Hydrology and Earth System Sciences
www.hydrol-earth-syst-sci.net
1027-5606
1607-7938
6
2
2002
10.5194/hess-6-167-2002
http://www.hydrol-earth-syst-sci.net/6/167/2002/
http://www.hydrol-earth-syst-sci.net/6/167/2002/hess-6-167-2002.html
http://www.hydrol-earth-syst-sci.net/6/167/2002/hess-6-167-2002.pdf
167
184
0000-00-00
Heterogeneity in catchment properties: a case study of Grey and Buller catchments, New Zealand
U. Shankar
C. P. Pearson
V. I. Nikora
R. P. Ibbitt
National Institute of Water and Atmospheric Research, P.O. Box 8602, Christchurch, New Zealand
Email for corresponding author: u.shankar@niwa.cri.nz
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 ν<sub>l</sub> ≈0.6 and ν<sub>w</sub>≈ 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 (Holder exponent) values and
maximum dimension at α<sub>0</sub>,
(also known as the capacity dimension <i>D<sub>cap</sub></i>), are obtained.
Other fractal dimensions (information <i>D<sub>inf</sub></i> and
correlation <i>D<sub>cor</sub></i>) are also calculated and compared. The dimensions
are connected by the
inequality <i>D<sub>cap</sub></i>≥<i>D<sub>inf</sub></i>≥<i>D<sub>cor</sub></i>.
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.</p>
<p style="line-height: 20px;"><b>Keywords: </b>fractal, multifractal, scaling, landscape, patchiness