Objective analysis of the vorticity field within a region of no data

Objective methods for estimating meteorological fields within so-called “data-holes” are compared. In particular, if Ψ is the streamfunction, a solution of the biharmonic equation ▽⁴Ψ = 0 subject to specified values of Ψ and δΨ/δn around the boundary of the hole is shown to provide a field whose mean square wind velocity error is comparable to that obtained by RICHARDSON (1961) for a hole 1200 km square using THOMPSON’S (1961) technique of sequential Lagrangian advection of known vorticity into the hole from outside. A scheme is suggested, combining certain advantages of both methods, which involves the Lagrangian advection of vorticity and periodic adjustment of the vorticity field to conform with the known changes in Ψ and δΨ/δn around the boundary.