Temperature Regime, Dynamics and Water Balance of Two Crater Lakes in the Nevado de Toluca Volcano, Mexico

*Anatoliy Filonov, Iryna Tereshchenko, María del Refugio Barba-López, David Avalos-Cueva and Cesar Monzon*

## **Abstract**

Volcanic lakes are ecosystems in which thermodynamic processes have a complex relationship with atmospheric variables. This study presents the results of an analysis of the thermal regime and dynamics of two high-altitude tropical lakes located in the crater of the Nevado de Toluca volcano in Mexico, at an altitude of more than 2200 m above sea level. Joint meteorological and hydrological measurements taken in two adjacent lakes revealed strong diurnal fluctuations in water temperature, which are caused by wind-induced internal gravity waves and free seiches oscillations. During the daytime, heating occurs in the near-surface layer of the lakes, which creates a thermocline at a depth of 2–3 m, but it is washed out at night. The heat penetration into the lakes is significantly different due to differences in water transparency and algae density, despite the small distance of only 200 m between the lakes separated by a 100-m high lava dome. Temperature and level fluctuations were analyzed using spectral analysis. The numerical model used in Lake El Sol allowed for the first-ever evaluation of the circulation and the impact of wind circulation regimes on lake-level fluctuations. Analyzing such physical processes is crucial in assessing the chemical and biological processes occurring in this reservoir. Field measurements uncovered unexpected temperature changes near the lake bottom, along with heat exchange between the bottom water layer and bottom sediments (during winter, sediments emit heat to the water column). The estimated heat fluxes through the lake bottom were less than 0.3 W/m<sup>2</sup> during winter and less than 0.1 W/m<sup>2</sup> for the rest of the year.

**Keywords:** Mexico, Nevado de Toluca volcano, lakes El sol and La Luna, thermal structure, hydrodynamic modeling, lakes' level fluctuation, water balance

## **1. Introduction**

Lake ecosystems exhibit a strong interrelationship between physical, chemical, and biological processes. A comprehensive understanding of these processes would enable the establishment of better management policies. Due to the dependence of the thermal and dynamic behavior of lakes on variations in atmospheric parameters, and in order to understand their correlation, wind speed, wind direction, solar radiation, and ambient temperature on the outer slopes and interiors of the volcano crater were analyzed.

High mountain lakes are located above the tree line, where the climatic conditions are extreme [1]. Mountainous regions around the world, including the Andes, the Alps, the Himalayas, and the Rockies, commonly feature bodies of water nestled within their peaks [1, 2].

The lakes, due to their location in high mountain areas, have specific characteristics in terms of their environment and climate. Their basins have steep slopes, and water inputs can come from glaciers, snowmelt, or strong rainfall [3–5]. Furthermore, the water temperature in high mountains is often low because of their high altitude and exposure to solar and ultraviolet radiation [6–8].

High mountain lakes can also be sensitive to environmental perturbations due to their geographic location, which limits water flow and interaction with other water bodies [9, 10]. Hence, they are important indicators of climate change and water quality in high mountain regions [11, 12].

It is also possible to establish a direct relationship between lake water level variations and the balance between precipitation and evaporation in the lake basin [13, 14]. The daily variations are the main factors determining the heat balance in tropical aquatic ecosystems.

Mountain lakes located in the craters of volcanoes at higher altitudes experience particularly complex interactions between the atmosphere and the lakes. As a result, turbulent flows can arise and affect the transport of matter, nutrients, pollutants, and phytoplankton dynamics [10]. However, these interactions have not been extensively studied in tropical high mountain systems. The tropical high mountain lakes in Mexico provide a natural laboratory to investigate the effects of atmospheric forcing on lake hydrodynamics and productivity, and to explore potential climatic impacts.

The volcano Nevado de Toluca is the fourth highest volcano in the mountains of Mexico and is classified as a strombolian volcano, with alternating explosions and lava emissions [15]. Several authors have reported that the volcano is situated at the convergence of three fault systems, and the most recent eruption occurred approximately 10,445 95 years ago [16–18]. The region encompassing Nevado de Toluca has undergone an extensive and intriguing geological history spanning over 1.5 million years [18, 19]. This area is situated within the Trans-Mexican Volcanic Belt and is characterized by a diverse array of volcanic rocks in its composition [17, 18, 20]. These rocks comprise andesite, basaltic andesite, dacite, and trachyte/trachydacite. Additionally, it is noteworthy to mention the presence of the Tilzapotla Formation, which consists of rhyolites, rhyodacites, and deposits of pyroclastic flows. These volcanic rocks originated from subvolcanic magmatic chambers, and their diversity reflects the intricate dynamics of magma emplacement processes [18].

In the Nevado de Toluca area, highly significant volcanic deposits have been identified, which can be attributed to a catastrophic eruption that resulted in lahars or mudflows of considerable magnitude [18]. During the Late Pleistocene, a remarkable Plinian eruption from the Nevado de Toluca volcano gave rise to a complex sequence of pyroclastic deposits known as the Upper Toluca Pumice [17]. There are two lakes in the crater, El Sol and La Luna, located at 4200 m above sea level. They are separated by a lava dome and are considered to be evidence of a moderate eruption that took place 3140 195 years ago [19]. Both lakes are separated by 200 m within the interior

### *Temperature Regime, Dynamics and Water Balance of Two Crater Lakes in the Nevado de… DOI: http://dx.doi.org/10.5772/intechopen.112196*

of the volcano and have been dated to have the same age, origin, and hydrological regime. However, several studies have described significant differences in the physicochemical and biological characteristics of lakes [21, 22].

For this research, we utilized *in situ* measurements of meteorological and water column variables over long-term and high-frequency periods. These measurements enabled us to determine the nonlinear dynamics of the crater lakes of the Toluca Volcano. For this purpose, we assume that the coupling properties between the atmosphere and the water column in El Sol and the Moon are different due to the characteristics caused by the crater walls and the dome. The analysis of the data revealed the existence of complex, coupled forcings at small spatiotemporal scales that are rarely considered in the literature. Forcings can cause substantial variations in lake productivity, which corroborate the meteorological and thermal findings described by Refs. [21, 22]. Interdisciplinary analysis of lake dynamics is essential in improving our understanding of how these ecosystems modulate productivity and subsequently impact climate.

This research aims to make a significant contribution to the understanding of the lakes located in the Nevado de Toluca volcano region. Through a comprehensive and in-depth approach, including precise measurements of meteorological variables, numerical modeling of circulation and currents, and analysis of heat transfer patterns in sediments, we endeavor to gain a profound understanding of the hydrodynamic processes and water balances in these high mountain ecosystems. What sets this research apart is its multidisciplinary approach and meticulous examination of crucial factors, such as solar radiation, thermal stratification, and wind influence. The outcomes of this study will enhance our comprehension of the dynamics of high mountain lakes, thereby establishing a solid scientific foundation for the effective management and conservation of these invaluable aquatic ecosystems.

## **2. Study area**

Limnology has been focused for several decades on the study of high mountain lakes, which are considered to be excellent sentinels of current global change because of their particular limnological characteristics. These lakes tend to occur in clusters, with several to many lakes forming lake districts, as mentioned by previous studies [1, 23]. In this study, we will focus on our interest in El Sol and La Luna lakes, which are two high mountain lakes located on the Nevado de Toluca volcano at coordinates 19°10<sup>0</sup> N 99°45<sup>0</sup> W and an altitude of 4200 m above sea level. During the warm rainy season, temperatures can reach up to 11°C in the water column. However, during the winter season, temperatures are closer to 4°C. The waters of the lake are transparent and well-oxygenated, with concentrations close to saturation (�7 mm/L) throughout the water column [24]. Lakes have a homogeneous mixture and a very distinctive polymictic pattern [24].

**Figure 1** shows the location and configuration of Nevado de Toluca volcano. It has a horseshoe shape that surrounds two central lakes, with a circular dome reaching a height of approximately 100 m in between. Due to the difference in height between the western and eastern walls of the volcano, wind currents enter the crater, with the former being 345 m higher than the latter [24]. It has been reported that the lakes exhibit a limited buffering capacity, leading to an acidic pH range of 4.9–5.6 [25]. Additionally, the conductivity levels were recorded between 18 and 24 μS c/m, with low levels of dissolved and suspended organic matter.

The maximum depth recorded in El Sol is 15 m, while its average depth is 6 m. Additionally, its area covers 237,321 m2 , with a length of 795 m and a width of 482 m

**Figure 1.** *Location and panoramic photos of Toluca Volcano (a) and (b).*

[21, 24]. Similarly, La Luna has a maximum depth of 10 m and an average depth of 5 m. Its surface area is 31,083 m2 , with a length of 227 m and a width of 209 m [24, 26]. The climate in Nevado de Toluca varies from cold to semi-cold and humid, with average monthly temperatures ranging between 2 and 12°C and an annual average of approximately 3.8°C [27]. The average annual precipitation is between 1200 and 2000 mm, concentrated between the months of May and September. In winter, there is precipitation in the form of snow, while after March, it occurs in the form of rain [24].

## **3. Data and methods**

## **3.1 Field measurements and instruments**

Field measurements in the lakes were conducted during two separate experiments. The first experiment took place from October to September 2010, while the second one occurred from May 2017 to September 2019. It is worth noting that the latter experiment was executed with greater precision and utilized additional equipment. During the first experiment, four buoys were deployed as shown in **Figure 2a**. On buoys numbered 1–3, five HOBO Water TempProV2 sensors from Onset Computer Corp. were installed with an accuracy of �0.2°C at depths of 1 to 5 m. On buoy number four, 10 sensors were installed at each meter up to a depth of 10 m, and an upward-facing current meter (ADP SONTEK 1000 kHz) was anchored on the bottom (**Figure 2b**). The sampling interval for all sensors was 1 minute. Also, in the two lakes, water level meters (tide and wave recorder SBE-26, Sea-Bird Electronics Inc.) were installed at the bottom of the coastal zone to record high-frequency water variations (seiches) with a sampling frequency of 1 second and a level resolution of 0.1 mm for 7 hours (**Figure 2b**).

The first theoretical period of the waves can be estimated by modeling the theoretical period of seiche in a rectangular basin using Merian's formula, where the first mode is given <sup>¼</sup> <sup>2</sup>*<sup>L</sup>*ffiffiffiffi *gH* <sup>p</sup> , where H is the mean depth and L is the length of the lake.

*Temperature Regime, Dynamics and Water Balance of Two Crater Lakes in the Nevado de… DOI: http://dx.doi.org/10.5772/intechopen.112196*

#### **Figure 2.**

*(a) Bathymetric maps from September 28, 2010, and may 9, 2017. The white circles indicate the positions of the moorings with HOBO thermographs and SBE-26 (white cross) in the two lakes. (b) Shows the location of the instruments in the water column and the position of the ADP (modified from ref. [26]).*

#### **3.2 Measurements in lakes in 2018: 2019**

To measure the temperature of two lakes, a HOBO© Water TempProV2 thermistor chain was deployed in the deepest part of each lake. The measurement period lasted for over 2 years, from May 10th, 2017 to September 8th, 2019. In Lake El Sol, the thermistor chain consisted of 13 sensors, which were connected to a floating weather station. Meanwhile, Lake El Sol and Lake La Luna had thermistor chains deployed in their deepest parts to measure their temperature. A HOBO© Water TempProV2 thermistor chain was used for this purpose. The measurement period lasted for over 2 years, from May 10th, 2017 to September 8th, 2019. Lake El Sol's thermistor chain had 13 sensors and was connected to a floating weather station. On the other hand, Lake La Luna's chain had 12 sensors. To monitor the temperature of Lake La Luna, several thermographs were placed vertically from the surface to a depth of 3 m, with seven devices every 0.5 m, and then at 1 m intervals to the bottom. The temperature was recorded every 15 minutes. An innovative approach was also employed in this study by installing a floating weather station in the center of Lake El Sol.

The study utilized data from two weather stations. One of the stations was installed directly in the crater of the El Sol Lake volcano, while the other station, registered under the National Meteorological Service of Mexico (NMS 00015062, 19° 7.171΄ N; 99° 44.851΄O), was situated on the slope near the volcano surveillance post. The straight-line distance between the two weather stations is 1.7 km, and the crater station sits approximately 47 m higher than the slope station. Both stations recorded wind speed and direction, relative humidity, barometric pressure, solar radiation, and rainfall.

**Figure 3** shows the structural diagram of the anchoring system for the floating weather station. The system consists of a metallic structure on which the weather station is mounted, with the anemometer positioned 2 m above the water level at the upper end of the structure. Whereas the other end of the structure was submerged at a depth of 4 m, supported by a 30 kg weight, and three buoys were attached to the

#### **Figure 3.**

structure to maintain the stability of the weather station and avoid recording errors caused by wind. Fifteen HOBO thermographs were installed in the same mooring. Two of them were placed on the water's surface, at a height of 0.1 and 2 m, and were protected inside two white, heat-reflecting plastic cylinders that were nested one inside the other. The remaining thermographs were placed below the lake level at depths of 0, 0.5, 1, 1.5, 2, 2.5, 3, 4, 5, 6, 7, 8, and 9 m.

Measurements of wind speed and air temperature were taken at a frequency of 15 minutes from June 19 to October 25, 2019. However, wind speed records were not available for the last 2 months of the period. It has been asserted that in shallow lakes, heat flux reaches the bottom [28, 29]. Hence, in this study, we will analyze the impact of this phenomenon on the bottom stratification of two lakes. We used an RBR TDR-2050 temperature and depth recorder to measure the heat fluxes between the water and the lake bottom sediment. This equipment is calibrated to an accuracy of 0.002° C (ITS-90) over a range of 5 to +35°C and was buried at a depth of 15 cm in the lake bottom sediments. In addition, we used an instrument that had a depth measurement range of 0–50 m, ensuring an accuracy of 2.5 mm in our level measurements. Moreover, spectral analysis was employed to study the spatiotemporal variation of temperature within the lakes.

## **3.3 Spectral analysis**

Spectral analysis was conducted on the measured water temperature series to assess the spatiotemporal variability of temperature fluctuations in Lake Sol y la Luna. The automatic spectral functions were calculated using the fast Fourier transform, and *Temperature Regime, Dynamics and Water Balance of Two Crater Lakes in the Nevado de… DOI: http://dx.doi.org/10.5772/intechopen.112196*

subsequently, the periodograms of the frequencies were smoothed. The functions were calculated to determine the spatial and temporal relationship of temperature fluctuations in both lakes [30–33]. The estimate of the spectrum of the smoothed periodogram was obtained as follows:

$$\hat{\mathcal{S}}\_{\text{xx}}(\boldsymbol{\alpha}) = \int\_{-\infty}^{\infty} \mathcal{S}\_{\text{xx}}(\boldsymbol{\alpha}') Z(\boldsymbol{\alpha} - \boldsymbol{\alpha}') d\boldsymbol{\alpha}' \tag{1}$$

where *Z*ð Þ *ω* is a smoothing function, and *Sxx*ð Þ *ω* is defined as the auto-periodogram:

$$\mathbf{S}\_{\mathbf{x}\mathbf{x}}(\boldsymbol{\alpha}) = \frac{1}{T} \mathbf{C}\_{\mathbf{x}}(\boldsymbol{\alpha}) \mathbf{C}\_{\mathbf{x}}^{\*}(\boldsymbol{\alpha}) \tag{2}$$

where *Cx*ð Þ *ω* is the amplitude spectrum:

$$C\_{\mathbf{x}}(\boldsymbol{\alpha}) = \int\_{0}^{T} \boldsymbol{\mathfrak{x}}(t) e^{-2\pi i \boldsymbol{\alpha}t} dt \tag{3}$$

of the time series *x t*ð Þ; *T* is the total length of the series; ð Þ ∗ denotes the complex conjugate of the amplitude spectrum. The standard algorithms described in the literature [30–33] were used to calculate the confidence intervals for all spectral estimates. The number of degrees of freedom *υ*, was found as *υ* ¼ 2 2ð Þ *F* þ 1 ; where *F* is the halfwidth of the filter that is used to smooth the periodograms. The mean square amplitudes of the harmonics of the dominant peaks in the spectra were found from the values of the spectral density.

#### **3.4 Hydrodynamic model**

Delft3D is an open-source numerical model developed by WL/Delft Hydraulics and the Delft University of Technology [34]. It includes implementations of several mathematical models for different physical phenomena (currents, transport, wave propagation, morphological developments, etc.). The Delft3D model solves the Navier-Stokes equations for an incompressible fluid, under the shallow water and the Boussinesq assumptions using a finite difference scheme.

This model is a tool made up of different modules (Delft3D-FLOW, Delft3D-WAVE, Delft3D-MOR and Delft Dash Board) open source and with a free version. It is made up of several program modules that focus mainly on coastal and river systems and that has been well evaluated in work on lentic systems [35–37]. In the present study, the model is used to predict the circulation in the lake system. The model includes the depth-averaged horizontal momentum equations:t

$$\frac{\partial u}{\partial t} + \mathfrak{u} \bullet \nabla u + \mathfrak{g}\frac{\partial \eta}{\partial \mathbf{x}} - f\flat + \frac{u||\mathfrak{u}||}{\mathbb{C}^2(d+\eta)} - \frac{F\_\mathbf{x}}{\rho(d+\eta)} - \nu \nabla^2 u = \mathbf{0}$$

$$\frac{\partial v}{\partial t} + \mathfrak{u} \bullet \nabla v + \mathfrak{g}\frac{\partial \eta}{\partial \mathbf{y}} + f\natural + \frac{v||\mathfrak{u}||}{\mathbb{C}^2(d+\eta)} - \frac{F\_\mathbf{y}}{\rho(d+\eta)} - \nu \nabla^2 v = \mathbf{0} \tag{4}$$

the depth-averaged continuity equation:

$$\frac{\partial \eta}{\partial t} + \frac{\partial (d + \eta)u}{\partial \mathbf{x}} + \frac{\partial (d + \eta)v}{\partial y} = Q(d + \eta) \tag{5}$$

and the vertical momentum equation, which reduces to the hydrostatic pressure relationship *via* the Boussinesq approximation: *<sup>∂</sup><sup>p</sup> <sup>∂</sup><sup>z</sup>* ¼ �*ρg*, where *u*, *v* are the depthaveraged velocity in the *x* and *y* directions, *C* is the Chézy coefficient, *d* is the water depth, *η* is the free surface elevation above the reference plane (at *z* ¼ 0), *u* is twodimensional current vector, with k k∙ the Euclidean norm, *Q* are sinks or sources of water, *f* is the Coriolis force, *Fx*,*<sup>y</sup>* is the Reynolds stress, *g* is the gravity, *ν* is the horizontal eddy viscosity, *p* is the pressure, and *ρ* is the water density.

Modeling was done only for Lake El Sol since no meteorological measurements were made for the other lake. The RFGRID module of Delft3D was used to generate the grid file. A mesh grid of 61 x 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 [26]. The time step allowed was Δt = 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/s<sup>2</sup> ; water density 1000 kg/m<sup>3</sup> ; air density, 1 kg/m<sup>3</sup> ; uniform Chézy roughness, 65 m1/2/s; background horizontal and vertical eddy viscosity and diffusivity of 1 and 10 m<sup>2</sup> /s, respectively. Delft3D is a model that has been tested and used globally for the study of lake systems [35, 37, 38]. In addition, it has been used specifically in the hydrodynamic analysis of Mexican crater lakes [36, 39].

## **4. Results**

#### **4.1 Meteorological variables**

Detailed information about the meteorological conditions at the Nevado de Toluca volcano can be found in various recent publications [14, 15, 18]. For our study, we utilized a three-year dataset of solar radiation, air temperature, and precipitation from 2017 to 2019, which was collected at the NMS meteorological station. This time frame corresponds to the period of our fieldwork within the volcano crater (**Figure 4a**–**c**). However, wind data could not be included due to the poor performance of the speed sensor.

In a recent study [24], researchers analyzed an eight-year dataset of meteorological parameters, including wind, collected at the NMS meteorological station located on the southern outer slope of the Nevado de Toluca volcano. The results showed that wind on the slope of the volcano is relatively weak and predominantly blows in two directions: 80° (southeast) and 200° (southwest) (**Figure 5a** and **b**). The wind speed throughout the year did not exceed 4–5 m/s, but during some winters, an increase in the average speed up to 10 m/s was observed (**Figure 5a** and **b**).

The total solar radiation entering the crater was lower than at the NMS station due to the obstruction of the sun's rays by the high walls of the crater in the morning and evening hours. Consequently, solar radiation input is closely related to temperature changes in the lakes, although the impact of wind currents cannot be overlooked, especially in Lake La Luna where mixing is more intense than in Lake El Sol. The latter lake is protected by the lava dome [24].

#### **4.2 Water temperature, rainfall, evaporation, current, and level fluctuations**

The meteorological regime around the Nevado de Toluca volcano has been extensively described in several recent publications [22, 24, 26]. According to these

*Temperature Regime, Dynamics and Water Balance of Two Crater Lakes in the Nevado de… DOI: http://dx.doi.org/10.5772/intechopen.112196*

**Figure 4.** *Hourly variability of solar radiation (a), air temperature (b), and precipitation (c) measured at the NMS station during the period of 2017–2019.*

#### **Figure 5.**

*Monthly dynamics of wind speed and direction vectors (a) inside and outside (b) the volcano crater for the 24 hour cycle of January 1 to December 31, 2007. The figures also show wind speed and direction histograms for the entire observation period on the right-hand side (modified from ref. [24]).*

publications, the slope of the volcano receives a maximum of 1000 W/m2 of solar radiation around 3 pm, and there is no radiation from 6 pm to 9 am the following day. Solar energy penetrates 20% less into the crater of a volcano due to its high walls, as reported in a study [24]. The supply of solar energy to the crater lakes is at its peak during March and April, and at its lowest between June and August, as well as during the rainy season when cloud cover reduces energy penetration. Fluctuations in air temperature are highest in April and May, particularly in the early afternoon, while the lowest temperatures occur during the rainy and winter seasons.

Another recent study [22] suggested that the difference in lake stratification (**Figure 6a** and **b**) during summer may be due to Lake El Sol's lower transparency, which absorbs more heat at the surface compared to the more transparent Lake La Luna. It also suggested that vortex diffusion, not wind mixing, causes heat exchange between the near-surface layer and deeper waters.

Although seiches fluctuations in lakes are a common occurrence, they are weak in the crater lakes studied due to their small size and depth, as well as protection from wind impact by the crater walls. Spectral analysis revealed two seiche oscillations in Lake El Sol with periods of 167 and 81 seconds and corresponding amplitudes of about 2 and 1.5 mm. The first oscillation was along the main axis of the lake, while the second was perpendicular to this axis. Lake La Luna had only one free oscillation with a period of 53 seconds and an amplitude of about 3 mm.

To examine the relationship between precipitation, evaporation, runoff area, and the level of Lake El Sol, the authors used data from the NMS weather station and time series of water level measured by the TDR-2050 instrument. The results of these experiments are presented in **Figure 7a**–**e**. Precipitation was the main source of water entering the lakes, which had small runoff areas due to their specific orography. The catchment area of Lake El Sol was only 2.17 km<sup>2</sup> , while Lake La Luna's catchment area was 2.0 km<sup>2</sup> . Average annual precipitation was 1.2771 m<sup>3</sup> , and evaporation was 0.9708 m<sup>3</sup> , with the largest average monthly evaporation in February (112 mm/ month) and the lowest in June (63 mm/month).

Currents measured in the upper 2-m layer at the floating weather station in September–October 2010 showed that wind currents only reached this depth and did not

#### **Figure 6.**

*Hourly variability of temperature at 13 depths of El sol Lake (a) and at 12 depths of La Luna Lake (b) for the same time period. The instrumental depths are clearly indicated in the legend.*

*Temperature Regime, Dynamics and Water Balance of Two Crater Lakes in the Nevado de… DOI: http://dx.doi.org/10.5772/intechopen.112196*

#### **Figure 7.**

*Zonal (a) and meridional (b) components of the currents were measured by the acoustic doppler profiler (ADP) in mooring 4, located in El sol Lake. The wind rose from the NMS station data is shown in (c), while (e) displays a histogram of the directions of the currents in the upper 1-m water layer. Additionally, a vector histogram of the same data is presented in (d).*

penetrate deeper (**Figure 7a** and **b**). The currents were weak, not exceeding 3–5 cm/s, and did not display strict daily periodicity as temperature fluctuations in the surface layers of the lake (**Figure 7a** and **b**). **Figure 7c** and **d** also displays the wind direction and speed during the experiment.

The level of Lake El Sol's annual variation was relatively smooth, sometimes disturbed by small jumps due to precipitation. The annual minimum temperature occurred in early January 2018 at the water-bottom sediment boundary in the deepwater part of the lake, reaching 4.8°C and increasing slightly to 5.7°C at the bottom before dropping again to 4.5°C in early February (**Figure 8**). In addition, as shown in **Figure 8**, it can be observed that during the summer season, the bottom temperature was approximately 10°C.

### **4.3 Lake level fluctuations and processes occurring at its bottom**

A precise time series spanning over 13 months was obtained by using the TDR-2050 RBR temperature and level meter, which was submerged in the sludge at the bottom of the lake (**Figure 8**). This was made possible due to the highly accurate temperature and level sensor, with an accuracy of 0.002°C and 0.05% full scale for

#### **Figure 8.**

*Annual series of temperature fluctuations of bottom sediments (1) and the water level of Lake El sol (2) in the area surrounding the floating meteorological station have been recorded.*

pressure, making it two orders of magnitude better than the temperature measured using the Hobo V2.

In the winter months, the water temperature near the bottom of the lake drops to a minimum of 4.7°C, which is close to the maximum density temperature of water. The diurnal variation is prominently observed at the lake's bottom, with a larger range from November to May (0.2–0.3°C) than the remaining months of the year (**Figure 8**).

Using temperature measurements taken from both the bottom of a body of water and the sediment at the bottom, heat fluxes were determined near the interface of the water and sediment using the gradient method [28, 29]. This was done through the use of the formula Q = <sup>λ</sup> <sup>∂</sup>T/(∂z), where Q represents the heat flow in W/m2 near the boundary between the water and sediment, λ represents the coefficient of molecular thermal conductivity of water in the 0–10 m layer (which is 0.5813 W/(m°C)), and ∂T/(∂z) represents the temperature gradient.

According to the calculations, the bottom of the lake had a steady heat flow during the entire observation period. The heat transfer from the lower layers of water to the sediment beneath was measured to be below 0.1 W/m<sup>2</sup> in the spring, summer, and autumn months, which is much lower compared to the solar radiation that enters the lake's surface [24]. This solar radiation can reach up to 1000 W/m2 , but gets absorbed and dissipated within the water column. However, during winter, the heat flow changed direction with heat moving from the sediment to the water column, and the heat flux measured during this period was almost 0.3 W/m2 .

#### **4.4 The water balance of the lake depending on precipitation and evaporation**

The water equilibrium of a crater lake relies on several factors, including the inflow of water from precipitation, as well as the loss of water due to processes such as evaporation, runoff, and gravity filtration. On Nevado de Toluca, the steep slopes act as collectors of atmospheric precipitation, which helps to maintain a hydrological balance through the processes of evaporation and filtration. The altitude of the volcano also facilitates groundwater retention, which is essential in determining the water balance of closed water bodies. To achieve this, physiographic and meteorological characteristics, such as the watershed area, precipitation rates, evaporation, and water seepage volume, must be considered. While precipitation has been measured in the Nevado de Toluca basin and the surface area of the basin is known, it is important to study the volumes of water lost due to seepage from the bottom.

The slopes on the southern and western sides of the volcano's crater are steep, which results in shading over the lake. As per a study [24], this shading reduces the penetration of solar energy into the lake by roughly 20% during the morning and afternoon hours compared to daytime hours. We have taken this factor into account during our calculations, and we have determined that the annual evaporation rate is 940.1 mm.

**Table 1** presents information obtained from our field measurements and estimates of the water balance of Lake El Sol during the dry season. According to the data, the area of the lake during this season is 200,330 m2 , while the runoff area is significantly larger, at 2,170,000 m2 . These results suggest that Lake El Sol's water level largely depends on runoff to maintain itself during the dry season, as well as on annual precipitation, which does not exceed 50.8 mm. However, the evaporation rate reaches 3.33 mm/day, indicating that the lake loses a significant amount of water due to evaporation.

Annual measurements of mean values (using CNA measurements) reveal that the average area of the lake during both the rainy and dry seasons is 201,165 m<sup>2</sup> .

*Temperature Regime, Dynamics and Water Balance of Two Crater Lakes in the Nevado de… DOI: http://dx.doi.org/10.5772/intechopen.112196*


#### **Table 1.**

*Annual average values as extracted from ref. [26].*

Furthermore, the runoff area amounts to 2,170,000 m<sup>2</sup> , indicating that a considerable amount of water flows into the lake from its catchment area.

Moreover, the rainfall rate reported by the NMS is 1.359 m, while the calculations show a rate of 1.2771 m. Similarly, the NMS records an evaporation rate of 0.941 m, whereas the calculations indicate a rate of 0.9708 m. These disparities could be attributed to differences in measurement techniques.

The accumulated volume in the lake is 907,060 m<sup>3</sup> , which represents the total amount of water in the lake at a given time. The expected elevation due to evaporation is 4.509 m, but the actual elevation only increases by 1.20 m. This difference could be due to other factors that affect the water balance of the lake, such as outflow.

### **4.5 Hydrodynamics of lake El sol**

Thermal stratification is the primary hydrodynamic force in high mountain lakes. However, other factors, such as wind shear, precipitation, and seismic activity, also contribute to the system. Furthermore, the interaction of these forcings can generate complex hydrodynamic processes that significantly affect circulation, mixing, and water quality in high-mountain aquatic ecosystems. Importantly, thermal stratification occurs due to the difference in water density in different layers of the lake, which is caused by solar radiation. Wind shear can break the thermal stratification, allowing vertical mixing of water and generating currents on the lake's surface. Precipitation can also affect lake hydrodynamics, especially in regions where rainfall is intense, and lakes have a direct connection to rivers and streams. Seismic activity can generate waves and disturbances in the water that affect the circulation and mixing of water in the lake.

**Figure 9** shows the results of numerical modeling performed using the Delft3D model. The objective of this simulation was to complement the findings described in [26], which focused on the current field in Lake El Sol. In the previous study, we employed a current meter (ADP Sontek) and determined that wind-induced currents are restricted to the uppermost layer of the lake, extending up to a depth of 2 m, and do not exceed speeds of 15 mm/s. Consequently, we have restricted the presentation of current simulation outcomes to the upper layer of the lake.

The model inputs were created using accurate temperature, wind direction, and wind speed data recorded at the surface of the lake. This was made possible through the installation of a floating weather station, which is marked with a red circle in the upper-left panel and located in the deepest part of the lake.

#### **Figure 9.**

*Modeling results of current and water level fluctuations in Lake El sol based on observations taken on September 5, 2018. The rectangles illustrate the simulated currents and level fluctuations for every 2 hours. The black and red patterned arrows in the lower left corner represent the scales for current velocities and measured wind, respectively.*

The modeling results indicate the existence of two distinct closed circulation patterns, each with an opposite direction of circulation. The weaker circulation, with speeds ranging from 2 to 4 mm/s, appears in the central-northeast regions of the lake and rotates counterclockwise (**Figure 9**). Variations in this circulation are directly linked to the wind patterns recorded at the floating meteorological station. On the other hand, the stronger circulation, with clockwise rotation and speeds ranging from 8 to 10 mm/s, is observed in the deep southern part of the lake (**Figure 9**).

Furthermore, it has been observed that the level fluctuations of Lake El Sol vary up to a maximum height of 25 mm. However, no numerical analysis was conducted for Lake La Luna because it is impossible to install a floating meteorological station in this body of water.

## **5. Discussion and conclusions**

During the period from 2017 to 2019, various meteorological variables were examined in the Nevado de Toluca volcano region, including solar radiation and air

### *Temperature Regime, Dynamics and Water Balance of Two Crater Lakes in the Nevado de… DOI: http://dx.doi.org/10.5772/intechopen.112196*

temperature outside the crater. The results obtained were consistent with the values reported in previous studies (e.g., [24, 26]), which covered the period from 2000 to 2007. With regards to the annual precipitation in the area adjacent to the volcano, values of 11,622 mm, 1359 mm, and 1198 mm were recorded during the studied period, which falls within the normal range of precipitation reported in Ref. [26] for the same area.

On the other hand, the magnitude and direction of the wind directly over the surface of Lake El Sol turned out to be much lower than outside the crater, due to the presence of the volcano walls and their shielding effect on the lake. This process has been well described in other works [40–44].

Although it is known that there is a decrease in temperature with altitude (for dry air, 9.9°C/km), the air is rarely dry and the actual relationship between temperature and altitude varies both temporally and spatially depending on climatic conditions (humidity, wind, and radiation) and topography [45]. In our study, the air temperature showed a diurnal oscillation, typical of tropical zones [46, 47]. In addition to a daily variation, a seasonal variation was also observed in air temperature, with greater amplitude from September to May (2 m above the lake surface), and amplitudes below 0.1 m above the lake surface for these same months. For both time series of air temperature, maximum and minimum values (9°C, 22°C) fall within the range of temperatures observed in other mountainous areas [46, 48].

The behavior of meteorological variables, specifically air temperature, affects the resistance of the water column to mixing processes [49]. Air temperature is a key factor in temperature changes in lakes [48, 50]. Spectral analysis has been used to study these relationships in alpine lakes [51], Mexican lakes [26, 36, 52, 53], and particularly in lakes El Sol and La Luna [24]. The spectrum was dominated by diurnal and semidiurnal oscillations, with high coherence values (0.920) between air temperature and lake temperature. Frequency spectra analysis was also used to describe fluctuations in the lake level, where diurnal and semidiurnal oscillations were observed (24- and 12-hour), as well as 4- and 8-day periods.

During our measurement period, the temperature of Lake El Sol fluctuated between 6 and 14°C, while Lake La Luna recorded temperatures between 6 and 13°C. These values are similar to those reported by [24]. Additionally, they are consistent with the maximum values previously reported by Alcocer, Roberson, Oseguera, and Lewis [22] for these same lakes.

Through *in situ* measurements, we observed unexpected changes in temperature near the bottom of the lake. We detected a heat exchange between the bottom water layer and the sediments that is distinct from the exchange pattern described in Ref. [54] for Lake Biwa (Japan). During winter, the sediments release heat to the water column, resulting in this unique pattern. These heat transfer patterns can often be complex and arise from a wide range of characteristics. The steady-state temperatures of volcanic lakes are primarily determined by the magnitude of the volcanic heat influx relative to the lake's surface area [55].

The level of the lake is a parameter that depends on rainfall and evaporation. In our lake, it was observed that the level increased less than what theoretical calculations would suggest [56]. Numerous studies have demonstrated links between water levels and climate variability or change [57, 58]. However, some studies suggest that although water levels and climate cycles may be correlated, it is challenging to isolate the effect of individual forcing or attribute water-level trends to that forcing [59, 60].

In our study, we analyzed the lake level data over a two-year time series and observed a discrepancy, for the first time at this site, between the measured levels and theoretical calculations. Our findings emphasize the challenges of planning and maintaining equipment in high mountain areas, as well as the complex relationships among meteorological drivers, thermal regimes, and water balances in these unique mountain lake ecosystems.

For the first time, we were able to observe the free surface level of Lake El Sol and the circulation patterns in its surface layer resulting from wind stress using a numerical model. Since the hydrodynamic behavior of this body of water largely dominates and regulates the chemical and biological processes within it, a structured analysis of these processes is crucial to evaluate and understand the lake system as a whole.

## **Acknowledgements**

The authors would like to express their gratitude to each participant of the expedition who made it possible to complete this work. Specifically, we would like to extend our thanks to Dr. Luis Alberto Oseguera, Dr. Omar Mireles-Loera, Arturo Orozco-Estrada, and Carlos Villarreal-Olavarrieta. Additionally, we would like to thank the Comisión Estatal de Parques Naturales y de la Fauna (CEPANAF) within the Secretaría de Ecología of the Government of the State of Mexico for providing the permit for scientific research at the Área de Protección de Flora y Fauna Nevado de Toluca. We are also grateful to the Mexican National Science Foundation (CONACyT) for providing financial support for projects No. 466674-F and 262979.

## **Author details**

Anatoliy Filonov, Iryna Tereshchenko, María del Refugio Barba-López, David Avalos-Cueva\* and Cesar Monzon Department of Physics, University of Guadalajara, Guadalajara, Jalisco, Mexico

\*Address all correspondence to: david.avalos@academicos.udg.mx

© 2023 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Temperature Regime, Dynamics and Water Balance of Two Crater Lakes in the Nevado de… DOI: http://dx.doi.org/10.5772/intechopen.112196*

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## **Chapter 11**
