Articles | Volume 20, issue 12
Research article
15 Dec 2016
Research article |  | 15 Dec 2016

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

Riccardo Rigon, Marialaura Bancheri, and Timothy R. Green

Abstract. The theory of travel time and residence time distributions is reworked from the point of view of the hydrological storages and fluxes involved. The forward and backward travel time distribution functions are defined in terms of conditional probabilities. Previous approaches that used fixed travel time distributions are not consistent with our new derivation. We explain Niemi's formula and show how it can be interpreted as an expression of the Bayes theorem. Some connections between this theory and population theory are identified by introducing an expression which connects life expectancy with travel times. The theory can be applied to conservative solutes, including a method of estimating the storage selection functions. An example, based on the Nash hydrograph, illustrates some key aspects of the theory. Generalization to an arbitrary number of reservoirs is presented.

Short summary
The goal of the paper is to analyze the theory of water age inside a catchment while accounting for multiple outflows. It tries to propose the material under a new perspective where it lines up concepts, cleans the notation, discusses some classical results, and offers some examples that help to relate the modern achievements to the theory of the IUH, clarifying assets of both of them. In doing all of this, it also produces various new results, and some regarding solute transport.