute deviation (NMAD), while IDW produces the worst results. Moreover, the reduction of data density to 50 % of the original data results in no obvious accuracy loss of DEMs for all the interpolation methods. For quantifying TSRs from DEMs, IDW shows the highest accuracy when data density is larger than 50 % in samp1 and samp2, and larger than 70 % in samp3, while TPS obtains the best results in the other densities; however, the surfaces of IDW are very coarse, which makes terrain details unrecognizable. Additionally, the DEM-based TSRs of all the interpolation methods can endure the reduction of LiDAR data to 50 % of the original samples without considerable accuracy decreases, especially for TPS. Overall, TPS can be considered as a promising method for LiDAR DEM production and TSR quantification.