Effect of Geothermal Heating on Deep-Water Temperature in Lake Baikal

Abstract

Geothermal heating that emanates from the interior of the Earth, including the Baikal Rift Zone, produces potential energy for water movement. The basic concept behind the mechanism of deep-water renewal in Lake Baikal is conditional instability, which is a consequence of the joint effects of temperature and pressure on water density. However, an exact trigger of this instability is unknown. In this study, based on a non-hydrostatic 2.5D numerical model taking into account the intraday variability of atmospheric conditions, it was shown that, due to geothermal heating, the water column near the lake bed becomes slightly warmer (0.1–0.2 °C) than ambient waters, which can lead to instability. Simulated temperature distributions showed that 3.4 °C waters gradually shifted along the bed slope to ~650 m on day 1, ~750 m on day 3, ~830 m on day 5, and >1200 m on day 10 in the presence of geothermal heat flux; however, in its absence these waters remained at the level of ~600 m. In view of these findings, a conceptual model of deep convection and a map with potential zones of high ventilation processes in Lake Baikal are proposed. According to the map developed, deep-water renewal is expected to be the most intense at the eastern shore of Lake Baikal because of abnormally high heat release.

1. Introduction

Lake Baikal, located nearly in the center of the Asian continent in the southern part of eastern Siberia, is not only the world’s oldest and deepest lake, but also home to an enormous number (>1500) of endemic plant and animal species and the largest by volume (23,013 km³) freshwater lake on our planet (~20% of global fresh surface water). Despite its great depth, Lake Baikal’s waters are enriched with oxygen (>9.5 mg L⁻¹) throughout the water column [1,2], and its water age according to tritium/helium [3,4] and fluorochlorocarbons [5] distributions does not exceed 18 years. The short time period of deep-water renewal, contrary to a permanent stable stratification below ~250 m (the mesothermal maximum where water temperature is equal to the temperature of maximum density and thermal expansion coefficient changes sign [6]), suggests the existence of a special mechanism that controls water exchange processes between the surface and deep regions of the lake.

The mechanism of deep-water renewal, or ‘ventilation’, in Lake Baikal has been a mystery for many years. Despite remarkable efforts of scientists to solve it, a clear description of the physical mechanism of the processes of vertical water exchange does not yet exist, and many results of direct observations are difficult to explain. The basic concept behind the ventilation of Lake Baikal waters is conditional instability that depends on the joint effects of temperature and pressure on water density [5,7]. The temperature of maximum density, T_md, is ~4 °C at the lake surface and decreases with depth by ~0.2 °C per 100 m [8,9]. Because a water column of Lake Baikal below the mesothermal maximum horizon has a relatively homogeneous temperature (3.2–3.6 °C) [2] and is permanently stratified, the stability of this column is expected to be very sensitive to small variations in water temperature.

However, it is unclear what triggers this instability in Lake Baikal. The most popular ideas are wind-forced mixing [5,10,11], highly mineralized inflow waters [12], and cabbeling near a thermal bar front [13] due to the density increase under the mixing of water masses of different temperatures [14]. Also, processes of ventilation in Lake Baikal are believed to be linked to near-coast downwelling and deep-water intrusions [9,15].

During spring and autumn transitions, the role of a unique phenomenon of nature, the thermal bar—a sinking of maximum density waters in a narrow zone [16,17,18]—is crucial in the ecological functioning of a temperate lake [19]. In Lake Baikal, thermal bars are observed in bays (Chivyrkujskij, Maloe More), shallow water zones (Selenga), and close to relatively steep littoral areas [20,21,22]. Vertical flows forming in the location of a thermal bar may promote the transport of oxygen, microorganisms, and suspended matter to deeper layers [6,23,24]. Tributaries are very important for the formation of thermal bars in Lake Baikal [23] because river waters entering the lake are involved in general cyclonic round-the-Baikal circulation [20,25,26].

Numerical modeling of the effects of geothermal heating during a thermal bar in temperate lakes has not been undertaken. Also, the novelty of the developed model consists in consideration of a cross-section of the example of the Lake Baikal deep-water bathymetry, taking into account the intraday variability of atmospheric conditions. The aim of this study was to estimate the contribution of geothermal heat flux to conditional instability that causes deep-water renewal in Lake Baikal. Herein, on the basis of numerical modeling and analysis of observational data, a conceptual model of deep convection in Lake Baikal and a map with potential zones of high ventilation are proposed.

2. Materials and Methods

2.1. Numerical Model

The non-hydrostatic 2.5D numerical model [27] for the reproduction of thermohydrodynamic processes takes into account the intraday variability of the fluxes of short- and longwave radiation and latent and sensible heat [28], as well as wind action at the water–air interface. The model, including the equations of momentum, continuity, energy, and salinity balance, is based on the Reynolds-averaged Navier–Stokes equations in the Boussinesq approximation with appropriate initial and boundary conditions, and considers the influence of river inflow [29] and the effect of the Coriolis force related to the Earth’s rotation [30]:

$${\displaystyle \frac{\partial u}{\partial t}}+{\displaystyle \frac{\partial u^2}{\partial x}}+{\displaystyle \frac{\partial uw}{\partial z}}=-{\displaystyle \frac{1}{{\rho }_0}}{\displaystyle \frac{\partial p}{\partial x}}+{\displaystyle \frac{\partial }{\partial x}}\left(K_x{\displaystyle \frac{\partial u}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial z}}\left(K_z{\displaystyle \frac{\partial u}{\partial z}}\right)+2{\Omega }_{z}v-2{\Omega }_{y}w;$$

(1)

$${\displaystyle \frac{\partial v}{\partial t}}+{\displaystyle \frac{\partial uv}{\partial x}}+{\displaystyle \frac{\partial wv}{\partial z}}={\displaystyle \frac{\partial }{\partial x}}\left(K_x{\displaystyle \frac{\partial v}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial z}}\left(K_z{\displaystyle \frac{\partial v}{\partial z}}\right)+2{\Omega }_{x}w-2{\Omega }_{z}u;$$

(2)

$${\displaystyle \frac{\partial w}{\partial t}}+{\displaystyle \frac{\partial uw}{\partial x}}+{\displaystyle \frac{\partial w^2}{\partial z}}=-{\displaystyle \frac{1}{{\rho }_0}}{\displaystyle \frac{\partial p}{\partial z}}+{\displaystyle \frac{\partial }{\partial x}}\left(K_x{\displaystyle \frac{\partial w}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial z}}\left(K_z{\displaystyle \frac{\partial w}{\partial z}}\right)-{\displaystyle \frac{g\rho }{{\rho }_0}}+2{\Omega }_{y}u-2{\Omega }_{x}v;$$

(3)

$${\displaystyle \frac{\partial u}{\partial x}}+{\displaystyle \frac{\partial w}{\partial z}}=0;$$

(4)

$${\displaystyle \frac{\partial T}{\partial t}}+{\displaystyle \frac{\partial uT}{\partial x}}+{\displaystyle \frac{\partial wT}{\partial z}}={\displaystyle \frac{\partial }{\partial x}}\left(D_x{\displaystyle \frac{\partial T}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial z}}\left(D_z{\displaystyle \frac{\partial T}{\partial z}}\right)+{\displaystyle \frac{1}{{\rho }_0{c}_p}}{\displaystyle \frac{\partial H_{sol}}{\partial z}};$$

(5)

$${\displaystyle \frac{\partial S}{\partial t}}+{\displaystyle \frac{\partial uS}{\partial x}}+{\displaystyle \frac{\partial wS}{\partial z}}={\displaystyle \frac{\partial }{\partial x}}\left(D_x{\displaystyle \frac{\partial S}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial z}}\left(D_z{\displaystyle \frac{\partial S}{\partial z}}\right),$$

(6)

where u and v are the horizontal velocity components along the Ox and Oy axes, respectively; w is the vertical velocity component; T is the temperature; S is the salinity; p is the pressure; Ω_x, Ω_y, and Ω_z are the vector components of the Earth rotation’s angular velocity; g is the acceleration of gravity; c_p is the specific heat capacity; and ρ₀ is the water density at standard atmospheric pressure.

The initial conditions for the model equations were set as

$$u=0; v=0; w=0; T=T_L; S=S_L,$$

(7)

where T_L and S_L are the lake’s water temperature and salinity, respectively.

Boundary conditions were considered, as follows:

(a)

At the surface of the lake

$$K_z{\displaystyle \frac{\partial u}{\partial z}}={\displaystyle \frac{{\tau }_{surf}^u}{{\rho }_0}}; K_z{\displaystyle \frac{\partial v}{\partial z}}={\displaystyle \frac{{\tau }_{surf}^v}{{\rho }_0}}; w=0; D_z{\displaystyle \frac{\partial T}{\partial z}}={\displaystyle \frac{H_{net}}{{\rho }_0\cdot c_p}}; {\displaystyle \frac{\partial S}{\partial z}}=0,$$

(8)

where H_net is the heat flux of latent and sensible heat and longwave radiation [28];

(b)

At the solid boundaries

$$u=0; v=0; w=0; {\displaystyle \frac{\partial T}{\partial n}}=0; {\displaystyle \frac{\partial S}{\partial n}}=0,$$

(9)

where n is the direction of the outward normal to the domain;

(c)

At the river inflow boundary

$$u=u_R; v=0; w=0; T=T_R; S=S_R,$$

(10)

where u_R is the river inflow velocity; T_R and S_R are the temperature and salinity in the river, respectively;

(d)

At the open boundary, where the following conditions for the radiation type [31] were set:

$${\displaystyle \frac{\partial \varphi }{\partial t}}+c_{\varphi }{\displaystyle \frac{\partial \varphi }{\partial x}}=0 \left(\varphi =u,v,T,S\right); {\displaystyle \frac{\partial w}{\partial x}}=0,$$

(11)

The phase velocity c_ϕ is calculated here from the space and time trends ϕ in the domain near the boundary.

To close the set of equations, Wilcox’s two-parameter k–ω turbulence model [32] consisting of equations for kinetic energy and turbulent fluctuation frequency and algebraic relations to find eddy diffusivity were used. The horizontal diffusion coefficients are set to constants K_x = D_x = 5.0 m²/s [33]. Conditions of no-slip are set on solid boundaries [33,34,35]. The Chen and Millero equation [36] connecting water density with temperature (T), salinity (S), and pressure (p), and valid within the range of 0 ≤ T ≤ 30 °C, 0 ≤ S ≤ 0.6 g/kg, 0 ≤ p ≤ 180 bar, was taken as the state equation.

The problem is solved using the finite volume method [37]. The scalar quantities (temperature, salinity, etc.) are calculated in the center of a grid cell, and the velocity vector components at the midpoints of the cell boundaries. The numerical algorithm for finding the flow and temperature fields is based on a Crank–Nicolson finite difference scheme. The convective terms in the equations are approximated with a second-order upstream scheme, QUICK [38]. The velocity and pressure fields calculated are correlated by a procedure for buoyant flows, SIMPLED (Semi-Implicit Method for Pressure Linked Equations with Density correction) [39]. The initial pressure field is specified by solving the state and hydrostatic equations with the boundary condition p = p_a on the surface (p_a is the atmospheric pressure) by a fourth-order Runge–Kutta method. The calculation domain with a length of 10,000 m and depth of 1200 m (Figure 1b) was covered by a uniform orthogonal grid with steps h_x = 50 m and h_z = 5 m. The time step is 30 s.

Validation of the model of the hydrodynamics of the thermal bar was conducted in [27,39]. Analyses of the effects of wind, surface heat fluxes, tributary water mineralization, and Coriolis force were presented in previous studies [27,28,29,30,40,41,42,43].

2.2. Study Area and Problem Parameters

The Boldakov River–Maloye More Strait cross-section, located 70 km north of the Selenga River delta, in the Central Baikal, was taken for this study (Figure 1a). The bottom topography (Figure 1b) was taken from Likhoshway et al. [23].

The initial temperature field in simulations approximately corresponded to the average data of the thermal regime of the Central Basin of Lake Baikal in October [2]. In the model, the initial water temperature in the Boldakov River was 1.5 °C and decreased by 0.02 °C every day. The river flowed into the lake at a velocity of 5 mm/s. Water mineralization in the lake was 96 mg/kg [2]; in the river it was set to 128.2 mg/kg, which is the mean value for all tributaries of Lake Baikal [44]. Heat flux components across the lake surface were calculated based on data on air temperature, relative humidity, air pressure, cloud cover, and wind speed and direction taken from the weather conditions archives of the meteorological station in Goryachinsk village from 1 November 2015, to 30 November 2015 [45]. Note that the initial conditions in simulations are the same, except for geothermal heat flux. Despite the short period of existence of a thermal bar phenomenon, earlier model results obtained for Lake Baikal are consistent with observational data [27,39].

3. Results and Discussion

3.1. Geothermal Heating and Deep Convection

Geothermal heat flux, H_geo, emanating from the interior of the Earth produces potential energy. In Lake Kivu, for example, convective mixing at the lake bottom induced by extensive geothermal springs can become the dominant mixing process [46]. In Frolikha Bay of Lake Baikal, the temperature in the lowest 20 m of water increases by 0.1–0.15 °C [47]. Regional scale studies of ocean circulation show that geothermal heating can modify local water properties [48,49,50] and contribute to an overall warming of bottom waters by ~0.4 °C [51].

Geothermal heat flux in the Baikal Rift Zone, including the Baikal depression, is sufficiently non-uniform [52,53,54]. H_geo is fairly low and poorly variable in the North basin of Lake Baikal and has positive anomalies located near the eastern shore in the South and Central basins [54]. The average value H_geo is 71 ± 21 mW/m² [53,54]. An abnormally high heat release (100–200 mW/m²) occurs only on separate sites—in fault zones against the lake shore; extreme values (200–3000 mW/m²) were registered in local centers of discharge of fissure hydrotherms at the lake bottom [52,54]. The value of H_geo = 138 mW/m² used in this study corresponds to observational data [55] at a region under simulation—a 10 km transect directed from the Boldakov River to the Moloye More Strait (Figure 1).

Simulated temperature distributions show that in the presence of geothermal heat flux the 3.4 °C waters along the bed slope gradually shift to ~650 m on day 1, ~750 m on day 3, ~830 m on day 5, and > 1200 m on day 10 (Figure 2b), and in the absence of geothermal heat flux they remain at the level of ~600 m (Figure 2a).

Due to geothermal heating, waters along the bed slope (Figure 2b) become slightly warmer (less compressible and less dense) than ambient waters. As a result, the water column near the slope becomes unstable, and dense (ambient) waters from the overlying layers move down the bed slope into the deeper part of the lake. Thus, deep convection occurs.

The results of simulations demonstrate that the velocity of the near-slope flows below 600 m is less than the velocity of the thermal bar circulation, which is ~0.3 cm/s. However, the impact of geothermal heat flux is clearly manifested on the temperature distributions in the near-slope zone (Figure 2b,d). It follows that geothermal heat flux can act in combination with and supplement other system parameters such as water mineralization, wind friction, or solar radiation, which can enhance the effect of thermobaricity. The circulation paths during thermal bar events on the Boldakov River–Maloye More Strait cross-section in November 2015 are presented in [43].

A similar deep convection mechanism below ~600 m is, however, not observed in the absence of geothermal heat flux (Figure 2a,c). In this situation, we see only a formation of vertical temperature homogeneity in the upper 600 m layer between thermoactive and thermoinert regions of the lake (Figure 2c). Note that geothermal heat flux, in contrast to other external sources of force (wind, solar radiation, river inflow, etc.), has the important feature of acting throughout the entire water column. As simulations showed, the energy of geothermal heat flux was enough to heat up the near-slope deep waters by 0.1–0.2 °C (Figure 2d), which can lead to the effect of thermobaricity (caused by pressure dependence of the thermal expansion of water) [14] near the bed slope of the lake. As a consequence, the upper layer waters shift downslope to the deeper region. The effectiveness of deep ventilation can be affected by slope gradient, because in a current flowing down a slope the direct entrainment increases with slope [56]. Simulations with different slopes during the thermal bar were performed in [57].

3.2. Impact of the Thermal Bar

The thermal bar originated by the end of day 2 (Figure 3a), but the amplification of northwest wind up to 8 m/s (Figure 4) blowing opposite to the direction of the thermal bar propagation on day 3 led to the destruction of the thermal bar front; after the wind weakened it was formed again at the beginning of day 4. When colder river water (<T_md) mixes with warmer lake water (>T_md) denser water (~T_md) forms, and due to the effect of cabbeling (caused by the temperature dependence of the thermal expansion of water [14]) it sinks at a front of the thermal bar to the horizon of the mesothermal maximum (Figure 3b). In the absence of geothermal heat flux, the density plume may drop below this horizon, but it is unable to penetrate to greater depths; the denser water reached a depth of ~600 m on day 10 (Figure 3b). The average velocity of water sinking in this case was ~0.3 cm/s, which is consistent with the value estimated by Shimaraev et al. [13].

If there is geothermal heat flux, denser surface water near the thermal bar can sink along the bed slope directly to the bottom, reaching the bed of the lake and then flowing down along the bed slope (Figure 3c). Along-slope downwelling, generated by geothermal heating, attracts the denser water that forms at the thermal bar. For this reason, the horizontal propagation of the thermal bar is more sensitive to atmospheric impacts. The position of the temperature of maximum density on the lake surface indicates that the front of the thermal bar on day 10 was located at 2.3 km in the absence of geothermal heat flux and 1.7 km from the shore in the presence of geothermal heat flux (Figure 3a), and this difference at the end of the day decreased by 2.4 km and 2.0 km, respectively (Figure 3b,c). As the distance from the river mouth to the thermal bar front increases, the influence of atmospheric parameters strengthens (after day 8) (Figure 3a).

Note that during the existence of the thermal bar, cold surface waters located relative to the thermal bar front in the shore side in autumn, or in the open lake side in spring, can directly move down to the abyss. The combination of cabbeling and geothermal heating can force the cold-water plume to sink to the lake bottom. Presumably, a similar picture can be observed in the case of a classic thermal bar (without river inflow), but the intensity of deep convection can be low because of the lack of additional mechanical energy from river inflow.

3.3. Mechanism of Water Renewal

This study suggests that the mechanism of water renewal in Lake Baikal during the thermal bar (Figure 5) can consist of three phases. The first phase (up to ~200 m) is the transfer of surface waters to the depth of the mesothermal maximum due to active wind forcing. Simulations with various wind speeds demonstrated that if winds with a speed < 10.8 m/s had an impact on water temperature in the upper 100 m layer of Lake Baikal, strong wind (10.8–13.8 m/s) had an impact only in the upper 200 m layer [40]. The second phase (up to ~600 m) can occur during the existence of a thermal bar, in spring and autumn transition periods, due to the effect of cabbeling. The third phase (up to maximum depths) is associated with the effect of non-linearities in the equation of state for fresh water; namely, a difference in the compressibility of water leads to conditional instability—the effect of thermobaricity—triggered by the high mineralization of tributary waters [43] and/or geothermal heating. Note that the phases listed can occur either individually or in combinations.

Because water is denser at the horizon of the mesothermal maximum, a parcel of water generates a compensatory circulation above this horizon during vertical mixing. Also, the formation of compensatory circulations and intrusions above the boundary between relatively flat and steep areas of lake bed can be affected by the joint effect of wind and lake morphology [41]. Along-slope downwelling, reaching the lake bottom, can induce bottom intrusions under the action of Coriolis forces [58].

3.4. Potential Zones with High Ventilation

On the basis of these findings and analysis of values of heat fluxes measured at the bottom of Lake Baikal [54], a Lake Baikal map was developed indicating zones where deep-water renewal can be especially pronounced (Figure 6). In this map, the marked points correspond to zones with high heat flux (>120 mW/m²). For reasons of specificity of heterogenic distribution of heat flow, the eastern shore of Lake Baikal produces more favorable conditions for generating conditional instability. Nevertheless, in the North basin (near Capes Malyi Solontsovyi, Zavorotnyi, and Tonkii) active water renewal processes are viable at the western shore. However, the effect of thermobaricity in the North basin appears to be manifested to a lesser degree due to lower depth (the average depth is 576 m [59]) in comparison with other basins of Lake Baikal.

Note that the existing in situ registrations of deep-water renewal in Lake Baikal [6,13,15] coincide with one of the points marked on the map. At the same time, numerical modeling with H_geo = 50 mW/m² (geothermal heat flux through the bottom of Lake Baikal exceeds 50 mW/m² almost everywhere [52]) also demonstrates deep convection, but its efficiency has been significantly reduced.

The results obtained are consistent with a hypothesis on the relationship of deep-water renewal and coastal downwelling [9,60]. In ocean studies, geothermal heating can lead to large-scale overturning circulation [61,62] and can increase the temperature by ~0.5 °C [48,63].

4. Conclusions

This study suggests that the mechanism of water renewal in Lake Baikal is carried out through

(i)

Wind forcing (up to ~200 m);

(ii)

Cabbeling at the thermal bar (up to ~600 m);

(iii)

Tributary mineralization and/or geothermal heating (up to maximum depths).

Based on simulations conducted here, we can conclude that geothermal heat flux can trigger conditional instability near the bed slope of Lake Baikal. Due to abnormally high heat release, deep-water renewal in Lake Baikal can be especially pronounced at the eastern shore. These results could be a starting point for more in situ observations on the study of the nature and extent of influence of geothermal heating on Baikal water renewal. Also, they have implications for selecting an effective strategy to prevent deep-water pollution in Lake Baikal, the largest repository of freshwater on our planet, in light of the noticeable worsening of its littoral ecological status in recent decades.