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The wind extraction due to assimilation of stratospheric trace gas (tracer)data is examined using a 4D-Var (four-dimensional variational) data assimilation system based on theshallow water equations coupled to the tracer continuity equation. Theprocedure is outlined as follows. First, a nature run is created, simulatingmiddle stratospheric winter conditions. Second, ozone (O3), nitrousoxide (N2O), and water vapor (H2O) (treated in this study aspassive tracers) are initialized using Aura Microwave Limb Sounder (MLS) mixingratios at 850 K potential temperature and are advected by the nature runwinds. Third, the initial dynamical conditions are perturbed by using a 6 hoffset. Fourth, simulated hourly tracer observations on the full model gridare assimilated with a 4D-Var system in which tracer and winds are coupledvia the adjoint of the tracer continuity equation. Multiple assimilationexperiments are performed by varying the amount of random observation erroradded to the simulated measurements. Finally, the wind extraction potential(WEP) is calculated as the reduction of the vector wind root mean square error(RMSE) relative to the maximum possible reduction. For a single 6 hassimilation cycle with the smallest observation error, WEP values are~60% for all three tracers, while 10-day multi-cyclesimulations result in WEP of ~90%, wind errors of~0.3 m s−1, and height errors of ~13 m.There is therefore sufficient information in the tracer fields to almostcompletely constrain the dynamics, even without direct assimilation ofdynamical information. When realistic observation error is added (based onMLS precisions at 10 hPa), the WEP after 10 days is 90% for O3,87% for N2O, and 72% for H2O. O3 and N2O providemore wind information than H2O due to stronger background gradientsrelative to the MLS precisions. The RMSE for wind reach a minimum level of~0.3–0.9 m s−1 for the MLS precisions, suggesting alimit to which realistic tracers could constrain the winds, given completeglobal cover age. With higher observation noise levels, the WEP valuesdecrease, but the impact on the winds is still positive up to noise levelsof 100% (relative to the global mean value) when compared to the case ofno data assimilation

atmospheric chemistry and physics

Wind extraction potential from 4D-Var assimilation of stratospheric O&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;, N&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;O, and H&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;O using a global shallow water model