Wind extraction potential from 4D-Var assimilation of stratospheric O<sub>3</sub>, N<sub>2</sub>O, and H<sub>2</sub>O using a global shallow water model

Abstract

Abstract. 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 (N 2 O), and water vapor (H 2 O) (treated in this study as passive tracers) are initialized using Aura Microwave Limb Sounder (MLS) mixing ratios at 850 K 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 ∼ 60 % for all three tracers, while 10-day multi-cycle simulations 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 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 N 2 O, and 72 % for H 2 O. O 3 and N 2 O provide more wind information than H 2 O due to stronger background gradients relative 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 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.

Wind extraction potential from ensemble Kalman filter assimilation of stratospheric ozone using a global shallow water model

“…Additional maps of potential vorticity and ozone for this TR are provided in Fig. 2 of Allen et al (2014).…”

“…The calculations of RMSE and SPREAD are not area-weighted and therefore may be somewhat biased to match the higher latitudes, since the Gaussian grid is used. This tuning takes a similar approach to the 4D-Var simulations of Allen et al (2014) in which the background error variances were modified to match the global RMSE of the tracer and wind components. This adaptive tuning provides a flexible way to examine how the system behaves over a wide range or parameters, without needing to separately tune the inflation factor for each case.…”

“…The TR is designed to simulate Northern Hemisphere (NH) winter conditions in the middle stratosphere (the same TR was used in the 4D-Var tracer assimilation study by Allen et al, 2014). The initial conditions for the SWM T include zero meridional wind and a zonally symmetric zonal wind that varies with latitude (φ) as u (φ) = u max sin (2φ) in the NH and is zero in the Southern Hemisphere (SH), with u max = 60 m s −1 .…”

“…However, attempts to assimilate stratospheric ozone using 4D-Var algorithms and the resultant dynamical coupling have previously resulted in problems in operational numerical weather prediction (NWP) (Han and McNally, 2010;Dragani and McNally, 2013). These assimilation challenges led Allen et al (2014) to re-examine the stratospheric tracer-wind problem at a more fundamental level using 4D-Var assimilation studies with a shallow water model (SWM) coupled to the tracer continuity equation. This idealized system allowed Allen et al (2014) to probe the limits of wind extraction from assimilation of three readily measured long-lived tracers: ozone (O 3 ), nitrous oxide (N 2 O), and water vapor.…”

“…These assimilation challenges led Allen et al (2014) to re-examine the stratospheric tracer-wind problem at a more fundamental level using 4D-Var assimilation studies with a shallow water model (SWM) coupled to the tracer continuity equation. This idealized system allowed Allen et al (2014) to probe the limits of wind extraction from assimilation of three readily measured long-lived tracers: ozone (O 3 ), nitrous oxide (N 2 O), and water vapor. It was shown that assimilation of global hourly tracer data was sufficient to analyze the horizontal wind components to a high degree of accuracy (∼ 0.3 m s −1 random error for O 3 and N 2 O).…”