## 2 Method
### Lakes in the Tibetan Plateau  
With the aim of defining the lakes' mass variations in Tibet, two databases have been analyzed: one based on outlines of lakes [27], and the other is DAHITI [24]. The gravity field has been calculated for the lake outlines of 2020 and the given lake height variation rates, based on satellite altimetry. In general, it is found (already seen by [28]) that the lake levels are systematically rising in a range between 0.2 m/yr and 0.6 m/yr (Figure 4). The rate is independent of the lake area and is consistent over the entire plateau. For example, the rate of one of the biggest lakes, the Qinghai Lake, is 0.2 m/yr. The only two lakes with negative rates are the Rakshastal Lake in SW Tibet and the Taruo Co. The database of the lakes' outlines [27] comprises over 2000 lakes; the histogram of the areal distribution (Figure 5) shows the prevalence of small lakes, between 1 and 100 km\({}^{2}\) (Figure 5a,d); rare lakes have a considerable area up to \(>\)4000 km\({}^{2}\) (e.g., Qinghai); the smallest lakes have an area in the order of \(10^{-5}\) km\({}^{2}\). Plots in Figure 5e,f show for each area bin the total area covered by the lakes; it is evident that lakes \(<\)10 km\({}^{2}\), although still numerous, will not contribute significantly to the total surface lake area. The monitored lakes of the DAHITI database pertain to the largest ones (areas \(>\) 100 km\({}^{2}\)) and the corresponding mass variations of individual lakes vary between 0.1 and 1 Gt/yr, with very rare negative rates (Figure 6c). Figure 4: Temporal variations of lake levels in Tibet area (cyan) for the DAHITI catalogue; extrapolated rates in black. Figure 5: Statistical distribution of lakes in the Tibetan plateau. The spatial distribution of lakes is shown in plot **(b)**, while plots (**a,d**) report the numerosity-size distribution as functions of latitude and longitude, respectively. Plot **(c)** illustrates the distribution of lakes as function of height. Finally, plots **(e,f)** are calculated by multiplying the histogram **(a)** by the area of each bin. From these last two plots we see that most of the areal coverage is due to lakes with areas \(>\) 10 km\({}^{2}\). In plots **(a,b,d)**, “# Lakes” stands for number of lakes. Figure 6: Level variations for 14 lakes in Tibet: **(a)** level rates as function of the lake area; **(b)** level rates as function of the lake average height; **(c)** yearly mass variations for lakes in Tibet (circle) and uncertainty on mass rate derived from confidence interval on fitting the time-series rates. **(d)** Spatial distribution of lakes (black outlines); the 14 lakes of the DAHITI database are also labelled. For these  
lakes, the color code is proportional to the yearly rate value in m/yr. The left and bottom plots of the map illustrate the mass variation rates in the Tibet area, as functions of latitude and longitude, assuming that the unmonitored lakes are subjected to a yearly level rise of 0.25 m/yr (average rate for the DAHITI lakes). The cumulative rates as a function of longitude are shown considering the error bounds on the average rate. The mass variations of the 14 lakes for which the increase rates are known have been used to calculate the total gravity change at 250 km altitude, which is shown in Figure 7a. The maximum signal amounts to 0.1 uGal/yr, over an area of about 5\({}^{\circ}\) radius. The dominant signal comes from the Siling Co, Nam Co, Tangra Yum Co, and Zhari Namco lakes. As already shown, the database of lake outlines shows that in Tibet many more lakes than those monitored in DAHITI exist, but for which the time series are not available. Given the homogeneity of the level increases over the Plateau, and the lack of correlation of the rates with latitude/longitude (Figure 6d), height (Figure 6b), or lake area (Figure 6a), we extrapolated the rates to the entire lake database.