We use the extended Canadian Middle Atmosphere Model (CMAM), a general circulation model (GCM), to investigate the nature of the terdiurnal tide. Temperature and horizontal winds from a model run are analyzed to delineate the character of this tide for zonal wave numbers s = −5 to +5. Descriptions of the annual mean amplitudes, seasonal variations, and total tide superposed from the migrating and 10 nonmigrating components are provided. The amplitudes and vertical wavelengths of the various components and the total terdiurnal tide are found to depend strongly on season, latitude, and altitude. The migrating terdiurnal component maximizes at mid and high latitudes with significant amplitudes (annual mean amplitude in wind (temperature) >10 m/s (K)) in the upper mesosphere and lower thermosphere (MLT) region. Between 80 and 100 km, maximum amplitudes occur in winter in both hemispheres, whereas above 100 km, maximum amplitudes occur during solstices. For the zonal wind field, the nonmigrating terdiurnal components Te5, Te3, Te4, Tw4, and Tw5 tend to peak at >50°N/S with amplitudes between 2 and 8 m/s. The other nonmigrating components maximize in the polar regions with amplitudes of 2–10 m/s. Possible generation mechanisms (solar heating and nonlinear interactions) for the migrating terdiurnal tide in the MLT region are also examined. Correlation analysis indicates that nonlinear interactions between the migrating diurnal and semidiurnal tides are unlikely to be the source of the migrating terdiurnal tide.
If you can't find a tool you're looking for, please click the link at the top of the page to "Go to old article view". Alternatively, view our Knowledge Base articles for additional help. Your feedback is important to us, so please let us know if you have comments or ideas for improvement.
 Very few theoretical and modeling studies have addressed the form of the terdiurnal tide and examined its generation mechanism. The two main generation mechanisms proposed to explain the observed characteristics of the migrating terdiurnal tide are direct solar heating [Chapman and Lindzen, 1970; Glass and Fellous, 1975; Smith and Ortland, 2001] and nonlinear interactions between the migrating diurnal and semidiurnal tides although the nonlinear interaction mechanism remains contentious [Teitelbaum et al., 1989; Smith and Ortland, 2001; Akmaev, 2001]. Miyahara and Forbes  offered a plausible alternative mechanism associated with tidal modulation of gravity wave momentum flux capable of generating local, short-term fluctuations with close to an 8 h period. Most of the nonmigrating terdiurnal tidal components are thought to be generated by zonal asymmetries in latent heat forcing due to land-sea modulations of tropical deep convection, or by nonlinear interactions between the migrating tidal components and stationary planetary waves with zonal wave numbers s = 1 and s = 2 [Forbes and Wu, 2006; Forbes et al., 2006, 2008].
 It is generally expected, from the form of the solar heating, that the amplitude of the terdiurnal tide would be smaller than that of the diurnal or semidiurnal tides [Chapman and Lindzen, 1970]. However, observations from several locations have indicated that occasionally this is not the case and the terdiurnal tide dominates [Cevolani, 1987; Teitelbaum et al., 1989; Raghava Reddi et al., 1993]. Furthermore, variabilities over a range of time scales are typical of the observed terdiurnal tide. The short-term variability has been thought to be correlated with that of the migrating diurnal and semidiurnal tides [Teitelbaum et al., 1989; Thayaparan, 1997]. Beldon et al.  and Younger et al.  observed quasiperiodic variation of 2–3 days in the terdiurnal tide at mid and arctic latitudes and explained this as a result of interactions between the quasi 2 day planetary wave and the terdiurnal tide.
 In this paper we use the extended Canadian Middle Atmospheric Model (CMAM) to study the migrating and nonmigrating terdiurnal tides. The extended CMAM is a three-dimensional general circulation model (GCM) with a fully resolved troposphere and an upper boundary at 2 × 10−7 mbar (∼210 km) [Beagley et al., 2000; Fomichev et al., 2002]. This high upper boundary allows dynamical processes to be studied from the ground to the lower thermosphere without the influence of sponge layers, which are often inserted in the mesosphere. The model includes realistic tidal forcing due to radiative heating, convective processes and latent heat release (see Scinocca and McFarlane  for details) and uses the gravity wave breaking parameterization of Hines [1997a, 1997b]. These processes have been shown to provide the forcing to generate the migrating and nonmigrating tides [McLandress, 1998, 2002; Ward et al., 2005; Du et al., 2007].
 Spatial spectral analysis (as described by Ward et al.  and Du et al. ) has been applied to the model temperature and horizontal wind fields to obtain the amplitudes and phases of the terdiurnal tide at different zonal wave numbers (from −5 to +5). Throughout this paper we use the following convention for naming the terdiurnal tides. Tws and Tes are used to denote a westward (with positive wave numbers) or eastward (with negative wave numbers) propagating terdiurnal tide, respectively, with absolute value of the zonal wave number ∣s∣ (from 1 to 5). The standing oscillation of the terdiurnal tide is denoted as Ts0.
 This study provides the first analysis of the migrating terdiurnal tide in a GCM and also is the first to discuss the existence and form of 10 nonmigrating terdiurnal components. We identify the primary migrating and nonmigrating terdiurnal tidal components in the horizontal winds and temperature fields and describe their altitude-latitude distributions and seasonal variations. Superposition effects are also considered and their impact on local observations noted. The generation mechanisms of the migrating terdiurnal tide are also discussed by examining the short-wave solar heating of 8 h period in the model and the correlations between the amplitudes of the migrating terdiurnal tide and the migrating diurnal and semidiurnal tides for seasonal and short-term variations.
 This study has several objectives.
 1. One objective is to broaden the general appreciation for the complexity of this tide. We provide a global overview of the terdiurnal zonal wave number components (from s = −5 to s = +5) based on our model results, substantiated through comparisons with published observations. The global aspect of the model results reveals some tidal characteristics that have not yet been reported in observational studies. We hope the presentation of this global perspective will stimulate more complete observations and further modeling studies. These should take into account the full complement of components which contribute to the terdiurnal field.
 2. We wish to sensitize the observational community to the impact of the superposition of tidal components. We show that the combined fields exhibit considerable longitudinal variability. The interpretation of local observations must be undertaken with care.
 3. Another objective is to refine the manner in which correlation analyses are used as indicators of nonlinear interactions. We examine correlations between the amplitudes of the migrating diurnal/terdiurnal and semidiurnal/terdiurnal tides for seasonal and short-term variations. Strong positive and negative correlations are associated with seasonal variation. Correlations over short time scales are not found to be significant.
 The paper is organized as follows. We begin by briefly describing the extended CMAM and our data analysis procedures in section 2. The terdiurnal tidal components associated with different zonal wave numbers are described in section 3. Annual mean latitudinal-height structures of the amplitudes of all 11 terdiurnal components are illustrated. Seasonal variations and vertical wavelengths of the terdiurnal tidal components are described with emphasis on the migrating terdiurnal component Tw3. The results from superposing all 11 terdiurnal components are presented at the end of section 3. In section 4, our model results are compared with observations and other modeling studies and the generation mechanisms of the migrating terdiurnal tide Tw3 are discussed. The conclusions of this study are provided in section 5.
2. Description of the Extended CMAM and the Data Analysis Method
 The GCM used for the present study—the extended CMAM–extends from the Earth's surface to about 210 km. It is a spectral model with triangular truncation at wave number 32 (T32), which corresponds to a latitudinal-longitudinal resolution of ∼6° × 6° near the equator. This version has 70 vertical layers, with a vertical resolution ranging from ∼150 m near the surface to ∼2 km near the tropopause and tending to a roughly constant value of ∼3 km in the middle atmosphere. The extended CMAM is based on the standard CMAM which was originally developed from a tropospheric general circulation model at the Canadian Centre for Climate Modeling and Analysis (CCCma) [McFarlane et al., 1992; Beagley et al., 1997]. Physical parameterizations appropriate to the MLT region were implemented in the extended CMAM (see Beagley et al. , McLandress , and Fomichev et al.  for details and for model validation). The tidal oscillations are generated self-consistently through internal processes associated with short- and long-wave radiation absorption, large-scale condensation, and convective heating. Details of this run are provided by Du et al. , who, using the same run, showed that the nonmigrating semidiurnal tides simulated from the model are in reasonable agreement with the observations.
 The model sampling time interval for the run is 3 h and the model output is converted to frequency/zonal wave number (σ/s) fields. The data analysis method is the same as that used by Ward et al.  and Du et al. . Since the model is a spectral model, all variables at each time step are resolved as spherical harmonics. By summing over the spatial part of the harmonics, complex amplitudes are obtained at each latitude and height (accurate to the level of the machine precision). A Fourier transformation of the 3-hourly amplitudes is used to generate the spectral components presented in this paper. The phases are defined as the universal time (in hours) of maximum amplitude at 0° longitude.
 Although the terdiurnal tidal period is close to the Nyquist period of our sampling, the tidal estimates presented in this paper are representative of the actual tidal components. The spectral power in the model decreases rapidly for higher frequencies so aliasing is minor. This was verified using spectral analyses for a run with half-hour sampling. The spectra obtained using the half-hour sampling are marginally different from the spectra obtained using a degraded sampling of 3 h for the same run (the comparison results between the two samplings can be found in the auxiliary material; see Figures S1a–S1d). All figures presented in this paper (Figures 1–9) are robust with respect to the temporal resolution of the time series.
 The reader is reminded that although in our presentation, the terdiurnal tide is resolved into components, each with a different zonal wave number, additional structure may be present in each component. Classically, this additional structure is associated with the various modes associated with each component. Depending on the latitudinal dependence of the tidal forcing, more than one mode can be excited and behave as an independent wave. Although this terminology is only exact for a Hough mode analysis for an isothermal, windless atmosphere [Chapman and Lindzen, 1970], it provides a useful means with some physical basis to explain the variations in structure which occur during the year for the various components [see, e.g., Zeng et al., 2008].
3. Terdiurnal Tides From the Extended CMAM
 In this section, we provide a detailed description (including latitude-height structure, seasonal variation, and vertical wavelength) of the terdiurnal tidal components for temperature and horizontal winds simulated by the model. We identify the form of individual terdiurnal zonal wave number components and the nature of the tidal fields resulting from the superposition of all 11 terdiurnal components. Since, in the past, the sun synchronous component (the migrating terdiurnal tide Tw3) has been emphasized without consideration of the nonmigrating components, the focus of this presentation is intended to demonstrate the complexity of terdiurnal signatures and to stimulate further observation and analysis of these signatures in the real atmosphere.
3.1. Overview of the Terdiurnal Tidal Components
 For this paper, 11 terdiurnal tidal components (from Te5 to Tw5) were analyzed. The relative significance of the various components and their variability with latitude and altitude are shown in Figure 1. The monthly mean amplitudes of the terdiurnal tide for March are presented as a function of zonal wave number (from −5 to +5) and latitude (from −85.7°S to 85.7°N) for temperature (T), the zonal (U) and meridional (V) winds at 95 and 110 km. The wave numbers represent tidal “components” or “tides,” where positive (negative) zonal wave numbers imply westward (eastward) propagation. The units for temperature and winds are Kelvin and m/s, respectively.
 In March (Figure 1), the dominant component is the migrating terdiurnal tide (Tw3). At 95 km, larger amplitudes are located in low to mid latitudes with the largest amplitudes occurring in the NH. At 110 km, the amplitude distribution is more symmetric about the equator and the maxima are located at mid and high latitudes in both hemispheres. The maximum amplitudes are about 3–4 K for the temperature and 6–8 m/s for the winds at 95 km and increase with height. The peak amplitudes at 110 km are 10–15 K for the temperature and 10–15 m/s for the winds. Although weaker than the migrating component (Tw3), the nonmigrating terdiurnal components, such as Tw1, Tw2, Ts0 and Te5, are also present in March with maximum amplitudes greater than 5 K for the temperature and 5 m/s for the winds at 110 km. At some locations, especially in the polar regions, the amplitudes of some of the nonmigrating components (such as Tw1 and Ts0) can be as large as or even larger than those of the migrating component.
 The spectral structures in other months over an annual cycle are similar to those of March, but with amplitudes maximizing at different latitudes (figures not shown). Seasonal variations of the terdiurnal components will be discussed in more detail in section 3.3. Figure 1 indicates the complexity of the various terdiurnal tides and their strong variation with latitude and altitude.
3.2. Annual Mean Structures of the Terdiurnal Tides
 The latitudinal structure of each component is presented in Figure 2. Included are the annual mean amplitudes of the migrating terdiurnal tide Tw3 and the 10 nonmigrating terdiurnal tides Tw5−Te5 as a function of latitude and altitude for temperature (Figure 2a); zonal wind (Figure 2b); and meridional wind (Figure 2c). The altitude range is limited to 70–135 km because we are primarily interested in the MLT region where amplitudes are greater than 1 m/s or 1 Kelvin. The latitude range is from −85.7°S to 85.7°N. The amplitude scales in Figure 2 are different for the various zonal wave number components. While Figure 2 is indicative of the typical or average structure of the various components, there are significant short-term and monthly deviations from this structure. Based on the calculation from the 4 day window data set, the variability associated with the migrating terdiurnal tide maximum amplitudes is ∼30–50%. The variability is much more significant for the nonmigrating components, and the maximum amplitudes can change from negligible to about twice of the maximum amplitude values. The latitude-height distributions of the various physical fields (T, U, and V) for each component are different. The salient features of these structures are discussed below.
 The temperature amplitudes exhibit three kinds of latitude-height structures for the various terdiurnal tidal components. The dominant structure occurs above 100 km and is associated with the annual mean T amplitude of the migrating terdiurnal tide (Tw3) (Figure 2a). Two broad features are symmetrically located in the low and mid latitudes (10°–50°) of each hemisphere with maxima generally centered on 30°–40°N/S. The maximum amplitudes increase with height and are <10 K below 110 km and increase to >15 K above 120 km. Broad structures similar to those of Tw3 are seen for the nonmigrating components Tw4, Tw5, Te3, Te4, and Te5 between 60°N and 60°S, but with maxima centered on different latitudes. Te3, Te4 and Tw5 with maxima of 2–3 K are centered at the midlatitudes of both hemispheres, whereas the maximum amplitudes for Tw4 and Te5 are centered in the equatorial region and reach 4–5 K. A second structure is associated with the nonmigrating terdiurnal tides of Tw1, Tw2, Te1, and Te2. The temperature amplitude remains significant from pole to pole above 100 km with multiple peaks. Maximum amplitudes for these components are in the range of 2–4 K. Finally, Ts0 has a distinct latitude-height structure and maximizes at both poles with amplitudes of 6 K.
 There are also three kinds of latitude-height structures for the annual mean U amplitudes of the terdiurnal tides (Figure 2b). The first structure is exhibited by the Tw3, Tw5, Te3 and Te4 components. Two maxima are symmetrically located in the mid and high latitudes of both hemispheres, centered on 40°–50°N/S. The maximum amplitudes are over 15 m/s above 110 km for the migrating terdiurnal tide Tw3 and over 2 m/s for the three nonmigrating terdiurnal components. The second structure has two maxima located symmetrically in the polar regions of both hemispheres. Of the components with this type of structure, Tw1 has maximum amplitudes of 8 m/s whereas Tw2, Ts0, Te1 and Te2 have maximum amplitudes of 3–5 m/s. The third structure is associated with Tw4 and Te5 and features significant amplitudes at most latitudes except the polar regions. Tw4 has maximum amplitude of 3 m/s in the Southern Hemisphere (SH) low and mid latitudes centered on 25°S. Multiple peaks are present for Te5 with maximum amplitudes of 4–5 m/s above 110 km.
 The annual mean V amplitudes of the terdiurnal tides (Figure 2c) exhibit two of the three latitude-height structures present in the T, U fields. Broad amplitude features from 60°N to 60°S with multiple peaks characterize the migrating component Tw3 and the nonmigrating components of Tw4, Tw5, Te3, Te4 and Te5. Maximum amplitudes reach >10 m/s for the migrating component Tw3 above 100 km and 2–3 m/s for the nonmigrating components. On the other hand, the remaining nonmigrating components Tw1, Tw2, Ts0, Te1, and Te2 tend to have moderate amplitudes from pole to pole with maxima of 2–4 m/s located in the polar regions of both hemispheres.
 As with the calculations of Akmaev  and Smith and Ortland , our annual mean zonal wind amplitudes (5–6 m/s) for both components of the migrating terdiurnal tide Tw3 at 95 km are smaller than those observed by HRDI (12 m/s) [Smith, 2000]. The annual mean amplitudes of meridional wind for Tw3 are about 5–6 m/s at 95 km which is similar to the HRDI observations [Smith, 2000]. The difference in zonal winds might be due to the interannual variability of the tide, differences in the height assignment, different source mechanisms in the models or aliasing effects in the observations.
 To compare with these observations, seasonal variations of the migrating terdiurnal tide from the model are presented at 95 km for temperature, zonal wind and meridional wind fields. Since the migrating terdiurnal component maximizes above 100 km (see Figure 2), similar plots as 95 km for the 110 km level are also included. Although only seasonal variations of the migrating terdiurnal tide at two height levels are shown, the seasonal variation at 95 km is representative of those in the height range of 82–95 km and the seasonal variation at 110 km is typical for that above 100 km. The model level of 97 km appears to be a transition layer between the two kinds of seasonal variations.
 The four seasons in the NH are defined as spring (April–June), summer (July–September), autumn (October–December), and winter (January–March); the seasons in the SH are opposite of the NH; for example, the SH summer corresponds to the same months as the NH winter. In these seasonal variation plots, deviations from the annual mean structure are evident. For different seasons, different modes associated with a given component are present, presumably through selective excitation or selective filtering by the background winds and temperature as they propagate upward. In the discussion below, the migrating terdiurnal component is described and illustrated in detail. This is followed by a summary of the main features of the nonmigrating terdiurnal components. The temporal window for the seasonal variation plots is monthly mean.
Figure 3 shows seasonal variations (latitude-time distributions) of the migrating terdiurnal Tw3 tidal amplitudes (Figure 3, left) and phases (Figure 3, right) of temperature, zonal wind, and meridional wind at 95 (Figure 3a) and 110 km (Figure 3b). At each altitude, the seasonal variations of the different fields are very similar although their latitudinal structures differ.
 At 95 km (Figure 3a), the dominant features in both hemispheres have a strong annual variation. Maximum amplitudes of 4–5 K and 8–15 m/s for the temperature and winds, are present during the late autumn and early winter in each hemisphere (December–February for the NH and June–August for the SH). The maximum amplitudes in the SH are located between 40°S and 60°S and centered on 50°S, whereas the maximum amplitudes in the NH are located between 20°N and 40°N and centered on 30°N. The SH maximum tends to be slightly stronger than that of the NH. In addition to these midlatitude maxima, secondary maxima are seen in the low latitudes of both hemispheres with multiple peaks throughout the year. Zonal wind maxima of 6–8 m/s occur during December–February at 10°S and shift to 5°N–10°N with amplitudes of 4–6 m/s in March–April, June–July and October. Minima occur in February, April/May, September and November. Similar seasonal variations in the equatorial region are seen for the temperature field with maximum amplitudes of 2–4 K. Seasonal structures of the meridional wind also show an annual variation in mid/high latitudes but are more complicated than those of the zonal wind and temperature fields in the equatorial region. Multiple peaks occur throughout the year in both hemispheres.
 The large seasonal and hemispheric asymmetries associated with the structure of this component suggest that a symmetric and an asymmetric mode are both excited with similar amplitudes with the phase of the asymmetric component changing with an annual variation. (Note that on their own, symmetric and asymmetric modes cannot change their global amplitude structures, i.e., the overall amplitude can change but not the relative amplitudes.) This would result in constructive interference in one hemisphere and destructive interference in the other, with the phase of the interference switching by 180 degrees between solstices. Smith and Ortland  by using a linear tidal model found that the dominant cause of the hemispheric asymmetry is the sensitivity of the modal propagation to the background state and specific modes are prohibited from propagation in large regions of the summer mesosphere.
 At 110 km (Figure 3b), the amplitude features in both hemispheres show strong semiannual variations with stronger amplitudes during the solstices than the equinoxes. There are four maxima as a function of latitude. In the NH, the strongest amplitudes (>20 K for the temperature and >20 m/s for the winds) are seen during the late autumn and early winter months (December–February) and secondary maxima (>10 K for the temperature and >10 m/s for the winds) are seen during the late spring and early summer months (June–July) and early autumn (October). This secondary maximum is minimal at 95 km in the mid and high latitudes (Figure 3a). For both wind components, the maximum amplitudes in winter are centered on 30°N whereas the secondary maxima are centered on 60°N.
 In the SH at 110 km, the seasonal variation in amplitude is similar to the NH. Amplitudes (>20 K for the temperature and >20 m/s for the winds) are strongest during SH late spring and early summer (December–February) and late autumn and early winter months (June–July). Significant amplitudes of 15 and 10 m/s (10 K and 10 K) are also present during late summer and early autumn (March–April) and late winter (September), respectively. As with the NH, the maxima showed during late summer and early autumn (March–April) in the mid and high latitudes are absent at 95 km. The maximum amplitudes are centered on 50°S for most months except in June and July when two maxima are present and centered on 40°S and 60°S, respectively.
 The seasonal variations of the Tw3 phases at 95 (Figure 3a) and 110 km (Figure 3b) are similar in overall structure although the latitudinal structure at 95 km is more complex. This complexity at 95 km is probably due to the presence of higher-order Hough modes which are damped out by 110 km. In both cases, the asymmetric solstice structures dominate with a fairly rapid transition between them during equinoxes. The phase structures during the two solstices are reflections of each other across the equator. Overall, the rough latitudinal phase structure of all three parameters consists of four latitude bands each 4 h (180 degrees of phase) apart from each other with one of the 4 h phase jumps occurring at the equator. Between solstices the phases of the bands change by 4 h. During the transition period (equinoxes), the phase structure briefly becomes symmetric. The phase associated with the meridional wind (especially at 95 km) deviates somewhat from this general structure and is close to a five-phase band structure which varies semiannually in latitude.
 Since the seasonal variations of temperature and horizontal winds are similar for each particular terdiurnal component, the discussion for the nonmigrating components is concentrated on the zonal wind field (auxiliary material Figures S2a and S2b are similar to Figure 3 for the nonmigrating components). Most of the nonmigrating terdiurnal components have amplitudes of <1 K for the temperature and of <2 m/s for the horizontal winds below 100 km (see Figure 2). The seasonal amplitude and phase variations of the nonmigrating terdiurnal components are quite irregular at 95 km and overall structures are difficult to discern. Only seasonal variations at 110 km (where the nonmigrating terdiurnal tides have significant amplitudes) are described.
 Nonmigrating terdiurnal components Tw1, Tw2, Ts0, Te1, and Te2 maximize in the polar regions in both hemispheres (>70°N/S for Tw1 and ∼ 70°N/S for Tw2, Ts0, Te1 and Te2). Tw1, Tw2 and Ts0 have distinct seasonal variations, whereas Te1 and Te2 with amplitudes of 2–4 m/s are present for most months throughout the year without a stable seasonal variation pattern. For Tw1, peak amplitudes of 8–10 m/s occur in February, May–June and September in the northern polar region, whereas peak amplitudes of 8 m/s occur in August in the southern polar region. For Tw2, maximum amplitudes (>4 m/s) occur in the months of January–February and May–September in the northern polar region and in the months of December–March, May–August and October in the southern polar region. For Ts0, amplitudes of 2–4 m/s are present for most months throughout the year except for an amplitude minimum (<2 m/s) in November–February in the SH.
 Nonmigrating terdiurnal components Tw4, Tw5, Te3, Te4, and Te5 maximize at high latitudes in both hemispheres. For Tw4, maximum amplitudes of 6–8 m/s are seen at 50°S in July–September and a secondary maximum of 4 m/s is present at 40°N–50°N in January. For Te5, the maximum amplitudes (4–8 m/s) centered on 60°S are present during June–September whereas maximum amplitudes (∼6 m/s) centered on 60°N are present during December–February. Besides these high-latitude amplitude features, amplitudes of 2–4 m/s are also seen in the low latitudes of both hemispheres in most months throughout the year for Te5. The nonmigrating terdiurnal components Tw5, Te3 and Te5 maximize at 50°N/S with amplitudes of 2–4 m/s for most months throughout the year without obvious seasonal variations.
 The phases associated with Tw1 at the latitudes of maximum amplitudes are out of phase with each other (the northern polar phases are ∼6 h, whereas they are ∼2 h for the southern polar phases). The Tw2 phases are symmetric about the equator. The phases at both polar regions and the equatorial region are similar (∼4–6 h) and the phases are ∼2 h at 40°N–50°N and 30°S–50°S. Both phases of Tw1 and Tw2 are stable with time over an annual cycle. Phases of the other nonmigrating terdiurnal components are highly variable without a stable pattern of seasonal variation.
 More work is required to specify the behavior and sources of the nonmigrating components. Some show clear seasonal variations with maxima during specific seasons. Others are present with small amplitudes during all seasons. The phase of these components relative to the dominant migrating component will determine the local terdiurnal amplitude and if this is variable then interference effects between components may be a significant cause of local variability in the terdiurnal tide.
3.4. Vertical Wavelengths of the Terdiurnal Tides
 Observations have shown that the vertical wavelength of the terdiurnal tide has a strong dependence on season and location. Thayaparan  recorded a very short vertical wavelength of 22 km over London, Canada (45°N) in summer. Namboothiri et al.  reported that the midlatitude vertical wavelengths of the terdiurnal tide over Wakkanai, Japan (45.5°N) are very long in winter and autumn (>1000 km), shorter in spring (mean of ∼125 km) and shortest in summer (∼107 km). Younger et al.  reported a vertical wavelength of about 25–35 km in winter and spring and 50–90 km in summer and autumn at the Esrange station (68°N). While these observed wavelengths are not under question, the superposition effects described below mean that the assignment of these wavelengths to the migrating terdiurnal component is tenuous. The wavelength analysis described below, is appropriate for component resolved tidal analysis and in general can only be compared to single station ground-based observations when it is clear that a single component is dominant.
 In this section, vertical wavelengths of the 11 terdiurnal components are estimated from our model results. Some comparisons are made against the observed seasonal characteristics of the terdiurnal tide vertical wavelength. Results using the zonal wind field are emphasized (similar conclusions hold for the other fields albeit with different latitudinal dependencies).
Figure 4 shows the zonal wind amplitude (m/s) and phase (h) of the migrating terdiurnal tide Tw3 at 60°N and 60°S over an annual cycle from 40 to 135 km. Since the migrating terdiurnal tide is mainly generated by the stratospheric ozone, it is generally absent below 40 km. The solid black (red) lines are phase (amplitude) at 60°S and the dashed black (red) lines are phase (amplitude) at 60°N. The phase difference between these two latitudes (60°N–60°S) is plotted as the dotted black lines. The phase range for terdiurnal tide is 8 h; that is, an 8 h range in the x axis corresponds to one vertical wavelength in the y axis. The range in these plots is larger than 8 h because the phases presented here are corrected for phase jumps. The latitudes of 60°N/S are chosen because the annual mean amplitudes of the migrating terdiurnal tide (Tw3) zonal wind maximize and dominate the terdiurnal field at these latitudes (see Figure 2b).
 The amplitudes at both latitudes increase with height from ∼80 to 120 km and decrease slowly or stay invariant above 120 km. Between ∼100 and 120 km, the amplitude at 60°S grows more rapidly than that at 60°N for most months of the year (January–April, May, September, and November–December) and is roughly twice as large as that at 60°N at 120 km for all these months except May. During June–August, the height variation changes with the variations at the two latitudes exchanging behavior and 60°N dominating. In addition there is a lower-altitude maximum in the amplitude at 60°S around 100 km.
 Above 100 km, the phases decrease with height with very similar slopes for all months at both latitudes. This is a strong indication that a single mode dominates the behavior at these heights and the seasonal variation of the vertical wavelength is insignificant above 100 km. However, there is a clear seasonal dependence in the latitudinal structure. During solstice conditions (November–February and June–July), the phases from the two hemispheres are ∼2–4 h apart and during equinox conditions (March–May and September–October) they are approximately in phase. This implies that during solstices the dominant mode is antisymmetric and during equinox it is symmetric. The vertical wavelength of the migrating terdiurnal tide at 60°N/S above 100 km is 55 ± 15 km.
 Between 70 and 100 km, the situation for the migrating component is more complicated. The phase decreases with height for most months but with more variability in the slopes at both latitudes than was the case above 100 km. This suggests that that either more than one mode is present at these altitudes or that there is significant local forcing. There is also strong seasonal variation in the height structure of the phase. Based on estimates using 70–100 km, the vertical wavelength at 60°N is 30–50 km during April–August whereas it is 60–80 km for the other months. At 60°S, it is 60–80 km except for the months of October and November when there are large phase shifts in the range of 70–100 km, making vertical wavelength calculation difficult. Our results at 60°N are consistent with previous modeling and observation studies which state that the vertical wavelength of the terdiurnal tide is longer during the winter than summer [Thayaparan, 1997; Smith, 2000; Akmaev, 2001; Namboothiri et al., 2004]. However, this behavior does not appear to present at 60°S in the model.
 A similar analysis was conducted to determine the vertical wavelengths of the nonmigrating terdiurnal components. Vertical wavelengths were calculated over an annual cycle at two latitudes, symmetric about the equator, where the amplitude of the component maximizes (figures not shown). Since the phases of the nonmigrating terdiurnal tides are very variable below 100 km, it is difficult to determine their vertical wavelengths in this height range. Consequently vertical wavelengths are only calculated for these components above 100 km. The results are summarized in the following paragraphs.
 The vertical wavelength at 80°N/S for Tw1 is generally 50–60 km with the phase decreasing with height with similar slopes at both latitudes for most months. The exceptions for the NH are in February (vertical wavelength ∼30 km) and May (vertical wavelength ∼80 km) and for the SH in May and June (vertical wavelength ∼80 km). The phases from the two hemispheres are approximately in phase for August, September and December and they are ∼2 h apart for the other months. The vertical wavelength of Tw2 at 65°N/S is generally 40–50 km and there is a slight difference between the two latitudes during December–March when the vertical wavelength at 65°S is ∼10 km longer than that at 65°N. The phases are symmetric at these two latitudes during June–November, and are asymmetric in April and differ by 4 h. The vertical wavelengths for Tw4 and Tw5 at 50°N/S and Ts0 at 75°N/S are 40–50 km for most of the months with phases decreasing with height with similar slopes. The exception is that the vertical wavelength of Tw4 in February and April is very long with the phase changing slowly with height above 100 km. The phases of Tw4 are symmetric about the equator for June, August–October and December and are asymmetric for the rest of the year. The phases of Tw5 at 50°N/S are in phase with each other for February, March, May–July, and November and out of phase with each other for the rest of the months. For Ts0, the phases are in phase for May–December and out of phase for January–April and November.
 The vertical wavelength for Te1 at 75°N/S is about 50–60 km above 100 km. During equinox conditions, the phases are ∼4 h apart and during solstice conditions they are approximation in phase. Phase variations for the other eastward terdiurnal components (Te2, Te3, Te4, and Te5) are more variable with season above 100 km. Phase can decrease with height with different slopes, or stay constant with height or even increase with height. As a result, the vertical wavelengths of these components are highly variable.
3.5. Superposition of the Terdiurnal Tides
 The terdiurnal tidal temperature or winds observed above a ground based station is the superposition of all the migrating and nonmigrating terdiurnal components present at that time. Our model results show that the contribution of different terdiurnal components to the total terdiurnal amplitude at a given location varies with time, latitude and altitude. The resulting terdiurnal signature depends on their phases and amplitudes. As noted earlier, this renders direct comparisons between specific components and single station observations tentative. In this section, latitude-longitude and longitude-height distributions of the superposed terdiurnal tide (including the migrating terdiurnal tide Tw3 and the 10 nonmigrating terdiurnal components) as modeled by the extended CMAM are presented to illustrate the longitudinal variability of the total terdiurnal tide. Only the zonal wind field is discussed since the results are similar in general form for the temperature and meridional wind fields.
Figure 5 shows the monthly averaged total terdiurnal zonal wind amplitude (m/s) and phase (h) at 95 km in March (Figure 5a) and at 110 km in June (Figure 5b). In Figure 5a (top), the amplitudes over the latitude-longitude cross section are very variable and range between 0 and 15 m/s. The longitudinal variation due to the nonmigrating terdiurnal tides is significant (the amplitude of a purely migrating tide would be independent of longitude). The associated phase (Figure 5a, bottom) is less variable than the amplitude with bands of similar phase in the NH tilting eastward with increasing latitude (from the equator to the North Pole), and the bands in the SH tilting westward with increasing latitude (from the South Pole to the equator). The phase structure is symmetric about the equator. The total terdiurnal zonal wind at 110 km in March (figure not shown) has a similar phase structure, but with less variability. The amplitude structure is quite different from that at 95 km and closer to that of the migrating terdiurnal tide Tw3 which is the more dominant component at 110 km than at 95 km.
 At 95 km in June (figure not shown), the migrating terdiurnal tide Tw3 dominates in the SH with the nonmigrating terdiurnal components modulating the amplitude in longitude. The total amplitudes are quite variable in the NH and the nonmigrating terdiurnal components dominate in the polar regions. At 110 km in June (Figure 5b, top), there are eight amplitude peaks at 40°S and three peaks at 60°S along a longitude circle. The amplitudes can vary by 30 m/s along a particular longitude circle, clearly demonstrating the potential for significant station to station variation in the observed tide. The phase structures at the two height levels in June are very similar to each other with the one at 110 km being less variable. However, the phase structure in June is very different from that in March (Figure 5a). In contrast to March, the phase strips with similar phase values are continuous across the equator (antisymmetric) and tilt eastward with increasing latitude (from the South Pole to the North Pole). As would be expected, the different seasonal variations of the terdiurnal components (section 3.3) result in significant month-to-month variability in the form of the total amplitude and phase of the terdiurnal tide (figures not shown).
Figure 6 provides a further illustration of the consequences of the superposition of these components. In this case, longitude-height cuts at 60°N/S of the superposed terdiurnal tidal amplitude and phase are presented from the ground to 130 km in June (Figure 6a). Four vertical profiles of the total terdiurnal tidal phase at different locations (60°N/0°W, 60°N/100°E, 60°S/130°E, 60°S/50°E) selected from Figure 6a are presented in Figure 6b. Because the relative amplitudes and phases of the various components vary with height, the height dependence of the total terdiurnal tide at a given location does not conform to a particular component unless that component dominates. At most locations in the mesopause region, although the migrating component is typically the largest, the sum of the amplitudes of the other components can be as large. This likely explains the differences between ground-based observations taken at different longitudes at the same latitude. This also means that it is difficult to use a phase profile above a single station to determine the vertical wavelength of a specific component. This point is clearly demonstrated by comparing the phase profile from 80 to 100 km at different longitudes at the same latitude (Figure 6b). The phase profile at 60°N/100°E decreases monotonically with height whereas the phase at 60°N/0°W behaves quite differently with phase first decreasing, then increasing and finally decreasing with height. On the other hand, the phase decreases with height at 60°S/130°E more quickly than that at 60°S/50°E. As a result, the vertical wavelength calculated from each profile is different. Comparisons with single station observations must be undertaken with care because the terdiurnal tide is longitude-dependent due to the superposition of several zonal wave number components.
4.1. Comparison With Observations
 Analysis of the CMAM results indicates that the terdiurnal motions in the model atmosphere are significant and involve a number of zonal wave number components. Each component has its own seasonal variation and latitude-altitude structure. Annual mean amplitudes of the migrating terdiurnal tide Tw3 dominate over the nonmigrating terdiurnal components in mid and high latitudes. Its zonal wind amplitudes can reach a maximum of 10–15 m/s at 95 km during winter. While ground-based observations at specific times and locations will be affected by interference between the various terdiurnal components, seasonal variations are expected to follow that of the dominant component (generally the migrating terdiurnal tide).
 The diagnosed results for this tide from our model show that the seasonal variations of the terdiurnal tides are dependent on latitude and height. The seasonal variations of the migrating terdiurnal tide Tw3 at 95 km are quite different from those at 110 km (Figure 3). Note also that the geometric altitudes of 95 and 110 km used to illustrate the model results are derived from pressure levels using the global-averaged geopotential heights. As a result, these geometric altitudes are approximate and may not represent those in the real atmosphere (deviations of ∼5 km are possible). Since there are steep height gradients in the seasonal variations of the migrating terdiurnal tide in the model results, small changes in the heights of comparison can affect the extent to which the model/observation comparisons are in agreement or not.
 Most terdiurnal tidal observations have been conducted in the NH mid and Arctic latitudes and in the height range of 80–100 km. Different seasonal behaviors of the terdiurnal tide were observed at various latitudes. In the NH low latitudes, Jiang et al.  used Maui meteor radar (20.75°N, 156.43°W) to study the terdiurnal tide from May 2002 to May 2007. Their study showed that the meridional wind exhibits a semiannual variation in amplitude and peaks near the equinoxes (March and October). However, the zonal component does not show these seasonal characteristics. Radar wind observations at Wuhan (30°N, 114°E) showed no obvious seasonal pattern [Zhao et al., 2005]. Our model also shows complex seasonal patterns with the migrating terdiurnal tide in 30°S–30°N (Figure 3a). These results are also in agreement with the High Resolution Doppler Imager (HRDI) satellite observations [Smith, 2000].
 There are more ground based observations of the terdiurnal tide in the NH midlatitudes. These observations were reported from Montpazier (44°N) and Garchy (47°N), France, and Saskatoon (52°N), Canada [Teitelbaum et al., 1989], London (43°N), Canada [Thayaparan, 1997], Wakkanai (45.5°N), Japan [Namboothiri et al., 2004], and Castle Eaton (52.6°N), UK [Beldon et al., 2006]. The observations between 40°N and 50°N indicated that there is a distinct NH amplitude maximum in the winter months and a minimum in the summer months. This winter maximum and summer minimum seasonal variation is consistent with our model results in the latitude range of ∼25°N–50°N at 95 km (see Figure 3a, zonal wind amplitude). In contrast, the observations conducted between 50 and 60°N confirm that the terdiurnal tidal amplitudes maximize in September–November and minimize in May. The autumn maximum of the terdiurnal tide is even stronger than the amplitudes during winter months. This behavior is similar to our model results at 110 km (which is representative of the seasonal variation above 97 km in the model) and in the range of 50°N–60°N (Figure 3b, zonal wind amplitude).
 At NH high latitudes, Younger et al.  used data from October 1999 to April 2001 over the height range of 81–97 km at the Esrange station (68°N, 21°E) to study the terdiurnal tide. They reported that the winter maximum usually observed in the midlatitudes is greatly reduced in the Arctic and that the largest terdiurnal amplitudes occur in September and October. In the model in Arctic latitudes (>60°N) (Figure 3b), a NH late spring/summer (May–August maximum) and an autumn (October) maximum are present and the winter amplitudes are significantly smaller. The autumn maximum occurs at altitudes above 95 km whereas the late spring/summer maximum occurs above 100 km in the model. This is maybe why only an autumn maximum was observed at the Esrange station.
 In the model, the terdiurnal tidal characteristics in the SH have a different temporal form than those in the NH (Figure 3). Below 100 km, maximum amplitudes are present during the SH winter; however, the magnitude of this amplitude maximum is stronger than its NH winter counterpart. Above 100 km, maximum amplitudes in the NH are strongest during December–February whereas maximum amplitudes in the SH are present during the same periods but corresponding to the SH summer. More observations of the terdiurnal tide at locations in the SH are needed to verify these model results.
 Overall, we consider the basic characteristics of the terdiurnal tide captured by the extended CMAM to be in reasonable agreement with the published observations. In addition, some new features (such as seasonal variations above 100 km in the NH and in the SH) that have not yet been reported by the observing community have been identified in the model results.
4.2. Generation Mechanisms of the Migrating Terdiurnal Tide
 Two main sources have been considered for the generation of the migrating terdiurnal tide: solar heating and nonlinear interactions. A numerical study by Teitelbaum et al.  for solstice conditions found that the effective terdiurnal components generated by the direct solar heating mechanism and nonlinear interactions between the migrating diurnal and semidiurnal components were of comparable amplitudes. This work initiated a general search for such correlations which when found were typically taken as evidence for nonlinear interactions. Solar heating as a source was generally taken for granted.
 Reports of significant correlation between these components using ground-based observations are generally based on short time scale variations (∼days). Thayaparan  presented evidence from radar observations that the terdiurnal wind variations at 43°N sometimes follow variations in the diurnal and semidiurnal tides for several weeks with correlation coefficients between 0.40 and 0.75. Similarly, Zhao et al.  found evidence for these correlations using radar observations from Wuhan (30°N) at the 0.64 and 0.75 levels. In contrast, using satellite wind observations from HRDI, Smith  found that these correlations were quite low (∼0.2–0.3) when determined with data on a monthly time scale within the latitude range of 40°N–40°S (the best that could be achieved with this platform).
 There have also been modeling studies of these generation mechanisms. Akmaev  presented results from a modeling study of the migrating terdiurnal tide between 70 and 105 km using a mechanistic model with a lower boundary at 100 mb. The main source for the migrating terdiurnal tide was found to be solar heating in the ozone layer. He also performed a numerical experiment in which all wave number 3 forcing was switched off and observed significant terdiurnal amplitudes in the 90–110 km region. As a result he concluded that nonlinear interactions between the migrating diurnal and semidiurnal tides make a noticeable in situ contribution to the excitation of the migrating terdiurnal tide at these heights. Smith and Ortland  also examined the migrating terdiurnal tide in a theoretical study using a mechanistic three-dimensional primitive equations model, Research for Ozone in the Stratosphere and its Evolution (ROSE), which extends from the tropopause to the lower thermosphere. In their study, they found that direct solar forcing of the terdiurnal tide is the dominant source mechanism at all latitudes with nonlinear interactions possibly playing a role as a source for the low-latitude terdiurnal tide.
 Neither of these models had a fully resolved troposphere, did not introduce terdiurnal oscillations at their lower boundary and only examined the role of nonlinear interactions on a longer-term basis (∼monthly). The terdiurnal tide was excited by direct heating of ozone in the stratosphere. These models had the advantage of allowing clean investigations of coupling between tidal components since the semidiurnal and diurnal components introduced at the lower boundary could be switched on and off and solar heating related to the terdiurnal tide turned off.
 There are several ways in which the extended CMAM can be used to further investigate the source mechanisms of this tide. Because this model has a fully resolved troposphere, the impact of the tropospheric heating missing from these earlier simulations can be examined. The ozone chemistry in this run of the extended CMAM is similar to the model runs mentioned above so our stratospheric heating is similar. It is of interest to examine whether the inclusion of the tropospheric heating results in significant differences in the form of the diagnosed tidal components in these various models. Finally, the extended CMAM can be used to examine the importance of nonlinear interactions as a source by considering correlations on various time scales between the three migrating tides. Since the model naturally includes long- and short-term variability, it can be used to examine the short-term correlations noted in the ground-based observations (which could not be examined using satellite observations and the mechanistic models mentioned above). As this model is a full general circulation model, the tests, possible with the mechanistic models involving the shutting off of specific components, are very difficult to accomplish.
 The migrating terdiurnal component of the direct solar short-wave heating (SWH) in March and June from the extended CMAM is presented in Figure 7 (for clarity, the heating in the various layers is plotted separately). The heating is mainly confined to three layers located between 10 and 15 km, 40–60 km, and above 100 km which correspond to the heating from water vapor, ozone, and O2, N2, and atomic oxygen, respectively. The heating is symmetric across the equator in equinox (March), and strongly asymmetric in solstice (June). The maximum heating rate is about 0.1 K/d in the troposphere, 2 K/d in the stratosphere, and 6 K/d in the upper mesosphere and lower thermosphere.
 Although the thermospheric heating is largest, it is unlikely to be an effective source for the migrating terdiurnal tide at lower altitudes. Tides excited at these heights will be viscously damped and downward propagation will be truncated because of the increase in density at lower altitudes. To be an efficient source, the thickness of the heating layer should be about half of the vertical wavelength of the generated tide. The thermospheric heating is a thick layer (∼80 km) so it is not an efficient source for the migrating terdiurnal tide. On the other hand, the thickness of the stratospheric ozone layer (30–40 km) is a good match to the vertical wavelength of the migrating terdiurnal tide (60–70 km).
 The stratospheric heating from the extended CMAM is very similar in form but slightly smaller than that in the ROSE model [Smith and Ortland, 2001]. The seasonal variation of the migrating terdiurnal tide in our model (Figure 3a) at 95 km is also very similar in form and amplitude to their seasonal variation [see Smith and Ortland, 2001, Figure 2]. This similarity suggests that the stratospheric radiative source is the main solar heating source for the migrating terdiurnal tide Tw3 and that tropospheric heating plays a minor role.
 The possibility that nonlinear interactions between the migrating diurnal and semidiurnal tides might be a significant source for the migrating terdiurnal tide in the extended CMAM is explored by examining the correlations between the amplitudes of these tides. Correlation analysis is difficult to interpret rigorously without supporting causal evidence since strong correlations could imply common source effects (i.e., a common heating source lower in the atmosphere), common filtering effects associated with the background atmosphere as well as nonlinear interactions. However, should nonlinear interactions be a significant source of the migrating terdiurnal tide one would expect it to be present at short-term and seasonal time scales. The lack of significant correlation on both these time scales is taken as evidence against these particular nonlinear interactions being a source of the migrating terdiurnal tide.
 The nature of the correlation will depend on the time scale over which the interaction takes place. For a short-term interaction on the order of a few days, correlation between these components would be expected close to the height where the interaction takes place. However, because of variations in the vertical velocities of the components, correlations would only be seen at altitudes away from the source if appropriate lags were considered. For longer persistent interactions, one would expect correlations to exist above the interaction region (assuming vertical propagation) over a range of heights. As the tides under consideration here are global components, the correlations would also be expected to have extensive latitudinal extent (at least hemispheric).
 In the extended CMAM, the character of the correlations is examined by considering seasonal (>2 months) and short-term variations (<2 months) of the three migrating tidal amplitudes. Tidal amplitudes were diagnosed using a 4 day window (as opposed to the monthly average presented earlier) stepped by 2 days to provide suitable time series for this analysis. Two time series are then created for each tide by filtering the initial time series using a high- and low-pass filter (accomplished in this case by reconstructing time series using the high (>2 month−1) and low (<2 month−1) frequency terms, respectively, of the initial annual time series). Correlations associated with long- (short-) term variations in these components are calculated using the low- (high-) pass time series. The model exhibits considerable internal variability so the amplitude time series associated with the migrating diurnal and semidiurnal tides vary significantly on both time scales. Should nonlinear interactions be important, significant correlations for both the long- and short-term variations would be expected (there should be no preference for either temporal scale).
 The correlation plots between components are presented in Figures 8 and 9. Figure 8 shows latitude/height plots of correlation coefficients (from −1 to 1) of the migrating diurnal/terdiurnal zonal wind amplitudes for seasonal (Figure 8a) and short-term variability (Figure 8b) in four seasons (NH seasons, in captions) from 40 to 120 km. Figures 9a and 9b are the same as Figures 8a and 8b but for the correlations of the migrating semidiurnal/terdiurnal tidal amplitudes. Significance test of the correlations is done with a Gaussian random model. White spaces represent the correlations below the 95% significance level.
 For the seasonal variations, Figures 8a and 9a show regions of very strong positive and negative correlation which alternate in height as well as latitude. Both high positive and negative correlation coefficients (>0.8 or <−0.8) are seen in patches at different heights and latitudes in all four seasons between the migrating terdiurnal amplitude and the migrating diurnal tidal amplitude (Figure 8a) and the migrating semidiurnal tidal amplitude (Figure 9a).
 Despite the complex patterns, common features exist for the correlations of the seasonal variations in these tides (Figures 8a and 9a). The amplitude correlations between the migrating diurnal/terdiurnal tides tend to be negative (Figure 8a) whereas those between the migrating semidiurnal/terdiurnal tides tend to be positive (Figure 9a). The correlations in spring are approximately mirror images of the correlations in autumn in Figure 8a for the diurnal/terdiurnal/correlations. This feature does not seem to be present for the semidiurnal/terdiurnal correlations. The diurnal/terdiurnal correlations are linked to the seasonal variation in the amplitudes of the two tides with diurnal maxima during equinoxes being associated with terdiurnal minima. The patterns for the semidiurnal/terdiurnal correlations are more difficult to explain in this manner since the seasonal variation of the migrating semidiurnal tide is more complicated that than of the diurnal tide. However, as discussed in sections 3.3 and 4.1, the seasonal variations of the terdiurnal tide depend on latitude and height which when combined with similar variability in the diurnal and semidiurnal components could possibly explain the alternating patterns in the correlations.
 For the short-term variations, the correlations between the migrating diurnal/terdiurnal tides (Figure 8b) and the migrating semidiurnal/terdiurnal tides (Figure 9b) are not significant at most locations. In addition, these correlations show little coherence in height and latitude. Local correlations can be significant for a single location over short periods of time but there does not appear to be global significance to these correlations.
 The lack of significant correlation for the short-term variability implies that nonlinear interactions at these time scales are not present. Short-term variations in the amplitudes of the diurnal and semidiurnal components would be expected to result in similar variations in the terdiurnal component and this does not occur. The model does not replicate the short-term correlations reported in ground-based observations and used as evidence for the existence of nonlinear interactions between these migrating tides.
 The strong correlations appearing in the seasonal correlation plots are most likely associated with the large-scale seasonal variations in the sources and propagation characteristics of the various tides. The amplitudes of the migrating terdiurnal tide and the migrating diurnal and semidiurnal tides are strongly correlated at some regions during all four seasons. At the same time, the sign and magnitude of the correlations exhibit significant variability with latitude, height and season. If there were a single common source (i.e., heating at a specific altitude range exciting all three tides), the resulting amplitude variations would be expected to result in correlations whose only variation would be associated with differential dissipation between the tides. This if combined with multiple heating sources could explain the observed correlations.
 Similar separation of the correlation significance as a function of temporal scale is seen for nonlocal correlation analyses (correlation of the terdiurnal amplitude at 60°N (the latitude of maximum terdiurnal amplitude) at heights of 60, 90 and 110 km with amplitudes of the diurnal and semidiurnal components at all locations).
 Overall this correlation analysis indicates that nonlinear interactions between the migrating diurnal/semidiurnal tides are unlikely to be the source of the migrating terdiurnal tide. There are strong correlations between tides but these are likely associated with the large-scale variability of each tide which is ultimately linked to solar heating. This analysis does not eliminate the possibility that nonlinear interactions with other tides might be possible. We suspect that more detailed analyses such as a Hough mode decomposition are needed in order to fully understand these processes, since different tidal modes are likely to interact differently with each other even when associated with the same component (see, for example, Smith and Ortland  for a discussion of Hough mode decomposition). Unraveling the nature of the coupling between these components will require intelligent and careful study.
 The extended CMAM is used to study the morphology of the terdiurnal tides (including the migrating and 10 nonmigrating components) in the MLT region. Annual mean altitude-latitude distributions of the amplitudes of all 11 terdiurnal components are presented for the temperature (T), zonal wind (U) and meridional wind (V) fields. The seasonal variations, vertical wavelengths and superposition effect of the terdiurnal components are discussed with an emphasis on the zonal wind field. The model results reveal strong seasonal, latitude and altitude variations for all terdiurnal components.
 The migrating terdiurnal component maximizes at mid and high latitudes with significant amplitudes (annual mean amplitude in wind (temperature) >10 m/s (K)) in the upper mesosphere and lower thermosphere (80–120 km). Below 100 km, the amplitudes maximize at the NH/SH December/June solstice with amplitudes of up to 2–4 K for the temperature and 8–10 m/s for the winds. The SH maximum (centered on 50°S) tends to be slightly stronger than that of the NH (centered on 30°N). The seasonal variation of the migrating terdiurnal tide agrees well with the published observational results which generally emphasize heights below 100 km in the NH.
 Above 100 km, the amplitudes are stronger during solstice seasons than equinox seasons. In the NH, the amplitude maxima are seen in December–February/25°N–50°N, June–August/>60°N and October–November/>50°N. Maximum amplitudes in the SH are found in order of strength: December–February/50°S–70°S, June–August/∼60°S and ∼20°S, March–May/∼50°S, and September–November/∼50°S. In addition to these mid and high-latitude maxima, secondary amplitude maxima are seen in the low latitudes of both hemispheres with multiple peaks throughout the year.
 The vertical wavelength of the migrating terdiurnal tide Tw3 at 60°N/S above 100 km is ∼55 ± 15 km without significant seasonal variation. During solstice conditions, the phases at 60°N/S are asymmetric, ∼2–4 h apart and during equinox conditions they are approximately in phase. In contrast, the vertical wavelength between 70 and 100 km at 60°N exhibits strong seasonal variations and lies in the 30–50 km range during April–August and in the 60–80 km range for the other months. However, this behavior is not present at 60°S where the vertical wavelength is generally 60–80 km for all months.
 In addition to the migrating terdiurnal tide, the nonmigrating terdiurnal components have nonnegligible amplitudes and strong seasonal variations. Taking the zonal wind behavior as characteristics of these components, the nonmigrating terdiurnal components Te5, Te3, Te4, Tw4, and Tw5 tend to peak at high latitudes (50°N/S) with amplitudes between 2 and 8 m/s and the nonmigrating terdiurnal components Te2, Te1, Ts0, Tw1 and Tw2 maximize in the polar regions (centered on ∼65°–75°N/S) in both hemispheres with amplitudes between 2 and 10 m/s. These polar nonmigrating components dominate over the migrating terdiurnal component in this region.
 The total terdiurnal tidal zonal wind field was calculated from the superposition of all 11 terdiurnal components. The nonmigrating terdiurnal components play an important role in the superposed total terdiurnal wind and contribute significantly to the longitude variation of the total terdiurnal tide. Variations in amplitude around a longitude circle are significant with minima close to zero and maxima of close to 30 m/s at some locations above 100 km. These variations indicate the difficulty of using single station observations to draw conclusions about the characteristics of individual tidal components. Amplitudes, phases and vertical wavelengths all vary with longitude as a result of these superposition effects.
 The basic characteristics of the terdiurnal tide captured by the extended CMAM are in reasonable agreement with previous published observation and modeling results. The model analyses presented in this paper have also revealed some new features that have not yet been reported by the observation community. These include the seasonal variations above 100 km in the NH, the seasonal variations in the SH and the complete latitudinal structures of the various terdiurnal components.
 Generation mechanisms of the migrating terdiurnal tide in our model are examined with an emphasis on the nature of the correlations between amplitudes of the migrating diurnal/terdiurnal and semidiurnal/terdiurnal tides and possible interpretation of these features through nonlinear interaction theory. The nature of the correlation depends on the time scale associated with the correlation and the vertical propagation of the components. The correlations in the model are only significant for time scales on the order of 2 months or more. What we see is significant variation in the seasonal correlation as a function of height and latitude. We suspect this corresponds more to the slow tidal amplitude variations associated with heating by the radiative sources than nonlinear interaction. We do not see short-term correlations in the model similar to those in observations which are interpreted as nonlinear interactions. Overall our correlation analysis indicates that nonlinear interactions between the migrating diurnal and semidiurnal tides are unlikely to be the source of the migrating terdiurnal tide in the model. Further analysis using Hough modes decomposition is a way to study this issue in more detail.
 Funding support for Jian Du and William Ward was through the Canadian Modeling of Global Chemistry for Climate Research Network (grants from the Natural Sciences and Engineering Research Council (NSERC), Meteorological Service of Canada, through the Canadian Foundation of Climate and Atmospheric Sciences (CFCAS)), and through an NSERC discovery grant.