Thermal regime, energy budget and lake evaporation at Paiku Co, a deep alpine lake in the central Himalayas

Evaporation from hydrologically-closed lakes is one of the largest components of their lake water budget, however, its effects on seasonal lake level changes is less investigated due to lack of comprehensive observation of lake water budget. In this study, lake evaporation were determined through energy budget method at Paiku Co, a deep alpine lake 15 in the central Himalayas, based on three years’ in-situ observations of thermal structure and hydrometeorology (2015-2018). Results show that Paiku Co was thermally stratified between July and October and fully mixed between November and June. Between April and July when the lake gradually warmed, about 66.5% of the net radiation was consumed to heat the lake water. Between October and January when the lake cooled, heat released from lake water was about 3 times larger than the net radiation. Changes in lake heat storage largely determined the seasonal pattern of lake evaporation. There was about a 5 20 month lag between the maximum lake evaporation and maximum net radiation due to the large heat capacity of lake water. Lake evaporation was estimated to be 975±39 mm between May and December during the study period, with low values in spring and early summer, and high values in autumn and early winter. The seasonal pattern of lake evaporation at Paiku Co significantly affects lake level seasonality, that is, significant lake level decrease in post-monsoon season while slight in premonsoon. This study may have implications for the different amplitudes of seasonal lake level variations between deep and 25 shallow lakes.

therefore the meteorological condition over the lake surface can be recorded. There was no data available between February and May 2017 because the instrument battery was too low.

>>Fig. 2<<
Radiation, including downward shortwave radiation and longwave radiation to lake, was measured by Automatic Weather 100 Station (AWS) at Qomolangma station for Atmospheric Environmental Observation and Research, Chinese Academy of Sciences (CAS). This station is located at the northern slope of Mount Everest, about 150 km east of Paiku Co (87°1.22′E, 28°25.23′N, 4276 m a.s.l). The 2 m air temperature, relative humidity, wind speed, radiation were recorded at an interval of 10 min. In this study, downward shortwave radiation and longwave radiation at this station were used because the climate conditions between Paiku Co and Qomolangma station were very similar, including topography, altitude, cloud cover etc. 105 Nonetheless, weekly averaged radiation was used to calculate lake evaporation in order to reduce the error caused by regional difference. The related information about hydro-meteorology observations at Paiku Co basin are listed in Table 1.

Energy budget derived lake evaporation
Lake evaporation was calculated using the energy budget (Bowen-ratio) method as described by Winter et al. (2003) and Rosenberry et al. (2007). The energy budget of a lake can be mathematically expressed as: 110 (1) where R is the net radiation on the lake, H is the sensible heat flux from lake surface, lE is the latent heat utilized for evaporation, S is the change in lake water energy, G is the heat transfer between lake water and bottom sediment, and A V is the energy advected into lake water. The units used for the terms of Eq (1) are W·m -2 . As a deep lake, the influence of river discharge on the total lake heat storage at Paiku Co is very small and can be neglected. Therefore, we do not consider the 115 influence of G and A V on the lake energy budget in this study.
The net radiation on the lake can be expressed as the following: (2) where R s is downward shortwave radiation, R sr is the reflection of solar radiation from lake surface, which is taken as 0.07 R s in this study (Gianniou and Antonopouls, 2007), R a is downward longwave radiation to lake, R ar is the reflected longwave 120 radiation from the lake surface, which is taken as 0.03 R a , and R w is the upward longwave radiation from the lake surface.
The units of the items in Eq (2) are W·m -2 .
The longwave radiation from lake is approached by the equation: where R a is the longwave radiation from lake, σ is the Stefan-Boltzmann constant (=5.67×10 -8 W·m -2 ·K -4 ), ε a is the water 125 emissivity (0.97 for water surface) and T w is surface water temperature of the lake ( o C). In this study, the water temperature at the depth of 0.4-0.8 m was use to represent the surface water temperature because the surface water temperature was not https://doi.org/10.5194/hess-2020-320 Preprint. Discussion started: 13 July 2020 c Author(s) 2020. CC BY 4.0 License. monitored. Although the water temperature at the depth of 0.4-0.8 m does not represent 'skin' temperature (Prats et al., 2018), the daily average between them is very similar during most time of a year because surface water can be mixed quickly by water convection or strong wind in the afternoon. 130 The sensible heat flux is related to the evaporative heat flux through the Bowen ratio (Henderson-Sellers, 1984): where β is Bowen ratio, T s is the surface water temperature ( o C), T a is air temperature at 2m high above the water surface ( o C), e sw and e d are the saturated vapor pressure at the temperature of the water surface and the air vapor pressure above the water surface (kPa), respectively, P is air pressure (kPa), and γ is the psychrometric constant, 6.5×10 -4 o C -1 . In this study, air 135 temperature, air pressure and specific humidity were monitored at the lake's shore. Saturated vapor pressure at the lake surface was calculated according to surface water temperature in the southern center of the lake. To match the radiation, all the input data were averaged at weekly interval before lake evaporation was calculated.
Changes in lake heat storage (S) were calculated according to the detailed lake bathymetry and water temperature profile: where is the specific heat of water (J·kg -1 ·K -1 ), is water density (=1000 kg·m -3 ), is the lake volume at certain depth (m 3 ), and is water temperature change at the same depth, is lake area (m 2 ). S was calculated at an interval of 5 m and therefore there are 13 layers in vertical direction. was acquired according to the 5m isobath of Paiku Co (Lei et al., 2018).

Thermal structure of lake water
Water temperature profiles between 2015 and 2018 show that Paiku Co was thermally stratified between July and October, and fully mixed between November and June in each year of the study period (Fig. 3). Lake water temperature increased 150 rapidly from 2 to 7 o C between April and June due to the strong solar radiation. During this period, temperature differences between the surface and bottom water was less than 1 o C. The temperature gradient on vertical profile increased dramatically in late June with clear stratification occurring in July, which corresponded to a significant reduction in wind speed (data not shown). Strong lake surface heating and the reduction in wind speed together contributed to the development of thermal stratification (Wetzel, 2001). During the summer stratification period, the surface water warmed rapidly from 7 to ~13 o C 155 between July and August, while the bottom water warmed slowly. As a result, the thermocline formed between 15 m and 30 m water depth, with the largest temperature difference of 5~6 o C occurring in late August. https://doi.org/10.5194/hess-2020-320 Preprint. Discussion started: 13 July 2020 c Author(s) 2020. CC BY 4.0 License. Lake surface temperature started to decrease gradually since September due to the decrease in solar radiation, however, the bottom water continued to warm slowly (Fig. 3). As a result, the water temperature gradient on vertical profile decreased, which caused the lake stratification to break down in late October of each year. Notably, the timing of the stratification 160 breaking down corresponded well to significantly increased wind speed during this time (data not shown). Unlike the rapid appearance of lake stratification in late June, the breakdown of stratification occurred more gradually, with the mixed layer deepening gradually throughout October (Fig. 4). The mixed layer reached to 40 m water depth on October 13th, 2016, and to 70 m water depth about two weeks later (October 30th). Following the complete breakdown of the water column's stratification, the bottom water experienced rapid warming in several days due to its mixture with the warmer water from the 165 upper layer. For example, the water temperature at 70 m water depth remained stable at ~6.9 o C from July to October, but increased abruptly from 6.9 to 8.6 o C in less than one weeks (October 25 th to October 30 th ).
Paiku Co's water column was fully mixed between November and May as indicated by the identical lake water temperature profiles at the two monitoring sites (Fig. 3, Fig. 4). Water temperature of the whole lake decreased gradually from 8.6 to 1 o C from November to January and remained stable at 1-2 o C until March. Landsat satellite images show that Paiku Co did not 170 completely freeze up in winter during the study period, therefore lake water stratification in winter did not appear as reported in other studies on the TP .
The thermal structure of Paiku Co indicates that it is a dimictic lake, which is similar to Bangong Co (Wang et al., 2014) and Nam Co , but different from Dagze Co (Wang et al., 2014). The water temperature gradients at Paiku Co and other lakes on the TP are considerably lower than those in other parts of the world (Livingstone, 2003;Stainsby et al., 175 2011, Zhang et al., 2015, which is probably due to the lower air temperature in summer in this high elevation area. As a deep lake, Paiku Co stored a large amount of energy in spring and summer and released it in autumn and early winter. The identical lake water temperature profile between November and June at Paiku Co indicates that changes in lake heat storage are not only affected by surface water, but also the bottom water. For deep lakes like Paiku Co, changes in lake heat storage can be significantly underestimated if only the surface water is considered. 180 >>Fig. 3<< >>Fig. 4<<

Spatial difference of lake water temperature
Spatial difference of lake water temperature was investigated using in-situ observations at different sites in 2016/2017. First, we compared water temperature difference between Paiku Co's southern and northern basins (Fig.5). Since the northern 185 basin is much deeper than the southern basin, lake water in the northern basin warmed more slowly than that in the southern basin during the spring and early summer, and cooled more slowly during the autumn and early winter. The surface water temperature in the southern basin was about 0.85 o C higher on average than that in the northern basin between April and September. The water temperature became spatially uniform in late October when the water column was fully mixed. In about 0.45 o C lower on average than that in the northern basin. Water temperature became spatially uniform at both basins again between January and March. Similar spatial difference can also be found at 10 m depth (Fig.5), indicating that this characteristics exists in the surface layer (the epilimnion).
Contrasting changes in water temperature occurred in the bottom water (the hyplimnion). Between the mid-August and mid-September, water temperature at 20 m depth was about 0.81 o C lower in the southern basin than in the northern basin, which 195 contrasts with that of the surface layer (Fig. 5c). Similar conditions occurred at 40 m depth, where water temperature was 0.75 o C lower in the southern basin relative to the northern basin between mid-September and mid-October (Fig. 5d). This contrasting pattern occurred in the late summer or early autumn when the vertical temperature gradient started to decrease.
As shown in Fig.3, both the start and end of lake stratification were about half a month earlier in the southern basin relative to the northern basin. However, water convection occurred earlier in the northern basin relative to the southern basin during 200 this period due to the relatively lower vertical temperature gradient (Fig. 3). Lower temperature gradient caused stronger water convection in the northern basin compared with the southern basin during the late summer and early autumn.
We further compared the water temperature between the lake centre and shoreline. Water temperature along the northern and eastern shorelines of Paiku Co was recorded by HOBO water level loggers (Fig. 1). The results show that the water temperature along the shoreline was very sensitive to air temperature and fluctuated with much larger amplitude than that in 205 the lake centre, although both exhibited similar seasonal fluctuations (Fig. 5E, 5F). For example, shoreline water warmed more quickly to higher temperature during the spring and summer as compared with that in the lake centre, but conversely the shoreline water cooled more quickly in the autumn. The spatial difference of water temperature indicates that large errors can result if only water temperature data collected at the shoreline are used to calculate lake heat storage and energy budget. >>Fig. 5<< 210

Lake hydrometeorology
Lake hydrometeorology was measured at the north and central shoreline of Paiku Co, respectively. Energy budget and lake evaporation at Paiku Co in this part are addressed according to the data at the north shoreline. The spatial difference between the north and central shoreline will be discussed in part 4.1.
Annual mean air temperature over Paiku Co was 4.7 o C in 2016 with the highest air temperature in July (11.2 o C) and the 215 lowest in January (-2.4 o C). There was a ~1.5 month lag between lake surface temperature and air temperature. The highest lake surface temperature occurred in late August and the lowest in February (Fig. 6). The temperature difference between the lake surface and the overlying atmosphere exhibited a linear increasing trend from June to November, and a linear decreasing trend from January to June. Positive temperature difference mainly occurred during the autumn and winter with the highest value of ~7 o C in late October and early November. Negative temperature difference occurred during the spring 220 and early summer with the lowest value of -3 o C in June.
Atmospheric water vapor content at Paiku Co was elevated from June to September (Fig. 6), which is consistent with the occurrence of Indian summer monsoon precipitation. During the non-monsoon season (October to May), the atmospheric https://doi.org/10.5194/hess-2020-320 Preprint. Discussion started: 13 July 2020 c Author(s) 2020. CC BY 4.0 License.
water vapor content was generally low. The water vapor pressure difference between the lake surface and the overlying atmosphere exhibited a linear increasing trend from June to September and then a linear decreasing trend from October to 225 February. High water vapor difference occurred between September and December (0.76 kPa), while low difference was observed between March and June (0.39 kPa).

>>Fig. 6<<
Radiation, including downward shortwave radiation, downward longwave radiation to lake and upward longwave radiation from the lake body, are the main drivers of lake's energy balance. Downward shortwave radiation at Paiku Co had an annual 230 average of 251.8 W·m -2 (Fig. 7), which is slightly higher than the TP average due to its lower latitude (Yang et al., 2009).
Downward longwave radiation to the lake had an average of 235.8 W·m -2 . Upward longwave radiation from the lake body had an annual average of 336.8 W·m -2 . The total incoming radiation was always higher than the outgoing radiation. The net radiation over Paiku Co varied seasonally between 19.0 and 212.1 W·m -2 , with an average value of 125.8 W·m -2 . Relatively high net radiation occurred from April to August (200.4 W·m -2 ), with the highest value in June (212.1 W·m -2 ). Relatively low 235 net radiation occurred from October to February (52.2 W·m -2 ), with the lowest value in December (19.7 W·m -2 ). >>Fig. 7<<

Impact of lake heat storage on the heat fluxes
Changes in lake heat storage at Paiku Co were quantified using in-situ observations of water temperature profile and detailed lake bathymetry. This also makes it possible to evaluate the impact of lake heat storage on the heat flux at lake surface (Fig.  240 8). Between April and July when Paiku Co warmed gradually, the lake water absorbed energy at an average rate of 128.6 W·m -2 , accounting for 66.5% of the net radiation during the same period. The lake heat storage increased most rapidly in June, with an average rate of 191.6 W·m -2 , accounting for 91.6% of the net radiation during the same period. The lake heat storage reached its peak in late August, when the surface water temperature was in the highest. Between October and January, when Paiku Co cooled, the lake heat storage decreased at an average rate of 137.5 W·m -2 , which was more than 3 245 times larger than the net radiation during the same period. The lake heat storage decreased most rapidly in November at an average rate of 193.6 W·m -2 , which was about 5 times larger than the net radiation during the same period.
The heat flux at lake surface was determined as the difference between the net radiation and changes in lake heat storage.
The lowest heat flux occurred in June and the highest in November, which is consistent with the seasonal pattern of changes in lake heat storage. The seasonal pattern of heat flux at Paiku Co is almost anti-phase with the net radiation ( Fig 8B). There 250 was a ~5 month lag between the maximum heat flux and maximum net radiation due to the large heat storage of lake water.
Although net radiation was high in spring and summer, a large portion of energy was consumed to heat lake water, which resulted in low heat flux. In the autumn and early winter, although net radiation was relatively low, a large amount of heat stored in the lake was released into the overlying atmosphere, which resulted in high heat flux.

>>Fig. 8<<
The Bowen ratio determines the distribution of sensible and latent heat flux. At Paiku Co, the Bowen ratio varied in a range of -0.26~+0.37, with an annual average value of +0.08 (Fig. 9, Tab. 2). Negative value occurred between April and July, with an average value of -0.12, indicating the lake water absorbed energy from the overlying atmosphere. Positive value occurred between August and January, with an average value of 0.20, indicating the lake water released energy to the overlying atmosphere. July with an average value of -5.6 W·m -2 (Fig. 9b), and was in positive value between August and December with an average of 23.0 W·m -2 . There was a high correlation between sensible heat and the water temperature difference between surface water and the overlying atmosphere (r 2 =0.86). >>Fig. 9<<

Lake evaporation at Paiku Co 270
Lake evaporation at Paiku Co between May and December is shown in Fig. 10. Lake evaporation was generally low between May and June with an average value of 1.7 mm/day. In July and August, lake evaporation increased rapidly from 2.9 to 4.1 mm/day. High lake evaporation occurred between September and December, with an average value of 5.4 mm/day. The total lake evaporation was estimated to be 975 mm between May and December during the study period. Lake evaporation between middle January and April is not determined because the energy budget during this period is also affected by 275 intermittent lake ice.

>>Fig. 10<<
Lake evaporation at Paiku Co lagged net radiation by ~5 months and exhibited a similar seasonal pattern with changes in lake heat storage. Regression analysis shows that lake evaporation at Paiku Co positively correlated with changes in lake heat storage (r 2 =0.63, P<0.001), but negatively correlated with net radiation (r 2 =0.22, P<0.001), which indicating that the 280 seasonal pattern of lake evaporation is significantly altered by lake heat storage. When the net radiation was high between May and July, most of the energy is used to heat the lake water and only a small part of it is consumed as to the latent heat flux. When the net radiation was low between November and December, a large amount of heat was released from the lake water as latent heat to the overlying atmosphere. Lake evaporation exhibited similar patterns with the water vapor pressure difference between surface water and the overlying atmosphere (r 2 =0.33). 285 Significant changes in lake ice phenology occurred at Paiku Co during the study period. Generally, Paiku Co was covered by lake ice between the mid-January and mid-April (e.g. the winter of 2013/2014). During ice covered period, lake level was https://doi.org/10.5194/hess-2020-320 Preprint. Discussion started: 13 July 2020 c Author(s) 2020. CC BY 4.0 License. very stable because lake ice can effectively prohibit evaporation. However, lake surface of Paiku Co did not completely frozen up between 2015/2016 and 2017/2018 with only intermittent lake ice in the shoreline region. Contrasting with the ice covered period, Paiku Co's water level decreased considerably by 199 mm on average between January and April. Assuming 290 lake evaporation between January and April is equal to lake level decrease because there was almost no surface runoff during this period, annual lake evaporation at Paiku Co is estimated to be 1174 mm during the study period. This also indicates that that annual lake evaporation increased by ~20.4% in recent years due to the disappearance of lake ice.

The representativeness of lake hydrometeorology 295
The components of energy budget are not uniform at large lake and the meteorological station near the lake centre is usually expected to produce more accurate estimation of heat flux (Sugita, 2019). To check the representativeness of hydrometeorology at the shoreline of Paiku Co, we first compare air temperature and relative humidity between shoreline and lake centre. We set up a platform in the southern centre of Paiku Co in September 2019 (water depth: 19 m; least distance from shoreline: 2 km) and a simple AWS station (GMX600) was installed on the platform. Meteorological data 300 between September 22 nd and October 26 th were acquired and compared with that from shoreline (Fig. 11). Result shows that both air temperature and relative humidity fluctuated very similarly between the shoreline and lake centre, indicating the meteorological data from the shoreline of Paiku Co can be used to represent the general condition of the whole lake at least during the observed period. Unfortunately, the platform was damaged by lake ice in winter 2019/ 2020, so there is no more data available. 305 Then we compare air temperature and relative humidity at the north and central shoreline of Paiku Co (Fig. 6). Results show that air temperature from the north and central shoreline of Paiku Co varied similarly throughout a year, except the considerable difference in early summer and early winter (Fig. 6a). Air temperature is about 2.7 o C lower in May and June in the north shoreline than that in the central shoreline, but about 4 o C higher in November and December. Different from air temperature, water vapour content at both sites varied very similarly throughout the year (Fig. 6b). Similar with air 310 temperature, Bowen ratio at both sites also varied similarly throughout a year, except the considerable difference in early summer and early winter. Bowen ratio is 0.22 higher in May and June in the north shoreline than that in the central shoreline, but 0.19 lower in November and December. Lake evaporation derived from the north and central shoreline of Paiku Co also exhibits very similar seasonal fluctuations throughout a year (Fig. 10), with slight difference in early summer and early winter. Lake evaporation derived from the north 315 shoreline is 0.47 mm/day lower in May and June than that from the central shoreline, but 0.66 mm/day higher in November and December. Total lake evaporation derived from the north shoreline is 22 mm lower between May and December than that from the central shoreline. Although there is some spatial difference, the similar seasonal patterns of energy budget and lake evaporation at different sites indicate that our results are reliable.

Uncertainty of lake evaporation estimation 320
There are several factors that can cause uncertainty of lake evaporation. The first one is the determination of solar radiation and atmospheric long wave radiation at Paiku Co. In this study, solar radiation and atmospheric long wave radiation at Qomolangma station, which is about 150 km away from Paiku Co, were used to represent values at Paiku Co. To evaluate the spatial difference, we made a comparison of solar radiation at Paiku Co and Qomolangma Station by using Hamawari-8 satellite data (Tang et al., 2019;Letu et al., 2020). The results show that daily solar radiation at the two sites exhibited very 325 similar seasonal fluctuations (R 2 =0.55, P<0.001), with standard deviation of 23.9 W·m -2 . Assuming approximately 70% of the net radiation was consumed by lake evaporation (Lazhu et al., 2016), the uncertainty of lake evaporation due to error in solar radiation was ~74.5 mm per year ( ).
mm/day in October, thereby partially offsetting lake level changes from lake evaporation. According to this difference of 0.9 mm/day during the post-monsoon season, the error of lake evaporation is estimated to be 82.8 mm/year.

Comparison of lake evaporation with other lakes on the TP 355
To further explore the impact of lake heat storage on the seasonal pattern of lake evaporation, we compared lake evaporation at Paiku Co with other lakes on the TP. We only selected lakes with direct measurements of lake evaporation, including the eddy covariance system or energy budget method. At Ngoring Lake (area, 610 km 2 ; mean depth, 17 m) on the eastern TP, Li Z. et al. (2015) investigated the lake's energy budget and evaporation in 2011-2012 using the eddy covariance system, and found that the latent heat at Nogring Lake was lowest in June, peaked in August and then decreased gradually from 360 September to November. At Qinghai Lake (area, 4430 km 2 ; mean depth, 19 m) on the northeast TP, Li X. et al. (2016) conducted studies concerning the lake's energy budget and evaporation in 2013-2015 using the eddy covariance system, and found that there was a 2-3 month delay between the maximum net radiation and maximum heat flux. Compared with the two larger but shallower lakes, there was longer time lag between the heat flux and net radiation at Paiku Co. As we have shown, Paiku Co has the mean water depth of ~41 m and the water column is fully mixed between November and June. This means 365 that the lake can store more energy in spring and early summer than shallow lakes, and can release more energy to the overlying atmosphere in the autumn and early winter.
At Nam Co, a large and deep lake on the central TP, there have been several studies regarding lake evaporation (Haginoya et al., 2009;Ma et al., 2016;Wang et al., 2016. Haginoya et al. (2009) found that lake evaporation at Nam Co was lowest in May and highest in October. The Bowen ratio-derived lake evaporation was estimated to be 916 mm in 2013 370 (Lazhu et al. 2016). Comparison with Paiku Co shows that both lakes exhibited similar seasonal pattern of lake evaporation, although lake evaporation at Paiku Co was slightly larger than that at Nam Co due to its higher solar radiation. In fact, although the maximum depth at Nam Co is greater than that at Paiku Co, the average water depth of the two lakes is similar (Wang et al., 2009;Lei et al., 2018), which resulted in similar seasonal pattern of lake evaporation. At Siling Co, another large and deep lake on the central TP, monthly lake evaporation was found to vary within a range of 2.4-3.3 mm/day 375 between May and September, 2014, with a total amount of 417.0 mm during the study period (Guo et al., 2016). Although the accumulative evaporation between Paiku Co and Siling Co was similar between May and September, lake evaporation at both lakes between October and December can not be further compared because the energy flux at the lake was not measured at Siling Co.

Implications for the seasonal lake level variations on the TP 380
The quantification of lake evaporation is important for understanding lake water budget and associated lake level changes.
Compared with the eddy covariance system that can only work until October/November when the lake surface begins to freeze (Li et al., 2015;Wang et al., 2017;Guo et al., 2016), our results give a full description of lake evaporation during the entire ice-free period. More importantly, our results indicate that for deep lakes on the TP, evaporation during the post-https://doi.org/10.5194/hess-2020-320 Preprint. Discussion started: 13 July 2020 c Author(s) 2020. CC BY 4.0 License. monsoon season can be much higher than that during the pre-monsoon seasons due to the release of large amount of stored 385 heat (Haginoya et al., 2009), despite both air temperature and net radiation are already much lower. In this sense, lake evaporation during the cold season (October to December) is of great importance to lake water budget and can significantly affect the amplitude of lake level changes, especially for deep lakes.
As shown in Fig. 11b, lake level at Paiku Co decreased considerably at a rate of 3.8 mm/day on average between October and December, which is in contrast to the slight decreasing rate of 1.3 mm/day in mid-April and May. So, what is the main 390 cause for the large difference of lake level decrease during the two dry seasons? Runoff measurements at the three main rivers feeding Paiku Co indicate that the surface runoff had a weak impact on lake level changes during the pre-monsoon and post-monsoon seasons (Tab. 3). The seasonal pattern of lake evaporation can explain this well. High lake evaporation rates during the post monsoon season led to the rapid lake level decrease, while low lake evaporation in pre-monsoon season led to much lower lake level decrease. This suggests that lake evaporation can largely determine the amplitude of lake level 395 changes in dry seasons.
In a larger sense, our result may have implication for the different patterns of lake level seasonality that have been observed on the TP. Phan et al. (2012) showed that seasonal lake level variations in the southern TP are much larger than those in the northern and western TP. Lei et al (2017) investigated the lake level seasonality across the TP and found that there were different amplitudes of lake level fluctuations even in similar climate regimes. For example, lake level at Nam Co and Zhari 400 Namco, two large and deep lakes on the central TP (Wang et al., 2009(Wang et al., , 2010, decreased considerably by 0.3-0.5 m in cold season (October to December), while lake level at two nearby small lakes, Bam Co and Dawa Co, decreased slightly by 0.1-0.2 m during the same period. Different lake heat storage can play an important role in the amplitude of lake level seasonality. For deep lakes (e.g. Paiku Co, Nam Co and Zhari Namco), the latent heat flux (lake evaporation) over lake surface may lag the solar radiation by several months due to the large heat storage of lake water. For this kind of lake, the 405 lake level drop is most dramatic in the autumn and early winter when lake evaporation is high. For shallow lakes, the latent heat flux closely follows solar radiation, with high lake evaporation during the pre-monsoon and monsoon seasons, and low lake evaporation during the post monsoon season (Morrill et al., 2004). Meanwhile, shallow lakes freeze up 1-2 months earlier than deep lakes. When the lake surface is covered by ice, lake evaporation is effectively prohibited. Consequently, lake level decreased more slowly in post monsoon season in shallow lakes than that in deep lakes. This phenomenon can also 410 be seen in some thermokarst lakes on the northern TP (Luo et al., 2015;Pan et al., 2017).

Conclusion
Lake evaporation and its impact on seasonal lake level changes were investigated based on three years' in-situ observations of lake water temperature profile and hydrometeorology at Paiku Co, a deep alpine lake in the central Himalayas. The results show that Paiku Co is a dimictic lake with clear lake stratification between July and October. The thermocline formed 415 between 15 m and 30 m water depth, with the largest temperature difference (5~6 o C) occurring in August. The lake is https://doi.org/10.5194/hess-2020-320 Preprint. Discussion started: 13 July 2020 c Author(s) 2020. CC BY 4.0 License.
completely mixed between November and June. Considerable spatial difference of lake water temperature was also investigated between the southern and northern basins of Paiku Co.
As a deep alpine lake, lake heat storage significantly affected the seasonal pattern of energy budget and lake evaporation.
The lake absorbed most of net radiation to heat the lake water in the spring and early summer and released it to the overlying 420 atmosphere in autumn and early winter. Between April and July, about 66.5% of the net radiation was consumed to heat the lake water. Between October and January, heat released from lake water was about 3 times larger than the net radiation. As a result, there was about a 5 month lag between the maximum heat fluxes and the maximum net radiation due to the large heat storage of lake water. Lake evaporation was estimated to be 975±82 mm between May and December during the study period, with low values between May and June (1.7 mm/day), and high values between October and December (5.4 mm/day). 425 Our result also indicates that that annual lake evaporation increased by ~20.4% during the study period due to the disappearance of lake ice.
This study may have implications for explaining the different seasonal lake level changes between shallow and deep lakes.
For deep lakes like Paiku Co, high lake evaporation during the post monsoon season may leads to the rapid decrease in lake    https://doi.org/10.5194/hess-2020-320 Preprint. Discussion started: 13 July 2020 c Author(s) 2020. CC BY 4.0 License.

Figure 6: Time series of hydro-meteorology at the north (blue lines) and central (red lines) shoreline of Paiku Co. a:
Daily surface water temperature (black), atmosphere temperature, and their differences. b: Actual vapor pressure at lake surface (black) and the overlying atmosphere, and their differences.