Water stream heating dynamics around extreme temperature events: An innovative method combining GAM and differential equations

Abstract : The highlighting and study of extreme water temperatures, which endanger numerous species, is of particular interest for river managers planning for future thermal conditions. Extreme water temperatures, defined as temperatures outside the normal range, are predicted to occur more frequently. This range includes seasonality and other trends in temperature time series.
First, extreme water temperatures were highlighted using generalized additive modeling (GAM) to extract within-year variations (seasonality) and long-term changes (trend). Second, the temporal dynamics of water temperature around extremes were modeled using specific differential equations. The period considered was 15 days, 7 days before and after each extreme considered day. The data were water temperatures measured every 10 min for 7 years (2012–2018) at 94 measurement sites. Sites were located evenly throughout the Walloon (southern Belgium) hydrological network.
Results showed that GAM was robust for capturing seasonality and trend, and highlighting extreme water temperatures. GAM had already been used in water temperature studies but not yet to detect extremes. The thermal dynamics of water temperature around extremes was successfully modeled using differential equations.
Several equations expressing heat flux processes between air and water interface were tested. Two correlations were analyzed: (i) between the model coefficients and the number of extreme days, and (ii) between the model coefficients and the number of days above a fixed thermal threshold. Significant positive correlations were found in both cases. Considering the value ranges of the model coefficients, it is thus possible to describe rivers’ thermal sensitivity. With our approach, river’s managers can now better address the important issue of extreme water temperature in the context of climate change.