Surface-water divides can be delineated by analyzing digital elevation models. They might, however, significantly differ from groundwater divides because the groundwater surface does not necessarily follow the surface topography. Thus, in order to delineate a groundwater divide, hydraulic-head measurements are needed. Because installing piezometers is cost- and labor-intensive, it is vital to optimize their placement. In this work, we introduce an optimal design analysis that can identify the best spatial configuration of piezometers. The method is based on formal minimization of the expected posterior uncertainty in localizing the groundwater divide. It is based on the preposterior data impact assessor, a Bayesian framework that uses a random sample of models (here: steady-state groundwater flow models) in a fully non-linear analysis. For each realization, we compute virtual hydraulic-head measurements at all potential well installation points and delineate the groundwater divide by particle tracking. Then, for each set of virtual measurements and their possible measurement values, we assess the uncertainty of the groundwater-divide location after Bayesian updating, and finally marginalize over all possible measurement values. We test the method mimicking an aquifer in South-West Germany. Previous works in this aquifer indicated a groundwater divide that substantially differs from the surface-water divide. Our analysis shows that the uncertainty in the localization of the groundwater divide can be reduced with each additional monitoring well. In our case study, the optimal configuration of three monitoring points involves the first well being close to the topographic surface water divide, the second one on the hillslope toward the valley, and the third one in between.

可以通过分析数字高程模型来划定地表水水位。但是，它们可能与地下水划分有很大不同，因为地下水表面不一定遵循地表地形。因此，为了划定地下水水位，需要进行水头测量。由于安装压力计成本高昂且费力，因此优化其位置至关重要。在这项工作中，我们介绍了一种最佳设计分析，可以确定压计的最佳空间配置。该方法基于将地下水分流局部化的预期后验不确定性的形式最小化。它基于前置数据影响评估器，即贝叶斯框架，该框架在完全非线性分析中使用随机模型样本（此处为稳态地下水流模型）。对于每个实现，我们都会在所有潜在的油井安装点上计算虚拟水头测量值，并通过粒子跟踪来描绘地下水的划分。然后，对于每组虚拟测量值及其可能的测量值，我们评估贝叶斯更新后的地下水划分位置的不确定性，最后将所有可能的测量值边缘化。我们测试了模仿德国西南部含水层的方法。在该含水层中的先前工作表明地下水分配与地表水分配有很大不同。我们的分析表明，每增加一口监测井，就可以减少地下水分界线的不确定性。在我们的案例研究中