Heterogeneity in catchment properties: a case study of Grey and Buller catchments, New Zealand

Abstract

The scaling behaviour of landscape properties, including both morphological and landscape patchiness, is examined using monofractal and multifractal analysis. The study is confined to two neighbouring meso-scale catchments on the west coast of the South Island of New Zealand. The catchments offer a diverse but largely undisturbed landscape with population and development impacts being extremely low. Bulk landscape properties of the catchments (and their sub-basins) are examined and show that scaling of stream networks follow Hack's empirical rule, with exponents ~0.6. It is also found that the longitudinal and transverse scaling exponents of stream networks equate to l v ≈ 0.6 and w v ≈ 0.4, indicative of self-affine scaling. Catchment shapes also show self-affine behaviour. Further, scaling of landscape patches show multifractal behaviour and the analysis of these variables yields the characteristic parabolic curves known as multifractal spectra. A novel analytical approach is adopted by using catchments as hydrological cells at various sizes, ranging from first to sixth order, as the unit of measure. This approach is presented as an alternative to the box-counting method as it may be much more representative of hydro-ecological processes at catchment scales. Multifractal spectra are generated for each landscape property and spectral parameters such as the range in α Such a relationship strongly suggests that the landscape patches are heterogeneous in nature and that their scaling behaviour can be described as multifractal. The quantitative parameters obtained from the spectra may provide the basis for improved parameterisation of ecological and hydrological models.

Power-law of Aggregate-size Spectra in Natural Systems

“…Equation 2 is commonly known as Hack's law in fluvial geomorphology [89] where C is the mainstream length and S is the size of a basin. The interchange of the mainstream with the basin boundary is supported by our ansatz and by the empirical evidence of the scaling of the basin perimeter with the mainstream length with a power of one (C ∼ l) [61,[84][85][86][87]. The Hack's law validity is proven in any embedded subbasins within river basins.…”

“…The aforementioned scaling relationship is verified for river basins. For river basins it was suggested that basin boundaries and mainstream courses are in essence mirror images of each other [61,[84][85][86][87]. This assumption generates the second allometric law in Equation 1 irrespectively of the constant.…”

“…Landscape ecology is the field in which the theory of aggregates received the highest attention due the importance of the species aggregate-size distribution for species conservation. [60] and [61], studied the patches of river ecosystem properties (for instance, slope, hydrogeology, erosion, and vegetation) in New Zealand. These are the first studies, to the best of our knowledge, that tried to unify theories, including the "Korčak's law", for the characterization of patches in heterogeneous ecosystems.…”

Lithologic control on the multifractal spectrum of river networks

“…doi:10. 1016/j.jhydrol.2005.11.025 Rinaldo et al, 1992;Rinaldo et al, 1993;Rigon et al, 1993;Lavallée et al, 1993;Rodriguez-Iturbe and Rinaldo, 1997;Veneziano and Niemann, 2000a,b;Shankar et al, 2002).…”

Comprehensive analysis of changes to catchment slope properties in the high-sediment region of the Loess Plateau, 1978–2010

“…The physical properties of a catchment, such as geologic substrate, topography (e.g., slope, aspect), soil type/depth, vegetation, and landscape patchiness, have long been known to influence runoff generation and sediment yield (Yang et al, 2001;Shankar et al, 2002;Roderick et al, 2011;Fenicia et al, 2014). For a given catchment, many of the properties, especially the geologic and topographic properties, will remain nearly constant over decadal to century time scales.…”