Contrasting hydrological and thermal intensities determine seasonal lake-level variations A case study at Paiku Co on the southern Tibetan Plateau

Evaporation from hydrologically-closed lakes is one of the largest components of lake water budget, however, its effects on seasonal lake-level variations remain unclear on the Tibetan Plateau (TP) due to a lack of comprehensive 15 observations. In this study, weekly lake evaporation and its effects on seasonal lake-level variations are investigated at Paiku Co on the southern TP using in-situ observations of thermal structure and hydrometeorology (2015-2018). Lake evaporation at Paiku Co was estimated to be 975±142 mm during the ice-free period (May to Dec), characterized by low values of 1.7±0.6 mm/day during the pre-monsoon season (May to Jun), high values of 5.5±0.6 mm/day during the post-monsoon season (Oct to Dec) and intermediate values of 4.0±0.6 mm/day during the monsoon season (Jul to Sep). There was ~5 20 months lag between the maximum net radiation (Jun) and maximum lake evaporation (Nov). These results indicate that the seasonal pattern of lake evaporation at Paiku Co was significantly affected by the large lake heat storage. Contrasting hydrological and thermal intensities may play an important role in the large amplitude of seasonal lake-level variations at deep lakes like Paiku Co. High inflow from monsoon precipitation and glacier melting and moderate lake evaporation, for instance, drove rapid lake-level increase during the monsoon season. In contrast, high lake evaporation and reduced inflow 25 caused lake level to decrease significantly during the post-monsoon season. This study implies that lake evaporation may play an important role in the different amplitudes of seasonal lake-level variations between deep and shallow lakes and between the southern and northern TP.


Introduction
The Tibetan Plateau (TP) hosts the greatest concentration of high-altitude inland lakes in the world. More than 1200 lakes (>1 km 2 ) are distributed on the TP, with a total lake area of more than 45000 km 2 in the 2010s (Ma et al., 2011;Zhang et al., 2014a). During the past few decades, lakes on the TP experienced significant changes in response to climate warming, increased precipitation, glacier mass loss and permafrost thawing (Song et al., 2014;. Most lakes on the 35 interior TP have expanded dramatically since the late 1990s, in contrast with lake contraction on the southern TP (Lei et al., 2014). For most lakes across the TP, water temperature has also increased (Zhang et al., 2014b;Su et al., 2019), while lake ice duration has shortened considerably at the same time in response to rapid climate warming since the 1970s (Ke et al., 2013;Cai et al., 2017).
Compared to numerous studies of inter-annual to decadal lake changes, seasonal lake-level changes and the associated 40 hydrological processes on the TP are less understood (Song et al., 2014). Phan et al. (2012) showed that seasonal lake-level variations on the southern TP were much larger than those on the northern and western TP. In-situ observations gave additional details of seasonal lake-level variations, showing that large lakes usually exhibited considerably greater seasonal lake-level variations relative to small lakes . For example, lake levels at Zhari Namco and Nam Co, two large and deep lakes on the central TP (Wang et al., 2009(Wang et al., , 2010, increased significantly by 0.3~0.6 m during the summer 45 monsoon season and decreased by a similar amount during the post-monsoon season. Two nearby relatively small and shallow lakes, Dawa Co and Bam Co, exhibited considerably less lake-level variability despite showing similar seasonal cycle . What caused these lake systems to experience different amplitudes of seasonal lake-level variations remains unstudied. Understanding how large and small lakes respond differently to similar forcing mechanisms is critical for understanding how continued warming will impact water storage on the TP. This work additionally may provide insight into 50 discrepancies in lake-level reconstructions from large and small lakes on the TP that are used to reconstruct and understand long-term relationships between climate and water storage. Evaporation from hydrologically-closed lakes is one of the largest components of lake water budget (Li et al., 2001;Morrill, 2004;Xu et al., 2009;Yu et al., 2011). Both the eddy covariance system and energy budget method are effective ways to determine lake evaporation (Blanken et al., 2000;Winter et al., 2003;Rouse et al., 2003Rouse et al., , 2008Lenters et al., 2005;55 Rosenberry et al., 2007;Giannoiu and Antonopoulos, 2007;Sugita, 2014Sugita, , 2019Sugita, , 2020. On the TP, several studies have used eddy covariance system to estimate lake evaporation, e.g. Nogring Lake (Li et al., 2015), Qinghai Lake (Li et al., 2016), Nam Co (Wang et al., 2017, Siling Co (Guo et al., 2016). Their results show that the seasonal pattern of lake evaporation is significantly affected by lake heat storage, especially for deep lakes. At Nam Co, for example, Haginoya et al. (2009) found that the sensible and latent heat fluxes were small during the spring and early summer, and 60 increased considerably during the autumn and early winter due to the large heat storage. However, lake evaporation during the late autumn and early winter is not typically investigated through eddy covariance system because it is difficult to maintain the measurement platform due to the influence of lake ice. Likewise, energy budget studies that investigate changes 3 in lake heat storage and its effects on lake evaporation have been limited on the TP. Although the energy budget method needs significant personnel commitment for fieldwork, it is more suitable for accurate, long-term monitoring of lake 65 evaporation (Winter et al., 2003).
To fully understand the process that affects lake water budget on the TP, we conducted comprehensive in-situ observations at Paiku Co, a deep alpine lake on the southern TP since 2013. In this study, lake evaporation from Paiku Co during the icefree period is estimated through energy budget (Bowen ratio) method and its effects on seasonal lake-level variations are investigated. We first show the thermal regime and changes in lake heat storage based on three years' water temperature 70 profile data (2015)(2016)(2017)(2018), then investigate energy budget and latent and sensible heat fluxes over the lake surface, and finally analyze the seasonal pattern of lake evaporation and its impact on seasonal lake-level variations. Meanwhile, the effects of lake evaporation on the different amplitude of seasonal lake-level changes between deep and shallow lakes and between the southern and northern TP is also discussed.

Site description
Paiku Co (85°35.12' E, 28°53.52' N, 4590m a.s.l) is a hydrologically closed lake on the southern TP with a surface area of 280 km 2 , watershed area of 2376 km 2 , and salinity of 1.7 g/L. Bathymetry survey showed that the lake has mean water depth of 41.1 m with the maximum water depth of 72.8 m (Lei et al., 2018). Glaciers are widely developed to the south of the lake, with a total area of ~123 km 2 . Dozens of paleo-shorelines are visible around Paiku Co. The highest paleo-shoreline is ~80 m 80 above the modern lake level. Wünnemann et al. (2015) found that there was a close relationship between glacier dynamics and lake-level changes since the Last Glacial Maximum (LGM). The lake has been shrinking since the 1970s (Nie et al., 2013;Dai et al., 2013). Between 1972 and 2015, lake level at Paiku Co decreased by 3.7 ± 0.3 m and water storage reduced by 8.5 % (Lei et al., 2018). According to rain gauge data collected between 2013 and 2016, annual rainfall in Paiku Co basin fluctuated significantly year to year. Typical annual precipitation varied between 150~200 mm, indicating that the lake basin 85 belongs to the dry belt in the northern slope of Himalaya mountains . The mean annual temperature was 4.4 o C between June 2015 and May 2016 (Lei et al., 2018).

Data acquisition
In-situ observations including lake water temperature, hydrometeorology, lake level and runoff were carried out in Paiku Co basin. HOBO water-temperature loggers (U22-001, Onset Corp., USA) were used to monitor water temperature with an 90 accuracy of ±0.2 o C. Two water-temperature profiles were monitored in Paiku Co's southern (0-42 m in depth) and northern (0-72 m in depth) basins (Fig. 1). In the southern basin, water temperature was monitored at the depths of 0.4 m, 5m, 10 m, 15 m, 20 m, 30 m and 40 m. In the northern basin, water temperature was monitored at the depths of 0.4 m, 10 m, 20 m, 40 m, 50 m, 60 m and 70 m. Since lake level fluctuates seasonally, the depth of water-temperature loggers may also have 4 fluctuated in a range of 0~0.5 m. Water temperatures were recorded at an interval of 1 hour and daily values were used to 95 investigate lake thermal structure and changes in lake heat storage. Three years' observational data from June 2015 to May 2018 from the southern basin was acquired, while only one year's data (June 2016 and May 2017) from the northern basin was acquired.

>>Fig. 1<<
Air temperature and relative humidity above the shoreline were monitored since June 2015 using HOBO air-temperature and 100 humidity loggers (U12-012, Onset Corp., USA). The instrument has an accuracy of 0.35 o C for air temperature and 2.5% for relative humidity. Two loggers were installed in an outcrop ~2 m above the lake surface. One is located in the north shoreline, the other is located in the central shoreline (Fig. 1). The instruments were under a large rock where there was a hole facing the lake. The monitoring site was ventilated and therefore the meteorological condition over the lake surface can be recorded (Fig. S1). Air temperature and relative humidity were recorded at an interval of 1 hour and daily values were 105 used to calculate Bowen ratio. The related information about hydrometeorology observations in Paiku Co basin are listed in Table 1. There was no data available between February and May 2017 because the instrument battery was too low. The air temperature and humidity measurements in the shoreline were further validated by a simple Automatic Weather Station (AWS) in the Paiku Co's southern center (Section 3.6).
Radiation, including solar radiation and downward longwave radiation to lake, was measured at Qomolangma station for 110 Atmospheric Environmental Observation and Research, Chinese Academy of Sciences (CAS). This station (87°1.22′E, 28°25.23′N, 4276 m a.s.l) is located at the northern slope of Mount Everest, about 150 km east of Paiku Co. The 2 m air temperature, relative humidity, wind speed and radiation were recorded at an interval of 10 min. In this study, daily solar radiation and downward longwave radiation at this station were used to calculate net radiation over the lake surface. The climate conditions between Paiku Co and Qomolangma station were similar, including topography, altitude, precipitation etc. 115 As an important part of lake water budget, runoff was measured at three main rivers, i.e. Daqu, Bulaqu and Barixiongqu (Fig.   1). The water level of the three rivers was recorded at an interval of 1 hour by using HOBO water-level loggers (U20-001-01). Runoff during the pre-monsoon and post-monsoon seasons was measured at least twice a day, including the largest runoff in the afternoon and lowest runoff in the morning during field expedition using a LS1206B propeller-driven current meter (Nanjing Institute of Hydrological Automatization). Meanwhile, lake level was recorded at an interval of 1 hour in the 120 littoral zone of north Paiku Co (Lei et al., 2018). Daily water levels of Paiku Co and its rivers were used to compare with the seasonal pattern of lake evaporation.

Energy budget derived lake evaporation
Lake evaporation was calculated using energy budget (Bowen-ratio) method, which has been described by Winter et al. (2003). The energy budget of a lake can be mathematically expressed as: 125 (1) where is the net radiation over the lake, H is the sensible heat flux from lake surface, lE is the latent heat utilized for evaporation, S is change in lake heat storage, 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 .
The energy advection into the lake (Av) can be roughly estimated according to total river discharge and the water 130 temperature difference between river and lake. Lake water temperature was similar to that of river between April and June, but 2-6 o C higher between July and December (Fig. S3). As a deep lake, total river discharge to Paiku Co was about 800-1000 mm water equivalent to lake level, accounting for 2-2.5% of total lake storage. The river discharge can accumulatively decrease lake water temperature by ~0.1 o C in summer, which corresponds to 2.1 W·m -2 of heat flux between July and September and 0.07 mm/day of lake evaporation. Therefore, we do not consider the impact of river discharge and 135 precipitation on the energy budget at Paiku Co because of its relatively small contribution to energy budget of Paiku Co.
Although it is still challenging to accurately quantify groundwater inflow, lake level variations during the ice-covered season can give us some evidence because both lake water input (snowfall and runoff) and output (sublimation) are very limited.
According to in-situ lake level observations, we found that there was no significant lake level variation during the icecovered season. Taking 2013/2014 as an example, the lake level decreased slightly at a rate of 13 mm per month between 140 mid-January and mid-April when the lake surface frozen up (Lei et al., 2018). Lake ice sublimation is estimated to be ~40 mm per month on average according to the results at Nam Co . Based on lake water budget, we can conclude that groundwater inflow should be less than the rate of lake ice sublimation, which has very limited impact on energy budget of Paiku Co. Therefore, we do not consider the heat transfer between lake water and bottom sediment (G) during the estimation of energy budget at Paiku Co. 145 The net radiation over the lake ( ) can be expressed as the following: ( 2) where is solar radiation, is the reflection of solar radiation from lake surface, which is taken as 0.07 (Gianniou and Antonopouls, 2007), is downward atmospheric longwave radiation to lake, is the reflected longwave radiation from the lake surface, which is taken as 0.03 , and is the upward longwave radiation from lake. The units of the items in Eq 150 (2) are W·m -2 .
The upward longwave radiation from lake ( ) is approached by the equation: where σ is the Stefan-Boltzmann constant (=5.67×10 -8 W·m -2 ·K -4 ), is the water emissivity (0.97 for water surface) and is lake surface temperature ( o C). In this study, the water temperature at the depth of 0.4 m was used to represent the lake 155 surface temperature. Note that the bulk temperature is slightly different from the 'skin' temperature (Wilson et al., 2013;Prats et al., 2018;Sugita et al., 2020). There exists surface warming during the day and surface cooling at night for high elevation lakes. However, the daily difference between them is small during most time of a year because surface water can 6 be mixed quickly by water convection or strong wind in the afternoon and the two uncertainties by surface warming and cooling can cancel each other on daily scale. 160 The sensible heat flux is related to the evaporative heat flux through the Bowen ratio (Henderson-Sellers, 1984): where β is Bowen ratio, is lake surface temperature ( o C), is air temperature ( o C) at 2 m high above the water surface, and are the saturated vapour pressure (kPa) at the lake surface and the air vapour pressure (kPa) above the lake surface, respectively, P is air pressure (kPa), and γ is the psychrometric constant, 6.5×10 -4 o C -1 . Air temperature, air pressure 165 and relative humidity were monitored at the lake's shoreline. Saturated vapour pressure at the lake surface was calculated according to the lake water temperature at the depth of 0.4 m in the lake centre. Daily Bowen ratio is calculated in this study.
Changes in lake heat storage (S) were calculated according to the detailed lake bathymetry and water temperature profile: 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 170 (m 3 ), and is water temperature change at the same depth, is lake area (m 2 ). Changes in lake heat storage were calculated at an interval of 5 m and therefore there are 15 layers in vertical direction (the maximum depth: 72.8 m). was acquired according to the 5 m isobath of Paiku Co (Lei et al., 2018). was calculated at 5 m interval as the average temperature of the top and bottom layer. Changes in lake heat storage for the bottom water (>40 m) were calculated according to the data in 2016/2017 since there is no data available in the other two years. Lake heat storage, sensible and 175 latent heat fluxes and lake evaporation were calculated at weekly interval in order to reduce their uncertainty caused by the spatial difference of solar radiation and lake water temperature.

Thermal regime
Water temperature profiles between 2015 and 2018 show that Paiku Co was thermally stratified between July and October, 180 and fully mixed between November and June in each year of the study period (Fig. 2). Lake water temperature increased rapidly from 2 to 7 o C between April and June due to the high solar radiation. During this warming period, water temperature between the lake surface and bottom was almost same, indicating the lake water was well mixed. The vertical temperature gradient increased considerably in late June and clear stratification occurred by July. The occurrence of thermal stratification corresponded to a significant reduction in wind speed between July and the middle of October (Fig. S2). Strong lake surface 185 heating and a 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 between July and August, while the bottom water warmed much more slowly. As a result, surface water reached its highest temperature by late August while 7 bottom water (>40 m) reached to its highest temperature by middle to late October. The thermocline formed between 15 m and 25 m water depth, with the largest temperature difference of 5~6 o C by late August. 190 Lake surface temperature started to decrease gradually since September, while the bottom water continued to warm slowly ( Fig. 2). As a result, the vertical temperature gradient decreased gradually. The lake stratification completely broke down by late October of each year, corresponding to significantly increased wind speed during this period (Fig. S2). Notably, the breakdown of stratification occurred gradually, with the mixed layer deepening throughout October (Fig. 2). The mixed layer reached 40 m water depth on 13 October, and to 70 m water depth about two weeks later (30 October). Following the 195 complete breakdown of the water column's stratification, the bottom water experienced rapid warming over several days due to its mixing with the warmer water from the 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 over several days (25 October to 30 October). Paiku Co's water column was fully mixed by November as indicated by the identical lake water temperature profiles at the two monitoring sites (Fig. 2, 3). Water temperature of the whole lake decreased gradually from 8.6 to 1 o C 200 from November to January and remained stable at 1-2 o C until March.
Changes in thermal structure indicate that Paiku Co is a dimictic lake, which is similar to Bangong Co  and Nam Co , but different from Dagze Co . The vertical temperature gradients of Paiku Co and other dimictic lakes on the TP are considerably lower compared with lakes in other parts of the world, for example Lake Qiaodaohu (area: 580 km 2 , maximum depth: 108 m) in east China , Lake Zurich (area: 65 205 km 2 , maximum depth: 136 m) on the Swiss Plateau (Livingstone, 2003) and Lake Simcoe (area: 580 km 2 , maximum depth: >40 m) in Canada (Stainsby et al., 2011). This may be mainly related to the high elevation of Paiku Co. Due to the elevation effect, the highest air temperature near Paiku Co is only ~12 o C in summer and the highest lake surface temperature is 13 o C, which is considerably lower than lakes in other parts of the world (e.g. Lake Qiaodaohu: ~32 o C, Lake Zurich: ~22 o C and Lake Simcoe: ~22 o C), while the bottom water temperature does not show much difference (e.g. Paiku Co: 7 o C, Lake 210 Qiaodaohu: ~10 o C, Lake Zurich: ~5 o C, and Lake Simcoe: ~4 o C).

Energy budget over the lake surface
The main components of radiation budget over the lake surface including solar radiation, atmospheric longwave radiation to 215 the lake and upward longwave radiation from the lake body are shown in Fig. 4a-c. Solar radiation had an annual average of 251.8 W·m -2 (Fig. 4), which is slightly higher than the TP average due to its lower latitude (Yang et al., 2010). Atmospheric longwave radiation and upward longwave radiation from the lake body had an annual average of 235.8 W·m -2 and 336.8 W·m -2 , respectively. The net radiation over Paiku Co varied seasonally in a range of 19.0~212.1 W·m -2 , with an average value of 125.8 W·m -2 . Relatively high net radiation occurred between April and August, with the highest value of 212.1 220 8 W·m -2 in June. Relatively low net radiation occurred between October and February, with the lowest value of 19.7 W·m -2 in December.

>>Fig. 4<<
Changes in heat storage at Paiku Co were quantified using in-situ observations of water temperature profiles and detailed lake bathymetry (Fig. 4d), which makes it possible to evaluate the impact of lake heat storage on the heat flux over the lake 225 surface. 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 by late August, when the surface water temperature was highest. Between October and January, when the lake water cooled, the lake released energy to the overlying atmosphere at an average rate of 137.5 W·m -2 , which 230 was more than 3 times greater 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 greater than the net radiation during the same period >>Fig. 5<<

Lake evaporation 245
Lake evaporation from Paiku Co between May and December was determined using energy budget method (Fig. 6). Lake evaporation between January and April was not determined because part of the lake surface was covered by lake ice which can significantly affect the energy balance over the lake surface. Monthly lake evaporation from Paiku Co during the ice-free season is shown in Fig.6. Lake evaporation was generally low during the pre-monsoon season (May and Jun) with an average value of 1.7 mm/day. During the monsoon season (Jul to Sep), lake evaporation increased rapidly from 2.9 to 5.1 250 mm/day. High lake evaporation occurred during the post-monsoon season (Oct to Dec), with an average value of 5.4 mm/day. Total lake evaporation from Paiku Co was estimated to be 975 mm between May and December. 9 >>Fig. 6<< Lake evaporation from Paiku Co was in anti-phase with the seasonal pattern of net radiation (Fig. 6), indicating that lake evaporation was not directly driven by the input energy. There is ~5 months lag between the maximum net radiation and 255 maximum lake evaporation from Paiku Co due to the large lake heat storage. When the net radiation was high between May and July, most of the energy was used to heat the lake water and only a small part of it was consumed as the latent heat flux, which led to low latent heat flux. When the net radiation was low between October and December, a large amount of heat was released from the lake water as latent heat to the overlying atmosphere, which led to high latent heat flux. Instead, lake evaporation exhibited a similar seasonal pattern with changes in lake heat storage, indicating that lake evaporation was 260 significantly affected by large lake heat storage. Regression analysis shows that lake evaporation from Paiku Co was 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). Lake evaporation exhibited similar patterns with the water vapour pressure difference between atmosphere and the underlying surface water (r 2 =0.33, P<0.001). According to bulk transfer relation, lake evaporation is mainly controlled by humidity gradient in the atmospheric layer . For deep lakes like Paiku Co, 265 although net radiation and air temperature decreases considerably during the post-monsoon season, lake water temperature was still high due to its large lake heat storage, which led to large water vapor difference and high evaporation. During the pre-monsoon season, the above process was reversed, which led to relatively low lake evaporation.

Impact of lake heat storage on the seasonal pattern of lake evaporation
To further explore the impact of lake heat storage on the seasonal pattern of lake evaporation, we compare lake evaporation 270 from Paiku Co with other lakes on the TP. We only select lakes with eddy covariance system measurements. At Ngoring Lake (area, 610 km 2 ; mean depth, 17 m) on the eastern TP, Z. Li et al. (2015) investigated the lake's energy budget and evaporation in 2011-2012, and found that the latent heat at Nogring Lake was lowest in June, peaked in August and then decreased gradually from September to November. At Qinghai Lake (area, 4430 km 2 ; mean depth, 19 m) on the northeast TP, X. Li et al. (2016) conducted studies concerning the lake's energy budget and evaporation in 2013-2015, and found that there 275 was a 2-3 month delay between the maximum net radiation and maximum heat flux. Compared with Paiku Co, there was shorter time lag between net radiation and evaporation from the two relatively shallow lakes. The different phase of lake evaporation among these lakes can be partly attributed to lake heat storage. As we have shown, Paiku Co has a mean water depth of ~41 m and the water column is fully mixed between November and June. This means that Paiku Co as a deep lake can store more energy during the pre-monsoon and monsoon seasons than relatively shallow lakes, and subsequently release 280 more energy to the overlying atmosphere during the post-monsoon season.
At Nam Co, a large and deep lake on the central TP, there have been several studies regarding lake evaporation Ma et al., 2016;Wang et al., 2017. Haginoya et al. (2009) found that lake evaporation from Nam Co was lowest in May and highest in October. Lake evaporation from Nam Co was estimated to be 916~986 mm through Bowen ratio method (Lazhu et al. 2016) and eddy covariance system . Fig. 6c shows that lake evaporation from 285 Paiku Co and Nam Co exhibits similar seasonal variations. 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 results in a similar seasonal pattern of changes in lake heat storage and lake evaporation (Fig. 6c). At Siling Co, another large lake on the central TP, monthly lake evaporation varied within a range of 2.4-3.3 mm/day between May and September with a total amount of 417.0 mm during the study period in 2014 (Guo et al., 2016). Although the cumulative evaporation between Paiku 290 Co and Siling Co is similar between May and September, lake evaporation during the post-monsoon season cannot be further compared because the heat flux at Siling Co was not measured after October.

The effects of lake evaporation on seasonal lake-level variations across the TP
The quantification of lake evaporation is important for understanding lake water budget and associated lake-level changes.
Compared with the eddy covariance system that is easily affected by lake ice after October/November when the lake surface 295 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-monsoon season can be much higher than that during the pre-monsoon season due to the release of large amount of stored heat, despite both air temperature and net radiation are already low. In this sense, lake evaporation during the postmonsoon season is of great importance to lake water budget and can significantly affect the amplitude of seasonal lake-level 300 changes, especially for deep lakes.

As a monsoon dominated region, Indian summer monsoon around Paiku Co usually starts in middle June and ends in late
September (Yu et al., 2016). For most years, more than 80% precipitation occurs during the summer monsoon season.
Glacier melting also occurs during the summer monsoon season. In contrast, heat flux from Paiku Co is still low during the summer monsoon season. During the post-monsoon season, precipitation and glacier melting decrease considerably while 305 heat flux from Paiku Co is high. This contrasting pattern of hydrological and thermal intensities plays an important role in the large amplitude of seasonal lake-level variations at Paiku Co. Precipitation and lake inflow, for instance, are mainly concentrated during the monsoon season, while lake evaporation is still low during this period ( Fig. 7a-b), which causes a positive lake water budget and a rapid increase in lake level (40~60 cm). During the post-monsoon season, precipitation and lake inflow are already very low, while lake evaporation is high, which leads to a negative lake water budget and a rapid 310 decrease in lake level (~40 cm). The slight lake-level decrease during the pre-monsoon season is mainly due to low lake evaporation and lake inflow during the pre-monsoon season.

>>Fig. 7<<
On a broader scale, lake evaporation may affect the different amplitude of seasonal lake-level variations between deep and shallow lakes on the TP.  investigated the lake-level seasonality across the TP and found that there were 315 different amplitudes of seasonal lake-level fluctuations even in similar climate regimes. For example, lake level at Nam Co and Zhari 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 during the post-monsoon season (Fig. 8), 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 seasonal pattern of lake evaporation may 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 320 evaporation) over lake surface may lag the net radiation by several months due to the large heat storage. For this kind of lake, the lake-level drop mainly occurs during the post-monsoon season when lake evaporation is high but lake water input is low.
For shallow lakes, the latent heat flux closely follows solar radiation due to relatively small lake heat storage. High lake evaporation occurs during the pre-monsoon and monsoon seasons, and low lake evaporation occurs 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 325 is covered by ice, lake evaporation (sublimation) is significantly reduced (Huang et al., 2019). Consequently, lake level at shallow lakes decreased slowly during the post-monsoon season compared with deep lakes. This phenomenon can also be seen at shallow thermokarst lakes on the northern TP (Luo et al., 2015;Pan et al., 2017).
Lake evaporation may also have significant impact on the different amplitude of seasonal lake-level variations between the northern and southern TP. Based on ICESat satellite altimetry data, Phan et al. (2012) showed that there was a larger 330 amplitude of seasonal lake-level variations on the southern TP relative to the northern TP. However, the main causes have not been investigated until now. Lakes on the northern TP usually freeze up earlier and break up later due to its lower temperature (Kropacek et al., 2013;Maussion et al., 2014), which results in longer ice cover duration on the northern TP (159-209 days) relative to the southern TP (126 days). Longer ice cover duration can considerably reduce lake evaporation during the post-monsoon season (Wang et al., 2020). Meanwhile, lakes on the southern TP are usually larger and deeper than 335 those on the northern TP (e.g. Wang et al., 2009Wang et al., , 2010, which indicates that it can store more energy during the premonsoon and monsoon seasons, and release it to the overlying atmosphere during the post-monsoon season. For endorheic lakes, relatively higher lake evaporation during the post-monsoon season may lead to larger lake-level decrease on the southern TP compared with the northern TP. Therefore, the different amplitudes of seasonal lake-level variations between the southern and northern TP can be partly attributed to the different seasonal patterns of lake evaporation. Note that other 340 factors including lake salinity and solar radiation may also have impact on lake evaporation across the TP besides lake ice phenology. More studies are still needed to quantify their impact on annual lake evaporation and the seasonal distribution. >>Fig. 8<<

Uncertainty of lake evaporation
In this study, energy budget and lake evaporation from Paiku Co are estimated based on in-situ measurements from a single 345 point. However, studies showed that there are considerable spatial differences in lake evaporation due to the different surface temperature and meteorological conditions over lake surface (Sugita et al., 2014). For example, Sugita (2019) showed that lake surface temperature and evaporation differs horizontally at Lake Kasumigaura due to the spatial variations of surface temperature, air temperature and wind speed. Lake evaporation was larger at the centre and the south of Lake Kasumigaura due to the strong wind regime. More detailed measurements from Paiku Co are still needed to investigate the spatial 350 variations of lake evaporation. Here, uncertainty of lake evaporation is estimated from the following aspects: solar radiation, lake surface temperature, changes in lake heat storage, meteorological data (air temperature and humidity).
Firstly, solar radiation and atmospheric longwave radiation at Qomolangma station were used to represent those 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 ( Fig. S4; Tang et al., 2019; Fig. S4). The results show that daily solar radiation at the two sites 355 exhibited similar seasonal fluctuations (R 2 =0.55, P<0.001). The mean difference of solar radiation at the two sites was estimated to be 3.8 W·m -2 ( ). The uncertainty in the atmospheric longwave radiation is not estimated, but the variations of solar radiation and atmospheric longwave radiation are usually opposite at a site, so their total uncertainty should not exceed the individual uncertainty (Yang et al., 2010).
Secondly, lake water temperature at the depth of 0.4-0.8 m, not lake skin temperature is used to calculate upward longwave 360 radiation. Studies show that lake skin temperature is higher than surface water temperature at daytime, and vice versa at nighttime (Prats et al., 2018). Here Aqua MODIS 8-day lake surface temperature product is used to determine the difference between lake bulk temperature and skin temperature. The product is produced with spatial resolution of about 1 km and the accuracy is estimated to be 1 K under clear sky conditions (Wan, 2013). During the pre-monsoon and monsoon seasons when the lake water got warm, the skin temperature derived from MODIS data was about 1.2 o C higher than lake body 365 temperature. During the post-monsoon season when the lake water got cool, the skin temperature derived from MODIS data was about 0.05 o C higher than lake body temperature. Because MODIS data is easily affected by cloud cover and other factors during the monsoon season, the mean difference of 0.05 o C during the post-monsoon season is used to estimate uncertainty of upward longwave radiation, which corresponded to be 7.6 W·m -2 of heat flux ( ) by using error propagation.
Thirdly, uncertainty of changes in lake heat storage mainly comes from the spatial distribution of lake water temperature. A 370 comparison of lake water temperature between Paiku Co's southern and northern basins in 2016/2017 is shown in Fig. S5.
Since the northern basin is deeper than the southern basin, lake water in the northern basin warmed more slowly than that in the southern basin during the pre-monsoon and monsoon seasons, and cooled more slowly during the post-monsoon season.
The daily 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, but was about 0.45 o C lower on average in November and December (Fig. S5). Water 375 temperature became spatially uniform at both basins between January and March. Similar spatial difference can also be found at 10 m depth, indicating that this phenomenon may exist in the entire epilimnion. Uncertainty of changes in lake water temperature is estimated to be 0.007 o C/day during the ice-free period, corresponding to 14.3 W·m -2 of heat flux ( ).
Fourthly, air temperature and relative humidity at the shoreline are used to calculate Bowen ratio and lake evaporation. To validate its representativeness, we set up a platform (water depth: 19 m; least distance from shoreline: 2 km) in the southern 380 centre of Paiku Co in September 2019 and a simple AWS station (GMX600) was installed on the platform. Meteorological data between 22 September and 26 October were acquired. We made a comparison of meteorological data between shoreline and lake centre. Results show that both air temperature and relative humidity fluctuated similarly between the shoreline and lake centre (Fig. 9), indicating the meteorological data from the shoreline of Paiku Co can be used to represent the general 13 condition of the whole lake at least during the observed period. The RMSE of daily air temperature and water vapour 385 pressure in the shoreline was estimated to be 0.91 o C and 0.069 kPa. The uncertainty of Bowen ratio was estimated to be 0.02 during the ice-free period by using error propagation, which corresponds to 2.2 W·m -2 of heat flux ( ). By using error propagation, the uncertainties of latent heat flux and lake evaporation are estimated to be 16.8 Wm -2 (=√ ) and 0.6 mm/day, respectively. The total uncertainty of lake evaporation is 142 mm during the ice-free period between May and December. 390 >>Fig. 9<< Lake evaporation is validated by comparing with lake-level changes during the pre-monsoon and post-monsoon seasons.
Runoff measurements at the three largest rivers feeding Paiku Co are shown in Tab. 3. During the pre-monsoon season (May), lake evaporation (1.7 mm/day) was similar with the rate of lake-level decrease (1.8 mm/day). During the postmonsoon season (Oct to Dec), lake evaporation (5.4 mm/day) was considerably higher than the rate of lake-level decrease 395 (3.8 mm/day). This discrepancy (1.6 mm/day) may be largely due to the contribution of precipitation and surface runoff. As shown in Table 3, runoff at the three large rivers can contribute to lake-level increase by 1.0 mm/day on average in October, thereby partially offsetting lake-level changes from lake evaporation. This difference (0.6 mm/day) between the estimated lake evaporation and the in-situ measurements of lake-level decrease and runoff during the post-monsoon season is very close to the uncertainty of lake evaporation estimated by error propagation. 400

Conclusion
Lake evaporation and its effects on seasonal lake-level variations at Paiku Co on the southern TP were are investigated based on three years' comprehensive observations of lake water budget. The results show that Paiku Co is a dimictic lake with clear lake stratification between July and October. The surface water reaches its highest temperature by late August while the bottom water reaches its highest two months later. The thermocline formed at the depth of 15~25 m, with the largest 405 temperature difference of 5~6 o C in late August.
As a deep alpine lake, the seasonal patterns of heat flux and lake evaporation are significantly affected by the large lake heat storage. The lake absorbed absorbs most of net radiation to heat the lake water during the pre-monsoon and monsoon seasons and released releases it to the overlying atmosphere during the post-monsoon season. 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 410 about 3 times larger than the net radiation. As a result, there was ~5 months lag between the maximum net radiation and the maximum lake evaporation due to the large heat storage of lake water. Lake evaporation from Paiku Co was estimated to be 975±142 mm during the ice-free period between May and December, with low values of 1.7±0.6 mm/day during the premonsoon season (May and Jun), and high values of 5.4±0.6 mm/day during the post-monsoon season (Oct to Dec).
14 Our results imply that lake evaporation plays an important role in the different amplitudes of seasonal lake-level variations 415 on the TP. For deep lakes like Paiku Co, contrasting hydrological and thermal intensities determines the large amplitude of seasonal lake-level variations. High lake evaporation and low lake inflow leads to the considerable lake-level decrease during the post-monsoon season. In contrast, relatively low lake evaporation but high lake inflow leads to rapid lake-level increase during the monsoon season. For relatively shallow lakes, the seasonal pattern of lake evaporation varies similarly with the net radiation, which results in slight lake-level decrease during the post-monsoon season and less amplitude of lake-420 level seasonality. Therefore, lake evaporation may play an important role in the different amplitudes of seasonal lake-level variations.

Data availability
All original data presented in this paper are publicly available via National Tibetan Plateau Data Center 425 (http://data.tpdc.ac.cn/en/).

Author contribution
Lei Y.B. and Yao T.D. conceived and designed the experiments; Lei. Y.B., Yao T.D., Yang K., Lazhu, and Ma Y.M. analyzed the data; Lei Y.B. performed the fieldwork and wrote the paper; Bird B.W. helped write the paper.

Competing interests 430
The authors declare that they have no conflict of interest.