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

这个可持续发展的关键方面-气候（CAS-气候）项目开发了大规模洪水事件的准确和快速的统计表示（也称为仿真），作为在每种情况下运行复杂物理模型的替代方案。这是通过在代表性洪水模拟上训练统计公式来实现的，但增加了灵活性，以推断不在训练集中的情况的结果。由于气候变化，预计大洪水将更频繁地发生，因此激发了对强大，高效和实时洪水建模的更多关注。对于大多数河流工程问题，包括洪水缓解，需要在不同的降雨和风暴潮情况下量化水深和水面高程。虽然许多水力模型（例如，TELEMAC模型）可以表示这些特征，但是使用高分辨率地形和基础设施数据的洪水的大规模水力模拟完成在计算上是昂贵的。因此，尽管有这些建模资源，但常规或快速地模拟可能的洪水情景是有限的。 这项工作的一个新的方面是专注于极端事件的统计分布，这是适当的洪水，而不是平均数量是不太有用的评估风险和危害。 此外，这种方法的统计基础本身的预测的不确定性的措施，因此支持决策和其他实际use.There是现有的方法来模拟计算机模型建立在空间极端分布，以表示洪水在一个复杂的域和这项工作的一个重要特点是匹配的洪水响应与适当的统计过程。这与机器学习相反，纯粹的数据驱动方法可能无法很好地表示极端事件。建模框架是变革性的，包括：马尔可夫随机场制定使用广义极值分布的特定站点的条件分布，选择邻域大小使用惩罚似然方法的空间极端，理论研究的有效性和大样本特性的仿真器，并开发计算算法来处理非常大的数据量。这项工作将通过TELEMAC模型模拟的概念验证研究进行验证，该研究受到极端降雨事件和风暴潮的现实模式的影响，并位于美国的一个城市地区。开源工具将基于该项目的结果生成，并与工程界共享，特别是在应对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NSF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.