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In the past 40 years, the surface water temperature of lakes worldwide has generally shown an upward trend, with a significant spatial heterogeneity. Previous studies generally attributed the change in lake surface water temperature to direct impact of climate change. However, few studies have explored the potential impact of additional anthropogenic factors, resulting in an incomplete understanding of the anthropogenic influence on lake surface water temperatures. We thus propose a new method to quantify the anthropogenic impact on the surface water temperature of lakes. We selected 11 lakes characterized by significant variations in the intensity of watershed urbanization development on the Yunnan-Guizhou Plateau in China for an empirical study, and discussed the trend of LSWT (lake surface water temperature) changes under the anthropogenic impact, as well as the potential link between these changes and human social policies. The research results show that (1) The mean annual rate of change in LSWT due to anthropogenic impact fluctuates of 0.06℃ per year. (2) LSWT is sensitive to changes in anthropogenic activities; a 1℃ increase in LSWT due to anthropogenic factors typically results in a mean temperature variation of 0.24℃. (3) During the three years of the COVID-19 pandemic, LSWT on the Yunnan-Guizhou Plateau was significantly affected by anthropogenic activities.

In the context of global warming, the lake surface water temperature (LSWT) exhibits a general upward trend. As an indicator of climate change, the surface water temperature of plateau lakes is particularly sensitive to climate warming. In this study, the machine learning model and physical process model are combined to predict water temperature in lake systems: The Air2water model and the long short term memory (LSTM) model are combined to form a prediction model for the inversion and prediction of 11 typical plateau lakes in the Yunnan–Guizhou Plateau. The modeling results show that the Air2water model performs best, followed by the LSTM model. Overall, the Air2water model and the LSTM model effectively reproduce the monthly, seasonal, and interannual variations of LSWT dynamics in the 11 lakes. The research results show that the LSWT dataset from 2021 to 2025 is constructed based on the forecast result, and it is found that six lakes, including Caohai, Dianchi, Erhai, Qionghai, Xingyun Lake, and Yangzonghai, showed significant warming in the next five years (the maximum warming rate was less than +0.2 °C/year), while the remaining five lakes showed no significant changes, and the size classification of LSWT data in different spaces on the interannual scale was consistent with the classification of altitudes. By conducting extensive exploration and research on the inversion of LSWT using physical process models and machine learning models, this study offers novel solutions for LSWT prediction and inversion. The study also provides a solid theoretical and practical foundation for future LSWT research, thereby holding practical significance and research value.

In the context of global warming, the lake surface water temperature (LSWT) exhibits a general upward trend. As an indicator of climate change, the surface water temperature of plateau lakes is particularly sensitive to climate warming. In this study, the machine learning model and physical process model are combined to predict water temperature in lake systems: The Air2water model and the long short term memory (LSTM) model are combined to form a prediction model for the inversion and prediction of 11 typical plateau lakes in the Yunnan–Guizhou Plateau. The modeling results show that the Air2water model performs best, followed by the LSTM model. Overall, the Air2water model and the LSTM model effectively reproduce the monthly, seasonal, and interannual variations of LSWT dynamics in the 11 lakes. The research results show that the LSWT dataset from 2021 to 2025 is constructed based on the forecast result, and it is found that six lakes, including Caohai, Dianchi, Erhai, Qionghai, Xingyun Lake, and Yangzonghai, showed significant warming in the next five years (the maximum warming rate was less than +0.2 °C/year), while the remaining five lakes showed no significant changes, and the size classification of LSWT data in different spaces on the interannual scale was consistent with the classification of altitudes. By conducting extensive exploration and research on the inversion of LSWT using physical process models and machine learning models, this study offers novel solutions for LSWT prediction and inversion. The study also provides a solid theoretical and practical foundation for future LSWT research, thereby holding practical significance and research value. [ABSTRACT FROM AUTHOR]

The air2water model is a simple and efficient tool for modeling surface water temperature in lakes based solely on the air temperature. In this article, we propose to modify the air2water model in such a way that different parameters would be associated with lake stratification of cold waters than with lake stratification of warm waters. The situation of a mix of both cold water and warm water is also considered. The model is tested on 22 lowland Polish lakes against two classical air2water variants. As the new air2water model variant is slightly more complicated than the basic versions, we focus on the importance of the choice of the calibration method. Each variant of the air2water model is calibrated with eight different optimization methods, which are also compared on various benchmark problems. We show that the proposed variant is superior to the classical air2water models on about 90% of tested lakes, but only if the calibration approach is properly selected, which confirms the importance of the links between the model and appropriate optimization procedures. The proposed air2water variant performs well on various lowland lakes, with exception of large but shallow ones, probably due to the weak stratification of the shallow lakes.

Sea surface temperature (SST) is an important indicator of marine system. In this study, the hybrid physically-statistically based air2water model was modified for the forecasting of SST. The hybrid model combines empiricism and theory, and balances the complexity and accuracy between the process-based physical models and statistical models. Daily observed SST data (2009–2019) from six stations in the Baltic Sea were used for the evaluation of model performance. Two metrics including the root mean squared error (RMSE) and the Nash-Sutcliffe efficiency coefficient (NSE) were used for model assessment. With the increase of air temperature, SST presents a clear warming trend (0.133°C/year–0.166°C/year), and air temperature warms faster than SST in the studied stations. The modelling results indicated that the model performs well for SST forecasting (in the validation period, mean value of RMSE is 1.245°C, and mean value of NSE is 0.961). Cross-validation results showed that the model is transferable in unknown stations. However, the model works a little bit worse in the warm period due to the impact of the upwelling phenomenon. Overall, the model is a promising tool for the prediction of SST.

Study region: Lowland lakes located at Poland. Study focus: There are thousands of lowland lakes in Poland, however, many of them don’t have observed data of water temperatures. How can we simply estimate lake surface water temperature (LSWT) is challenging, and a few studies tried to deal with this issue. In this study, we proposed a simple method using the air2water model for regional estimation of LSWT for Polish lowland lakes: Firstly, a literature review was conducted to collect parameter values of the air2water model applications in different lakes with diverse lake morphologies (e.g., mean depth). Secondly, correlations of model parameters with mean lake depth were analyzed. Finally, model parameters of the Polish lowland lakes (25 lakes with three lakes for testing) were derived using the corresponding mean lake depth and model performance was evaluated afterwards. New hydrological insights for the region: The results showed that the proposed method performs generally well for the 25 Polish lowland lakes, better than the previous method. Reasonable results were obtained for three Polish lakes that were not used for regression analysis, what encourages application of the proposed approach on unmonitored lakes. The results indicated that the method proposed in this study can be used to estimate LSWT of Polish lowland lakes as daily data of air temperatures are readily available in most of the meteorological stations.

Sea surface temperature (SST) is an important indicator of marine system. In this study, the hybrid physically-statistically based air2water model was modified for the forecasting of SST. The hybrid model combines empiricism and theory, and balances the complexity and accuracy between the process-based physical models and statistical models. Daily observed SST data (2009–2019) from six stations in the Baltic Sea were used for the evaluation of model performance. Two metrics including the root mean squared error (RMSE) and the Nash-Sutcliffe efficiency coefficient (NSE) were used for model assessment. With the increase of air temperature, SST presents a clear warming trend (0.133°C/year–0.166°C/year), and air temperature warms faster than SST in the studied stations. The modelling results indicated that the model performs well for SST forecasting (in the validation period, mean value of RMSE is 1.245°C, and mean value of NSE is 0.961). Cross-validation results showed that the model is transferable in unknown stations. However, the model works a little bit worse in the warm period due to the impact of the upwelling phenomenon. Overall, the model is a promising tool for the prediction of SST. [ABSTRACT FROM AUTHOR]

How fast does lake surface water temperature (LSWT) react to climate warming or cooling? The thermal response of lakes varies with the season and, typically, day‐to‐day fluctuations are larger in summer. The reason is that lakes are stratified systems where the thermally reactive volume is smaller in summer and, hence, its heat capacity (thermal inertia) is reduced. We define the dimensionless parameter δ as the ratio between the surface volume reacting to the net heat flux through the air‐water interface and the volume of the whole lake. By referring to a fully controlled case study obtained by means of a one‐dimensional physically based model (Simstrat), we investigate the variability of δ throughout the year and its dependence on LSWT. Then, we compare the results with the parameterization adopted in the hybrid data‐driven model air2water. Our analysis confirms that δ follows an exponential decay with increasing LSWT (i.e., a thinner surface layer in summer), and shows that this functional dependence varies between the warming and the cooling periods. These findings contribute to the understanding of the effect of a warming climate on water bodies and ecosystems by providing a simple tool to estimate the rate of change in lakes' water temperature. Plain Language Summary: The temperature of lake surface waters varies mostly because heat is exchanged with the atmosphere, in either direction. When heat is entering into the lake (spring‐summer), it generates a surface layer with nearly uniform water temperature, which is almost isolated from the bottom by a region with localized temperature change. The rate of change of surface water temperature grows when the depth of this layer decreases, and is higher in summer when the vertical variation of water temperature is stronger. This produces positive feedback (water temperature tends to grow faster as it becomes warmer) that may exacerbate the effect of climate warming on lake ecosystems. In this analysis, we discuss how these dynamics can be parameterized as a function of lake surface water temperature, and we claim that this is a fundamental element that all simplified (bulk, statistical, etc.) lake models should include. The high performance of a model based on this concept, and that has been extensively applied (air2water), supports this argument. Key Points: Only a portion of the lake volume reacts to the net heat flux exchanged at the surface, and this depends on stratificationThe size of the thermally reactive volume determines the thermal inertia and hence controls the warming rate at the surfaceThe reactive volume depth is inversely dependent on surface water temperature through an exponential decay for direct stratification [ABSTRACT FROM AUTHOR]

Study region: The study region comprises 25 lowland Polish lakes in the northern part of the country. The studied lakes provide domestic, industrial and agricultural water supply, and are major attractions for tourism, thus playing a significant role in the Polish economy. Study focus: The expected impact of future climate change on lake surface water temperature (LSWT) was predicted using the air2water model, which relies solely on daily air temperature (AT) as model input. LSWT and AT observations for the period 1987–2016 were used for model calibration and validation. Then, historical (1987–2005) and future (2006–2100) AT time series from nine EURO-CORDEX climate models were used to project future LSWT under emission scenarios RCP4.5 and RCP8.5. New hydrological insights for the region: The results showed that air2water can well reproduce daily LWST with root mean square errors lower than 1 °C on average. The warming trends of both AT and LSWT are expected to be lower than those observed in the past decades (after the 1980s), and ice cover and weak stratification conditions are expected to partially buffer the LSWT response to the high AT warming expected in future winters. However, the overall enduring warming will substantially alter future thermal dynamics, leading to a shortening of ice cover and inverse stratification periods, possibly leading to serious consequences for lake water quality and ecosystem health.

Lake surface water temperatures (LSWTs) are sensitive to climate change, but previous studies have typically focused on temperatures from only the last few decades. Thus, while there is good appreciation of LSWT warming in recent decades, our understanding of longer-term temperature change is comparatively limited. In this study, we use a mechanistically based open-source model (air2water), driven by air temperature from a state-of-the-art global atmospheric reanalysis (ERA-20C) and calibrated with satellite-derived LSWT observations (ARC-Lake v3), to investigate the long-term change in LSWT worldwide. The predictive ability of the model is tested across 606 lakes, with 91% of the lakes showing a daily root mean square error smaller than 1.5 °C. Model performance was better at mid-latitudes and decreased towards the equator. The results illustrated highly variable mean annual LSWT trends during the twentieth century and across climatic regions. Substantial warming is evident after ~ 1980 and the most responsive lakes to climate change are located in the temperate regions. [ABSTRACT FROM AUTHOR]

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 air2water, 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.The aim of the present work is to provide the reader with useful and practical guidelines for proper use of the air2water 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 air2water, with a particular emphasis on possible cross-sectoral applications.

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 air2water, 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. The aim of the present work is to provide the reader with useful and practical guidelines for proper use of the air2water model and for critical analysis of results. Two case studies have been selected for the analysis: Lake Superior and Lake Erie (USA). 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 modeling or physics. This work is also an attempt to foster the communication and interaction among colleagues of a branch of science, limnology, which suffer of significant fragmentation. This is summarized in the future perspectives and challenges concerning potential improvements of the air2water, with a particular emphasis on possible cross-sectoral applications. [ABSTRACT FROM AUTHOR]

The air2water model is a physically-based model in which major physical processes are parameterized. It allows to predict the surface lake temperature based solely on the time series of the air temperature. Due to its simplicity and very limited data requirements, it has found numerous applications around the globe. The air2water model defines the normalized depth of the well-mixed surface layer using a fixed parameter. This parameter is a threshold value that is set to 4 °C – the temperature of water with maximum density – for dimictic lakes, and to the minimum or to the maximum water temperature for warm or cold monomictic lakes, respectively. In this paper we propose to calibrate the threshold value as the ninth parameter of the model, instead of setting it fixed. We test the proposed approach on a set of 30-years long daily data from 22 lakes located in the lowland part of Poland and 25-years long daily data from the two Great Lakes – Huron and Eire. The proposed modification is very simple and improves the performance of the model, especially for winter-spring season, for the vast majority of lakes not only for the calibration, but also for the independent 8–10 years long validation data. [ABSTRACT FROM AUTHOR]

• 12 algorithms were implemented for the air2water model. • Impact of the number of function calls was evaluated. • The HARD-DE algorithm performed the best. The air2water model is a widely used tool for the forecasting of lake water temperatures and projection of climate change. It has been applied in thousands of lakes worldwide. However, it employed the Particle Swarm Optimization (PSO) as the calibration method, which was proposed more than 20 years ago. In this study, 12 advanced optimization algorithms proposed during the recent few years were implemented to calibrate and validate the air2water model. Daily observed water temperature in temperate lakes (22 lowland lakes in Poland) were used to evaluate the model performance. Each optimizer was run 30 times with 3 different settings of the maximum number of function calls, 5000, 20,000, and 100,000. We have found that the PSO method used in the original air2water model performs relatively poor compared with most of the recent algorithms, and the majority of recently proposed algorithms reach the similar best solutions on many lakes when the highest number of function calls is allowed. However, only the HARD-DE (hierarchical archive-based mutation strategy with depth information of differential evolution) algorithm is never outperformed by any competitor, irrespective which lake and maximum number of function calls is considered. As a result, we highly recommend using HARD-DE as the calibration method for the air2water model in the future studies. [ABSTRACT FROM AUTHOR]

• Four models are applied and compared for forecasting lake surface water temperature in Polish lakes. • All four models perform reasonably well in forecasting lake surface water temperature. • The hybrid air2water model performs the best, better than the machine learning and non-linear regression models. • The air2water and the machine learning models well reproduce the thermal dynamics of lakes. Accurate water temperature forecasting in lake systems is important for environmental impact assessment and fisheries management, among others. In this study, two models are developed and applied for water temperature forecasting in lake systems: (1) the multi-layer perceptron neural network (MLPNN) model; and (2) the wavelet transform and MLPNN integrated model (WT_MLPNN). The models are applied to forecast daily lake surface water temperature (LSWT) of eight lowland Polish lakes. Long-term daily LSWT from eight lakes and daily air temperatures from seven meteorological stations are used for daily LSWT forecasting. The results from the two models are compared with those obtained from two other widely used models: the physically-statistically based hybrid air2water model and a non-linear regression model (S-curve). The modelling results show that the air2water model performs the best, followed by the WT_MLPNN, MLPNN, and the non-linear regression model. Overall, the air2water , WT_MLPNN, and MLPNN models reproduce well the seasonal and inter-annual variations of the LSWT dynamics in the eight lakes. The non-linear regression model, although providing the lowest accuracy, can still provide good preliminary estimates of the LSWT for the eight lakes. The outcomes of the present research can provide references for forecasting lake surface water temperature and sustainable management of lake ecosystems. [ABSTRACT FROM AUTHOR]