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Ice‐Covered Lakes of Tibetan Plateau as Solar Heat Collectors

The Qinghai‐Tibet Plateau possesses the largest alpine lake system, which plays a crucial role in the land‐atmosphere interaction. We report first observations on the thermal and radiation regime under ice of the largest freshwater lake of the Plateau. The results reveal that freshwater lakes on the Tibetan Plateau fully mix under ice. Due to strong solar heating, water temperatures increase above the maximum density value 1–2 months before the ice break, forming stable thermal stratification with subsurface temperatures >6°C. The resulting heat flow from water to ice makes a crucial contribution to ice cover melt. After the ice breakup, the accumulated heat is released into the atmosphere during 1–2 days, increasing lake‐atmosphere heat fluxes up to 500 W m−2. The direct biogeochemical consequences of the deep convective mixing are aeration of the deep lake waters and upward supply of nutrients to the upper photic layer.

Due to lack of regular monitoring, the physical regime of the Tibetan lakes remains largely unknown, making it difficult to estimate their contribution to regional-scale energy and mass exchange between land and the atmosphere. Observational data on the physical properties of Tibetan Plateau lakes are scarce and mostly confined to lake surface characteristics obtained by remote sensing (Lin et al., 2011;Zhang et al., 2014). Especially little is known about the thermal dynamics under ice. First reports on the mixing conditions and vertical heat transport in Tibetan lakes during the open water seasons were presented only recently Kirillin et al., 2017;Wang et al., 2014;Wen et al., 2016), and the winter regime remains largely unexplored. The importance of the ice covered period for seasonal lake dynamics was only recognized in the last decade (Kirillin et al., 2012). Modern regional climate models either highly simplify or completely neglect thermodynamics of ice-covered lakes. As a result, large errors are produced in estimates of seasonal ice formation and thaw with consequences for the entire regional heat and mass balance in the land-atmosphere system. Development of more sophisticated lake models requires observational data on the thermal regime under ice and its major drivers. The specific heat budget of alpine ice-covered lakes is formed by the dry cold atmospheric conditions and relatively strong solar radiation. The resulting balance of heat in the water-ice-air system is different from that known in (sub)-polar lakes and temperate lakes. In the latter, solar radiation in winter is low, and the snow cover additionally isolates the surface from the radiation flux. Thus first insights into the winter regime of Tibetan lakes are particularly intriguing.
We measured the vertical temperature distribution and short-wave radiation flux under ice of the largest freshwater lake of Tibet during the entire ice season of 2015-2016. We observed anomalous warming of the lake water under ice. In the middle of the ice season, warming produced strong convection, which evolved into stable thermal stratification when the temperature exceeded the maximum freshwater density value of ≈4°C. Consequently, heat accumulated in the bulk of the water column accompanied by strong mixing at the water-ice boundary. The thermal regime differs radically from that in the majority of ice-covered lakes, where water temperatures stay below the maximum density value for the largest part of the ice-covered period. Below, we discuss the driving mechanisms of this specific thermal regime and its importance for the dynamics of the lake system of Tibet.

Study Site
Ngoring Lake (Figure 1) is the largest freshwater lake of Tibet (surface area 610 km 2 ) located in the north-eastern part of the Plateau at 34.5-35.5°N and 97-98°E and belongs to the origin area of the Yellow River. The lake's altitude is ≈4,300 m a.s.l., which counts it among the world's highest freshwater lakes. The mean and maximum depths are 17 and 32 m, respectively. Cold semi-arid continental climate prevails in the lake basin, the long-term (1953-2012) monthly mean air temperature varies from 7.7°C in July to −16.2°C in January, with an annual mean of −3.7°C (Z. Li et al., 2015).
The lake is ice-covered from early December to mid-April. As the majority of Tibetan lakes, Ngoring is oligotrophic, that is, presumably transparent for short-wave radiation. However, according to the early observations of Przhevalsky (Пржевальский, 1888), the Yellow River inflow can produce strong variability in water transparency between the seasons, as well as between the different areas of the lake.

Measurements Configuration
A chain with 18 RBR T-Solo temperature loggers (declared accuracy 0.002°C) was moored in Ngoring Lake on September 25, 2015. The mooring site was chosen by both logistic and lake-specific reasons. Located ∼2 km away from the shore, the site is close to the deepest part of the lake 1 and has the water depth of 26.2 m, which exceeds the mean lake depth of ∼17 m. The Yellow River inflow is located in the south-western part of the lake, the outflow is in the north-east. The temperature loggers were suspended from a float at 1 m intervals to a depth of about 17 m and at 2-3 m intervals below. The uppermost logger was suspended 3.1 m beneath the water surface. During winter, ice thickness grows to more than 0.7 m according to modeling results (Kirillin et al., 2017) and own measurements. The ice thickness measurements were taken occasionally, 1-2 times a year in mid-winter (Dec-Jan) by drilling and/or taking ice cores. The ice cover always consisted of transparent congelation ice. A thin (<0.1 mm) yellow dust skin typically formed on the ice cover during the winter, potentially reducing ice transparency. The uppermost temperature logger was at a depth of 2.4 m below the ice-water interface during the main winter period. Water temperatures were sampled at 0.1 Hz throughout the entire ice-covered period. Depth was monitored continuously with a pressure sensor at the lake bottom corrected for initial local air pressure. Downwelling short-wave radiation was measured at 10-min intervals with two cosine-corrected photosynthetically active radiation (PAR, 400-700 nm) sensors (model DEFI2-L by JFE Advantech, the manufacturer's declared measurement accuracy is ± 4%) moored at depths of 2.4 and 3.6 m, which corresponds to 1.8 and 3.0 m below the ice-water interface. The radiation sensors showed only weak biofouling when recovered, which developed presumably after iceoff. To check, we compared radiation data from ERA5 reanalysis (Hersbach et al., 2020) and from a clear-sky KIRILLIN ET AL.  . Bathymetry is adopted from (Defu et al., 2011). The elevation data are from (GLOBE Task Team, 1999). astronomical model (Kyba et al., 2020) with our mean measured radiation just before and after ice cover. We observed small sensor drift (−7% to +5%) relative to the external data sources, and conclude that biofouling had a negligible effect on the measurements.

Vertical Heat Fluxes
The spectrum of solar (wavelengths range 200-2500 nm) radiation is strongly modified by lake water, which absorbs the long-wave (infrared) part of the spectrum, while yellow substance absorbs the short-wave (ultraviolet) part. As a result, at <1 m depth, >95% of the transmitted radiation falls within the PAR spectral range of 400-700 nm (see e.g., Jerlov, 1976;Leppäranta et al., 2010). Therefore, the measured PAR values at 2.4 and 3.6 m water depths were adopted as characteristic of the corresponding total downward short-wave radiation flux. We converted the measured quantum irradiance R q (μmol s −1 m −2 ) to the net downward short-wave radiation I R (W m −2 ) using the relationship obtained for ice-covered lakes R q /I R = 4.6 μmol J −1 (see Leppäranta et al., 2010). The light extinction coefficient γ and the radiation value at the ice-water interface I 0 were determined from a one-band exponential approximation of the short-wave radiation profile I R (z) in the water column, The light extinction coefficient was calculated using underwater radiation measurements between 10:00 h and 14:00 h.
The vertical "convective" heat flux within the bulk of the water column Q conv (z, t) as function of time t and depth z was estimated from temperatures measured by the thermistor chain T (z, t) using the "flux-gradient method" which adopts the one-dimensional equation of heat transfer, neglecting horizontal advection: where C p ρ ≈ 4.18 10 6 J K −1 m −3 is the product of the water heat capacity and density. The solar radiation flux profile I R (z, t) was recovered from PAR measurements and Equation 1. Integration of Equation 2 from a reference depth H, usually chosen close to the lake bottom, to a depth z, and assuming negligible heat flux close to the lake bottom Q conv (H) ≈ 0, yields the expression which was solved numerically using finite differences for differentiation and the trapezoid method for integration. Q conv in this formulation is the sum of all "non-radiative" fluxes including buoyancy-driven convection, small-scale turbulence, and molecular heat conduction.

Analytical Model
In order to analyze the vertical heat transport by radiation and conduction in an ice-covered lake with water temperatures higher than the temperature of maximum density of freshwater T m ≈ 3.98°C, we applied the analytical solution of the one-dimensional heat transfer equation derived by Kirillin and Terzhevik (2011). The conduction-radiation equation reads as with the boundary conditions, , Here, I 0 is the radiation penetrating the ice normalized by the density and the specific heat of water; γ is the extinction coefficient, assumed to be uniform in the whole daylight spectrum; ϰ ≈ 1.4 10 −7 m 2 s −1 is the thermal diffusivity of water. The first two boundary conditions in 5 are straightforward: the first fixes the temperature of the ice-water interface at the freezing point, whereas the second expresses the fact that the deeper parts of the water column are at the temperature of maximum density T m and have been completely mixed by preceding convection. Due to the convection the initial temperature profile ϕ(z) is homogeneous everywhere except for the "conductive layer" (CL) under ice (red marked part of the temperature profile in Figure 4a). The temperature profile within the CL can be accurately reproduced by the stationary form of the heat transfer equation, that is, Equation 4 without the first term on the left-hand side (Mironov et al., 2002). Then, the initial profile ϕ(z) ≡ T (z, t), is given by and the boundary conditions are The solution of Equation 6 is The thickness of the layer δ can be found from the additional condition ∂T/∂z = 0 at z = δ. This leads to an algebraic equation for δ as function of the mixed layer temperature T m , I 0 and γ (Barnes & Hobbie, 1960)  The non-homogeneous heat transfer PDE problem Equation 4 is closed through the conditions Equations 8 and 9 and can be solved analytically, assuming the solar heat flux I 0 is constant in time. The final solution is where Here, erf, erfc and erfc 1 are the error function, the complimentary error function and the first order iterative complimentary error function, respectively (see e.g., Carlslaw & Jaeger, 1959). The derivative of Equation 10 with respect to z can be used to calculate the heat flux at the ice-water interface (z = 0), which is given by KIRILLIN ET AL. 10.1029/2021GL093429

Surface Cooling and Ice Formation
According to the water temperature data, the ice cover formed at the lake surface on 12 December ± 1 day.
Here, we used the evidence of the sudden drop in the latent and sensible heat release at the lake surface after the ice cover formation (Kirillin et al., 2012). As a result, the water column quickly ceased cooling and the mean temperature began to rise when the entire lake surface froze (see the temperature minimum at the "ice-on" mark in Figure 2). Noteably, the surface and bottom temperatures increased at nearly the same rate suggesting the heat supply was evenly distributed across the water column rather than concentrated near the bottom. Apparently, both solar radiation and heat release from sediment potentially contributed to the under-ice warming, while convective mixing redistributed the heat across the water column. The moment of the "ice-off" was identifiable in the water temperature data by a sudden drop of the mean water temperature to the maximum density value T m on 18 April (Figure 2). The total ice-cover duration was 126 days.
10.1029/2021GL093429 6 of 12 Figure 2. Succession of mixing states in the ice-covered season of Ngoring Lake as revealed by the mean water temperature and its vertical gradient. The icecovered period is split in two parts: Labels (1) and (2) mark the "normal" (mean water temperatures ≤ T m ) and "anomalous" (mean water temperatures > T m ) winters.
Prior to formation of the ice cover, cooling at the lake surface continued for several weeks at a nearly constant rate of 0.2°C day −1 , which corresponds to a net heat loss from a 17 m deep lake of >150 W m −2 . The water column started to re-stratify around 24 November, when the water temperature dropped below T m (Figure 2) changing the sign of the surface buoyancy flux to positive and thereby canceling convection. However, at depths above the mean depth of the lake, the water column remained nearly thermally homogeneous, indicating surface mixing by strong winds, typical for the Tibetan Plateau, which destroy the near-surface stratification. As a result, at the moment of ice formation, the entire 26 m deep water column cooled down to <1°C. Such a strong cooling rarely occurs in lowland freshwater lakes, where stable stratification at temperatures below T m develops near the lake surface and decelerates the cooling of the bulk of the water column. It took only about 3 weeks for the surface temperature of the lake to cool from T m to the freezing point and the stable stratification at the begin of the ice-covered period did not exceed 1°C over 20 m of the water column.

Convection by Solar Radiation at Temperatures Below T m ("Normal Winter")
Because of the weak stratification at the moment of ice formation, a thermally homogeneous convective layer quickly developed driven by absorption of under-ice solar radiation in the upper part of the water column. In early January, only 20 days after the ice cover formation, the convective mixed layer achieved the mean depth of the lake (∼17 m). Afterwards, the character of mixing changed: the gradual water temperature increase was superimposed by irregular short-term oscillations with characteristic time scales of a few days (Figure 2). Heat intrusions at water depths beneath 17 m were clearly identifiable by repeated temperature increases of several tenths of a Kelvin throughout January, with the strongest one lasting from 27 Jan to 12 Feb (Figure 2). The upper waters revealed in turn short-term temperature drops, which were destroyed within 1-2 days by continuous heat supply from the solar radiation absorption. After 12 Feb, 2 months after ice-on, free convection mixed the entire 26 m deep water column at the observational site, but several warm intrusions intermittently restored the near-bottom stratification. The temperature pattern is characteristic of advective heat transport from the warmer shallow littoral to the deep central part of the lake by downslope density currents with upwelling of colder water into the convective layer by transient residual currents (Kirillin et al., 2015). Eventually, on 04 Mar, the water column warmed up to T m and was fully homogenized by convective mixing.

Strong Heating and Inverse Stratification Under Ice ("Anomalous Winter")
As soon as the water temperature beneath the ice achieved T m , the free convection was halted, and stable vertical stratification developed in the bulk of the water column. Here, a distinct 3-layer vertical structure was created by the interplay of the volumetric heating by radiation absorption and the upward heat release at the ice base. The radiation absorption depresses convection and produces stable stratification with downward temperature decrease in the bulk of the water column, akin to formation of the summer stratification. On the other hand, the heat release from the water column to the ice cover produces an upward decrease of the water temperature near the ice-water interface. This resulted in a subsurface temperature maximum in the uppermost part of the water column covered by measurements, with temperatures growing continuously until the ice broke up in mid-April, when temperature values beneath the ice cover exceeded 6°C (Figure 2). The fixed temperature T f = 0°C at the ice base requires a thermally stable interfacial layer with temperatures increasing downwards from T f and T m to exist immediately under ice. This uppermost layer apparently did not exceed 1 m in thickness and was too thin to be covered by the moored sensors. The thermally unstable "inversion" layer with temperatures decreasing upwards from its maximum to T m (see the schematic temperature profile Figure 4b) was also not completely covered by the measurements. The modeling results (see below) and the temporal variability in the upper part of the measured temperature profiles suggest the thickness of the "inversion" layer to vary within 1-2 meters due to diurnal variations in solar radiation and the resulting convection.
Ice began to break up at midday on April 16 and had thawed completely within 36 h. During this 36 h period, the temperature within the near-surface peak decreased from 5.8°C to 3.8°C. The corresponding drop of the mean lake temperature from 4.7°C to 3.8°C was equivalent to an average heat loss flux from the lake surface of up to 500 W m −2 .

Under-Ice Solar Radiation
Underwater radiation measurements showed that the extinction coefficient γ = 0.25 m −1 . Using the extinction coefficient and the Lambert-Beer law, we estimated the radiation at the ice-water interface from the measurements at the depth of the sensors. The mean downward radiation at the ice-water interface was 42.2 W m −2 during the "normal" winter, and 46.5 W m −2 during the "anomalous" winter. The mean solar radiation reaching the ice-surface during these periods was 171 and 280 W m −2 , respectively, according to the ERA5 reanalysis (Hersbach et al., 2020). Considering that the visible band (400-700 nm) accounts for about 45% of broadband solar radiation on the Tibetan Plateau (R. Li et al., 2010), roughly 55% of visible radiation penetrated the ice cover during the normal winter, and about 37% during the anomalous winter. This suggests little snow cover, especially during the earlier ice cover period, and an increase in light attenuation as the ice cover matured. Overall, this strong radiative warming suggests that all lakes on the Tibetan Plateau heat to above 4°C during the ice-covered period.

Modeling Results
To analyze mixing conditions during the "anomalous winter" we fitted the model (Equation 10) using the measured solar radiation I 0 and extinction coefficient γ to the measured temperature profiles and obtained the estimation of the thermal diffusivity under ice ϰ = 1.41 10 −6 ± 4.6 10 −8 m 2 s −1 . The model described the observed daily mean temperatures well with a root mean square error of 0.19°C and bias of 0.012°C (Figure 3).
Since the radiation-diffusion model assumed a stationary radiation flux and neglected gravitational instability, it did not capture the diurnal temperature variations and the development of the nearly homogeneous vertical temperature distribution in the upper part of the measured temperature profiles created by convective mixing in the "inversion" layer ( Figure 3d). However, the model adequately reproduced both the strength of the subsurface temperature peak and the shape of the temperature profile in the stably stratified water column beneath, indicating the simple radiation-diffusion balance to hold true in the bulk of the water column. It is worth noting that the fitted value of the vertically constant diffusion   6 (10 )   m 2 s −1 is an order of magnitude higher than the molecular value, suggesting additional mixing mechanisms contributed to the vertical heat transport, such as breaking of internal waves in the stably stratified water column. Using Equation 11, the model suggested that the heat flux from the water to the ice was on average 22.3 W m −2 . In reality this heat flux can be much higher due to strong mixing under the ice caused by secondary convection, which the model does not account for.

Heat Budget
The critical differences in the heat budget of the lake water column for the "normal" and the "anomalous" winter are distinguishable in the mean profiles of the vertical heat flux during both periods (Figure 4) calculated from Equation 3. In the first period, the profile of the total flux Q conv + I R is linear, corresponding to the homogeneous vertical temperature distribution produced by convective mixing. At the upper boundary of the water column covered by the measurements (water depth ≈ 3 m), the downward flux is around 6 W m −2 . Using this value as a boundary condition and taking into account the fixed temperature of 0°C at the ice-water interface, application of Equation 3 to the layer 0 − 3 m yields the estimation of the mean flux at the ice base as ≈ −13 W m −2 . In the second period, after formation of the stable density stratification, the downward heat flux dropped significantly in the bulk of the water column (Figure 4b), and changed its sign to negative (upward) at 3-6 m water depth. The boundary value of −7 W m −2 at 3 m depth, when substituted to Equation 3, results in the ice base heat flux of ≈ −29 W m −2 , which is about 1/3 higher than the estimate obtained with the analytical model above.

Discussion
Our results elucidate novel aspects of the thermodynamics of alpine ice-covered lakes that are particularly relevant not only to their behavior as aquatic ecosystems, but also to the role that the world's largest high-mountain lake system-the Qinghai-Tibetan Plateau-plays in the land-atmosphere interaction. The combined effect of strong solar radiation and the cold atmosphere produces cardinal differences between ice-covered Tibetan lakes and lowland high-latitude freshwaters in terms of the thermal and radiation regime.
The most striking feature of the observed thermal structure is the heating of the water column up to the maximum density value several weeks before the ice breakup. Early limnological studies (Rossolimo, 1929;Kozmiński & Wisznewski, 1934) reported the phenomenon of anomalous heating of ice-covered freshwater lakes up to temperatures exceeding T m followed by a "temperature dichotomy" with a subsurface temperature maximum. However, the situation was rather short-lived, appearing just days before the ice breakup KIRILLIN ET AL.
Both high transparency of the oligotrophic lake water and dry thin atmosphere determine the particular role of the short-wave solar irradiance I R in the heat budget of alpine lakes. The surface value of total (direct and diffuse) I R at heights of the Tibetan Plateau is close to the solar constant (C. Li et al., 2000;. As a result, a high amount of solar radiation penetrates the snow-free ice cover and is stored throughout the transparent water column. On the other hand, the strong heat loss from the ice surface prevents ice melt and release of the heat accumulated in the water back to the atmosphere. The strong surface heat loss also ensures low heat content and weak stratification of the water column at the moment of ice-on as compared to the non-alpine ice-covered lakes, where dense warm waters with temperatures ≲ T m typically accumulate near the lake bottom (Bengtsson & Svensson, 1996;Kirillin et al., 2012). Strong autumn cooling additionally contributes to the weak thermal stratification and quick penetration of the convective mixing into the water column after the ice-on. Lake Ngoring was mixed down to its mean depth within less than a month. Assuming the observed conditions as typical for freshwater Tibetan lakes, convection would completely mix any lake with total depth of ≲100 m (i.e., virtually any freshwater lake on the Tibetan Plateau) during the 4 months of the ice-covered period. It should be noted however that vertical salinity gradients may prevent convection development in brackish and saline lakes, which comprise about 3/4 of all Tibetan lakes (Jiang & Huang, 2004).
Another remarkable feature of convective mixing in Tibetan lakes indirectly evidenced by our results is the strong horizontal heat exchange during the later stage of the convective period. As soon as the mixed layer depth exceeds the mean lake depth, a significant shallow part of the lake gets mixed by convection to the bottom and starts to warm faster than the deeper pelagic areas, where the solar energy is fractionated between the mixed layer warming and convective entrainment into the stratified water column. As a result, warm dense waters sink along the bottom slope, increasing the thermal stratification in the central part of the lake and contributing simultaneously to homogenization of the water column, as exemplified by the temperatures observed in late February (Figure 2). Differential heating of shallow and deep lake areas by solar radiation is the most plausible explanation of deep temperature increase and re-stratification of the water column almost two months after the ice-on. The effect has been previously reported at the concluding stage of the ice-covered period in high-latitude lakes (Kirillin et al., 2015;Ramón et al., 2021;Ulloa et al., 2019), but may contribute more strongly to mixing of alpine lakes due to the stronger solar heating and, as a result, higher lateral temperature gradients lasting for a significant part of winter.
The "anomalous" winter with under-ice water temperatures exceeding the maximum density value lasts in Tibetan lakes for more than a month, or about one third of the entire ice-covered period. Consequently, the thousands of lakes of the Qinghai-Tibet Plateau act as "lenses" spotted around the landscape and accumulating solar heat in a thin subsurface layer under ice. The heat stored under lake ice accelerates the ice melt: our estimations of the water-ice heat flux of 10-30 W m −2 are about an order of magnitude higher than estimates from temperate and polar lakes (Bengtsson & Svensson, 1996;Jakkila et al., 2009;Kirillin et al., 2018). Immediately after the ice breakup, the heat is released to the atmosphere within 1-2 days, creating "hot spots" in land-atmosphere interaction with strong upward heat fluxes of about 500 W m −2 , which are several times higher than those from the surrounding land (Z. Li et al., 2015;Wen et al., 2016). The resulting effects on the atmospheric boundary layer include strong horizontal temperature differences, intensification of convection driven by surface heat flux, and strong water mass flux into the atmosphere. Taking into account the large lake-covered area of the Qinghai-Tibet Plateau and importance of its water budget, the cumulative lake effect is regional or even global rather than local.
It is important to mention the potential biogeochemical and ecological projections of the specific mixing and temperature regime. The full mixing by convection of the entire water column in mid-winter ensures supply of the dissolved oxygen to the near-bottom layers, suggesting the Tibetan lakes are much less prone to winter hypoxia typical for small ice-covered lakes in higher latitudes (Golosov et al., 2007;Terzhevik et al., 2009). The high amount of subsurface radiation is in turn favorable for under-ice plankton primary production, while relatively warm conditions in the subsurface temperature maximum stimulate microbial activity. Particularly the deep convective mixing, which brings deep nutrients to the surface, followed by formation of a shallow stably stratified layer with high light availability are precisely the conditions that cause large phytoplankton blooms in lowland lakes (Kong et al., 2021). The high biological production under the ice cover may contribute significantly to the carbon and nutrients cycles, as well as stimulate oxic methane production (Günthel et al., 2019;Tang et al., 2016) suggesting potential (though not necessarily high) contribution of the Tibetan lakes to the greenhouse gas emissions to the atmosphere.

Conclusions
Our findings suggest that all freshwater (and apparently the majority of brackish) lakes on the Tibetan Plateau fully mix under ice, so that the convenient concept of winter stagnation, as known from traditional lake science, is inapplicable for these lakes. The 1-2 months long period of stable stratification at water temperatures above the maximum density value is an exceptional feature of high-altitude freshwaters. The resulting strong temperature gradient at the ice-water interface and a thin unstable layer right beneath the ice base intensify the heat flow from water to ice, making a crucial contribution to ice cover melting. The direct consequences of the deep convective mixing are aeration of the deep lake waters and upward supply of nutrients to the upper photic layer, both suggesting versatile biogeochemical and ecological interactions specific for high-altitude lakes.