Mixing and uptake of solutes in catchments: model development

Abstract

Simple mixing models are widely used to explain temporal variations in streamwater chemistry and to infer the relative contributions of old and new water during runoff events. These models assume conservative mixing of fixed end members and ignore solute uptake while new water is resident in the ground. A simple modelling approach is proposed which combines two-component mixing with solute uptake using a first-order kinetic rate equation. In this approach new and old water have the same origin in precipitation but old water, by virtue of its longer residence time, is more enriched. Equations are presented and illustrated for predicting the chemical evolution of old, new and mixed water and for inferring new water contributions. One consequence of the model is that solute rating plots do not exhibit a unique and reversible concentration-discharge relationship but a set of shifted counter-clockwise loops. Methods of parameter estimation are discussed. If intensive time-series data are not available, estimation of the chemical uptake parameter is not possible for a single solute but is possible for two solutes given information on several runoff events.