Variational data‐assimilation experiments using flow‐dependent dynamical constraints

Mass–wind and vorticity–divergence balance constraints based on the linearized Charney and quasi‐geostrophic omega equations, respectively, are assessed in a developmental version of the global, three‐dimensional variational data‐assimilation system at Environment Canada. Unlike traditional balance constraints, which are averaged in time, the new constraints are flow‐dependent and reflect a more complete set of dynamics. Single observation experiments demonstrate that the new covariance model leads to asymmetrical increments that are qualitatively aligned with the instantaneous background wind field. Data‐assimilation experiments using real observations are performed for a period of five weeks during two different seasons, employing the control and experimental constraints. Subsequent forecast verification against radiosondes shows a definite benefit of the new covariances in the Tropics; however, the impact in the Extratropics is neutral or slightly negative. Verifications against analysis show virtually no change in the troposphere; however, a significant improvement is observed in the stratosphere at all lead times. Compared with the Charney mass–wind balance, the contribution of the quasi‐geostrophic omega constraint is rather minimal, at least in its current adiabatic form. The new balance scheme requires a considerable amount of computational time in the context of our 3D‐Var system, although the relative cost in a 4D‐Var setting may be far less significant. Moreover, the present experiments are useful in elucidating several important aspects of covariance modelling, particularly the dependence of balance dynamics on spatial scale. © 2012 Crown in the right of Canada. Published by John Wiley & Sons Ltd.