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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.

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

Title: Scaling of Peak Flows with Constant Flow Velocity in Random Self-similar Networks : Volume 18, Issue 4 (22/07/2011)  
Author: Mantilla, R.
Volume: Vol. 18, Issue 4
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Historic
Publication Date:
2011
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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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 pi and pe, 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
Furey, P. and Gupta, V. K.: Effects of excess rainfall on the temporal variability of observed peak discharge power laws, Adv. Water Resour., 28, 1240–1253, 2005.; Furey, P. R. and Gupta, V. K.: Diagnosing peak-discharge power laws observed in rainfall-runoff events in Goodwin Creek experimental watershed, Adv. Water Resour., 30, 2387–2399, 2007.; Furey, P. R. and Troutman, B. M.: A consistent framework for Horton regression statistics that leads to a modified Hack's law, Geomorphology, 102, 603–614, 2008.; Gupta, V. K. and Waymire, E. C.: Spatial variability and scale invariance in hydrologic regionalization, in: Scale dependence and scale invariance in hydrology, edited by: Sposito, G., Cambridge University Press, Cambridge, UK, 88–135, 1998.; Gupta, V. K., Castro, S. L., and Over, T. M.: On scaling exponents of spatial peak flows from rainfall and river network geometry, J. Hydrol., 187, 81–104, 1996.; Gupta, V. K., Troutman, B. M., and Dawdy, D. R.: Towards a Nonlinear Geophysical Theory of Floods in River Networks: An overview of 20 years of progress, in: Nonlinear Dynamics in Geosciences, edited by: Tsonis, A. A. and Elsner, J. B., Springer, New York, NY, 121–151, 2007.; Gupta, V. K., Mantilla, R., Troutman, B. M., Dawdy, D., and Krajewski, W. F.: Generalizing a nonlinear geophysical flood theory to medium-sized river networks, Geophys. Res. Lett., 37, L11402, doi:10.1029/2009GL041540, 2010.; Liu, Y. B., Gebremeskel, S., Smedt, F. D., Hoffmann, L., and Pfister, L.: A diffusive transport approach for flow routing in GIS-based flood modeling, J. Hydrol., 283, 91–106, doi:10.1016/S0022-1694(03)00242-7, 2003.; Lovejoy, S., Agterberg, F., Carsteanu, A., Cheng, Q., Davidsen, J., Gaonac'h, H., Gupta, V., L'Heureux, I., Liu, W., Morris, S. W., Sharma, S., Shcherbakov, R., Tarquis, A., Turcotte, D., and Uritsky, V.: Nonlinear Geophysics: Why We Need It, Eos Trans. AGU, 90, doi:10.1029/2009EO480003, 2009.; Mandapaka, P. V., Krajewski, W. F., Mantilla, R., and Gupta, V. K.: Dissecting the effect of rainfall variability on the statistical structure of peak flows, Adv. Water Resour., 32(10), 1508–1525, doi:10.1016/j.advwatres.2009.07.005, 2009.; Marani, A., Rigon, R., and Rinaldo, A.: A note on fractal channel networks, Water Resour. Res., 27, 3041–3049, 1991.; Mantilla, R.: Physical Basis of Statistical Scaling in Peak Flows and Stream Flow Hydrographs for Topologic and Spatially Embedded Random Self-similar Channel Networks, Ph.D. thesis, University of Colorado, Boulder, CO, 2007.; Mantilla, R., Gupta, V. K., and Mesa, O.: Role of coupled flow dynamics and real network structures on Hortonian scaling of peak flows, J. Hydrol., 322, 155–167, 2006.; Mantilla, R., Troutman, B. M., and Gupta, V. K.: Testing statistical self-similarity in the topology of river networks, J. Geophys. Res., 115, F03038, doi:10.1029/2009JF001609, 2010.; Mc{C}onnell, M. and Gupta, V. K.: A proof of the Horton law of stream numbers for the Tokunaga model of river networks, Fractals, 16, 227–233, 2008.; Menabde, M. and Sivapalan, M.: Linking space-time variability of rainfall and runoff fields on a river network: A dynamic approach, Adv. Water Resour., 24, 1001–1014, 2001.; Menabde, M., Veitzer, S., Gupta, V. K., and Sivapalan, M.: Tests of peak flow scaling in simulated self-similar river networks, Adv. Water Resour., 24, 991–999, 2001.; Mesa, O. and Mifflin, E.: Scale Problems in Hy

 

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