Geomorphological Theory of the Hydrological Response

Abstract

The geomorphological theory of the hydrological response, originated by Rodriguez-Iturbe and Valdes, is reviewed with reference to the general framework of the formulation of transport processes by travel time distributions. This review, by no means exhaustive of the publications on this subject, collects in a reasonably organic manner some relevant theoretical developments and a few significant applications.

Scaling of peak flows with constant flow velocity in random self-similar networks

“…This method of expressing flow in terms of the width function is given in a number of publications in the context of GIUH (see for example Mesa and Mifflin, 1986;Marani et al, 1991;Rinaldo and Rodríguez-Iturbe, 1996 and Rodríguez-Iturbe and Rinaldo, 1997, Eq. 7.112).…”

“…Gupta et al (1996) first derived the scaling of peak flow versus drainage area in a self-similar Peano channel network. Their derivation was based on analysis of geometric properties of the network width function, which is defined to be the number of channel links as a function of distance from the outlet (Rodríguez-Iturbe and Rinaldo, 1997). Denoting W ω (x) as the width function for a stream of Strahler order ω, the scaling relationship with respect to the upstream contributing area A ω follows from the fractal structure of the maximum contributing set and is given by max x W ω (x) = c β A β ω .…”

Improving Flood Prediction Assimilating Uncertain Crowdsourced Data into Hydrological and Hydraulic Models

“…(2.7) in case of n=1, H=k and I t replaced by R sur . In particular, in case of Q sur the value of the parameter k, which is a function of the residence time in the catchment slopes, is estimated relating the slopes velocity of the surface runoff to the average slopes length L. However, one of difficulties involved is proper estimation of the surface velocity, which should be calculated for each flood event (Rinaldo and Rodriguez-Iturbe, 1996). According to Rodríguez-Iturbe et al (1982), such velocity is a function of the effective rainfall intensity and event duration.…”

“…The platform, already operating on the Bacchiglione catchment, processes the weather and climate data (with a forecast horizon of 3-days), determines the outflows through a geomorpho-climatic model (Rinaldo and Rodriguez-Iturbe, 1996) and estimates the flood wave propagation. The system contains also an automatic optimization module of hydrological model parameters that compares the measured and the simulated discharges at the available measuring points.…”

Age-ranked hydrological budgets and a travel time description of catchment hydrology

“…Some researchers (Rodriguez-Iturbe and Valdes, 1979;Rinaldo and Rodriguez-Iturbe, 1996), as reviewed by Rigon et al (2016), looked at the construction of the hydrologic response using geographical information. Others (e.g., Uhlenbrook and Leibundgut, 2002;Birkel et al, 2014) used travel times to understand catchment processes in relation to tracer experiments, while new experimental techniques were being developed (e.g., Berman et al, 2009;Birkel et al, 2011).…”