Prediction of long-term changes of weak diurnal stratification in shallow lakes using artificial neural networks

Thermal stratification has a significant role in lakes' ecological status, potentially causing oxygen depletion at the lake's bottom. In deep lakes, when stratification occurs, the water column can be divided into three layers: epilimnion, hypolimnion, and thermocline. Out of these, the hypolimnion plays a crucial role in maintaining stratification, as in typical circumstances, low mixing characterizes this layer, allowing stratification to persist. As a result, oxygen depletion can develop over the bottom, leading to eutrophication through nutrient release (Pettersson et al. 2003; Salmaso 2005). In contrast, epilimnion and hypolimnion may not develop in shallow lakes because driving forces of mixing acting at the lake's surface can reach the bottom of the lake, resulting in more frequent mixing periods and shorter stratification durations (Wilhelm & Adrian 2008). The stratification usually lasts for months in deep lakes and ranges from hours to days in shallow lakes. Despite the frequent mixing, oxygen depletion can also develop in the latter case if meteorological conditions are met in such a way that an intermittent – a few days long – but continuous stratification develops, leading to severe ecological problems, such as the record-setting algae bloom in 2019 in Lake Balaton (Istvánovics et al. 2022). Thus, stratification can significantly influence the trophic state of shallow lakes (Shinohara et al. 2023).

In shallow lakes, meteorological effects can substantially affect stratification, so it is necessary to reveal their influence and their long-term changes (Zhou et al. 2023). The dominant driving forces of stratification are the solar radiation, the surface air temperature, and the wind speed. The former two are responsible for building up stratification by warming the water layers with different intensities, while the latter is mainly responsible for breaking it up by current- and wave-induced mixing processes (Torma & Krámer 2017). Just mentioning two examples, as a consequence of climate change, the number of lake heatwaves increases (Wang et al. 2023) as well as the intensity of evaporation (Tong et al. 2023). In mid-latitude climates, solar radiation, and surface air temperature tend to increase, warming lakes and prolonging stratification periods in the warm seasons (Woolway et al. 2020).

In addition to climate change, anthropogenic effects also have a significant impact on the stratification of lakes. Among the effects, those that result in a change in the water level should be highlighted, as the water depth plays a crucial role in the stability of stratification. The higher the depth, the more stable stratification can develop (Kraemer et al. 2015). Due to climate change, lake and reservoir water levels may decrease if precipitation and, as a result, runoff rates from the lake's watershed decrease. Consequently, stakeholders try to keep higher water levels to provide a puffer for drought periods. However, more extended stratified periods can develop by a higher water level, increasing the possibility of oxygen depletion even in shallow, polymictic environments (Istvánovics et al. 2022).

In the case of shallow lakes, only weak stratification can develop with a typical diurnal cycle. This means that stratification develops over the day and breaks up due to surface cooling during the nighttime (Torma & Wu 2019). For example, in the very shallow Lake Balaton (Hungary), a stratification that forms over the day (with a maximum temperature difference of 5–6 °C between the surface and the bottom) mostly entirely disappears for the following day. Besides surface cooling, wind can also mix the water column through waves and currents, leading to even shorter stratified periods. Because of the diel cycle, at least hourly measurements are needed to capture the stratification in such environments. Nevertheless, in some cases, neither nighttime cooling nor the wind can mix the whole water column so that a stable stratification can continuously persist near the bottom for a few days. In such cases, anoxic conditions may occur with the consequences mentioned above. Overall, stratification and mixing processes in shallow lakes with a diurnal cycle must be modeled on short time scales of a few hours.

Physical-based models with different dimensions and empirical methods are also available to model stratification (Amorim et al. 2023; Naumenko & Guzivaty 2023). Due to the rapid growth of lake water temperature data, machine learning techniques, as powerful empirical tools, have gained immense potential and have been used more and more widely (Yousefi & Toffolon 2022). In contrast to physics-based models, machine learning techniques lack physical laws and theory; they make predictions based on data alone. One of their drawbacks arises from this, as their inaccuracy can increase if they are forced to make predictions for conditions outside the range used to train the model (Read et al. 2019). Nonetheless, various data-driven techniques, e.g., different artificial neural networks (ANNs), are successfully used to simulate the temperature conditions of lakes.

An ANN model can be a fast way to calculate water temperatures, and it is superior to regression models as they can accurately determine the nonlinear relationships between meteorological driving forces and water temperature changes. Nevertheless, they are usually used for deep lakes and reservoirs and mostly to predict lake water surface temperatures (Kimura et al. 2021; Wang et al. 2022). Regarding stratification, ANNs were only applied to simulate water temperatures at specific depths instead of directly determining stability conditions (Liu & Chen 2012; Saber et al. 2019; Saber et al. 2020). In short, based on a literature review, ANNs were not tested for polymictic lakes and for directly predicting stratification, even though they might be quick and reliable methods for these purposes.

The aim of this study is twofold. First, to prove that a simple artificial neural network model can simulate weak diurnal stratification for a shallow lake with high temporal resolution using routine meteorological data alone. Second, to show that an ANN model can quantify the long-term effects of climate change and anthropogenic impacts based on limited observational data.

Hydrometeorological measurements were carried out in the westernmost basin of the lake in the pelagic area in 2019, 2020, and 2022 in the warm season, from late spring to early autumn. The mean depth of this location was around 3.3 m for the three periods. During the measurement campaign, routine meteorological variables and water temperature profiles were recorded with high temporal resolution. The setup was very similar in each year. For 2019, detailed information about the lake, station location, and measurement setup can be found in Lükő et al. 2020 and 2022. The wind speed (U) was measured by CSAT3 and Windsonic2D anemometers (Campbell Sci.). The radiation components – incoming and outgoing shortwave (SW_in, SW_out) and longwave radiations (LW_in, LW_out) – were recorded by a CNR1 net radiometer (Kipp & Zonen). The air temperature (T_a) and relative humidity (RH) were measured by a HygroVue10 sensor (Campbell Sci.). The water temperature profile was recorded by T107 sensors or a CS225-L thermistor string (both Campbell Sci.) at fixed depths with 0.5 m resolution. A floating sensor attached to a buoy 2 cm below the water surface measured the water surface temperature. During the campaign, both air and underwater instruments were regularly (2 weeks on average) checked, cleaned, and maintained.

In the easternmost basin of the lake, water temperature measurements were carried out by the Hungarian Meteorological Service between 1981 and 2020 near the south shoreline, where the average water depth is around 2.5 m. At this site, daily measurements were taken at a depth of 1 meter below the water surface. The stratification model was set up based on the measurements in the westernmost basin's open water area. In addition, the long-term daily data from the eastern basin was used to check the simulated daily average water temperatures (and thus the energy balance). It can be assumed that this eastern measurement is also representative due to the lake's relatively small thermal inertia and low spatial variability arising from the shallowness. Furthermore, the mean depth of the westernmost basin is around 2.5 m, which is equal to the depth at this eastern measurement location.

The long-term simulations covered a 40-year-long period from 1981 to 2020. For this period, the input meteorological data was gathered from the ECMWF ERA5 reanalysis database, including surface wind speed, wind direction, air temperature, RH, solar radiation, and downward longwave radiation with 1-h time resolution. Comparing the measured and ECMWF meteorological time series, bias correction was needed in the case of U, T_a, and SW_in variables. It has been performed by matching their cumulative distribution functions employing second-degree polynomials. Daily water level time series, from which monthly mean values were derived, was available from the Hungarian Water Directory.

The second module is an ANN model, which uses the water temperature and its temporal change obtained from the 0D model, routine meteorological data (U, T_a, RH, SW_in), and water depth (h) as inputs (Figure 2) and calculates the stratification index called the potential energy anomaly (⁠⁠) as output (see details in the following subchapter). It also uses the preceding 6-h average of U and SW_in to consider the dominant antecedent meteorological conditions for mixing and stratification, respectively. In the case of water depth, monthly averaged values were used. The model has one hidden layer and consists of six neurons. It is a nonlinear input-output network without using the estimated from the previous timestep.

The ANN model was trained for 3 years of data with a Bayesian regularization algorithm. The training and testing were done at 80–20%. Because of the Bayesian regularization, the validation process was unnecessary (Burden & Winkler 2009). The ANN model simulations were performed in the Matlab software environment. For stratification modeling, a 3-h time resolution was used as it was frequent enough to describe the daily cycle of stratification without considering the highly short-term fluctuations. After the training, historical simulations were carried out for four decades, from 1981 to 2020. Each year, the simulations were run from May to September to include the lake's warming up and cooling periods. In the results, only the summer months were examined. After the ANN simulations, a final bias correction was performed to improve the model's performance. A first-order polynomial was used for the correction, whose coefficients were calculated using the measured and trained data in 2019, 2020, and 2022.

The calibrated 1D General Ocean Turbulence Model (GOTM, Burchard et al. 1999) was considered as a reference to assess the ANN m'del's reliability for long-term simulations. GOTM is a 1D model that uses a k-ε turbulence model for vertical mixing, providing stratification results on a physical basis. The model was driven by the same routine meteorological data as the 0D and the ANN model (Table 1). The sensible and latent heat fluxes were calculated by Equations (2) and (3) bulk formulas (Kondo 1975). The GOTM model has one further parameter to calibrate: the light extinction coefficient. In the absence of measurement data, we presumed it to be constant, and following a sensitivity analysis, it was set to 0.4 m⁻¹. For water depth, monthly averaged values were used. The water column was divided into 20 layers with an increasing resolution to the water surface and the bottom. The calibration and validation of the model were conducted for the years 2019 and 2022; after that, it was run for the 1981–2020 period with an hourly time resolution.

The mean water depth of Lake Balaton for the summer months in the 1980s was 3.21 m, but after some drought periods in the early 2000s – between 2000 and 2003 – it dropped to 2.93 m (Figure 4). The lowest summer water depth was recorded in August 2003, at 2.63 m. After that, water level regulation was made for the lake, and the maximum control water level was increased by 10 cm. It took three years for the lake to reach the new regulation level, so its effect can only be seen starting in 2006. In 2016, due to a new regulation, it has been increased by 10 cm again. Accordingly, the mean water depth for the summer months between 2006 and 2015 was 3.31 m, while from 2016 to 2020, 3.43 m.

The reference GOTM model was calibrated and validated for two parameters – T_w and ϕ – for 2019 and 2022. For depth-averaged water temperature, the model provides good results, with a slight overestimation in the case of sudden cooling periods. In the case of an unstable stratification (resulting in negative ϕ values), the model immediately mixes the water column and couldn't reproduce unstable situations. However, these events are negligible in the summer because they cannot last long and are very weak. Therefore, the rarely occurring negative ϕ values produced by the ANN were also neglected. Overall, the model provided satisfactory results for T_w and ϕ, which made it suitable for further investigations. Table 2 shows the statistical indicators for the calibration and validation periods regarding the two parameters.

As mentioned in the Introduction, periods when stratification does not entirely vanish by the next day may be crucial in the lake's ecology. Thus, the number of stratification periods that lasted at least 24 h were looked at using two different thresholds, 0.5 and 1.0 J m⁻³. In both cases, similar increasing trends experienced. The thresholds were selected to ensure that the stratification would exhibit sufficient strength to be classified as stable. Figure 8 shows how the number of stratified periods evolved in the last 40 years for the 0.5 J/m³ limit.

Both models showed the same tendencies. The GOTM resulted in 5.4 and 7.2 events per year for the two water depth periods, while the ANN gave 4.8 and 7.1 events, respectively. In contrast to the summer median ϕ values, the number of events didn't possess an increasing trend before 2006, meaning that climate change-related intensification of stratification was not strong enough to maintain a stable thermal structure that could survive by the next day. It also has to be mentioned that till 1997, the ANN model suggested a higher variability, having also years without 1-day-long stratification periods. This can be partly explained by the relationship between water depth and light extinction (see Discussion). Overall, the ANN model can assess the same trends for more extended stratification periods as the physics-based GOTM and adequately captures the interactive effect of water depth increase and climate change from 2006.

Lake Balaton's thermal stratification is primarily driven by wind speed, incoming shortwave radiation, and air temperature, which all show an increasing trend (Figure 4). SW_in and T_a are working in favor of the stratification by increasing vertical water temperature and density differences. In contrast, the U works against it by inducing waves and currents, which make the water column mix and the stratification dissipate. Considering their integrated effect, an increasing trend can be seen in the strength of the lake's thermal stratification (Figure 8), which was captured by the ANN model with a suitable accuracy (Figure 7). Water depth also has a crucial effect on the stratification, as it not only increases its strength but amplifies the impact of climate change. As a result, the observed increasing trend after 2006 is a combined, synergistic effect of the varying climate and the heightened water levels. This interaction increases not just the average stability but also results in longer-lasting stratification, and with this, the 24-h-long events occur more and more often.

Turbidity also greatly affects the lake's stratification. In the case of turbid water, incoming shortwave radiation can penetrate only to a limited depth, warming up only the layers it manages to traverse. This creates a temperature difference between the layers, contributing to the development of stratification. In the other case, when the water is more transparent, solar radiation can penetrate deep and warm up the whole water column, so the temperature difference between the layers will be slighter, resulting in a very weak stratification. Light extinction (or attenuation coefficient), which quantifies the efficiency of water absorbing the incoming light, depends linearly on turbidity (Brown 1984). Turbidity, and thus water transparency, is determined by the concentration of organic and inorganic substances, like phytoplankton and suspended sediments, respectively. As a result, light extinction is a highly variable parameter both on small and large time scales. However, external factors such as meteorology also directly and strongly determine it.

In the case of smaller water depths, sediment resuspension can occur more often as the wind-induced mixing can reach the lake's bottom more quickly and with higher intensity, resulting in more variable water transparency conditions. In the ANN model, this might be indirectly incorporated through nonlinear relationships with wind forcing. Regarding the 1-day-long stratification events, the ANN model showed higher variability for the first period (1981–2006) with lower water levels. In contrast, light attenuation was fixed to a constant in the GOTM model. For example, on the 4th and 5th of August, GOTM underestimated ϕ, and the ANN model provided better results (Figure 7). These two days were preceded by a wind event, likely with sediment resuspension. The suspended fine sediments require quite a long time to settle, and until that, they result in higher turbidity, light attenuation, and stratification, as explained above. This means that in some cases, the ANN may provide better results than the GOTM, even though the latter operates on a physical basis.

Sensitivity analysis was carried out on three main elements of the ANN model setup: (i) the role of the water depth range in the training, (ii) the quantity of the training data, and (iii) the role of antecedent wind and solar radiation conditions. The model was trained using 3 years of data: 2019, 2020 and 2022. This version is referred to as S0. For (i) and (ii), the model was trained with only 2 years of data and then ran it for all the 3 years. The S1 model version was trained for 2019 and 2022, with a wide range of water depths, while the S2 model version was trained for 2019 and 2020 when water levels were significantly higher than in 2022. To assess the differences between the training cases the NS efficiency was used (Table 3).

In 2019 and 2020, the water level was high; the depth varied between 3.55 and 3.30 m at the measurement station, while in 2022, it was between 3.32 and 2.98 m. Due to this difference in water depths, the S2 model had to perform extrapolation for almost the whole of 2022. As a result, the S2 model mostly underestimated ϕ and provided unreliably strong, unstably stratified periods. In the S1 case, the water depth in the training period covered the whole range of the 3-years, so the model did not have to extrapolate. Compared to the accepted S0 version, the NS worsened by less than 5% due to the reduced training data providing fewer possible meteorological states (Table 3). Since the difference between S0 and S1 was not convincing for the three years, both models were run for the 1981–2020 period and compared based on the cumulative distribution functions. The distribution of the S1 case shows a more considerable variability than the one obtained using GOTM or the S0 version (Figure 9). In our case, this means that the S1 version is unreliable and usually overestimates the strength of stratification. However, the three-year dataset proved sufficient to establish reliable connections between meteorological driving factors and thermal structure.

Lastly, a simple sensitivity analysis was made for SW_in and U as the most dominant driving forces of stratification formation and break-up, respectively. In the S0 model, the input data included the mean U and SW_in from the preceding 6 h besides their instantaneous values. Since the NS index declined by only 8% for three years of training, the model was run without the averaged values for the 1981–2020 period. As a result, the cumulative distribution functions again possess a more significant variability than the physics-based GOTM model. This means that even though the statistical indicators do not clearly support the usage of the 6-h averaged values, they are not negligible because their impacts become pronounced when we consider the long-term changes.

Machine learning recently became a common and efficient tool for simulating, hindcasting, and predicting lakes' water temperature. A very simple and, thus, robust model has been developed that can simulate shallow lakes' weak stratification and its diurnal cycle with similar accuracy to a complex physics-based 1D model. The presented model system possesses two submodules, both forced by the same routine meteorological variables. The first submodule is a 0D energy balance model, which estimates the depth-averaged water temperature and its temporal change as further inputs for the ANN submodule. As its output, the ANN model calculates the potential energy anomaly index, which characterizes the strength of thermal stratification. The model proved to be reliable both on short and long time scales. Besides capturing the diurnal variation and the intensity of stratification, it was able to explore the effect of climate change, anthropogenic water level regulation, and the synergistic interaction of these two.

Our study provides at least two main novelties. First, it proves that a simple ANN model can simulate a delicate environment with rapidly changing and weak stratification conditions. Of course, to train the model, it is required to have a suitably long and high-frequency time series, including both temperature profiles and meteorological variables. In our case, the time series from three summer seasons proved sufficient. Second, instead of directly estimating water temperature in different depths, the potential energy anomaly index was simulated that adequately describes a shallow lake's stratification. Water temperatures are estimated based on the energy balance equation, which requires only routine meteorological data, and its calibration is also straightforward. This method also has the advantage that water temperature estimates satisfy the energy conservation in contrast to temperatures estimated by machine learning techniques.

The ANN model's predictivity can be improved in the future. Firstly, the hydrometeorological measurements have continued in Lake Balaton, so the training dataset can be extended with further seasons. Secondly, the most simple ANN structure was used for the modeling. It is conjectured that the ANN model's accuracy will increase by including estimated ϕ values from previous time steps in the inputs. Similarly, real-time in-situ measurements can be easily introduced to such a system, making it suitable for nowcasting purposes. Finally, if turbidity or light extinction data are also available, a more complex system would be worth establishing that estimates turbidity conditions first and stratification in a second step. The simultaneous availability of these two parameters would also be fruitful for simulating habitat conditions.

The proposed model system offers an efficient tool for examining several changes in shallow lake environments in the long term. The ANN model can capture intra-daily stratification and its alteration by slowly varying climate change-driven meteorological forces and by much faster human interventions like water level regulation, incorporating their synergistic effect, too. Since the system includes an energy balance submodule, evaporation changes can also be tracked. Evaporation plays a crucial role in the lake's water resource as it is the main loss component of the water balance. For water resources management, accounting for the changes in stratification and evaporation is inevitable, and this model system offers a simple and fast method for their joint calculation. In light of these changes, stakeholders can make informed decisions to ensure sustainable management of the lake's environment.

The research presented in the article was carried out within the framework of the Szechenyi Plan Plus program with the support of the RRF 2.3.1 21 2022 00008 project. This research was also funded by the Ministry of Culture and Innovation and the National Research, Development and Innovation Office (Grant Nr: TKP2021-NVA-02 and K134559). In the case of the first author, the project was supported by the Doctoral Excellence Fellowship Programme (DCEP) is funded by the National Research Development and Innovation Fund of the Ministry of Culture and Innovation and the Budapest University of Technology and Economics, under a grant agreement with the National Research, Development and Innovation Office. Finally, for the second author, funding was also provided by the Hungarian Academy of Sciences (Award: Janos Bolyai fellowship 00906/23).

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.