Inversion of Potential Vorticity Density

Abstract

Inversion of potential vorticity density Ph * 5(va � =h)/(›h/›z) with absolute vorticity va and function h is explored in h coordinates. This density is shown to be the component of absolute vorticity associated with the vertical vector of the covariant basis of h coordinates. This implies that inversion of Ph* in h coordinates is a two-dimensional problem in hydrostatic flow. Examples of inversions are presented for h5u (u is potential temperature) and h5p (p is pressure) with satisfactory results for domains covering the North Pole. The role of the boundary conditions is investigated and piecewise inversions are performed as well. The results shed new light on the interpretation of potential vorticity inversions.