A greedy-based multiquadric method for LiDAR-derived ground data reduction

A high-fidelity multiresolution digital elevation model for Earth systems

“…However, as numerical simulation systems evolved to incorporate broader scales and finer processes to produce more exact predictions (Ringler et al, 2011;Weller et al, 2016;Wilson, 2012;Zarzycki et al, 2014), how to accurately assimilate or transform the finePublished by Copernicus Publications on behalf of the European Geosciences Union. 240 X. Duan et al: A high-fidelity multiresolution DEM for Earth systems resolution topography has proven to be a quite difficult task (Bilskie et al, 2015;Chen et al, 2015;Tarolli, 2014).…”

“…But a mesh constructed from interpolated vertices does not necessarily comply with the terrain relief, and elevation errors are frequently reported as an input uncertainty (Bilskie and Hagen, 2013;Hunter et al, 2007;Nunalee et al, 2015;Wilson and Gallant, 2000). Although there are many situations where dynamic conditions are stressed as stronger impacts on predictions (Cea and Bladé, 2015;Budd et al, 2015), the underlying topography is still very important due to its increasingly improved fidelity to the Earth's surface (Bates, 2012;Tarolli, 2014), and a sophisticated topography transformation would be beneficial to reduce discrepancies arising from physical inconsistencies (Chen et al, 2015;Glover, 1999;Ringler et al, 2011).…”

“…Systematic scale transformation of topographic data has long been studied under terrain generalisation, where precise surface approximation and terrain structural feature retention have both been pursued (Ai and Li, 2010;Chen et al, 2015;Guilbert et al, 2014;Jenny et al, 2011;Weibel, 1992;Zhou and Chen, 2011). Triangulated irregular networks (TINs) are generally chosen as a substitute for the regularly spaced grids (RSGs), and terrain feature points (critical points or salient points from some significance metric) are selected for constructing the network.…”

“…It thus forces existing research to employ some heuristic strategy, in which insertion (or deletion) refinements on feature points are adopted, to find a sub-optimal approximation that is computationally practical. In each insertion (or deletion), rearranging the entire existing grid to obtain a better approximation is also computationally prohibitive and thus not adopted (Chen et al, 2015;Heckbert and Garland, 1997;Lee, 1991); this may result in the clustering of feature points . Among those existing heuristic approaches, trenching the pre-extracted terrain features (drainage streamlines, for example) into the TIN surface seems quite appealing (compound method) (Chen and Zhou, 2012;Zhou and Chen, 2011), but the quality of the generalised TIN surface cannot be guaranteed, and the existence of sliver triangles makes it difficult to be incorporated with simulation numerical stability (Kim et al, 2014;Weller et al, 2009).…”

“…The second class of approaches recognised the TIN surface constructed from locally computed feature points as not a good approximation to the original DEM surface. Much research thus considered global approximation instead of relying on an elaborate feature point selection scheme, such as bi-linear, bi-quadric, multi-quadric, Kriging, or general radial base function-based fitting (Aguilar et al, 2005;Chen et al, 2015;Schneider, 2005;Shi et al, 2005). The proposed multi-quadric method (Chen et al, , 2015, for example, well approximates the original DEM surface with a high-order smooth surface, and the smooth surface provides a kind of rejection mechanism to cure the feature point clustering problem.…”