Domain-independent attribution. Part I: Reconstructing the wind from estimates of vorticity and divergence using free space Green's functions

Abstract

Free space Green's functions may be used to reconstruct the wind over a limited domain from vorticity, divergence, and the wind at the boundary of the domain. When standard finite-difference estimates of the vorticity/divergence field are used, the technique fails to accurately reconstruct the wind in regions where the vorticity or divergence change markedly between grid boxes. The standard finite-difference estimate of vorticity/divergence is accurate provided that the wind varies linearly with distance along the edges of grid boxes. An estimate of vorticity/divergence is derived that accounts for the fact that these requirements are not met when the vorticity/divergence field is locally he..