Multivariate space-time models and methods to combine large disparate spatial data and numerical models

将大量不同的空间数据与数值模型相结合的多变量时空模型和方法多变量时空统计问题在环境科学中很普遍，特别是在大气和海洋数据应用中。在许多情况下，感兴趣的过程本质上是非线性和动态的。这些系统的不同信息来源包括观测数据和基于物理的数值模型。在过去十年中，实时观测的可获得性有所增加，确定性大气和海洋模型的精确度和分辨率也有所提高。提出了一种结合数值模型和观测数据的建模框架，该框架允许估计数据的多变量统计模型以及基于物理的确定性模型的参数，同时考虑了观测数据中潜在的相加和相乘偏差。发展了一类广泛的多变量时空模型来解释多变量时空数据的变异性，以及不同变量之间的交叉依赖关系。这类一般模型超越了协方差函数的对称性、可分离性和平稳性的标准假设，并提出了对非高斯过程的扩展。风暴潮是与飓风相关的陆上海水涌动，可能导致财产损失、数十亿美元的损失和大量人员死亡。数值海洋模型被用来确定何时何地向受影响地区发送疏散警告和恢复单位。海洋模型的主要输入之一是地面风场，它是基于物理模型计算的。目前，来自浮标和卫星的物理风速测量不能用于预测风暴潮。建议的统计框架和模型用于通过用来自浮标和卫星的风信息补充基于物理的模型输出来更好地模拟飓风表面风场。使用统计多变量时空模型将这些数据组合在一起进行预测。统计模型已被证明是环境科学中描述物理过程复杂的空间和时间行为的基本工具。统计模型还允许在新的地点和时间预测潜在的时空过程。通过科学家和统计学家之间的合作，预计本提案中提出的多变量时空过程的新统计模型和方法将通过改进海洋沿岸预测和引入新的方法来分析海量数据集，从而提高科学水平。调查人员将使用部分资金进行旅行，并广泛传播这里提出的方法，以增进对数学和科学的理解。首席调查员将在拉美裔国家进行一些演讲和短期课程，以扩大代表性不足的地理和族裔群体的参与。调查人员将继续努力扩大少数群体和妇女的参与。

Multivariate space-time models and methods to combine large disparate spatial data and numerical modelsMultivariate spatial-temporal statistical problems are prevalent in the environmental sciences, particularly in atmospheric and oceanic data applications. In many cases the processes of interest are inherently nonlinear and dynamic. Different sources of information for these systems include observational data as well as physics-based numerical models. Over the past decade there has been an increase in the availability of real-time observations as well as advances in the sophistication and resolution of deterministic atmospheric and oceanic models. A modeling framework to combine numerical models and observations is proposed, this framework allows for estimation of a multivariate statistical model for the data as well as parameters of physically-based deterministic models, while accounting for potential additive and multiplicative bias in the observed data. A broad class of multivariate spatial-temporal models is developed to explain the variability in the multivariate space-time data, as well as the cross-dependency between different variables. This general class of models goes beyond the standard assumptions of symmetry, separability and stationarity of the covariance function, and an extension to non-Gaussian processes is presented. Storm surge is the onshore rush of seawater associated with hurricane winds and can lead to loss of property, billion of dollars in damage, and large number of fatalities. Numerical ocean models are used to determine when and where to send evacuation warnings and recovery units to affected areas. One of the main inputs to the ocean models is the surface wind field, which is calculated based on a physical model. Currently, physical wind measurements from buoys and satellites are not used to forecast storm surge. The proposed statistical framework and models are used to better model hurricane surface wind fields by supplementing the physics-based model output with wind information from buoys and satellites. Statistical multivariate space-time modeling is used to combine these data to make predictions. Statistical models have proven to be an essential tool in the environmental sciences to describe complex spatial and temporal behavior of physical processes. Statistical models also allow for prediction of the underlying spatial-temporal processes at new locations and times. Through collaborations between scientists and statisticians, it is anticipated that the new statistical models and methods presented in this proposal for multivariate space-time processes will enhance science by improving ocean coastal prediction, and by introducing new methodology to analyze massive datasets. The investigators will use part of the funds to travel and disseminate broadly the methods proposed here to enhance mathematical and scientific understanding. The principal investigator will give some talks and short courses in Hispanic countries to broaden the participation of underrepresented geographic and ethnic groups. The investigators will continue their efforts to broaden the participation of minorities and women.