Kuai Fang ^1* Jef Caers ² Kate Maher ¹

• ¹ Department of Earth System Science, School of Earth, Energy & Environmental Sciences, Stanford University, Stanford, California, United States
• ² Department of Geological Sciences, School of Earth, Energy & Environmental Sciences, Stanford University, Stanford, California, United States

The temporal dynamics of solute export from catchments are challenging to quantify and model due to confounding hydrological and biogeochemical processes, as well as the inadequate measurements. Conventionally, the concentration-discharge relationship (C-Q) and statistical approaches to describe it, such as the Weighted Regressions on Time, Discharge and Seasons (WRTDS), have been widely used. Recently, deep learning (DL) approaches, especially Long-Short-Term-Memory (LSTM) models, have shown predictive capability for discharge and stream-dominated variables. However, it is not clear if such advances can be expanded to water quality variables driven by complex subsurface biogeochemical processes. This work evaluates the performance of LSTM and WRTDS for 20 water quality variables across ~500 catchments in the continental US. We find that LSTM does not markedly outperform WRTDS in our dataset, potentially limited by the current measurement capabilities of water quality across CONUS. Both models present similar performance patterns across water quality variables, with the LSTM displaying better performance for nutrients and worse on weathering-derived solutes. Additionally, the LSTM does not benefit from additional flexibility in the inputs. For example, incorporation of climate data that constrains streamflow generation, does not significantly improve the LSTM performance. We also find that data availability is not a straightforward predictor of LSTM model performance, although higher availability tends to stabilize its performance. To fully assess the potential of the LSTM model, it may be necessary to use a higher frequency dataset across the CONUS, which does not exist now. To evaluate the dynamics of C-Q patterns relative to model performance, we introduce a "simplicity index" considering both the seasonality in the concentration pattern and the linearity in the C-Q relationship, or the C-Q-t pattern. The simplicity index is strongly correlated with model performance and differentiates the underlying controls on water quality dynamics. Further DL experiments and model-intercomparison highlight the strengths and deficiencies of existing frameworks, pointing to the need for further hydrogeochemical theories that are amenable to complex basins and solutes.