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Time-dependent variational data assimilation allows the possibility of extracting wind information from observations of ozone or other trace gases. Since trace gas observations are not available at sufficient resolution for deriving feature-track winds, they must be combined with model background information to produce an analysis. If done with time-dependent variational assimilation, wind information may be extracted via the adjoint of the linearized tracer continuity equation. This paper presents idealized experiments that illustrate the mechanics of tracer–wind extraction and demonstrate some of the limitations of this procedure. We first examine tracer–wind extraction using a simple one-dimensional advection equation. The analytic solution for a single trace gas observation is discussed along with numerical solutions for multiple observations. The limitations of tracer–wind extraction are then explored using highly idealized ozone experiments performed with a development version of the Navy Global Environmental Model (NAVGEM) in which globally distributed hourly stratospheric ozone profiles are assimilated in a single 6 h update cycle in January 2009. Starting with perfect background ozone conditions, but imperfect dynamical conditions, ozone errors develop over the 6 h background window. Wind increments are introduced in the analysis in order to reduce the differences between background ozone and ozone observations. For "perfect" observations (unbiased and no random error), this results in root-mean-square (RMS) vector wind error reductions of up to ~4 m s<sup>−1</sup> in the winter hemisphere and tropics. Wind extraction is more difficult in the summer hemisphere due to weak ozone gradients and smaller background wind errors. The limitations of wind extraction are also explored for observations with imposed random errors and for limited sampling patterns. As expected, the amount of wind information extracted degrades as observation errors or data voids increase. In the case of poorly specified observation error covariances, assimilation of ozone data with imposed errors may result in increased RMS wind error, since the assimilation is constrained too tightly to the noisy observations

Limitations of wind extraction from 4D-Var assimilation of ozone