Qinghai Lake (36∘32′–37∘15′ N, 99∘36′–100∘ 47′ E) is the largest inland lake in China, with a surface area of 4497 km2 (in 2017) and a catchment area of 29 660 km2. The maximum length and width of the lake are approximately 106 and 67 km, respectively. It is an endorheic, brackish lake (salinity 12.5 g L-1, pH 9.3; Deng et al., 2010) located on the northeastern margin of the TP (Fig. 1) at the height of about 3194 m a.s.l. The mean and maximum depths of the lake are 21 and 32.8 m, respectively. The lake is ice-covered from December–January to early April; the average annual lake water temperature is 5.4 ∘C, with the maximum monthly temperature of 17.2 ∘C (August) and the minimum of -2.0 ∘C (January; Li et al., 2016). The average annual air temperature (1959–2015) at the lake is 1.9 ∘C. The mean annual precipitation in 1959–2015 was about 340 mm (Ding et al., 2018), with more than 65 % occurring in summer. Annual evaporation from the lake surface was 924 mm, and surface runoff water inflow and groundwater inflow were 348 and 138 mm, respectively (Li et al., 2007).

Qinghai Lake is sensitive to climate variability. Because the evaporation was generally larger than river runoff and precipitation from 1961 to 2004, the water level of Qinghai Lake decreased at an average rate of 7.6 cm per year (Cui and Li, 2016). However, the precipitation continuously increased in 1970–2015 by 15.603 mm per decade, according to the data from the Gangcha station (the nearest meteorological station approximately 13 km north to Qinghai Lake). Simultaneously, the runoff from the melting of Qilian Mountain glaciers was also increasing because of the regional warming trend of 0.319 ∘C per decade, coupled with the decreasing evaporation by 1.343 mm per year (observed by Gangcha station) during 1970–2003 (Tang et al., 2018). Since 2004, as the runoff and precipitation exceeded evaporation and the regional climate gradually turned to the direction of “warm and humid”, the Qinghai Lake level increased at a rate of 14 cm per year during 2004–2012 (Dong and Song, 2011; Zhang et al., 2011, 2014b; Cui et al., 2016).

The FLake model (Mironov, 2008) is used to simulate the vertical temperature profile and the energy budget of the different layers of the lake on the timescales from several hours to many years. The model divides the lake water body vertically into two layers, the upper layer being the mixed layer with uniform temperature. Beneath the mixed layer, the temperature profile is parameterized using the concept of self-similarity (Kitaigorodskii and Miropolsky, 1970), which means that the characteristic shape of the temperature profile is conserved irrespective of the depth of this layer. The parameterization formula is 1θs(t)-θ(z,t)Δθ(t)=Φθζht≤z≤D, where t is time, z is the depth, θs(t) is the temperature of the upper mixed layer of depth ht, Δθt=θst-θb(t) is the temperature differences across the thermally stratified layer of the depth of Δht=D-h(t), D is the lake depth, and θb(t) is the temperature at the lake bottom. Φθ(ζ) is a dimensionless “universal” function of the dimensionless depth ζ=z-h(t)Δht which satisfies the boundary conditions Φθ0=0 and Φθ1=1. Based on the self-similarity assumption, the temperature profile can be expressed as a two-layer approximation: 2θ(t)=θs(t)0≤z≤h(t)θst-[θst-θbt)Φθζ]h(t)≤z≤D.

Substitution of Eq. (2) over the lake water column with subsequent substitution into the heat transport equation yields a set of ordinary differential equations, including the lake in form of the shape factor Cθ=∫01Φθ(ζ). The resulting equation system is complemented by an equation for evolution of the mixed layer depth ht, which is calculated based on the convective entrainment or relaxation-type equation in terms of wind mixing (see Mironov, 2008 for details).

The shape factor Cθ is parameterized by a relaxation formula: 3dCθdt=signdhtdtCθmax-CθmintrcCθmin≤Cθ≤Cθmax, where trc is the empirically estimated relaxation time or times of the temperature profile in the thermocline from one limiting curve to the other, following the change of sign in dh(t)dt. Cθmin=0.5 and Cθmax=0.8 are the minimum and maximum values of the shape factor.

Additionally, FLake includes the representation of the thermal structure of the ice layer, snow layer and the thermally active upper layer of bottom sediments, all using the self-similarity concept. The snow module of FLake has not been comprehensively tested so far. Compared with other lake models, it is relatively easy to adjust FLake to a specific application due to a small number of lake parameters to be specified, the major ones being the lake depth and the optical characteristics of the lake water.

To partially account for salinity effects in a brackish lake, the freshwater equation of state used by FLake was adjusted by changing the temperature of maximum water density (Tm) and the freezing point temperature (Tf). The parameterization formula of Tm and Tf obtained from linear approximations of the empirical function of state of seawater (Caldwell, 1978; UNESCO, 1981) are 4Tm∘C=3.98–0.216S,5Tf∘C=-0.055S, where the S is salinity taken in parts per thousand (‰ or g L-1). For the salinity of S=12.5 g L-1, which is the case of Qinghai Lake, the equation gives Tm=1.28 ∘C and Tf=-0.69 ∘C. In addition, the lake depth was set to the mean depth of Qinghai Lake (21 m). The simulation started at the beginning of the year in 1979. The forcing data of 1979 were used to drive the Flake model 10 iterations for a spin-up. Then the actual modelling period started in 1979 and ended in 2012. The simulation duration was 34 years, with the simulation step of 3 h. The model runs were performed using both the original freshwater equation of state and the brackish water approximation (Eqs. 4–5). Here we defined the simulation with original freshwater equation of state as a freshwater lake (FL) experiment and the simulation with the brackish water approximation as a saltwater lake (SL) experiment.

Introduction of salinity remarkably affected the ice regime but not the lake surface temperatures. Therefore, only the simulation results of the SL experiment are analysed in this subsection. Comparison of the simulated lake surface temperatures against MODIS LST (Fig. 3) demonstrated that the FLake model can nicely simulate the seasonal variations in the lake surface temperature: the correlation coefficient amounted to 0.93. The simulated temperature was, however, generally higher than the MODIS LST, with a positive bias of 1.98 ∘C and a root-mean-square error (RMSE) value of 3.97 ∘C for the annual mean, except in springtime, when the simulated LST had a negative bias of -0.74 ∘C compared to MODIS LST.

In order to evaluate the effect of the forcing data deviation on the simulation results, we applied a correction to the ITPCAS forcing data. Since the buoy observations are mainly available from June to October, only forcing data for this period of the year were corrected. The air temperature was adjusted with the linear relationship (y=0.76x+3.27, x for ITPCAS and y for buoy observations), and the wind speed was corrected by adding a constant bias of 1.19 m s-1 between the mean buoy observation and the mean ITPCAS data. After the correction, the bias and RMSE between simulated LST and MODIS LST were both reduced for the open-water period (from 2.85 and 3.71 to 2.82 and 3.58 ∘C, respectively), especially for the summer (3.30 to 1.60 ∘C) and the autumn (2.97 to 1.06 ∘C). Through the correction of the driving data, we found that the positive bias between simulated LST and satellite data can be partly explained by the differences in the forcing weather data measured over the lake and provided by the ITPCAS data. The remaining bias may be partly attributed to the cool skin effect in the LST sensed by MODIS.

The effect of salinity stratification on the lake mixing was not accounted for by the FLake model, assuming purely thermal stratification. The modelled seasonal stratification of Qinghai Lake corresponded to that of a dimictic lake (Fig. 4) with typical features of this type of mixing regime (Kirillin and Shatwell, 2016). Winter and summer stratified periods are divided by two short periods of full vertical mixing (overturns) in late spring and late autumn. During the overturn period, dimictic lakes are supposed to be fully mixed with the bottom. From the simulation, we found that the spring overturn of Qinghai Lake, occurring around May, lasted for 2–3 weeks, and the depth of mixed layer reached the bottom of the lake in most but not all simulation years. The autumn overturn appeared around November–December, lasting approximately for a month, and the mixed layer reached the bottom of the lake in all simulated years. In the summer stratified period, the mixing process was mainly caused by the wind forcing and the stratification instability due to diurnal temperature variations, and the depth of the mixed layer reached 10–15 m, gradually increasing with time.

Although the modelled LSTs are slightly lower in the spring and higher in other seasons, especially in summer and autumn, and the deviations in nighttime are larger than in daytime, the model simulated the variations in the LST and its typical magnitudes well and produced a reasonable vertical thermal structure.

According to the ITPCAS data from 1979–2012, the air temperature and longwave radiation had positive trends of 0.58 ∘C (p<0.01) and 3.22 W m-2 (p<0.01) per decade, respectively, while the wind speed and shortwave radiation had negative trends of -0.11 m s-1 (p>0.05) and -2.41 W m-2 (p<0.05) per decade, respectively. These values are consistent with other reports on climate change over the TP. The air temperature at different weather stations on the TP is rising by an average of 0.09 to 0.74 ∘C per decade from 1961 to 2007 (Guo and Wang, 2012), while the wind speed and shortwave radiation is decreasing (Yang et al., 2014).

From 1979 to 2012, the simulated LST, mixed-layer temperature and the lake mean temperature in the SL experiment was increasing at 0.74, 0.38 and 0.26 ∘C per decade, respectively (p<0.01 for all three trends); the bottom temperature revealed a slower trend at 0.2 ∘C per decade (p>0.05; Fig. 5). For the first decade from 1979 to 1989, all temperatures demonstrated a stronger warming trend, especially for the surface layer (1.4 ∘C per decade, p>0.05). Later on, the trend slowed down to 0.54 ∘C per decade (p<0.05) for the surface temperature, same as the mixed layer (0.32 ∘C per decade, p<0.05) and mean water column (0.14 ∘C per decade, p>0.05) during the rest of years. The bottom water temperature even demonstrated a slightly decreasing trend of -0.25 ∘C per decade (p>0.05).

Due to the importance of the lake surface as an interface of heat and mass exchange between the lake and atmosphere, the relationship between the LST variation trend and main atmospheric characteristics was investigated (Fig. 6). The trend of LST simulated by FLake was consistent with rising air temperature (0.58 ∘C per decade), but with a higher rate of 0.74 ∘C per decade. Meanwhile, the simulated LST had a positive correlation coefficient of 0.71 (p<0.01) with air temperature. A negative correlation coefficient of -0.35 (p<0.05) was found between the simulated LST and the wind speed. The downward shortwave radiation had a negative correlation coefficient of -0.29 (p>0.05) for the LST. The LST and the downward longwave radiation were positively correlated (coefficient of 0.74, p<0.01).

Compared with the FL experiment, the salinity parameterization for Tm and Tf in the SL experiment has a certain effect on the ice phenology (Fig. 7): the maximum ice thickness is reduced, the freeze-up date is delayed and the break-up date is advanced, leading to a shorter ice duration period. Nevertheless, the interannual changes between them remained consistent. The simulated freeze-up and break-up date in the FL and SL experiments are both later than satellite observations, with some differences in interannual variations but a similar range in ice duration. In the SL experiment, the maximum ice thickness and the break-up date are closer to the observations; the former was reported at 0.7 m by Chen et al. (1995). Hence the ice phenology results from the SL experiment were used for further analysis.

The variations in break-up and freeze-up dates are sensitive to the meteorological conditions, e.g. air temperature, solar radiation and wind (Duguay et al., 2006; Latifovic and Pouliot, 2007; Ye et al., 2011; Kirillin et al., 2012; Yao et al., 2016). In the SL experiment, the simulated maximum ice thickness demonstrated a negative correlation of -0.52 (p<0.01) to the mean air temperature anomaly from January to April in Qinghai Lake. With the increase in air temperature, the maximum ice thickness of Qinghai Lake reveals a decreasing trend of -0.1 m decade-1 (p<0.01; Fig. 7a). Simulated ice cover of Qinghai Lake started in the late December to January and ended in early April to early May. The correlation coefficient of -0.68 (p<0.01) was found between the freeze-up date and mean air temperature anomaly for November–December (Fig. 7b), while a 0.48 (p<0.01) correlation coefficient was found between a break-up date and mean temperature anomaly for March–April (Fig. 7c). With the increasing trend in the air temperature and LST, the freeze-up date was delayed by about 4.5 (p<0.01) days every decade, and the break-up date advanced about 5.7 d (p<0.01) earlier every decade, resulting in a shortening of the ice cover period by about 10.2 d (p<0.01) per decade (Fig. 7d).

Lake mean temperature is the indicator of the heat storage in the lake water body, whose changes are mainly driven by the heat exchange at the lake surface, which is composed of the net (shortwave and longwave) radiation budget, sensible heat flux (SH) and latent heat flux (LH). Quantification of the energy balance at the lake surface is necessary for understanding the mechanisms of the lake response to climate change. The heat transfer from precipitation, runoff and the bottom sediments of the lake are ignored here due to their small magnitudes and observational difficulties.

According to ITPCAS data, the solar radiation flux over Qinghai Lake was decreasing at -2.41 W m-2 per decade (p<0.05; not shown), while simulation results produce a positive trend of 0.78 W m-2 (p>0.05) per decade in the net annual shortwave radiation gain by the lake (Fig. 8a). This was caused apparently by shortening the ice-covered period from 125 d (1979) to 72 d (2012) that reduced the lake surface albedo from the ice values (between 0.1 and 0.6) to the open-water albedo (∼0.07), significantly increasing the amount of net annual solar radiation absorption by the lake. The net longwave radiation reduced at -0.21 W m-2 per decade (p>0.05; Fig. 8b). Concurrently, the downward longwave radiation increased at 3.22 W m-2 per decade (p<0.01; not shown). Hence, the decreasing trend of net longwave radiation was caused by the increased upward longwave radiation (3.4 W m-2 per decade, p<0.01) due to the rising LST during the open-water period and a shortening of the ice cover duration.

From 1979 to 2012, SH at Qinghai Lake decreased slightly at -0.14 W m-2 per decade (p>0.05; Fig. 8c), while LH become stronger at 1.57 W m-2 per decade (p<0.05; Fig. 8d). Hence, the additional heat gained due to the net radiation increase (0.57 W m-2 per decade, p>0.05) was mainly balanced by the increased LH due to evaporation. The average annual energy storage in the water body (Qs, ice cover not included) of Qinghai Lake was close to equilibrium and showed a slight downward trend (-0.58 W m-2 per decade, p>0.05; Fig. 8e). The long-term interannual cumulative energy storage in turn showed an increasing trend (4.68 W m-2 per decade, p<0.01; Fig. 8f), which was consistent with the increasing lake mean water temperature.

The strong seasonal variation in the surface-air temperature differences is driven by the different thermal properties of the lake and the surrounding land surface (Haginoya et al., 2009; Desai et al., 2009). In the seasonal course averaged over the period 1979–2012, the 5 d moving average air temperature was higher than LST during the ice-covered period (Fig. 9a), with the minimum lake–air temperature differences as low as -6.9 ∘C (Fig. 9b). After the ice-off between early April to mid-May, LST increased rapidly, particularly due to heating by the intense solar radiation (maximum 285.4 W m-2 for 5 d average), characteristic of high-altitude conditions on the TP (Fig. 9c), and exceeded the air temperature in June, reaching the maximum of 18.7 ∘C in August (Fig. 9a). LST was generally higher than air temperature from June to January of the next year, which roughly coincided with the end of the open-water period. The mean lake–air temperature difference (5 d moving average) became positive in June and kept increasing to a maximum of 12.8 ∘C in December, just about 20–30 d before the ice cover formation (Fig. 9b). Owing to the large heat capacity of the lake, a clear phase lag existed between LST and air temperature. The time difference between the seasonal temperature maximums of the LST and the air temperature was about 20 d, and the time difference between both values dropping to the freezing temperature of water of 0 ∘C was about 2 months.

From the perspective of interannual variability, both air temperature and LST had an increasing trend all year round, with stronger warming in winter than in summer (Fig. 9a). Although the downward longwave radiation increased in summer and autumn (average of 0.33 W m2 a-1, maximum of 0.47 W m2 a-1 in September; Fig. 9d), the LST increased slower than the air temperature, resulting in a reduction of lake–air temperature difference in autumn (average of -0.04 ∘C a-1, maximum of -0.05 ∘C a-1 in November; Fig. 9b). This behaviour can be attributed to the apparent decrease in the downward shortwave radiation in summer (average of -0.59 W m2 a-1) and in autumn (average of -0.11 W m2 a-1), which reduced the net shortwave radiation absorption by the lake in summer and autumn (average of -0.55 and -0.10 W m2 a-1, respectively, Fig. 9c, e). In turn, the increased upward longwave radiation in summer and autumn (average of ∼0.22 W m2 a-1; not shown) partially damped the effect of the downward longwave radiation increase (average of 0.33 W m2 a-1), which lead to a decrease in the net longwave radiation from the lake to air (average of ∼0.19 W m2 a-1) between mid-summer and late autumn (Fig. 9f).

In contrast to the inhibited positive trend of LST increase during the ice-free period, the monthly mean LST in early winter and late spring increased more rapidly than the air temperatures, with two apparent peaks of 0.24 and 0.12 ∘C a-1 in January and May, respectively (Fig. 9a, b). The significant increase in LST in these periods may be related to the shift of the ice-on and break-up dates (grey areas in Fig. 9), as well as to the slight increase in solar radiation in December and April. The same seasonal pattern was reflected in the variations in the radiation balance (Fig. 9e, f): during the open-water period, the absorbed net shortwave radiation and released longwave net radiation at the lake surface had a generally consistent trend with downward shortwave radiation and downward longwave radiation, respectively, while during the ice formation period (the grey area around December–January in Fig. 9) and the thawing period (the grey area around April–May in Fig. 9), the absorbed net shortwave radiation and released longwave radiation had opposite trends to the downward shortwave radiation and downward longwave radiation, respectively. The net shortwave radiation increased obviously in these two periods (average of 0.57 and 0.53 W m2 a-1, respectively), while the downward shortwave radiation was not (average of -0.05 and -0.13 W m2 a-1, respectively; Fig. 9c, e). The same is true for the net longwave radiation that decreased obviously in these two periods (-0.31 and -0.40 W m2 a-1, respectively), although the downward longwave radiation had an increasing trend in each period (0.34 and 0.16 W m2 a-1) (Fig. 9d, f).

Since the dates of the lake ice break-up and freeze-up strongly affect the seasonal energy budget of the lake (Rouse et al., 2003; Jakkila et al., 2009), the heat budget and its long-term trends were considered in more detail. During the thawing period (the grey area around April–May in Fig. 10; same as in Fig. 9), the solar radiation was the strongest (average of 270.6 W m-2; Fig. 9c) on the background of appreciable downward longwave radiation (average of 246.1 W m-2; Fig. 9d). An earlier break-up date significantly reduced the albedo of the lake (from ice ∼0.6 to water ∼0.07), which led to an increase in the net shortwave radiation into the lake (Fig. 9e), which is same for the net radiation in April (1.1 W m-2 a-1; Fig. 10c). Concurrently, the small lake–air temperature differences also ensured small SH and LH (average of -3.3 and 10.4 W m-2, respectively; Fig. 10a, b), which means that the heat release from the lake surface (the compound of net longwave radiation, SH and LH) was low (Fig. 10d). As a consequence, the energy storage (Qs) of the lake water body in this period (average of ∼91.7 W m-2) increased due to earlier ice break-up at ∼1.0 W m-2 a-1 or at ∼1.1 % per year (Fig. 10e).

In contrast, the freezing period (the grey area around December–January in Fig. 10) was characterized by the weakest levels of both downward shortwave and downward longwave radiation (average of ∼125.9 and ∼166.5 W m-2, respectively; Fig. 9c, d). However, the upward longwave radiation (not shown) in this period was ∼1.7 times larger than downward longwave radiation, causing a minimum of net radiation of -45.3 W m-2 in December (Fig. 10c). Also, unlike in the thawing period, the values of upward SH and LH (average of 20.4 and 26.9 W m-2, respectively; Fig. 10a, b) both cannot be ignored because of a large lake–air temperature difference during this period. Hence, a later ice-on leads to an intense cooling of the lake water because the upward longwave radiation, SH and LH were not obstructed by the ice cover (Fig. 10a, b, c, d). The additional heat absorbed by the lake caused by earlier break-up in previous seasons released before freeze-up partly contributed to the delay of the freeze-up date of Qinghai Lake.

The validation results indicate that FLake performed well for the extreme climatic conditions of the TP. Although there is an underestimation to the lake surface temperature in spring and an overestimation of it in rest of the seasons, it reproduced the observed seasonal variation in LST well and simulated the thermal structure of the mixed layer and the thermocline reasonably. FLake can be considered a useful tool for studying the impact of the climate change to lakes on the TP.

The ITPCAS forcing data incorporating observations from land weather stations produced a constant bias when applied directly to model the lake surface conditions. The reason is the difference in the physical characteristics, in particular, air temperatures and wind speeds, between land and water, which is especially strong over the TP (Lazhu et al., 2016). The result is consistent with the findings of Kheyrollah Pour et al. (2012), who applied the FLake model to Great Slave Lake and Great Bear Lake in Canada. They also found that the model overestimated the LST when compared with the MODIS data because the forcing data were obtained at the land station rather than over the lake surface. In our case, the ITPCAS air temperatures are 0.71 ∘C larger during daytime and 2.49 ∘C smaller during nighttime compared to the buoy observations in summer and autumn. The ITPCAS wind speeds are 0.63 m s-1 lower during daytime and 1.83 m s-1 lower during nighttime. In turn, the daily variations in the air temperatures in ITPCAS data are almost 2.85 times higher than in the buoy observations. Lower wind speeds from ITPCAS forcing data weaken the heat transfer and lead to a warmer lake surface temperature simulated by FLake. Additionally, the wind speeds of ITPCAS data are smaller at night, corresponding with a higher simulated LST in the nighttime. This result proves that the deviation of the ITPCAS forcing data indeed leads to a warmer simulated LST. Hence, the choice of atmospheric forcing is crucial for the simulation of large lakes in the extreme highland conditions of the TP. In the absence of long-term weather observations over the lake surface, a correction procedure can be applied to the forcing data based on the available short-term observations from moored stations (buoys) and/or satellite information. In this study, a comparison with short-term observation data from the buoy on lake surface allowed correction of the ITPCAS forcing data, significantly reducing the bias between the model and the remote sensing data.

The simulated seasonal stratification regime suggests that Qinghai Lake is dimictic, with the spring overturn taking place around May and the autumn overturn appearing around November–December. Currently, there is no long-term information available on the vertical thermal structure of Qinghai Lake. The stratification pattern simulated in this study is, however, very similar to the observations from another Tibetan lake, Bangong Co (Wang et al., 2014). Salinity can influence the temperature of maximum density (Tm) and the freezing temperature of water (Tf). According to the 12.5 g L-1 salinity of Qinghai Lake, these two parameters equal 1.28 and -0.69 ∘C instead of the default model configurations of 4 and 0 ∘C, respectively. Considerations of the salinity effects lead to a slightly earlier spring overturn and a later autumn overturn, and consequently to an extension of the lake stratification period. Because the salinity stratification effects cannot be completely included in the model designed for freshwater lakes, the simulated mixing regime may have some differences from the actual situation of Qinghai Lake.

Despite incorporation of the salinity effects on Tm and Tf improved simulation accuracy of maximum ice thickness and break-up date, the ice phenology modelled by FLake still differs from the remote sensing observations. The discrepancy may be related to a number of factors not included in the model. One of them is the effect of salinity on the ice structure, density and porosity; the others are precipitation, inflows, circulation under ice cover and wind, which are especially important for large-area lakes (Kirillin et al., 2012; Kouraev et al., 2007) such as Qinghai Lake. However, the air temperature apparently has the strongest effect on ice regime, especially in long-term changes, which appear to be simulated well by FLake, allowing us to study the effect of climate change on lake ice regime within the model ability.

Following the studies of Lazhu et al. (2016) on Nam Co Lake (salinity ∼1.78 g L-1) and Kirillin et al. (2017) on freshwater lakes Ngoring and Gyaring, the good prediction of the LST over the largest, brackish lake of the TP by the relatively simple, highly parameterized model FLake, verified by satellite and buoy data, is one of the core results of this study. Both the importance of the TP for global climate interactions and the lack of continuous observations in this region demand reliable modelling schemes to take into account the complexity of the land–atmosphere interactions. FLake is currently among the few lake parameterization schemes actively used in regional climate models and numerical weather prediction (NWP). Complementary to the recent study of Kirillin et al. (2017), who successfully applied FLake to the freshwater lakes of the TP, the present study demonstrates that the model adequately simulates the major mechanisms of the air–lake interaction in large brackish lakes of the TP. Hence, FLake can significantly improve the simulation of the land–atmosphere interaction in regional climate models and NWP, which is crucial for understanding the climate-driven changes in this key region. To a first approximation, the result suggests the applicability of FLake to the simulation of all large brackish waters. The latter are characteristic features of arid regions worldwide, having a strong impact on regional climate and the water budget.

We have found that the duration of the ice-covered period is crucial for the lake–atmosphere interaction on the TP, with periods of ice-on and ice-off having the strongest effect both on the radiation balance and the boundary heat exchange by SH and LH. To simulate the ice cover duration properly, the heat storage in winter and the vertical heat transport across the ice-covered water column should be adequately described. In its present version, FLake treats these in a simplistic way, neglecting the heating of water column by solar radiation penetrating the ice cover (Kirillin et al., 2017). This simplification is a source of potential errors in the simulated ice break-up date and LST after the break-up, which errors can be significant for the Tibetan conditions, taking into account the strong solar radiation and low snow precipitation on the TP in winter. In earlier studies on lowland lakes, FLake tended to predict earlier break-up dates because of the absence of snow in the FLake model (Bernhardt et al., 2012; Kheyrollah Pour et al., 2012). In this study, the simulated break-up date is generally later than observation, which can be treated as an indication of the importance of the under-ice water column heating by solar radiation neglected in the model. Another factor potentially introducing the uncertainty into the simulation of the ice duration is the ice albedo. The latter was recently estimated in Qinghai Lake to be much lower than typical estimates for lakes: ice albedo obtained by MODIS was less than 0.25 under the snow-free condition and less than 0.4, even under the snow cover condition (Li et al., 2018; Lang et al., 2018). Among the reasons for such a low ice albedo that may be mentioned are the effects of salt on the ice structure and deformation of the ice surface under the influence of the strong solar radiation. As a result, standard modelling approaches may underestimate the amount of shortwave radiation penetrating the ice, with subsequent errors predicting the ice duration and underestimation of the LST after ice break-up.

The LST acquired by the MODIS, which is used as a reference for validation of simulation results, is generally lower than the in situ LST. This discrepancy may partly be contributed by the cool skin effect (Crosman and Horel, 2009), which is also found to be stronger in high-altitude lakes than in the ocean due to strong solar radiative heating and cooler air temperature at lake surface (Li et al., 2015; Wen et al., 2016). This suggests that the model predictions of the bulk LST may be better than what the comparison against the satellite data shows, though exact estimation and correction of the cool skin effect is out of the scope of this study.

As expected, the correlation analysis shows that the changes in LST are closely related to air temperatures, downward longwave radiation and wind speed (Fig. 6). The increase in the air temperature and downward longwave radiation plays a key role in lake surface temperature warming, and the decrease in wind speed also promoted the warming of the lake surface temperature. The downward shortwave radiation is negatively and insignificantly (R<0.3) correlated with the water temperature, which can also explain the slower increase in the water temperature compared with the air temperature (see Kirillin et al., 2017). The decrease in ice cover duration increases, in turn, the annual amount of shortwave radiation penetrating the water column, accelerating the net warming. Annual mean LST simulated by FLake increased at a rate of 0.74 ∘C per decade, primarily due to rising air temperature and decreasing wind speed. The warming trend of simulated LST significantly exceeded that of the regional air temperature (0.58 ∘C per decade). This discrepancy may be caused by declining winter ice cover, which leads to an earlier start of the stratified season that significantly increases the LST (Austin and Colman, 2007). Mixed-layer and water mean column temperature increased by 0.38 and 0.26 ∘C from 1979 to 2012, respectively, while the bottom temperature increased slowly from 1979 to 1989 and has even a slight decreasing trend from 1989 to 2012. The slight decrease in the deep temperatures agrees with findings of Kirillin et al. (2017) from freshwater Ngoring Lake on the TP and the research of Huang et al. (2017) that uses the General Lake Model (GLM) at another TP lake, Nam Co. The apparent reason for the deep cooling is the increase in stability of the lake due to surface warming, which restricts heat transfer from surface to bottom and produces a decrease in the bottom water temperature. This behaviour has been reported as a characteristic in previous studies on lowland dimictic lakes (Hondzo and Stefan, 1993; Danis et al., 2004; Kirillin, 2010).

As mentioned above, climate change is found to have a strong impact on lake ice phenology. The maximum ice thickness of Qinghai Lake decreases in simulations, and significant tendencies to later ice-on and earlier ice-off are predicted. These three ice phenology characteristics are correlated with the January–April, November–December and March–April air temperature, respectively. The ability to accurately represent ice cover on lakes is essential for the improvement of global circulation models, regional climate models and numerical weather forecasting (Brown and Duguay, 2010). We have shown that the net shortwave radiation increase caused by a shortening of the ice duration plays a key role in net radiation increase. Hence, the declining winter ice cover has a significant influence on the annual radiation balance of the lake.

In total, the annual energy storage in water body of Qinghai Lake (Qs) decreased at a slow rate of -0.58 W m-2 per decade, influenced primarily by the increase in received net radiation and released LH at the lake surface (Fig. 8e). Still, the cumulative energy storage of the lake is increasing at 4.68 W m-2 per decade (p>0.01; Fig. 8f), consistent with the trend of the mean water column temperature. Change of freeze-up or break-up date dramatically influenced the lake energy and heat budget during the ice formation or decay period. The earlier thaw of ice causes an increase in energy absorbed by the lake in late spring, since more solar radiation comes into the lake without reflection by the ice cover. The delayed freeze-up date leads to an increase in energy lost before freeze-up due to strong upward longwave radiation, SH and LH.

For low-altitude temperate and boreal lakes, the air temperatures are typically higher than LST after the ice-off and remain higher until temperature equilibrates around mid-summer. In the subsequent period down to ice-on, the LSTs are typically higher than the air temperatures. Hence, the atmospheric boundary layer is generally stable throughout much of the summer season over low-altitude lakes (Scott and Huff, 1996; Rouse et al., 2003; Gianniou and Antonopoulos, 2007; Momii and Ito, 2008; Nordbo et al., 2011). Due to a higher altitude, the lakes on the TP have a lower atmospheric thickness and air density, and the solar radiation over the plateau is much stronger than in other areas of the same latitude, while the air temperatures are comparably low (Wen et al., 2016; Haginoya et al., 2009; Li et al., 2016). These specific climatic conditions cause a significantly different seasonal interaction between the lake and the atmosphere. In this study, the LST of Qinghai Lake increased very fast after ice melt in mid-April under the strong solar radiation and equilibrated with air temperature in June, which is much earlier than in low-altitude lakes. The difference between air temperature and LST is the fundamental property of lake–air interaction, determining the intensity of the surface heat exchange by means of atmospheric stability. When the LST is higher than air temperature, which is the case for the TP lakes in summer, the atmosphere over the lake becomes increasingly unstable, accelerating the release of heat to the atmosphere by convection. In that sense, the role of lakes, as hotspots of the land–atmosphere interaction on the TP, consists of the accumulation of the solar radiation and release of the accumulated heat into the air by the convective exchange. This fact also determines the differences in the response of TP lakes to regional climate change compared to that found previously in low-altitude areas.