SESSION:        River Networks and Flows
ORGANIZERS:   Harry Pavlopoulos (Greece) and Vijay K. Gupta (Colorado, USA)
 
 

The search for connections between river flow and the geometric properties of the channel network  transporting the flow has long been a major theme of surface-water hydrologic research. We consider different approaches to stochastic modeling of channel networks and how these approaches may yield insights into geometric scaling and hydrologic flow properties. Among the models reviewed are the "random model" in geomorphology, recursive replacement trees, and lattice trees. In the context of these models we discuss scaling properties of two random variables associated with uniformly sampling points in a drainage network, namely distance to the outlet and upstream area.
Geometric mass exponents are defined which characterize how the distribution of these random variables changes as a function of scale, and interpretations of these exponents in terms of flow are given. The distribution of distance to the outlet is proportional to the so-called "width function" of  the network, which is hydrologically important because, under certain assumptions, it gives information about the time distribution of storm flow at the network outlet. Behavior of the two mass exponents for different network models is discussed, and some results on the effect of spatially varying rainfall patterns are presented.

BRENT M. TROUTMAN
Denver Federal Center
U.S. Geological Survey
Box 25046, Mail Stop 413
Lakewood, CO 80225, USA
troutman@usgs.gov
 
 

Much of river basin hydrology is focussed on connections between rainfall/landforms/flows in terms of scaling exponents and
self-similarities. We present two recent results within this framework which illustrate some of the mathematical/statistical theory. The first result concerns the statistical estimation of scaling exponents associated with rainfall and the second concerns a stochastic self-similarity observed in river networks. This talk is based on recent work with Mina Ossiander, Greg Burd, and Ronald Winn.

EDWARD C. WAYMIRE
Department of Mathematics
Oregon State University
Kidder Hall
Corvallis, OR 97331, USA
waymire@math.orst.edu
 

A general approach to the evaluation of the sampling variance of flood quantile estimates by the index-flood method is presented. An approximate formulation for the variance of the estimated quantiles at the regional scale is combined with an uncertainty model accounting for the variance of estimation of the index-flood in a given river site. This approach also provides a method for discriminating between the at-site analysis and the index-flood method based on relative estimation efficiency. The appropriate selection is shown to depend on the return period required for risk assessment, and it is also dictated by the flood frequency regime at the regional scale. A preliminary application of the approach to the assessment of flood frequency regime in North Western Italy is given.

CARLO DE MICHELE
D.I.I.A.R.
Politecnico di Milano
Piazza L. da Vinci, 32
Milano, I-20122, Italy
carlo.demichele@polimi.it
 

The present paper provides some physically-based arguments to support the application of the Generalized Extreme Value (GEV) distribution for representing extreme flood flows in flashy streams. The approach moves from a simplified but physically-based description of precipitation and surface runoff dynamics. The assumptions on precipitation dynamics include the hypotheses that the storm depth has a Generalized Pareto distribution and a Poisson chronology. As a first result we show that, considering different temporal durations and proper power-law relations between the position and scale parameters of the corresponding random variables involved, yields a scaling law for the storm depth. Then we show that the maximum annual storm depth has a GEV distribution and how the scaling of the storm depth induces that of its maximum. Finally, we study two possible stream-flow models using two different transfer functions, which provide a synthesis of the rainfall-runoff transformation for impervious and pervious catchments respectively. In both cases we show that the peak discharge takes on an asymptotic GEV law, and we also illustrate how its scaling properties are affected and tuned by the transfer dynamics.

CARLO DE MICHELE
D.I.I.A.R.
Politecnico di Milano
Piazza L. da Vinci, 32
Milano, I-20122, Italy
carlo.demichele@polimi.it