Water temperature controls many biochemical and ecological processes in rivers, and theoretically depends on multiple factors. Here we formulate a model to predict daily averaged river water temperature as a function of air temperature and discharge, with the latter variable being more relevant in some specific cases (e.g., snowmelt-fed rivers, rivers impacted by hydropower production). The model uses a hybrid formulation characterized by a physically based structure associated with a stochastic calibration of the parameters. The interpretation of the parameter values allows for better understanding of river thermal dynamics and the identification of the most relevant factors affecting it. The satisfactory agreement of different versions of the model with measurements in three different rivers (root mean square error smaller than 1 o C, at a daily timescale) suggests that the proposed model can represent a useful tool to synthetically describe medium-and long-term behavior, and capture the changes induced by varying external conditions.

Temperature of the surface layer of temperate lakes is reconstructed by means of a simplified model on the basis of air temperature alone. The comparison between calculated and observed data shows a remarkable agreement (Nash-Sutcliffe efficiency indices always larger than 0.87, mean absolute errors of approximately 1uC) for all 14 lakes investigated (Mara, Sparkling, Superior, Michigan, Huron, Erie, Ontario, Biel, Zurich, Constance, Garda, Neusiedl, Balaton, and Baikal, in west-to-east order), which present a wide range of morphological and hydrological characteristics. Differently from a pure heat flux balance approach, where the different fluxes are determined on the basis of independent relationships, the input data directly inform parameters of a simple model that, in turn, provides meaningful information about the properties of the real system. The dependence of the model parameters on the main morphological indicators is presented, which allows for a quantitative description of the strong influence of the mean depth of the lake on the thermal inertia and the hysteresis pattern between air and lake surface temperatures.The temperature of the surface layer is a crucial factor for the hydrodynamics and ecology of lakes. Water temperature changes may have important direct and indirect ecological effects via their influence on the lifehistory processes of organisms (metabolism, growth, reproduction) and the properties of the habitats (Winder and Sommer 2012). Temperature variations affect foodweb structures and the availability of nutrients for the biological systems in a lake. The effects of temperature on physical and chemical characteristics of lakes may also modify the distribution of individual taxa from the microbiological to the top predator scale (Eggermont and Heiri 2012;Wojtal-Frankiewicz 2012;De Senerpont Domis et al. 2013).Surface temperature is the result of heat fluxes at the lake surface (short-wave solar radiation, long-wave radiation from and to the lake, sensible and latent heat exchange) and at the boundaries (inflows and outflows, groundwater exchange, precipitation, etc.), and of heat transport due to mixing within the lake. All these fluxes depend on several variables (solar radiation, air temperature, wind speed and direction, cloudiness, relative humidity, etc.), some of which may be difficult or expensive to measure reliably and with sufficient precision. Moreover, some of the variables can change significantly over the lake surface and in time (e.g., wind), and reconstructing their spatial variation can be a particularly hard task. Predicting water temperature is nonetheless a desired goal and models of different types and of different complexity have been proposed, ranging from simple regression models (Livingstone and Lotter 1998;Sharma et al. 2008) to more complex process-based numerical one-dimensional Perroud et al. 2009;Thiery et al. 2014) and three-dimensional models (Wahl and Peeters 2014).In this work, we aim at obtaining results that are accurate enough to reliably p...

During the last several decades, the Great Lakes region has been experiencing a significant rise in temperatures, with the extraordinary summer warming that affected Lake Superior in 1998 as an example of the marked response of the lake to increasingly warmer atmospheric conditions. In this work, we combine the analysis of this exceptional event with some synthetic scenarios, to achieve a deeper understanding of the main processes driving the thermal dynamics of surface water temperature in Lake Superior. The analysis is performed by means of the lumped model air2water, which simulates lake surface temperature as a function of air temperature alone. The model provides information about the seasonal stratification dynamics, suggesting that unusual warming events can result from two factors: anomalously high summer air temperatures, and increased strength of stratification resulting from a warm spring. The relative contribution of the two factors is quantified using the model by means of synthetic scenarios, which provide a simple but effective description of the positive feedback between the thermal behavior and the stratification dynamics of the lake.

Abstract. Water temperature in lakes is governed by a complex heat budget, where the estimation of the single fluxes requires the use of several hydro-meteorological variables that are not generally available. In order to address this issue, we developed Air2Water, a simple physically based model to relate the temperature of the lake superficial layer (epilimnion) to air temperature only. The model has the form of an ordinary differential equation that accounts for the overall heat exchanges with the atmosphere and the deeper layer of the lake (hypolimnion) by means of simplified relationships, which contain a few parameters (from four to eight in the different proposed formulations) to be calibrated with the combined use of air and water temperature measurements. The calibration of the parameters in a given case study allows for one to estimate, in a synthetic way, the influence of the main processes controlling the lake thermal dynamics, and to recognize the atmospheric temperature as the main factor driving the evolution of the system. In fact, under certain hypotheses the air temperature variation implicitly contains proper information about the other major processes involved, and hence in our approach is considered as the only input variable of the model. In particular, the model is suitable to be applied over long timescales (from monthly to interannual), and can be easily used to predict the response of a lake to climate change, since projected air temperatures are usually available by large-scale global circulation models. In this paper, the model is applied to Lake Superior (USA-Canada) considering a 27 yr record of measurements, among which 18 yr are used for calibration and the remaining 9 yr for model validation. The calibration of the model is obtained by using the generalized likelihood uncertainty estimation (GLUE) methodology, which also allows for a sensitivity analysis of the parameters. The results show remarkable agreement with measurements over the entire data period. The use of air temperature reconstructed by satellite imagery is also discussed.

Abstract:River water temperature is a key physical variable controlling several chemical, biological and ecological processes. Its reliable prediction is a main issue in many environmental applications, which however is hampered by data scarcity, when using datademanding deterministic models, and modelling limitations, when using simpler statistical models. In this work we test a suite of models belonging to air2stream family, which are characterized by a hybrid formulation that combines a physical derivation of the key equation with a stochastic calibration of parameters. The air2stream models rely solely on air temperature and streamflow, and are of similar complexity as standard statistical models. The performances of the different versions of air2stream in predicting river water temperature are compared with those of the most common statistical models typically used in the literature. To this aim, a dataset of 38 Swiss rivers is used, which includes rivers classified into four different categories according to their hydrological characteristics: low-land natural rivers, lake outlets, snow-fed rivers and regulated rivers. The results of the analysis provide practical indications regarding the type of model that is most suitable to simulate river water temperature across different time scales (from daily to seasonal) and for different hydrological regimes. A model intercomparison exercise suggests that the family of air2stream hybrid models generally outperforms statistical models, while cross-validation conducted over a 30-year period indicates that they can be suitably adopted for long-term analyses.

<p>Water temperature plays a primary role in controlling a wide range of physical, geochemical and ecological processes in lakes, with considerable influences on lake water quality and ecosystem functioning. Being able to reliably predict water temperature is therefore a desired goal, which stimulated the development of models of different type and complexity, ranging from simple regression-based models to more sophisticated process-based numerical models. However, both types of models suffer of some limitations: the first are not able to address some fundamental physical processes as e.g., thermal stratification, while the latter generally require a large amount of data in input, which are not always available. In this work, lake surface temperature is simulated by means of <em>air2water</em>, a hybrid physically-based/statistical model, which is able to provide a robust, predictive understanding of LST dynamics knowing air temperature only. This model showed performances that are comparable with those obtained by using process based models (a root mean square error on the order of 1°C, at daily scale), while retaining the simplicity and parsimony of regression-based models, thus making it a good candidate for long-term applications.</p><p>The aim of the present work is to provide the reader with useful and practical guidelines for proper use of the <em>air2water</em> model and for critical analysis of results. Two case studies have been selected for the analysis: Lake Superior and Lake Erie. These are clear and emblematic examples of a deep and a shallow temperate lake characterized by markedly different thermal responses to external forcing, thus are ideal for making the results of the analysis the most general and comprehensive. Particular attention is paid to assessing the influence of missing data on model performance, and to evaluating when an observed time series is sufficiently informative for proper model calibration or, conversely, data are too scarce thus leading to the risk of overfitting. The final aim of the work is to facilitate the use of the model also by scientists that do not necessarily have a solid background on modelling or physics. However, this work should not be considered simply as a collection of best practices, but also as the attempt to foster the communication and interaction among colleagues of a branch of science, limnology, that suffer of significant fragmentation. This is summarized in the future perspectives and challenges concerning potential improvements of the <em>air2water</em>, with a particular emphasis on possible cross-sectoral applications.</p>

Water temperature in lakes is governed by a complex heat budget, where the single fluxes are hardly assessable over long time periods in the absence of high accuracy data. In order to address this issue, we developed Air2Water, a simple physically-based model to relate the temperature of the lake superficial layer (epilimnion) to air temperature only. The model accounts for the overall heat exchanges with the atmosphere and the deeper layer of the lake (hypolimnion) by means of simplified relationships, which contain a few parameters (from four to eight in the different proposed formulations) to be calibrated with the combined use of air and water temperature measurements. In particular, the calibration of the parameters in a given case study allows one to estimate, in a synthetic way, the influence of the main processes controlling the lake thermal dynamics, and to recognize the atmospheric temperature as the main factor driving the evolution of the system. In fact, the air temperature variation implicitly contains proper information about the variation of other major processes, and hence in our approach is considered as the only input variable of the model. Furthermore, the model can be easily used to predict the response of a lake to climate change, since projected air temperatures are usually available by large-scale global circulation models. In this paper, the model is applied to Lake Superior (USA – Canada) considering a 27-yr record of measurements, among which 18 yr used for calibration and the remaining 9 yr for model validation. The results show a remarkable agreement with measurements, over the entire data period. The use of air temperature reconstructed by satellite imagery is also discussed

Can we predict long‐term trends of lake surface temperature based on air temperature alone? We explore this question by analyzing the performance of a hybrid model (air2water) as a predictive tool for defining scenarios of lake surface temperature in the framework of climate change studies. Employing Lake Tahoe (U.S.A.) as a case study, we apply the model using different air temperature datasets (in situ measurements, gridded observations, and downscaled General Circulation Models). Through a data‐driven calibration of the model parameters based on surface water temperature records, we show that air2water provides good performance (root mean square error ∼ 0.5°C, on a monthly scale) regardless of the input dataset. The model is able to accurately capture the historical long‐term trend and interannual fluctuations over decades (from 1969 to present), using only 7 yr of monthly measurements of surface water temperature for calibration. Additionally, when used to predict future surface water temperature of the lake, air2water produces the same projections irrespective of the air temperature dataset used to drive the model. This is certainly desirable, but not immediately expected when using a relatively simple model. Overall, the results suggest the high potential and robustness of air2water as a predictive tool for climate change assessment. Lake surface temperature warming of up to 1.1°C (RCP 4.5) and 2.9°C (RCP 8.5) was simulated at the end of the 21st century during summer months in Lake Tahoe. Such a scenario, if realized, would lead to serious consequences on lake water chemistry, primary productivity, plankton community structure, and nutrient cycling.