CAS-Climate/Collaborative Research: Prediction and Uncertainty Quantification of Non-Gaussian Spatial Processes with Applications to Large-scale Flooding in Urban Areas

可持续发展的关键方面-气候（CAS-Climate）项目开发了大规模洪水事件的准确和快速的统计表示（也称为模拟），作为在每个实例中运行复杂物理模型的替代方案。这是通过训练代表性洪水模拟的统计公式来实现的，但增加了灵活性，可以推断不在训练集中的情况的结果。由于气候变化，大洪水预计会更频繁地发生，因此人们越来越关注强大、高效和实时的洪水建模。对于大多数河流工程问题，包括防洪，都需要量化不同降雨和风暴潮情景下的水深和地表高程。虽然许多水力模型（例如TELEMAC模型）可以表示这些特征，但使用高分辨率地形和基础设施数据进行大规模水力模拟的计算成本很高。因此，尽管有这些建模资源，常规或快速模拟可能的洪水情景是有限的。这项工作的一个新颖方面是关注极端事件的统计分布，这适用于洪水，而不是对评估风险和危害不太有用的平均数量。此外，这种方法的统计基础有助于衡量预测中的不确定性，从而支持决策制定和其他实际用途。现有的方法很少模拟建立在空间极端分布上的计算机模型来表示复杂域的洪水，这项工作的一个重要特征是将洪水响应与适当的统计过程相匹配。这与机器学习、纯数据驱动的方法形成对比，在这种方法中，极端事件可能无法很好地表示。建模框架具有变革性，包括：使用特定地点条件分布的广义极值分布的马尔可夫随机场公式，使用空间极值的惩罚似然方法选择邻域大小，对模拟器的有效性和大样本特性的理论研究，以及开发处理非常大数据量的计算算法。这项工作将通过TELEMAC模型模拟的概念验证研究来验证，该模型将在美国城市地区的极端降雨事件和风暴潮的现实模式下进行。开源工具将基于该项目的结果生成，并与工程界共享，特别是在处理空间依赖数据和不确定性方面经常面临挑战的民用基础设施界。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This Critical Aspects of Sustainability - Climate (CAS-Climate) project develops an accurate and fast statistical representation (also known as emulation) of large-scale flooding events as an alternate to running complex physical models in every instance. This is achieved by training the statistical formulation on representative flood simulations but adding flexibility to infer results for situations that are not in the training set. Large floods are expected to occur more frequently due to climate change and so motivate increased attention for robust, efficient, and real-time flood modeling. For most river engineering problems, including flood mitigation, there is a need for quantification of water depth and surface elevation under different scenarios of rainfall and storm surges. While many hydraulic models (e.g., the TELEMAC model) can represent these features, large-scale hydraulic simulations of flooding using high-resolution topographic and infrastructure data, are computationally expensive to complete. Thus, despite these modeling resources, simulating possible flood scenarios routinely or in a rapid manner is limited. A novel aspect of this work is to focus on statistical distributions for extreme events, which are appropriate for flooding, rather than average quantities that are less useful for assessing risks and hazards. Also, the statistical basis of this approach lends itself to measures of uncertainty in the predictions and so support decision making and other practical uses.There is little existing methodology to emulate computer models built on spatial extreme distributions to represent flooding in a complex domain and an important feature of this work is matching the flooding response with the appropriate statistical processes. This is in contrast with a machine learning, purely data-driven approach where extreme events may not be as well represented. The modeling framework is transformative including: a Markov random field formulation using generalized extreme value distributions for site-specific conditional distributions, selecting neighborhood size using a penalized likelihood method for spatial extremes, a theoretical investigation into the validity and large sample properties of emulators, and developing computational algorithms to handle very large data volumes. This work will be validated through proof-of-concept studies with TELEMAC model simulations, forced by realistic patterns of extreme rainfall events and storm surges and located in an urban area of the US. Open-source tools will be generated based on the results from this project and shared with the engineering communities, especially civil infrastructure community that frequently faces challenges in coping with spatially-dependent data and uncertainties.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.