Scaling properties in landscape patterns: New Zealand experience

Abstract

In this paper we present a case study of spatial structure in landscape patterns for the North and South Islands of New Zealand. The aim was to characterise quantitatively landscape heterogeneity and investigate its possible scaling properties. The study examines spatial heterogeneity, in particular patchiness, at a range of spatial scales, to help build understanding on the effects of landscape heterogeneity on water movement in particular, and landscape ecology in general. We used spatial information on various landscape properties (soils, hydrogeology, vegetation, topography) generated from the New Zealand Land Resource Inventory. To analyse this data set we applied various methods of fractal analyses following the hypothesis that patchiness in selected landscape properties demonstrates fractal scaling behaviour at two structural levels: (1) individual patches; and (2) mosaics (sets) of patches. Individual patches revealed scaling behaviour for both patch shape and boundary. We found self-affinity in patch shape with Hurst exponent H from 0.75 to 0.95. We also showed that patch boundaries in most cases were self-similar and in a few cases of large patches were self-affine. The degree of self-affinity was lower for finer patches. Similarly, when patch scale decreases the orientation of patches tends to be uniformly distributed, though patch orientation on average is clearly correlated with broad scale geological structures. These results reflect a tendency to isotropic behaviour of individual patches from broad to finer scales. Mosaics of patches also revealed fractal scaling in the total patch boundaries, patch centers of mass, and in patch area distribution. All these reflect a special organisation in patchiness represented in fractal patch clustering. General relationships which interconnect fractal scaling exponents were derived and tested. These relationships show how scaling properties of individual patches affect those for mosaics of patches and vice-versa. To explain similarity in scaling behaviour in patchiness of different types we suggest that the Self-Organised Criticality concept should be used. Also, potential applications of our results in landscape ecology are discussed, especially in relation to improved neutral landscape models.