Domain-Independent Attribution. Part I: Reconstructing the Wind from Estimates of Vorticity and Divergence Using Free Space Green's Functions

Abstract

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 st...