| This work focuses on the scaling, or power law, properties of hydrographs with respect to drainage area in Random Self-similar Networks (RSNs). We study hydrographs under two assumption of flow velocity in channels: (i) constant, and (ii) variable velocity in space and time. We begin by determining the family of RSNs that best represent topological features observed in real networks. The validity of RSN model assumptions are tested on 28 basins spread across the US. The scaling characteristics of four hydrograph properties with respect to drainage area A, namely E[maxt ho(t)], maxt E[ho(t)], E[ T(maxt ho( t))], and T(maxt E[ho(t)]) are investigated. T() means time-to, E[] denotates expectation, and ho(t) represents streamflow from an order o sub-basin at time t > 0. Results indicate that simulated hydrographs provide good estimates of scaling properties and their functional relationship with independent variables governing flood generation. This relationships collapse the macro features of a system with many degrees of freedom into very simple formulas. However, the RSN model is topological and it provides no information about the distribution of the river networks in space, which limits the ability of this framework to address questions regarding the spatial variability of runoff generation processes (e.g. rainfall, infiltration, interception). To address this problem and generalize the framework, the problem of embedding topologic binary rooted trees (BRTs) on the plane is addressed. Some examples of applying the embedding algorithm to Tokunaga trees and to RSNs are presented. Finally, a technique is presented that maps the resulting tiled region into a 3-dimensional surface that corresponds to a landscape drained by the chosen network. The combined results of this work represent new advances on spatially variable flood-governing processes and hydraulic geometric conditions that are required in the study of peak flows scaling. |
