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Characteristics of gravity waves revealed in high-resolution radiosonde observations at Pohang, Korea

In-Sun Song and Hye-Yeong Chun

Department of Atmospheric Sciences, Yonsei Univertisy, Seoul, Korea

FIGURES

Abstract

1. Introduction

     Vertically propagating gravity waves generated in the troposphere can transport their momentum and energy into the middle atmosphere. As gravity waves propagate vertically in the middle atmosphere, they experience the increase of their amplitudes due to the density decrease with the altitude. However, gravity wave saturation process generates turbulence field so that the atmosphere can not be dynamically or statically unstable due to the amplified gravity waves(Fritts 1984). Because gravity waves in the turbulence field can deposit their momentum and energy to the large-scale flow, the gravity waves can play an important role in the dynamics of the middle atmosphere.
     Lindzen (1981) theoretically investigated the interaction between zonal mean flow and turbulence field induced by wave saturation, and proposed a simple gravity wave parameterization scheme. Holton(1982) numerically simulated the zonal mean wind to be changed by the drag and diffusion of gravity wave with a specified phase speed. Since such theoretical and numerical studies showed that the gravity wave characteristic like phase speed distribution is essential for the realistic simulation of the large-scale mean flow in the middle atmosphere. There have been many attempts to observe several gravity wave characteristics, for example wave energy, dominant spatial and temporal scales of gravity waves, phase speed, propagation direction, and anisotropy using radiosonde, rocketsonde, radar, or lidar(e.g., Thompson 1978; Hirota and Niki 1985; Fritts et al. 1988; Kitamura and Hirota 1989; Hamilton 1991; Allen and Vincent 1995; Vincent et al. 1997; Guest et al. 2000). Kitamura and Hirota (1989) pointed out the importance of the subtropical jet as the source of inertia-gravity wave through the latitudinal(  $ 27^{\circ}$N -  $ 45^{\circ}$N ) distribution of inertia-gravity wave characteristics observed by daily rawinsonde observation in the lower stratosphere. Allen and Vincent (1995) investigated the latitudinal(  $ 12^{\circ}$S -  $ 68^{\circ}$S ) and vertical( 2 - 24 km ) distribution of gravity wave activity using sounding data observed at radiosonde stations of Austrian Bureau of Meteorology. Guest et al. (2000) studied the properties of inertia-gravity waves in the lower stratosphere, their seasonal variation, and the likely source of the inertia-gravity waves using high-resolution ozonesonde launched at Macquarie Island.
     In this study, several gravity wave characteristics are investigated using linear gravity wave theory and high-resolution rawinsonde data observed in Pohang, Korea during a year of 1998. The seasonal and vertical variations of the characteristics are also analyzed.

2. Observation and data analysis

     We used sounding data observed by Vaisala Digicora2 MW 15 rawinsonde in Pohang(  $ 120^{\circ}~ 23'$E,  $ 36^{\circ}~ 3'$N ), Korea during a year of 1998. The ascending rate of the balloon is approximately 50 - 60 $ m~s^{-1}$, and all the observation variables are recorded every 10 second. As a result, the vertical resolution of data is roughly 50 - 60 m. However, because the rawinsonde automatically smooth horizontal wind data using low-pass filter in order to reduce observational errors, the vertical resolution of horizontal wind data becomes approximately 500 m. For the convenience, all observed variables used in this study are interpolated into 50 m grids using cubic-splint method.
     Figure 1 shows time-height cross sections of monthly mean temperature and zonal wind observed at Pohang. In this figure we used sounding data that reached the higher altitude than 30 km. Temperature in the troposphere decreases rapidly with height, while temperature in the stratosphere increases slowly with height. The vertical lapse rate remains nearly constant in the stratosphere regardless of the change of season. This suggests that the static stability in the stratosphere is nearly constant during a year of 1998.  The jet stream in winter(January and December) are much stronger than that in summer(July, August). Figure 1b also shows the clear seasonal variation of zonal wind that the zonal wind in the winter stratosphere is generally westerly, while that in the summer stratosphere is easterly. However, it should be taken note that easterly wind regions are also observed near z = 33 km in January and November.

Figure 1. Time-height cross sections of monthly mean (a) temperature and (b) zonal wind. Contour intervals for temperature and zonal wind are 5 K and 5 $ m~s^{-1}$, respectively. The regions of easterly zonal wind are shaded in (b).
\includegraphics[scale=0.60]{fig01}

     For the analysis of gravity wave characteristics in the stratosphere and the troposphere, the temperature and wind profiles within 17 - 30 km and 2 - 9 km altitude ranges are used, respectively. The rapid changes of temperature and wind at the tropopause can be excluded in the data analysis using the two separated analysis regions. The sounding data observed at 00UTC and 12UTC are used except for July in which there were only 7 soundings that reached the higher altitude than 30 km at 00UTC and 12UTC. Accordingly, in July, the sounding data observed at 06UTC and 18UTC are also used in addition to 00UTC and 12UTC.
     To obtain gravity wave perturbation from temperature and wind profiles in the stratosphere and the troposphere, basic state profiles are estimated by fitting second order polynomial into sounding profile for individual variables, and perturbation profiles are calculated by removing the basic state profile from the each sounding profile.

3. Gravity wave characteristics

     For the analysis of the seasonal variation of gravity wave activity, monthly mean gravity wave energy densities, $ E_0$ and $ E_t$, are calculated in the stratosphere and the troposphere. $ E_0$ and $ E_t$ are given by

$\displaystyle E_0$ $\displaystyle =$ $\displaystyle \frac{g^2}{N^2} \frac{1}{B_0 C_{In} } \overline{ \bigg(\frac{T'}{\overline{T} } \bigg)^2 } ,$ (1)
$\displaystyle E_T$ $\displaystyle =$ $\displaystyle \frac{1}{2} \left[ \overline{u'^2} + \overline{v'^2} + \frac{ g^2}{N^2} \overline{ \bigg(\frac{T'}{\overline{T} } \bigg)^2 } \right] ,$ (2)

where $ B_0$ and $ C_{In}$ can be derived using three-dimensional gravity wave spectrum model suggested by Fritts and VanZandt (1993).
     Figure 2 shows time series of monthly mean $ E_t$ and $ E_0$ in the stratosphere and the troposphere. Although gravity wave energy $ E_0$ are derived in the vertically uniform basic state zonal wind and static stability, the magnitude and tendency of $ E_T$ and $ E_0$ in the stratosphere are almost the same. However, $ E_T$ is quite different from $ E_0$ in the troposphere. The similarity between $ E_T$ and $ E_0$ in the stratosphere suggests that the calculated perturbation variables in the stratosphere can be referred to as gravity wave perturbations.

Figure 2. Time series of monthly mean $ E_T$ and $ E_0$ in (a) the stratosphere and (b) the troposphere. In each panel, $ E_T$ and $ E_0$ are plotted with solid and dash lines, respectively.
\includegraphics[scale=0.60]{fig02}

     In the stratosphere, $ E_T$ is much larger in January and November than in the other months. The gravity wave activity in the stratosphere can be controlled by the basic state flow and the characteristics of wave sources. The stationary mountain waves can propagate vertically into the stratosphere in winter because they do not meet critical level for the zonal wind structure in the troposphere(Figure 1b). However, those stationary waves can not propagate into the stratosphere in summer because of the reversed zonal wind near the tropopause. For the summer zonal wind structure, non-stationary waves induced by convective storms may not propagate into the stratosphere, either. Thus the strong wave activity in the winter stratosphere can be determined by the combination of the above-mentioned wave sources and basic state flow conditions.
     In the atmosphere, there are many possible sources for gravity waves besides mountain and convection. Kitamura and Hirota(1989) showed the relevance of the subtropical jet to the wave activity through the anaysis of the propagation direction of waves. Their study suggests that the observed gravity waves in this study are generated near the subtropical jet region far away form Pohang. Accordingly, wave propagation characteristics should be estimated in order to precisely analyze the strong gravity wave activity in the winter stratosphere. However, the spectral characteristics and dominant spatial and temporal scales of gravity wave should be calculated in advance in order to estimate wave propagation characteristics.
     In this study, we calculated the power spectral densities of the normalized temperature as a function of the vertical wavenumber. Allen and Vincent (1995) fitted their model spectra into the monthly mean PSD to obtain several spectral characteristics of gravity waves. The model spectra used in Allen and Vincent is given by

$\displaystyle F(m) = F_0 \frac{ m/m_* }{ 1 + (m/m_* )^{t+1} },$ (3)

where $ m$ is vertical wavenumber( $ = 1/ \lambda_z $), $ m_*$ is the characteristic vertical wavenumber( $ = 1/{\lambda_z}_*$), and $ t$ is the log-scale spectral slope in the large vertical wavenumber region.
     The characteristic vertical wavenumber($ m_*$) indicates the dominant vertical scale in the observed gravity wave field because the gravity wave energy is concentrated near the vertical scale corresponding to $ m_*$ in the area-preserving form of PSD(not shown).  Yearly mean $ m_*$s are $ 2.29 \times 10^{-4}$(4.37 km) and $ 2.55 \times 10^{-4}$(3.92 km) in the stratosphere and the troposphere, respectively. The spectral slopes($ t$) of monthly mean PSDs in the large vertical wavenumber region are slightly less than -3 except for the stratospheric PSD in May, July, and August. Yearly mean $ t$ are 2.66 and 2.86 in the stratosphere and the troposphere, respectively.
     The intrinsic frequency and mean propagation direction of the wave are estimated using Stoke's parameter method(Eckermann and Vincent 1989) and Hilbert transform, and mean horizontal and vertical wavenumber are obtained assuming that the observed perturbation variables are due to inertia gravity waves. The monthly mean vertical wave lengths are about 2.94 km and 2.55 km in the stratosphere and the troposphere, respectively. The estimated monthly mean horizontal wave lengths are about 430.94 km and 96.59 km in the stratosphere and the troposphere, respectively. Thus it can be immediately seen that the horizontal scales of waves are, on average, 200 times as large as the vertical scales of waves in the stratosphere. The ratio of intrinsic frequency to inertia frequency ( $ = \hat{\omega} / f $) are about 2.26 with small seasonal variations in the stratosphere. The intrinsic phase speed and group velocity are written as

$\displaystyle \hat{c}_x = \frac{ \hat{\omega}}{\overline{k}} \cos \overline{\phi} \qquad \hat{c}_y = \frac{\hat{\omega}}{\overline{k}} \sin \overline{\phi} ,$ (4)
$\displaystyle c_{gx} \approx \overline{u} + \hat{c}_{x} \qquad c_{gy} \approx \overline{v} + \hat{c}_{y} ,$ (5)

where  $ \displaystyle \hat{\omega}$ is the intrinsic frequency,  $ \displaystyle \overline{k}$ is mean horizontal wavenumber, and  $ \displaystyle \overline{\phi}$ is mean propagation direction.
     Figure 3 shows the intrinsic phase velocity and group velocity vectors in the stratosphere in January and July. In the stratosphere, the mean direction of intrinsic phase velocities in winter is mainly toward the northwest, while that in summer is toward the northeast. That is, the observed gravity waves in the stratosphere have the anisotropic propagation characteristics. The monthly mean  $ {\hat{c}}_{ix}$s in the stratosphere show an interesting seasonal variation that there exist the negative $ {\hat{c}}_{ix}$ in winter, and positive in summer.  In the troposphere, however, the propagation characteristics do not have the anisotropy that exists in the stratosphere.

Figure 3. The intrinsic phase velocity and group velocity vectors in the stratosphere in January and July.
\includegraphics[scale=0.60]{fig04}

     The monthly mean $ c_{gx}$ shows the seasonal variation opposite to that of  $ {\hat{c}}_{ix}$ in the stratosphere. Thus we can see that the basic state wind significantly affects the dominant direction toward which the gravity wave energy propagates.
     In this study, because $ w'$ is not directly observed, the zonal and meridional momentum fluxes are indirectly estimated in order to examine the interaction between the observed gravity waves and the large-scale circulation. the zonal and meridional momentum fluxes are calculated using

$\displaystyle \overline{\rho} \overline{u' w'} = \frac{\overline{\omega} g}{N^2} \overline{ u' \hat{T}'_{+90} } \delta_- ( \overline{\omega} ),$ (6)
$\displaystyle \overline{\rho} \overline{v' w'} = \frac{\overline{\omega} g}{N^2} \overline{ v' \hat{T}'_{+90} } \delta_- ( \overline{\omega} ),$ (7)

where  $ \displaystyle \overline{\omega} $ is the spectral average value,  $ \hat{T}'_{+90}$ is the Hilber transformed normalized temperature perturbation, and  $ \displaystyle \delta_- (\omega)= 1 - \bigg\{ 1 - \bigg(\frac{f}{\omega} \bigg) \bigg\}$.

     From the monthly mean zonal and meridional momentum flux in the stratosphere, we can see a clear seasonal variation of zonal momentum flux. In the stratosphere, zonal momentum is transported downward in winter, while that is transported upward in summer.
     Because the intrinsic phase velocities in the winter stratosphere are mainly westward, the downward trasfer of the zonal momentum should be observed for the gravity waves that propagate their energy upward. Thus it is expected that the gravity waves will deposit their negative momentum to the large-scale flow, and accelerate the large-scale zonal flow westward in the region where the diffusion or breaking of the gravity waves exist. As a result, the easterly zonal mean flow in the winter stratosphere in January and November may be due to the deposition of gravity wave momentum to the large-scale zonal flow. Non-zero vertical gradient of zonal and meridional momentum flux in January and November can be clearly seen in the vertical profiles of monthly mean zonal and meridional momentum fluxes in the stratosphere. In January, the magnitude of the zonal momentum flux above z = 20.5 km decreases with the altitude, and approaches to zero above z = 28 km. In November, the magnitude of zonal momentum flux decrease rapidly with height in the altitude range between z = 19.5 km and 22 km. This vertical structure of the zonal momentum flux in the winter stratosphere indicates that the gravity waves can accelerate the large-scale zonal wind westward.

4. Summary

     We investigated the characteristics of gravity waves using the high-resolution rawinsonde data made at Pohang, Korea during a year of 1998.
     The seasonal gravity wave activities were examined though the calculation of mean gravity wave energy densities, $ E_0$ and $ E_T$. $ E_T$ was directly calculated from the observed perturbation. while $ E_0$ was estimated assuming the observed perturbations to be due to the gravity waves. In the stratosphere, $ E_T$ and $ E_0$ were almost the same in their magnitude and seasonal variation. This similarity suggests that the calculated perturbation variables in the stratosphere can be considered to be due to gravity waves. The strong gravity wave activity in the stratosphere appeared in January and November. Because the gravity wave activity depends on wave sources and mean flow conditions, further information on the wave sources was needed. In this study, the characteristics of wave sources were estimated through the caculation of the group velocity $ \vec{c}_g$ and intrinsic phase velocity  $ \vec{\hat{c}}_i$.
     Through the nonlinear fitting, we can estimate spatial scales of gravity wave.  The vertical gravity wave scales of 4.37 km and 3.92 km were dominant in the stratosphere and the troposphere, respectively. The spectral slopes were slightly less than -3 except for the stratospheric PSD in May, July, and August, and the spectral slopes in the stratosphere were usually less than those in the troposphere.
Mean intrinsic frequencies( $ \hat{\omega}$) of gravity waves were calculated using Stoke's parameter methods. In the stratosphere, the calculated  $ \hat{\omega}$s were about 2.26 times as large as the inertial frequency at Pohang, Korea, and any significant seasonal variation of  $ \hat{\omega}$ was not found.
     Mean horizontal scale of gravity waves was estimated using the dispersion relation for the inertia gravity waves, mean vertical wavelength in PSD, and the estimated intrinsic frequency. The aspect ratio of horizonal scale to vertial scale of gravity waves was about 200 in the stratosphere. This indicates that the observed wave motion is almost horizontal. That is, the large portion of wave energies can be explained by horizontal kinetic energy.
     The intrinsic phase velocities showed a clear seasonal variation in the stratosphere. Westward propagation was dominant in winter, while there exist a weak eastward progation in summer. For the gravity waves propagating their energy upward, such a anisotropy of the wave propagation in the stratosphere suggests that the downward and upward transfer of zonal momentum will be observed in winter and summer, respectively. As we expected, The momentum flux estimated in this study showed the seasonal variation similar to that of the intrinsic phase velocity. The significant vertical gradient of zonal momentum flux was seen in the stratosphere in January and November when the $ E_T$ and $ E_0$ were much stronger compared to those in the other months. Thus the revesal of zonal wind near z = 33 km in January and November is thought to be greatly associated with the activity of gravity waves and the vertical structure of zonal momentum flux.

5. References

Allen, S. J., and R. A. Vincent, 1995: Gravity wave activity in the lower atmosphere: Seasonal and latitudinal variations. J. Geophys. Res.,100, 1327-1350.

Eckermann, S. D., and R. A. Vincent, 1989: Falling sphere observations of anisotropic gravity wave motions in the upper stratosphere over Australia. Pure Appl. Geophys., 130, 509-532.

Fritts, D. C., 1984: Gravity wave saturation in the middle atmosphere: A review of theory and observations. Rev. Geophys. Space Phys.,22, 275-308.

Fritts, D. C., T. Tsuda, T. Sato, S. Fukao, and S. Kato, 1988: Observational evidence of a saturated gravity wave spectrum in the troposphere and lower stratosphere. J. Atmos. Sci., 45, 1741-1759.

Fritts, D. C., and T. E. VanZandt, 1993: Spectral estimates of gravity wave energy and momentum fluxes. Part I: Energy dissipation, acceleration, and constraints. J. Atmos. Sci., 50, 3685-3694.

Guest, F. M., M. J. Reeder, C. J. Marks, and D. J. Karoly, 2000: Inertia-gravity waves obsered in the lower stratosphere over Macquarie island. J. Atmos. Sci., 57, 737-752.

Hamilton, K., 1991: Climatological statistics of stratospheric inertia-gravity waves deduced from historical rocketsonde wind and temperature data. J. Geophys. Res., 96, 20831-20839.

Hirota, I., and Niki T., 1985: A statistical study of inertia-gravity waves in the middle atmosphere. J. Meteor. Soc. Japan, 63, 1055-1066.

Holton, J. R., 1982: The role of gravity wave induced drag and diffusion in the momentum budget of the mesosphere. J. Atmos. Sci., 39, 791-799.

Kitamura, Y., and I. Hirota, 1989: Small-scale disturbances in the lower stratosphere revealed by daily rawin sonde observations. J. Meteor. Soc. Japan, 67, 817-831.

Lindzen, R. S., 1981: Turbulence and stress owing to gravity wave and tidal breakdown. J. Geophys. Res., 86, 9707-9714.

Thompson, R. O. R. Y., 1978: Observation of inertial waves in the stratosphere. Quart. J. Roy. Meteor. Soc., 104, 691-698.

Vincent, R. A., S. J. Allen, and S. D. Eckermann, 1997: Gravity wave parameters in the lower stratosphere. Gravity Wave Processes: Their Parameterization in Global Climate Models Springer-Verlag, 404pp.

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