Quantification of the gravity wave forcing of the migrating diurnal tide in a gravity wave resolving general circulation model

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114,, doi: /2008jd011218, 2009 Quantification of the gravity wave forcing of the migrating diurnal tide in a gravity wave resolving general circulation model Shingo Watanabe 1 and Saburo Miyahara 2 Received 30 September 2008; revised 3 February 2009; accepted 12 February 2009; published 15 April [1] The interaction of gravity waves (GWs) and the migrating diurnal tide are studied in a GW-resolving general circulation model (GCM) by calculating the tidal components of zonal wind accelerations and equivalent Rayleigh friction due to tidal induced GW dissipation. Two 15-day periods for perpetual equinoctial and solstice simulations are analyzed, which are performed with the Japanese Atmospheric General circulation model for Upper Atmosphere Research (JAGUAR) high-resolution GCM. The model can directly simulate GWs with horizontal wavelengths greater than about 190 km, and, thus reproduce the general features of the mean winds and temperatures from the surface to the mesosphere and lower thermosphere (MLT). The amplitudes of the migrating diurnal tide are successfully simulated during both seasons, and the tidal winds affect the altitudes of GW dissipation in the low-latitude MLT. The tidal component of GW forcing has maximal values of about 15 m s 1 d 1 near the maximal vertical shears of the tidal winds and generally works to shorten the vertical wavelength of the migrating diurnal tide. The phase relationship between the tidal winds and the tidal induced GW forcing is not exactly 90 out of phase, causing amplification/suppression of the tide. The GW forcing amplifies the migrating diurnal tide during the equinox, while during the solstice, it suppresses the tidal winds in the upper mesosphere of both hemispheres. This difference in behavior can be attributed to a seasonal variation of the mean zonal winds, because combination of the mean and tidal winds affects the altitudes of GW dissipation. Citation: Watanabe, S., and S. Miyahara (2009), Quantification of the gravity wave forcing of the migrating diurnal tide in a gravity wave resolving general circulation model, J. Geophys. Res., 114,, doi: /2008jd Introduction [2] The migrating diurnal tide is a Sun-synchronous, atmospheric thermal tide with zonal wave number 1 [e.g., Chapman and Lindzen, 1970], which is one of the most prominent disturbances in the low-latitude mesosphere and lower thermosphere (MLT) [e.g., McLandress et al., 1996; Tsuda et al., 1999; Shepherd et al., 1999; Zhang and Shepherd, 2005; Forbes et al., 2006; Huang et al., 2006; Wu et al., 2006, 2008]. Vertically propagating, small-scale gravity waves with horizontal wavelengths of tens to hundreds of kilometers are ubiquitous and have equally large amplitudes in the MLT [e.g., McLandress, 1998; Fritts and Alexander, 2003]. Both of these wave types are known to originate in the lower atmosphere and to propagate upward with an increase in amplitude as a result of decrease in the atmospheric density. Because of the ubiquitous nature of small-scale gravity waves, frequent occurrences of the wave-tide interactions with the migrating diurnal tide are expected in the low-latitude MLT. 1 Frontier Research Center for Global Change, Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan. 2 Department of Earth and Planetary Science, Kyushu University, Fukuoka, Japan. Copyright 2009 by the American Geophysical Union /09/2008JD [3] Momentum deposition due to small-scale gravity waves can act to suppress or amplify the migrating diurnal tide. The large-amplitude tidal winds likely affect favorable altitudes of gravity wave dissipation, and resultant phase relationships between the tidal winds and tidal induced gravity wave forcing may affect the amplitude and phase of the tide itself [e.g., Walterscheid, 1981; Miyahara and Forbes, 1991; McLandress, 1998; Mayr et al., 1998; McLandress 2002a]. Such interactions have been numerically simulated using mechanistic models and general circulation models (GCMs), in which the effects of smallor subgrid-scale gravity waves are represented by gravity wave parameterizations [e.g., Lindzen, 1981; Hines, 1997a, 1997b]. One numerical study concluded that the parameterized gravity wave forcing strongly suppress the amplitudes of the migrating diurnal tide [Miyahara and Forbes, 1991] (see Appendix A), while other studies have reached the opposite conclusion [e.g., McLandress, 1998; Mayr et al., 1998]. In a numerical study using the Canadian Middle Atmosphere Model (CMAM) that employs Hines s gravity wave parameterization, McLandress [2002a, 2002b] compared all possible factors that can modulate the amplitude of the migrating diurnal tide. He concluded that the effects of parameterized gravity waves on the tidal amplitude were substantially weaker than other effects, such as wave-mean flow interaction between tides and mean wind fields, that can modulate the tidal amplitude. 1of14

2 [4] The conclusions of the abovementioned studies could depend on a number of assumptions and parameters used in the gravity wave parameterizations [e.g., McLandress, 1998; Fritts and Alexander, 2003], as well as on different mean flows in their models. Thus, it is worthwhile to perform a high-resolution GCM simulation in which small-scale gravity waves are directly simulated without using any gravity wave parameterizations. The present study aims at quantifying the interaction of the migrating diurnal tide and small-scale gravity waves simulated in a gravity wave resolving GCM. In this study we analyze two 15-day periods for perpetual equinoctial and solstice simulations, which are performed using the JAGUAR (Japanese Atmospheric General circulation model for Upper Atmosphere Research) gravity wave resolving GCM. [5] Section 2 describes the model and experimental settings. Section 3.1 gives results for mean zonal winds and temperatures during the two seasons. Section 3.2 presents the amplitude for the simulated migrating diurnal tide. In section 3.3, interactions of gravity waves and the migrating diurnal tide are evaluated by calculating the tidal components of horizontal wind accelerations and equivalent Rayleigh friction due to tidal induced gravity wave dissipation. Phase relationships between the tidal winds and the tidal induced gravity wave forcing are mainly investigated. Section 4 gives a summary. 2. Model Description [6] JAGUAR is based on the T213L256 middle atmosphere GCM developed for the KANTO project, which explicitly resolves small-scale gravity waves and reproduces the general circulation in the troposphere, stratosphere, and mesosphere (0 to 85 km) [Watanabe et al., 2008a]. The current version of JAGUAR has a horizontal-triangularly truncated spectral resolution of T213, corresponding to a latitude-longitude grid interval of (62.5 km near the equator), and comprises 270 vertical layers from the surface to the geopotential height of approximately 150 km, with a uniform log-pressure vertical spacing of 500 m throughout the middle atmosphere. No parameterization of subgrid gravity waves is used in the present study in order to focus on the effects of directly resolved gravity waves on the migrating diurnal tide. The T213 horizontal resolution is insufficient to resolve very small-scale gravity waves with horizontal wavelengths of km, which can propagate from the lower atmosphere to the mesopause height of the real atmosphere [e.g., Preusse et al., 2008]. Nonhydrodynamic processes, such as wave-ducting, wave-reflection, turbulent breakdown, and secondary generation of very small-scale gravity waves are also not resolved in the model. The turbulent breakdown processes associated with shearing and convective instabilities due to resolved gravity waves are instead represented by a Richardson number dependent vertical diffusion parameterization in the model, as well as the dry convective adjustment. These limitations in the model s framework can affect the results presented in this paper. [7] The newly implemented physical parameterization for the MLT region is briefly described here, since the dynamical and physical processes below the MLT are described in detail by Watanabe et al. [2008a]. The physical parameterizations used in the MLT region are similar to those used in the Kyushu-GCM [e.g., Yoshikawa and Miyahara, 2003a, 2003b, 2005], which has been referred to as the Middle Atmosphere Circulation Model at Kyushu University (MACMKU) in earlier studies [e.g., Miyahara et al., 1993, 1999; Miyahara and Miyoshi, 1997; Watanabe et al., 1999; Yamashita et al., 2002]. Radiative transfer processes, including the nonlocal thermodynamic equilibrium (non-lte) effects for infrared cooling, are calculated using Fomichev s parameterization [Fomichev et al., 1993, 1998]. Solar radiation heating due to molecular oxygen and ozone in the MLT region is calculated using Strobel s scheme [Strobel, 1978]. At a height of 70 to 77 km, the heating rates calculated by the abovementioned MLT schemes are gradually merged with those calculated using mstrnx, a radiative transfer scheme with very high accuracy below the height of about 70 km [Sekiguchi and Nakajima, 2008; Watanabe et al., 2008b]. The effects of the molecular viscosity and thermal conductance are introduced, which exceed the effects of the eddy vertical diffusion above a height of about 110 km. A simple ion-drag parameterization is introduced, whose effects are negligible below about 120 km. [8] Strong horizontal hyperviscosity diffusion is introduced above the turbopause height, which is approximately 110 km. The r 16 hyperviscosity diffusion is used in this study with a standard e-folding time constant for the smallest resolved motion of 1 day below a height of about 100 km. The time constant is rapidly decreased at altitudes between 100 km and 110 km, which implies that most of the small-scale gravity waves are absent above such an artificially introduced global turbopause in the model, while large-scale atmospheric waves, including thermal tides, are not directly affected by the horizontal diffusion. This treatment is necessary for two reasons. The first reason is simply associated with computational instability, which is a common problem in GCMs (see for instance in CMAM [Fomichev et al., 2002]). The second reason is probably a unique problem for this high-resolution GCM. In the simulated lower thermosphere without strong horizontal diffusion, horizontally small-scale structures are ubiquitous. They do not have the typical structures of vertically propagating gravity waves, and are not efficiently damped by the molecular viscosity and thermal conductance in the model. Such small-scale and probably unrealistic disturbances produce strong eddy vertical mixing in the lower thermosphere, which rapidly destroys the large-scale thermal structure. In practice, a rapid increase in the mean temperature in the lower thermosphere cannot be maintained without the enhanced horizontal diffusion. It is assumed that the energies of such small-scale disturbances are cascaded into far smaller-scale disturbances in the real lower thermosphere, and such processes should somehow be parameterized in GCMs. Therefore, it should be noted that the effects of simulated gravity waves on the migrating diurnal tide can only be evaluated below a height of about 100 km in this study. [9] The simulations described in this study were performed on the Earth Simulator for two perpetual conditions, that is, the equinox and austral winter solstice. The initial conditions were constructed by combining the results of a T42L250 version of the Kyushu-GCM [Yoshikawa and 2of14

3 Figure 1. Zonal mean zonal wind (contours) and temperature (color and thin contours) in (a) equinox simulation, (b) Met Office and CIRA86 for April, (c) June solstice simulation, and (d) Met Office and CIRA86 for July. Contour intervals are 10 m s 1 and 5 K. Met Office data are averaged over and displayed below 50 km. The color scale is changed below and above a height of 80 km. 3of14

4 Miyahara, 2005] (above 80 km) and the T213L256 GCM for the KANTO project [Watanabe et al., 2008a] (below 80 km). A time step of 10 s was used in this study, although the model might be safely integrated with longer time steps (10 20 s). The model was run for the two perpetual conditions for successive 105 days, and the last 15 days of each simulation were analyzed. The simulated mean fields are sufficiently stable throughout the analysis period. For example, mean temperatures in the MLT have no apparent linear trend, and no sudden warming occurs in the stratosphere. During the last 15 days for each simulation, the three-dimensional meteorological elements were sampled every hour as hourly averages. The analysis period of 15 days is sufficiently long to evaluate the interactions between small-scale gravity waves and the migrating diurnal tide. 3. Results 3.1. Mean Winds and Temperatures [10] Figure 1 compares the zonal mean zonal wind and the zonal mean temperature obtained with this simulation to the Met Office assimilation data (below 1 hpa) [Swinbank and O Neill, 1994] and the 1986 Committee on Space Research (COSPAR) International Reference Atmosphere (CIRA) data (above 1 hpa) [Fleming et al., 1990]. Of the currently available observational data sets, CIRA86 is used here, because of the consistency between the zonal mean zonal winds and temperatures. The standard height (STD Height), which corresponds to the global average of geopotential height simulated in the model, is used as a proxy of the altitude in this study. The model qualitatively reproduces the majority of the observed meridional structures of the zonal mean zonal wind and temperature during both the equinox and the austral winter solstice, although the model has been run with the perpetual conditions. For the equinox simulation, the meridional structure of the zonal mean westerly winds in the Southern Hemisphere is similar to that observed in April. For example, the location and strength of the maximum of the westerly jet in the mesosphere are successfully reproduced in the model. The westerly winds have a minimum at a height of km, and have a maximum near a height of 100 km. The zonal mean thermal structures are also reproduced from the troposphere to the lower thermosphere, while the CIRA86 data are not available above about 125 km. The model has the global cold-point mesopause near a height of 98 km, which is similar to observation. [11] For the austral winter simulation, the Southern Hemisphere polar night jet has similar meridional structures to the observations in the stratosphere and mesosphere. Although the simulated polar night jet is slightly weak in the lower stratosphere, the location and strength of the westerly wind maximum are generally reproduced in the model. The meridional structure of the simulated zonal winds differs from observations in the Southern Hemisphere above 90 km altitude. While the zonal mean westerly winds gradually reverse to easterly winds for CIRA86, the simulated zonal mean westerly winds decrease at a height of km, but they never reverse to easterly winds. The maximal westerly winds appear around a height of 100 km, which is associated with the minimal mesopause temperature in the southern polar region. Such wind and temperature structures are unrealistic, and probably associated with the experimental setup of the model, such as the artificial global turbopause represented by the strong horizontal diffusion. Detailed investigations for the zonal momentum budget in this region of the present simulation are underway and will be reported in the near future. [12] In the Northern Hemisphere, the summertime easterly wind jet in the stratosphere and mesosphere is reproduced by the model, including the location and strength of the jet core. The easterly winds rapidly reverse to westerly winds at a height of about 85 km near the North Pole, while the reversal occurs at lower altitudes (about 70 km) in the midlatitudes. In this simulation, the westerly wind maximum in the lower thermosphere is stronger (80 m s 1 ), and confined to the higher latitudes, compared to CIRA86. Such a distribution of the zonal mean zonal wind is associated with the extremely cold mesopause temperature (about 110 K) in the polar region (between 70 N and 90 N) near a height of km, which is separated from the global cold-point mesopause (about 170 K) located near a height of 98 km. The vertical profile of the temperature near the summer polar mesopause is qualitatively similar to observations using ground-based lidars and falling spheres [e.g., Lübken and von Zhan, 1991], although the minimum temperatures are underestimated by about K in the present simulation. The westerly winds in the lower thermosphere again reverse to weak easterly winds at about 115 km near the North Pole, and at about 90 km in the northern midlatitudes. [13] A vertically stacked structure of the equatorial zonal mean zonal wind in the present result is not a realistic phenomenon, but is likely associated with perpetual simulations. It is probably generated by inertial instability in the simulated equatorial atmosphere. While in the real atmosphere with a seasonal variation in the solar zenith angle, the stratopause semiannual oscillation probably plays an important role in regulating such zonal wind oscillations in the equatorial atmosphere [e.g., Baldwin et al., 2001]. The temporal evolution of the equatorial zonal wind profiles presented by Watanabe et al. [2008a] indicates that the model would simulate realistic equatorial winds when seasonally varying conditions are used Amplitude of the Migrating Diurnal Tide [14] After removing the linear trend in the time series, a space-time Fourier analysis [e.g., Hayashi, 1971] is applied to the hourly sampled data to obtain the migrating diurnal tidal component. Figure 2 shows the amplitudes of the migrating diurnal tidal components for zonal and meridional winds. The tidal amplitudes for the zonal winds have broad maxima at altitudes between 90 and 110 km, maximizing at latitudes of about 25 N and 25 S. The peak amplitude during the equinox is about 30 m s 1, while during the solstice it is 20 m s 1. The latitudinal distribution at low latitudes and below 115 km resembles the Hough mode solution (1, 1) for the diurnal migrating tide, indicating the dominance of upward propagation from lower-altitude sources versus in situ generation. Another peak at higher latitude in the Northern Hemisphere and altitude above 110 km occurs during the austral winter solstice simulation, which probably indicates the predominance of in situ tides. 4of14

5 Figure 2. Amplitudes of the migrating diurnal tide for (a) zonal winds and (b) meridional winds in the equinox simulation and (c) zonal winds and (d) meridional winds in the June solstice simulation. The contour interval is 10 m. [15] The tidal amplitude for the meridional winds in the equinox simulation has two distinct maxima at altitudes of about 90 km and 105 km, which are located at about 19 N and 19 S. The peak amplitude is about 60 m s 1. The amplitude for the meridional winds decreases to about 30 m s 1 in the solstice simulation, while the peak in the Southern Hemisphere has a broad maximum at altitudes between 60 and 110 km. The simulated amplitude distributions of the migrating diurnal tide are in good agreement with satellite observations using the Wind Imaging Interferometer (WINDII) [e.g., McLandress et al., 1996], as well as the earlier GCM simulations [e.g., Miyahara and Miyoshi, 1997; Yoshikawa and Miyahara, 2005; McLandress, 2002a; Achatz et al., 2008]. Recently, Wu et al. [2008] reported strong interannual variations of the tidal amplitude during March equinox observed by the TIMED Doppler interferometer (TIDI). The tidal amplitude in the present equinox simulation roughly corresponds to the largest amplitude that is observed by TIDI Gravity Wave Tide Interactions [16] In this study, gravity waves are defined on the basis of total horizontal wave number n = , corresponding to horizontal wavelengths of km. The gravity wave components of three-dimensional winds (u 0, v 0, w 0 )are extracted using a spherical high-pass filter in the spatial domain [see Watanabe et al., 2008a]. Spherical filtering is more appropriate than the zonal wave number filtering to obtain three-dimensionally propagating gravity waves. The eastward and northward components of gravity wave forcing at each grid location are calculated as [e.g., Miyahara, Fx; Fy 0 u w w where the overbar denotes the 15-day mean of each of the hourly values. Note that Fx and Fy are calculated as a function of universal time (UT). The effect of rotation is neglected in this calculation, and the third term in rhs of (1), representing the vertical divergence for the vertical flux of horizontal momentum, has the largest contribution to Fx and Fy. [17] In what follows, phase relationships between the tidal winds and gravity wave forcing are mainly investigated. If the gravity wave forcing is in phase with the tidal winds, the amplitude of the migrating diurnal tide would be amplified, while it would be damped if they are in antiphase. If the gravity wave forcing is 90 out of phase with the tidal winds and works to pull down the vertical wind shear of tidal winds, the vertical wavelength of the tide would be shortened [e.g., McLandress 2002a]. In order to evaluate such effects of the gravity wave forcing on the amplitude and phase of the migrating diurnal tide more quantitatively, a coefficient of the equivalent Rayleigh friction (ERF) is calculated as a ¼ Fx tide =u tide ; ð1þ ð2þ 5of14

6 Figure 3. Results for the equinox simulation. (a) Eastward components and (b) northward components. Latitudinal averages are taken in latitude ranges where wind amplitudes of the migrating diurnal tide are large: 20 S 30 S (Figure 3a) and 13 S 23 S (Figure 3b). Color denotes gravity wave forcing. Contours denote large-scale flows consisting of the total horizontal wave number n = The contour interval is 10 m s 1. for each hour of the day, where subscript tide denotes the migrating diurnal tidal component. In this definition, a conventional complex expression for a real quantity is used to express both the amplitude and phase of Fx tide and u tide [e.g., Miyahara and Forbes, 1991; McLandress 2002a]. Re{a} > 0 indicates the suppression effect of the tidal winds due to gravity wave forcing, while Re{a} < 0 indicates the amplification effect. Im{a} < 0 indicate the shortening effect of the vertical wavelength, and Im {a} > 0 means the converse effect Equinox [18] Figures 3a and 3b show the longitude-height cross sections of Fx and Fy at 0030 UT for the equinox simulation, along with 15-day averaged large-scale horizontal winds (u and v) with n = 0 21 for the same hour. Latitudinal averages are taken in latitude ranges where wind amplitudes of the migrating diurnal tide are large, that is, 20 S 30 S for the zonal component and 13 S 23 S for the meridional component. The large-scale winds show the dominance of a zonal wave number one component, a signature of the upward-propagating migrating diurnal tide, which propagates through a weak vertical shear of the zonal mean zonal winds (see Figure 1a). Local effects of the gravity wave forcing (Fx and Fy) on the migrating diurnal tidal winds appear to be large. The magnitude of local maxima for Fx and Fy exceeds 80 m s 1 d 1. Some correspondence between gravity wave forcing and the tidal winds can be seen. At a height from 70 to 100 km, Fx and the zonal component of the tidal winds are in phase, which implies that the gravity wave forcing acts to amplify the tide. On the other hand, Fy generally corresponds to vertical shear zones of v. Positive Fy occurs in regions which leads to shortening of the vertical wavelength of the migrating diurnal tide. 6of14

7 Figure 4. Same as Figure 3 but for the migrating diurnal tidal component. [19] In order to see the effects of gravity wave forcing on the migrating diurnal tide more clearly, the space-time Fourier analysis is applied to u, v, Fx and Fy to obtain the migrating diurnal tidal components, which are plotted as longitude-height cross sections in Figure 4. The migrating diurnal tidal components are denoted as u tide, v tide, Fx tide, and Fy tide. It can clearly be seen that Fx tide peaks at about 2 km above the zero contour lines of u tide. The vertical wavelength of the migrating diurnal tide is about 18 km. The amplitude of Fx tide ranges from 8 to 15 m s 1 d 1 depending on the altitude, which roughly corresponds to 8 9% of the local time derivative for u tide, which ranges from ±90 to ±200 m s 1 d 1 depending on altitude. Therefore, the amplifying effect due to Fx tide on u tide is small, but not negligible in this equinox simulation. As for the meridional wind components, Fy tide peaks in the vicinity of the zero contour lines of v tide, resulting in only weak effects on the amplitude of v tide. Instead, Fy tide acts to pull down the phase lines of v tide, shortening the vertical wavelength of the migrating diurnal tide. A certain portion of Fx tide also causes a similar effect. The amplitude of Fy tide exceeds 16 m s 1 d 1 and is larger than that for Fx tide. However, the ratio of Fy tide to the local time derivative for v tide is small, about 4 5%, because of the large amplitude of v tide. The total modulation effects due to gravity wave forcing on the migrating diurnal tide in the equinox simulation are the amplification of u tide and the shortening of the vertical wavelength via both u tide and v tide Solstice [20] In this section, the zonal wind component of the gravity wave tide interactions will be considered, since the seasonal variation in the background zonal mean zonal winds strongly affects the interactions. On the other hand, the effect of gravity wave forcing on the meridional wind component of the migrating diurnal tide has only a weak seasonal variation (not shown). [21] Figures 5a and 5b show the longitude-height cross sections of Fx and large-scale u with n = 0 21 at 0030 UT during the austral winter solstice simulation, which are averaged over 20 S 30 S and 20 N 30 N. Unlike in the 7of14

8 Figure 5. Results for the austral winter solstice simulation. Latitudinal averages are taken in latitude ranges where wind amplitudes of the migrating diurnal tide are large: (a) 20 S 30 S and (b) 20 S 30 N. Color denotes eastward gravity wave forcing. Contours denote eastward large-scale flows consisting of total horizontal wave number n = The contour interval is 10 m s 1. equinox simulation, the zonal mean zonal winds in the upper mesosphere have significant vertical shears at 20 S 30 S and 20 N 30 N. In the region of 20 S 30 S, Figure 5a, the wintertime westerly winds are dominant below a height of about 75 km (see also Figure 1c). The zonal gravity wave forcing (Fx) causes a strong deceleration of the westerly winds at a height of 60 to 85 km. The local maximum of negative Fx exceeds 100 m s 1 d 1. Fx shows significant longitudinal variation depending on the phase of the tidal winds, that is, the westward forcing mostly occurs below the height of the zero wind line for the large-scale zonal winds consisting of the zonal mean and tidal components. Such dependence strongly suggests the occurrence of critical level filtering and/or wave breaking of gravity waves that propagate westward relative to the background westerly winds. The longitudinal variations in the gravity wave sources in the troposphere may also contribute to the longitudinal variation of the gravity wave forcing. For example, a distinct peak of Fx around 290 E is a unique feature in the solstice simulation (see Figure 3a) and is associated with breaking orographic gravity waves originating near the Andes [e.g., Watanabe et al., 2008a; Watanabe, 2008]. [22] In contrast to the winter subtropics (20 S 30 S), the summertime easterly winds are dominant in the summer subtropics (20 N 30 N) below a height of about 75 km (Figures 1c and 5b). The zonal gravity wave forcing (Fx) causes strong decelerations of the easterly winds below the zero wind line for the large-scale zonal winds, suggesting occurrence of critical level filtering and/or wave breaking of gravity waves that propagate eastward relative to the background easterly winds. As is the case with the results from 20 S 30 S, Fx shows significant longitudinal variation, which is likely associated with the phase of the migrating 8of14

9 Figure 6. Same as Figure 5 but for the migrating diurnal tidal component. diurnal tide. At a height of km, the westerly (easterly) phase of the migrating diurnal tide lowers (raises) the zero wind line for the zonal winds in the eastern (western) hemisphere, while simultaneously lowering (raising) the altitudes of Fx. [23] Figures 6a and 6b show the migrating diurnal component of the gravity wave forcing and zonal winds shown in Figures 5a and 5b, respectively. The vertical wavelength of the migrating tide is about 21 km. In the upper mesosphere (70 80 km), the amplitude of the zonal wind component of the migrating diurnal tide (u tide ) is larger in the winter subtropics (Figure 6a) than in the summer subtropics (Figure 6b). Although a significant positive (eastward) acceleration is found in the upper mesosphere of the winter subtropics (Figure 6a), it only results from the zonal Fourier decomposition for the zonal wave number 1 component of Fx. In fact, no positive acceleration occurs in that region (see Figure 5a). Since the negative (westward) acceleration due to Fx tide occurs below the local zero wind line, including the zonal mean westerly winds and tidal winds, phase relationships between Fx tide and u tide are less clear than in the equinox simulation (Figure 4a). For example, the negative Fx tide matches negative u tide in a longitude-height region of (180 E 360 E, km), which causes amplification of u tide. On the other hand, negative Fx tide matches positive u tide in longitude-height regions of (0 90 E, km) and ( E, km), which causes suppression of u tide. Both of these effects are not negligible (jfx tide j = m s 1 d 1 ) compared to the local time derivative for u tide, which is about ± m s 1 d 1 depending on the altitude. A similar situation occurs in the upper mesosphere (60 80 km) of the summer subtropics (Figure 6b), where Fx tide is in antiphase with u tide, acting to suppress the migrating diurnal tide. These results strongly suggest the importance of the background zonal mean zonal winds on the gravity wave tide interactions in the present simulations Equivalent Rayleigh Friction Coefficient [24] Figures 7a and 7b show the altitude-latitude cross sections for the real part of the ERF coefficient in the 9of14

10 Figure 7. (a) Equinox simulation. (b) Austral winter solstice simulation. Color denotes real part of the equivalent Rayleigh friction coefficient (see text). Thick contours denote zonal mean zonal wind with a contour interval of 10 m s 1. Thin contours denote amplitude of zonal wind for the migrating diurnal tide with a contour interval of 10 m s 1. equinox and solstice simulations, respectively. According to the definition of the ERF coefficient (equation (2)), the magnitude of the coefficient becomes large at locations, where the amplitude of u tide is small. However, large values of the ERF coefficient outside the latitudes of the maximal tidal amplitude, that is, outside the subtropics of both hemispheres, are not important for the amplification/ suppression of the migrating diurnal tide. As was mentioned earlier (section 3.3.1), Fx tide acts to amplify the migrating diurnal tide in the subtropics of the equinox simulation (Figure 7a). The negative real part of 2 to s 1 is seen near the altitudes of 75, 85, and 95 km in the subtropics of both hemispheres. In the solstice simulation, Fx tide suppresses the migrating diurnal tide in the upper mesosphere of both hemispheres (Figure 7b). The positive real part of 4 to s 1 is seen near the vertical shear zones of the zonal mean zonal winds (70 80 km) in both hemispheres. These values for the real part of the ERF coefficient are the same order of magnitude as those for McLandress [2002a]. [25] Figures 8a and 8b show the imaginary part of the ERF coefficient in the equinox and solstice simulations, respectively. Negative values represent the tidal component of gravity wave forcing which acts to shorten vertical wavelength of the migrating diurnal tide, although the correspondence between the imaginary part of the ERF coefficient and the phase of the migrating tide is not obvious from Figure 8. The magnitude of the imaginary part of the ERF coefficient is roughly proportional to the amplitude of Fx tide shown in Figure 9, and inversely proportional to the amplitude of u tide. This relationship is expected from the definition of the ERF coefficient, as well as the fact that gravity wave forcing generally acts to pull down the overlying vertical shear zone of the background flows. 10 of 14

11 Figure 8. (a) Equinox simulation. (b) Austral winter solstice simulation. Color denotes imaginary part of the equivalent Rayleigh friction coefficient (see text). Thick contours denote amplitude of zonal wind for the migrating diurnal tide with a contour interval of 10 m s 1. Thin contours denote phase of the migrating diurnal tide with a contour interval of 3 h. The magnitude of the imaginary part of the ERF coefficient in the subtropics of both hemispheres is 2 to s 1 during the equinox and 2 to s 1 during the solstice. These values agree well with the earlier evaluation of McLandress [2002a]. 4. Summary [26] We performed the perpetual equinoctial and solstice simulations using the JAGUAR gravity wave resolving GCM to investigate the interactions between the migrating diurnal tide and the directly simulated small-scale gravity waves in the low-latitude MLT. The model directly simulates gravity waves with horizontal wavelengths greater than 190 km, and generally reproduces mean zonal winds and temperatures from the surface to the MLT. The interactions between the migrating diurnal tide and the directly simulated small-scale gravity waves in the low-latitude MLT were investigated by calculating the tidal components of zonal wind accelerations and the equivalent Rayleigh friction due to the tidal induced gravity wave dissipation. [27] The amplitudes of the migrating diurnal tide were successfully simulated during the both seasons, and the tidal winds affected the altitudes of gravity wave dissipation, and therefore, the altitudes of gravity wave forcing. The phase relationships between the zonal components of the tidal winds and the tidal induced gravity wave forcing were investigated. The tidal component of zonal wind acceleration due to the gravity wave forcing had maximal values of about 15 m s 1 d 1 near the maximal vertical shear of the tidal winds, which generally shortened the vertical wavelength of the migrating diurnal tide. During the equinox, when the vertical shear of the mean zonal winds in the lowlatitude MLT is weak, the tidal winds primarily affect the altitudes of gravity wave dissipation. In such a case, the tidal winds and the tidal induced gravity wave forcing are in 11 of 14

12 Figure 9. (a) Equinox simulation. (b) Austral winter solstice simulation. Color denotes amplitude of the migrating diurnal tidal component of the zonal gravity wave forcing.thick contours denote zonal mean zonal wind with a contour interval of 10 m s 1. Thin contours denote amplitude of zonal wind for the migrating diurnal tide with a contour interval of 10 m s 1. phase, so that the gravity wave forcing acts to amplify the migrating diurnal tide. On the other hand, the zonal mean zonal winds have a strong vertical shear in the low-latitude upper mesosphere during the solstice. Hence, the combination of the zonal mean zonal winds and the tidal winds affects the altitudes of gravity wave dissipation. As a result, the tidal winds and the gravity wave forcing are in antiphase in the low-latitude upper mesosphere of both hemispheres, and the gravity wave forcing acts to suppress the migrating diurnal tide. The ERF coefficients calculated in this study had a similar order of magnitude to those for McLandress [2002a]. Appendix A [28] As was mentioned by Akmaev [2001] in his Appendix, Miyahara and Forbes [1991] equation (2.2) for the damping condition of gravity wave momentum flux was incorrectly written in the article. The correct expression, which corresponds to those given by Akmaev in his Appendix, equations (A2), (A3), and/or (A6), was used in the FORTRAN program to calculate the momentum flux. Thus, Akmaev s [2001] suggestion that this misprint is the source of the discrepancies between Miyahara and Forbes [1991] and Akmaev et al. [1996, 1997], McLandress [1998], and Norton and Thuburn [1999] cannot be correct. These other factors need to be identified. However, the possible causes are not discussed in the present paper, since the objective of this paper is not to find the possible causes, but to analyze the direct interaction between gravity waves and the diurnal tides. [29] Acknowledgments. The authors thank two anonymous reviewers for many constructive comments. Discussions with William Ward and members of the KANTO project were helpful in improving the original manuscript. This work is a contribution to the Innovative Program 12 of 14

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14 Yoshikawa, M., and S. Miyahara (2003a), Longitudinal variations of amplitudes of diurnal tides in the MLT region simulated by a general circulation model, Adv. Space Res., 32, , doi: /s (03) Yoshikawa, M., and S. Miyahara (2003b), Zonal mean meridional circulation in the low to middle latitude of MLT region: A numerical simulation by a general circulation model, Adv. Space Res., 32, , doi: /s (03) Yoshikawa, M., and S. Miyahara (2005), Excitations of nonmigrating diurnal tides in the mesosphere and lower thermosphere simulated by the Kyushu-GCM, Adv. Space Res., 35, , doi: /j.asr Zhang, S. P. P., and G. G. Shepherd (2005), Variations of the mean winds and diurnal tides in the mesosphere and lower thermosphere observed by WINDII from 1992 to 1996, Geophys. Res. Lett., 32, L14111, doi: /2005gl S. Miyahara, Department of Earth and Planetary Science, Kyushu University, Fukuoka , Japan. (sbm@geo.kyushu-u.ac.jp) S. Watanabe, Frontier Research Center for Global Change, Japan Agency for Marine-Earth Science and Technology, Showa-machi, Kanazawa-ku, Yokohama city, Kanagawa , Japan. (wnabe@jamstec.go.jp) 14 of 14