River network fractal geometry and its computer simulation

Nikora, Vladimir; Sapozhnikov, Victor B.

doi:10.1029/93wr00966

Cited by 54 publications

(43 citation statements)

References 21 publications

(8 reference statements)

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“…The plot of total river length against catchment area also shows the expected value of near unity for ε (Nikora et al, 1996). reported elsewhere (Nikora et al, 1996, Nikora andSapozhnikov, 1993a). Combining these values and using…”

Section: Scaling Of Morphological Parametersmentioning

confidence: 99%

“…The scaling behaviour of channel networks is studied using previously established methods (Nikora and Sapozhnikov, 1993a;Nikora et al, 1996). The method uses relationships which connect longitudinal (l) and transverse (w) scales of a channel network with the total length (L) of the network through scaling exponents v l (longitudinal) and v wl (transverse).…”

Section: Scaling In Catchment Properties (A) Morphometric Parametersmentioning

confidence: 99%

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

Shankar

Pearson

Nikora

et al. 2002

Hydrol. Earth Syst. Sci.

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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.

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Section: Scaling Of Morphological Parametersmentioning

confidence: 99%

Section: Scaling In Catchment Properties (A) Morphometric Parametersmentioning

confidence: 99%

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

Shankar

Pearson

Nikora

et al. 2002

Hydrol. Earth Syst. Sci.

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“…In a subsequent paper [10] they demonstrated the manner in which these models also capture the effects of random influences in driving the processes of landscape evolution. In particular, their results provided a physical basis for explaining various fundamental scaling relationships [44,70,55,42,60,61,59,48,54,69,62,58,32,56,21,22] that characterize fluvial landscapes and supply a bridge between deterministic and stochastic theories of drainage basin evolution.…”

Section: Complexity In Geomorphologymentioning

confidence: 99%

The Stochastic Theory of Fluvial Landsurfaces

2006

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A stochastic theory of fluvial landsurfaces is developed for transport-limited erosion, using well-established models for the water and sediment fluxes. The mathematical models and analysis is developed showing that some aspects of landsurface evolution can be described by Markovian stochastic processes. The landsurfaces are described by nondeterministic stochastic processes, characterized by a statistical quantity the variogram, that exhibits characteristic scalings. Thus the landsurfaces are shown to be SOC (Selforganized-critical) systems, possessing both an initial transient state and a stationary state, characterized by respectively temporal and spatial scalings. The mathematical theory of SOC systems is developed and used to identify three stochastic processes that shape the * and the University of Iceland, 107 Reykjavík 1 surface. The SOC theory of landsurfaces reproduces established numerical results and measurements from DEMs (digital elevation models).

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“…Basically, the scaling laws state that the ratio of a morphologic parameter 213 (area or slope of the watershed, number or length of streams within the watershed) measured at 214 order i and order i+1 is constant. According to Rosso et al (1991), the Horton laws of network 215 composition are geometric-scaling relationships because they hold regardless of the order or 216 resolution at which the network is viewed and because they yield self-similarity of the catchment-217 stream system, or at least self-affinity in cases where the scaling factors in the longitudinal and 218 transverse directions are not equal (Nikora and Sapozhnikov, 1993) …”

Section: Spring Water Sampling and Analytical Techniques 163mentioning

confidence: 99%

Integrating topography, hydrology and rock structure in weathering rate models of spring watersheds

Pacheco

Weijden

2012

Journal of Hydrology

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We are very pleased with your decision regarding our manuscript. We addressed the very minor corrections pointed out by reviewer #2, as can be consulted in the DOC file Revision_Notes. The revised version of the manuscript is given in the DOC file Reviewer #1No corrections to be made. Reviewer #21)The abstract contains some formulas. I think it is better to delete them from the abstract.The formulas were deleted. 2)p.7, 155: Please check the calculation of percolation time of soil water to reach the bedrock. Based on the given K, it should be at least 3.75 days, i.e. >3.75 days.The sentence was corrected: where the text was "< 3,75 days" is now "at least 3,75 days". 3)p.8, 188-190: The sequence of sentences beginning with "Altogether." do not make sense. How does a model operating with a minimum amount of information affects the type of methods used in the model?The sentence was deleted (in fact, it was not an essential sentence). 4)Perhaps a better phrase can be used instead of the term "aquifer formation constant". It sounds like the hydraulic conductivity and porosity have something to do with the formation of the aquifer.Throughout the text (in 7 places), the term "formation constants", although used regularly in hydrologic texts to describe aquifer hydraulic parameters such as K and n e , was replaced by "hydraulic parameters". 5)p.19, 461-64: Here the authors mention that no spring flow discharge was information was available. However, it is not clear what was done to compensate for this. The authors should make it clear to the reader by rephrasing the sentence and using better wording, what was done exactly. Perhaps this issue can be clarified in the previous methods section of the manuscript.The way how we compensated for the lacking of spring flow discharges is explained in the section "Aquifer Formation Hydraulic Parameters and Travel Times of Spring Watersheds". However, in the section ("Aquifer Formation Hydraulic Parameters and Travel Times of Stream Watersheds") we now added the following sentence to make this more clear: "The hydraulic conductivities (K) and effective porosities (n e ) resulting from this characterization were then used as proxies of the K and n e values of the spring watersheds, as explained in the next section, which also describes how groundwater travel times were downscaled from the larger (stream) the smaller (spring) scales." The papers corresponding to the reference numbers are given in the legend of RESEARCH HIGHLIGHTS• develop a weathering model that incorporates rock structure in the rate equation• conceive a weathering model especially designed for fracture artesian springs•Create a model that integrates topography, hydrology, rock structure and weathering evaluation of morphologic parameters is subjective due to difficulties in conceiving the catchment 21 geometry. Besides, when springs emerge from crystalline massifs, rock structure must be accounted 22 in formulas describing the area of minerals exposed to the percolating fluids, for a realistic 23 evaluation of th...

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River network fractal geometry and its computer simulation

Cited by 54 publications

References 21 publications

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

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

The Stochastic Theory of Fluvial Landsurfaces

Integrating topography, hydrology and rock structure in weathering rate models of spring watersheds

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