NOTES AND CORRESPONDENCE On the Geostrophic Balance of ...

Journal of the Meteorological Society of Japan, Vol. 78, No. 5, pp. 683-688, 2000 683

NOTES AND CORRESPONDENCE

On the Geostrophic Balance of Mean Zonal Winds in the Mesosphere

and Lower Thermosphere

By Saburo Miyahara, Daisuke Yamamoto and Yasunobu Miyoshi

Department of Earth and Planetary Sciences, Kyushu University, Fukuoka, Japan

(Manuscript received 7 September 1999, in revised form 10 July 2000)

1. Introduction

It is well known in dynamic meteorology that the tonally averaged meridional momentum equation can be accurately approximated by the geostrophic balance, or by the gradient-wind balance if the cur-vature of the Earth is considered, except for the equatorial region (e.g., Andrews, Holton and Leovy 1987). Based on this fact, mean zonal thermal winds can be calculated from an observed zonal mean tem-perature distribution using the thermal wind rela-tion to infer a mean zonal wind distribution. The calculated mean zonal wind distribution is consid-ered to be a good approximation of unknown, not directly observed, actual mean zonal wind distribu-tion, if deviations from the geostrophic balance or gradient-wind balance are small.

It is shown by Lieberman (1999) that the gradient wind calculated using. HRDI observed temperature data captures the essential features of the HRDI ob-served mean zonal wind field in the summer middle latitudes in the lower thermosphere, while the con-sistency between them diminishes at tropical lati-tudes due to tidal contamination of the sampled ob-served data, and it is also suggested that gravity wave, tidal wave, and planetary wave eddy-forcing cannot be neglected in the zonally averaged merid-ional momentum equation.

In this short note the balance in the Mesosphere and Lower Thermosphere (referred as MLT) region is examined, using the output data of the middle atmosphere circulation model at Kyushu University (referred as MACMKU), in which the tidal contam-ination is completely removed in contrast to the HRDI data. It is shown that the balance is not in a

good approximation in the MLT region.

2. Results and discussions

MACMKU is a general circulation model cov-ering atmospheric layers from the ground through the lower thermosphere (ca. 150km). The detailed model description is found in Miyahara et al. (1993), and some recent revisions are found in Miyahara and Miyoshi (1997) and Miyahara et al. (1999). In this analysis one-month data for the perpetual equinox condition is used. Figure 1 shows the latitude-height cross section

of mean zonal wind averaged over one month. The magnitudes of the westerlies, especially the weak mesopause winds, are in agreement with those in the real atmosphere (e.g., CIRA: 861). Above the mesopause region easterlies of the order of 20ms-1 exist, which are consistent with the results obtained from LIARS observations (e.g., McLandress et al. 1996). To examine the accuracy of the gradient-wind balance for this wind distribution, each term of the gradient-wind balance equation and the devi-ation from the gradient-wind balance are calculated. Figure 2 shows the latitude-height cross section of the deviation S that is defined by

1au2tanq5 b=-2fusinq-a-a, (1)

where the notations are conventional. Apart from above 110km where other physical factors such as ion drags and molecular viscosity are playing important role, there are two regions around the stratopause (50 to 60km) and the lower thermo-sphere (90 to 110km) where systematic deviation

Corresponding author: Saburo Miyahara, Department of Earth and Planetary Sciences, Faculty of Science, Kyushu University, Hakozaki, Fukuoka 812-8581, Japan. E-mail: [email protected]

(C) 2000, Meteorological Society of Japan

1 The mean zonal wind of CIRA: 86 is calculated from tem-

perature data assuming the gradient-wind balance, which is not correct in the lower thermosphere as will be shown in the present note. However, overall distribution mentioned here is not greatly affected by the unbalance.

684 Journal of the Meteorological Society of Japan Vol. 78, No. 5

exists. To see the relative magnitude of each term of (1) and the deviation at these heights, the latitu-dinal distributions of each term and b at 60km and 90km are shown in Figs. 3a, and 3b, respectively. It is found that the Coriolis force and the pressure gradient force have a tendency to balance each other for all latitude regions at 60km height. The mag-nitude of centrifugal force is less than 30% even in the highest latitude regions in both hemispheres. The deviation 6 is much smaller than the Coriolis force and the pressure gradient force at almost all the latitudes, except for the latitude region higher than 40 degrees north, where the deviation is still small but not negligible. In contrast to the 60km height, the pressure gradient force at 90km height has a tendency to balance with the Coriolis force only in the latitude region higher than 40 degrees in the northern hemisphere, and higher than 30 de-grees in the southern hemisphere. The deviation S becomes remarkable less than 50 degrees indicating the geostrophic balance (centrifugal force is negligi-ble at this height) is violated. It is notable that the pressure gradient force and the Coriolis force have the same direction at some latitudes less than 40 de-grees. The pressure gradient force has no counter-part to balance with in the region lower than 20 de-grees, and the deviation S almost coincides with the pressure gradient force. To find the cause of the deviation from the

gradient-wind balance, rectified eddy-forcing (diver-gence of the Reynolds stress) in the tonal mean meridional momentum equation, which is given by

1av'v'tantanav'w' Fv=-u'u'+vw'- (2) aaqaaap

is calculated, and the latitude-height cross section is shown in Fig. 4, where u', v', and w' denote east-ward, northward velocities, and vertical p-velocity disturbances, respectively. It is obvious that the eddy-forcing term has a tendency to balance system-atically with the deviation from the gradient-wind balance shown in Fig. 2. In Fig. 5, the latitudinal distributions of these two terms at 90km are shown to see the balance more clearly. It is found that these two terms have a tendency to balance each other at all latitude regions. This result shows that the meridional eddy-forcing term is playing an im-portant role in the zonal mean meridional momen-tum equation at this height region, in contrast to the case of lower atmosphere (e.g., Andrews, Holton, and Leovy 1987). The main disturbance which produces the eddy-

forcing at this height of the present model is the migrating diurnal tide, which is the dominant wave motion in the MLT region of the present model (Miyahara and Miyoshi 1997; Miyahara et al. 1999). The importance of the diurnal tide dissipation in the MLT region dynamics is pointed out based on

Fig. 1. Latitude-height cross section of mean

tonal wind averaged over 30 days. Solid

lines show westerlies, and dotted lines

show easterlies. The unit is ms-1. Con-

tour interval is 10ms-1.

Fig. 2. Latitude-height cross section of

the deviation from the gradient-wind bal-

ance. Solid and dotted lines show posi-

tive and negative deviations, respectively.

The unit is ms-2. Contour interval is

2.0x10-4ms-2.

October 2000 S. Miyahara, D. Yamamoto, and Y. Miyoshi 685

Fig. 3a. Latitudinal distributions of Cori- olis force (dotted line), pressure gradient force (dashed line), centrifugal force (Solid line), and total (dash-dotted line), at 59.65km. The unit is ms-2.

Fig. 3b. As in Fig. 3a., except for the distri-

butions at 90.53km.

Fig. 4. Latitude-height cross section of mean

meridional eddy-forcing. Solid and dot-

ted lines show positive and negative de-

viations, respectively. The unit is ms-2.

Contour interval is 2.0x10-4 ms-2.

Fig. 5. Latitudinal distributions of mean meridional eddy-forcing (dash-dotted line), deviation from the gradient-wind balance (dashed line), and the difference of these two terms (solid line). The unit is ms-2.


the WINDII observations (e.g., Fauliot et al. 1997), and empirical wind model (Miyahara et al. 1991). The importance is predicted by Miyahara (1978a, b), Miyahara (1984), and Miyahara and Wu (1989) using quasi-nonlinear tide/mean inds interaction models. However, all these are related to the zonal momentum balance but not to the meridional mo-mentum balance.

In the same papers, Miyahara (1978a,b), Miyahara (1984), and Miyahara and Wu (1989) ob-tained the similar latitude-height distribution of the meridional eddy-forcing due to the migrating diur-nal tide in the MLT region. They did not stress the importance of the eddy-forcing term due to the diurnal tide in the meridional momentum equation, but it was simply mentioned in the same paper by Miyahara (1978a,b). As mentioned above, the main disturbance in the

present model, which produces the eddy-forcing at the MLT region, is the diurnal tide. On the other hand, it is known that tonal momentum flux associ-ated with internal gravity waves play an important role in the MLT region (e.g., Andrews, Holton, and Leovy 1987). It is reported that the meridionally propagating internal gravity waves are frequently observed in the mesosphere (e.g., Namboothiri et al. 1996; Taylor et al. 1997; Vincent and Fritts 1987). This suggests that the meridional momentum flux may play an important role as the zonal momentum flux. The present GCM is a low horizontal resolu-tion model (truncated at zonal wavenumber 21), so that the description of internal gravity waves in the model is insufficient. If any high horizontal resolu-tion model, which has the ability to resolute gravity waves, were used, meridional momentum flux asso-ciated with internal gravity waves would possibly play an important role, and the distribution of the deviation from the gradient-wind balance would be possibly changed. Lieberman (1999) showed the violence of the

gradient-wind balance in the lower thermosphere using HRDI data particularly due to substantial tidal contamination caused by a daytime only sam-pling. In the present analysis the tidal contamina-tion is completely removed, and the effect of tide due to the meridional eddy-forcing term is not spu-rious but substantial. The remaining unbalanced quantity shown in Fig. 5 might be attributable to mean meridional advection term, eddy dissipation term, and time derivative of mean meridional wind. As the present analysis is based on the perpetual equinox data, some readers might think that the ef-fects of time derivative are not correctly reflected in the present analysis. However, even though an extremely strong time derivative 10ms/month (about 4x10-6ms-2) exists, the value is more than one order smaller than the remaining amount. Contributions of the mean meridional advection and

eddy dissipation terms will be discussed in a sepa-rate paper. The disturbance, which produces the eddy-forcing at 50 to 60km heights in the northern hemisphere, is a stationary planetary wave having zonal wavenum-ber one propagated from the troposphere. The am-plitude of the geopotential height associated with the stationary planetary wave in the model is about 1000m at the stratopause region. Although the sim-ulation is done for the equinox condition, the simu-lated amplitude is comparable to the observed am-plitude in the midwinter northern hemisphere (e.g., CIRA: 86). This overestimation of the wave ampli-tude is due to the unrealistically strong mean zonal wind in the northern hemisphere (see, Fig. 1), which is comparable to the real zonal wind distribution in the midwinter. The perpetual equinox condition is a cause of the strong westerly in the model. How-ever, the present results suggest that the deviation from the gradient-wind balance in the midwinter in the real atmosphere would be the same order as the present results. The winter time balance in a sea-sonal march model is now under investigation, and the result will be published in a separate paper. As usually done, tonal mean winds are calculated

using the zonal mean temperature distributions ob-tained by the MACMKU, assuming the thermal wind relation,

2Ilsinq5+utanau1101 (3) n71nr

where R is the gas constant for dry air. (3) is solved iteratively taking the lower boundary value of tonal mean winds at about 12km height of the model out-put. Figs. 6a and 6b shows the latitude-height cross section of the calculated winds and the difference from the simulated winds (Fig. 1), respectively. As shown in these Figs., even in the higher than 20 de-grees, significant deviations (more than 12ms-1) from the actual mean zonal winds are found in the lower thermosphere and around the stratopause in the northern hemisphere. These deviations are of course due to the effects of eddy-forcing terms.

It is noteworthy that even though the deviation from the gradient-wind balance is small enough as in the case of the stratopause of the present model result, the thermal wind could be considerably dif-ferent from the actual mean winds. If the devia-tion is systematic and not random, the difference is accumulated with the vertical integration, and the resulting difference could be remarkable.

3. Concluding remarks

In this short report, we have shown the im-portance of the eddy-forcing term in the zonally averaged meridional momentum equation, which brakes the geostrophic balance or gradient wind bal-ance in the MLT region, using the output data of

October 2000 S. Miyahara, D. Yamamoto, and Y. Miyoshi 687

Fig. 6a. Latitude-height cross section of thermal wind. Lower boundary condition of the thermal wind is given at 12km, and the boundary value is taken from the model output (Fig. 1). The unit is ms-1.

Contour interval is 10ms-1.

Fig. 6b. Latitude-height cross section of the difference between the simulated mean zonal wind and the

thermal wind. The unit is ms-1. Contour interval is 5ms-1.


MACMKU. This result is incompatible with the meteorological knowledge that the zonally aver-aged meridional momentum equation can be ac-curately approximated by the geostrophic balance or gradient-wind balance. If it is the case in the real atmosphere, we must be cautious to estimate a mean zonal winds distribution from an observed tonal mean temperature distribution using the ther-mal wind relation.

Acknowledgments

The figures were produced by GFD-DENNOU Li-brary. This research was partly supported by a Grant-in-Aid for Scientific Research (B) 05452079 of the Ministry of Education, Science and Culture, Japan.

References

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中間圏下部熱圏帯状平均東西風の地衡風平衡について

宮原三郎・山本大介・三好勉信

(九州大学大学院地球惑星科学)

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