Modeling Tangential Vector Fields on a Sphere

• 成果类型: Article
• 署名作者: Fan, Minjie; Paul, Debashis; Lee, Thomas C. M.; Matsuo, Tomoko
• 署名单位: University of California System; University of California Davis; University of Colorado System; University of Colorado Boulder
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2017.1356322
• 发表日期: 2018
• 页码: 1625-1636
• 关键词: multivariate random-fields; cross-covariance functions; Spatial Data; FRAMEWORK; streamfunction; interpolation; computation; prediction; variogram; ozone

摘要

Physical processes that manifest as tangential vector fields on a sphere are common in geophysical and environmental sciences. These naturally occurring vector fields are often subject to physical constraints, such as being curl-free or divergence-free. We start with constructing parametric models for curl-free and divergence-free vector fields that are tangential to the unit sphere through applying the surface gradient or the surface curl operator to a scalar random potential field on the unit sphere. Using the Helmholtz-Hodge decomposition, we then construct a class of simple but flexible parametric models for general tangential vector fields, which are represented as a sum of a curl-free and a divergence-free components. We propose a likelihood-based parameter estimation procedure, and show that fast computation is possible even for large datasets when the observations are on a regular latitude-longitude grid. Characteristics and practical utility of the proposed methodology are illustrated through extensive simulation studies and an application to a dataset of ocean surface wind velocities collected by satellite-based scatterometers. We also compare our model with a bivariate Matern model and a non-stationary bivariate global model. Supplementary materials for this article are available online.