Mechanism and effects of warming water in ice-covered Ngoring 1 Lake of Qinghai-Tibet Plateau 2

. Ngoring Lake is the largest freshwater lake in the Qinghai-Tibet Plateau (TP). The lake water temperature was observed to be generally rising during the ice-covered 18 period from November 2015 to April 2016. This phenomenon appeared in the whole 19 water column, with slowing in deep water and accelerating in shallow water before ice 20 melting. The process is different from low-altitude boreal lakes. There are few studies 21 on its mechanism and effects on lake-atmosphere interaction. Based on the observation 22 data of Ngoring Lake Station, ERA5-Land data, MODIS surface temperature data, and 23 precipitation data of Maduo Station of China Meteorological Administration, the 24 characteristics of water temperature rise in the ice-covered Ngoring Lake are analyzed. 25 LAKE2.3 model, which is currently little used for TP lakes, is applied to explore the 26 influence of local climate characteristics and the main physical parameters on the 27 radiation transfer in water body. The study questions are the continuous rise of water 28 temperature in the ice-covered period, and the effects of different water temperature 29 profiles prior to ice breakup on the lake heat storage per unit area and sensible and latent 30 heat release. The results show that LAKE2.3 represents well the temperature evolution 31 and thermal stratification in Ngoring Lake, especially in the ice-covered period. The 32 strong downward short-wave radiation plays a dominant role, low precipitation gives 33 2 positive feedback, and smaller downward long-wave radiation, lower temperature and larger wind speed give negative feedback. Increase of ice albedo and ice extinction coefficient reduces the heating rate of water temperature before reaching the maximum density temperature, and increases the maximum temperature that can be reached during ice-covered period, while increasing the water extinction coefficient has little influence on water temperature. The lake temperature in Ngoring Lake rising during 39 the ice-covered period, and the temperature at the upper layer of lake body was higher 40 than that at the maximum density temperature before ice breaking. Compared with the 41 characteristics of three typical ice-covered periods which the lake temperature remained 42 fixed in each layer, and the lake temperature was less than or equal to the maximum 43 density temperature, the difference of heat release after ice breaking lasted for 59-97 44 days. The higher the lake temperature before breakup, the more heat is stored in the 45 lake, and the more sensible heat and latent heat is released when the ice melts 46 completely and the faster is the heat release.


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The Tibetan Plateau (TP), with an average altitude of 4000-5000 m, is known as the 50 "roof of the world". It is the highest plateau on Earth. There are many alpine lakes in 51 TP constituting the largest number, largest area and highest altitude plateau lake group 52 in China, known as the "Asian water tower" (Immerzeel et al., 2010). There are more 53 than 1400 lakes with an area of more than 1 km 2 , and the total area of lakes is more 54 than 5 × 10 4 km 2 , accounting for 57.2 % of the total lake area in China (Wan et  found out that in several lakes in TP the temperature rises during the ice-covered period. 110 The temperature of Bangong Co and Nam Co Lakes have risen from freezing to melting, 111 but the rise is greater in the latter due to the difference in lake depth. The temperature 112 in Dagze Co Lake remained fixed in each layer in the early ice-covered period and 113 began to rise in the late ice-covered period, because this lake is meromictic with high  Although previous studies have revealed the warming phenomenon of TP lakes during 119 ice-covered period with qualitative analysis pointing out that temperature rise is 120 affected by salinity and depth (Lazhu et al., 2021), they did not consider the influence 121 of ice, meteorological conditions, and physical processes in the warming. 122 Numerical models are often used to reveal the phenomena and mechanisms of TP lakes. 123 At present, the lake models widely used in the TP are the Flake model (Freshwater Lake  This paper 1) applies the LAKE model for a typical TP lake to evaluate its capability to 131 simulate the rising lake temperature in ice-cover period; 2) uses the LAKE model to 132 analyze the influence of the meteorological driving factors and the main parameters that 133 affect the radiation transmission on the warming process during the ice season in 134 Ngoring Lake; 3) discusses the influence of temperature distribution prior to ice 135 breakup on lake heat storage and lake-air heat transfer. grow only in the riparian area. The lake is thermally stratified in summer and ice-145 covered from the end of November or early December to late April (Wen et al., 2016).

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Ngoring Lake basin is dominated by the cold, semi-arid continental climate, which is 147 sensitive to the Westerly jet, Indian monsoon and Asian monsoon (Zhang et al., 2013).    The water temperature is calculated according to the one-dimensional thermal diffusion 208 equation:

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where is heat capacity of water, is density of water, is temperature of water,  which is calculated by the following formula:

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Snow cover is formed by accumulation of precipitation during the cold season. It is 236 characterized by liquid water content and temperature. The equations are as follows:

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The indexes to evaluate the accuracy of the model are the root mean square error 268 ( ), BIAS, and correlation coefficient (CC): In order to more intuitively analyze the changes of lake temperature over time, the 302 observed water temperature of Ngoring Lake was averaged daily (Fig. 3a) difference in air temperature between the two sites ( Fig. 4f). However, apart from the 335 surface layer, the water temperature of K Lake basically maintained at Tρ,max during the 336 ice-covered period (Fig. 3b). Therefore, we suspected that the warming characteristics 337 of Ngoring Lake were related to the local climate, and to show that we shall analyze 338 the climate characteristics of the two sites in Sect. 4.2. The daily averages of meteorological variables near the two lakes are shown in Fig. 4 348 during November to June, and the ranges and averages from December 12 to April 18 349 of the next year (ice-covered period of Ngoring Lake) were compared ( Table 1). The 350 differences in the average air temperature, specific humidity and downward LR 351 between Ngoring Lake and K Lake were -0.42 ℃, -0.38 g kg -1 and 41.9 W m -2 , 352 respectively. The wind speed of Ngoring Lake was 1.7 times that of K Lake, and the 353 downward SR was 159.0 W m -2 greater in Ngoring Lake than in K Lake. However, the 354 precipitation was much less in Ngoring Lake than in K Lake, by the factor of 0.037.

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In general, there were not many differences in temperature, specific humidity and 356 downward LR between the two places, but there was lower precipitation, and higher 357 downward SR and wind speed in the TP. Since the surface pressure has little effect on 358 water temperature, this paper does not consider that.  In order to reveal the mechanism of water temperature increase during ice-covered 370 period in Ngoring Lake and its influences, we set up one control simulation (CTL) and 371 28 experimental simulations (SIM) in this study (Table 2).  Compared with the observations (Fig. 2a), the simulation results of CTL (Fig. 2b) were 408 basically consistent with the observations, but the whole ice season was shifted to occur 409 about half a month earlier than observed. The water temperature was slightly higher Lake.

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The simulation was evaluated by comparing RMSE, BIAS, CC (Table 3)    temperature of 3 m was stable keeping in the range of 0-0.1 °C (Fig. 6a). The date of 454 ice formation was earlier and the melting date was delayed, which led to the growth of 455 the whole ice-covered period. Compared with CTL, the depth of the mixed layer 456 increased (Fig. 6d). Thus, during the ice period, the strong downward SR on the TP 457 caused the water temperature to rise, because SR in Ngoring Lake transferred more heat 458 through the ice, resulting in the accumulation of heat and continuous warming of the 459 lake.

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In SIM_Precip simulation, the precipitation of K Lake was substituted for Ngoring Lake.

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In the sensitivity experiment SIM_Precip, the water temperature at 3 m kept horizontal 462 in the early and then increased but did not exceed Tρ,max (Fig. 6a). Compared with CTL 463 (Fig. 2b), the layering and the temperature maximum centers between March and April 464 disappeared, and the lake was fully mixed (Fig. 6g). This was because the mean to more snowfall, more radiation reflected and absorbed by snow and less radiation 468 entering water. More precipitation damped the rise in water temperature.

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In SIM_LR simulation, the downward LR of K Lake was substituted for Ngoring Lake.

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In the ice-covered period, the average downward LR of SIM_LR was 233.62 W m -2 , 471 which was larger than in CTL (191.73 W m -2 ). In SIM_LR, the water temperature at 3 472 m still kept rising, and the time of complete melting of ice was earlier than in CTL, in 473 the end of February or early March. After the ice breakup, the air temperature was lower, 474 and the lake transferred heat to the atmosphere, and water temperature underwent a 475 cooling process (2 ℃) until reaching a new equilibrium with the atmosphere (Fig. 6b).

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Compared with the CTL, mixing in the ice-covered period was more uniform, the 477 stratification between March and April was weakened, and the temperature maximum 478 center was about 15 days earlier (Fig. 6e).

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In SIM_U simulation, the wind speed of K Lake was substituted for Ngoring Lake. The 480 wind speed of SIM_U was less than in CTL for the whole simulation period, and the 481 average wind speed in ice-covered period was 2.21 m s -1 , smaller than in CTL. In the 482 sensitivity experiment SIM_U, the water temperature at 3 m was rising, but it was about 483 3 ℃ higher than in the CTL in the whole simulation period (Fig. 6b). Due to the stratification increased (Fig. 6h).

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In SIM_Tair simulation, the air temperature of K Lake was substituted for Ngoring Lake.

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The average air temperature difference between SIM_Tair (-9.83 °C) and CTL (- Lake was continuously decreasing (Fig. 6f). The lake stratification was enhanced, and 493 the maximum center of water temperature was about 10 days ahead of time (Fig. 6f).

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In SIM_q simulation, the specific humidity of K Lake was substituted for Ngoring Lake.

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The difference of specific humidity between SIM_q and CTL were 0.38 g kg -1 during 496 the ice-covered period. In the sensitivity experiment SIM_q, the simulation results were 497 similar to the CTL, and thus the specific humidity had little effect on the water 498 temperature (Figs. 6c and 6i).

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On the whole, the stronger downward SR and lower precipitation in the TP played a 500 positive role to increase the water temperature during the ice-covered period in Ngoring 501 Lake. Less downward LR, lower air temperature and larger wind speed has an opposite 502 effect, and specific humidity had no significant influence.  Table 4. formation, but it delayed the time of ice melting remarkably, thus prolonging the ice-535 covered period. When the albedo increased from 0.1 to 0.8, the increase was equivalent 536 to 0.1-step, and the ice-covered period was extended for 15-30 days (Fig. 7a).

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In the sensitivity experiment SIM_Ei, changes of extinction coefficient of ice did not 538 all give a continuous rising of the water temperature, but at 3 m depth the temperature 539 decreased by 1-2 °C for the increase of ice extinction coefficient by 1 m -1 (Fig. 7b). The 540 greater was the extinction coefficient of ice, the more heat the ice absorbed, and the less 541 heat entered the lake water under ice.

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In order to further explore the influence of Ai on lake temperature in ice-covered period. 543 We divided ice-covered period into two periods in CTL and the sensitivity experiment the T_max decreases, the heating rate and duration fluctuate in Period-B. When Ai ≥ 555 0.6, the heating rate during ice-covered period decreases and will not rise to Tρ,max, so 556 the heating rate and duration of the entire ice-covered period are shown in Table 5.

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In the sensitivity experiment SIM_Ew, the water extinction coefficient had just little 558 influence on winter water temperature, which was shown as the late ice temperature 559 decrease with the increase of Ew (Fig. 7c). The main reason was that in the later period   The thermal conditions in an ice-covered lake just before ice melting have significant 579 influence on the air-lake energy exchange. In order to explore the effects of lake 580 temperature characteristics on the atmosphere at ice melting, three experiments -581 SIM_E1, SIM_E2 and SIM_E3 (Table 1)  corresponding to Thrush Lake (Fang and Stefan, 1996).

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In the CTL, the first layer was at the melting point, and May 24, and the heat release rate of the lake was different under different circumstances.

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After the late May, the heat balance between the lake and the atmosphere was the same, 613 and so the heat storage per unit area of the lake is basically the same after that. The temperature of the lake surface also affected the sensible and latent heat release 620 from the lake surface. The sensible and latent heat differences between CTL and the 621 three experimental simulations were calculated (Fig. 9) 17) for latent heat (Fig. 9b), and in SIM_E3 they were 51.5 W m -2 (March 31 to May 630 23) for sensible heat and 86.0 W m -2 (April 1 to June 5) for latent heat (Fig. 9c).

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Compared with the three lake temperature characteristics, the heating characteristics of

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Sensitivity simulations with perturbed local climate data showed that strong downward 662 SR in TP played a dominant role in the water temperature rise during the ice-covered 663 period in Ngoring Lake, and also the low precipitation played a positive feedback role.

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The smaller downward LR, lower air temperature and larger wind speed had negative 665 feedback to the water temperature.

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The sensitivity simulation results of the main physical parameters that affect the 667 radiation transfer showed that with the increase of the albedo of ice, the rising trend of 668 water temperature decreased and the length of the ice season increased. When albedo 669 increased to 0.6, the lake water temperature no longer rose but tended to remain on a 670 stable level. With the increase of extinction coefficient of ice, the increase of the 671 temperature of the lake in the ice-covered period of Ngoring Lake decreased. The 672 extinction coefficient of water had just a minor effect on water temperature under ice.

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Compared with three more stable lake temperature profiles, the warming of Ngoring