Irreversible vertical mixing of ozone caused by inertio-gravity wave breaking in the lower stratosphere K. Noguchi, T. Imamura and K. -I. Oyama Japan Aerospace Exploration Agency, Tokyo, Japan Abstract. The irreversible vertical mixing of ozone due Shear instability region Altitude Group velocity Wave front to the breaking of inertio-gravity waves is investigated based on a case study with the aid of ozone density and meteorological data obtained by ozonesondes at Santa Cruz Phase velocity (28.46˚N). The altitude regions where the conditions of shear instability and convective instability were satisfied Wind had locally flat vertical distributions of ozone mixing ratio Wind velocity in the and potential temperature. A hodograph analysis showed direction of horizontal Material surface Convective instability region that a gravity wave observed simultaneously caused such propagation instabilities and the vertical mixing of potential tempera- ture and ozone. Statistical analysis is also conducted to Figure 1. Schematic of the regions of shear instability and con- show how often the condition of shear instability is satis- vective instability in the field of a gravity wave whose group ve- locity is upward. fied in the lower stratosphere. Case study of vertical mixing Introduction The ozonesonde data which are used in the present study It has been recognized that the Brewer-Dobson circula- are supplied by World Ozone and Ultraviolet Radiation tion governs the transport of trace gases in the stratosphere Data Centre (WOUDC), which contains ozonesonde data [Holton et al., 1995]. Besides the large-scale vertical obtained at over 400 stations in the world. We pick up transport associated with the Brewer-Dobson circulation, Santa Cruz (28.46˚N) stations since the data of Santa Cruz the vertical mixing by small-scale sporadic turbulence due have high vertical resolution (~20 m). to gravity wave breaking also causes the transport across Figure 2 shows an example of the case where tempera- isentropic surfaces [Lindzen, 1981; Garcia and Solomon, ture and ozone distributions seem to be strongly affected by 1983]. In the present study, the contribution of gravity wave the vertical advection and mixing associated with gravity breaking to the vertical mixing of ozone is discussed using wave breaking. At altitudes of 15-25 km, the zonal and me- ozone density data and meteorological data obtained by ridional wind velocity profiles have distinct wavelike ozonesondes. structures, which strongly suggest that a gravity wave ex- ists. Conditions of instabilities Small-scale vertical mixing is caused by the breaking of gravity waves through shear instability and convective in- stability [Fritts and Rastogi, 1985]. The condition for convective instability is given by θ/z < 0, where θ is po- tential temperature and z the altitude, and the condition for Meridional shear instability is Ri < 0.25, where Ri is the Richardson wind number defined by 2 Ozone u Ri N 2 . z Here N is the Brunt Väisälä frequency defined by Temperature ln N2 g , z where g is the gravitational acceleration and u the horizon- Zonal tal wind. In the middle atmosphere, these instabilities are wind usually initiated by gravity waves as illustrated in Figure 1. Taking the coordinate of wind velocity fluctuation u’ in the direction of horizontal propagation, convective instability occurs around the regions where u’ peaks, while shear in- stability occurs around the regions where u’ ≈ 0. The re- gions where these instabilities occur should have vertical- ly-smoothed distributions of tracers and potential tempera- ture due to vigorous vertical mixing. Such regions are easi- Figure 2. Ozonesonde data on August 11, 1999 at Santa Cruz ly found in ozonesonde data, as shown later. (28.46˚N). (Left) Ozone mixing ratio and temperature. (Right) Zonal and meridional wind velocity. To investigate the relationship between these small-scale shear or convective instability at Santa Cruz (28.46˚N). The structures and the instabilities which are illustrated in Fig- altitude where the probability of ~0.25 occurs varies with ure 1, ozone mixing ratio and potential temperature are season similarly to that of the tropopause, below which the compared with N2 and Ri in Figure 3. The vertical distribu- instability occurs more frequently than above. This result is tions of ozone mixing ratio and potential temperature tend consistent with the fact that the background atmosphere is to be locally flat in the regions where N2 ~ 0 and/or Ri < less stable in the troposphere than in the stratosphere. 0.25, i.e., the condition of convective and/or shear instabil- The probability decreases above the tropopause more ity is satisfied. Then, it is suggested that vertical mixing has sharply in summer than in winter. The activity of gravity occurred in those regions due to the instabilities. Consi- waves is inferred from temperature data. As the index of dering that these regions have thickness of 200-300 m and gravity wave activity, the potential energy typically include 10-15 data points in each layer, the fea- 1 g2 T (1) Ep 2 N 2 T0 tures should not be artificial. is adopted, where T’ is the fluctuation component of tem- perature and T0 the background component of temperature. Comparison of the probability distribution (Figure 4a) with the Ep distribution (Figure 4b) suggests that the gravity wave enhancement around the tropopause cause more in- Ozone stability in winter than in summer. This is consistent with the results of the radar observations of the eddy diffusivity, which were shown to have a maximum around the winter tropopause jetstream [Fukao et al., 1994]. The present study suggests that such an enhancement of the eddy diffu- sivity is attributed to an active occurrence of turbulence by shear instability due to gravity waves. Potential (a) (b) Temperature Figure 3. An altitude section of the ozonesonde observation shown in Figure 2. (a) Ozone mixing ratio and potential tempera- Month Month ture. (b) Static stability. (c) Richardson number. (d) Wind velocity fluctuation with λz ≤ 3 km along the direction of horizontal prop- Figure 4. (a) Probability of the occurrence of shear or convective agation. Shaded regions indicate the regions where shear instabil- instability at Santa Cruz (28.46˚N). (b) Potential energy of gravity ity or convective instability is expected to occur. waves with λz ≤ 2 km defined by (1) in unit of J kg-1. White cir- cles in (a) and (b) indicate tropopause. In order to relate the regions of instability to the gravity wave field, a hodograph analysis is applied to the data Acknowledgments The ozonesonde data are supplied by adopting the procedure described by Hamilton . The WOUDC. I thank Dr. Yoshihiro Tomikawa of National Institute of result suggests that the observed fluctuations of wind and Polar Research (NIPR), Japan for his useful comments and dis- cussion. The global ozonesonde data are supplied by World temperature are attributed to an inertio-gravity wave with Ozone and Ultraviolet Radiation Data Centre. horizontal wavelength λx = 410 km, vertical wavelength λz = 1.0 km and the intrinsic period of 19.8 hours. The propaga- References tion direction was also determined, and u’ in this direction is compared with other variables in Figure 3. Considering Fritts, D. C. and Rastogi, P. K., Convective and dynamical insta- bilities due to gravity wave motions in the lower and middle the phases where instabilities are expected to occur (Figure atmosphere: theory and observations, Radio Sci., 20, 1), the mixing regions A-C are attributed to shear instability, 1247-1277, 1985. while the region D, convective instability. Fukao, S., M. D. Yamanaka, N. Ao, W. K. Hocking, T. Sato, M. Yamamoto, T. Nakamura, T. Tsuda, and S. Kato, Seasonal va- Probability of occurrence of shear instability riability of vertical eddy diffusivity in the middle atmosphere 1. Three-year observations by the middle and upper atmosphere The result in the previous section implies that the occur- rader, J. Geophys. Res., 99, 18973-18987, 1994. rence of instabilities and subsequent mixing can be de- Garcia, R. R. and S. Solomon, A numerical model of the zonally tected in meteorological data by using the criterion Ri < averaged dynamical and chemical structure of the middle at- 0.25. Then, the question of how often such instabilities mosphere, J. Geophys. Res., 88, 1379-1400, 1983. occur can be answered by evaluating the ratio of the num- Hamilton, K., Climatological statistics of stratospheric iner- ber of data which satisfy Ri < 0.25 to the total number of tia-gravity waves deduced from historical rocketsonde wind data in each altitude region. The probability of the occur- and temperature data, J. Geophys. Res., 96, 20,831-20,839, rence of shear or convective instability is calculated at each 1991. Holton, J. R., P. H. Haynes, M. E. McIntyre, A. R. Douglass, R. B. altitude (1 km step) by using data within 1 km altitude Rood, and L. Pfister, Stratosphere-troposphere exchange, Rev. span. Geophys., 33, 403-439, 1995. Figure 4a shows the probability of the occurrence of Lindzen, R. 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