[Insert Table 2 here]
2.2.3 Climate data
To investigate the climate impact of lake water level changes, the annual and monthly precipitation data for the period 1990-2018 from 10 stations in the TP was collected from the China Meteorological Network (http://data. cma.cn). The locations of the ten stations are shown in Fig. 1. In addition, we analyzed the changes of water vapor transport modes over the TP and its surroundings based on ERA-interim reanalysis data with a spatial resolution of 0.75°×0.75° (Dee et al. 2011). The sea surface temperature (SST) from the National Oceanic and Atmospheric Administration was also applied to investigate the association of the TP lake level changes and precipitation anomalies driven by El Niño and La Niña events.

2.3 Methods

2.3.1 Altimetry water level processing
We retrieved important variables such as time, latitude, longitude, water level elevation, and geoid from the collected raw data files. Since the parameter information contained in each altimeter satellite is not completely consistent, the formulas for calculating water level are also not the same. Thus, this part of the work also needs to refer to the data manual for each altimeter satellite. We calculated water levels by the following the formula below (Hwang et al., 2016):
\(H_{\text{water}}=h_{\text{sat}}-R_{\text{alt}}-C\) (1)
where \(H_{\text{water}}\) refers to ellipsoidal height of the waterbody, \(h_{\text{sat}}\) refers to ellipsoidal height of the satellite, \(R_{\text{alt}}\) refers to distance between satellite and waterbody, and \(C\) refers to the integration of all corrections. Considered corrections include inverted barometer height correction (\(C_{\text{inv}}\)), wet and dry tropospheric corrections (\(C_{\text{wet}}\),\(C_{\text{dry}}\)), ionospheric correction (\(C_{\text{iono}}\)), solid earth tide (\(C_{\text{solid}}\)), ocean earth tide (\(C_{\text{ocean}}\)), poletide (\(C_{\text{pole}}\)), sea state bias correction (\(C_{\text{stb}}\)), and high frequency fluctuations correction (\(C_{\text{hf}}\)).
2.3.2 Removal of measurement outliers
For all lakes, the original tracks of the satellite are observed as it passes through the lake, then the track data falling within the lake will be selected. As the observations contain outliers, it is necessary to eliminate them for subsequent work. Outlier elimination for the selected orbit data was divided into two steps.
Step 1: Apply a median filter with a six-month window size to smooth the original time series during the study period, and remove the outliers out of two standard deviations from the median for all the measurements.
Step 2: Remove the data other than twice the standard deviation for single-day measurements.
2.3.3 Unifying the reference system of different altimetry sources
In order to reduce the differences caused by different altimeter instruments, all lake levels from multi-source altimetry satellite were first converted to the same geographic reference system. The system biases calculated by the data from different altimetry satellites at the same period was subtracted from the elevation measurements for each lake (Crétaux et al. 2011a; Jarihani et al. 2013).

3 Results and discussions

3.1 Long-term lake level variations based on Hydroweb and DAHITI data archives

The best way of altimetry data validation is to compare the altimeter-derived lake level with the in situ data. At present, only a few lakes such as Qinghai Lake and Nam Co have long-term continuous water level observations in the TP which are extremely limited compared with more than 1,200 lakes (>1km2) across the TP (Zhang et al. 2014). The altimetry data archives, such as Hydroweb and DAHITI, play an critical role in verifying the lake level changes obtained by other satellite altimetry data. In order to verify the reliability of Hydroweb and DAHITI altimetry data archives, the annual means of water level for Qinghai Lake was validated against the in situ water levels measured by the hydrological station. As shown in Fig. 2, the altimetry levels follow a robust linear correlation with in situ measurement, with a R² value of 0.90. This agreement indicates that the lake level time series obtained from Hydroweb and DAHITI have a high reliability, and therefore, were used as a reference for validating our level time series processed from SARAL and Sentinel-3 altimeters.