Brief introduction of storm hysteresis effects in solute concentration-stream discharge (C-Q) relationship

What are storm hysteresis effects?

Generally, in order to investigate the dynamics of stream discharge and solute concentrations (C-Q relationship) in a watershed, researchers and environmental engineers usually set up monitoring stations in the watershed outlet. As the temporal dynamics of discharge and solute concentration is an integration of complex hydrological and biochemical processes, the relationship between solute concentration and discharge, hereafter called C-Q relationship, is mostly non-linear. If we plot the concentration against discharge within one storm event in a plot, we are supposed to see a non-linear loop, instead of a linear regression curve. The tweet below demonstrated the hysteresis effects in one event happened in 1991.

Bored of seeing time-series data? Maybe there is another way of visualizing your discharge and nutrient concentration measurements in streams. pic.twitter.com/PSIEWpJp8E

— Wenlong Liu (@tianya0423) November 13, 2017

How to describe a hysteresis loop?

As the shapes of hysteresis loops vary because of the different hydrogeochemical processes, it is important to describe a hysteresis loop to compare across spatial and temporal scales. For a fictitious hysteresis loop in Fig. 1a，adapted from Long et al. (2017), there are three variables to characterize a loop:

• Direction: the direction of loops based on time or any x-axis variable, e.g. clockwise and anti-clockwise;

• Amplitude: the strength of hysteresis effects;

• Slope: to indicate the dilution/leaching of solute during an event compared with the base flow.

Fig. 1 Depiction of hysteresis loops

Why are we interested in hysteresis effects?

Due to the complexity of hydrogeochemical processes in the watershed, the watershed is mostly a black box for us. It is impossible to identify the exact sources and reactions contributing to the nutrient export. Luckily, we can employ hysteresis effects as a proxy to internal reactions in watersheds.

For example, Blaen et al. (2017) monitored high-frequency stream discharge and nutrients data in a headwater catchment for 8 months and delineated 29 storm events representing 31% of observation period. Based on the analysis of storm hysteresis patterns, Blaen et al. (2017) identified the key drivers and processes of nutrient export, showing in Fig. 2. Further details are available from an open-source publication here.

Fig. 2 Conceptual model highlighting the spatial distribution of NO3-N and DOC across the catchment and key processes that control stream nutrient export under different hydroclimatological conditions.

With the help of rapidly developing in-situ measuring techniques, we are going to gain more access to intensive measurements from different research interests. Therefore, the analysis of C-Q relationship with high-frequency dataset becomes more popular. The author, Wenlong Liu, is working on this topic right now, and going to update his latest research in this blog. Further Content will include the methods to quantify the hysteresis patterns and to identify the drivers based on various approaches.

Hope this blog helps. Cheers!