Modeling Tangential Vector Fields on a Sphere
Minjie Fan
Debashis Paul
Thomas C. M. Lee
Tomoko Matsuo
10.6084/m9.figshare.5279992.v2
https://tandf.figshare.com/articles/Modeling_Tangential_Vector_Fields_on_a_Sphere/5279992
<p>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.</p>
2017-08-14 19:59:57
Curl-free
Divergence-free
Helmholtz–Hodge decomposition
Matérn model
Ocean surface wind