Atmospheric Tides Appearing in a Global Atmospheric ...

June 1987 T. Tokioka and I . Yagai 423

Atmospheric Tides Appearing in a Global Atmospheric General Circulation Model

By Tatsushi Tokioka and Isamu Yagai

Meteorological Research Institute, Tsukuba, Ibaraki 305, Japan

(Manuscript received 3 December 1986, in revised form 20 April 1987)

Abstract

Atmospheric tides induced in a global atmospheric general circulation model in January are

analyzed. The model produces detailed structure in the thermal forcings of diurnal and semi-diurnal

modes within the planetary boundary layer (PBL) in the subtropics and within the mid-troposphere

in the tropics. Compared with the forcings by Forbes (1982a, b), the model gives larger ones in the lower part of the troposphere for both modes. The thermal forcings of diurnal and semi-diurnal tides

within the stratosphere roughly agree with the forcings by Forbes (1982a, b).

The model produces tidal forcings other than the migrating tides, such as (*=-1, m=5), (*=1,

m=3), (*=-1, m=9), (*=1, m=1),*, where * is the frequency in day-1 and m is the zonal wavenum-

ber. Such non-migrating modes* have large thermal forcings within the PBL and the mid-troposphere

in the tropics. Strong diurnal heating over land in low latitudes essentially forces them.

1. Introduction

Despite progress in the theoretical study of atmospheric tides, the detailed structure of the thermal forcings of the atmospheric tides is still not clear. Because of complicated distributions of land and sea, topography, sea-ice, sea surface temperature, ground temperature and ground wetness, the thermal forcings of the atmospheric tides realized in a model are expected to yield detailed structures hitherto uncovered.

Tokioka and Yagai (1984) found a dominant non-migrating tidal mode in a global general circulation model (the Meteorological Research Institute (MRI) GCM-I). The zonal wavenumber

(m) of the non-migrating mode is five and the mode propagates westward with the frequency

(f) of 1 day-1. Kato, Tsuda and Watanabe (1982) studied characteristics of non-migrating atmos-pheric tides forced by hypothetical localized heating near the equator and found that the resultant perturbations have generally fairly short

*We use this term to indicate tidal modes other than

migrating modes which move in synchrony with the

sun.

©1987 Meteorological Society of Japan

vertical wavelengths around 10km. Their solu-tions, however, do not explain the dominance of the (*=-1, m=5) mode over the possible non-migrating modes. Tokioka and Yagai (1984)

pointed out that the actual land-sea distributions in low latitudes selectively force the (*=-1, m=5) mode.

In Tokioka and Yagai (1984), thermal forc-ings of atmospheric tides are described very briefly. This paper supplements details of the at-mospheric tides realized in the MRI.GCM-I in-cluding those of (*=-1, m=5). An outline of the model is described in section 2. The thermal forc-ings of the atmospheric tides are presented in section 3. As the model is not designed for simulating atmospheric tides, the vertical resolu-tion of the model is too coarse, and the top of the model is too low, to describe tidal motions. Therefore tidal motions realized in the model in-clude unsatisfactory features for vertically prop-agating modes. The description of the motion fields is covered very briefly in section 4.

2. An outline of the model and the analyses

2.1 The model The model used in the present experiment was

424 Journal of the Meteorological Society of Japan Vol. 65, No. 3

developed at the Meteorological Research Insti-tute (MRI) and is described by Tokioka et al.

(1984). Governing equations are approximated by a finite differencing method in both the hori-zontal and the vertical directions. A modified

*-coordinate, *=(p-pI)/*p, is used in the vertical direction, where p is the pressure and pI the pres-sure near the tropopause (=100mb). *p is de-fined as

where ps and pt are pressures at the surface and the top of the model, respectively. The top is located at 1mb. The model atmosphere is di-vided into twelve layers in the vertical direction as shown in Fig. 1. The vertical levels above p=pI are located at equal intervals in in p after Toki-oka (1978) to simulate dispersion relations reasonably. The Arakawa C grid scheme (Ara-kawa and Lamb, 1977) is used with a horizontal resolution of 5* by 4* in the longitudinal and the latitudinal directions, respectively.

The model uses Katayama's parameterization

(1972) of radiation modified by Schlesinger (Arakawa and Mintz, 1974). Ozone is predicted based on a simplified photochemical model by Schlesinger and Mintz (1979), and the predicted amount is used for the calculation of radiative heating rate. Predicted amounts of water vapor and cloud are also used in the calculation as well

as the prescribed amount of carbon dioxide. The dry convective adjustment, middle level convec-tion and penetrative cumulus parameterization by Arakawa and Schubert (1974) are used for

parameterizing convective processes. Surface fluxes of sensible heat, water vapor and momen-tum are computed by the bulk method with the transfer coefficient proposed by Deardorff

(1972). Ground temperature, snow depth and ground wetness are predicted by considering ground thermodynamics and hydrology after Katayama (1972).

The present model simulates diurnal cycles of the planetary boundary layer (PBL) well qualita-tively (Tokioka et al., 1984). Therefore, tidal forcings of thermal origin realized in the present model with a realistic geography and topography may give us useful information on atmospheric tides in the actual atmosphere. The January per-formance of the present model is described in Tokioka and Yagai (1984).

2.2 Data The data used for the analyses are taken from

January in an annual march simulation. The data are sampled in every six hours throughout one month. For particular two days, they are sam-

pled in every one hour.

2.3 Analyses We adopted a very simple way of extracting

tidal modes from a dataset sampled in every six hours. At first, data of the same time of day are averaged over a month and the monthly mean values are subtracted from them. Let us denote such data as aL, where L is the Greenwich Stand-ard Time and takes values of either 00, 06, 12 or 18. We know that tidal modes include a west-ward propagating diurnal mode of the zonal wavenumber one (*=-1, m=1), and a westward

propagating semi-diurnal mode of the zonal wavenumber two (*=-2, m=2). In the present model an eastward propagting diurnal mode of the zonal wavenumber one (*=1, m=1) is also found. Therefore we introduce the following filtering operator;

Fig. 1. Location of vertical levels in the present experi-

ment.

June 1987 T. Tokioka and I. Yagai 425

Table 1. Perfect response pair of the zonal wavenumber "m" and frequency "f" (day-1) to the filter-

ing operator b1, b2 and b3. The perfect response pair (m, f) to the operator bi (i=1, 2, 3) is marked with bi.

aL(i) indicates the value of aL at the longitudinal

grid point "i". As the longitudinal grid size is 5*, "i" varies from 1 to 72. The response character-istics of b1 is

where i is an imaginary unit. The filter b1 elimi-nates (*=-2, m=2) and (*=1, m=1) modes. The response characteristics of b2 and b3 are

The filter b2 eliminates (*=-1, m=1) and the filter b3 eliminates (*=-1, m=1) and (*=-2, m= 2). The perfect response pairs (*, m) to the filter-ing b1, b2 and b3 are marked with b1, b2 and b3 in Table 1, respectively. For example, b1 (a) in-cludes not only (*=-1, m=1) but also (*=3, m=1), (*=l, m=3), (*=-1, m=5),* Modes with a different zonal wavenumber are separated further by a Fourier decomposition of b1 (a) in the longi-tudinal direction. The m=1 component of b1(a), for example, includes all oscillations of *=-1+4n

(n=0, *1, *2, ... ). Each mode can be separated with the help of special data sampled every hour. Fortunately, we confirmed that the Fourier de-composition of bl(a) (l=1, 2, 3) in the longitudi-nal direction is enough, in practice, to isolate a single dominant mode (*, m).

3. Thermal forcing of atmospheric tides

Thermal forcing of atmospheric tides has been estimated by many workers to investigate excited tidal motions. Tidal motions synchronous with the movement of the sun are often called "mi-

grating modes". The forcings estimated so far are those of migrating modes, such as (*=-1, m= 1), (*=-2, m=2) and (*=-3, m=3). Recently, Forbes and Garret (1978) and Walterscheid and Derome (1981) have presented improved heating rates of the migrating modes compared with those described in Chapman and Lindzen (1970). One of the purposes of this section is to compare the thermal forcings of the migrating modes realized in the model atmosphere with those esti-mated so far which are based on the climatologi-cal distribution of ozone and water vapor.

The present model includes realistic surface boundary conditions. As the surface conditions, such as the land-sea distribution, topography, snow coverage, sea-ice distribution, are com-

plicated, the present model includes thermal tidal forcings other than those of migrating modes

(Tokioka and Yagai, 1984). Here the character-istics of the non-migrating mode heating as well as those of the migrating ones are given in detail.

Figures 2(a) and (b) show the power spectra of the heating rate in the space-time domain at 2*S at 700mb and 5.18mb, respectively. As the analysis is based on data sampled every six hours, high frequency modes over |*|=2 are not covered. In Fig. 2(a) there are four peaks at |*|=1, i.e., (*= -1 , m=1), (*=-1, m=5), (*=-l, m=9) and (*=1, m=3) besides low frequency powers. At 5.18mb and |*|=1, we notice spectral peaks at (*=*l, m= 1), (*=-l, m=5) and (*=1, m=3). At this level.


Fig. 2. The power spectra of the heating rate in the space-time domain at (a) 7 00mb, 2*S and (b) 5.18mb and 2*S. The data used for the analysis are

sampled every 6 hours for a month. Units are (0.1K day-1 )2 day. Areas over

10 in these units are shaded. The abscissa indicates frequency in day-1 and

the ordinate the zonal wavenumber.

Fig. 3. The same quantities as in Fig. 2 but for the data sampled every one hour for two days. (a) 700mb,

2*S and (b) 5.18mb and 2*S.

relative powers in the low frequency range to those at |*|=1 are reduced from those at 700mb.

Figures 3(a) and (b) show the same quantities as in Fig. 2 but for the data sampled every one hour for two days to cover frequency ranges up to |*|=12. At 700mb, significant power peaks are not found in the range higher than |*|=2. At 5.18mb powers are found mostly for the migrat-ing tidal modes.

3.1 Diurnal mode heating The amplitude of the diurnal mode heating

rate is shown in Fig. 4 in the latitude-height domain. There are major heating regions both in

Fig. 4. The amplitude distribution of diurnal mode heating (*=-1, m=1) in the latitude-height domain.

Units are 1K day-1. Areas over 10 in this unit are shaded.

the troposphere and the stratosphere. In the troposphere major heating is found near the sur-face boundary (within the PBL) at 20*N and 25*S. Another maximum of the PBL heating is found along the periphery of Antarctica. These maxima are closely related to the dominant diur-nal heating variation within the PBL over land. This feature is quite different from the heating adopted in the theoretical calculations summa-rized in Chapman and Lindzen (1970). A sec-ondary peak is found over the equatorial region around 400mb, this is due to penetrative cumu-


lus convection. The important role of the latent heat release by cumulonimbi in the atmospheric tides is stressed by Hamilton (1981), who no-ticed a significant diurnal component in rainfall variation (over the low latitude continents). In the stratosphere, the heating structure in the lati-tudinal direction is simpler than that in the tro-

posphere. There is one maximum heating latitude at each level, although it is shifted in the summer hemisphere. The horizontal distribution of the heating rate at 06Z is shown in Fig. 5(a) and (b) at both 900 mb and 5.18mb. The maximum heating occurs at noon at 5.18mb except near the North Pole regions. The maximum value is about 7K/day and occurs at 20*S. At 900mb, the time of the maximum heating occurs about one hour after noon. There are three peaks in the subtropics and the greatest of them being found at 16*N. At other levels in the troposphere, the time of the maximum heating is close to that at 900mb.

Usually the heating function is expanded into Hough tidal components. Figure 6 shows the ver-tical distribution of the expanded coefficient of the diurnal mode heating. The heating functions are decomposed into each Hough component in the same way as was done in Forbes (1982a). Each component is multiplied by a factor e-*/2,

where *=-ln(p/p0) and p0=l000mb. The co-efficients estimated by Forbes (1982a) are also shown in the same figure with thin lines. Rough-ly speaking, the coefficient of each Hough diur-nal component agrees well with Forbes (1982a)' above 10km. This suggests indirectly that the ozone photochemistry adopted in the present model describes the diurnal variation of ozone reasonably well. Below 10km, we find two peaks in each Hough coefficient, one near the surface and the other near the 7 to 8km level. The former is due to the heating within the PBL and the latter to the penetrative cumulus heating. Compared with Forbes (1982)', the present model gives stronger forcing below 10km. Very large differences are found in the (1,1), (1,3) and

(1,-2) Hough components, especially below 2 km. These differences have to be clarified further in future. The negative antisymmetric compo-nent (1,-1) indicates that the Northern Hemi-sphere (NH) is less heated than the Southern Hemisphere (SH). The agreement of the coeffi-

Fig. 5. The horizontal distribution of the heating rate

of (*=-1, m=1) at 06Z at (a) 900mb and (b) 5.18

mb. Contour interval is 0.2K day-1. Negative areas

are shaded.

Fig. 6. The vertical distribution of the coefficients of Hough tidal components as defined in Forbes

(1982a). The notation of Hough components also follows him. Thin lines correspond to the results of

Forbes (1982a). Each component is multiplied by the pressure factor e-x/2, where x=-1 n(p/p0) and

p0=1000mb.

cient of (1,-1) is fairly good throughout the atmosphere.

428 Journal of the Meteorological Society of Japan Vol . 65, No. 3

3.2 Semi-diurnal mode heating Figure 7 shows the latitude-height distribution

of the amplitude of the semi-diurnal mode heat-ing. Characteristic profiles of the heating in the troposphere are similar to those in Fig. 4. There are two maxima in the PBL in the subtropics and a maximum in the mid-troposphere of the equa-torial latitudes. In the stratosphere, it is interest-ing to note that the maximum heating latitude both in the lower stratosphere and above 40km lies not in the SH but in the NH.

Figures 8(a) and (b) show the horizontal dis-tribution of the heating rate at both 900mb and 5.18mb. At 900mb the maximum around 20*N occurs close to noon (mid-night). In the SH, the maximum precedes noon (mid-night) by an hour. The maximum is about 0.8K/day at 20*N. At 5.18mb, the maximum occurs about a half hour before noon between 60*S and 65*N.

Figure 9 shows the same quantities as in Fig. 6 but for the semi-diurnal component. The mod-el heating functions (thick lines) roughly agree with those of Forbes (1982b)' (thin lines). How-ever, the model gives larger heating in the tropo-sphere than Forbes (1982b)' especially near the surface. On the other hand, the mode (2,2) gives less heating in the model upper stratosphere than Forbes (1982b)'. The antisymmetric heating with respect to the equator is represented by the modes (2,3), (2,5),* The positive coefficient of (2,3) indicates more heating in the NH than in the SH at noon (mid-night).

Fig. 8. The same as in Fig. 5 but for the semi-diurnal

mode heating (*=-2, m=2).

Fig. 9. The same as in Fig. 6 but for the semi-diurnal

mode heating (*=-2, m=2).

Fig. 7. The amplitude distribution of semi-diurnal

mode heating (*=-2, m=2) in the latitude-height

domain. Units are 0.1K day-1. Areas over 10 in this

unit are shaded.

3.3 Non-migrating mode heating In Figs. 2 and 3, we already pointed out

power peaks at (*=-1, m=5), (*=1, m=3), (*=1, m=5), ... , besides the migrating tidal modes. In order to make clear the causes of those non-migrating modes, a hypothetical heating model is considered, where heating occurs only over sunlit parts of the continents in proportion to the co-sine of the solar zenith angle, with the maximum


Fig. 10. The same as in Fig. 2 but for the hypothetical heating where heating

occurs only over sunlit parts of the continents in proportion to the cosine

of the solar zenith angle with the maximum set to unit. The heating rate be-

tween 30*S and 20*S is averaged latitudinally.

Fig. 11. The same as in Fig. 5 but for the mode (*=-1, m=5).

heating set to unity. Figure 10 shows the power spectra of the hypothetical heating averaged be-tween 20*N and 30*S. The spectral peaks found in Fig. 10 correspond well with those in Figs. 2 and 3. There is a clear peak at (*=-l, m=5) and

(*=1, m=3) and a weak peak at (*=1, m=5). This suggests strongly that those components are forced by the heating over low latitude conti-nents under the present land-sea configuration. Similar hypothetical heating averaged between 20*S and 20*N produces peaks of non-migrating


modes at (*=-1, m=5), (*=1, m=3) and (*=-l, m=2). Mathematical reasoning for the occurrence of non-migrating modes is presented in the Ap-

pendix. The horizontal distribution of the heating rate of the mode (*=-1, m=5) at 900mb and 06Z is shown in Fig. 11. The phase in the subtropics of the NH precedes that in the subtropics of the SH due to the present land-sea configurations. Fur-ther details on this are also found in the Appen-dix. The maximum heating rate is about 1.2K/ day at 14*S. The heating rate at 5.18mb is less than 0.2K/day. The major forcing of this mode is in the low latitude troposphere. This is con-firmed more celarly in Fig. l2,where the latitude-height distribution of the amplitude of (*=-1, m=5) mode heating is shown. Most heating is confined to low latitudes in the troposphere. This again suggests that this mode is forced by heating originating from the land-sea distribution


in low latitudes. The horizontal distribution of the heating rate

of (*=1, m=3) at 900mb, 06Z is shown in Fig. 13. Latitudinal phase tilt in low latitudes resem-bles that of (*=-1, m=5). The maximum heating rate is 1.4K/day at 26*S and 14*S. The maxi-mum heating rate at 5.18mb (not shown) is about 0.2K/day. The latitude-height distribution of the heating amplitude of (*=1, m=3) has simi-lar characteristics to those in Fig. 12.

Fig. 13. The same as in Fig. 5 but for the mode (*=l, m=3).

Fig. 14. (a) The horizontal map of wind and geopotential filed of (*=-1, m= 1) at 06Z and 5.18mb. The contour interval is 20gpm, and negative areas

are shaded. (b) The horizontal wind of (*=-1, m=1) at the December sol- stice, 36.378km and 06Z reproduced from the table by Forbes (1982). Aso (Radio Atmospheric Science Center, Kyoto Univ.) made this figure and permitted its use.


Fig. 15. The same as in Fig. 14(a) but for 900mb. The contour interval of

geopotential is 2.5gpm.

4. Tidal mode structure

4.1 Migrating mode The horizontal map of wind and geopotential

field of (*=-1, m=1) at 06Z and 5.18mb is shown in Fig. 14 together with the wind field obtained by Forbes (1982a)*. In the regions equatorward of 30* latitude, vertically propagat-ing modes, especially the Bough mode (1,1), are dominant. In those regions correspondence be-tween the model results and Forbes (1982a)' is poor. The present model has failed to describe internal modes well probably due to the upper boundary condition and also due to the coarse vertical resolution. The sponge term is included in the highest level to eliminate artificial wave reflection at the upper boundary. Although the model works well when only a single mode is

present (see Chapter 2 of Tokioka et al. (1984)), artificial reflections of waves are not suppressed well in the realistic situation. This is confirmed by examining the vertical distribution of phase in the equatorial regions. Another type of error could be due to the omission of thermal forcings in the mesosphere and above. Forcings in those regions influence motions below the stratopause level, especially through internal modes. In the

*Dr . T. Aso of Radio Atmospheric Science Center, Kyoto Univ., did the authors the courtesy of drawing

the map based on the data by Forbes (1982a) .

region poleward of 60*, the wind pattern of the model agrees with Forbes (1982a)'. In those regions, the vertically evanescent diurnal modes with negative equivalent depth dominate (Kato, 1966; Lindzen, 1966).

Figure 15 shows the same quantities as in Fig. 14 (a) but for 900mb, winds are dominant in the subtropics of the SB. The amplitude of geo-

potential height is confined near the equator and the maximum is about 5.2gpm. The amplitude may be compared with the observed surface pres-sure amplitude of 0.593mb by Haurwitz (1965), although the phase lags behind the observation by 100min.

The vertical distribution of the ampltide and phase of meridional wind are compared with the observed (Reed et al., 1969) and theoretical

(Lindzen, 1967; Forbes, 1982a) values at 61*N and 30*N (Fig. 16). The observed values are based on the analyses of meteorological rocket observations for 9 years. White circles indicate model values in the NH. Black ones are the values at the same latitude in the SH. At 61* very good agreement is found between the SH values of the model and the observed or theoretical (Lindzen, 1967) ones. At 30*, again the SH values compare well with the observed or theoretical ones.

Figure 17 shows the same quantities as in Fig. 14 except for the semi-diurnal mode (*=-2, m= 2). The model's results agree well with Forbes


Fig. 16. The vertical distribution of the amplitude (left) and phase (right) of meridional wind for (*=

-1 , m=1) at 61*N (left) and 30*N (right). Model results are plotted by circles on the figure reproduced from Reed et al. (1969). White and black

circles indicate the values at the nearest grid points

to 61* and 30* in the NH and SH, respectively. The

solid line shows the results by Reed et al. (1969), the

dashed line by Lindzen (1967) and the thin solid

line by Forbes (1982a).



(1982b)' in the extratropical latitudes. Although some discrepancies are found in the intervening equatorial latitudes, the phase of the cross-equa-torial wind is in rough agreement.

The same quantities as in Fig. 17 but for 900 mb are shown in Fig. 18. Although the overall horizontal wind pattern for the model resembles Forbes (1982b)', there is a phase lag in the model by 80min at the equator. Compared with the observed analysis by Haurwitz (1956), the phase of the model lags behind by 40min. In the model, phase precedes with latitude in the NH. The geopotential amplitude near the equator is about 8.2gpm. This is about 75% of the ob-served amplitude of 1.1mb at the equatorial sur-face (Haurwitz,1965).

4.2 Non-migrating mode Firures 19(a) and (b) show the horizontal

structure of (*=-1, m=5) at both 900mb and 5.18mb, respectively. The motion at 900mb in-cludes a symmetric component with respect to the equator with the center of divergence (con-vergence) at the equator. The motion is intensi-fied in the subtropics of the SH, where this mode shows northward transport of zonal momentum. The same sense of the momentum transport ex-ists at 5.18mb except near the equator. The geo-

potential phase inclines in the NE-SW direction. The horizontal map of wind and geopotential

field of (*=1, m=3) at 900mb, 06Z is shown in Fig. 20. The mode has narrow structures in the

Fig. 18. The same as in Fig. 14 but for the mode (*=-2, m=2) at 900mb. The

contour interval of geopotential field is 2.5gpm.

434 Journal of the Meteorological Society of Japan Vol . 65, No. 3

Fig. 19. The same as in Fig. 14(a) but for the mode (*=-1, m=5) at (a) 900 mb and (b) 5.18mb.

Fig. 20. The same as in Fib. 14(a) but for the mode (*=1, m=3) at 900mb. The contour interval is 2.5gpm.


latitudinal direction. Wind amplitude is large in the subtropics of the SH, although the amplitude itself is about a half of that of (*=-l, m=5). The maximum geopotential amplitude is 3.1gpm at 14*S.

5. Summary

Atmospheric tides induced in a global atmos-

pheric general circulation model are analyzed. As the model includes realistic distributions of complicated surface conditions, thermal tidal forcings realized in the model may give us useful informations about them. The model is not de-signed to simulate tidal motions well. The pres-ent vertical resolution is not enough for the inter-nal modes with vertical wavelengths less than 10 km (see Fig. 2.1 in Tokioka et al., 1984). The top of the model is located near the stratopause level, which is unsatisfactory for the simulation of tidal motions because of the artificial wave reflection caused by the upper boundary and because the neglection of thermal forcings in the mesosphere and above causes differences in the tidal motions below the stratopause, especially through the modifications of internal modes.

We summarize the following from the present analyses:

i) The model produces detailed structure in the thermal forcings of diurnal and semi-diurnal modes within the planetary boundary layer

(PBL) in the subtropics and in the mid-tropo-sphere in equatorial latitudes. Compared with the forcings by Forbes (1982a, b), the present mod-el gives larger ones in the lower level of the tro-

posphere for both modes. ii) The thermal forcings of diurnal and semi-

diurnal tides within the stratosphere agrees fairly well with the forcings by.Forbes (1982a, b). This suggests indirectly that the ozone photochemical model included in the GCM describes the diurnal variation of ozone properly.

iii) The mdoel produces tidal forcings other than the migrating tides, such as (*=-1, m=5), (*=1, m=3), (*=-1, m=9), (*=1, m=1), * ,where

* is the frequency in day-1 and m is the zonal wavenumber. Such non-migrating modes have large thermal forcings within the PBL and the mid-troposphere in low latitudes.

iv) Large diurnal heating over land in low lati-

tudes essentially forces the non-migrating tidal modes mentioned in iii).

v) Diurnal tidal motions realized in the model do not agree with the theoretical ones obtained by Forbes (1982a) in low latitudes, where inter-nal modes prevail. At 900mb, the maximum geo-

potential amplitude is 5.2gpm at 6*S. The phase lags behind the observed analysis of Haurwitz

(1965) by 100min. vi) In the extratropics, especially of the SH,

diurnal tidal motions in the model are compared favorably with the observed analysis by Reed et al. (1969) and also with the theoretical results by Lindzen (1967) and Forbes (1982a).

vii) Comments similar to v) and vi) are appli-cable for semi-diurnal tidal motions in the model. At 900mb the maximum geopotential amplitude is 8.2gpm at 6*N, which is about 75% of the ob-served analysis by Haurwitz (1956). The phase lags behind the observed analysis by Haurwitz

(1965) by 40min. viii) The non-migrating mode is detected in

the wind field in low latitudes, especially in the subtropics of the SH in January. The maximum geopotential amplitude at 900mb for (*=1, m= 5) is 2.5gpm at 18*S.

Acknowledgements

The authors thank members of the MRI GCM

group for useful discussions. Thanks are ex-tended to Dr. M. Aihara, the head of the forecast research division of the MRI, and Mr. T. Yoshida, the former head of the division, for their en-couragement throughout this work.

Computations are made with the HITAC M200-H of the MRI.

Appendix

Non-zonal Stationary effects in generating non-migrating modes

The thermal forcing of atmospheric tides is mainly determined by ozone heating, water vapor heating and by the PBL plus cumulus heat-ing. If the distributions of ozone, water vapor and ground surface conditions are uniform in the zonal directton, the thermal forcing of tides, JG, can be written following Chapman and Lindzen

(1970);


where *=2*/1 solar day; *, latitude; *, longitude; t, time; *n , a constant phase angle. In this case, tidal modes migrating in synchrony with the movement of the sun are generated.

In the actual atmosphere, the land-sea dis-tribution is complicated. The time-averaged dis-tribution of ozone and water vapor have non-zonal planetary scale variations. Those non-zonal effects modify Jn(z, *) in (Al) toJn(z, *, *). Jn (z, *, *) may be written as

Fig. A1. Fourier components of topography in the

zonal direction averaged from 20*S to 30*S. The

solid line corresponds to actural topography and the

dashed line to flat continents. The height of the flat

continents is assumed to coincide with the zonal

mean value of actual topography.

where *ni is a constant phase angle. Substitution of (A2) into (Al) gives

Fig. A2. Horizontal distribution of the zonal wave-

number 4 of topography (unit: m).

In (A3), the last term indicates the thermal forc-ing of non-migrating tidal modes. It is interesting to note that the zonal wavenumber i component, Jni, generates two types of non-migrating modes, i.e., (*=-n, m=n+i) and (*=sign(i-n)*n, m=|n-i|).

A solid line in Fig. Al shows the Fourier am-

plitude of topography in the zonal direction aver-aged between 20*S and 30*S. A dashed line in the same figure shows that of flat continents at the same latitude belt, where a constant eleva-tion is assigned over land instead of actual one. Clear peaks are found at the zonal wavenumber 4 and 8 in the solid line. We find a peak at 4 in the dashed line also. As the PBL and cumulus heating in low latitudes is enhanced over land in the daytime,Jni for the PBL and cumulus heating must have peaks at i=4 and 8. If i=4 and n=1 in

(A3), the non-migrating mode (*=-1, m=5) and (*=1, m=3) are generated. Those peaks are found in Figs. 2(a) and 10. If i=8 and n=1, (*=-1, m= 9) and (*=1, m=7) are generated. We can also find those peaks in Fig. 2(a).

Figure A2 shows the horizontal distribution of the zonal wavenumber 4 of topography. The

phase has a southeast to northwest tilt between the equator and 30*N, while it has almost no

phase tilt between the equator and 40*S. These features are commonly seen in Figs. 11(a) and 19(a). This supports the notion that the non-migrating mode (*=-l, m=5) is closely related with the zonal wavenumber 4 of the land-sea distribution (or topography).

Ozone distribution has dominant stationary components of the zonal wavenumber 1 and 2 in winter of the NH. Therefore the following modes are expected to be genrated in the NH, i.e., (*=-1, m=2), (*=-1, m=3), (*=1, m=1),


(*=-2, m=3), (*=-2, m=1), (*=-2, m=4). Spec-tral powers are found at several of those points in the total heating (figure is not shown), al-though the powers themselves are not large com-pared to those of migrating modes.

References

Axakawa, A. and Y. Mintz, 1974: The UCLA atmospheric general circulation model. Notes distributed

at the workshop 25 March - 4 April 1974, Dept. of Meteorology, UCLA, 404pp.

- and W.H. Schubert, 1974: Interaction of a cumulus ensemble with the large-scale environment,

Part I. J. Atmos. Sci., 31, 674-701. - and V. Lamb, 1977: Computational design of

the basic dynamical processes of the UCLA general circulation model. Methods in Computational

Physics, Advances in Research and Application, Vol. 17: General circulation models of the atmos-

phere, Academic Press, Inc., 337pp. Chapman, S. and R.S. Lindzen, 1970: Atmospheric

Tides, Reidel, Dordrecht-Holland. Deardorff, J.W., 1971: Parameterization of the plane-

tary boundary layer for use in general circulation models. Mon. Wea. Rev., 100, 93-106.

Forbes, J.M. and H.B. Garrett, 1978: Seasonal-latitudinal structure of the diurnal thermospheric tide. J.

Atmos. Sci., 35,148-159. - and -, 1978: Theoretical studies of

atmospheric tides. Rev. Geophysics. Space Phys., 17,1951-1981.

-, 1982a: Atmospheric tides 1. Model description and results for the solar diurnal component. J.

Geophys. Res., 87, 5222-5240. -, 1982b: Atmospheric tides 2. The solar and

lunar semidiurnal components. J. Geophys. Res., 87, 5241-5252.

Hamilton, K., 1981: Latent heat release as a possible forcing mechanisms for atmospheric tides. Mon.

Wea. Rev., 109, 3-17. Haurwitz, B., 1956: The geographical distribution of the

solar semidurnal pressure oscillation, Meteorol. Pap. 2(5), New York University.

-, 1965: The diurnal surface pressure oscillation. Archiv. Meteorol. Geophsy. Biokl. A14, 361-

379. Katayama, A., 1972: A simplified scheme for comput-

ing radiative transfer in the troposphere. Technical Report No. 6, Department of Meteorology, Univer-

sity of California, Los Angeles, 77pp. Kato, S., 1966: Diurnal atmospheric oscillation, 1.

Eigenvalues and Hough functions. J. Geophys. Res., 71, 3201-3209.

-, T. Tsuda and F. Watanabe, 1982: Thermal excitation of non-migrating tides. J. Atmos. Terr.

Phys., 44,131-146. Lindzen, R.S., 1966: On the theory of the diurnal tide.

Mon. Wea. Rev., 94, 295-301. -, 1967: Thermally driven diurnal tide in the

atmosphere. Quart. J. Roy. Met Soc., 93,18-42. Reed, R.J., Oard, M.J, and Sieminski, M., 1969: A com-

parison of observed and theoretical diurnal tidal motions between 30 and 60km. Mon. Wea. Rev., 97, 456-459.

Schlesinger, M.E, and Y. Mintz, 1979: Numerical simulation of ozone production, transport and distribu-

tion with a global atmospheric general circulation model. J. Atmos. Sci., 36,1325-1361.

Tokioka, T., 1978: Some considerations on vertical differencing. J. Meteor. Soc. Japan, 56, 98-111.

-, K. Yamazaki, I. Yagai and A. Kitoh, 1984: A description of the Meteorological Research Insti- tute atmospheric general circulation model (MRI*

GCM-I). Technical Report of the Meteorological Research Institute, No. 13, MRI, Tsukuba, 249pp.

- and I. Yagai, 1984: On the January simulation of stratospheric circulations with the MRI gen-

eral circulation model: Preliminary results. Dynamics of the Middle Atmosphere, Ed. JR. Holton and T.

Matsuno, Reidel, Dordrecht-Holland, pp. 527-537. Walterscheid, R.L, and Devore, J.G., 1981: The semi-

diurnal atmospheric tide at the equinoxes: A spectral study with mean-wind-related influences and im-

proved heating rates. J Atmos. Sci., 38, 2291-2304.


大気大循環モデルに現われた潮汐について

時岡達志・谷貝勇

(気象研究所予報研究部)

全球大気大循環モデルによる1月の再現実験の結果を解析して大気潮汐を調べた。モデルの対流圏で

は亜熟帯域の大気境界層(PBL)と熱帯域の対流圏中層に1日周期および半日周期の強い熱的強制力が

ある。Forbes(1982a,b)と比較すると,対流圏の下層においてモデルは両方のモードでより大きな値に

なっている。成層圏における1日周期と半日周期の熱的強制力はForbes(1982a,b)とほぼ良い対応を

している。

モデルは太陽と同期する起潮力以外のモード,(f=-1,m=5),(f=1,m=3),(f=-1,

m=9),(f=1,m=1),*を作っている。ここでfは振動数(day-1),そしてmは東西方向の

波数を表わす。このような非同期モード*の起潮力は熱帯におけるPBLと対流圏の中層で大きな値を持

っており,低緯度の陸上で日中に受ける大きな加熱が本質的な役割を果している。

*我々は,この用語を太陽と同期しているモード以外の潮汐モードを表わすために用いる。

Atmospheric Tides Appearing in a Global Atmospheric ...

Documents

Transcript of Atmospheric Tides Appearing in a Global Atmospheric ...