The first step of our effort in producing the integrated LSWT dataset is to derive the satellite-based observation from the MOD11 (version 6) provided by NASA's Earth Observing System Data and Information System (EOSDIS, https://earthdata.nasa.gov, last access: 13 July 2022). The MOD11 (Wan, 2013) is the land surface temperature and emissivity products retrieved at 1 km pixels by the generalized split-window algorithm and 6 km grids by the day/night algorithm mainly based on bands 31 (10.78–11.28 µm) and 32 (11.77–12.27 µm) of MODIS (moderate-resolution imaging spectroradiometer) aboard the Terra and Aqua satellite, where Terra overpasses the Equator at around 10:30 (22:30) LT (local time) and Aqua at around 01:30 (13:30) LT. The MOD11 includes products with temporal resolutions of daily, 8 d, and monthly readings. Validation of the MODIS LST product for water surface temperatures against in situ measurements has been conducted and the absolute differences have been reported to be within the range of 0.8–1.9 ∘ (Crosman and Horel, 2009, 2009; Hulley et al., 2011; Reinart and Reinhold, 2008). The bias of MODIS-based LSWT was reported to be around -1.74 ∘C (Song et al., 2016) and -1.4 ∘C (Zhang et al., 2014) over the TP when compared to the limited in situ observations. Different from the 8 d dataset by Wan et al. (2017), herein, we used MOD11A1 (Terra product of Land Surface Temperature/Emissivity Daily L3 Global 1 km) instead of MOD11A2 to produce the daily lake surface temperature dataset. The daily product is used also because it is more suitable to calibrate and validate the air2water model at the same temporal resolution. The MOD11A1 is a tile of daily Level 3 product at 1 km spatial resolution corresponding to the earth locations on the sinusoidal projection.

In our dataset, the satellite observation of LSWT for a specific lake is the lake-wide mean temperature of all 1 km pixels within the lake, which is different to the temperature of the centroid pixels presented by Zhang et al. (2014) and is more consistent with our model settings. In calculating the lake-wide mean surface water temperature, pixels within a lake are identified by the boundaries of the lakes (shapefiles included in the dataset), which are mainly from the National Tibetan Plateau Data Center (TPDC, http://data.tpdc.ac.cn, last access: 13 July 2022) and cross-checked by lake boundary maps from HydroLAKES (http://www.hydrosheds.org/, last access: 13 July 2022) (Messager et al., 2016) and Google Earth. To remove the boundary effects (i.e., where pixels could be a mix of land and water), the boundaries are buffered inward by 1 km. The daily surface water temperature is the mean of daytime and nighttime LST in the MOD11A1. All the data-processing procedures are conducted via Google Earth Engine (GEE). In addition, the MOD11A1 product has noticeable missing values because of cloud effects and the limitation of the algorithm. The gaps in our MODIS LSWT series were marked as “-999”.

The satellite-based LSWT has been accessible since 2000 and with missing data due to the limitation in the MODIS. To investigate the long-term changes in surface water temperature for lakes in the TP and their responses to climate change, in our integrated datasets, we used a slightly modified air2water model to reconstruct the daily LSWT for the period 1978–2017 based on daily air temperature data from the dataset of daily climate data from Chinese surface stations (V3.0) provided by the China Meteorological Data Service Centre of the National Meteorological Information Centre (http://data.cma.cn/data/cdcdetail/dataCode/SURF_CLI_CHN_MUL_DAY_V3.0.html, last access: 2 July 2021).

The air2water (Piccolroaz et al., 2013) is a semi-physical model designed to simulate lake surface temperature principally based on lake surface heat balance and can be expressed as 1ρcpVsdTwdt=AHnet, where Tw is surface water temperature, Hnet is the net heat flux per unit surface, A is the surface area of the lake, Vs is the volume of water involved in the heat exchange with the atmosphere, and ρ and cp is the density and specific heat capacity of water. The model considers all contributions to the heat balance (Hnet), which are represented as a function of air temperature or are parameterized (Piccolroaz et al., 2013; Piccolroaz, 2016). The original air2water model has simplified the lake heat balance by introducing eight calibratable parameters a1–8 with air temperature as the only required input, which can be expressed as 2dTwdt=1δa1+a2Ta-a3Tw+a5cos⁡2πtty-a6,3δ=exp⁡-Tw-Tha4,forTw≥Thexp⁡-Th-Twa7+exp⁡-Twa8,forTw≤Th, where, Ta is air temperature and ty is days of a year. δ=D/Dr is normalized well-mixed depth, where D is the depth of well-mixed surface layer (the epilimnion thickness) and Dr is the maximum thickness. Th is the deep water temperature with the default value being 4 ∘C. The a1–4 in Eq. (2) are the most sensitive parameters determining model performance (Piccolroaz et al., 2013).

The original air2water is limited in simulating the surface temperature of open water, which results in difficulties for applications in lakes with a long duration of ice cover. Therefore, we assume that when the lake is completely covered by ice, the heat exchange between air and water is blocked and the surface energy balance becomes 4dTidt=a9+a10Ta-a11Tw+a12cos⁡2πtty-a13, where Ti is the ice surface temperature and a9–13 have similar physical significance to a1,2,3,5,6. To represent the state-shift of the lake between open water and ice-covered parts, two additional parameters a14 and a15 are introduced to determine the states. The lake surface temperature TL can be expressed as 5TL=Tw,forTL≥a15Ti,forTL≤a141-KiceTw+KiceTi,fora15>TL>a14, where, Kice=a15-TL/a15-a14 is the proportion of ice on the surface of the lake. As in the original model, the model equations were solved numerically using the Crank–Nicolson numerical scheme at the daily time step.

The daily air temperature data used to drive the modified air2water model are from 31 meteorological stations in the TP (Fig. 1). The air temperature above each lake is interpolated from the nearest station and adjusted by a lapse rate of 0.65 ∘C per 100 m (Hu et al., 2014). The model is calibrated against the derived remotely sensed LSWT described in Sect. 3.1 using the particle swarm optimization (PSO) approach (Kennedy and Eberhart, 1995; Piccolroaz, 2016). The objective function of model calibration is the widely adopted Nash–Sutcliffe efficiency coefficient (NSE) (Nash and Sutcliffe, 1970). To ensure the rationality of the calibrated model parameters, a physically consistent a priori range is assigned to each parameter (Piccolroaz, 2016) and Dr is bounded by the average depth of the lake obtained from Records of Lakes in China (Wang and Dou, 1998) and HydroLAKES (Messager et al., 2016). The calibration period is set to be 2000–2012, while 2013–2017 is considered as the validation period. It should be noted that the satellite-derived water temperature is a measurement of instantaneous water temperature at the top of the surface (∼10–20 µm deep), known as “skin temperature”. The skin temperatures can differ from surface water temperature because the thermal structure of the first meters of the water column is not uniform under all conditions. Nevertheless, satellite-derived water temperatures (skin temperatures) are relevant and sufficient for the calibrating and validating hydrodynamic or water quality models of lakes (Andréassian et al., 2012; Prats and Danis, 2019; Prats et al., 2018). For comparison and further validation, the dataset produced by Liu et al. (2019) based on AVHRR was also used.

Three subsets of lake-wide mean surface water temperature are derived and included in our integrated dataset, which are daily daytime LSWT, daily nighttime LSWT, and daily mean LSWT for the period 2000–2017. The LSWT derived from the MOD11A1 is compared with two satellite-based datasets released by other researchers, which were based on AVHRR (Liu et al., 2019) and ARC-Lake (Layden et al., 2015).

Figure 3 shows the comparison between our MOD11A1-based LSWT and the AVHRR-based LSWT (i.e., the TPlake_Temp dataset by Liu et al., 2019) for 77 shared lakes. The TPlake_Temp provides daily LSWT for the period 1981–2015 and for 97 lakes in the TP, which, however, has a different length of data gaps among the lakes. It should be noted that the LSWT from the TPlake_Temp is that of the daytime instead of the daily mean, hence, it is compared against our MODIS-based daytime LSWT instead of mean daily LSWT herein. The LSWT from the two sensors (i.e., AVHRR and MODIS) are largely comparable for the studied lakes, where the NSE and R2 between the LSWT from the two datasets is greater than 0.7 for more than 80 % of the lakes, and the bias ranges from 0.6 to 3.38 ∘C. It is worth mentioning that the MODIS-based LSWT would be better for investigating the long-term changes in lake surface temperature in the TP since the AVHRR-based LSWT from the TPlake_Temp dataset has more missing data and was reported to have abrupt shifts in LSWT due to inconsistent calibration among the successive satellites (Liu et al., 2019).

We further compare the MODIS-based LSWT with that from the ARC-Lake dataset. The ARC-Lake dataset (version 3) included ATSR-2/AATSR-based lake surface temperatures for the period 1995–2012 for 1628 target water bodies distributed globally. Here the daytime and nighttime LSWTs in ARC-Lake are averaged to present daily mean LSWT. Since the ARC-Lake LSWT product is only for open water and a tag temperature during the frozen season with a value of 0 ∘C, in the comparison, only the period in which both MODIS-based and ARC-Lake LSWTs are above 0 ∘C is considered. The LSWTs of 11 studied lakes (location shows in Fig. S1 in the Supplement) are available from the ARC-Lake dataset for the comparison. Besides some outliers where the difference between the two satellite observations is greater than 5 ∘C (around 8 % of the observations in the studied periods), as shown in Fig. 4, the two satellite-based observations of LSWT are mostly comparable to NSE > 0.7 with bias ranging from -1.23 to 0.94 ∘C.

The reconstructed LSWT by the slightly modified air2water model is compared and validated by the MODIS-based LSWT. As shown in Fig. 5a and b, the spatial pattern of the long-term mean annual LSWT from the reconstructed LSWT is close to that based on MOD11A1 with overall NSE = 0.977 and R2=0.987. For the period 2000–2017, NSE and R2 of most lakes (>90 %) are both over 0.8 with bias ranging at ±0.55 ∘C. The bias for the validation period (2013–2017) is slightly higher than that for the calibration period (see Fig. S2) ranging from -1.7 to 0.9 ∘C. Although there is a tendency showing that NSE is relatively higher for lakes with lower altitude and higher latitude, model performance is found to be weakly related to the altitude and latitude of the lakes (see Fig. S3). The results indicate there is no substantial systematic bias in the reconstructed LSWT. The modified air2water model hence is reliable in reconstructing LSWT for lakes at different altitude or latitude zones. However, it should be noted that uncertainties exist in the reconstructed LSWT due to the uncertainties not only in the calibrated model but also in the air temperature inputted to the model. Summaries of model performance for each month presented in Fig. S4 show that the simulated LSWT has a smaller bias in July and November. As mentioned in Sect. 3.2, the daily air temperature above the lakes is that interpolated from the nearest meteorological stations with elevation adjustment, where the performance of the interpolation would be affected by the density and locations of the stations. Currently, the available meteorological stations are sparsely located in the western TP (Fig. 1), which may result in inherent uncertainties of the reconstructed LSWT for lakes in the western TP. As shown in Fig.5c and 5d, although there is no significant difference in model performance with respect to the locations of the lakes, it is worth exploring further in the future the effects of the interpolation approaches on the simulation of LSWT.

The in situ observed LSWT is not widely available for lakes in the TP to conduct an overall validation of the modeling results. Nevertheless, we have compared the modeling results against the best publicly available in situ surface water temperature data for lakes in the TP (Table S1 in the Supplement, Figs. S6 and S7), which include sequential observations (Guo et al., 2016; Li et al., 2015; Wang and Hou, 2018) of four lakes (i.e., Ngoring Lake, Serling Co, Dogze Co, Bangong Co) and sporadic observations (simulated LSWT of same day as observation) of 41 lakes (Liu et al., 2015). As shown in Fig. 6, the simulated lake surface temperature is in good agreement temporally with the sequential observations (R2=0.97, 0.92, 0.90, 0.97 for Ngoring Lake, Serling Co, Dogze Co, Bangong Co, respectively) and spatially with the sporadic observations (R2=0.94). Compared with the in situ observations, the RMSE of the simulated temperature is around 2.0 ∘C for the 45 lakes listed in Table S1. It is noted that the bias in the simulation is mainly due to its underestimation for the warmer seasons. Taking Ngoring Lake, for example, for the season when the in situ observed temperature is above 10 ∘C, the RMSE could reach 2.42 ∘C although R2 is greater than 0.70. The bias of the simulated water temperature could be reduced or corrected if the model is calibrated against the observations. However, it is important to note that the simulated water temperature is not completely equivalent to the in situ observations. This is because the simulations represent the lake-wide mean temperature of the skin layer, while the in situ observation used herein is the profile mean temperature for a fixed location in the lake.

On the basis of the reconstructed daily LSWT dataset, the long-term changes of surface water temperatures of lakes across the TP are detected by using the Mann–Kendall trend analysis approach (Kendall, 1949; Mann, 1945). The daily and annual variation of a sample lake is shown in Fig. S5. Figure 7 shows that, for the period 1978–2017, the annual LSWT of most lakes (except for Lake Beidao and Lake Changhong) increase significantly at rates ranging from 0.01 to 0.47 ∘C per 10 years, which is consistent with but comparably smaller than that of the increasing rate in air temperature (0.26–0.87 ∘C per 10 years) indicating the contributions of heat storage capacity of the lakes. Lakes in the southern TP are generally found to have higher warming rates than those in the northern TP. The increase in LSWT is more evident in the winter season (December to February) than in the summer season (June to August). Except for Lake Kuhai, the LSWTs of all the other lakes increase significantly at a rate ranging from 0.06 and 0.96 ∘C per 10 years. In summer, while most of the lakes (125 out of 160) show a significant increase in LSWT, the LSWTs of 13 lakes located in the northern part of the TP decrease nonsignificantly. It should be noted that the warming and cooling trends could inherit uncertainties from the modeling, which needs further validation when more in situ observations become available.