全球水循环中地表水量是非常重要的影响因素之一，而地表水量中包含的诸多元素中湖泊水量又占据了绝对优势。所以研究湖泊储水量的热度日益增长，同时湖底数字地形对于湖泊水量和变化的计算的作用不言而喻。然而由于较高的测量成本以及复杂的地形地貌，导致依靠实地测量来获得全球数以万计的湖泊水下地形的方法很难行得通。学者们也曾探索出测量湖底地形和储水量的其他方法，但各有不足，例如光谱法仅限于浅清水体才可应用；经验公式法不能生成每个湖泊的水下地形地貌；机载重力计法难以进行大尺度的测量；各类样条曲线法需要待测区域的实测数据等。 本文提出了一种基于数字高程模型（DEM）的湖泊水下地形三维模拟方法（DLBM），利用原创的逐步退水计算方法（WRM），无需水体内实测数据的输入，仅依靠湖泊周围的DEM数据和形态学函数（MFM）对水下地形进行数学模拟，最后生成湖泊的三维水下地形图，以此估算整体湖泊储水量。该方法拥有两大假设：（1）湖泊内的水下地形和周围的陆上地形在形态上连续；（2）湖泊内的沉积率处处相等，即湖泊内各处沉积层厚度和水深之比为定值。程序以Matlab编写，并可以进行批处理，能够自动搜寻相应位置的DEM数据，完成世界范围内的湖泊水下地形计算，并分类储存出来。 本文以安大略湖的实测水下地形、纳木错湖的时序体积、面积数据对模型进行了实例分析，同时采用HydroLAKES的全球湖泊数据集对模型结果进行统计学检验，并与形态学公式法进行比较。最终本模型的模拟结果能够一定程度上反映水下地形的地貌特征；在水文要素曲线的对比中，尽管面积有一定差异，但体积曲线拟合较好；在统计学分析中拟合优度达到0.627，超过了形态学公式法的0.588。 总结来说，本模型能够适应包括湖心岛等复杂湖泊边界的情况，在无实测数据仅利用遥感数据的情况下，根据地质学假设完成了由边界向内部的推演，在所研究问题领域内是一次大胆的尝试，初步取得了良好的效果，但仍存在一定的改进空间和发展潜力。
The surface water volume is one of the most important component of global water cycle, and the lake volume accounts for the vast majority of total surface water volume, so researcher and studies on lake volume are getting more attention. The availability of lake bathymetry maps is imperative to estimate lake water volumes and their variability. It has been difficult to obtain all the bathymetric measurements of thousand lakes across the globe, due to costly labors and/or harsh topographic regions. There are also some other methods to estimate the bathymetry or storage, but they all have limitations. Such as spectrum method will fail in deep or turbid lakes; equation method can not generate the whole bathymetry; airborne gravity method also costs much when measuring globally; spline method needs field measured data as input and so on. In this study, we develop a new digital lake bathymetry model (DLBM) using the step-wise water recession method (WRM) and morphologic function module (MFM) to generate 3-Dimensional lake bathymetric and estimate the lake volume based on digital elevation model (DEM). There are two assumptions: 1) the lake’s bathymetry was formed and shaped by the similar geological processes as the surrounding landmass, and 2) the agent of water (the thickness of the sedimentary deposit proportional to lake water depth) was uniform. DLBM is programed by Matlab for batch processing, and it can search the location then calculate the lake bathymetry automatically. Ontario Lake and Namco Lake are used as examples to demo the model development, calibration, and refinement. Finally we conclude that DLBM can basically express some topographical features; when compared with water element curves, although area curve is not satisfied, the volume fitting is acceptable; and in the statistical analysis with the data from HydroLAKES, the final R-squared of our model is 0.627 which is better than the result 0.588 from the equation method. DLBM will work when the lake boundary is complicated without internal measured data. It’s a bold attempt in this field with satisfied result, but there is still room for developing and improving.
