Multi-objective fitting of concentration-discharge relationships

Concentration–discharge ($C–Q$) relationships are widely used to assess the link between hydrological and biogeochemical processes at the catchment scale. $C–Q$ relationships are mainly calibrated using mono-objective methods to represent, either concentrations or discharge-weighted concentrations (i.e., load). Based on its wide use in hydrological modelling, we test a multi-objective calibration for the $C–Q$ relationship parameters, using both concentration and load, and compare it to a mono-objective calibration applied on either concentrations or load. This work is carried out on a high-frequency dataset (ORACLE-Orgeval Observatory, France). Our findings show that the multi-objective calibration yield a better representation of $C–Q$ relationships parameters during the high and low-flow events. The multi-objective calibration can be used for all forms of $C–Q$ relationships and avoids issues of under-representation of dilution processes characterized by high-discharge, low-concentration periods.