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 heterogeneous. This improved estimate is named the G4 estimate. It is not derived from Taylor series. When the G4 estimate of vorticity/divergence is used to reconstruct the wind field, the magnitude of the reconstruction error is an order of magnitude smaller than the reconstruction error associated with the standard estimate of vorticity/divergence.