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Scaling of Peak Flows with Constant Flow Velocity in Random Self-similar Networks : Volume 18, Issue 4 (22/07/2011)

By Mantilla, R.

Book Id:WPLBN0003974686 Format Type:PDF Article : File Size:Pages 14 Reproduction Date:2015

Troutman, B. M., Gupta, V. K., & Mantilla, R. (2011). Scaling of Peak Flows with Constant Flow Velocity in Random Self-similar Networks : Volume 18, Issue 4 (22/07/2011). Retrieved from http://www.ebooklibrary.org/

Description
Description: IIHR-Hydroscience & Engineering, The University of Iowa, Iowa City, IA, 52242, USA. 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 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.

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

Excerpt
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