Stream temperature prediction in ungauged basins: review of recent approaches and description of a new physics-derived statistical 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 inter-annual variation of stream temperature. This study presents a new statistical model to estimate the monthly mean stream temperature of ungauged rivers over multiple years in an Alpine country (Switzerland). Contrary to similar models developed to date, which are mostly based on standard regression approaches, this one attempts to incorporate physical aspects into its structure. It is based on the analytical solution to a simplified version of the energy-balance equation over an entire stream network. Some terms of this solution cannot be readily evaluated at the regional scale due to the lack of appropriate data, and are therefore approximated using classical statistical techniques. This physics-inspired approach presents some advantages: (1) the main model structure is directly obtained from first principles, (2) the spatial extent over which the predictor variables are averaged naturally arises during model development, and (3) most of 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 rootmean-square error (RMSE) 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 aspects contained in the model structure can be used to gain more insight into the stream temperature dynamics at regional scales.

StreamFlow 1.0: an extension to the spatially distributed snow model Alpine3D for hydrological modelling and deterministic stream temperature prediction

“…This standard design pattern, illustrated in Fig. 3b, enables the dynamic extension of the functionality of a class (Gamma et al, 1994). In the figure, the parent class "Interface" stands for any of the abstract classes (LumpedSubwatershedInterface, LumpedStreamReachInterface or DiscretizedStreamReachInterface) described above (see Fig.…”

“…Riparian forest shading is currently not represented in the model, hereby restricting the application of StreamFlow to high-altitude catchments. This limitation might be relaxed in the near future through the implementation of an appropriate shade model, taking, for instance, advantage of the improvements brought by Gouttevin et al (2015) to the canopy module of Snowpack.…”

“…The latter was developed to study multiple subjects such as the impact of climate change on snow cover (Bavay et al, 2009(Bavay et al, , 2013, the effect of wind and topography on snow deposition (Mott and Lehning, 2010;Mott et al, 2014) or the sublimation of drifting snow (Groot Zwaaftink et al, 2013 evolution of the vertical snow profile, as well as the vertical profiles of soil moisture and soil temperature (Bartelt and Lehning, 2002;Lehning et al, 2002b, a). It accounts for the canopy layer (Gouttevin et al, 2015) and can simulate the vertical water transport using either the Richards equation or a simple bucket scheme (Wever et al, 2014(Wever et al, , 2015. StreamFlow is implemented as a semi-distributed model, i.e.…”

“…The computation of in-stream temperature assumes a constant cross-sectional profile in each stream reach separately; it is based on the one-dimensional mass and energy-balance equations solved over each stream reach (adapted from Gallice et al, 2015):…”

“…On the contrary, more credit is generally given to the long-term forecasts of the deterministic (2000) hourly, daily forested catchments in Canada UBC Morrison et al (2002) hourly large river basins GISS GCM Ferrari et al (2007) monthly large river basins SWAT Ficklin et al (2012) daily, monthly medium-to large-scale catchments MIKE-SHE MIKE11 Loinaz et al (2013) hourly (Ficklin et al, 2014) -than that of the statistical models. It should be mentioned that an intermediate sort of model, referred to as hybrid, has recently been developed (Gallice et al, 2015;Toffolon and Piccolroaz, 2015) and shown by Piccolroaz et al (2016) to be suitable for climate change studies. As opposed to the separate simulation of discharge and stream temperature, the coupled modelling of the two offers new perspectives to investigate the effects of climate change on mountain hydrology (e.g.…”