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

多变量时空模型和方法，以联合收割机大规模不同的空间数据和数值模型多变量时空统计问题是普遍存在的环境科学，特别是在大气和海洋数据的应用。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以及基于物理的数值模型。在过去十年中，实时观测的可用性有所增加，确定性大气和海洋模型的复杂性和分辨率也有所提高。提出了一种结合联合收割机数值模型和观测的建模框架，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，同时考虑观测数据中潜在的加性和乘性偏差。一个广泛的类的多元时空模型的发展，以解释在多元时空数据的变异性，以及不同变量之间的交叉依赖。这类一般的模型超越了标准假设的对称性，可分性和平稳性的协方差函数，并扩展到非高斯过程。风暴潮是与飓风相关的海水向岸上的冲击，可能导致财产损失，数十亿美元的损失和大量人员死亡。数值海洋模型用于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根据物理模型计算的表面风场。目前，来自浮标和卫星的实际风力测量并不用于预报风暴潮。拟议的统计框架和模型被用来更好地模拟飓风表面风场，补充物理模型输出与风信息浮标和卫星。 统计多变量空间-时间建模用于联合收割机这些数据进行预测。统计模型已被证明是环境科学中描述物理过程的复杂时空行为的重要工具。统计模型还允许在新的位置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海岸预测和引入新方法来分析大量数据集来加强科学。 研究人员将使用部分资金旅行和广泛传播这里提出的方法，以提高数学和科学的理解。首席研究员将在西班牙裔国家举办一些讲座和短期课程，以扩大代表性不足的地理和种族群体的参与。调查人员将继续努力扩大少数民族和妇女的参与。

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.