FRG: Collaborative Research: Prediction and Risk of Extreme Events Utilizing Mathematical Computer Models of Geophysical Processes

FRG：协作研究：利用地球物理过程的数学计算机模型预测极端事件和风险

• 批准号: 0757367
• 负责人: E Bruce Pitman
• 金额: $ 28.56万
• 依托单位: SUNY at Buffalo
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-07-01 至 2012-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0757367&HistoricalAwards=false
• 关键词: FRG; Collaborative; Research; Prediction; Risk

The goal of this project is to develop the mathematical, statistical and computational tools needed to assess and predict the risk associated with geophysical hazards such as volcanic pyroclastic flows. Based on a preliminary data analysis, the investigators develop stochastic models beginning with stationary independent increment processes employing (possibly tapered) Pareto distributions for the volumes of pyroclastic flows exceeding some observational threshold, in the domain of attraction of an alpha-stable process governing the aggregate flow volume of multiple smaller eruptions. Von Mises distributions are used for flow initiation angles. The deterministic TITAN2D two-dimensional computational environment is employed, which uses available digital elevation maps to predict the impact at various sites of interest from flows of specified volume and initiation angles. TITAN2D is a depth-averaged, thin-layer computational fluid dynamics code based on an adaptive grid Godunov solver, suitable for simulating geophysical mass flows. A rapid emulator based on a simple Gaussian random-field approximation to the TITAN2D model enables the investigators to emulate hundreds of thousands of TITAN2D runs and construct an estimate of the set of possible flow volumes and initiation angles that would lead to significant impact; a hierarchical Bayesian statistical model then reflects the probability of such an impact over a specified period of time.Recent advances in computing power and algorithms have led to the application of mathematical and computer modeling to such highly complex phenomena as storms, floods, earthquakes and volcanic eruptions. It is increasingly being understood that development of mathematical models of these phenomena is only one part of a much more complex process needed for making reliable estimates and predictions of risk. This project develops the mathematical, statistical and computational tools needed for assessing and predicting the risk associated with such natural hazards. A particular focus of the work is the study of how these risks vary in space and time, and of how uncertain they are. This methodology is developed in context of the specific problem of volcanic avalanches and pyroclastic flows (so-called geophysical mass flows), but much of it will be applicable more broadly to problems in the analysis and quantification of risk in problems featuring spatial variability and model uncertainty. It brings together a unique team of scientists with specialties including volcanology, to guide the development of realistic models for the geophysical processes under study; in stochastic processes, to reflect uncertainty and variability about initial conditions, flow frequencies, and other features in realistic and verifiable ways; in deterministic computer modeling, for the difficult task of making detailed spatial predictions of the consequences of the most probable and of the most hazardous possible events; in computer model emulation, to accelerate many thousand-fold the computations necessary for predicting the risk of rare events under a wide range of possible scenarios; and in statistical modeling and analysis, to reflect honestly all the different sources of uncertainty and variability in this analysis, leading to a full quantification of the risk of hazardous events. Only with such a broad range of expertise can investigators build the tapestry of science that is required to develop tools for studying devastating natural hazards.

该项目的目标是开发评估和预测与火山碎屑流等地球物理灾害有关的风险所需的数学、统计和计算工具。 初步数据分析的基础上，研究人员开发随机模型开始与固定的独立增量过程采用（可能是锥形）帕累托分布的火山碎屑流的体积超过一些观测阈值，在域的吸引力的α稳定的过程中，管理多个较小的喷发的总流量。 流动起始角采用Von Mises分布。 确定性TITAN 2D的二维计算环境，它使用现有的数字高程图来预测的影响，在不同的网站的利益，从指定的体积和启动角度的流量。 TITAN 2D是一个深度平均的薄层计算流体动力学代码，基于自适应网格Goddom求解器，适用于模拟地球物理质量流。 一个基于TITAN 2D模型的简单高斯随机场近似的快速模拟器使研究人员能够模拟数十万次TITAN 2D试验，并对可能导致重大影响的一组可能的流量和起爆角度进行估计;一个分层贝叶斯统计模型反映了在一个特定的时间段内这种影响的概率。算法导致了数学和计算机建模应用于风暴、洪水、地震和火山爆发等高度复杂的现象。 人们越来越认识到，发展这些现象的数学模型只是对风险进行可靠估计和预测所需的更为复杂的过程的一部分。 该项目开发评估和预测与此类自然灾害有关的风险所需的数学、统计和计算工具。 这项工作的一个特别重点是研究这些风险在空间和时间上的变化，以及它们的不确定性。 这种方法是在火山雪崩和火山碎屑流（所谓的地球物理物质流）的具体问题的背景下开发的，但其中大部分将更广泛地适用于分析和量化具有空间变异性和模型不确定性的问题中的风险。 它汇集了一个独特的科学家团队，具有火山学等专业知识，以指导研究中的地球物理过程的现实模型的开发;在随机过程中，以现实和可验证的方式反映初始条件，流动频率和其他特征的不确定性和可变性;在确定性计算机建模中，用于对最可能和最危险的可能事件的后果进行详细的空间预测的困难任务;在计算机模型模拟中，将预测各种可能情况下罕见事件风险所需的计算加速数千倍;在统计建模和分析中，诚实地反映分析中所有不同的不确定性和可变性来源，从而全面量化危险事件的风险。 只有拥有如此广泛的专业知识，调查人员才能建立科学的挂毯，这是开发研究毁灭性自然灾害的工具所必需的。