Thermal Regime and Water Balance of Two Tropical High-Mountain Lakes in the Nevado de Toluca Volcano, Mexico

Abstract

High-mountain lakes are unique ecosystems with very few examples at tropical latitudes for experimentation. A two-year, high-frequency meteorological and water-column dataset from the crater of the Nevado de Toluca volcano, in Mexico, at an altitude of about 4200 m above sea level, allowed for the study of temporal changes in the thermal structure, water level, and water balance in the Lakes El Sol and La Luna, separated by about 500 m by a lava dome. Annual fluctuations in the water level of the lakes and calculations of the annual variability of the water balance showed that the lakes accumulated almost four times less water from rainfall than expected. Furthermore, the temperature measured at a depth of 15 cm in the bottom sediments of Lake El Sol revealed an unexpected warming during the cold season. Estimated heat fluxes through the lake bottom were less than 0.3 W m⁻² during the winter and less than 0.1 W m⁻² during the rest of the year. Although the variability of the hydrometeorological regime of high-mountain lakes remains relatively poorly understood, our results significantly improve the understanding of these complex processes of stratification and mixing in these unique lake ecosystems.

1. Introduction

High-mountain lakes (HML) occur above the tree line [1]. The altitude at which the tree line is observed depends on the latitude, and it occurs at higher altitudes at lower latitudes [2,3]. Mountain lakes share many features, regardless of their latitude, including catchments with steep topographic gradients, cold temperatures, and high-incident solar and ultraviolet radiation (UVR) [4,5].

Warming above the planetary average associated with climate change is higher in mountain areas, and warming rate increases with elevation. High-mountain areas experience more rapid changes in temperature than environments at lower elevations [5,6,7], and for that reason, HML are useful sentinels of global change effects, particularly those located in remote areas with limited direct human influence [8,9]. Moreover, variation in lake water level can be directly associated with the precipitation/evaporation relationship present in the lake basin [10,11,12].

Most studies on HML have focused on temperate mountain ranges with limited information from tropical systems in the literature. Tropical HML occur predominantly in the Andes, and to a lesser extent in East Africa [13,14]. The main distinction between temperate and tropical HML arises from the seasonal patterns of heat exchange and the external loadings [15], with notable water-column mixing and stratification differences. Tropical lakes are generally more sensitive than temperate lakes to environmental alterations. For example, nutrient-load increases can lead to rapid eutrophication, reduction of water quality, and loss of deep-water dissolved oxygen concentration, all of which affect aquatic biota. The differences between the limnology of temperate and tropical lakes might require different conservation strategies and are important to consider in management plans [16].

Due to the lower latitude and their high altitude, tropical HML are exposed to intense solar and UV radiation [17]. The water temperature distribution of any lake is directly controlled by solar radiation and is one of their most basic intrinsic characteristics. The upper two-meter water layer absorbs over one-half of incoming radiation, while light energy decreases exponentially with increasing water depth [18,19]. In tropical areas, the heat balance in a lake is driven principally by daily variations.

Although the impacts of local climatic conditions and complex topographical conditions on the physical behavior of lakes has been studied in general [20,21,22,23,24], there are only a few studies [25] exploring the effects of meteorological parameters on tropical HML. There are only two tropical HML in Mexico: El Sol and La Luna, both within the crater of the Nevado de Toluca volcano. The geochemistry and biology of these lakes have been studied with much less attention paid to their physics [26,27,28,29,30,31]. Recent research [25,32] shows alternating patterns of heating and cooling for ~30 days during the warmest months related with the solar irradiance reaching the lake surface. However, despite being within the same crater and very close to each other (about 500 m), these lakes show significantly different thermal responses. Lake El Sol has a discontinuous warm polymictic regime where, between each heating and cooling episode, it develops a stable mixed layer and a deeper layer separated by a weak thermal gradient. Lake La Luna also showed the same heating and cooling cycle, but it mixes and stratifies daily and not over multiple days, showing a continuous warm polymictic regime [32].

Barba-López et al. [25] used long-term time series of meteorological and water-column parameters to study the dynamics of these two HML, showing that the wind regime and solar radiation are different when measured on the outer slope of the volcano versus inside the crater, where Lake El Sol is located. At the center of the volcanic crater, the wind speed weakens, the wind direction changes, and the solar radiation is reduced by almost 20% [25]. Soto et al. [33] showed that topography affects climatic conditions by using climate series in the Nevado de Toluca volcano area. These findings highlight the relevance of studying the spatial–temporal variation of temperature, precipitation, evaporation, and wind inside the volcano to understand how these factors affect the thermal and hydrodynamic behavior of the lakes [25].

The aim of the current study was to reveal how prevailing climate variability affects the hydrophysical behavior of the lakes, including temporal changes in the thermal structure, water balance fluctuations, and surface currents, from more accurate in situ data and a numerical simulation for the last two parameters. We use a continuous two-year dataset of water-column temperature as the basis for analyzing the thermal structure dynamics from the surface to the bottom of both lakes and the water balance in Lake El Sol. A further goal was to explore the thermal interactions between the sediments and the bottom water layer.

We show that in Lake El Sol, similar to shallow lakes of middle latitudes [34], there is an exchange of heat between the bottom sediments and the water bottom layers of water. In winter, heat is transferred from bottom sediments to the water layers, and in summer, heat is accumulated in sediments. Herein, temperature fluctuations in the bottom water layers of a shallow crater lake have been measured for the first time, providing critical new information on bottom stratification and its effect on lake mixing.

2. Study Area

Lakes El Sol and La Luna are in Central Mexico (19°06″ N, 99°45″ W, 4200 m above sea level, see Figure 1). Average monthly mean temperatures ranged between 2.8 °C in February and 5.8 °C in April, with an annual mean temperature of 4.2 °C. Total annual precipitation is 1243.5 mm, ranging from 17.2 mm in December to 270 mm in July [26]. The waters of these two lakes are transparent and cold. Their highest temperatures (~11 °C) occur in the warm, rainy season, and are lowest in the cold, dry winter (~4 °C). Both lakes are well-oxygenated, with concentrations close to saturation (~7 mg/L) throughout the entire water column [10,31]. They are well-mixed lakes with a warm polymictic regime [25,32]. Both lakes have an acidic pH (4.9–5.6) and reduced buffering capacity. Their conductivity is low (18–24 µS/cm) with low dissolved and suspended organic matter [26,28].

The volcano inner slopes are shaped like a horseshoe around the two lakes in the center, where there is a circular lava dome rising almost 115 m above the lakes, separating them. The western slope of the crater is about 345 m higher than its lower eastern part, through which wind currents can enter the crater.

The hydrological parameters for Lakes El Sol and La Luna, according to Filonov et al. [35], are described in Table 1.

3. Data and Methods

3.1. Field Measurements

3.1.1. Floating Weather Station

Previous measurements [25,35] suggested an issue with estimating the wind direction and speed within the volcano crater associated with the presence of the lava dome in the center of the crater preventing their accurate estimations. In this study, we used a novel approach to avoid this issue by installing a floating weather station at the center of Lake El Sol.

The floating weather station was mounted on a metal pipe about 6 m long. The anemometer was at the upper end of the pipe, 2 m above the water level. The other end of the pipe was submerged in the water to a depth of 4 m with a 30-kg weight attached to the lower end (Figure 2). In the middle part, three buoys were attached to the pipe, keeping the station afloat. They were fixed by three ties preventing the station from horizontal oscillations and thereby avoiding errors in wind-direction measurement. Fifteen thermographs (HOBO © Water TempProV2, accuracy ±0.2 °C) were attached to the station. Two of them were above the water level (0.1 m and 2 m), and the other thirteen thermographs below the lake level, distributed every 0.5 m from the surface to 3 m depth, and then every meter to the bottom. Thermographs located above the water level were in two heat-reflecting white plastic cylinders nested inside each other, avoiding inaccuracies due to logger resin heating during the day.

Wind and air temperature measurements were carried out with a time rate of 15 min from 19 June to 25 October 2019; however, wind speed records were unavailable for the last two months of the record.

3.1.2. National Meteorological Service (NMS) Weather Station

To analyze the meteorological regime during the period of our experiment, we use long-term data (2017–2019) from the weather station 15062-Nevado de Toluca, provided by the (NMS 00015062, 19°7.171′ N; 99°44.851′ O, with altitude 4139 m a.s.l.). This weather station is located on the outer slope of the Nevado de Toluca volcano and recorded temperature, wind speed and direction, relative humidity, atmospheric pressure, solar radiation, and rainfall every 10 min. Wind data was not used due to poor performance of the speed sensor.

3.1.3. Temperature on the Internal Slope of the Nevado de Toluca Volcano

One HOBO thermistor (HOBO © Water TempProV2) was placed on the western internal slope of the volcano. The device recorded the temperature every 15 min from June to November 2018 (the measurement point is marked in Figure 1a, number 6).

3.1.4. Lake Level and Bottom Sediment Temperature Measurements

Because the heat flow in shallow lakes reaches the bottom, we assessed its role in the variability of bottom stratification [34,37]. To measure heat fluxes through the bottom of the lake (sediment water), an RBR TDR-2050 temperature and depth recorder was buried into the bottom sediment at a depth of about 15 cm. The temperature channel of the TDR-2050 was calibrated to an accuracy of ±0.002 °C (ITS-90) over a range of −5 to +35 °C. The depth channel was calibrated to an accuracy of 0.05% of full scale. We used an instrument with a depth-measurement range from 0 to 50 m, which ensured the accuracy of our measurements of 2.5 mm. These measurements were taken continuously at a sampling interval of every 2 min for 15 months (from June 2018 to August 2019).

3.1.5. Water Temperature Measurements

A mooring with a chain of HOBO thermistors (HOBO © Water TempProV2) was placed in the deepest part of each lake. The measurement period for both moorings was more than two years, from 10 May 2017, to 8 September 2019. The chain in Lake El Sol had 13 thermographs (attached to the floating weather station, see above), with 12 thermographs in Lake La Luna. All thermographs were distributed vertically from the surface to 3 m depth with seven devices every 0.5 m, and then to the bottom every meter and recorded temperature every 15 min.

3.1.6. Hydrodynamic Modeling

To estimate the circulation in Lake El Sol, we used the hydrodynamic model Delft3D, which is an open-source numerical model developed by WL/Delft Hydraulics and the Delft University of Technology [38]. The Delft3D model solves the Navier-Stokes equations for an incompressible fluid under the shallow water and the Boussinesq assumptions. The model includes the depth-averaged horizontal momentum equations

(1)$\frac{\partial u}{\partial t}+\mathit{u}·\nabla u+g\frac{\partial \eta }{\partial x}-fv+\frac{u\Vert \mathit{u}\Vert }{C^2\left(d+\eta \right)}-\frac{F_x}{\rho \left(d+\eta \right)}-\nu {\nabla }^{2}u=0$

(2)$\frac{\partial v}{\partial t}+\mathit{u}·\nabla v+g\frac{\partial \eta }{\partial y}+fu+\frac{v\Vert \mathit{u}\Vert }{C^2\left(d+\eta \right)}-\frac{F_y}{\rho \left(d+\eta \right)}-\nu {\nabla }^{2}v=0$

and the depth-averaged continuity equation

(3)$\frac{\partial \eta }{\partial t}+\frac{\partial \left(d+\eta \right)u}{\partial x}+\frac{\partial \left(d+\eta \right)v}{\partial y}=Q\left(d+\eta \right)$

and the vertical momentum equation, which reduces to the hydrostatic pressure relationship via the Boussinesq approximation: $\frac{\partial p}{\partial z}=-\rho g,$ where $u,v$ are the depth-averaged velocity in the $x$ and $y$ directions, $C$ is the Chézy coefficient, $d$ is the water depth, $\eta$ is the free surface elevation above the reference plane (at $z=0$), $\mathit{u}$ is two-dimensional current vector, with $\Vert ·\Vert$ the Euclidean norm, $Q$ are sinks or sources of water, $f$ is the Coriolis force, $F_{x,y}$ is the Reynolds stress, $g$ is the gravity, $\nu$ is the horizontal eddy viscosity, $p$ is the pressure, and $\rho$ is the water density.

The RFGRID module of Delft3D was used to generate the grid file. A mesh grid of 61 × 60 cells and 1 layer were used in the horizontal and vertical direction, respectively. Bathymetry measurements obtained during the field campaigns were used to interpolate the depth file by using the QUICKIN module of Delft3D. The time step allowed was ∆t = 0.6 seg. The model was run for 34 days, with the first 4 days used as warm-up in the model. The other physical parameters had typical values: gravity, 9.81 m/s², water density 1000 kg/m³, air density, 1 kg/m³, uniform Chézy roughness, 65 m^1/2/s, background horizontal and vertical eddy viscosity and diffusivity of 1 and 10 m²/s, respectively.

The Murakami model for heat flux was applied with the default values of 75% sky cloudiness and Dalton number of 0.0013. The Secchi depth was set to 2 m.

Delft3D is a model that has been tested and used globally for the study of lake systems [39,40,41]. In addition, it has been used specifically in the hydrodynamic analysis of Mexican crater lakes [42,43].

3.2. Data Analysis

3.2.1. Meteorological Variables

We analyzed the meteorological variables at the floating weather station in Lake El Sol and the nearby weather station of the National Meteorological Service, separated by a horizontal distance of 1.7 km. To show how wind speed and direction changed during the day at the floating weather station, as well as at the NMS weather station, time series with hourly data were presented in the form of two-dimensional matrices, in which the analyzed values measured during the day were plotted along the vertical axis, and the values, by days of measurement, were located along the horizontal axis (these matrices are graphically shown in Figure 3a,b and Figure 6a,b).

Cross-spectral analysis was used to calculate coherence matrices and phase differences between the time series of all measured values. This process was carried out with the objective of recognizing the relationship between the meteorological characteristics and the temperature regime of the lakes [44].

A comparison was made between the air-temperature fluctuations on the western slope of the volcano and the temperature fluctuations in the surface water layer in Lake El Sol (near the floating weather station). The distance between the thermographs was about 200 m.

3.2.2. Water Temperature

The initial series were smoothed with a cosine filter, and the hourly time series were analyzed by using auto- and cross-spectral analysis. The spectral functions were calculated by using the Fourier transform with subsequent smoothing of the periodograms in frequency. The spectra were calculated to explore the periods and amplitudes of the dominant oscillations, as well as the coherence and phase difference between them [11,25,44,45].

3.2.3. Heat Flux between the Water-Bottom Sediments Interface

Based on water temperature measurements at the bottom and temperature in bottom sediments for the 2018–2019 time period, heat fluxes near the water-bottom interface were calculated by the gradient method [34,37] according to the formula $Q=-\lambda \partial T{\left(\partial z\right)}^{-1}$, where Q is the heat flow near the water-bottom boundary in W/m²; $\lambda$ = W/m °C is the coefficient of molecular thermal conductivity of water in the 0–10 m layer 0.5813; ∂T/(∂z)-temperature gradient [46].

3.2.4. Rainfall, Evaporation and Level Fluctuations

To analyze the relationship of precipitation, evaporation from the surface of the water and the area of runoff with fluctuations in the level of Lake El-Sol, data from the NMS weather station and time series of the water level measured by the TDR-2050 instrument were used. To estimate the evaporation rate, we used the simplified version of the Penman [47] method proposed by Valiantzas [48].

For the calculations, we used a catchment area of Lake El Sol at 2.17 km² and Lake La Luna at 2.0 km², which allowed us to evaluate the response of Lake El Sol level response in one case of heavy precipitation.

The horizontal distance between the weather station and the mirror of Lake El Sol in a straight line is 1.7 km, and it is 47 m below the lake, that is, they are located at almost the same height [25].

4. Results and Discussion

4.1. Long-Term Series. NMS Weather Station (2017–2019)

Figure 3c shows the annual precipitation amount, and the total daily (1) and average monthly precipitation (2). The red polygon in (d) and (e) shows the period of intense rainfall, and with the effect on the level of Lake El Sol discussed in Section 4.5.1.

The influx of solar radiation on the slope of the volcano reaches a maximum value of 1000 W/m² at about 15:00, and from 18:00 to 9:00 in the morning it is zero. Barba-López et al. [25] showed that due to the high walls, 20% less solar energy penetrates into the crater of the volcano than on its outer slope, and this must be taken into account in thermodynamic calculations. The supply of solar energy to these crater lakes is at maximum in March and April and at minimum from June to August, and low also during the rainy season due to cloud cover. Intra-annual fluctuations in air temperature in the volcano area depend mainly on the influx of solar radiation and are consistent with its variability. Fluctuations in air temperature have their maximum values in April and May in the early afternoon hours of the day (2 to 3 p.m.). The minimum temperatures were observed during the rainy season and during the winter months (Figure 3a,b).

Barba-López et al. [25] presented an analysis of an eight-year series of observations of wind and other meteorological elements at the NMS meteorological station located on the southern outer slope of the Nevado de Toluca volcano. The three-year field measurements analyzed herein, presented in Figure 3a,b, confirm previously obtained results [25].

The values of annual precipitation for the area surrounding the volcano (1162 mm, 1359 mm and 1198 mm) (Figure 3c) are within the range of normal precipitation values mentioned in Soto et al. [33] for the same study area. Precipitation was the main source of water entering the lakes. Due to their specific orography, they have a very small runoff area (Figure 3d,e). According to observations at the NMS station, an average of 1.2771 m³ of precipitation, and 0.9708 m³ evaporation, occurs per year.

4.2. Data Obtained at the Floating Weather Station

4.2.1. Water Temperature

Temperature fluctuations between 6 °C and 14 °C occurred for Lake El Sol, while on Lake La Luna values ranged between 6 °C and 13 °C (Figure 4). These values are similar to those reported by Barba-López et al. [25] and the maximum values found in Alcocer et al. [32] for these same lakes.

4.2.2. Relationship between Air Temperature Fluctuations on the Western Slope of the Volcano and Surface Temperature Fluctuations of Lake El Sol

The cross-spectral analysis of the annual time series (Figure 5) was dominated by diurnal oscillations and their subharmonics (Figure 5b) with a 0.920 agreement, with a confidence interval of 95%. The phase shift of the fluctuations was 3.5 h, with the fluctuations in water temperature leading the fluctuations in air on land (which lagged water fluctuations). That is, unexpectedly, the water warmed and cooled faster than the inner walls of the volcano.

4.2.3. Wind Speed and Direction

In Figure 6, two-dimensional plots (hours of the day/days of measurements) of the hourly variability of speed (a) and wind direction (b) measured at the floating weather station in July–October 2018 are shown. Due to the failure of the wind speed sensor, data was only available during the first two months. Nevertheless, for the first time, we obtained reliable data of the wind speed over the water surface of the lake, which was at maximum from 11:00 to 19:00 and did not exceed 3 m/s, during which time the wind had an almost stable direction of 210°, i.e., blowing over the lake from the north to its south side. The rest of the time, the wind speed was less than 1 m/s and at times, zero. The diurnal wind direction had a bimodal structure with a direction of 90–360° at night and in the morning until 10:00, also shown by the histograms of wind speed and direction measured from June–October 2018 at the station.

The values recorded by our station neared 3 m/s, somewhat lower than the average value reported by Alcocer et al. [32] (4.2 m/s).

4.2.4. Fluctuations in Air Temperature above Water and at the Near-Surface Layer of the Lake

Air-temperature fluctuations from September to May (Figure 7a) had a large amplitude (as well as a greater value by 5–7 °C) at the surface than at a height of 2 m above the water. The minimum temperatures during these months dropped to 2–3 °C at night.

From October to March, there was a balance between the temperature of the water and the air near the surface of the lake. A significant drop in air temperature at night to −5–8 °C was compensated by the influx of heat to the surface from the deep layers of the lake, which did not allow the water to freeze and form an ice cover. Winter vertical circulation was observed here, typical for lakes of middle and high latitudes [49]. In the near-surface layers of the lake during the winter months, the temperature was stable and near 4 °C, i.e., close to the temperature of the maximum density of fresh water. Seasonal fluctuations in water temperature in the near-surface layer of the lake occurred synchronously and did not create significant vertical gradients (Figure 7b).

The air temperature presented a diurnal oscillation, which is typical in tropical areas [50,51]. Besides a daily variation, a seasonal variation with greater amplitude in the months of September to May (2 m above the surface of the lake) and smaller amplitudes to 0.1 m above the surface of the lake for these same months also occurred in air temperature. For both time series of air temperature, the maximum and minimum values (−9 °C, 22 °C) are within the range of temperatures observed in other mountain areas [50,52].

4.3. Modeling Results of Currents and Level Fluctuations in Lake El Sol

In Filonov et al. [35], field measurements of currents carried out in Lake El Sol by using an ADP Sontek 1.0 MHz current meter with a vertical resolution of 0.5 m and a time rate of 1 min were presented. A monthly time series of currents made it possible to explore their structure and circulation in the lake, showing that wind currents exist only in the upper 2-m layer and do not penetrate deeper. The measured currents were weak, did not exceed 10–15 mm/s, and did not demonstrate the strict daily periodicity inherent in temperature fluctuations in the surface layers of the lake. To expand on these data, we estimated the circulation in Lake El Sol with the hydrodynamic model Delft3D.

The use of the floating weather station allowed for the reliable measurement of the direction and speed of the wind directly on the lakes without the confounding influence of the lava dome to then be used for hydrodynamic modeling (Figure 8). Numerical modeling showed that the lake contains two closed circulation patterns with opposite directions of rotation. The more intense one is in the southern, deep-water part of the lake, with a clockwise rotation with current amplitudes up to 8–10 mm/s. The second circulation pattern almost completely covers the central and northeastern parts of the lake. It is weaker, only 2–4 mm/s, and has a counterclockwise rotation. Fluctuations in current speed and direction correlate well with changes in wind speed and direction measured at the floating weather station (Figure 6) and penetrate the near-surface layer to no more than 2 m [35]. Thus, because the lakes under study are protected by high crater walls, the currents in them are very weak and mainly thermal processes drive vertical mixing.

Level fluctuations also correlated well with fluctuations in wind and currents in the lake. They have a maximum height of about ±25 mm, but their role can be significant in the mixing of lake water.

Modeling of currents and water levels in Lake La Luna were not conducted as we did not have data on the wind and fluctuations in the level of this lake.

4.4. Lake-Level Fluctuations and Processes Occurring at Its Bottom

By using the TDR-2050 RBR temperature and level meter immersed in the bottom sludge, it was possible to obtain an accurate time series of more than 13 months (Figure 9), due to the high resolution of the temperature and level sensor (accuracy of ±0.002 °C and accuracy of 0.05% full scale for pressure), which is two orders of magnitude higher compared to temperature measured with the Hobo V2. During the winter months, the temperature near the bottom of the lake drops to a minimum value of 4.7 °C, i.e., it becomes close to the temperature of the maximum density of water. The diurnal variation is well-manifested at the very bottom of the lake, where it has a larger range from November to May (0.2–0.3 °C) than the rest of the year (Figure 9a,b).

4.4.1. Heat Fluxes between the Water-Bottom Sediments Interface

In the autumn–winter period, Lake El Sol was in a state of weak thermal stratification, followed by homothermal conditions. The bottom sediments accumulated heat in summer and released it back into the water column in winter. This is the reason for the well-manifested annual temperature variation of the bottom layer of water and the upper layer of bottom sediments of the lake. In summer and autumn, the heat flow is directed from the water to the bottom sediments; in winter, on the contrary, the heat flow is directed from the bottom sediments to the water layers (Figure 9b).

Calculations showed that heat flowed through the bottom of the lake during the entire measurement period. In spring, summer and autumn, the heat flux from the bottom layers of water to the bottom sediments did not exceed 0.1 W/m²; that is, it was 10⁻⁴ times less than the flux of solar radiation penetrating the lake surface [25], where it has a maximum value of about 1000 W/m². This is due to the dissipation and absorption of solar energy in the water column. On the contrary, in the winter months, the heat flux was directed from bottom sediments into the water column. During these months, it reached almost 0.3 W/m².

Our results are distinct from the exchange pattern described by O’Niell et al. [53] for Lake Biwa (Japan). The difference is because the heat transfer patterns are often complex and result from a wide range of characteristics. The steady-state temperatures of volcanic lakes are largely determined by the magnitude of the volcanic heat influx relative to the surface area of the lake [54].

4.4.2. Variability of Level Fluctuations and Stratification in Lake El Sol

The annual variation of the level of Lake El Sol is quite smooth, sometimes disturbed by small sharp jumps due to precipitation. Two such time intervals are shown in Figure 9a (see rectangles). The figure shows that the annual minimum temperature in Lake El Sol at the water-bottom sediment boundary in the deep-water part of the lake reached 4.8 °C in early January 2018, where the temperature at the bottom increased slightly to 5.7 °C and dropped again in early February to 4.5 °C. In summer, the temperature at the bottom was close to 10 °C.

4.4.3. Spectra of the Level and Temperature Fluctuations

The frequency spectra of temperature and level fluctuations are shown in Figure 10. Oscillations with periods of 8 and 4 days dominate the spectra, as well as the daily period of 24 h and its overtone at 12 h. Moreover, the semidiurnal peak is higher than the diurnal one in the level spectrum due to the two maxima in atmospheric pressure near 10 and 22 h, and two minima near 4 and 16 h. The presence of these peaks in pressure variability is especially noticeable in tropical latitudes [55] and is generally associated with daily fluctuations in air temperature.

Spectral analysis has been used to study the oscillations in some alpine lakes [56], in Mexican lakes [11,12,43,57], and particularly in the Lakes El Sol and La Luna by Barba-López et al. [25]. Our results are in accordance with Barba-López et al. [25]. For another closed body of water, Arnon et al. [58] detected frequencies of 8, 12, and 24 h, as well as 2 and 3 days. The differences in the dominant frequencies of the parameters analyzed by spectral analysis may be due to the morphology of the aquatic bodies in question [59,60] and variables such as precipitation and runoff area [61].

4.5. Fluctuation of the Water Balance of the Lake Depending on Precipitation and Evaporation

The high slopes of the Nevado de Toluca crater form a drainage basin that fills with atmospheric precipitation and reaches equilibrium through the evaporation and filtration of water. The inflow of groundwater into crater lakes is not possible due to the high altitude of the volcano in comparison with the surrounding space. Thus, to calculate the water balance of a closed lake, it is necessary to know the area of its catchment, the mode of precipitation and evaporation, as well as the volume of water filtration. Of the listed values, we know only the amount of precipitation and the catchment area. This makes it possible to calculate the volume of lost water due to its filtration through the bottom.

Because the crater of the volcano has very steep southern and western slopes that shade the lakes, the penetration of solar energy in the morning and evening hours is limited with about 20% less solar radiation than during the day [25]. We took this factor into account in our calculations and obtained an annual evaporation rate of 940.1 mm/year. The evaporation calculation algorithm is detailed in Appendix A.

4.5.1. Lake El Sol Level Response in One Case of Heavy Precipitation

It is known that a thunderstorm cloud has, on average, a horizontal size of 8–15 km and rises up to 12–15 km [62,63]. That is, the height of the clouds is 2–2.5 times greater than the height of the volcano, and the dimensions of its crater are small (about 2 km) to affect the local microclimate and the patron of precipitation. Therefore, we assumed that the precipitation measurements at the meteorological station on the slope of the volcano will, on average, be the same as in its crater.

To assess the response of the lake level to intense short-term precipitation, we took such a case that occurred at the end of 2018, when the lake level almost reached its minimum annual value. During the day on 29 November, more than 50 mm of precipitation fell; a rise in the lake level by 11 cm was recorded (Figure 11). The initial data used for the calculations and their result are shown in Table 2 and Appendix A (Table A2). Note that considering evaporation from the water surface changes the calculated level rise by an insignificant amount, by only 4%.

Measurements and calculations showed that the real rise in the level of Lake El Sol as a result of heavy rains on 29 November 2018 (11 cm, Table 3) should be about five times higher than that measured by the device. When rainwater enters the lake, it is filtered through its bottom and side walls and seeps through loose volcanic rocks down the slope.

Hydrogeologists often use radioactive or fluorescent tracers and measure their presence in the water and in a drilled section across the slope of the volcano as an accurate method of confirming these calculations. Unfortunately, we were unable to make such measurements and calculations of level fluctuations in Lake La Luna. For this reason, we do not calculate the water budget in Lake La Luna.

4.6. Annual Water Budget of Lake El Sol

The data obtained as a result of our field measurements allow for rough estimates of the water balance of the lakes located in the crater of the Nevado de Toluca volcano (Table 3).

The calculation gave results close to those obtained in the previous paragraph. Over the course of the annual inflow of precipitation into the closed lake, its level in 2018 should have increased by 4.5 m, but the measured level change was only 1.2 m (Table 3).

Williams and Pelletier [61] indicate that a determining factor in these fluctuations may be the size of the lake when the analysis corresponds to long time series (tens of years), although most lake levels are studied under the assumption that they respond quickly and linearly to precipitation and runoff (dependent parameters of precipitation runoff, snowmelt, and groundwater discharge into streams and lake bottoms), in such a way that they are directly attributable to climate variability and climate change. These and many other studies show links between water level and climate variability or climate change [64,65]. However, other studies show that while water levels and climate cycles may be correlated, it is difficult to either isolate the effect of individual forcing or attribute water-level trends to that forcing [66,67].

5. Conclusions

The analysis for the years 2017–2019 of meteorological variables, such as solar radiation and air temperature outside the Nevado de Toluca volcano crater are similar to the values reported for the years 2000–2007 by Soto et al. [33] and Barba-López et al. [25].

However, the magnitude and direction of the wind directly on the surface of Lake El Sol turned out to be much smaller than on the exterior of the crater due to the presence of the walls of the volcano and their shielding of the lake. This process is well-described in works such as [20,22,68,69,70]. The values recorded herein are somewhat lower than the average value reported in the study by Alcocer et al. [32], potentially due to the difference in the measurement period and the location of the weather stations.

In our study, the air temperature presented a diurnal oscillation, which is typical in tropical areas [50,51]. The maximum and minimum values are within the range of temperatures observed in other mountain areas [50,52]. The difference in range oscillations is due to the real relationship between temperature and altitude, which varies both temporally and spatially depending on climatic conditions (moisture, wind, and radiation) and topography [21,71].

The use of spectral analysis allowed us to observe temperature and level oscillations in Lake El Sol. The morphology of the lake basin produces spectral peaks that differ from other lakes.

The numerical model allowed us to observe for the first time the wind-driven free surface level and circulation patterns. The analysis of such physical processes is of key importance as one of the first steps in the evaluation of the chemical and biological processes present in this body of water.

By using in situ measurements, unexpected changes in the temperature near the bottom of the lake were detected, with heat exchange between the bottom water layer and the sediments (in the winter the sediments give heat to the water column).

Finally, our study found that the level of the lake increased less than the theoretical calculations would suggest. The analysis of the level of the lake corresponds to a time series of two years and the difference between the measured levels and the theoretical calculations is observed for the first time at this site.

Our results highlight the difficulty of planning and maintaining equipment in high-mountain areas, in addition to the complicated relationships between meteorological drivers and the thermal regime and water balances in these unique mountain lake ecosystems.

Author Contributions

A.F.: conceptualization, investigation, writing original draft, methodology, software, validation, visualization, project administration. M.d.R.B.-L.: writing original draft, formal analysis, investigation, data processing and modeling. L.B.L.: investigation, writing—review & editing. I.T.: data analysis, investigation, review & editing. D.A.P.: field work, data processing and modeling. J.A.: financial support, review & editing. F.Á.V.-M.: investigation, data processing and modeling. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Universidad Nacional Autónoma de México DGAPA/PAPIIT through projects IN105009 and ES209301, and Programa de Investigación en Cambio Climático (PINCC 2020–2021).

Data Availability Statement

Data are available from the authors upon reasonable request.

Acknowledgments

The authors express their gratitude to each of the expedition participants who made it possible to complete this work. Omar Mireles-Loera provided assistance in the field work. We are also very grateful to the graduate students at the University of Guadalajara, Arturo Orozco-Estrada and Andrea Manrique-Cantillo who, in cold weather, rain or snow, performed the difficult work of measuring at the top of the volcano. Special thanks to graduate student Carlos Villarreal-Olavarrieta for his work as an equipment diver. We also thank the Comisión Estatal de Parques Naturales y de la Fauna (CEPANAF, Secretaría de Ecología, Gobierno del Estado de México) for providing the permit for scientific research at the Área de Protección de Flora y Fauna Nevado de Toluca.

Conflicts of Interest

The authors declare that they have no known competing financial interest or personal relationships that could have appeared to influence the work reported in this paper.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures and Tables

Figure 1. (a) Geographical location of the Nevado de Toluca volcano and Lakes El Sol and La Luna. Photograph of the volcano crater is available in [36]. The numbers indicate: 1—Lake El Sol, 2—Lake La Luna, 3—Lava dome, 4—the position of the floating weather station, 5—the position of the meteorological station installed on the shore in 2007–2010, 6—location of the Hobo V-2 thermograph on the western slope of the crater. (2). (b) A topographical chart of the volcano. The red dots indicate the location of the floating weather station in Lake El Sol (1), and the location of the SMN weather station on the outer slope. Volcano diagram adapted from [29].

Figure 2. Structural diagram of a floating weather station. In the right corner is a photograph of the part of the station above the water level.

Figure 3. Hourly variability of solar radiation (a), air temperature (b) and precipitation (c) measured during 2017–2019 at the NMS station. In (d,e), the red curves show the runoff areas in the crater lakes of the Nevado de Toluca volcano.

Figure 4. Hourly variability of temperature (a) at thirteen depths of Lake El Sol (a) and at twelve depths of Lake La Luna (b) for the same time period (instrumental depths are indicated in the legend).

Figure 5. (a) Variability of water temperature in the surface layer of Lake El Sol in the area of the floating meteorological station (1) and air temperature on the western slope of the volcano crater (2), from June-November 2018. (b) The corresponding spectra of these time series. The vertical line in Figure 5b shows the 95% confidence interval.

Figure 6. Hourly variability of speed (a) and wind direction (b) measured at the floating weather station located in the center of Lake El Sol. (c,d) Representations of the histograms of (a,b). The red vertical line shows the day for which the numerical modeling of fluctuations of currents and the level of Lake El Sol was carried out.

Figure 7. Hourly variability of air and water temperature in the area of the floating weather station. (a) At a height of 0.1 m above the level of the lake (1) and at a height of 2 m (2). (b) Temperature fluctuations directly below the water surface (3) and at a depth of 2 m (4).

Figure 8. Modeling results of currents and level fluctuation in Lake El Sol from observations of wind and air temperature on 5 September 2018. In the upper left, a bathymetric map of the lake shows the floating meteorological station marked with a white circle (in the rest of the figures, the position of the weather station is marked with a black dot). The remaining rectangles show simulated currents and level fluctuations every two hours. In the lower left, black and red pattern arrows indicate the corresponding scales of current velocities and measured wind.

Figure 9. (a) Annual series of temperature fluctuations (1) of bottom sediments and (2) the level of Lake El Sol in the area of the floating meteorological station. Moments of a sharp change in the measured characteristics are marked by black and red rectangles. (b) Vertical gradient of water temperature between the bottom and 1 m above the bottom (9 and 8 m depth) (1). The red curve (2) is the calculated heat flux across the water-bottom sediment interface (positive values are heat flux from bottom sediments to water layers).

Figure 10. Spectra of lake level fluctuations (1) and temperature fluctuations (2) in bottom sediments in 2018–2019 in the area of the floating weather station (see Figure 2). The vertical line in Figure 10 shows the 95% confidence interval.

Figure 11. Daily precipitation (NMS data) and level values (TDR 2050 data) measured on 27–30 November 2018 at the time of heavy precipitation. This segment of observations corresponds to the red rectangle inn Figure 9a.

Table 1

Hydrological parameters for Lake El Sol and Lake La Luna. Modified from Filonov et al. [35].

	At the End of the Rainy Season (October)		At the End of the the Dry Season (May)
	El Sol Lake	La Luna Lake	El Sol Lake	La Luna Lake
Surface area	2.020 × 105 m2	0.203 × 105 m2	2.003 × 105 m2	0.202 × 105 m2
Maximum depth	13.8 m	10.2 m	10.9 m	7.6 m
Average depth	6.4 m	5.7 m	4.0 m	3.5 m
Volume	13.022 × 105 m3	1.172 × 105 m3	8.102 × 105 m3	0.725 × 105 m3

Table 2

Parameters used to calculate the response of Lake El Sol to heavy rainfall on 29 November 2018.

Dry season area of the lake El Sol [35]	200,330 m2
Runoff area	2,170,000 m2
Evaporation rate (November 2018)	3.33 mm/day
Rain case	50.8 mm
Real level rise	0.11 m
Accumulated in runoff area	110,236 m3
Expected level rise with evaporation	0.550 m
Expected level rise without evaporation	0.586 m

Table 3

Annual average values (with CNA measures).

Lake El Sol average area for the rainy and dry seasons [35]	201,165 m2
Runoff area	2,170,000 m2
Rain rate	1.2771 m(NMS measures)	1.359 m(calculations)
Evaporation rate	0.9708 m(NMS measures)	0.941 m(calculations)
Accumulated volume	907,060 m3
Expected level rise with evaporation	4.509 m
Real level rise	1.20 m

Appendix A. Calculation of Evaporation from the Surface of the Lake

Various authors have developed methods and equations for calculating evaporation through adjustments, correlations of climatic variables, as well as through theories of energy balance, water balance, aerodynamic methods and others [72]. One of the most used methods is the one proposed by Penman [47], where evaporation is calculated from the effects of wind speed and radiation solar. To do this, he suggested using the following formula:(A1)$$PE=\frac{\Delta }{\Delta +\gamma }+\frac{\left(R_n\right)}{\lambda }+\frac{\gamma }{\Delta +\gamma }\frac{6.43\left(f_u\right)D}{\lambda }$$ where PE is the potential evaporation (mm/ day); R_n is the net radiation on the surface of the water body (MJ/m²day), ∆ is the water vapor saturation curve (kPa/°C); γ corresponds to the psychrometric constant (kPa/°C); λ represents the latent heat of vaporization (MJ/kg) $f_u$ is the function of the wind, and D is the vapor pressure deficit. Valiantzas [48] simplified Equation (A1) by calculating evaporation from more readily available measured data. This new approximation is equivalent in accuracy to Equation (A1) and allows calculating the daily evaporation rate for each month of the year.

The simplified Penman formula proposed by Valiantzas [48] is represented:(A2)$$PES\approx 0.047R_S\sqrt{T+9.5}-2.4{\left(\frac{R_s}{R_A}\right)}^2+0.09\left(T+20\right)\left(1-\frac{RH}{100}\right)$$ where $R_s$ is the solar radiation (MJ/m² day, T is the monthly average temperature (°C) at 2m above the surface, RH is the relative humidity and (MJ/m² day) is the extraterrestrial radiation. In this case, the extraterrestrial radiation values can be traced using the formula:(A3)$$R_A=\frac{24\left(60\right)}{\pi }{G}_{SC}{d}_r[{\mathsf{\omega }}_s\sin \left(\Phi \right)\sin \left(\delta \right)+\cos \left(\Phi \right)\cos \left(\delta \right)\sin \left({\mathsf{\omega }}_s\right)]$$ where R_A is the extraterrestrial radiation (MJ/m² day), $G_{SC}$ is the solar constant $G_{SC}$ = 0.0820 MJ/m² min, $d_r$ is the mean distance from the Earth to the Sun, $\mathsf{\omega }$_s corresponds to the sunset angle of sun (radians), Φ is latitude (radians) and $\delta$ solar declination (radians). To calculate the evaporation in the crater Lakes El Sol and La Luna, the values given in Table A1 were used.

Table A1

Parameters for estimating the evaporation rate in Lakes El Sol and La Luna.

Year	Month	T2 m Average (°C)	RS Average (MJ/m2 day)	RA (MJ/m2 day)	HR Average (%)
2018	July	5.2	14.4	26.8	85.8
	August	4.7	16.7	30.6	98.3
	September	5.4	14.8	34.7	85.3
	October	5.0	11.8	37.9	79.4
	November	3.0	14.9	39.3	61.9
	December	2.6	17.4	39.5	65.2
2019	January	2.1	17.9	39.3	62.3
	February	3.2	19.6	38.3	52.6
	March	4.3	23.3	35.8	64.4
	April	4.6	22.4	31.8	62.5
	May	6.4	22.6	27.7	79.1
	June	5.8	13.9	25.6	73.4

Where average T2 m corresponds to the average monthly temperature at 2 m above the surface of the lake, RS average is the monthly solar radiation calculated from data recorded by the automatic meteorological station Nevado de Toluca (NMS) with the monthly extraterrestrial solar radiation values calculated from Equation (A3), and average RH corresponds to the monthly average values of relative humidity recorded by a meteorological station located inside the crater of the volcano. Substituting the values from Table 2 in Equation (A2); we obtain the evaporation values in Table A2.

Table A2

Monthly and annual evaporation in Lakes El Sol and La Luna.

	MonthlyEvaporation(mm/month)
July 2018	68.8
August 2018	70.7
September 2018	77.4
October 2018	72.5
November 2018	87.9
December 2018	95.5
January 2019	96.7
February 2019	112.2
March 2019	107.2
April 2019	107.7
May 2019	97.0
June 2019	76.3
Annualevaporation	1070.0(mm/year)

CRediT authorship contribution statement.

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