Modeling Tangential Vector Fields on a Sphere. Issue 524 (2nd October 2018)

• Record Type: Journal Article
• Authors: Fan, Minjie; Paul, Debashis; Lee, Thomas C. M.; Matsuo, Tomoko
• Is Part Of: Journal of the American Statistical Association. Volume 113:Issue 524(2018)
• Page Start: 1625
• Page End: 1636
• Publication Date: 2018-10-02
• Subjects: Curl-free -- Divergence-free -- Helmholtz–Hodge decomposition -- Matérn model -- Ocean surface wind; Statistics -- Periodicals; Statistics -- Periodicals; Statistiques -- Périodiques; États-Unis -- Statistiques -- Périodiques; 519.5
• DOI: 10.1080/01621459.2017.1356322
• Languages: English
• ISSNs: 0162-1459

Abstract

ABSTRACT: 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 Matérn model and a non-stationary bivariate global model. Supplementary materials for this article are available online.