A simple triangular approximation of the area function for the calculation of network hydrological response

The hydrological response of a catchment is the result of combined hillslope and channel network delays in the translation of rainfall to discharge at the catchment outlet. In this paper we examine three simple descriptions of the channel network response following an instantaneous hillslope runoff input within a general framework in which the role of network morphology is described using the probability density function (pdf) of network path lengths, and the role of hydrodynamic dispersion is described using a solution of the linear advection dispersion equation. We show that the pdf of path lengths, represented by the area function, can be adequately approximated by a triangular distribution with just two parameters (the mean and maximum network path lengths). The triangular pdf can be combined with a description of residence times in individual paths to derive an analytical expression for the hydrological response of the channel network. This expression provides a better approximation of the network response than both the original geomorphological instantaneous unit hydrograph (GIUH), based on Horton-Strahler ratios, and a single-channel representation, based on the concept of geomorphological dispersion. Using the same expression, we show that geomorphological factors generally prevail in controlling the mean and variance of network residence times. In contrast, hydrodynamic dispersion is shown to have a significant influence on the skewness of the network response over a wide range of catchment characteristics, strongly influencing the hydrograph peak and time to peak values in these cases.