Ertel potential vorticity inversion using a digital filter initialization method

A new Ertel-potential-vorticity inversion method is proposed and tested in the framework of a low-order model as well as in Meteo France's operational primitive-equation spectral model, ARPEGE. The potential-vorticity (PV) inversion procedure is designed so that its result lies within the subspace of model solutions, without the use of any explicit balance condition. The inversion is based on a variational problem in which one minimizes simultaneously the distance to the dynamical initialized solution following a digital-filter method and the PV to be inverted. Since the inverted solution results from model backward and forward integrations, and not from a set of algebraic equations, it possesses a strong dynamical consistency. In the framework of a low-order model, it is found that for small Rossby number, digital-filter initialization lies between nonlinear normal-mode initialization and quasi-geostrophic methods. The method has also been successfully used to rebuild the non-divergent flow, the temperature, and a significant part of the divergent flow, knowing only the three-dimensional PV field and a boundary condition. Copyright (c) 2008 Royal Meteorological Society.