An Investigation On The Non-linear Relationship Between The Water Level And Lake Area In The Badain Jaran Desert

The Badain Jaran Desert, located on the Alxa Plateau in Inner Mongolia, is the second largest desert in China and is famous for the existing of the tallest sand hills in the world as well as ~100 lakes. The water levels in the lakes range between 1150 m and 1200 m above sea level at present. However, it was suggested by previous studies that higher lake water levels were exhibited in some periods in the past 30 ka. Assuming that the shapes of the sand dunes and inter-dune depressions were not changed, the distribution of the lakes and the total lake area during those high-lake-level periods could be modeled from the three-dimensional shape of the landscape at present.Based on the 90 m resolution DEM data and the Google earth data, the morphological characteristics of some depressions are quantitatively studied in this paper. It shows that the flattenings of the lakes are less than 0.35, which indicates that the shape of the lake can be regarded as a circle; The axials of the lakes are mostly in the northwest; And the maximum gradients in these lake-depressions are 30? more or less; Profiles’ shapes of the depressions are all like the shape of "U" font, the steep both sides, and flat bottom.Based on these facts, the relationship between the area of the plan with an equal height and the elevation of the plan are analyzed for several typical depressions in this paper. It indicates that the relationship could be approximated with two kinds of nonlinear formulas: power or polynomial functions. In most cases the third-order polynomial formula is available. The bottom elevation of a lake basin is usually unknown because the lack of the lake depth data. It could be estimated using the nonlinear formulas with the optimized parameters for the best fitting on the area-level data in the zone above the lake surface, however, with some uncertainties. This has no impacts on rebuilding the shape and size of lakes with higher water levels in the history.Based on the characteristics of the beaded distribution appearing on the lake depressions, it is predicted that the merger phenomena of multiple depressions may appearing in the higher-lake-water-level period. The typical lake depressions of Shaobaijilang and Sumujilin are taken for example in this paper to explain the range discipline of the number of lakes and the total area of the lakes in the depression with the water level. It indicates that when water level downs, the number of lakes in the depression may be up and down and the relationship among water level, the number of lakes and the lake area is really complex.