Vertical distribution of annual water temperature maxima in the southern coastal zone of Lake Baikal

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1. Introduction

The current knowledge of thermal structure and interannual variability in large lake require much more simulations and observations than available today (Beletsky et al., 2006). Especially, it concerns a large dimictic lake, Lake Baikal, with the biggest depth and largest freshwater volume among the world`s lakes (Minoura, 2000; Sherstyankin et al., 2006). According to many publications, it is known that the lakes in the world are exposed to climate change (Adrian et al., 2009; O’Reilly et al., 2015). In fact, during the last 30-year period, the water surface temperature of world lakes increased, ice–covered period decreased, date and duration of stratification period changed. The Lake Baikal ecosystem is undergoing rapid change on a local and global scale (Hampton et al., 2008; Izmest`eva et al., 2016). The vertical and horizontal exchange of heat and momentum determines the distribution of water temperature from surface to bottom. Quantification of hydrophysical processes is necessary to understand the changes in many aquatic processes. For these reasons, as well as for monitoring climatological temperature conditions in lakes, knowledge of the spatial and temporal distribution of lake water temperature can be extremely valuable (Carpenter et al., 2011).

The thermal regime of a large dimictic lake is determined by the seasonal course of heat input to the water surface, the interaction of the moving air layer with water, and the propagation of heat into the depths of the lake. Dimictism of the lake stratum is manifested in the fact that the lake is stirred twice a year from the surface to the bottom due to the anomaly of fresh water density at a temperature of 3.98°С on the surface. Usually, between two basic mixing events, the lake is stable and stratified for a few months. The classic three-layer vertical temperature distribution is formed: 1) the surface mixed layer (epilimnion), 2) the middle layer with big vertical temperature gradients (metalimnion) and 3) the bottom layer, which is colder, and denser than every upper layer (hypolimnion) (Boehrer and Schultze, 2008).

Usually, the annual maximum temperature on the water surface layer $T_{\max }$ occurs in the middle of summer. In Lake Baikal, due to its huge size, the annual water temperature maxima (AWTM) near the shore is observed in late July-August and in the open parts of the lake in August-September. The largest vertical temperature and density gradients arise during the heating period in metalimnion, 20–30 days before the surface water temperature reaches its maximum (Naumenko and Guzivaty, 2022). Then the cooling begins, initiating convective mixing, which accelerates the deepening of the epilimnion, and the gradients deccrease. Heat is transferred to the underlying horizons, resulting in a shift of temperature maxima to greater depths and a decrease in their values. On every date, the penetration of heat to underlying horizons can be traced as the deepening of annual water temperature maxima from surface layer to bottom on a certain vertical (James, 1971; Stepanenko et al., 2018). In autumn, when the heat reaches the bottom, the overturn (that is, a vertical isothermia) arises, and the temperature at the bottom becomes the highest for the year in the large dimictic lake.

Seasonal variations in thermal stratification can influence phytoplankton and zooplankton population dynamics (Eckert and Walz, 1998; Brandão et al., 2012). The vertical extent of the epilimnion (i.e., the mixed layer depth) and the magnitude of the thermal gradient in the water column affect plankton growth and primary production (Vincent et al., 1984; O’Brien et al., 2003; Brighenti et al., 2015) and thereby regulate light penetration and internal nutrient loading. Thus, the absolute annual maximum temperature $T_{\max }$ and time of occurrence of annual peakat $t_{T_{\max }}$ at certain depth $Z_{T_{\max }}$ are to influence the position of the chlorophyll concentration maximum during the seasonal course of the lake ecosystem parameters. Therefore, the deepening of the temperature maximum in stratified lakes can be considered not only as an important hydrophysical process but also as a parameter influencing the structure of the ecosystem. Moreover, the climatic maxima change may affect fish populations and communities (Gillis et al., 2021).

Obviously, knowledge of the magnitude and date of onset of temperature maxima at different horizons is necessary to understand changes in many water processes in different types of lakes. There are publications about the importance of these extreme events (Sharma et al., 2008; Minns et al., 2018; Ptak et al., 2019; Dokulil et al., 2021), and unfortunately, they practically concern only surface water temperature except for the article (Hondzo and Stefan, 1996), which deals with the bottom temperature.

There are no publications about the vertical distribution of AWTM in dimictic lakes, in particular in the deep regions of Lake Baikal. The interannual variability of temperature and the depth of occurrence of the mesothermal maximum temperature during the period of winter stratification in Lake Baikal are considered in the article (Aslamov et al., 2024). The only two articles on the distribution of maximum water temperatures in the coastal zone of Lake Baikal concern the bottom depths of 15 meters or less (Rossolimo, 1957; Fedotov and Khanaev, 2023). Therefore, the objective of this study was to present for the first time the data of annual water temperature maxima $T_{\max }$ by using stationary long-term high-precision temperature measurements at different horizons (since 2005 to 2016 except 2009) referring to the bottom depths up to 500 m in the southern coastal zone of Lake Baikal. After analyzing the observed vertical temperature profiles data sets the empirical relationship between both the absolute annual maximum temperature $T_{\max }$ and the date $t_{T_{\max }}$ and depth of its appearance $Z_{T_{\max }}$ were established.

2. Data and Study area

Lake Baikal has been studied extensively since 1990, when the Baikal International Center for Ecological Research (BICER) was created. Stationary long-term high-precision temperature measurements have been carried out since March 1999 by Research Institute of Applied Physics of Irkutsk State University in cooperation with the Swiss Federal Institute of Environmental Science and Technology (EAWAG) and Limnological Institute SB RAS on the base of the Lake Baikal Neutrino Experiment (Baikal Neutrino Telescope NT200+ in operation) (Aynutdinov et al., 2009). Several stations were set up in the southern coastal zone of the lake.

We used data from the buoy station closest to shore at a distance of 1.0 km and a bottom depth of 550 m (Fig. 1a). Seven temperature loggers distributed along the lake bed and 15 m deep recorded the temperature profile throughout the year at 15 min intervals for eleven years from 2005 to 2016 (except 2009). Measurement horizons were: 1) 14.7 to 26.5 m, 2) 50 to 52.3 m, 3) 100 to 102.3 m, 4) 150 to 152.3 m, 5) 200 to 202.3 m, 6) 250 to 252.3 m, and 7) 300 to 302.3 m. The characteristics of the measurements performed are given in Aslamov et al., 2024. Some of the variation in logger depths is due to technical difficulties in installation from year to year. Figure 1a shows the location of the buoy station in Southern Baikal, near Cape Ivanovsky (51°47′22.7″ N, 104°24′53.4″ E).

 

Fig.1. Location of the buoy station in Southern Baikal (A) and seasonal course of water temperature for two different stratification periods, namely the very warm (2005) (B) and the very cold periods (2010) (C).

 

The average bottom slope in the station area is 33° (Bathymetric map..., 2024), which exceeds the critical value for sliding processes (Hakanson and Jansson, 2002). This indicates that both the sliding of water masses and the movement of substances can occur on this slope.

The southern part of Lake Baikal has pronounced peculiarities associated with the influence of the bordering shores with various heights and wind action in the semi-enclosed area of the lake. As Kozhova and Izmest’eva (1998) reported, in the southern part of Lake Baikal, strong northwestern winds disrupt often the summer stratification, generating cold-water upwellings along the western coast and causing surface water temperatures to plunge to 4 °C from 14° to 16 °C within hours. Strong winds can accelerate the mixing, and some warm pulses, followed by a return to 4 °C, can cause the thermocline to disappear. A well-mixed surface layer is formed by coastal downwelling due to inshore Ekman transport generated by a wind blowing parallel to the coast.

3. Results and Discussion

3.1. Basic features of vertical distribution of annual water temperature maxima in the southern coastal zone

The timing of the annual surface temperature maximum $t_{T_{\max }}$ is the most active period for the air-lake surface interaction (Naumenko and Guzivaty, 2022). The dates are important phenological indicators for assessing the long-term change in the thermal regime of large lakes, in particular Lake Baikal. Long-term year-round temperature measurements at certain horizons allow precise identification of key temperatures in the thermal cycle of Lake Baikal. For every available horizon (usually from 15–19 m to 300 m), both the maximum temperature $T_{\max }$ and its date $t_{T_{\max }}$ were estimated in the southern coastal zone of Lake Baikal based on the dataset used. This was done for the stable stratification period over eleven years, from 2005 to 2016, except 2009. Fig.1 shows the seasonal course of water temperature for two different data sets, namely the very cold stratification period and the very warm period. As the depth of measurement increases, the temperature change from higher to lower values is clearly visible. Obviously, there is a significant difference in temperature and the timing of the occurrence of maximum temperatures $t_{T_{\max }}$ at the two upper horizons, while at the lower horizons, these differences are much smaller. As for upwelling, it can be recognized by a sharp decrease in temperature in the upper horizons (Troitskaya et al., 2023).

In general, the most pronounced shape of the temperature graph for the upper layer of the lake has the shape of a pointed peak each year. It is well known that Lake Baikal is a typical dimictic lake up to a depth of the active layer of 200-300 m, where the annual seasonal temperature fluctuations are observed (Shimaraev, 1977; Shimaraev et al., 1994; Shimaraev et al., 2012).

The deeper temperature structure demonstrates more gentle curves with a short maximum period. At a depth of more than 100 m, seasonal fluctuations are insignificant (Fig. 1).

The statistical characteristics of the parameters of annual temperature maxima $T_{\max }$ and the dates of their occurrence $t_{T_{\max }}$ for the coastal zone of Southern Baikal are given in Table 1.

 

Table 1. Statistical characteristics of the parameters of temperature maxima $T_{\max }$ and the dates of their occurrence $t_{T_{\max }}$

Parameters	Z1	Z2	Z3	Z4	Z5	Z6	Z7
Annual temperature maximum $T_{\max }$, °C
Minimum	10.87	8.39	6.93	5.49	4.41	3.94	3.84
Maximum	18.15	16.04	10.35	7.29	6.11	5.37	4.18
Range	7.28	7.65	3.42	1.80	1.70	1.43	0.34
Mean	15.00	11.06	8.34	6.16	5.14	4.34	3.99
Std. dev.	2.64	2.20	1.32	0.56	0.55	0.41	0.11
Date of annual temperature maximum $t_{T_{\max }}$, day of year
Minimum	Aug.6	Aug.16	Sep.23	Oct.3	Oct.12	Oct.12	Oct.12
Maximum	Sep.16	Oct.8	Nov.2	Nov.19	Nov.24	Nov.25	Dec.17
Range	41	54	40	46	44	44	66
Mean	Aug.22	Sep.19	Oct.10	Oct.28	Nov.5	Nov.10	Nov.16
Std. dev.	14	15	13	15	14	15	19

Note: Z₁ conforms to the depth of measurement from 14.7 to 26.5 m, Z₂ from 50 to 52.3 m, Z₃ from 100 to 102.3 m, Z₄ from 150 to 152.3 m, Z₅ from 200 to 202.3 m, Z₆ from 250 to 252.3 m, and Z₇ from 300 to 302.3 m.

 

The annual maximum water temperatures in the years 2005-2016 varied from 10.9 °C in 2010 to 18.2 °C in 2005 at the highest horizon of about 20 m (Fig. 1). The average maximum annual temperature (15 °C) decreases from the upper horizon to a maximum density of 4 °C at a depth of 300 m. The smallest variability in maximum water temperatures was observed at the same depth. The interannual $T_{\max }$ range decreased dramatically with depth by 20 times compared to the upper horizon, as well as the standard deviation (Table 1).

Table 1 indicates that date of annual temperature maximum $t_{T_{\max }}$ varied from August 6 (2012) to September 16 (2013) at the highest horizon. The date difference is about one month and a half, with an average date $t_{T_{\max }}$ August 22.

On average, the occurrence of peaks $t_{T_{\max }}$ from horizon to horizon varied from 28 days between the upper horizons, with a deacrease to five days from 250 to 300 m.

However, in 2013, the difference between the dates of maxima at the neighboring upper horizons was the largest over the entire eleven-year period and was approximately 52 days.

The difference between the dates of maxima at the uppermost horizon and the lowest horizon averaged 86 days, with a maximum of 111 days in 2016. This phenomenon confirms the unevenness of heat input at depth from year to year, related to differences in weather conditions, the intensity of vertical mixing processes, stratification stability, and the degree of warming of the upper water layer.

The standard deviation of $t_{T_{\max }}$ is large and almost identical at all horizons (13 – 19 days), indicating a large scatter of dates.

Seven data sets for every studied horizon during eleven years illustrate how the annual maximum water temperatures varied versus day of year with linear dependence for every horizon (Fig. 2).

 

Fig.2. Annual maximum water temperatures depending on the day of year, with linear dependence for every horizon.

 

We can see that in the three upper horizons (up 100 m), there is a decrease in maximum temperatures with increasing dates. This means that the later the maximum temperature occurs, the lower it is. Starting from the horizon at 150 m, this pattern stops, and regardless of the date, the maximum temperature remains constant.

This supports the conclusion that a negligible amount of heat from the surface penetrates to these depths. Obviously, the variation of the maximum temperature with depth is strongly nonlinear.

In terms of climate trends, we found no significant trends for the eleven-year study period, for either $T_{\max }$ or $t_{T_{\max }}$.

3.2. Empirical relationship of variation of maximum temperature by time and depth

The upper layer of Lake Baikal reaches its maximum temperature in July and August in the southern part of the lake. Maximum temperatures are recorded at depths of more than 200 m between October and December. We hypothesize that for every specific dimictic lake (or some area of lake), the annual extreme temperatures can be a function of depth. It is obvious that if the summer vertical temperature distribution is stable, the maximum temperature will gradually decrease with depth due to surface heat penetration and horizontal exchange (Naumenko and Guzivaty, 2022). We wonder at what rate this deepening occurs and whether there are correlations between the magnitude of the maximum, its depth, and the time of the occurrence. To quantify changes in the AMWT, the previously developed approximation forms of empirical functions were used to find three dependencies, namely

$T_{\max }=F\left(h\right)$

$Z_{T_{\max }}=F\left(t\right)$

$T_{\max }=F\left(t\right)$

where h is depth in m, t is time, and day of year.

The forms of empirical dependencies and the coefficients of determination R² are given in Table 2 and Fig. 3.

 

Table 2. Empirical coefficients for dependencies developed for parameters of annual maximum water temperatures

Dependences	Formula	Coefficients
		a	b	c	R2
$T_{\max }=F\left(h\right)$	$a*\mathrm{Exp}(b*\mathrm{ArcTan}(\mathrm{Log}(h/1000)+c\left)\right)$	6.91	-0.72	2.11	0.87
$Z_{T_{\max }}=F\left(t\right)$	$a**\left(t/100\right)+c)$	5.47	-	0	0.66
$T_{\max }=F\left(t\right)$	$a*\mathrm{POW}\left(\left(t/100\right),b\right)*\mathrm{Exp}\left(c*\left(t/100\right)\right)$	351.46	-0.67	-1.12	0.87

 

Fig.3. Empirical dependences for estimation of the magnitude of the annual water temperature maxima, its depth, and the time of occurrence (left panel). The right panel demonstrates rates for the same parameters.

 

It is evident that each dependence has a nonlinear character (Fig. 3). Empirical dependence describes from 66 to 87% of the variability of the studied parameters.

To construct empirical relationships, we used the values found for only eight years, which amounted to 54 values for each sample. The values for the three remaining years were highlighted in orange in Fig. 3. They were used to verify the dependencies as independent data. Evidently, they lie within the same boundaries as the data used to construct the relationships. Independent observed data were compared with those estimated by the three empirical relationships. Root Mean Square Errors (RMSE) are 1.3 °C, 49 m, and 1.9 °C, respectively. It should be noted that the error in depth is quite large. This is due to the large variation of date $t_{T_{\max }}$ across the studied horizons.

Differentiation of the obtained dependencies enables to estimate the rates of change of the studied parameters. Due to the nonlinearity of relationships for the studied seasonal cooling period of the southern part of Lake Baikal, the greatest variability of the maximum annual temperatures with time $T_{\max }/\text{t}$ was observed in early August, right after the beginning of regular convective mixing at a depth of up to 50 m (Fig. 3, right upper and lower graph). At the same time, the rate of deepening $T_{\max }/\text{h}$ is also maximum.

Fig. 3, right center graph shows the rate of deepening $Z_{T_{\max }}/\text{t}$ over time. The minimum rate $Z_{T_{\max }}/\text{t}$ is observed in early August at about 0.5 m/day, and then it increases to 6 m/day in early December.

In this way, the empirical dependences obtained for the first time allow us to estimate the background seasonal evolution of the vertical distribution of AWTM values in the southern part of Lake Baikal and the rate of change of these parameters.

4. Conclusion

We analyzed in-situ measurements of water temperature with discreteness of 15 minutes for stable stratification period in the southern coastal zone of Lake Baikal with a bottom depth of 550 m for eleven years from 2005 to 2016, except 2009. For the first time, the absolute annual temperature maxima $T_{\max }$ and time of occurrence $t_{T_{\max }}$ at seven horizons were determined based on the dataset used. The statistical characteristics of the parameters are estimated. It should be noted that these characteristics will vary depending on the depth of the bottom and the distance from the shore of the lake. $T_{\max }$ at the upper horizon corresponds to the data on the maximum water surface temperature in Listvaynka (Fedotov and Khanaev, 2023). In contrast to the shallow zone of Lake Baikal, the maximum temperatures do not occur at the same time at all horizons. There are significant time shifts (about 86 days) between the uppermost horizon (~20 m) and the lowest horizon (~300 m).

The annual maximum temperature goes from the surface to a depth of 300 m, where it reaches ~4 °C. Attempts have been made to derive equations to approximate the vertical distribution of annual extreme water temperature with depth as background for analysis of possible climatic variations. The resulting dependencies are non-linear. They are verified using independent data. Much of the variation in extreme lake water temperature can be explained by the vertical heat exchange, which depends on the depth.

The rates of change of the annual maximum temperature with depth have been determined. The maximum rate of change occurs immediately after the beginning of seasonal surface cooling and free vertical convection. The rate of deepening of the maximum is a measure of the vertical penetration of heat to the depth and can serve as the hydrophysical basis for Lake Baikal. These conclusions correspond to similar results for Lake Ladoga (Naumenko and Guzivaty, 2023). Dokulil et al. (2021) indicate a substantial increase in annual maximum lake surface temperatures in several lakes. Our results provide significant evidence of the existence of the background empirical dependencies necessary for detecting the features in terms of regional climate changes.

Acknowledgements

Financial support for the research was mainly provided by the federal budget funds for the State Assignment FFZF-2024-0001 “Ecosystems of Lake Ladoga, water bodies of its basin, and adjacent territories under the influence of natural and anthropogenic factors against the background of climatic changes”.

Limnological Institute Siberian Branch of the Russian Academy of Sciences provided the initial data within the State Assignment LIN SB RAS (0279-2021-0004), and the results were jointly discussed on the basis of the State Assignment of the Ministry of Education and Science FZZE-2023-0004.

The authors thank colleagues from EAWAG (Switzerland) for joint field work and data collection and members of the Baikal Collaboration for assistance in expedition work.

Conflict of interest

The authors declare that they have no competing interests.

About the authors

M. A. Naumenko

Institute of Limnology of the Russian Academy of Sciences – St. Petersburg Federal Research Center, Russian Academy of Sciences

Author for correspondence.
Email: m.a.naumenko@mail.ru
Russian Federation, Sevastyanova Str., 9, St. Petersburg, 196105

V. V. Guzivaty

Institute of Limnology of the Russian Academy of Sciences – St. Petersburg Federal Research Center, Russian Academy of Sciences

Email: m.a.naumenko@mail.ru
Russian Federation, Sevastyanova Str., 9, St. Petersburg, 196105

S. V. Lovtsov

Research Institute of Applied Physics of Irkutsk State University

Email: m.a.naumenko@mail.ru
Russian Federation, Gagarin Blvd, 20, Irkutsk, 664033

E. S. Troitskaya

Limnological Institute Siberian Branch of the Russian Academy of Sciences

Email: m.a.naumenko@mail.ru
ORCID iD: 0000-0002-6575-0465
Russian Federation, Ulan-Batorskaya Str., 3, Irkutsk, 664033

N. M. Budnev

Research Institute of Applied Physics of Irkutsk State University

Email: m.a.naumenko@mail.ru
Russian Federation, Gagarin Blvd, 20, Irkutsk, 664033

References

Supplementary files