Slow and Quick Flow Models Explain the Temporal Dynamics of Daily Salinity in Streams

The availability of long-term high-frequency water quality data sets provides an opportunity to investigate transport pathways within catchments. The simple “C-Q” log-regression equation is commonly used to investigate the relationship between water quality concentrations and streamflow. However, significant variability within high-frequency data sets can result in poor explanation of temporal dynamics using the simple C-Q equation. C-Q equations with multiple flow components may better capture these dynamics, but they often only provide empirical interpretations and require subjective procedures to partition streamflow. Here, we aim to improve the simulation of water quality data over time by evaluating existing and newly derived quick-slow C-Q equations. We derive eight quick-slow C-Q equations and evaluate their performance along with seven existing equations. The equations are applied to over 20 years of daily salinity records in 23 catchments in Victoria, Australia. The evidence ratio between equations identifies our quick-slow version of the Hubbard Brook equation as the most acceptable equation at 14 of the 23 catchments. The Hubbard Brook equation is a mixing model that explains in-stream concentrations as a function of volumes mixing in the subsurface, and our quick-slow version differs with an additional slower mixing volume. Compared to the simple C-Q equation, this equation explained the temporal dynamics with an average increase of 0.17 in the Nash-Sutcliffe efficiency coefficient. Global parameter estimation gave an objective estimate of baseflow with a plausible baseflow index ranging between 0.05 and 0.40 across catchments. The modified Hubbard Brook equation provides a basis for further examining transport pathways in catchments.