Wind extraction potential from 4D-Var assimilation of stratospheric O3, N2O, and H2O using a global shallow water model

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 the shallow water equations coupled to the tracer continuity equation. The procedure is outlined as follows. First, a nature run is created, simulating middle stratospheric winter conditions. Second, ozone (O-3), nitrous oxide (N2O), and water vapor (H2O) (treated in this study as passive tracers) are initialized using Aura Microwave Limb Sounder (MLS) mixing ratios at 850K potential temperature and are advected by the nature run winds. Third, the initial dynamical conditions are perturbed by using a 6 h offset. Fourth, simulated hourly tracer observations on the full model grid are assimilated with a 4D-Var system in which tracer and winds are coupled via the adjoint of the tracer continuity equation. Multiple assimilation experiments are performed by varying the amount of random observation error added 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 h assimilation cycle with the smallest observation error, WEP values are similar to 60% for all three tracers, while 10-day multi-cycle simulations result in WEP of similar to 90 %, wind errors of similar to 0.3 m s(-1), and height errors of similar to 13 m. There is therefore sufficient information in the tracer fields to almost completely constrain the dynamics, even without direct assimilation of dynamical information. When realistic observation error is added (based on MLS precisions at 10 hPa), the WEP after 10 days is 90% for O-3, 87% for N2O, and 72% for H2O. O-3 and N2O provide more wind information than H2O due to stronger background gradients relative to the MLS precisions. The RMSE for wind reach a minimum level of similar to 0.3-0.9m s(-1) for the MLS precisions, suggesting a limit to which realistic tracers could constrain the winds, given complete global cover age. With higher observation noise levels, the WEP values decrease, but the impact on the winds is still positive up to noise levels of 100%(relative to the global mean value) when compared to the case of no data assimilation.