Utilizing Multi-Source Datasets for the Reconstruction and Prediction of Water Temperature in Lake Miedwie (Poland)

Abstract

Water temperature is a fundamental parameter of aquatic ecosystems. It directly influences most processes occurring within them. Hence, knowledge of this parameter’s behavior, based on long-term (reliable) observations, is crucial. Gaps in these observations can be filled using contemporary methodological solutions. Difficulties in reconstructing water temperature arise from the selection of an appropriate methodology, and overcoming them involves the proper selection of input data and choosing the optimal modeling approach. This study employed the air2water model and Landsat satellite imagery to reconstruct the water temperature of Lake Miedwie (the fifth largest in Poland), for which field observations conducted by the Institute of Meteorology and Water Management—National Research Institute ended in the late 1980s. The approach based on satellite images in this case yielded less accurate results than model analyses. However, it is important to emphasize the advantage of satellite images over point measurements in the spatial interpretation of lake thermal conditions. In the studied case, due to the lake’s shape, the surface water layer showed no significant thermal contrasts. Based on the model data, long-term changes in water temperature were determined, which historically (1972–2023) amounted to 0.20 °C per decade. According to the adopted climate change scenarios by the end of the 21st century (SSP245 and SSP585), the average annual water temperature will be higher by 1.8 °C and 3.2 °C, respectively. It should be emphasized that the current and simulated changes are unfavorable, especially considering the impact of temperature on water quality. From an economic perspective, Lake Miedwie serves as a reservoir of drinking water, and changes in the thermal regime should be considered in the management of this ecosystem.

1. Introduction

Water temperature is one of the fundamental parameters of inland waters, as evidenced by extensive research on this topic. Water temperature has been analyzed in the context of the spawning process of Grass carp (Laurentian Great Lakes region). It was determined that spawning is most likely when the water temperature is below 25 °C and the discharge is above 10 m³/s [1]. Studies of several cascade reservoirs in China have shown that water temperature can directly or indirectly affect the diversity of microorganisms, where an increase in temperature caused an increase in the diversity of planktonic bacteria, while archaea showed the opposite situation. In the case of Lake Poyang, Yan et al. [2] demonstrated that water temperature regulates the dynamics of organophosphate esters in the food chain. According to Haddout et al. [3], water temperature in the lake is one of the key parameters in determining its ecological properties. Water temperature is closely related to qualitative parameters such as biochemical oxygen demand, chlorophyll-a, and transparency [4]. Due to the above, understanding the thermal characteristics of rivers or lakes is crucial for the proper interpretation of the processes and phenomena occurring in these ecosystems. This issue takes on particular significance in an era of rapidly changing climatic conditions, which have a clear impact on the components of the hydrosphere. Air temperature is commonly used in statistical models of water temperature as a surrogate variable for physical processes [5]. The currently observed increase in air temperature [6] has a clear translation into an increase in water temperature in lakes [7]. Changes in the thermal regime of lakes have further consequences for their functioning. Due to the complexity of the interactions between individual processes, their broader effects are often difficult to assess.

Originally, for many years, the primary source of information on water temperature in lakes was instrumental field measurements [8]. However, acquiring in situ data is not always satisfactory, i.e., it is limited both spatially and temporally. The first situation pertains to lakes in inaccessible areas, and the second relates to insufficiently long observation series or situations where measurements have been discontinued. The lack of knowledge about thermal conditions is particularly important in the case of large lakes, which have a real impact on the entire region in which they exist. An example of such a situation is Lake Miedwie—the fifth largest lake in Poland [9], for which water temperature measurements ended in 1989. Nowadays, in such cases, the environmental sciences are supported by a range of tools that allow for a detailed reconstruction and further prediction of various processes—including those concerning water temperature in lakes. Currently, an important role in studying the thermal characteristics of lakes is played by methodologies based on remote sensing [10], machine learning [11], or a combination of both approaches [12]. Difficulties in reconstructing water temperature arise from the selection of an appropriate methodology, and overcoming them involves the proper selection of input data and choosing the optimal modeling approach. According to research by Heddam et al. [11], the air2water model outperformed other water temperature modeling options. Therefore, this approach was used in the present article. The dataset obtained through this modeling method was enriched with Landsat satellite data, representing the first such combination compared to previous methods used in lake studies in Poland.

The goal of this study is the reconstruction and prediction of the water temperature of Lake Miedwie, followed by an assessment of changes in the thermal regime of the analyzed lake. The implementation of these objectives is based on the use of satellite imagery and modeling based on air temperature. Regarding other lakes in Poland where stationary water temperature measurements are lacking, this new approach, based on the proposed methodology, allows for a detailed understanding of one of the fundamental parameters of these ecosystems.

2. Materials and Methods

2.1. Study Area

In Poland, there are over 7000 natural lakes [13], primarily located in the northern part of the country [14]. However, the vast majority of these are small—nearly 3000 lakes fall within the 1–5 hectare range [13]. As mentioned previously, one of the largest is Lake Miedwie in the northwestern part of the country (Lon 14.88205116, Lat 53.26781949, 13.9 m a.s.l., Figure 1). Genetically, it is a post-glacial lake with a meridional trough shape [15]. Its surface area is 3500 ha; it has a maximum depth of 43.8 m and an average depth of 19.3 m, classifying it as a cryptodepression. The length of the lake’s shoreline is 39 km, and its surroundings are dominated by arable land. According to the climatic classification of Poland [16], Lake Miedwie is located in region 6—Szczecin Coastland. This region is characterized by an average annual temperature of 8.4 °C, with January being the coldest month (−0.7 °C) and July the warmest (17.6 °C). The average annual precipitation amounts to 558 mm. From an economic perspective, the lake serves as a water reservoir for the nearby city of Szczecin (with 400,000 residents), located approximately 20 km away. Additionally, there are recreational centers operating along the lake.

2.2. Materials

To achieve the study objective, a diverse dataset including in situ measurements and satellite images was utilized. Water temperature measurements at Lake Miedwie were carried out from 1972 to 1989. Temperature registration was conducted in the surface water layer (at a depth of 0.4 m) at a permanent hydrological station in the northern part of the lake (Figure 1). Additionally, to verify further model calculations, water temperature data from Lake Lubie during the years 1972–2022 were used, where measurements were performed in a similar way. Lake Lubie is located 63 km to the northeast. Meanwhile, air temperature, serving as an explanatory variable for water temperature, was recorded at the Szczecin station (1.0 m a.s.l., Figure 1). These included records obtained from a meteorological gauge at a height of 2 m above ground level. Both water and air temperature observations were conducted as part of the standard monitoring by the Institute of Meteorology and Water Management—National Research Institute.

2.3. Methods

2.3.1. Reconstruction and Prediction of Water Temperature with the Application of the Air2water Model

In the first stage, the water temperature of Lake Miedwie from 1990 to 2023 was reconstructed using the air2water model. Subsequently, predictions of water temperatures in Lake Miedwie for the period 2024 to 2100 were made, utilizing estimated daily air temperatures (Section 2.3.3).

The air2water model is a widely used tool to forecast lake surface water temperatures (LSWT) that has been well demonstrated in lakes worldwide [17,18,19,20]. Compared to other water temperature modeling options, it was shown that for the validation dataset, the air2water model had an average RMSE of 1.031, while the RMSE for ERT, MARS, M5Tree, MLPNN, and RF was 1.413, 1.520, 1.582, 1.726, and 1.499, respectively [11]. It is a lumped model coupling energy balance of the surface layer of the lake and stochastic calibration of model parameters. Among the available model versions, e.g., 3-para, 6-para, 8-para, and 9-para versions, the 6-para version has been widely used to model LSWT in different lakes worldwide [21,22], hence it is used in this study as well.

$${\displaystyle \frac{d{T}_w}{dt}}={\displaystyle \frac{1}{\delta }}\left[a_1+a_2{T}_a-a_3{T}_w+a_{5}cos\left(2\pi \left({\displaystyle \frac{t}{t_y}}-a_6\right)\right)\right]$$

(1)

$$\delta \left\{\begin{array}{c}\exp \left(-{\displaystyle \frac{T_w-T_h}{a_4}}\right) T_w\ge T_h\\ 1 T_w<T_h\end{array}\right.$$

(2)

where T_h is a reference value for the deep lake water temperature (4 °C for dimictic lakes and the minimum or maximum water temperature for the other lakes), δ is a dimensionless term representing the ratio between the volume of the surface lake layer and a reference volume, T_w is daily lake surface water temperature (°C), T_a is daily air temperature (°C), t is time step, and a₁~a₆ are model parameters that need to be determined during the calibration process.

For each lake, the available observed water temperatures are divided into two parts, around 75% for model calibration, and around 25% for model validation. To evaluate model performance, two widely used metrics are employed, namely root mean square error (RMSE) and the Nash–Sutcliffe efficiency coefficient (NSE). Once the models are sufficiently calibrated and the model performance is acceptable, the calibrated models will be used to project the daily water temperatures of lakes to 2100 considering two scenarios, namely SSP245 and SSP585.

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n(T_o-T_s{)}^2}$$

(3)

$$NSE=1-{\displaystyle \frac{{\sum }_{i=1}^n(T_o-T_s{)}^2}{{\sum }_{i=1}^n(T_o-T_m{)}^2}}$$

(4)

where T_o is observed water temperature (°C), T_s is the modeled water temperature (°C), T_m is the average value of T_o, and n is the number of samples.

2.3.2. Reconstruction of Water Temperature with the Application of Satellite Data

In addition to the air2water model, the reconstruction of the water temperature of Lake Miedwie also utilized a second source of data, specifically the Landsat Collection 2 Level-2 [23]. This dataset includes publicly available information on the Earth’s surface temperature in degrees Kelvin. Detailed information about the data used and the method of processing them to calculate the Earth’s surface temperature is presented in the instructions developed by the USGS for Landsat 4–7 and Landsat 8–9 [24,25]. The surface temperature data contained in Collection 2 are available for the period from 1982 to 2024 (

Table 1. Access to Landsat data.

Satellite	Instrument	Operation Period	Number of Acquired Data Points	Number of Used Data Points (April–October)
Landsat 4	Thematic Mapper (TM)	August 1982 to December 1993	8	8
Landsat 5	Thematic Mapper (TM)	March 1984 to May 2012	343	280
Landsat 7	Enhanced Thematic Mapper Plus (ETM+)	July 1999 to April 2022	323	233
Landsat 8	Operational Land Imager (OLI)	April 2013 to present	195	142
Landsat 9	Operational Land Imager 2 (OLI-2)	February 2022 to present	31	19

). The Collection 2 data were released in 2020 by the USGS Earth Resources Observation and Science (EROS) Center. Data from Collection 2 have improved geometric accuracy and radiometric calibration compared with previous Collection 1 products. Due to the fact that the hydrological station performing in situ lake water temperature measurements is located within the shoreline range, it is not possible to obtain surface temperature data (Landsat 4–9) for this location specifically. That results in spatial resolution of the Landsat surface temperature science product. Pixels within the range of the hydrological station where the lake water temperature is measured also extend over land or shoreline vegetation. Therefore, surface temperature data were collected from a point with coordinates Lon 14.918857, Lat 53.347478, located 120 m towards the center of the lake in relation to the lake hydrological station. Similar procedures were used in an earlier study focused on lake water thermometry using Landsat 8 satellite data [12]. Water temperatures were determined based on all available data from Landsat 4, 5, 7, 8, and 9, when this point was not covered by clouds. This process resulted in a total of 900 surface temperature results, from which measurements from November to March were discarded due to possible ice cover on the lake. Consequently, 682 observations were retained for analysis. A script created in Google Earth Engine (GEE) [26] was used to gather the data, which were obtained in the form of a *.csv file arranged as follows: acquisition date; cloud cover; satellite name; and water temperature. Additionally, to determine water temperatures, GEEcode developed by Ermida et al. [27] was utilized, updated for use with Collection 2 and to determine the emissivity of snow and water surfaces. In this method, the surface water temperature is computed using the Statistical Mono-Window (SMW) algorithm developed by the Climate Monitoring Satellite Application Facility (CM-SAF). The results were obtained in the form of a *.csv file.

In the first stage of acquiring water temperature data for Lake Miedwie, quality statistics collected in the QA_PIXEL file were used, calculated based on image data and cloud mask information for the scene. In the second stage, the data underwent filtering based on water temperature results obtained from in situ measurements for Lake Lubie. For this purpose, minimum and maximum temperature values were calculated for each day from 1 April to 31 October based on long-term data from 1972 to 2023. These boundary values were used to filter the data in such a way that temperatures lower than the minimum values and higher than the maximum values were excluded from the analysis. The results obtained in this manner were compared with in situ measurement data from the period 1984–1989 and with results obtained from the air2water model for the period 1990–2023.

Additionally, satellite data were used to present the seasonal variability of surface water temperature in Lake Miedwie. For this purpose, visualizations were created using Landsat Collection 2 Level-2 data by selecting one image from each month of the year 2022 for the period from April to October.

2.3.3. Air Temperature Prediction

This study employed multi-model ensembles (MMEs) utilizing the Bayesian model averaging (BMA) technique to obtain the surface air temperature data from multiple datasets from the Global Climatic Model (GCM) based on Coupled Model Intercomparison Project Phase 6 (CMIP6), as listed in

Table 2. List of Global Climate Models (GCMs) and their corresponding institutions.

GCM	Institutions
NorESM2-MM	Norwegian Climate Centre (NCC)
MPI-ESM1-2-HR	Max Planck Institute for Meteorology (MPI-M)
EC-Earth3	EC-Earth-Consortium
AWI-CM-1-1-MR	Alfred Wegener Institut (AWI)
BCC-CSM2-MR	Beijing Climate Center (BCC)
MRI-ESM2-0	Meteorological Research Institute (MRI)
GFDL-ESM4	Geophysical Fluid Dynamics Laboratory (GFDL) of the National Oceanic and Atmospheric Administration (NOAA)
CESM2-WACCM	National Center for Atmospheric Research (NCAR)
CMCC-CM2-SR5	Euro-Mediterranean Centre on Climate Change (CMCC) Foundation

. These datasets encompassed both historical and projected climate data. MMEs are a highly efficient method for reducing the uncertainty associated with individual models.

The NorESM2-MM dataset encompasses the time period from the pre-industrial era to the year 2100. It runs on a grid resolution of roughly 1 × 1 degree latitude/longitude, with a particular focus on marine biogeochemical processes. This model [28] highlights the significance of marine biogeochemical processes within its framework. The MPI-ESM1-2-HR dataset provides climate forecasts with a high level of detail on a 0.5-degree grid spanning the years 1850 to 2100. This dataset demonstrates exceptional proficiency in establishing connections between atmospheric observations and ocean models [29]. The EC-Earth3 dataset encompasses the time period from 1850 to future forecasts beyond 2100. It has a grid resolution of approximately 1 × 1 degree and is specifically designed to simulate the climate and variability of Europe [30]. The AWI-CM-1-1-MR dataset, which spans from the late 20th century to 2100, offers valuable insights into polar processes with a resolution of around 1 degree [31]. The BCC-CSM2-MR model covers a wide range of time periods, starting from 1850 and extending up to 2100 with a projected change of around 1 degree. It provides comprehensive information on the specific climate characteristics of East Asia and the West Pacific region [32]. The MRI-ESM2-0 dataset provides accurate simulations of atmospheric and oceanic dynamics, with a grid resolution ranging from 0.5 to 1.5 degrees [33]. The GFDL-ESM4 dataset encompasses the time period from the pre-industrial era to 2100. This dataset effectively combines the carbon cycle with physical climate aspects, hence offering valuable insights into the mechanisms of carbon feedback [34]. The CESM2-WACCM dataset encompasses time periods ranging from 1850 to 2100, featuring atmospheric resolution of up to 0.25 degrees. It includes a comprehensive model of the entire atmosphere [35]. The CMCC-CM2-SR5 encompasses a range of historical periods spanning from the 20th century to future possibilities in the 21st century, with a specific emphasis on the climate of the Mediterranean region [36].

To ensure consistency and facilitate direct comparisons, we employed a bilinear interpolation method to regrid various climate model datasets onto a standardized 1 × 1 degree latitude/longitude grid. Our study involved multiple datasets, including NorESM2-MM, MPI-ESM1-2-HR, EC-Earth3, AWI-CM-1-1-MR, BCC-CSM2-MR, MRI-ESM2-0, GFDL-ESM4, CESM2-WACCM, and CMCC-CM2-SR5, which span different time periods and geographic focuses. Bilinear interpolation calculates the interpolated value at a target grid point using values from the four nearest neighboring grid points on the source grid. Specifically, the interpolated value V′ at the target grid (x_t, y_t) is computed as follows:

$$V^{\prime }\left(x_t,y_t\right)={\sum }_{i=1}^4{w}_i·V(x_s^i·y_s^i)$$

(5)

$$w_i={\displaystyle \frac{1}{∆x·∆y}}·(x_{dist}^i·y_{dist}^i)$$

(6)

$V(x_x^i·y_x^i)$ represents the values of the variable at the four nearest neighboring grid points to the source grid that surrounds the target point (x_t, y_t), while the calculation of the weights, denoted as w_i, is based on the distance that exists between each of the four locations and the target point. The variables denoted as Δx and Δy correspond to the intervals between adjacent points on the source grid. The variables $x_{dist}^i$ and $y_{dist}^i$ denote the horizontal and vertical distances, correspondingly, between the ith adjacent point and the target grid point. For instance, the NorESM2-MM dataset, with a grid resolution of roughly 1 × 1 degree, aligns directly with our standardized grid, while the MPI-ESM1-2-HR dataset, which has a 0.5-degree grid, is upscaled to match the 1 × 1 degree resolution using bilinear interpolation. Similarly, datasets with coarser resolutions, such as MRI-ESM2-0 (0.5 to 1.5 degrees), are regridded to achieve consistency. This interpolation process ensures that all datasets, regardless of their original resolution, are uniformly regridded, enabling a direct comparison of climate variables across different models and enhancing the robustness of our analyses.

The study employs Bayesian Model Averaging (BMA) as proposed by Hoeting et al. [37] to integrate data derived from several global climate models (GCMs). The Bayesian Model Analysis (BMA) is a statistical framework that facilitates the integration of predictions generated by several models, employing principles from probability theory. The underlying premise of this approach is the theorem of Bayes, which can potentially effectively be expressed mathematically within the framework of model averaging in the form that follows:

$$p\left(\left.M_i\right|y\right)={\displaystyle \frac{p\left(\left.y\right|M_i\right)·p\left(M_i\right)}{p\left(y\right)}}$$

(7)

$p\left(\left.M_i\right|y\right)$ denotes the posterior probability of model Mi given the data y, $p\left(\left.y\right|M_i\right)$ denotes the likelihood of the data y under model M_i, $p\left(M_i\right)$ denotes the prior probability of model M_i, and p(y) denotes the marginal likelihood of the data y and serves as a normalizing constant.

To determine the BMA prediction distribution for a new data $\tilde{y}$, a weighted average is taken from the predictive distributions of each model. The equation incorporates the predictive distribution, denoted as $p\left(\left.\tilde{y}\right|M_i\right)$, which signifies the probability distribution of the new data $\tilde{y}$ to the model $M_i$. Furthermore, the weight for model $M_i$, denoted as $p\left(\left.M_i\right|y\right)$, is computed under the previously elucidated methodology. It can be expressed mathematically in the form that follows:

$$p(\left.\tilde{y}\right|y{\sum }_{i=1}^{M}p\left(\left.\tilde{y}\right|M_i\right)·p\left(\left.M_i\right|y\right))$$

(8)

The climate model ensemble provides a consolidated BMA prediction for the surface air temperature (T) at a particular grid point (x, y) and time (t) as follows:

$$T_{BMA}\left(x,y,t\right)={\sum }_{i=1}^M{w}_i\left(x,y,t\right)·T_i(x,y,t)$$

(9)

The prediction provided by model i is denoted as T_i (x, y, t), whereas the BMA weight assigned to model i at grid point (x, y) and time t is represented as w_i (x, y, t). The weight in question is defined by the posterior probability p(M_i∣y), which is specific to the location and time in question. The determination of uncertainty in the combined prediction of the BMA model is based on the standard deviation of the predictive distribution of the BMA model as follows:

$${\sigma }_{BMA}\left(x,y,t\right)=\sqrt{{\sum }_{i=1}^M{w}_i\left(x,y,t\right)·{(T_i\left(x,y,t\right)-T_i\left(x,y,t\right))}^2}$$

(10)

σ_BMA (x, y, t) represents the degree of uncertainty at the given coordinates (x, y) and time t on the grid. The degree of uncertainty in the aggregated forecast and the level of agreement across the models can be inferred from the variability of the posterior distribution. The weighting factors from the BMA method for each model are listed in

Table 3. BMA weighting factors for each model.

Model	SSP245	SSP585
AWI-CM-1-1-MR	0.11	0.12
BCC-CSM2-MR	0.08	0.08
CESM2-WACCM	0.12	0.11
CMCC-CM2-SR5	0.09	0.10
EC-Earth3	0.12	0.13
GFDL-ESM4	0.10	0.09
MPI-ESM1-2-HR	0.12	0.12
MRI-ESM2-0	0.14	0.13
NorESM2-MM	0.12	0.12

.

We utilized the nearest neighbor methodology [38] to choose surface air temperature data for a particular geographic location after applying the MME method. This approach involves calculating the distance between the target point and each location within the grid, and then choosing the closest grid point’s data as representative of the target location to ensure the selection of the most representative grid point. The notion of the nearest neighbor was articulated through the calculation of the distance between the target point and every location inside the grid.

The Euclidean distance d between a target point with geographic coordinates (x_target, y_target) and each grid point (x_i, y_i) in the dataset can be calculated as follows:

$$d_i=\sqrt{{(x_i-x_{target})}^2+{(y_i-y_{target})}^2}$$

(11)

In this study, we applied a bias correction method to adjust the outputs of air temperature data from the MME method to better match observed historical climate data. This process corrects both the mean and the temporal variability in the GCM outputs, ensuring that the corrected data reflects the observed climate patterns more accurately. The corrected outputs are then used for future climate projections.

For the historical period up to 2014, we used observed temperature data and air temperature data from the MME method to calculate the necessary bias correction factors. Specifically, we computed the mean and standard deviation of the observed temperature data ($O_{REF}$, ${\sigma }_{O,REF}$) as well as the mean and standard deviation of the air temperature data from the MME method ($T_{REF}$ and ${\sigma }_{T,REF}$). The bias correction was applied as follows [39,40]:

$$T_{BC}\left(t\right)=O_{REF}+{\displaystyle \frac{{\sigma }_{O,REF}}{{\sigma }_{T,REF}}}(T_{RAW}\left(t\right)-T_{REF})$$

where $T_{BC}\left(t\right)$ is the bias-corrected GCM output, $O_{REF}$ is the mean of the observed data for the reference period, ${\sigma }_{O,REF}$ is the standard deviation of the observed data for the reference period, $T_{RAW}\left(t\right)$ is the raw GCM output, $T_{REF}$ is the mean of the GCM data for the reference period, and ${\sigma }_{T,REF}$ is the standard deviation of the GCM data for the reference period.

This correction formula was applied to the GCM outputs for the future periods 2015–2023 and 2024–2100. By adjusting the raw GCM outputs based on the observed data’s mean and variability, the corrected data more closely align with historical observations. To evaluate the performance of the bias-corrected data, we calculated several statistical metrics for the period 2015–2023, including the correlation coefficient, root mean squared error (RMSE), and mean absolute error (MAE). The correlation coefficient measures the strength and direction of the linear relationship between observed and corrected temperatures, with values closer to 1 indicating a stronger positive correlation. RMSE and MAE measure the average magnitude of the errors and the average absolute difference between observed and corrected temperatures, respectively, with lower values indicating better performance.

2.3.4. Analysis of Trends of Changes in Water Temperature in Lake Miedwie

The study of long-term changes in air and water temperatures was conducted for different time periods. Initially, the analysis covered the entire period for which data were obtained from the air2water model, i.e., from 1990 to 2023. Subsequent analyses were performed for four 30-year periods. Firstly, the analysis was conducted for the past period from 1994 to 2023, and secondly for the near, mid, and far future periods, respectively from 2024 to 2053, 2047 to 2076, and 2071 to 2100. Future temperature changes were analyzed separately for the SSP245 and SSP585 scenarios. In order to determine the directions of long-term changes in average annual air and water temperatures in Lake Miedwie, non-parametric Mann–Kendall [41] and Sen [42] tests were used. In order to test the existence of a monotonic trend using the Mann–Kenadal test, two hypotheses were formulated. The null hypothesis (H0) states that the data show no monotonic trend, while the alternative hypothesis (HA) states that there is a monotonic trend in the data over time. To determine the magnitude of changes in air and water temperatures, the nonparametric Sen’s slope test was used. Sen’s test is insensitive to the presence of outliers in the dataset that significantly differ from the general population. Moreover, a trend-free prewhitening procedure was used to remove autocorrelation from the data series [43]. Meanwhile, to detect discontinuities in the data series, the nonparametric Pettitt test was applied. The Pettitt test allows for the detection of individual change points in time series data [44]. For the analysis of the directions and magnitudes of changes using the Mann–Kendall and Sen’s tests, the modifiedmk package developed by Patakamuri and O’Brien [45] was utilized. For change point detection, the trend package developed by Pohlert [46] was utilized.

3. Results

3.1. Historical Reconstruction of Water Temperature

The average annual water temperature of Lake Miedwie during the period covered by field measurements was 9.3 °C, ranging from 8.5 °C (in 1980 and 1984) to 10.4 °C (in 1989). On a monthly basis, February was the coldest month (2.1 °C), and July was the warmest (18.1 °C). Due to the cessation of stationary measurements in 1989, further thermal characterization of Lake Miedwie was conducted by reconstructing water temperatures based on air temperatures up to 2023. For this purpose, the Air2Water model was used, which achieved calibration period results with an RMSE of 1.34 and an NSE of 0.95, and validation period results of 1.54 and 0.94, respectively. A similar analysis was also conducted for Lake Lubie (located 63 km away), which, due to ongoing continuous observations to the present day, serves as a reference base. The results of these statistics for Lake Lubie were similar, confirming the model’s assumptions as correct. The reconstructed water temperature of Lake Miedwie during the period with available air temperatures (1990–2023) was close to that for the period covered by field monitoring (1972–1989), with an average temperature of 9.6 °C, and the lowest and highest temperatures being 8.2 °C (in 1996) and 10.4 °C (in 2019 and 2020), respectively. Similarly, during this period, February remained the coldest month (2.1 °C), and July the warmest (18.5 °C). Long-term changes from 1972 to 2023 showed an increase in the average annual temperature by 0.20 °C per decade (statistically significant, p 0.05) (

Table 4. Water temperature changes (Miedwie Lake) and air temperature changes (Szczecin).

Period	Mann–Kendal and Sen Tests				Pettitt Test
	S	z-Value	p-Value	Sen Slope Value (°C per Decade)	Change Point	p-Value
Water temperature
1972–2023	545	4.30	0.000	0.20	1988	0.003
1994–2023	180	3.21	0.001	0.31	2014	0.004
2024–2053 a	237	4.27	0.000	0.17	2036	0.006
2047–2076 a	133	2.41	0.016	0.09		0.214
2072–2100 a	150	2.74	0.006	0.08	2079	0.035
2024–2053 b	278	5.02	0.000	0.30	2037	0.000
2047–2076 b	317	5.68	0.000	0.35	2061	0.000
2072–2100 b	344	6.15	0.000	0.42	2084	0.000
Air temperature
1972–2023	680	5.21	0.000	0.41	28	0.000
1994–2023	201	3.57	0.000	0.49	20	0.007
2024–2053 a	225	4.00	0.000	0.28	11	0.007
2047–2076 a	124	2.19	0.028	0.14		0.195
2072–2100 a	155	2.75	0.006	0.14		0.077
2024–2053 b	281	5.00	0.000	0.49	11	0.000
2047–2076 b	298	5.30	0.000	0.55	14	0.000
2072–2100 b	343	6.10	0.000	0.67	13	0.000

^a SSP245; ^b SSP585.

). Over the last 30 years, the thermal changes in the waters of Lake Miedwie were even greater, at 0.31 °C per decade (statistically significant, p 0.05). In the same period, the recorded increase in air temperature was 0.41 °C per decade (p 0.05).

3.2. Future Water Temperature

The analysis of the bias-corrected outputs compared to the observed temperatures for the period 2015–2023 demonstrates the effectiveness of the bias correction method applied in this study. The plot compares observed temperatures (black line, Figure 2) with bias-corrected GCM outputs for both scenarios SSP245 and SSP585. Several statistical metrics, including the correlation coefficient, Root Mean Squared Error (RMSE), and Mean Absolute Error (MAE), were used to evaluate the performance of the corrected data.

The spatial resolution of the GCMs used in this study, with a grid cell size of approximately 100 km, poses a limitation when studying Miedwie Lake, which has a size of about 10 to 20 km. This coarse resolution leads to the loss of fine-scale spatial details and the inability to accurately represent the lake’s dynamics and surrounding microclimate, potentially resulting in errors in temperature, precipitation, and other climate-related variables. The resolution of GCM outputs can be improved through dynamical downscaling based on Regional Climate Model (RCM) methods; however, these methods are computationally demanding and complex. Generally, RCMs can provide more detailed data and offer higher resolution. However, they are computationally intensive and require significant resources, making them less feasible for extensive temporal and spatial studies [47]. In order to address these constraints, we implemented a bias correction methodology that was inspired by the methodologies outlined by Hawkins et al. [39] and Ho et al. [40]. Bias correction methods are advantageous in this context because they can effectively adjust systematic biases in GCM outputs without the need for high computational resources [48,49]. This method aligns the GCM outputs more closely with observed data by adjusting both the mean and temporal variability. The efficacy of this methodology is illustrated by statistical metrics: the correlation coefficients for SSP245 and SSP585 are 0.79 and 0.77, respectively, indicating a robust positive correlation between the observed and corrected temperatures. The RMSE values for SSP245 and SSP585 are 6.28 and 6.62, respectively, indicating that the corrected outputs closely align with the observed data. Additionally, the MAE values for SSP245 and SSP585 are 4.95 and 5.17, respectively, further corroborating the accuracy of the bias-corrected data. Future research could explore advanced downscaling techniques, high-resolution models, and integrated approaches that combine multiple methods to maximize data accuracy and resolution.

Further analysis is based on the prediction of future climate changes (until the end of the 21st century) related to air temperature. Two commonly considered scenarios were adopted: SSP245 and SSP585. The study of the directions and pace of changes in water temperature of the analyzed lake is presented in Table 4. The data analysis was divided into three 30-year periods: near, mid, and far future (Figure 3). The results indicate that under the SSP245 scenario, an increase in water temperatures in Lake Miedwie is still projected, but the changes are expected to decrease over successive 30-year periods, amounting to 0.17, 0.09, and 0.08 °C per decade respectively. Considering the SSP585 scenario, an acceleration in the warming of the lake’s waters is expected in subsequent 30-year periods. For the period 2024–2053, the increase in water temperature at Lake Miedwie is forecasted to be 0.30 °C per decade. In the following 30-year periods, 2047–2076 and 2071–2100, the rate of change will be higher than in the last three decades (1994–2023), amounting to 0.35 and 0.42 °C per decade, respectively. Similar trends are observed for air temperatures. Assuming the SSP245 scenario, it is predicted that the pace of increase in air temperatures will be at a lower level than what occurred in the years 1994–2023 (Table 4). However, under the SSP585 scenario, the rate of increase in air temperatures in the near, mid, and far future will be higher than that observed in the years 1994–2023. Furthermore, the rate of change in air temperatures in subsequent 30-year periods is expected to increase.

3.3. Application of Satellite Images in Water Temperature Analysis

In the next phase, an attempt was made to use satellite images to reconstruct water temperatures in Lake Miedwie using data recorded by Landsat satellites 4, 5, 7, 8, and 9. For the period from April to October (ice-free) from 1984 to 2023, 682 observations were collected. After filtering using historical daily minimum and maximum temperatures, 511 observations remained for analysis. Comparing these results with in situ measurements (from the period 1984–1989) and results from the air2water model (from the period 1990–2023), deviations ranged from −4.9 to 5.2 °C. The RMSE value was 2.41 °C, MAE was 2.04 °C, and the coefficient of determination was 0.84 (Figure 3a). Using the SMW algorithm and code developed by Ermida et al. [27] and performing filtering based on long-term data for the reference Lake Lubie (as above), 516 observations remained for analysis. Comparing these results with in situ measurements (from the period 1984–1989) and results from the air2water model (from the period 1990–2023), deviations ranged from −5.5 to 4.9 °C. The RMSE value was 2.28 °C, MAE was 1.88 °C, and the coefficient of determination was 0.83 (Figure 4b).

The spatial variability in surface water temperatures in 2022, from April to October, is presented in Figure 5.

These results show that the surface water temperature in Lake Miedwie exhibits relatively low spatial variability in subsequent months. In the year analyzed, the water temperature within the reservoir ranged from approximately 3.5 °C to 27.8 °C. The relative homogeneity of the surface water temperature is due to the shape and catchment conditions. In the first case, there are no bays where water could heat up more quickly. Additionally, the absence of obstacles such as peninsulas means that water circulation evens out the thermal characteristics of the surface layer of water. Regarding the catchment conditions, it should be noted that the lake is not fed by a river with a high flow rate, which would alter the thermal system in the area of its mouth. Nonetheless, slight differences are visible (April, June), where the shallowest zones are characterized by higher water temperatures than the central sectors of the lake.

4. Discussion

The ability to interpret long-term, and therefore reliable, changes that various components of the natural environment undergo requires the most accurate data possible. This becomes particularly significant in the era of global warming for assessing the scale of current and future transformations. According to Obrębska-Starkel and Starkel [50], direct data provide the most accurate information about climate changes. However, it is not always possible to rely on such compilations, which can be supplemented by various methodological approaches. Rapid progress in the field of modeling and the continuous development of remote sensing techniques create new possibilities for interpreting hydrological processes. This approach was used for one of the largest lakes in Poland, where field measurements of water temperature were completed in the late 1980s. The results obtained in the study enrich the widely developed contemporary research direction concerning changes in the thermal regime of lakes. Referring to specific situations, it was noted, for instance, that in the case of Lake Nam Co (China), the water temperature during the summer increased by 0.52 °C per decade, and at the same time, the onset of stratification accelerated and its duration extended [51]. Between 1984 and 2019, two morphometrically different lakes in Italy showed an increase in water temperature by 0.05 °C/year (Lake Bracciano, larger and deeper) and 0.06 °C/year (Lake Martignano, smaller and shallower) [52]. The largest of the lakes in Poland (Śniardwy Lake), over the last five decades, experienced a temperature rise of 0.44 °C per decade [53]. In this context, Lake Miedwie is similar, i.e., from 1972 to 2023 (during which period there were stationary measurements and taking into account model data based on air temperature), there was a statistically significant increase in average annual water temperature, at a rate of 0.20 °C per decade. At the same time, it can be observed that despite maintaining a uniform direction of changes similar to that of Lake Śniardwy, the scale is lower. This difference may result from the morphometry of both lakes, with Miedwie being significantly deeper (the average depth is 5.8 m and 19.3 m, respectively). The inflow of cooler water masses from the extensive hypolimnion zone may cause the observed difference. Such a situation has been presented, among others, in the case of Lake Hańcza (the deepest in Poland), where the rate of water temperature increase was lower compared to other cases [54].

The approach based on satellite imagery in the considered case yielded worse results than modeling using the air2water model. It can be therefore said that with access to appropriate input data, i.e., continuous recordings of air temperature as a variable explaining water temperature trends, the use of such methodology is more justified. Nonetheless, it is important to emphasize that in the absence of reliable data, namely data related to areas not covered by any field observations (including mountainous areas), satellite data are crucial for understanding the thermal conditions of lakes [55,56,57]. Another issue is the impact of local conditions on the thermodynamics of lakes, where air–water relationships can be obscured by the morphometric parameters of the lakes or their watershed characteristics [58]. Furthermore, issues of spatial variability in water temperature are significant, where point field measurements may not reflect the dynamics of changes within a single lake. For example, such an illustration for Lake Drawsko (located 85 km from Lake Miedwie) showed significant spatial variability, with the warmest water in narrow, sheltered bays. In the case of Lake Miedwie, its relatively compact shape (without bays and peninsulas) influenced the absence of major thermal contrasts in different months (Figure 5).

The rapid progress of civilization necessitates a priority understanding of future changes, which also pertains to aquatic ecosystems. So far, studies on this matter do not look optimistic, and the recorded increase in water temperature is evident. By the end of the 21st century, the water temperature in Southeast Asian lakes will rise by 0.38 °C in the best-case scenario, while the most extreme simulation indicates an increase of 2.29 °C [59]. Lake temperature projections are based on one-dimensional, vertically resolved hydrodynamic simulations for 29 lakes. A prediction of water temperature for 29 lakes in Switzerland by the end of the 21st century showed an average increase of 3.3 °C (RCP8.5) [60]. Referring to predictions of water temperature changes in Lake Miedwie, two commonly used scenarios were applied (SSP245 and SSP585). According to them, the analyzed lake will be warmer by the end of the 21st century (compared to the initial period of study) by an average of 1.8 °C and 3.2 °C, respectively. Piccolroaz et al. [61] conducted studies for 25 lakes and found that the average increase in water temperature in the discussed region will be 0.15 °C/decade in the case of the RCP4.5 pathway and 0.34 °C/decade for the RCP8.5 pathway. Therefore, in the first case, Lake Miedwie achieved the same result, and in the second, it is lower, which may be due to the presence of shallower lakes in the set analyzed by Piccolroaz et al. [61]. In the case of polymictic lakes, due to multiple circulations, the water exhibits similar thermal characteristics from the surface to the bottom. The SSP585 pathway shows a continuous increase in temperature (Figure 3b), consequently leading to greater differences between shallow and deep lakes.

These are therefore significant changes in the thermal regime that will be reflected in the course of most processes occurring in the lake. As noted by Chen et al. [62], water temperature is a fundamental parameter of water quality in lakes and reservoirs. Water quality issues are particularly important for Lake Miedwie given that it serves as a source of drinking water for Szczecin. As Stepanowska et al. [63] note, Lake Miedwie was classified as eutrophic at the turn of the 20th and 21st centuries and has been classified as mesotrophic in recent years. Wilmański [64] addresses plankton issues, noting that current blooms are less intense. Maintaining the lake’s waters in a mesotrophic state depends on maintaining the appropriate level of various components that determine water quality. According to the data obtained, meeting such conditions will be more difficult in the future due to changes in one of the fundamental characteristics of water, namely its temperature. For example, based on the RCP4.5 scenario, an analysis of water temperature changes in the case of Fairy Lake (USA) showed that there will be an extension of the duration of cyanobacterial blooms by more than 39% [65]. Simulations of changes in water temperature and dissolved oxygen in the case of Lake Mississippi show that an increase in the former by 9.2% and 18.4% (RCP4.5 and RCP8.5) will be noticeable alongside a decrease in oxygen by 6.2% and 14.3%, respectively [66]. Reduced oxygen levels will impact the limited possibilities for the oxidation of organic matter [67]. In this light, the institutions managing Lake Miedwie will face new challenges, where alongside actions aimed at reducing pollution at the watershed level, it will be necessary to consider threats to water quality on a macroscale level—associated with progressing global warming.

5. Conclusions

The article reconstructs and subsequently predicts changes in the water temperature of one of the largest lakes in Poland, Lake Miedwie, for which stationary measurements had ceased over 30 years ago. Utilizing contemporary models that define the interaction between water and the atmosphere, as well as thermal satellite imagery, it was possible to obtain results characterizing the thermal regime of Lake Miedwie, including an analysis of long-term changes. Using field measurements of water temperature and subsequently modeling results based on air temperature and Landsat images (1972–2023), it was determined that over the past five decades, the analyzed lake has been warming at an average rate of 0.19 °C per decade. Further analysis concerning future changes indicated that the increase in water temperature by 2100 will average 0.15 °C per decade (SSP245) and as much as 0.25 °C per decade (SSP585). Both contemporary and projected future changes are significant, which, given the fundamental importance of water temperature, will impact the ecosystem discussed in the article. Given that Lake Miedwie serves as a source of drinking water, issues concerning the maintenance or improvement of water quality in the era of global warming will be crucial for water management authorities.