Global Non-Gaussian Stochastic Partial Differential Equation Models for Assessing Future Health of Ecohydrologic Systems

近几十年来，计算能力的急剧增加，加上便携式和遥感设备的技术进步，使数据的数量、种类和速度呈指数级增长，促进了新的科学和工程突破。该项目的重点是全球时空数据，这是一种受大数据革命影响很大的数据类型，旨在为高分辨率实时（每日或每小时）监测的过程开发一个新的全球动态模型。该应用程序将侧重于降雨的发生和强度，该模型将用于评估各种水文系统所面临的风险，包括湖泊，湿地和地表水/地下水相互作用区。拟议的全球统计模型将具有足够的灵活性，能够解释当地模型可能忽略的大规模大气/海洋模式（例如厄尔尼诺/南方涛动）造成的洪水和干旱事件。该应用程序将集中在四个地区在美国大陆已知的是敏感的降水事件。计划在不同级别开展外联活动，从为高中生举办讲座到为当地社区举办活动，以提高人们对健康水文系统价值的认识，一个计算机程序将使用户能够探索美国哪些地区面临更高的洪水和干旱风险。研究生的支持将用于跨学科研究和编写代码。 全球数据的模型是一个理论上的挑战，因为在定义有效的过程中有限制的领域和时间。由于这些模型必须足够灵活，以捕获地球仪上的重要数据结构，并且能够适应现代数据集的极大规模（数十亿个点），因此也存在实际和计算挑战。提出了一种用于全球时空数据的潜在高斯模型，该模型将通过随机偏微分方程控制空间依赖性，该方程具有能够捕获具有局部张量变形的非平稳性的算子，并改变陆地和海洋的行为以允许在两个域之间平滑过渡。该模型将采用有限体积方法求解，该方法将保证潜在过程中精度矩阵的稀疏性，从而允许超大数据集的可扩展性。该应用程序将解决水文生态水文系统未来健康的不确定性评估的关键问题。全球每日降水量模拟和质量守恒方程将提供美国四个地区未来干旱和洪水风险的估计。该奖项反映了NSF的法定使命，并被认为值得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。

In recent decades, the dramatic increase of computational power, coupled with technological advances in portable and remote sensing devices has exponentially increased the volume, variety and velocity of data, facilitating new scientific and engineering breakthroughs. This project focuses on global spatio-temporal data, a data type highly affected by this Big Data revolution and aims to develop a new global dynamical model for processes monitored at high resolution in time (daily or hourly). The application will focus on the occurrence and intensity of rainfall, and the model will be applied to assess risks faced by diverse hydrologic systems, including lakes, wetlands, and the surface/groundwater interaction zone. The proposed global statistical model will be flexible enough to explain floods and drought events governed by large scale atmospheric/oceanic patterns (for example, the El Niño Southern Oscillation) that a local model could miss. This application will focus on four regions in the continental USA known to be sensitive to precipitation events. Outreach activities at different levels, from lectures to high school students to events for the local community, are planned to increase awareness on the value of healthy hydrological systems, and a computer program will allow users to explore which areas in the United States are at higher risk of floods and droughts. The graduate student support will be used on interdisciplinary research and writing codes. Models for global data represent a theoretical challenge, as there are restrictions in defining valid processes over the sphere and time. Practical and computational challenges also exist as these models must be both flexible enough to capture non-trivial data structure across the globe, and be able to fit the extremely large size of modern data sets (billions of points). A latent Gaussian model for global spatio-temporal data is proposed, which will control the spatial dependence by a Stochastic Partial Differential Equation with an operator able to capture non-stationarity with a local tensor deformation, and changing behavior across land and ocean to allow for a smooth transition across the two domains. The model will be solved with a finite volume approach which will guarantee sparsity of the precision matrix in the latent process, thus allowing scalability for extremely large data sets. The application will address the critical issue in hydrology of the assessment of the uncertainty in future health of ecohydrological systems. Global simulations of daily precipitation and a mass conservation equation will provide estimates of the future risk to droughts and floods in four regions in the United States.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.