Statistical self-similarity of width function maxima with implications to floods

Veitzer, Seth; Gupta, Vijay

doi:10.1016/s0309-1708(01)00030-6

Cited by 50 publications

(38 citation statements)

References 21 publications

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“…The parameter ω has been studied by Veitzer and Gupta (2000) for RSNs and by Mantilla et al (2006) for real networks as it has a direct bearing on the scaling relation for peak flows. The random variable ω is of particular interest because it has been shown by Veitzer and Gupta (2001) to exhibit statistical self similarity (SSS); …”

Section: The Scaling Exponent βmentioning

confidence: 99%

Scaling of peak flows with constant flow velocity in random self-similar networks

Mantilla

Gupta

Troutman

2011

Nonlin. Processes Geophys.

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Abstract.A methodology is presented to understand the role of the statistical self-similar topology of real river networks on scaling, or power law, in peak flows for rainfall-runoff events. We created Monte Carlo generated sets of ensembles of 1000 random self-similar networks (RSNs) with geometrically distributed interior and exterior generators having parameters p i and p e , respectively. The parameter values were chosen to replicate the observed topology of real river networks. We calculated flow hydrographs in each of these networks by numerically solving the link-based mass and momentum conservation equation under the assumption of constant flow velocity. From these simulated RSNs and hydrographs, the scaling exponents β and φ characterizing power laws with respect to drainage area, and corresponding to the width functions and flow hydrographs respectively, were estimated. We found that, in general, φ > β, which supports a similar finding first reported for simulations in the river network of the Walnut Gulch basin, Arizona. Theoretical estimation of β and φ in RSNs is a complex open problem. Therefore, using results for a simpler problem associated with the expected width function and expected hydrograph for an ensemble of RSNs, we give heuristic arguments for theoretical derivations of the scaling exponents β (E) and φ (E) that depend on the Horton ratios for stream lengths and areas. These ratios in turn have a known dependence on the parameters of the geometric distributions of RSN generators. Good agreement was found between the analytically conjectured values of β (E) and φ (E) and the values estimated by the simulated ensembles of RSNs and hydrographs. The independence of the scaling exponents φ (E) and φ with respect Correspondence to: R. Mantilla (ricardo-mantilla@uiowa.edu) to the value of flow velocity and runoff intensity implies an interesting connection between unit hydrograph theory and flow dynamics. Our results provide a reference framework to study scaling exponents under more complex scenarios of flow dynamics and runoff generation processes using ensembles of RSNs.

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Section: The Scaling Exponent βmentioning

confidence: 99%

Scaling of peak flows with constant flow velocity in random self-similar networks

Mantilla

Gupta

Troutman

2011

Nonlin. Processes Geophys.

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“…SSS is discussed in detail by Veitzer and Gupta (2000), and Veitzer et al (2003) both empirically and for RSNs. Veitzer and Gupta (2001) investigated SSS in the peaks of the width functions, Θ ω , ω = 1, 2, 3, . .…”

Section: Geomorphologic Analysismentioning

confidence: 99%

“…Gupta et al (1996) published the first paper on the statistical scaling theory of floods on a highly idealized channel network known as Peano basin. Results in Gupta et al (1996) have been generalized in many directions for idealized mean self-similar channel networks (Gupta and Waymire, 1998;Veitzer and Gupta, 2001;Troutman and Over, 2001;Morrison and Smith, 2001). However, there is a pressing need to further generalize and test the scaling theory of floods on real channel networks.…”

Section: Introductionmentioning

confidence: 99%

“…Section 3 analyses the channel network geomorphology of the Walnut Gulch basin. It introduces some terminology, and gives some background on estimation of scaling exponent of the peak of the width function following Veitzer and Gupta (2001). Section 4 describes HidroSig, our GIS numerical simulation environment, and its application to solving link-based mass and momentum balance equations on the Walnut Gulch.…”

Section: Introductionmentioning

confidence: 99%

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Role of coupled flow dynamics and real network structures on Hortonian scaling of peak flows

Mantilla

Gupta

Sánchez

2006

Journal of Hydrology

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We investigate how channel flow dynamics on real river networks produces scaling in peak flows. Scaling relations have been defined by log-log linearity between peak flow statistics and drainage areas for idealized mean self-similar networks like Peano and Mandelbrot Viscek. Unlike idealized basins, drainage areas and link lengths in real basins vary statistically. We use Horton-Strahler order as scale parameter instead of drainage area, and use the Hortonian framework to analyze these network structures. A river-network oriented GIS is used to extract the drainage network for the Walnut Gulch basin, Arizona in the United States. It provides the link connectivity structure and the geometric variables for numerically solving coupled link-based mass and momentum conservation equations. The equations are solved for spatially uniform and instantaneous injection of runoff under three different scenarios of flow in the channels: 1) Constant Velocity, 2) Constant Friction, and 3) Spatially Variable Friction. We find that Hortonian scaling in peak flows does not hold for the constant friction scenario. The scaling exponents of peak flows for the other two cases are larger than the scaling exponent of the peaks of the width functions. This property of scaling exponents for a real network is opposite to previous findings for idealized mean self-similar networks. An empirical scaling analysis of peak flows on the Walnut Gulch basin is briefly explained to provide preliminary empirical support to our theoretical findings.

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“…There are important works that explore a similar strategy in a variety of hydrologic processes and highlight the importance of its adaptation. Among those are the nature of the heterogeneity of the earth's surface that drives the run-off networks and rain fields, applying the heuristics of self-organization and self-similarity (Gorenburg et al, 2001;Veitzer & Gupta, 2001), the temporal spatial variability associated with the process of evapotranspiration, and identifying diverse control factors in relevant scales and patterns Katul et al, 2001;Mahrt et al, 2001;Coronel et al, 2008). Terrestrial memory processes that are fundamental to long-term water balance are identified, among them vegetation and soil adjustments that relate energy and water balances and nutrient cycling (Post & Jones, 2001;Mackay, 2001;Coronel & Mora, 2008a;Coronel & Mora, 2008b).…”

Section: Conceptual Elements and Heuristics From Complexity Paradigm mentioning

confidence: 99%

Conceptual Elements and Heuristics from Complexity Paradigm Suitable to the Study of Evapotranspiration at the Landscape Level

Coronel¹,

Silva²,

Hernández³

et al. 2011

Evapotranspiration

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Statistical self-similarity of width function maxima with implications to floods

Cited by 50 publications

References 21 publications

Scaling of peak flows with constant flow velocity in random self-similar networks

Scaling of peak flows with constant flow velocity in random self-similar networks

Role of coupled flow dynamics and real network structures on Hortonian scaling of peak flows

Conceptual Elements and Heuristics from Complexity Paradigm Suitable to the Study of Evapotranspiration at the Landscape Level

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