Data-Driven Inverse Sensitivity Analysis for Predictive Coastal Ocean Modeling

该项目的目标是通过将一种新的测量理论方法与实验数据相结合，提高沿海海洋计算模型的预测能力。沿海海洋的先进计算机模型，如先进环流（ADCIRC）模型，可用于预测模式，在飓风接近登陆时估计风暴潮，以便进行紧急疏散和应对。然而，ADCIRC和其他计算机模型的准确性依赖于基于不确定输入参数的模型校准过程。研究人员研究了某些关键参数的估计和模型敏感性，特别是水深、底部摩擦和风应力。将解应用于逆问题进行预测由于两个问题而变得复杂。首先，从输入数据和参数空间到可观测空间的映射通常会降低维数，这意味着逆问题具有集值解。其次，尽管本项目中考虑的模型提供了确定性的物理描述，但所有可用的数据都受到自然随机变率以及实验/观测误差和通常随机描述的不确定性的影响。测量理论算法计算整个参数空间的概率度量，从中可以选择模型选择的集合，以提供对关键数量的可靠预测，例如沿海的最大水位。pi研究各种数学问题，包括在测量理论方法的非侵入性实现中固有的各种误差源的估计。实验数据和ADCIRC模型的使用为验证和验证所提出的方法创造了独特的机会。沿海海洋状况的定量预测对于沿海可持续性的长期研究、制定沿海生态系统恢复和维护的优先事项和政策、增强沿海社区的经济活力以及评估沿海人口面临自然灾害的风险至关重要。尽管各种复杂的海岸预测已经被开发和常规使用了几十年，但过去7年的一系列事件推动了一场革命。也就是说，卡特里娜飓风（2005年）以一种毁灭性的方式展示了低估沿海社区对风暴潮的脆弱性的危险。卡特里娜飓风之后是丽塔飓风（2005年）、古斯塔夫飓风（2008年）和艾克飓风（2008年），这些飓风都对墨西哥湾北部地区造成了巨大的破坏，最近发生在路易斯安那州海岸的深水地平线石油泄漏事件威胁到整个海湾生态系统。这些事件促使人们认真而持续地努力提高预测沿海海洋状况的能力。然而，预测可观测范围以外的海岸状况，例如，根据当前和近过去的海岸观测数据实时预测未来最大风暴潮，是一个极具挑战性的数学、统计和计算问题。在这个项目中，研究人员研究和应用最先进的技术，以提高用于预测风暴潮的沿海海洋模型的预测能力。本项目开发的计算方法和工具适用于海岸工程、海洋科学、材料科学和其他工程学科的其他问题。在本项目下开发的数学和数值方法的技术转让将与沿海海洋建模社区以及美国陆军工程兵团、NOAA、国土安全部、州和地方机构、工业界以及美国和国外的其他大学等机构进行。

The goal of this project is to improve the predictive capabilities of computational models of the coastal ocean, by combining a novel measure-theoretic approach for inverse sensitivity with experimental data. Advanced computer models of the coastal ocean, such as the Advanced Circulation (ADCIRC) model, can be used in predictive mode to estimate storm surge as hurricanes approach landfall for the purposes of emergency evacuation and response. However, the accuracy of ADCIRC, and other computer models, relies on the painstaking process of model calibration based on uncertain input parameters. The investigators study the estimation and model sensitivity for certain critical parameters, in particular bathymetry, bottom friction, and wind stress. Applying the solution to the inverse problem for prediction is complicated by two issues. First, the map from the input data and parameter space to the observable space generally reduces the dimension which implies the inverse problem has set-valued solutions. Second, even though the models considered in this project provide deterministic physical descriptions, all of the data available is subject to natural stochastic variability as well as experimental/observational error and uncertainty generally described stochastically. The measure-theoretic algorithm computes a probability measure over the entire parameter space from which an ensemble of model selections may be chosen to deliver reliable predictions of critical quantities of interest such as maximum water elevation along the coast. The PIs study various mathematical issues including estimation of various sources of error inherent in a non-intrusive implementation of the measure-theoretic approach. The use of experimental data and the ADCIRC model creates a unique opportunity for verification and validation of proposed methods.Quantitative predictions of coastal ocean conditions is central to long-range studies of coastal sustainability, the development of priorities and policies for the restoration and maintenance of coastal ecosystems, enhancing the economic vitality of coastal communities, and assessing risk of coastal populations to natural disasters. While coastal predictions of various complexity have been under development and used routinely for decades now, a series of events over the past seven years has driven a revolution. Namely, Hurricane Katrina (2005), in devastating fashion, demonstrated the perils of underestimating the vulnerability of coastal communities to storm surge. Following on the heels of Katrina were hurricanes Rita (2005), Gustav (2008) and Ike (2008), which all caused tremendous damage to communities along the northern Gulf of Mexico, and more recently the Deepwater Horizon Oil Spill, which occurred off the coast of Louisiana and threatened the entire Gulf ecosystem. These events spurred a serious and sustained effort to improve the ability to predict coastal ocean conditions. However, the prediction of coastal conditions beyond what can be observed, e.g. predicting future maximum storm surge from current and near past coastal observation data in real-time, is an exceedingly challenging mathematical, statistical, and computational problem. In this project, the investigators study and apply state-of-the-art techniques in order to improve the predictive capabilities of coastal ocean models used to predict storm surge. The computational methodology and tools developed under this project are applicable to other problems in coastal engineering, marine science, material science and other engineering disciplines. Technology transfer of the mathematical and numerical methodologies developed under this project will occur with the coastal ocean modeling community, and with agencies such as the U.S. Army Corps of Engineers, NOAA, the Department of Homeland Security, state and local agencies, industry, and other universities in the U.S. and abroad.