A New Analytical Model for the Prediction of Stream Temperature in Ungauged Basins

Stream temperature is a hydrological factor which affects the habitat suitability of many aquatic species, and is therefore of great concern in the actual context of climate change. Its prediction in ungauged basins is usually based on statistical approaches, such as multi-linear regression models or machine learning techniques. These models typically predict temperature metrics corresponding to yearly aggregates, such as the popular annual maximum weekly mean temperature (MWMT). As a consequence, they 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 model to estimate the monthly mean stream temperature of ungauged rivers over multiple years in an Alpine country (Switzerland). Contrary to the current statistical approaches, this model rests upon the analytical solution of a simplified version of the energy-balance equation over an entire stream network. This physically-based approach presents some advantages, among which the possibility to interpret the model coefficients from a physical point of view, hereby enabling the restriction of their calibration range. The evaluation of the model over a new 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 standard multi-linear regression models. 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.

Stream temperature prediction in ungauged basins: review of recent approaches and description of a new physics-derived statistical model

Aurélien Gallice, Michael Lehning, Marc Parlange, Bettina Schaefli

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.

European Geosciences Union2015

Comparison of stream temperature modeling approaches: the case of a high Alpine watershed

Francesco Comola, Aurélien Gallice, Wolf Hendrik Huwald, Michael Lehning

Stream temperature controls important aspects of the riverine habitat, such as the rate of spawning or death of many fish species, or the concentration of numerous dissolved substances. In the current context of accelerating climate change, the future evolution of stream temperature is regarded as uncertain, particularly in the Alps. This uncertainty fostered the development of many prediction models, which are usually classified in two categories: mechanistic models and statistical models. Based on the numerical resolution of physical conservation laws, mechanistic models are generally considered to provide more reliable long-term estimates than regression models. However, despite their physical basis, these models are observed to differ quite significantly in some aspects of their implementation, notably (1) the routing of water in the river channel and (2) the estimation of the temperature of groundwater discharging into the stream. For each one of these two aspects, we considered several of the standard modeling approaches reported in the literature and implemented them in a new modular framework. The latter is based on the spatially-distributed snow model Alpine3D, which is essentially used in the framework to compute the amount of water infiltrating in the upper soil layer. Starting from there, different methods can be selected for the computation of the water and energy fluxes in the hillslopes and in the river network. We relied on this framework to compare the various methodologies for river channel routing and groundwater temperature modeling. We notably assessed the impact of each these approaches on the long-term stream temperature predictions of the model under a typical climate change scenario. The case study was conducted over a high Alpine catchment in Switzerland, whose hydrological and thermal regimes are expected to be markedly affected by climate change. The results show that the various modeling approaches lead to significant differences in the model predictions. It is also shown that the temperature of groundwater discharging into the stream has a marked impact on the modeled stream temperature at the catchment outlet. This supports the development of more accurate methodologies to estimate groundwater temperature in current hydrological models.

2015

Modeling the monthly mean stream temperature dynamics

Aurélien Gallice, Wolf Hendrik Huwald, Michael Lehning, Bettina Schaefli

Water temperature is a hydrological factor which affects the habitat suitability of many aquatic (fish) species, and is therefore of great concern in the actual context of climate change. Two types of models are currently used to simulate stream temperature: physically-based models, which are typically applied only over limited areas, and regression models, which usually lack the ability to make predictions in ungauged areas. As an attempt to bridge the gap between these two types, we propose a hybrid model based on the energy-balance equation, in which the terms are related to catchment physiographic variables via empirical relationships. The physiographic variables are chosen so as to be available over the entire country (Switzerland), enabling the model to be used in ungauged catchments. This approach is on the one hand more physically-based than the usual regression models – hereby limiting the degree of empiricism associated with its derivation – but on the other hand seeks simplicity and applicability over large areas – making it more practical than the usual physically-based models. In order to test this model, we use it to predict the monthly mean stream temperature over 23 selected medium-sized catchments (3–300 km2) in Switzerland. While selecting the catchments, particular attention is given to cover a large range of different geomorphological conditions, especially regarding altitude, slope and aspect. It is shown that the model compares favorably with standard empirical models such as multi-linear regression.