# Predicting surface temperature in Lake Villarrica (Chilean Patagonia) using a long short-term memory model

Lien Rodríguez-López, David Bustos Usta, Lisandra Bravo Alvarez, Iongel Duran-Llacer, Luc Bourrel, Frederic Frappart, Roberto Urrutia

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Lien Rodríguez-López, David Bustos Usta, Lisandra Bravo Alvarez, Iongel Duran-Llacer, Luc Bourrel, et al.. Predicting surface temperature in Lake Villarrica (Chilean Patagonia) using a long short-term memory model. Scientific Reports, 2025, 15 (1), pp.40091. 10.1038/s41598-025-23937-5. hal-05533354

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# Predicting surface temperature in Lake Villarrica (Chilean Patagonia) using a long short-term memory model

Lien Rodríguez-López<fnref n="1" />✉, David Bustos Usta², Lisandra Bravo Alvarez³, Longel Duran-Llacer⁴,⁵, Luc Bourrel⁶, Frederic Frappart⁷ & Roberto Urrutia⁸

In this study, we analyze water-temperature time series was measured over 34 years, between 1986 and 2020, at the water surface at seven stations across Lake Villarrica (Southern Chile). The spring and summer seasons show an increment in the superficial temperature during the study period. The annual maximum temperature, ranging between 17.35 and 21.65 °C were observed in 1997 and 2009, respectively, while the annual minimum, ranging between 16.8 and 21.5 °C were observed in 2001 and 2009, respectively. In addition, we employ a machine learning based estimation model to predict surface temperatures in a South American lake spanning the period 1989 to 2021. Our model uses data in situ of physical, chemical, and biological parameters of lake quality water, along with meteorological data and spectral bands, including combinations of images from the Landsat 8 satellite, as input variables. The 7 lake monitoring stations were classified into 4 regions according to their geographical location: north, south, east, and west. Our findings demonstrate the exceptional performance of the long short-term memory (LSTM) model in accurately estimating temperatures across Lake Villarrica. The best results were obtained for the west region of the lake with good statistical metrics from the estimation model of RMSE = 2.79, Bias = -0.06, max error = 5.93, MSE = 7.83 and median absolute error (MedAE) = 2.13. This approach represents a significant advance in the integration of remote sensing and machine learning techniques to monitor and manage inland water systems.

**Keywords** Aquatic ecosystem, Remote sensing, Machine learning, Long short-term memory model

Climate change is causing a global increase in temperature, with significant consequences for both natural ecosystems and human societies<fnref n="1" />,². The Intergovernmental Panel on Climate Change (IPCC) has reported that the Earth's average surface temperature has already increased by approximately 1 °C (1.8 degrees Fahrenheit) compared to pre-industrial levels and is projected to increase further in the coming decades³,⁴. This temperature increase is mainly due to the accumulation of greenhouse gases, such as carbon dioxide, in the Earth's atmosphere due to human activities such as fossil fuel burning and deforestation⁵,⁶. The effects of this temperature increase include more frequent and severe heat waves, changes in precipitation patterns, sea level rise, and more intense storms⁷,⁸. These changes are already affecting communities around the world and are likely to have even greater impacts in the future.

Temperature plays a crucial role in the processes that take place in a lake, affecting everything from water circulation to the growth of aquatic organisms⁹,¹⁰. Temperature influences the physical properties of water, such

<footnote n="1">¹Facultad de Ingeniería, Universidad San Sebastián, Lientur 1457, Concepción, Chile. ²Facultad de Oceanografía, Universidad de Concepción, Concepción 4030000, Chile. ³Department of Electrical Engineering, Universidad de Concepción, Edmundo Larenas 219, Concepción 4030000, Chile. ⁴Escuela de Ingeniería en Medio Ambiente y Sustentabilidad, Escuela de Ingeniería Forestal, Facultad de Ciencias, Ingeniería y Tecnología, Universidad Mayor, Camino La Pirámide 5750, Santiago 8580745, Chile. ⁵Hémera Centro de Observación de la Tierra, Escuela de Agronomía e Ingeniería Forestal, Facultad de Ciencias, Ingeniería y Tecnología, Universidad Mayor, Camino La Pirámide 5750, Huechuraba 8580745, Chile. ⁶Géosciences Environnement Toulouse, UMR 5563, Université de Toulouse, CNRS-IRD-OMP-CNES, 31000 Toulouse, France. ⁷UMR 1391 INRAE, Bordeaux Sciences Agro, UMR 1391, 33140 Villenave- d'Ornon, France. ⁸Facultad de Ciencias Ambientales, Universidad de Concepción, Concepción, Chile. ✉email: lien.rodriguez@uss.cl</footnote>
as its density, viscosity, and thermal conductivity, which in turn affect the movement of water within the lake<sup>11,12</sup>. In addition, temperature influences the rates of biological processes, such as photosynthesis, respiration, and nutrient uptake, which are vital for the growth and survival of aquatic organisms<sup>13</sup>. Thus, changes in temperature can have significant impacts on the ecology of a lake, with consequences for the entire food web.

In addition, the temperature is a critical factor influencing primary productivity, which is the rate at which plants and other photosynthetic organisms produce organic matter through photosynthesis<sup>14,15</sup>. This process is the basis of all life on Earth, as it provides the energy and nutrients needed for the growth and survival of higher trophic levels<sup>16</sup>. The rate of primary productivity is strongly influenced by temperature, as warmer temperatures generally lead to higher rates of photosynthesis. Understanding the role of temperature in these processes is critical to managing and protecting freshwater resources.

Remote sensing methods have revolutionized the way lake surface water temperature (LSWT) is measured, allowing large-scale, non-invasive monitoring of aquatic systems<sup>17,18</sup>. A widely used remote sensing technique for measuring water surface temperature is thermal infrared remote sensing in passive sensors<sup>19,20</sup>. It consists of using a sensor to measure the thermal radiation emitted by the water surface, which is proportional to its temperature. This method can be carried out from the air, with airplanes or drones equipped with thermal cameras, or from space, with satellites equipped with thermal sensors. In addition, some satellites are equipped with microwave radiometers, which can measure water surface temperature from their microwave emissions<sup>21</sup>. Remote sensing methods offer several advantages over traditional methods, such as the ability to monitor large areas of water over time, without the need for physical contact with the water<sup>22,23</sup>.

There are several satellite-based platforms that measure the surface temperature of aquatic systems using algorithms. Among the most widely used are the Moderate Resolution Imaging Spectroradiometer (MODIS)<sup>23,24</sup>, the Landsat Thermal Infrared Sensor (TIRS)<sup>25,26</sup>, and the Visible Infrared Imaging Radiometer Suite (VIIRS)<sup>27,28</sup>. The algorithms used by each platform are slightly different, resulting in variations in accuracy and precision. In general, the choice of satellite platform depends on the specific needs of the user, such as the desired spatial and temporal resolution, as well as the environmental conditions of the aquatic system under study<sup>29</sup>. Regardless of the platform used, remote sensing provides a powerful tool for monitoring and managing aquatic systems, allowing researchers and managers to make more informed decisions about the health and sustainability of these important resources. The objective of this work is to analyse the spatial and temporal trends and behavior of the surface temperature of Lake Villarrica, in southern Chile, between 1986 and 2020, using Landsat satellite imagery and the LSTM estimation model. This research will contribute to providing useful data on the effects of climate change in Chilean lakes.

## Materials and methods

### Site description

Lake Villarrica is a large lake located in southern Chile, specifically in the Araucanía Region, between the Andes Mountains and the Coastal Range (Fig. 1). It has an approximate surface area of 174 km² and is located 227 m above sea level<sup>30</sup>. Its shape is elongated, with an approximate length of 22 km and a maximum width of about 8 km<sup>31</sup>. Its coastline is irregular and is marked by numerous bays, inlets, and islets. It is fed by several rivers, such as the Toltén, the Liucura and the Trancura, and its waters flow into the Pacific Ocean. The main morphological parameters of Lake Villarica are summarized in (Table 1). The landscape surrounding the lake is characterized by the presence of volcanoes, the Villarrica volcano being the most prominent. The volcano is an active stratovolcano, with a height of 2847 m, and is located on the eastern shore of the lake<sup>32</sup>. The Villarrica volcano is known for its frequent eruptions, which have resulted in the formation of a crater lake at the top of the volcano. The area surrounding Lake Villarrica is covered by dense forests, composed mainly of native trees such as araucaria, coigue and lenga. The lake is also surrounded by a varied flora and fauna, including several species of fish, birds, and mammals, such as the pudú, a small deer endemic to southern Chile. In general, Lake Villarrica and the surrounding landscape are characterized by their natural beauty and unique geological features, making it a popular destination for tourists and lovers of outdoor activities<sup>33,34</sup>.

### In situ data

In situ measurements in the period 1986–2020 were carried out in several monitoring campaigns of the Chilean General Directorate of Water through the free web-based hydrometeorological service available online (http://www.dga.cl/servicioshidrometeorologicos/access) (accessed 20 January 2024). The first was reported in "Redefinición de la red mínima de lagos" by POCH AMBIENTAL S.A. in the study "Informe final n° 1. Analysis of phytoplankton in water samples. Tender N° 1019-98-LE13". The second was reported in the study "Analysis and reformulation of the monitoring network of the river lakes region" (DGA, 2020), and the third was carried out by the Eula Center in 2021. This downloadable database is available for 16 lakes that are part of the Minimum Lake Network (RML), in which Lake Villarrica is included. From it, Secchi disk depth (SD), chlorophyll a (Chl-a), surface temperature (°C), dissolved oxygen (OD), phosphorus and nitrogen total (PT and NT respectively), conductivity (Conduct) and turbidity (NTU) were obtained at 7 sampling stations (V1-V7). The monitored parameters were surface temperature (thermometry 2250 B standard methods 22 Ed, method used as a reference for temperature analysis according to the NCh 2313 compendium), surface Chl-a (fluorometric method), determination of total phosphorus (4500 P B Standard Methods 22 Edit. EAM), determination total nitrogen (4500-N C Standard Methods 22 Edit-EAM) and transparency (measured by SDD). At each of the lake stations, water samples were collected at 5 depths using a 5 L Niskin sampling bottle. Niskin 5 L sampling bottle. Samples were stored and transported in thermally insulated boxes, properly cooled with ice at a temperature of approximately 5 °C for subsequent analysis. Chemical analyses were performed at the chemistry laboratory of the Dirección General de Aguas de Chile (DGA). This laboratory is accredited by the Instituto Nacional de Normalización (National Standards Institute) for the Chilean Standard NCh ISO 17.025 of 2005.
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Study area. (A) Lake Villarrica; (B) Chile in South America continent and (C) IX Araucanian Region in Chile. Source: Created for authors using free software QGIS version 3.40 (https://qgis.org/).</figcaption></figure>

<table><caption>**Table 1.** Morphometric parameters that influence LSWT: location, elevation, surface area, perimeter, volume, mean depth, and maximum depth.</caption><thead><tr><td>Parameter</td><td>Unit</td><td>Villarrica</td></tr></thead><tbody><tr><td>Latitude</td><td>°</td><td>39°18'S</td></tr><tr><td>Longitude</td><td>°</td><td>72°05'</td></tr><tr><td>Altitude</td><td>m.a.s.l</td><td>250</td></tr><tr><td>Max. length</td><td>km</td><td>23</td></tr><tr><td>Max. width</td><td>km</td><td>11</td></tr><tr><td>Avg. width</td><td>km</td><td>7.6</td></tr><tr><td>Perimeter</td><td>km</td><td>71</td></tr><tr><td>Surface area</td><td>km²</td><td>176</td></tr><tr><td>Max. depth</td><td>m</td><td>165</td></tr><tr><td>Avg. depth</td><td>m</td><td>120</td></tr><tr><td>Volumen</td><td>km³</td><td>20,9</td></tr><tr><td>Drainage Area</td><td>km²</td><td>2884,15</td></tr><tr><td>Avg. drainage/surface area</td><td></td><td>16.4</td></tr><tr><td>Renovation Time</td><td>years</td><td>4</td></tr></tbody></table>
## Landsat satellite images

### Preprocessing satellite images

This study used 25 Landsat 8 Collection 2 Level 1 images (L8, C2-L1) (see Table S1). The bands of the visible and infrared spectrum (Blue-B, Green-G, Red-R, Near Infrared-INR, Short Wavelength Infrared-SWIR1) were used from the Operational Land Imager (OLI) sensor at a spatial resolution of 30 m, and the thermal bands (TIRS 1, TIRS2) were used from the Thermal InfraRed Sensor (TIRS) at 100 m spatial resolutions. The images were downloaded from the Earth-Explorer site (https://earthexplorer.usgs.gov/), from United States Geological Survey (USGS). Landsat 8 was developed in collaboration with National Aeronautics and Space Administration (NASA) and the United States Geological Survey (USGS). The study area of interest (Roi) was covered by trajectories 232/233 and row 87 of the imagery. The selected images met certain criteria, including low cloud cover (less than 12%) and proximity to the sampling date (within ±9 days of satellite overpasses). Quality assessment (QA) bands were used to mask clouds, shadows, and cirrus clouds. Only cloud-free areas were included in the analysis.

To atmospherically correct images, the ACOLITE program (version 20211124.0) was used. ACOLITE incorporates atmospheric correction protocols and processing software developed at RBINS for water remote sensing applications. Dark Spectrum Fitting (DSF) and Exponential Extrapolation (EXP) algorithms were used for atmospheric correction for the bans of visible and infrared spectrum. The resulting values represent the surface level reflectance (ps) for L8. X-Y band values were then extracted into a 3 × 3-pixel matrix. The lake contour was established using geospatial information obtained from the Dirección General de Aguas de Chile (DGA). Only the water body was considered for the analysis. In the case of thermal bands, they were also corrected in ACOLITE but using the Thermal Atmospheric Correction Tool (TACT). TACT is the thermal atmospheric correction tool for Landsat developed at RBINS. Retrieves ERA5 atmospheric profiles and uses libRadtran to calculate atmospheric transmittance and ascending and descending radiances. Currently, TACT generates the water surface temperature (WST) in each thermal band present in the Landsat sensor, assuming a constant (water) emissivity over the scene. This methodology can be consulted in detail in³⁵.

## Data processing and feature engineering

Rows with more than 80% of features with null values were removed from the in-situ database water quality data. Therefore, the data cleaning process started with the detection of outliers, data integrity analysis and imputation of missing values.

The cleaning steps were:

(1) Eliminate non-numeric values for each of the selected variables and replace them with null values.

(2) Extract the year, month, and day of each measurement, verifying consistency and completeness.

(3) Apply a sensitive imputation for the null values in each column using a robust central tendency measure, the median.

(4) Construct monthly time series from 1997 to 2021 for each variable, ensuring continuous data periods. For this we implemented the Akima interpolation algorithm³⁶ for incomplete series. We ensure not include extrapolation issues by grouping stations into 4 groups: EAST (V6 and V7), WEST (V1 and V2), NORTH (V3), and SOUTH (V5), excluding V4 due to over 50% null values.

(5) Match-ups between in-situ data and satellite images were identified. A maximum time lag of 9 days was considered. The match-ups identified are listed in (Table 2). Subsequently, satellite ratio variables and satellite intensity bands were added as a new data matrix.

(6) Create correlation matrices ( heatmaps) to identify variables significantly correlated with surface Temperature (ST). Results encompass the four variable groups: Atmospheric, meteorological, satellite ratio, and band intensity variables. Only significant variables were considered for the LSTM models.

(7) Split the data for test validation and training. Of the total of all measurements, the first 70% collected (training period) at each sampling station over time were selected for training and the remaining 30% (validation period) for testing in each group of stations (Table 2). A 5-fold cross validation is conducted only during the training period to tune hyperparameters, validate model performance, and prevent overfitting (see K-fold cross-validation section).

## LSTM models

Long short-term memory (LSTM) models are a type of recurrent neural network (RNN) that has been designed to handle the challenges of long-term dependencies in sequential data. Traditional RNNs can have difficulty retaining information over long periods of time, leading to the problem of vanishing gradients³⁷. This is where gradients in the backpropagation algorithm become very small as they are propagated through many time steps, making it difficult to update the weights of the network. LSTM models address this issue by introducing memory cells and gating mechanisms that allow the model to selectively remember or forget information over time³⁸.

<table><caption>**Table 2.** Train and test samples size for the LSTM training in the 4 groups of stations selected for the analysis.</caption><thead><tr><td>Group</td><td>Train size</td><td>Test size</td><td>Training period</td><td>Validation period</td></tr></thead><tbody><tr><td>South</td><td>172</td><td>74</td><td>Aug 1997 - Dec 2011</td><td>Jan 2012 - Jan 2018</td></tr><tr><td>North</td><td>189</td><td>81</td><td>Aug 1997 - Jan 2013</td><td>Feb 2013 - May 2019</td></tr><tr><td>West</td><td>189</td><td>81</td><td>Aug 1997 - Dec 2012</td><td>Jan 2013 - May 2019</td></tr><tr><td>East</td><td>189</td><td>81</td><td>Aug 1997 - Jan 2013</td><td>Feb 2013 - May 2019</td></tr></tbody></table>
Unlike standard recurrent neural networks, which can have trouble retaining information over the long term, LSTM networks are designed to be able to do so. They use a gating mechanism that allows them to control how much information they retain and how much they discard at each time step. In an LSTM network, each neural network unit has three main gates: the input gate, the forget gate and the output gate. These gates allow the network to decide what information to retain and what information to discard at each time step. The input gate decides what information is added to the network's short-term memory. The forgetting gate decides what information is retained in long-term memory and what information is discarded. Finally, the output gate decides what information will be used to make predictions or decisions at that point in time³⁹.

We applied a tanh activation function to scale values within a range of -1 to 1 and used the Adam optimizer during training. The input variables were constructed using the most recent lag (t-1) along with seasonal lags of 12 and 24 months (t-12, t-24) to explicitly incorporate both short-term dynamics and long-term seasonal patterns. The number of units in the LSTM layer was iteratively tuned based on RMSE and MSE performance metrics, resulting in the tailored unit allocations for each region: SOUTH (35), NORTH (40), WEST (30), and EAST (25). A dense layer was appended to the topology to generate final predictions. This configuration aligns with established architectures for time series forecasting using LSTMs⁴⁰. A schematic overview of the training structure is provided in (Fig. 2).

## Statistical analysis

A linear fit between Landsat and in situ data was performed following the methodology of²³. The adjustment was performed by the least squares to find the relationship between the water surface temperature acquired by processing Landsat images and in situ measured data.

The data were analyzed at three temporal resolutions: monthly, seasonal, and annual measured temperatures. To quantify estimation errors, basic statistical analyses such as the coefficient of determination (R²), root mean square error (RMSE) and mean absolute error (MAE) were used.

### K-fold cross-validation

After creating the models described in the section before, we had to determine the performance of each model. To this end, we applied the k-fold cross-validation (CV) method described by⁴¹, which is considered a statistical method to evaluate and compare algorithm performance by dividing data into two segments: one used for learning and the other to validate results without overlapping data instances between groups. We used the most applied alternative, known as k-fold, cross-validation with k = 5 folds⁴².

### Mann Kendall and Sen's slope tests

To analyze temperature and precipitation trends, the non-parametric Mann Kendall and Sen's slope tests were applied, which do not require a normal distribution and can be applied to time series⁴³⁻⁴⁵. The level of significance used in all tests was a p value < 0.05⁴⁶. The tests were applied to annual and seasonal precipitation, while temperature was only analyzed in summer and spring.

## Results

### Behavior of mean superficial temperature in the study period

The water-temperature time series measured over 34 years, between 1986 and 2020, at the water surface at seven stations across Lake Villarrica. Figure 3 shows the behavior of mean superficial temperature in all seasons of year. The spring and summer seasons show an increment in the superficial temperature during the study period. The annual maximum temperature, ranging between 17.35 and 21.65 °C were observed in 1997 and 2009, respectively, while the annual minimum, ranging between 16.8 and 21.5 °C were observed in 2001 and 2009, respectively. Furthermore, figure shows the behavior of the surface temperature for the period 1986-2009 in the autumn and winter seasons since the Dirección General de Aguas only conducted monitoring campaigns in these seasons during this period. The maximum temperatures were in the range of 18.0 and 10.10 °C in the autumn season and the minimum values moved in the ranges 10.10 and 6.33 °C in the winter season.

### Behavior of meteorological parameters

The behavior of the meteorological variables is shown in (Table 3). Observations made at Lake Villarrica between 2017 and 2021 reveal that the daily monthly mean photosynthetically active radiation (PAR) values were 677.04 mmol/m², ranging from a maximum of 1237.38 mmol/m² during summer (December) to a minimum of 181.04 mmol/m² in winter (June). Likewise, the monthly average daily temperature was 11.84 °C, with a maximum of 16.64 °C in summer (February) and a decrease to 7.39 °C in winter (July). Generally, cloudiness increases during the winter months due to the decrease in PAR and conversely decreases during the summer months. Average cloudiness in the area was 23.67%, with a maximum of 26.76% in winter (August) and a minimum of 17.37% in summer (February). According to hydrometric statistics, total precipitation during the study period was 6,210.0 mm.

Figure 4 presents a time series plots illustrating the interannual variability of temperature and rainfall during summer and spring from 1986 to 2020. During summer, temperatures range between 18 and 21 °C, while rainfall shows marked variability, with some years exceeding 350 mm. In spring, temperatures fluctuate between 11 and 17 °C, with rainfall reaching values as high as 900 mm in certain years. Both seasons exhibit considerable interannual variability, with no clear long-term trend, although warmer years often coincide with lower rainfall, suggesting potential inverse relationships in certain periods.

Trend analysis of non-parametric tests did not yield significant results. A statistically significant pattern could not be found because the p-values were greater than the level of significance (> 0.27). It can only be mentioned that rainfall in summer and spring showed a slight increase, this being not the case for the annual values and the
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Schematic representation of LSTM structure for the training in the regions defined (section X). Xs represent the independent variables including a near lag (Xt-1) and two seasonal lags (X t-12 and X t-24) and yt the dependent variable (ST) at the moment t. k = 11 indicates the number of variables (including independent and dependent outcome) and L the number of LSTM units for the training with four possible values SOUTH (35), NORTH (40), WEST (30), and EAST (25) according to the data complexity.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Temporal evolution of superficial temperature (minimum, average and maximum in dark orange, light orange, respectively) in Villarrica Lake during summer (top)/spring (bottom) from 1986–2020.</figcaption></figure>

<table><caption>**Table 3.** Meteorological and radiometric parameters.</caption><thead><tr><td>Month</td><td>T (°C)</td><td>WS (m/s)</td><td>RH (%)</td><td>Rain (mm)</td><td>PAR (mmol/m²)</td><td>Cloud (%)</td></tr></thead><tbody><tr><td>Jan</td><td>16.62</td><td>2.68</td><td>69.82</td><td>2521.7</td><td>1235.37</td><td>18.69</td></tr><tr><td>Feb</td><td>16.64</td><td>2.78</td><td>66.58</td><td>2164.8</td><td>1082.19</td><td>17.37</td></tr><tr><td>Mar</td><td>14.90</td><td>2.79</td><td>73.79</td><td>3397</td><td>764.56</td><td>20.47</td></tr><tr><td>Apr</td><td>11.83</td><td>3.33</td><td>84.08</td><td>5586.7</td><td>436.46</td><td>21.89</td></tr><tr><td>May</td><td>9.74</td><td>3.76</td><td>88.28</td><td>8888</td><td>249.21</td><td>22.91</td></tr><tr><td>Jun</td><td>7.90</td><td>5.32</td><td>86.29</td><td>13154.4</td><td>181.04</td><td>22.82</td></tr><tr><td>Jul</td><td>7.39</td><td>5.62</td><td>85.84</td><td>9508.2</td><td>220.51</td><td>24.87</td></tr><tr><td>Aug</td><td>8.16</td><td>5.82</td><td>84.41</td><td>9272.3</td><td>345.55</td><td>26.76</td></tr><tr><td>Sep</td><td>9.79</td><td>4.27</td><td>80.64</td><td>6181.5</td><td>550.76</td><td>25.48</td></tr><tr><td>Oct</td><td>11.23</td><td>3.65</td><td>78.03</td><td>5741.9</td><td>801.51</td><td>28.82</td></tr><tr><td>Nov</td><td>12.99</td><td>3.95</td><td>76.44</td><td>4174</td><td>1019.96</td><td>28.82</td></tr><tr><td>Dec</td><td>14.93</td><td>3.01</td><td>72.87</td><td>3929.3</td><td>1237.38</td><td>25.16</td></tr><tr><td>Total</td><td>11.84</td><td>3.92</td><td>78.92</td><td>6210.0</td><td>677.04</td><td>23.67</td></tr></tbody></table>

remaining seasons of the year. In relation to temperature, in summer there was a slight increase and in spring there was a slight decrease, but as they were not statistically significant, it cannot be said that there was a trend in the series.

Figure 5 displays four wind rose diagrams representing seasonal wind direction and frequency for winter, autumn, spring, and summer. It can be observed that the wind is well distributed between NNE and ESE in autumn and winter and has a speed greater than 5.82 m/s in winter. While in summer and spring the wind directions become more dispersed, indicating a more variable wind regime during these seasons. These seasonal differences reflect changes in regional atmospheric circulation throughout the year.
<figure><img src="image_6.png" /><figcaption>Fig. 4. Seasonal behavior of temperature and precipitation on lake Villarrica.</figcaption></figure>

## Pearson correlation matrix

Figure 6 shows four correlation matrixes between regressors and surface temperature. Results encompass the four variable groups: Atmospheric, meteorological, satellite ratio, and band intensity variables. Only significant variables were considered for the LSTM models. The best variables considered for the model were: Conductivity, Chl-a, Air Temperature radiation UV and PAR, INFR/R, INFR/G, G + R, G/R, B11 and B10. The variables were normalized to obtain a Gaussian probability distribution following a power transformation⁴⁷,⁴⁸.

## LSTM Estimation model

Figure 7 illustrates the behavior of estimated surface temperature (ST) across the four groups of stations throughout the study period. While the models capture the overall variability observed during the test period, the only drawback arises when attempting to reproduce peak values which are expected in high noise signals.

The error metrics from the LSTM models reveal distinctive performance characteristics across geographical groups of stations (Table 4). In the SOUTH group of stations, all the metrics are higher compared to the other groups of stations with RMSE = 5.25° C, Bias = 0.09° C, Max Error = 8.99° C, MSE = 27.65° C and Median Absolute Error (MedAE) = 4.13° C, indicating the lower prediction accuracy. Conversely, in all the remaining groups the error metrics are considerably lower with RMSE ranging from 2.79 and 3.41° C, Bias between -0.12 and 0.02° C, Max Error between 5.75 and 5.91° C and MedAE between 2.13 and 2.65° C, being the WEST region the best in performance. Overall, the LSTM model demonstrates controlled levels of accuracy across geographical regions, with a reliable performance considering the high variability in the time series.

## Discussion

LSWT is an essential climate variable that highlights regional weather and climate variability and trends. Temperature is a critical factor that significantly impacts various physical, chemical, and biological processes within aquatic ecosystems. Its influence extends to the solubility of gases, such as oxygen and carbon dioxide, which are indispensable for the survival of aquatic organisms. As temperature rises, the solubility of these gases decreases, resulting in warmer water containing less oxygen dissolved, thereby posing challenges for aquatic organisms' respiratory processes. Moreover, temperature dictates the pace of essential chemical reactions, including nutrient cycling, photosynthesis, and respiration. These reactions, in turn, dictate nutrient
<figure><img src="image_7.png" /><figcaption>Fig. 5. The wind rose in each season.</figcaption></figure>

availability, productivity levels, and decomposition rates within aquatic ecosystems, thus shaping food webs and biogeochemical cycles. In addition, temperature exerts a fundamental influence on the distribution and abundance of aquatic organisms. Various species of fish, invertebrates and algae have different temperature preferences for optimal growth and reproduction. Changes in temperature can alter the timing of life cycles, migratory patterns, and overall population dynamics of aquatic organisms. In addition, temperature influences the physical properties of water, such as density and viscosity, which in turn affect water movement and circulation patterns. These alterations in circulation subsequently influence the mixing of water masses, nutrient distribution, and overall ecosystem dynamics.

The analysis of surface temperature (ST) modelling based on LSTM network presents insightful findings. Results indicate that the model correctly captures the overall variability with problems only regarding peak values. Despite this limitation, the LSTM models exhibit promising performance across geographical regions, as evidenced by distinct error metrics showcased in (Table 4). Notably, in the SOUTH group of stations, all the metrics are higher, indicating the lower prediction accuracy signifying comparatively lower prediction accuracy. In all the remaining groups the error metrics are considerably lower with RMSE ranging from 2.79 to 3.41 °C, Bias between – 0.12 and 0.02° C, Max Error between 5.75 and 5.91 °C and MedAE between 2.13 and 2.65 °C, being the WEST region the best in performance. These results are correspondence with⁴⁹ where measured data from the monitoring station and the remote sensing satellite data as the data source and obtain similar results with relative root-mean-square error (rRMSE), and the mean relative error (MRE) values of 0.83, 0.16, and 0.18, respectively. However, in lake other variables were used like entrance variables of the LSTM model. While in⁵⁰ LSTM and XGBoost models used with the goal of predicting wave heights and periods in Lake Erie and⁵¹ used LSTM for Estimating Particulate Organic Carbon from Remote Sensing in Lakes.

In our study, overall, the LSTM model demonstrates controlled levels of accuracy across geographical regions, with a reliable performance considering the high variability in the time series. However, to improve the reliability of the model estimates through the combination of in-situ data, meteorological and satellite sources, it will be tested in other lakes in Chile for which data is available. In the future, the results of this study will be used to evaluate the effects of temperature on primary producers in the lake, specifically when algal blooms appear in the lake during the summer. In addition to its importance in ecological processes, temperature is also a key factor in water management and conservation. Changes in temperature can indicate changes in the hydrological cycle, such as alterations in precipitation patterns or alterations in river and stream flow. Temperature monitoring can help identify water quality problems, such as thermal pollution caused by human activities such as power plants and industrial processes. Therefore, understanding the role of temperature in aquatic systems is crucial for maintaining ecosystem health, conserving biodiversity, and implementing sustainable water management practices.
<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Correlation between regressors (Section X) and Surface Temperature (ST). Variables are grouped into Atmospheric (a), Meteorological (b), Satellite ratio (c), and satellite band intensity (d) categories, with red indicating higher positive and blue lower negative correlation values.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 7.** SST monthly real values and estimation across four groups of station (Sect. 2.5) using data from Villarrica Lake between 1997–2020. Training, Test and Predictions are in blue, orange and crimson respectively.</figcaption></figure>
<table><caption>Table 4. Validation metrics for all the four groups selected.</caption><thead><tr><td>Group/metric (°C)</td><td>RMSE</td><td>Bias</td><td>Max error</td><td>MSE</td><td>Medae</td></tr></thead><tbody><tr><td>South</td><td>5.25</td><td>0.09</td><td>8.99</td><td>27.65</td><td>4.13</td></tr><tr><td>North</td><td>3.08</td><td>0.02</td><td>5.75</td><td>9.51</td><td>2.65</td></tr><tr><td>West</td><td>2.79</td><td>-0.06</td><td>5.93</td><td>7.83</td><td>2.13</td></tr><tr><td>East</td><td>3.41</td><td>-0.12</td><td>5.91</td><td>11.69</td><td>2.34</td></tr></tbody></table>

## Conclusions

This study analyzed surface water temperature time series collected over 34 years (1986–2020) at seven monitoring stations across Lake Villarrica. Results indicate a warming trend during spring and summer, with notable increases in surface temperature over the study period. The annual maximum temperatures ranged from 17.35 °C (1997) to 21.65 °C (2009), while the annual minimum temperatures ranged from 16.8 °C (2001) to 21.5 °C (2009). Additionally, we used 25 Landsat 8 satellite images, in situ water quality data, and meteorological records to estimate lake surface temperature using a combined data-driven algorithm.

However, the study has some limitations. The temporal resolution of satellite data was constrained by cloud cover and the revisit time of Landsat 8, which limited the number of usable scenes. In situ measurements were not always taken simultaneously with satellite overpasses, which may have affected model accuracy. Furthermore, the model's performance varied spatially across the lake, suggesting that local environmental heterogeneity influences temperature estimations. Future work should focus on improving temporal alignment between satellite and in situ data, incorporating higher-resolution sensors or alternative satellite missions, and refining the model to better account for spatial variability in lake conditions.

## Data availability

Data is provided by the website of General Directorate of Water, Chile https://dga.mop.gob.cl/.

Received: 16 June 2025; Accepted: 9 October 2025

Published online: 17 November 2025

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## Acknowledgements

L.R-L thank to Fondecyt Iniciación 2025 Project ANID/11250177 and Project ANID/FOVI/240030 and thank to Vicerrectoría de Investigación y Doctorados USS. L.R.-L. and R.U are grateful to the Centro de Recursos Hídricos para la Agricultura y la Minería (CRHIAM) (Project ANID/FONDAP/15130015 and ANID/FONDAP/1523A0001).

## Author contributions

“Conceptualization, L.R-L.; methodology, L.R-L, D.B-U and I.D.; software, D.B-U, I.D and L.B-A.; validation, L.R-L and D.B-U.; formal analysis, L.R-L.; investigation, L.R-L.; resources, F.F, L.B and R.U.; data curation, D.B-U and L.B-A.; writing—original draft preparation, L.R-L.; writing—review and editing, L.R-L, D.B-U, L.B, F.F and I.D.; visualization, L.B-A and I.D.; supervision, R.U.; project administration, R.U.; funding acquisition, L.B. All authors have read and agreed to the published version of the manuscript.”

## Funding

Fondecyt Iniciación 2025 Project ANID/11250177 and Project ANID/FOVI/240030 and VRID USS.

## Declarations

### Competing interests

The authors declare no competing interests.

## Additional information

**Supplementary Information** The online version contains supplementary material available at https://doi.org/10.1038/s41598-025-23937-5.
**Correspondence** and requests for materials should be addressed to L.R.-L.

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