Vector analysis theory on landscape pattern (VATLP)

Landscape indices are popular for the quantification of landscape pattern. However, all landscape indices being used so far are scalar quantities, and measure patterns without considering sufficiently the pattern shape and the directionality together. Based on planar characteristics defined in mechanics such as centroid, moment of inertia, product of inertia and principal axes, vector analysis theory on landscape pattern (VATLP) is explored here. Firstly, we establish a coordinate system of centroidal principal axes (CSCPA). Three related new indices including those describing the direction of pattern distribution (patch orientation (PO), vectorial patch orientation (VPO)), and that indicating the shape of patch's equivalent ellipse (eccentric rate (ER)) are deduced. These landscape metrics are then applied to the pattern analysis of the lakes in Qian-an county (the study area), Jilin province, China. The vector-based data sets of the study area come from the National Land Use/Cover Database (NLUCD). The application of the theory help us better understand the pattern formation of the lakes and the related ecological processes that occur on both ends of the major principal axis, e.g., the transportation of energy and materials flow, and the ecological gradients.