Geomorphological dispersion

Abstract

The hydrologic response of a channel network is defined by decomposing the process of runoff formation into two distinct contributions, one accounting for the mechanisms of travel time within individual reaches (hydrodynamic dispersion), and the other accounting for the morphology of the network structure (geomorphological dispersion). Exact Laplace transforms of first passage time distributions at the outlet of a network are obtained by a consistent approximation of travel time distributions through individual reaches. The moments of such distributions are obtained analytically in the general case. Closed-form first-passage distributions are obtained in the particular case of basin-constant hydrodynamic dispersion. The variance of the resulting travel time distributions is shown in this paper to be made up of two additive contributions corresponding to the two dispersion mechanisms considered. The geomorpho}ogic dispersion coefficient is shown to depend on the ratios of bifurcation, length and area of the network suggesting that, at the scale of an organized network, heterogeneities other than those related to the convection field shape the dispersive character of transport. In particular, a significant application of the general solution to Hortonian channel networks suggests that models based on accurate specification of the geometry and the topology of the network and a simplified dynamics capture the foremost features of the travel time distributions in a broad range of dispersivities within individual reaches. channel networks [e.g., Shreve, 1966; Smart, !972; Mandelbrot, 1983; Abrahams, 1984; Tarboton et al., 1988; La Barbera and Rosso, 1989; A. Marani et al., A note on fractal channel networks, Paper number 90WR02501, •3-t 397/91/90WR-0250 ! $05.00 1990 (hereinafter Marani et al. (submitted manuscript, 1990))]. Similar ideas have been explored with reference to random networks (modeling, somewhat arbitrarily, porous media as a random resistor network [De Arcangelis et al., 1986]), whereas we propose, in the framework of studies on transport by travel time distributions, the geomorpho!ogic analysis of channel networks. Recent contributions have provided new significant inroads toward a unifying approach for transport processes based on travel (first-passage, arrival or residence) time distributions. It is granted in this study that (1) the arrival time distribution at the outlet of a channel network after an instantaneous pulse is the geomorphologic unit hydrograph (GUH) which is the core of the hydrologic response [Rodriguez-!turbe and Valdes, 1979; Gupta et al., 1980; Gupta and Waymire, 1983]; and (2) travel time distributions may be related in a rational manner to approaches based on the solution of the mass and momentum balance equations in an Eulerian framework, are of general nature and robust in characterizing the transport process, and blend all sources of uncertainty into a unique curve [Rinaldo and Marani, 1987; Shapiro and Cvetkovic, 1988; Dagan and Nguyen, 1989; Rinaldo et al., 1989; Dagan, 198...

Best linear unbiased design hyetograph

“…In particular, (16), which applies to the case of slow decay of the unit hydrographs u i(r) relative to the correlation function of rainfall intensity, remains very simple. Notice, however, that n large implies a fine spatial discretization and hence more peaked IUHs; in the limit as n --• o•, the functions u i(r) have only hydrodynamic dispersion, as the geomorphological component of dispersion vanishes [Rinaldo et al, 1991]. Therefore, for distributed basins the limiting assumption of wide IUH is not expected to apply as accurately as in the lumped case.…”

Chloride circulation in a lowland catchment and the formulation of transport by travel time distributions

“…The assumption of random sampling was proved to be quite robust in single hillslopes characterized by heterogeneous soils . Moreover, the nonpoint source nature of the inputs and the integrative nature of the network geometry [Rinaldo et al, 1991] seem to favor the robustness of this assumption also in larger catchments with complex network structures.…”

Constraining frequency–magnitude–area relationships for rainfall and flood discharges using radar-derived precipitation estimates: example applications in the Upper and Lower Colorado River basins, USA

“…This diversion creates a "gap" between the two curves and indicates that flood discharge is not a simple power-law function of contributing area. Three mechanisms have been proposed to explain the "gap" and characteristic concave-down shape of FECs: (1) integrated precipitation (i.e., total precipitation over an area) is more limited over larger contributing areas compared to smaller contributing areas (Costa, 1987), (2) a relative decrease in maximum flood discharges in larger contributing areas due to geomorphic dispersion (RodriguezIturbe and Valdes, 1979;Rinaldo et al, 1991;Saco and Kumar, 2004), and (3) a relative decrease in maximum flood discharges in larger basins due to hydrodynamic dispersion (Rinaldo et al, 1991). The first explanation, proposed by Costa (1987), suggests that there is a limitation to the size of a storm and the amount of water that a storm can precipitate.…”