Use of potential vorticity for incremental data assimilation

Abstract

Decomposing the mass and wind fields in a data assimilation scheme into balanced and unbalanced flow is part of the process of defining a covariance model. It is not uncommon to assume that the dynamic balanced part of the flow is approximated solely by the rotational part of the wind, which is obtained from a Helmholtz decomposition of the horizontal momentum (with an associated balanced pressure being diagnostically inferred from a balance equation, for example). The unbalanced flow is then represented by the divergence and the residual unbalanced pressure. The assumption that the rotational part of the momentum is a good approximation to the total balanced flow is only valid in certain regimes. We propose a new approach that incorporates flow regime dependence, where we assume that the balanced part of the flow is approximated instead by a linearized potential vorticity increment. We show the benefit of such a formulation in the context of shallow-water equations defined on a hemisphere. © Royal Meteorological Society, 2006.