Stream temperature prediction in ungauged basins: review of recent approaches and description of a new physically-based analytical model

Abstract

Abstract. The development of stream temperature regression models at regional scales has regained some popularity over the past years. These models are used to predict stream temperature in ungauged catchments to assess the impact of human activities or climate change on riverine fauna over large spatial areas. A comprehensive literature review presented in this study shows that the temperature metrics predicted by the majority of models correspond to yearly aggregates, such as the popular annual maximum weekly mean temperature (MWMT). As a consequence, current models are often unable to predict the annual cycle of stream temperature, nor can the majority of them forecast the interannual variation of stream temperature. This study presents a new model to estimate the monthly mean stream temperature of ungauged rivers over multiple years in an Alpine country (Switzerland). Contrary to the models developed to date, which mostly rely upon statistical regression to express stream temperature as a function of physiographic and climatic variables, this one rests upon the analytical solution to a simplified version of the energy-balance equation over an entire stream network. This physically-based approach presents some advantages: (1) the functional form linking stream temperature to the predictor variables is directly obtained from first principles, (2) the spatial extent over which the predictor variables are averaged naturally arises during model development, and (3) the regression coefficients can be interpreted from a physical point of view – their values can therefore be constrained to remain within plausible bounds. The evaluation of the model over a new freely available data set shows that the monthly mean stream temperature curve can be reproduced with a root mean square error of ±1.3 °C, which is similar in precision to the predictions obtained with a multi-linear regression model. We illustrate through a simple example how the physical basis of the model can be used to gain more insight into the stream temperature dynamics at regional scales.

Development of spatial regression models for predicting summer river temperatures from landscape characteristics: Implications for land and fisheries management

“…For example, differences in the scale of characterisation between river lines and land use maps or imprecise DTMs directly influence the covariate values (Gallice et al . , ). Detailed discussion of these potential errors and methods to correct them can be found in Millar et al .…”

“…All possible model combinations were explored, giving 126 possible models. Due to the small sample size, corrected Akaike information criterion (AICc) was used for model selection (Gallice, Schaefli, Lehning, Parlange, & Huwald, ; Hurvich & Tsai, ) with the “best” model having the lowest AICc value. AICc values were tabulated for the top 10 models for each metric to identify other candidate models (models with similarly low AICc values).Where smoothed terms in the selected models had an effective degrees of freedom of 1, they were replaced with linear terms.…”

“…Covariate characterisation was another potential source of uncertainty in the Tw models (Gallice et al, 2015;Millar, Millidine, Middlemass, & Malcolm, 2015). For example, differences in the scale of characterisation between river lines and land use maps or imprecise DTMs directly influence the covariate values (Gallice et al, 2015).…”

A hybrid model for river water temperature as a function of air temperature and discharge

“…The three cases are briefly described below and in table 1 (for further details please refer to the supplementary material). For a more extensive description of the Swiss database see, e.g., Schaefli et al (2015).…”

A multifaceted analysis of the relationship between daily temperature of river water and air

“…the inflow of wastewater, thermal pollutants, and hydromorphological changes occurring within the channel of the water course (Sinokrot et al 1995;Caissie 2006;Webb and Nobilis 2007;Graf 2018). The specific utilisation of the catchment area and the selected method of development of the river valley may also modify the thermal characteristics of river waters (Younus et al 2000;Wiejaczka 2007; Gallice et al 2015;Lisi et al 2015).…”