巴丹吉林沙漠湖泊面积与水位的非线性关系模拟研究

Modeling the nonlinear relationship between lake area and water level in Badain Jaran Desert,China

位于内蒙古阿拉善盟的巴丹吉林沙漠是中国第二大沙漠,以其存在世界上最高的沙山以及约100个湖泊而著称.现今湖面海拔一般为1150~1200 m,前人研究认为在过去3万年以来的某些时期存在更高的湖面.假设沙丘洼地的形态基本保持不变,可以根据现今湖泊洼地的三维形态来模拟高湖面时期的湖泊群分布特征和总面积.以90 m分辨率的DEM数据为基础,对若干典型洼地等高面面积随高程的变化进行了分析,发现可以用幂函数和多项式2种非线性方程模拟.多数情况下需要多项式,但一般只要达到3阶就可以精确拟合.对于湖泊洼地,由于很少有湖水最大深度的数据,湖底最低高程往往是未知的.利用湖面以上的等高面数据建立拟合程度最佳的非线性函数可以反推最低高程,但仍然存在不确定性.这一点对恢复历史上的高湖面形态并没有影响.

Badain Jaran Desert located on the Alxa Plateau in Inner Mongolia is the second largest desert in China.It is renowned for its tallest sand hills in the world as well as for about 100 lakes.The water level in the lakes ranges from 1150 m and 1200m above the sea level.Previous studies have suggested higher water levels in the past 30 ka.Assuming that shapes of sand dunes and inter-dune depressions do not change,distribution of lakes and total lake area during those high-lake-level periods could be modeled from three-dimensional shape of the landscape.The 90 m-resolution DEM data are used to analyze relationship between area of the plan with an equal height and elevation of the plan in several typical depressions.Relationship is found to be approximated with two kinds of nonlinear equations：power or polynomial functions.In most cases third-order polynomial equation is available.The bottom elevation of a lake basin is usually unknown due to the lack of lake depth data.It can be estimated by nonlinear equations with optimized parameters for best fitting on area-level data in zone above the lake surface,but with certain uncertainties.This has no impact on rebuilding shape and size of lakes with higher water levels in history.