
^{1}IIHRHydroscience & Engineering, The University of Iowa, Iowa City, IA, 52242, USA ^{2}Department of Civil, Environmental and Architectural Engineering, Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, CO,~80309, USA ^{3}US Geological Survey, Denver Federal Center, Lakewood, CO, 80225, USA Abstract. A methodology is presented to understand the role of the statistical selfsimilar topology of real river networks on scaling, or power law, in peak flows for rainfallrunoff events. We created Monte Carlo generated sets of ensembles of 1000 random selfsimilar 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 linkbased 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. Citation: Mantilla, R., Gupta, V. K., and Troutman, B. M.: Scaling of peak flows with constant flow velocity in random selfsimilar networks, Nonlin. Processes Geophys., 18, 489502, doi:10.5194/npg184892011, 2011. 
