Characterization of export regimes in concentration-discharge plots via an advanced time-series model and event-based sampling strategies

Abstract

Currently, the export regime of a catchment is often characterized by the relationship between compound concentration and discharge in the catchment outlet or, more specifically, by the re-gression slope in log-concentrations versus log-discharge plots. However, the scattered points in these plots usually do not follow a plain linear regression representation because of different processes (e.g., hysteresis effects). This work proposes a simple stochastic time-series model for simulating compound concentrations in a river based on river discharge. Our model has an ex-plicit transition parameter that can morph the model between chemostatic behavior and che-modynamic behavior. As opposed to the typically used linear regression approach, our model has an additional parameter to account for hysteresis by including correlation over time. We demonstrate the advantages of our model using a high-frequency data series of nitrate concen-trations collected with in situ analyzers in a catchment in Germany. Furthermore, we identify event-based optimal scheduling rules for sampling strategies. Overall, our results show that (i) our model is much more robust for estimating the export regime than the usually used regres-sion approach, and (ii) sampling strategies based on extreme events (including both high and low discharge rates) are key to reducing the prediction uncertainty of the catchment behavior. Thus, the results of this study can help characterize the export regime of a catchment and manage water pollution in rivers at lower monitoring costs.