## 2 Geographic Background  
Lake Ta-Lung-Chi (Figure 1) is a freshwater lake with an altitude of 2402 m, located on the southern slope of the middle Tian Shan. The bedrocks in this region are mainly composed of carbonate sedimentary rocks, pyroclastics, mixed sedimentary rocks, and a small cover of intermediated plutonic [35]. The east-west length of the lake is \(\sim\)2.6 km, the north-south width is \(\sim\)0.6 km, the area is \(\sim\)2 km\({}^{2}\), and the deepest point is 5.5 m. The lake is mainly supplied by glacier melt water from the surrounding mountain and precipitation in the valley, which is blocked by the moraine embankment west of the lake. Glacial and snow-melt water are injected into the lake through the Muzilik River on the east side of Lake Ta-Lung-Chi. The lakeside area consists of dense grassland, with dense spruce forest in the south, spruce forest, bushes, and meadows on the western slope, and seasonal rivers and underflows in the western lake area; the northern mountains are relatively bare, with some low bushes. The lake has no obvious surface water outlets, but water passes through an underground underpass formed by gaps in the huge rock stacks under the final embankment, and enters Lake Hsiao-Lung-Chi downstream at \(\sim\)1.4 km through infiltration. During the high-water period, water in Lake Hsiao-Lung-Chi overflows the west bank where a waterfall dropping 150 m forms. Overflow water from Lake Hsiao-Lung-Chi enters the Kuqa River through the river channel. Based on CRU data [22](grid coordinates 42.0\({}^{\circ}\) N-42.5\({}^{\circ}\) N; 83.0\({}^{\circ}\) E-83.5\({}^{\circ}\) E, central coordinates 42.25\({}^{\circ}\) N, 83.25\({}^{\circ}\) E), the average annual temperature within this grid for the period 1960 to 2019 was 1.4 \({}^{\circ}\)C. The hottest month was July, with an average temperature of 14.7 \({}^{\circ}\)C; the coldest period was January, with an average temperature of \(-\)16.0 \({}^{\circ}\)C. The total annual precipitation was 159.4 mm; the average monthly precipitation was 25.6 mm, with the maximum precipitation occurring in May. The closest meteorological station to Lake Ta-Lung-Chi is Bayanbulak Station with an elevation of 2458 m. The average annual temperature recorded at Bayanbulak Station from 1960 to 2019 was 3.2 \({}^{\circ}\)C. The hottest month was July, with an average temperature of 18.3 \({}^{\circ}\)C; the coldest period was January, with an average temperature of \(-\)19.6 \({}^{\circ}\)C. The average precipitation for the period was 283.7 mm; the average monthly precipitation was 71.4 mm, with the maximum occurring in July.  
Figure 1: Geographical map of the study area. (**a**) Location of the Tian Shan where Lake Ta-Lung-Chi is located. Monthly precipitation and monthly average temperature data for Lake Ta-Lung-Chi are from the climatic research unit (CRU) ([PERSON] et al., 2020) while data for the Bayanbulak Station are from the Meteorological Data Center of China Meteorological Administration. (**b**) Lake Ta-Lung-Chi water system. The base map of (**a**) was derived from a SRTM30 PLUS color-encoded shaded relief world topography (approximately 4 km) GeoTTFF image ([PERSON] et al., 2019). The base map of (**b**) was derived from global topographic data at 1 arc-second (\(\sim\)30 m) horizontal resolution (NASADEM) from NASA Land Processes Distributed Active Archive Center (LP DAAC) Distribution Server hosted at the USGS Earth Resources Observation and Science (EROS) Center ([PERSON] et al., 2020). (**c**) Vegetation around the lake. (**d**) Core sediment TLC01 and field sub-sampling.