Replication data for: A multivariate semiparametric Bayesian spatial modeling framework for hurricane surface wind fields

Storm surge, the onshore rush of sea water caused by the high winds and low pressure associated with a hurricane, can compound the effects of inland flooding caused by rainfall, leading to loss of property and loss of life for residents of coastal areas. Numerical ocean models are essential for creating storm surge forecasts for coastal areas. These models are driven primarily by the surface wind forcings. Currently, the gridded wind fields used by ocean models are specified by deterministic formulas that are based on the central pressure and location of the storm center. While these equations incorporate important physical knowledge about the structure of hurricane surface wind fields, they cannot always capture the asymmetric and dynamic nature of a hurricane. A new Bayesian multivariate spatial statistical modeling framework is introduced combining data with physical knowledge about the wind fields to improve the estimation of the wind vectors. Many spatial models assume the data follow a Gaussian distribution. However, this may be overly-restrictive for wind fields data which often display erratic behavior, such as sudden changes in time or space. In this paper we develop a semiparametric multivariate spatial model for these data. Our model builds on the stick-breaking prior, which is frequently used in Bayesian modeling to capture uncertainty in the parametric form of an outcome. The stick-breaking prior is extended to the spatial setting by assigning each location a different, unknown distribution, and smoothing the distributions in space with a series of kernel functions. This semiparametric spatial model is shown to improve prediction compared to usual Bayesian Kriging methods for the wind field of Hurricane Ivan.

风暴潮（Storm surge）是指由飓风伴随的强风与低压引发的海水向岸涌升现象，它会加剧降雨引发的内陆洪涝灾害，给沿海地区居民造成财产损失与人员伤亡。数值海洋模式（numerical ocean models）是制作沿海区域风暴潮预报的关键工具，此类模式主要依靠地表风强迫（surface wind forcings）驱动。当前海洋模式所采用的格点风场（gridded wind fields），由基于风暴中心气压与位置的确定性公式（deterministic formulas）设定。尽管这些公式纳入了描述飓风地表风场结构的重要物理知识，但往往无法准确捕捉飓风的非对称与动态特性。本文提出一种全新的贝叶斯多元空间统计建模框架（Bayesian multivariate spatial statistical modeling framework），该框架融合观测数据与风场相关物理知识，以优化风矢量（wind vectors）的估算精度。多数空间模型假设数据服从高斯分布（Gaussian distribution），但对于风场数据而言，此类假设可能过于严苛——风场数据通常会表现出不稳定的特征，例如时空维度上的突变。针对这类数据，本文构建了一种半参数多元空间模型（semiparametric multivariate spatial model）。我们的模型以折断先验（stick-breaking prior）为基础，该先验在贝叶斯建模中常被用于刻画结果参数形式的不确定性。我们将折断先验拓展至空间场景中，为每个空间位置赋予独立的未知分布，并通过一系列核函数（kernel functions）实现分布的空间平滑。相较于针对飓风伊万（Hurricane Ivan）风场的常规贝叶斯克里金法（Bayesian Kriging），该半参数空间模型的预测性能得到了显著提升。