Basin scale model of solute transport

Abstract

A mathematical model based on conditional probability distributions is proposed for solute yield response to rainfall impulses at the basin scale. Solutes enter the mass balance because of sorption processes between fixed phases and the carrier flow. The present approach allows to be addressed the individual role and the mutual connection of the hydrologic response and of macroscopic sorption kinetics controlling basin scale release processes. Mass response functions (MRFs) from geomorphology and statistical mechanics are derived and used to analyze experimental records. A synthesis of nonlinear effects in the mechanism of chemical supply to the carrier and the derivation of concentration distributions are also attempted in the paper. It is shown that three‐parameter generalized gamma distributions provide sound physical and statistical insight and are suited to the interpretation of field data. A dimensionless number is defined as the ratio of 2 times the characteristic of the sorption kinetics and of the residence in the basin. The number is shown to be related to total solute loads in the runoff. It is also shown that the mathematical construct leading to the MRF accounts for the observed variability of the instantaneous and time‐averaged concentration/discharge relations. As an example, discharge characteristics of NO 3 ‐N are analyzed via suitable MRFs. The results compare favorably with extensive evidence collected in a small Japanese catchment and capture the dominant modes of the process behavior.