By using a general circulation model, behaviors of the eastward propagating diurnal tide with zonal wavenumber 3 (DE3) and their relation with the convective activity in the tropical troposphere are examined. The amplitude of the DE3 is significant in the equatorial mesosphere and lower thermosphere (MLT). Day-to-day variations of the DE3 amplitude are evident in the MLT region, and are closely related with temporal variations of the rainfall rate in the tropics. Estimates of the EP flux divergence due to the DE3 indicate that this convective modulated DE3 activity induces day-to-day variations of the wave-induced driving of the zonal mean zonal wind in the MLT region. Our results show that temporal variations of the zonal mean zonal wind in the equatorial MLT region are influenced by the moist convective activity in the tropics.
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 In low latitudes of the mesosphere and lower thermosphere (MLT), the upward propagating mode of the migrating diurnal tide plays an important role on the general circulation of the atmosphere. Recently, observational studies have revealed that nonmigrating diurnal tides also have considerable amplitudes in the MLT region [e.g., Talaat and Lieberman, 1999; Forbes et al., 2003]. By using UARS data, they showed that the eastward propagating diurnal tide with zonal wavenumber 3 (s = 3), the standing (s = 0) diurnal oscillation, and the westward propagating diurnal tide with s = 2 were prominent components of nonmigrating diurnal tides. Fourier decomposition of longitudinal rainfall distribution involve a range of zonal wavenumbers of both westward and eastward propagating diurnal tides, and these nonmigrating components of the rainfall are plausible excitation sources of nonmigrating diurnal tides [Forbes et al., 1997; Tokioka and Yagai, 1987]. By using a global scale wave model (GSWM), Hagan and Forbes  showed that latent heat release associated with the moist convection was important for excitation of nonmigrating diurnal tides. On the other hand, Hagan and Roble , Ward et al. , and Yoshikawa and Miyahara  suggested that the westward propagating diurnal tide with s = 2 was excited by wave-wave interaction in the middle atmosphere.
 By using MF radar observations, Isoda et al.  and Gurubaran et al.  indicated that temporal variations of the diurnal tide in the MLT region were closely related with the moist convective activity in the tropics. However, there are only a few studies concerning the relation between the diurnal tide in the MLT region and the moist convective activity in the tropics.
 A general circulation model (GCM) is a quite useful tool for investigating behaviors of the diurnal tide. By using a GCM developed at Kyushu University, Miyoshi and Fujiwara  showed that fluctuations of the migrating diurnal tide amplitude with periods of 12 and 25 days were evident from the height range from 20 to 300 km heights, indicating dynamical coupling between the mesosphere and thermosphere and the lower atmosphere. Miyahara and Miyoshi  investigated behaviors of nonmigrating diurnal tides in the MLT region. In this study, by using the GCM, we examined behaviors of the eastward propagating diurnal tide with s = 3 (DE3), which is one of prominent components of the nonmigrating diurnal tides. The purpose of this study is to investigate day-to-day variations of the DE3 in the MLT region and their relation with the moist convective activity in the tropical troposphere. Furthermore, by calculating the EP flux divergence due to the DE3, the wave-induced driving of the zonal mean zonal wind is studied.
2. Descriptions of the GCM and Numerical Simulation
 The GCM used in this study is an extension of the middle atmosphere GCM developed at Kyushu University [Miyahara et al., 1993; Miyoshi, 1999]. The GCM is a global spectral model with a triangular truncation of T21 (the maximum horizontal wavenumber is equal to 21). The GCM has 75 vertical levels, and contains the region from the ground surface to the exobase (about 500 km height). The GCM has a vertical resolution of 0.4 scale height above the tropopause. The GCM has a full set of the physical processes appropriate for the troposphere, stratosphere, mesosphere and thermosphere. The detailed descriptions of the physical processes are found in the work by Miyoshi and Fujiwara , so that the description of the physical processes is briefly mentioned here.
 The GCM includes schemes for hydrology, a boundary layer, radiation process, eddy diffusion and moist convection. The distributions of water vapor and cloud are predicted in the GCM. The cumulus parameterization developed by Kuo  is used. Effects of the topography of the surface are also taken into account. The monthly mean of zonally symmetric distribution of O3 is climatologically prescribed. The distributions of sea surface temperature, ground surface albedo and ground wetness, which are used in a boundary layer process, are also climatologically prescribed.
 The neutral composition in the thermosphere is obtained from the empirical model of MSISE-90 [Hedin, 1991], and specified as a function of time, latitude and pressure. The atmospheric molecules of N2, O2, and O are assumed as major species, and the concentrations of CO2 and NO are also prescribed for calculations of the infrared cooling. Schemes for the infrared cooling, absorption of solar extreme ultraviolet (EUV) and ultraviolet (UV) radiations, the ion drag and the Joule heating are included in the GCM.
 Day-to-day variations of solar UV and EUV fluxes and geomagnetic activity (e.g., the solar 27-day rotation effect) are frequently observed, and affect the migrating and non-migrating diurnal tides in the MLT region. In order to exclude effects of day-to-day variations of solar EUV and UV fluxes and geomagnetic activity, the numerical simulation is conducted under solar cycle moderate and geomagnetically quiet conditions. The solar F10.7cm flux is fixed at 135 in units of 10−22 W/m2/Hz during the numerical simulation. The data are sampled every 1 hour for 12 months. The procedure of spectral analysis follows. The grid-point data are expanded into zonal Fourier harmonics at each latitude and each vertical level. The resulting time-dependent Fourier coefficients of zonal wavenumber 3 are treated as separate time series. By performing a space-time cross-spectral analysis [e.g., Hayashi, 1971], an eastward propagating diurnal component with zonal wavenumber 3 is extracted.
Figure 1a shows the annual-mean amplitude of the temperature component of the DE3. The amplitude has a maximum near the equator and is symmetric about the equator. The amplitude increases with height until 115 km height, and reaches a maximum (11 K) at 115 km height. Figure 1b shows the annual mean amplitude of the zonal wind component. The meridional structure of the zonal wind component is quite similar to that of the temperature component. The amplitude of the zonal wind component peaks at 115 km height near the equator. The maximum value is 14 m/s. Above 120km height, the amplitude attenuates, and the dissipation of the DE3 occurs. The amplitude of the meridional wind component is about half of that of the zonal wind component (not shown). Thus, in the MLT region, the amplitude of the DE3 is significant.
Figure 2 shows the time-height cross section of the zonal wind component of the DE3 at 0°E and 2.8°N. The phase line descends with time, indicating upward propagating wave. Below 110km height, the vertical wavelength is 40–45 km. These features are in good agreement with those obtained by the UARS data [Talaat and Lieberman, 1999; Forbes et al., 2003]. The DE3 simulated in this study is identified as the gravest symmetric eastward propagating tidal mode (a diurnal Kelvin wave).
 Next, day-to-day variations of the amplitude of the DE3 zonal wind component are examined. Figures 3a–3c show time series of the DE3 amplitudes at 2.8°N at the altitudes of (a) 160 km, (b) 115 km and (c) 80 km, respectively. Fluctuations of the amplitude with periods of 20–60 days are clearly seen. The amplitude at 115 km height ranges from 5 to 28 m/s, indicating marked day-to-day variations. The amplitudes at 80 and 160 km heights vary between 1.5 and 6.5 m/s and between 3 and 12 m/s, respectively. In the height range from 80 to 160 km heights, the enhancement of the amplitude occurs simultaneously.
 In order to investigate the relation between day-to-day variations of the DE3 amplitude and the moist convective activity in the troposphere, eastward moving diurnal component of the rainfall rate with zonal wavenumber 3 is calculated. Figure 3d shows time series of the eastward s = 3 diurnal component of rainfall rate near the equator (averaged between 10°N and 10°S). When the amplitude of the rainfall rate is enhanced, the amplitude of the DE3 also becomes large; examples include the end of January, the beginning of March, the beginning of April, the beginning of May, the end of May, the end of September, and mid-October. We found a clear relationship between the DE3 amplitude in the MLT region and the amplitude of the rainfall rate near the equator except for the period from the end of June to mid July. Because the vertical group velocity of the DE3 which is the vertical speed of the wave energy associated with the DE3 is large, it takes only a few days to propagate from the upper troposphere to the lower thermosphere. The EP flux vector associated with the DE3 shows upward propagation from the upper troposphere to the MLT region (not shown). These results indicate that the DE3 is excited by the latent heat release associated with the moist convection.
 By using MF radars, Isoda et al.  and Gurubaran et al.  showed that temporal variations of the tidal amplitude in the equatorial MLT region were closely related with variations of the outgoing longwave radiation (OLR), which was as indicator of the convective activity in the tropics. Furthermore, by using the GSWM, Hagan and Forbes  indicated importance of latent heat release in the tropics for excitation of non-migrating diurnal tides. These results are in good agreement with our results.
 In the tropical troposphere, the global-scale convective activity varies with periods of 30–70 days (Madden-Julian Oscillation [Madden and Julian, 1994]). These day-to-day variations of convective activity influence the amplitude of the eastward s = 3 diurnal component of rainfall rate near the equator. Thus, the excitation of the DE3 may be modulated by the connective activity associated with the Madden-Julian Oscillation.
 In GCMs, moist convection is not resolved explicitly because of its sparse horizontal resolution. In this study, Kuo's cumulus parameterization is used. In other GCMs, various types of cumulus parameterizations, such as moist convective adjustment and Arakawa-Schubert's scheme, are used. Horinouchi et al.  investigated effects of cumulus parameterization on the variability of rainfall rate and simulated waves in the equatorial middle atmosphere. They showed that the choice of cumulus parameterization had an impact on the vertically propagating waves in the equatorial middle atmosphere. The amplitude of the nonmigrating diurnal tide simulated by the GCM with Kuo scheme was comparable with or slightly larger than that obtained by Hagan et al.  from satellite-observed brightness temperature data. However, the excitation of nonmigrating tides is dependant on the choice of cumulus parameterization. A series of GCM experiments with other cumulus parameterizations may be necessary.
 In order to investigate the wave-induced driving of the zonal mean zonal wind, the EP flux divergence (EPFD) due to the DE3 is calculated. Figure 4a shows time series of the EPFD due to the DE3 at 2.8°N of 115 km height. The dissipation of the DE3 produces westerly acceleration in the lower thermosphere. The EPFD fluctuates with periods of 20–60 days. Strong westerly acceleration (8–13 m/s/day) occurs when the DE3 amplitude is enhanced. The EP flux divergence peaks around 115 km height. The westerly acceleration due to the EPFD at 100 and 150 km heights ranges from 1 to 5 m/s/day.
Figure 4b shows time series of the zonal mean zonal wind at 2.8°N of 115 km height. The zonal mean zonal wind also has significant temporal variations with periods of 20–60 days. During the periods of strong westerly acceleration due to the EPFD, such as the beginning of March, the beginning of May, the beginning of July, the end of September and mid-October, the westerly wind is intensified. On the other hand, in the beginning of April and the end of May, strong westerly acceleration due to the EPFD does not induce the strong westerly wind. During these periods, the amplitude of the migrating diurnal tides is also enhanced, and strong easterly acceleration due to the migrating diurnal tide appears (Figure 4c). Moreover, in the end of May, easterly acceleration due to the westward s = 2 diurnal tide is also enhanced (not shown).
 Based on these results, we can propose that day-to-day variations of the DE3 in the MLT region, which are modulated by the moist convective activity in the troposphere, produce day-to-day variations of the zonal mean zonal wind in the MLT region. There is a clear connection between the zonal mean zonal wind in the MLT region and the convective activity in the tropical troposphere.
 By using the GCM developed at Kyushu University, behaviors of the DE3 in the MLT region and their relation with the convective activity in the tropical troposphere are examined. Day-to-day variations of the DE3 amplitude are evident, and are closely related with temporal variations of the rainfall rate in the tropics. Furthermore, this convectively modulated DE3 activity induces similar periodicity in westerly acceleration of the wave-induced driving of the zonal mean zonal wind in the MLT region. Thus, the convective activity in the troposphere influences temporal variations of the zonal mean zonal wind in the MLT region.
 Long-term MF radar observations revealed that interannual variation of the diurnal tide in the equatorial MLT region is correlated with the OLR variation [Gurubaran et al., 2005]. This result suggests that interannual variation of the zonal wind in the MLT region is influenced by the El Nino Southern Oscillation that influences the convective activity in the tropics. In the next step, by using a GCM, we will investigate interannual variation of the general circulation in the MLT region and its relation with interannual variability in the troposphere.
 The author thanks the anonymous reviewers for their suggestions to improve the manuscript. This work was financially supported by a Grant-in-aid for Scientific Research by the Ministry of Education, Science, Sports and Culture, Japan. The GFD/DENNOU Library was used for drawing figures.