Geometric approaches to computing 3D-landscape metrics

The relationships between patterns and processes lie at the core of modern landscape ecology. These dependences\udcan be quantified by using indices related to the patch-corridor-matrix model. This model conceptualizes\udlandscapes as planar mosaics consisting of discrete patches. On the other hand, relief variability is a key factor for\udmany ecological processes, and therefore these processes can be better modeled by integrating information concerning\udthe third dimension of landscapes. This can be done by generating a triangle mesh which approximates\udthe original terrain. The aim of this methodological paper is to introduce two new constructions of triangulations\udwhich replace a digital elevation model. These approximation methods are compared with the method which was\udalready used in the computation of 3D-landscape metrics (firstly for parameterized surfaces and secondly for two\udlandscape mosaics). The statistical analysis shows that all three methods are of almost equal sensitivity in reflecting\udthe relationship between terrain ruggedness and the patches areas and perimeters. In particular, either of the methods\udcan be used for approximating the real values of these basic metrics. However, the two methods introduced\udin this paper have the advantage of yielding continuous approximations of the terrain, and this fact could be useful\udfor further developments