1. Introduction
Convection in the tropics is often coupled with large-scale dynamics, especially equatorial waves (Chang 1970; Madden and Julian 1971, 1972, 1994, 2005; Nakazawa 1986, 1988; Takayabu 1994; Wheeler and Kiladis 1999; Houze et al. 2000; Wheeler et al. 2000; Yanai et al. 2000; Straub and Kiladis 2002, 2003a; Kiladis et al. 2005; Masunaga et al. 2006). Observational studies have revealed the dynamical properties and detailed structures of convectively coupled waves (Nakazawa 1986; Takayabu and Murakami 1991; Wheeler et al. 2000; Straub and Kiladis 2002, 2003a; Yang et al. 2003; Roundy and Frank 2004; Kiladis et al. 2005; Masunaga et al. 2006; Murata et al. 2006). Intensive investigations have particularly focused on Kelvin waves, showing them to be coupled with super–cloud clusters (SCCs) and characterized by “boomerang-like” vertical phase tilt and eastward phase velocity of 15–20 m s−1. The Madden–Julian oscillation (Madden and Julian 1971, 1972, 1994, 2005) has the horizontal structure of a coupled equatorial Kelvin and Rossby wave (Rui and Wang 1990) or a “Kelvin–Rossby wave” (Houze et al. 2000) with a planetary horizontal scale. Despite a growing body of detailed observations, the mechanisms by which convection interacts with large-scale dynamics are not fully understood (Houze et al. 2000; Wheeler et al. 2000; Yanai et al. 2000).
Theoretical studies have provided useful guidelines for understanding convectively coupled waves, including wave-conditional instability of the second kind (CISK) (Yamasaki 1969; Hayashi 1970; Lindzen 1974; Yoshizaki 1991; Matthews and Lander 1999), wind-induced surface heat exchange (WISHE) (Emanuel 1987; Neelin et al. 1987; Xie et al. 1993; Raymond and Torres 1998), frictional wave-CISK (Wang 1988; Xie and Kubokawa 1990; Wang and Rui 1990; Wang and Li 1994; Oouchi and Yamasaki 1997), and stratiform instability (Mapes 2000; Majda and Shefter 2001).1 Although such individual mechanisms provide helpful information, they do not necessarily account for every aspect of the observed waves (Straub and Kiladis 2003b). Furthermore, differences among theoretical frameworks, in which assumptions are inevitable for simplification, have made comprehensive evaluations difficult.
Another major research approach has been numerical simulation using general circulation models (GCMs). Hayashi and Sumi (1986) first simulated a planetary-scale convectively coupled wave disturbance for an aquaplanet. Based on simulations using a similar aquaplanet, Numaguti and Hayashi (1991a, b) concluded that the convective signal (SCCs) was driven by the wave-CISK mechanism, whereas the planetary-scale disturbance (k = 1 moist Kelvin wave) was driven by the WISHE mechanism. However, one of the critical problems of the GCM approach is the uncertainty of convective parameterization (Yano et al. 1995; Slingo et al. 1996, 2005; Suzuki et al. 2006). Lin et al. (2006) reported that even state-of-the-art models still tend to underpredict the variances of convectively coupled waves and to overpredict the phase velocities, with high dependency on the convective parameterization scheme.
A cloud-resolving simulation is a promising method with which to overcome the uncertainty of convective parameterization. This approach has led to progress in understanding the interaction between convection and large-scale wave dynamics (Oouchi 1999; Oouchi and Yamasaki 2001; Grabowski and Moncrieff 2001; Tulich et al. 2007), although discussion in these studies has been limited to two-dimensional geometry without surface stress. Cloud-resolving convection parameterization (CRCP; Grabowski 2001, 2004) or superparameterization (Khairoutdinov and Randall 2001; Khairoutdinov et al. 2005), in which a cloud-resolving model is operated instead of conventional convective parameterization schemes, and the diabatic acceleration and rescaling (DARE)/reduced acceleration in the vertical (RAVE) approach (Kuang et al. 2005) are examples of methods that demand fewer computational resources. The CRCP approach (Grabowski 2003; Grabowski and Moncrieff 2004) and simple multimode models based on cloud-resolving model (CRM) simulations (Kuang 2008) and a multicloud framework (Khouider and Majda 2006) have demonstrated the importance of free-atmospheric humidity to large-scale convectively coupled disturbances, or the “moisture–convection feedback” (Raymond 2000; Tompkins 2001).
Recently, improvements in computational technology have allowed global explicit simulation of convection with horizontal mesh sizes as low as 3.5–7 km (Tomita et al. 2005; Satoh et al. 2005, 2007, 2008; Miura et al. 2005, 2007a, b; Iga et al. 2007; Nasuno et al. 2007). Beginning from an idealized aquaplanet (Miura et al. 2005; Satoh et al. 2005; Tomita et al. 2005; Nasuno et al. 2007; hereafter M05, S05, T05, and N07, respectively), month-long simulations with realistic setups have been executed (Miura et al. 2007a, b; Iga et al. 2007). Since the pioneering work by Hayashi and Sumi (1986), aquaplanet setups have been used as a standard approach to basic research problems (Numaguti and Hayashi 1991a, b; Flatau et al. 1997; Hayashi and Golder 1997; Grabowski 2001, 2003, 2004, 2006; Innes et al. 2001; Neale and Hoskins 2001; Woolnough et al. 2001; Nakajima et al. 2004). An aquaplanet case of global explicit simulation (S05, T05, N07) showed the spontaneous organization of tropical convection at the thousand-kilometer scale (i.e., SCCs) embedded in a planetary-scale Kelvin wave–like structure; the entire systems propagated eastward at 15–25 m s−1. In this sense, these results are similar to those of previous aquaplanet experiments (Hayashi and Sumi 1986; Numaguti and Hayashi 1991a). Our objective was to investigate the mechanisms of these large-scale disturbances, simulated without a prescribed relationship between convection and large-scale dynamics. In particular, the evaluation of convective effects on the wave structure is a central issue.
The rest of this paper is arranged as follows. Section 2 provides a brief description of the numerical model and the experimental design. Section 3 presents the horizontal and vertical structures of the simulated large-scale convective disturbances and moisture budgets. Section 4 provides a discussion of the simulated results in comparison with previous observational, theoretical, and modeling studies. Section 5 presents the conclusions.
2. Numerical model and experimental design
The numerical experiment was conducted using the Nonhydrostatic Icosahedral Atmospheric Model (NICAM; Satoh et al. 2008). This model was designed for fine-mesh [O(1 km)] global simulations and includes explicit moist processes in a nonhydrostatic framework (Satoh 2002, 2003). The icosahedral grid system is used to boost computational performance in parallel computing (Tomita and Satoh 2004). The cloud processes are explicitly calculated by a cloud microphysical scheme (Grabowski 1998),2 and no cloud parameterization is used. Other physical processes are modeled in the same way as in the Center for Climate System Research–National Institute for Environmental Studies–Frontier Research Center for Global Change (CCSR–NIES–FRCGC) atmospheric GCM (Numaguti et al. 1997; K-1 Model Developers 2004), that is, Mellor and Yamada’s (1974) level-2 scheme for subgrid-scale turbulence and Louis’s (1979) bulk formula for surface fluxes of heat and momentum.
The aquaplanet setup was documented by T05. The sea surface temperature (SST) was fixed to a zonally uniform value, with the meridional distribution given by Neale and Hoskins (2001) (control run). The model was run with horizontal grid spacings of 14, 7, and 3.5 km for 90, 40, and 10 model days, respectively. The top level of the domain was near 40 km, and 54 stretched layers were included in the vertical. The initial conditions for the 3.5-km (7 km) mesh run were interpolated from 7-km (14 km) mesh run results on the 20th (60th) day.
One may debate the applicability of explicit cloud processes to 7- and 14-km grid spacings. The 7-km mesh run represented the large-scale structure of the 3.5-km mesh run for a corresponding period (T05, their Fig. 1; S05, their Fig. 1), although the results did not converge quantitatively (T05, their Fig. 4). The multiscale organization of convection, including mesoscale cloud systems, was reasonably reproduced by the 3.5-km mesh run (S05, N07). We present results for the 7-km mesh run because month-long data were available at this scale.
3. Results
a. Definition of modes
Figure 1 shows time–longitude sections of outgoing longwave radiation (OLR) and surface pressure (3°N–3°S). Deviations from the zonal mean at each time are divided into equatorially symmetric and antisymmetric components (40-day-averaged zonal mean profiles are shown in Figs. 2a and 2b). The most prominent signals appear in symmetric components, which propagate eastward at around 15–25 m s−1. A zonal size of several thousand kilometers is dominant in OLR (SCC in N07), whereas the planetary scale is more distinct in the dynamical field (e.g., surface pressure). The time-averaged power spectra of these variables confirm the dominance of the planetary scale (zonal wavenumber k = 1) in the surface pressure and of the SCC scale (e.g., k = 3–5) in the OLR (Figs. 2c and 2d). In addition, the power of the OLR (Fig. 2c) in the planetary scale is comparable to that in the SCC scale. Turning back to the time–longitude section (Figs. 1a and 1c), the organized convection (SCCs) and planetary-scale dynamical signal are roughly coherent. These results indicate a link between the k = 1 signal and convection. The dominance of the coherent structure of the eastward-propagating k = 1 dynamical signal and the SCCs is similar to the results of previous aquaplanet experiments (Hayashi and Sumi 1986; Numaguti and Hayashi 1991a, b; Woolnough et al. 2001; Grabowski 2003, 2006). However, when examined closely, the movement of the planetary-scale signal seems slightly faster than that of the SCCs (e.g., approximately 23 versus 17 m s−1) for the 40-day period shown in Fig. 1. N07 also showed evidence of SCC-scale circulations superimposed on the planetary-scale structure, both of which were similar to Kelvin waves in dynamical structure (N07, their Figs. 2 and 4). Thus, the relationship between the SCC and planetary scales is not straightforward. Our goal was to extract the typical structure of these disturbances using composites of eastward propagation and zonal scale filtering.
Figure 3 shows space–time power spectra of equatorially symmetric OLR, calculated following the method of Takayabu (1994) and Wheeler and Kiladis (1999). A single series of 3-hourly data for the 40-day period was used. The zonal mean was subtracted at each time to remove the zonal mean tendency. The “tapering” technique was not used so as to avoid losing lower-frequency signals, which were of interest. The double fast Fourier transform (FFT) was applied to obtain the raw space–time spectra at individual latitudes. These spectra were divided into eastward- and westward-propagating modes using Hayashi’s (1977) method. Raw spectra were normalized by the total power at each latitude and averaged between 0° and 3°. As expected from Fig. 1, eastward-propagating modes of k = 1–5 are dominant in Fig. 3. These are primarily interpreted as convectively coupled equatorial (Kelvin) waves. The corresponding equivalent depths were in the range of those observed [12–50 m; Wheeler and Kiladis (1999)]. The k = 1 signal shows peaks of 0.05 cycles per day (cpd), whereas the k = 3, 4, and 5 signals peak at 0.1, 0.15, and 0.2 cpd, respectively. The eastward phase velocities corresponding to the above wavenumber–frequency relationship are 23.1, 15.4, 17.3, and 18.5 m s−1 for k = 1, 3, 4, and 5, respectively.
Although the wavenumber and frequency in Fig. 3 are discrete, they support the adequacy of the visually estimated phase velocities of the SCC-scale and planetary-scale disturbances (Fig. 1). Based on Figs. 1 and 3, we present the components of zonal wavenumbers 3–5 (1) of the average (composite) having 17 (23) m s−1 eastward propagation to represent the structures associated with SCC-scale (planetary scale) disturbances.3 These are defined as the “SCC” and “40 000 km” modes, respectively. Separation of the two modes by scale filtering facilitates discussion of their interaction. Zonal wavenumber 2 is excluded from the planetary-scale mode for clarity; the signal was weak and the spectral properties were slightly different from the Kelvin wave mode (Figs. 1 and 3). Outputs from the 0–30-day period are used for the analysis.
b. Horizontal and vertical structures
Figures 4 and 5 show the horizontal view of OLR and surface pressure for the SCC and 40 000-km modes, respectively. A comparison of the unfiltered composite plots (Figs. 4a and 5a) with plots of filtered zonal wavenumber (Figs. 4b and 5b) confirms that the selected zonal scale accounts for the major part of the respective eastward-propagating signals. Zonal flow (Figs. 4d and 5d; vector) is dominant along the equator and is led by a quarter wavelength by a zonal pressure gradient to the east. This implies that both modes are primarily equatorially trapped eastward-propagating gravity waves (i.e., Kelvin waves). Two additional points are worth noting. One is the meridional component of wind. In the upper troposphere (Figs. 4c and 5c), meridional wind is evident in both modes, invading equatorward of the equatorial Rossby deformation radius [λR = (c/β)0.5; around 9° for c = 23 m s−1 and 7.7° for c =17 m s−1] in some phases (e.g., 60°W–60°E, Fig. 4c; 30°W and 60°–120°E, Fig. 5c). The SCC mode also includes meridional flow associated with midlatitudinal pressure anomalies (centered around 30°N/S), both in the upper and lower troposphere. Rotational flow patterns are prominent from 15° to 30°N/S (Figs. 4c and 4d). This relates to the second point. The meridional width of the Kelvin wave–like equatorial structure is highly deformed poleward of λR in the SCC mode (Fig. 4d), whereas the zonal structure is generally coherent between 0° and 20°N/S in the 40 000-km mode (Fig. 5d). Such differences between the two modes are consistent with the meridional distribution of pressure anomalies; the anomalies in the SCC mode keep phase with the equatorial anomalies, with another peak along 30°N/S (e.g., 40°W, 10°E, and 60°E; Fig. 4d). In contrast, pressure anomalies in the 40 000-km mode monotonically reverse poleward from the equator, keeping the sign of the meridional pressure gradient the same between 0° and 30°N/S, with the phase lagging by a quarter wavelength at 30°N/S (e.g., 0° and 90°W; Fig. 5d).
Figures 6 and 7 show the equatorial height–longitude sections of the SCC and 40 000-km modes, respectively. Both modes exhibit warm anomalies in phase with the easterly (low pressure) anomalies in the lower to middle troposphere, which is again typical of eastward-propagating gravity waves (30°E, Figs. 6a and 6b; 10°E, Figs. 7a and 7b). The low-level zonal convergence is in phase with positive anomalies of the diabatic heating and vertical motion (0°, Fig. 6c; 60°W, Fig. 7c). Maxima of the diabatic heating rate appear at altitudes of 6–8 km (z = 6–8 km), nearly the same as the zonal mean profile. These maxima are positively correlated with warm anomalies in the upper troposphere (Figs. 6b and 7b) because of the westward tilt (with height) of the temperature anomalies. Here, eddy available potential energy is generated and converted to eddy kinetic energy. The zonal pressure gradient (Figs. 6a and 7a) is in phase with the zonal velocity around the upper divergent levels (z > 12 km), implying stationary growth. Clearly, the structures of the two modes are typical of unstable waves in the upper troposphere.
In addition to these dynamical similarities, there are some differences between the two modes. The vertical tilt of the temperature deviation (Figs. 6b and 7b) is more significant in the SCC mode (1/4 wavelength) than in the 40 000-km mode (1/10 wavelength). The westward tilt with height is also evident in the zonal wind in the SCC mode, and zonal convergence coincides with maximum upward motion up to z = 10 km (Figs. 6a and 6b). The 40 000-km mode is rather similar to the first baroclinic mode with zonal divergence starting at z = 5 km (Figs. 7a and 7b). These results indicate the difference in the coupling of convection and wave dynamics.
c. Mass divergence
Both modes are accompanied by meridional flow, not only on the poleward side of λR, but also on the equatorward side (Figs. 4c, 4d, 5c and 5d). Differences between the two modes are found in the phase structure of zonal convergence and vertical motion (section 3b). We examined the zonal and meridional components of mass divergence along the equator for each mode. Figure 8 shows the mass divergence in the SCC mode in the domain 90°W–90°E. The meridional component (Fig. 8b) is generally comparable to or larger than the zonal component (Fig. 8a). In the lower troposphere, both components are nearly in phase. The meridional component reverses sign in the midtroposphere and accounts for the primary part of the mass divergence in the upper troposphere (30°W–0°), which is expected from the vertical motion (Fig. 6b). A peak in meridional convergence is found around z = 3 km in the rear part of the maximum updraft (20°W–0°; Figs. 6b and 8b). This meridional equatorward flow is connected to westerlies to form a weak equatorial Rossby wave–like flow pattern around z = 3–5 km (not shown). Meridional convergence in the boundary layer (z < 1 km, 50°E; Fig. 8b) precedes that in the lower troposphere (see section 3d).
To identify the major force that realizes such three-dimensional flow fields, the rotational (beta) effect, pressure gradient force, and advection terms were evaluated (Fig. 9). The advection term includes the advection of the time-averaged zonal mean (basic) field by perturbation (associated with the wave mode) wind, the advection of the perturbation field by basic wind, and the advection of the perturbation field by perturbation wind. The third component is first calculated using unfiltered composite data for the respective eastward propagations (17 and 23 m s−1 for the SCC and 40 000-km modes, respectively). The respective zonal wavenumber component (3–5 for the SCC mode and 1 for the 40 000-km mode) is then extracted. In this way, the effects of all perturbations that move at the same speed as the SCC and 40 000-km modes are counted. In contrast, components that do not match in zonal wavenumber are excluded from the perturbation advection associated with the SCC and 40 000-km modes. The 1°N/S sections are displayed as representative of the equatorial zone (i.e., <3°N/S). Because the rotational effect is weak around the equator (Fig. 9a), the zonal pressure gradient (Fig. 9c) is the leading term of the zonal component for z < 12 km, as expected from the Kelvin wave–like properties of the SCC mode (sections 3a and 3b). The advection term (Fig. 9e) forces convergence to the convective region (around 0°; Fig. 6c) throughout the troposphere with the same order of magnitude as the pressure gradient term. Vertical transport of zonal momentum is the major component of total advection (not shown). The net effects (Fig. 9g) demonstrate a tendency for the eastward propagation of the zonal wind structure in the main troposphere (a growth tendency remains in the upper divergent levels). The meridional components are more complex. The rotational term (Fig. 9b) and pressure gradient term (Fig. 9d) have the same sign, implying ageostrophic dynamics. The advection term (Fig. 9f) is again comparable to the pressure gradient term, with opposite sign. The resultant tendency is roughly in phase with the meridional velocity field, suggesting stationary growth rather than eastward propagation. The positive (negative) pressure gradient in the upper (lower) troposphere (Fig. 9d) coincides with the convective phase (Fig. 6c), indicating convective acceleration of the meridional circulation.
Figures 10 and 11 show mass divergence and forcing terms, respectively, in the 40 000-km mode. The 40 000-km mode (Fig. 10) is similar to the SCC mode (Fig. 8) in the general coherence of zonal and meridional divergence in the lower troposphere, with meridional convergence ahead (in the rear part) of the convective phase at z < 1 km (around z = 3 km). The meridional convergence in the boundary layer is even clearer than that in the SCC mode (Figs. 8b and 10b). The level of major upper-tropospheric divergence in the 40 000-km mode is higher (z = 14 km; Fig. 10) than that in the SCC mode (z = 12 km; Fig. 8), implying deeper vertical circulation in the 40 000-km mode. This recalls the slightly faster phase velocity of the 40 000-km mode than of the SCC mode. Unlike in the SCC mode, the zonal and meridional components have a positive correlation in the upper-level divergence (Fig. 10). This difference is attributed to the different vertical tilts of the zonal components in these modes (Figs. 8a and 10a). In the lower levels, the vertical range of the low-level convergence in the 40 000-km mode (4–6 km; Figs. 10a and 10b) is not as deep as in the SCC mode (10 km; Fig. 8a). The forcing terms in the 40 000-km mode (Fig. 11) are similar to those in the SCC mode (Fig. 9) in the phase structure of each component; however, the net tendencies of the zonal wind appear to be quite different (Figs. 9g and 11g). In this mode, the advection term (Fig. 11e) exceeds other terms in exerting deep zonal convergence to the center of the upward motion (60°W; Fig. 7b). The meridional pressure gradient force (Fig. 11d) drives deep divergent flow in the major upward region, and the resultant tendencies generally coincide with the flow pattern (Fig. 11h). These are common to the SCC mode (Figs. 9d and 9h). Thus, the flow field of the 40 000-km mode is only weakly controlled by the geostrophic balance and gravity wave dynamics near the equator, but convective forcing is of importance through advection (mainly vertical) and deformation of the pressure field. The forcing terms at 5° and 10°N/S were also examined (not shown). The 40 000-km mode generates an eastward-propagating tendency for zonal wind at these latitudes (with similar structure to the equatorial section; Fig. 7). The meridional tendency is analogous to Fig. 11h, with increasing cancellation of the pressure gradient force by the rotational term. The SCC mode begins to lose the Kelvin wave–like structure at 5°N/S and is completely deformed at 10°N/S.
d. Moisture distribution
Figure 12 (Fig. 13) exhibits the equatorial section of water vapor content and zonal and meridional moisture convergence in the SCC (40 000 km) mode, with OLR indicating the convective phase. Moisture flux from the sea surface is also quantified. Maxima of water vapor content appear in the convective phases (15°W, Fig. 12a; 10°W, Fig. 13a) at z = 5 (2) km in the SCC (40 000 km) mode. These are mainly due to the vertical transport of moisture (not shown), as expected from the wind fields (Figs. 6b and 7b). The moist anomalies in the boundary layer leading the convective phase (Figs. 12a and 13a) are reminiscent of meridional mass divergence (Figs. 8b and 10b). In fact, meridional convergence is the primary component of the moisture convergence (Figs. 12c and 13c), especially in the 40 000-km mode. Convergence in the boundary layer precedes the column integrations. This at least partly accounts for the moisture buildup in the boundary layer. Another source of moisture, evaporation from the sea surface (Figs. 12d and 13d), is one order of magnitude smaller than the horizontal moisture convergence, with a negative anomaly leading the convective phase on the equator. It is noteworthy that the surface flux of the 40 000-km mode (Fig. 13e) has positive anomalies 1/4 wavelength ahead of the convective phase in the off-equatorial flanks. This is relevant to the meridionally coherent structure of the zonal velocity in the 40 000-km mode (section 3b). In addition, the higher-wavenumber components are more significant in the meridional convergence and surface flux than are other variables, as observed in the difference between the unfiltered and SCC- and 40 000-km-filtered profiles.
Figure 14 evaluates the forcing terms (shown in Figs. 9 and 11) at z = 1.5 km and at the lowest level in the SCC and 40 000-km modes along 1°N/S. The meridional pressure gradient maintains nearly the same magnitude and phase at both levels (the 40 000-km mode), whereas the rotational term decreases in the boundary layer to approximately one-half of that in the free atmosphere. This is consistent with the reduction in zonal flow by frictional force. Noticeably, the advection term is also comparable in magnitude (decreasing downward), with a minimum in the convective phase. Consequently, the net tendency in the boundary layer leads the convective phase in both modes. The same holds true along 5°N/S, except for the reduced contribution of the advection term.
4. Discussion
a. Convectively coupled Kelvin waves
The SCC mode is similar to convectively coupled Kelvin waves in the real atmosphere (Wheeler and Kiladis 1999; Wheeler et al. 2000; Straub and Kiladis 2002, 2003b) in the structure along the equator (e.g., westward tilt with height in the troposphere and cold anomalies in the lower troposphere of the convective phase, preceded by warm anomalies) and in the propagation speed (15–20 m s−1). These properties have also been found for gravity waves simulated by regional CRMs (Grabowski and Moncrieff 2001; Tulich et al. 2007), despite the absence of surface stress and meridional dimension in these studies. The meridional flow in the SCC mode accounts for a significant part of the mass divergence (Fig. 8), but it is primarily an adjustment to the vertical motion that is driven by convection (Fig. 9) and, therefore, keeps the nature of the eastward-propagating gravity wave unchanged. The equatorially untrapped meridional structure in the 40 000-km mode is common to the planetary-scale moist Kelvin wave modes in previous studies (Hayashi and Sumi 1986; Xie and Kubokawa 1990; Salby et al. 1994). In the meridional divergence in the free atmosphere, the 40 000-km mode is reminiscent of the unstable mode of Xie and Kubokawa (1990). However, the structure of their unstable wave simply reversed sign between the two free-atmospheric layers. This is different from the 40 000-km mode, in which the phase relationship between the pressure gradient force and the zonal velocity differed between the upper and lower troposphere (Figs. 5c, 5d and 7a). More importantly, the effect of convection, which does not necessarily match the wave structure, was significant along the equator in the 40 000-km mode. The meridional pressure gradient around the equator was not balanced with the rotational term, but forced the meridional circulation in the convective phase (Figs. 11d and 11h). This is in contrast with the geostrophic balance relationship in previous studies (Hayashi and Sumi 1986; Salby et al. 1994). The phase velocity of 23 m s−1 is slower than that for dry Kelvin waves with the same vertical scale (approximately 50 m s−1), and it would be interesting to know whether the stationary growth tendency by convection (in both the zonal and meridional directions) has some influence on the propagation speed.
b. Phase velocities and frictional convergence
Why were the phase velocities of the SCC and 40 000-km modes not slowed as expected from frictional wave-CISK theories [i.e., <10 m s−1; Wang (1988); Wang and Rui (1990); Xie and Kubokawa (1990); Salby et al. (1994); Wang and Li (1994); Oouchi and Yamasaki (1997)]? Wang and Rui (1990) argued that Rossby wave responses are essential to the slow eastward propagation of the equatorial convection associated with a Kelvin wave; they enhance convection on the eastern side through boundary layer convergence, together with the frictional convergence associated with the Kelvin wave, and at the same time, they retard the eastward migration of the coupled mode through their tendency of westward propagation. Neither the SCC nor the 40 000-km modes were accompanied by Rossby wave responses in such a phase relation, which seems to be critical to the realization of slow phase speed.
The contribution of frictional convergence to the moisture buildup is roughly estimated from the ratio of the boundary layer convergence to the column-integrated amount. The convergence in the free atmosphere represents the effects of wave structure and the convective transport. The boundary layer convergence is comparable to the total convergence (one-half of the total convergence) in the 40 000-km (SCC) mode. The precedence of boundary layer convergence for the deep convective phase was attributed to the frictional convergence (Fig. 14). However, the deep moist layer in the convective phase of the SCC mode (Fig. 12a) and the moisture convergence in higher-wavenumber components (Figs. 12c and 13c) suggest that the moisture–convection feedback mechanism (Raymond 2000; Tompkins 2001; Grabowski 2003; Grabowski and Moncrieff 2004; Khouider and Majda 2006; Kuang 2008) operates efficiently in this mode.
c. Moisture flux from the sea surface
Previous studies have discussed the importance of the WISHE mechanism to the growth and eastward propagation of large-scale wave disturbances (Numaguti and Hayashi 1991b; Xie et al. 1993; Wang and Li 1994; Raymond and Torres 1998; Oouchi 1999; Grabowski 2003; Straub and Kiladis 2003b), with different perspectives. Oouchi (1999) and Grabowski and Moncrieff (2001) came to opposite conclusions using similar experiments with two-dimensional CRMs. Grabowski (2003), based on aquaplanet experiments, argued that surface fluxes contribute to the development of a k = 1 disturbance, but not necessarily to the maintenance of the disturbance; this is contrary to the conclusions of Numaguti and Hayashi (1991b). In our case, evaporation from the sea surface was one order of magnitude smaller than the moisture convergence (Figs. 12c, 12d, 13c and 13d), and the WISHE mechanism was not considered to work efficiently along the equator. Moreover, the equatorial surface moisture flux in the SCC and 40 000-km modes had negative anomalies in the easterly phase (i.e., maximum absolute surface velocity). The moisture flux in the NICAM (Louis 1979) depends on the degree of undersaturation, as well as the absolute surface wind speed. High humidity along the equator leads to negative feedback. However, the off-equatorial positive feedback in the 40 000-km mode suggests a possible contribution of the WISHE mechanism to the eastward propagation of the equatorially untrapped structure of this mode.
d. Sea surface temperature
Previous studies (Wang and Rui 1990; Salby et al. 1994; Wang and Li 1994) reported that the unstable modes in their studies were highly sensitive to the SST. They argued that an SST exceeding 28°–29°C is critical to the growth of the unstable mode. We used an SST of 27°C at the equator, dropping to 25.2°C at 10°N/S (Neale and Hoskins 2001). This is considered a major reason for the suppressed convection outside the 5°N–5°S zone (Fig. 2a). A series of experiments using SST elevated by 2 K was also conducted, keeping other parameters the same as in the control run (M05). The result was insensitive to the change in SST with respect to the propagation of the dominant tropical convective disturbances (not shown). One possibility is that a 2-K increase may not be sufficient to allow cooperative interaction between Kelvin and Rossby responses. Another possibility is that the zonal contrast of SST in the real atmosphere may favor such coupling. When the results obtained using different types of models (e.g., theoretical models and explicit GCMs) are compared, how a model links convective forcing (e.g., heating profile) with SST and convection with large-scale dynamics must be taken into account. In NICAM, SST affects convective activity through surface fluxes and radiation, but is not as directly linked with convective heating as Wang and Rui (1990) assumed. Further investigation is warranted.
e. Scale interactions
The explicit representation of interactions between different modes (with different horizontal scales) is an advantage of global explicit cloud modeling. The structures of the SCC and 40 000-km modes (Figs. 6c and 7c) demonstrate that the major upward motions in these modes are associated with latent heating by the explicitly represented clouds. Figure 11 also suggests that the horizontal wind fields in the 40 000-km mode are forced by convection, which typically appeared as SCCs (Fig. 1a). In reverse, once the 40 000-km mode is excited, it facilitates the development of convection through low-level convergence and the initiation of convection through moisture buildup to the east (N07). A noticeable event took place around days 20–25 (Fig. 1a), with weakening of the most active SCC and simultaneous activation of the next SCC to the east. This event suggests the possible control of SCC organization by the 40 000-km mode (e.g., via frictional convergence or off-equatorial surface moisture fluxes). The robustness of the behavior of the 40 000-km mode and its potential effects on the SCC mode observed in this particular 40-day simulation are still arguable. However, at the least, we can say that the k = 1 signal was of primary significance to various variables (e.g., surface pressure, zonal velocity at z = 12 km) in this experiment, and the convective signal also included the k = 1 component, which was synchronized with the dynamical signal (Figs. 1a, 1c, 3 and 5b). Longer integrations using the explicit GCM will provide useful information to challenge this issue.
5. Conclusions
A month-long dataset of the 7-km-mesh aquaplanet experiment using the NICAM was analyzed to elucidate the mechanisms of large-scale tropical convective disturbances. The results indicate spontaneous organization of convection with a zonal size of several thousand kilometers (SCC) that is embedded in a planetary-scale circulation, and Kelvin wave–like structures with respective zonal sizes (T05, S05, N07). In these aspects, our results are similar to those of previous aquaplanet experiments (e.g., Hayashi and Sumi 1986; Numaguti and Hayashi 1991a, b). We focused on these convectively coupled waves with the aim of evaluating the relationship between convective disturbances and wave dynamics simulated without any prescribed interrelationship. Based on the analysis of the power spectrum and time–longitude sections of OLR and dynamical variables, two dominant modes, the SCC and 40 000-km modes, were represented by typical eastward phase velocities of 17 and 23 m s−1 and zonal wavenumbers 3–5 and 1, respectively. The convective effects were evaluated by explicit calculation of the moisture and momentum transport associated with all zonal scales. The effects on the SCC/40 000-km scale were then extracted.
In the structure along the equator, the SCC mode resembled the convectively coupled Kelvin waves in the real atmosphere (Wheeler and Kiladis 1999; Wheeler et al. 2000; Straub and Kiladis 2002, 2003b) and as reproduced by numerical models (Matthews and Lander 1999; Mapes 2000; Grabowski and Moncrieff 2001; Majda and Shefter 2001; Majda et al. 2004; Kuang et al. 2005; Khouider and Majda 2006; Kuang 2008; Tulich et al. 2007). Meridional structure was also evident in the SCC mode. A pair of off-equatorial rotational flows accompanied the equatorial convection. Similar gyres were found in a previous aquaplanet experiment (Woolnough et al. 2001) and in observed convectively coupled Kelvin waves (Straub and Kiladis 2002). Noticeably, the off-equatorial gyres were coherent with the equatorial convection, which led to a configuration different from the well-known Matsuno–Gill pattern (Matsuno 1966; Gill 1980). The meridional mass divergence along the equator exceeded the zonal component by a factor of 2–3 in the SCC mode.
The 40 000-km mode kept a Kelvin wave–like structure, even at the poleward side of the equatorial Rossby deformation radius (approximately 9°), similar to the results of previous modeling studies (Hayashi and Sumi 1986; Xie and Kubokawa 1990; Salby et al. 1994). However, geostrophic balance did not account for the equatorial wind field in the 40 000-km mode. Common to the SCC mode, meridional mass divergence was pronounced not only in the boundary layer but also in the free atmosphere. Compared with the SCC mode, the top of the circulation in the 40 000-km mode was elevated by 2 km, with less significant vertical tilt. Low-level zonal convergence was not as deep (4–5 km) as in the SCC mode (8–10 km), reflecting weaker coupling with convection.
In terms of Kelvin wave dynamics, the equatorial structures in both modes matched those of the neutral eastward-propagating gravity waves in the lower troposphere and unstable (growing) waves in the upper troposphere. Diabatic heating and upward motion were positively correlated with warm anomalies in the upper troposphere because of the tilted structure, implying the generation of eddy-available potential energy and its conversion to eddy kinetic energy. The zonal pressure gradient in the upper divergent levels (z > 12 km) was in phase with zonal velocity, indicating a stationary growth tendency.
To identify which process was responsible for the three-dimensional nature of the wind fields in both modes, forcing terms (rotation, pressure gradient, and advection) were examined. Convection significantly affected the equatorial wind field through pressure anomalies and advection, which included forcing from higher-wavenumber components. The net meridional tendency roughly meant stationary growth in both modes, suggesting that the meridional winds in the SCC and 40 000-km modes were primarily driven by convective forcing via deformations in the pressure fields and vertical circulations.
Low-level moisture buildup preceding the convective phase was common to both the SCC and 40 000-km modes. Moisture convergence, in which the meridional component exceeded the zonal component, accounted for the major part of this buildup, with the amount of moisture flux from the sea surface being one order of magnitude smaller and having the opposite sign. The WISHE mechanism (Emanuel 1987; Neelin et al. 1987; Numaguti and Hayashi 1991b; Xie et al. 1993; Raymond and Torres 1998; Oouchi 1999) is not considered to be important to the development and eastward propagation of the 40 000-km mode along the equator. The deep moist layer in the convective phase of the SCC mode suggests that the moisture–convection feedback mechanism (Raymond 2000; Tompkins 2001; Grabowski 2003; Grabowski and Moncrieff 2004; Khouider and Majda 2006; Kuang 2008) operates efficiently in this mode.
The boundary layer convergence in the easterly phase, observed in both modes, is analogous to frictional convergence (Wang 1988; Wang and Rui 1990; Salby and Hendon 1994; Salby et al. 1994; Wang and Li 1994; Oouchi and Yamasaki 1997; Maloney and Hartmann 1998; Takayabu et al. 1999; Kemball-Cook and Weare 2001). Frictional stress on the zonal wind accounted for the eastward shift of the meridional convergence in the boundary layer in both modes, but with advection terms of comparable magnitude in this nonhydrostatic explicit framework.
A cooperative link between Kelvin and Rossby waves is regarded as the key to the growth and slow eastward propagation of the unstable mode by frictional wave-CISK theory (Wang and Rui 1990) and observational studies (Matthews 2000). For example, the Madden–Julian oscillation, which typically has such a combined Kelvin wave and Rossby wave structure (Houze et al. 2000; Kiladis et al. 2005), is characterized by a slow phase velocity of approximately 5 m s−1 (Hendon and Salby 1994; Salby and Hendon 1994; Yanai et al. 2000). The fast phase velocities of the SCC and 40 000-km modes may be attributed to the associated Rossby wave responses, which were adjacent to and not cooperatively linked with the Kelvin waves. This also accounts for the similarity of the SCC mode to the results of previous CRMs (Grabowski and Moncrieff 2001; Tulich et al. 2007), despite the absence of surface stress and the meridional dimension in these studies.
The reason for the different meridional extents of the Kelvin wave–like zonal structure in the SCC and 40 000-km modes remains uncertain. One possibility is that the zonal size of the SCC mode allows meridional propagation of the signal, as suggested by the train of pressure anomalies along 30°N/S. The pair of rotational flows accompanying the equatorial convection was one of the most robustly observed configurations in this simulation. The zonal size of the SCC mode may favor the excitation of a gyre with comparable diameter. Comparisons of the aquaplanet case with realistic simulations using the same approach [e.g., the simulation of a Madden–Julian oscillation event using NICAM; Miura et al. (2007a)] will shed new light on the mechanisms that link convection and large-scale dynamics.
Acknowledgments
We are indebted to Drs. Yukari Takayabu, Tetsuo Nakazawa, Taroh Matsuno, Brian Mapes, Bin Wang, Shang-Ping Xie, Hirohiko Masunaga, and Tsuneaki Suzuki for valuable discussions and comments. Three anonymous reviewers and the assigned editor are also acknowledged for helpful comments that have improved the manuscript. Simulations were performed on the Earth Simulator, and the ispack library was used for the fast Fourier transform. This research was supported by the Core Research for Evolutional Science and Technology (CREST) program of the Japan Science and Technology Agency.
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Hovmöller diagram of (a), (b) OLR (W m−2) and (c), (d) surface pressure (hPa). Deviations from the zonal means are divided into equatorially (a), (c) symmetric and (b), (d) asymmetric components. Averages between 0° and 3°N/S are plotted. Solid lines indicate eastward phase speeds of 17 (black) and 23 (white) m s−1.
Citation: Journal of the Atmospheric Sciences 65, 4; 10.1175/2007JAS2395.1
Zonal mean distributions of (a) OLR (W m−2) and (b) surface pressure (hPa), and the zonal wavenumber variance spectra of (c) OLR (W m−2) and (d) surface pressure (hPa), averaged over the 40-day period. Equatorially symmetric components averaged between 0° and 3°N/S are depicted in (c) and (d).
Citation: Journal of the Atmospheric Sciences 65, 4; 10.1175/2007JAS2395.1
Space–time power spectra of the symmetric component of OLR. The ordinate is the frequency (cpd) and the abscissa is the zonal wavenumber. Averages between 0° and 3°N/S, weighted by the ratio of the total power at each latitude to the 0°–3°N/S average, are plotted.
Citation: Journal of the Atmospheric Sciences 65, 4; 10.1175/2007JAS2395.1
Composite horizontal plots of (a) OLR (W m−2; color) and pressure (hPa; contour lines) on an eastward phase velocity of 17 m s−1 (deviations from zonal mean) and (b) the k = 3–5 components (SCC mode). Pressure (hPa; color) and wind vectors of the SCC mode at z = (c) 14 and (d) 1.5 km (m s−1). The period of the composite is 0–30 days. Base longitudes are those at the initial time. Solid (broken) lines in (a) and (b) indicate positive (negative) values. The contour interval in (b) is 0.1 hPa.
Citation: Journal of the Atmospheric Sciences 65, 4; 10.1175/2007JAS2395.1
As in Fig. 4 but for a phase velocity of 23 m s−1 and a k = 1 component (40 000-km mode).
Citation: Journal of the Atmospheric Sciences 65, 4; 10.1175/2007JAS2395.1
Vertical cross sections of the SCC mode along the equator: (a) zonal velocity (m s−1) and pressure (hPa; thick contour lines), (b) temperature (K), and (c) diabatic heating rate (K s−1). Zonal mean profiles are shown in the left panels. In the bottom panel, OLR along the equator is plotted. Vectors in (b) and (c) represent the zonal vertical mass flux. The vertical mass flux is multiplied by 200 to account for the aspect ratio of the plot.
Citation: Journal of the Atmospheric Sciences 65, 4; 10.1175/2007JAS2395.1
As in Fig. 6 but for the 40 000-km mode.
Citation: Journal of the Atmospheric Sciences 65, 4; 10.1175/2007JAS2395.1
As in Fig. 6 but for the (a) zonal and (b) meridional components of the horizontal mass divergence (×10−6 kg m−3 s−1).
Citation: Journal of the Atmospheric Sciences 65, 4; 10.1175/2007JAS2395.1
As in Fig. 6 but for major terms of the (left) zonal and (right) meridional momentum equations: (a), (b) rotational effects, (c), (d) pressure gradient, (e), (f) advection, (g), (h) sum of the above three (× 10−5 m s−2; contour lines), and the zonal–meridional velocity (m s−1; shading).
Citation: Journal of the Atmospheric Sciences 65, 4; 10.1175/2007JAS2395.1
As in Fig. 8 but for the 40 000-km mode.
Citation: Journal of the Atmospheric Sciences 65, 4; 10.1175/2007JAS2395.1
As in Fig. 9 but for the 40 000-km mode.
Citation: Journal of the Atmospheric Sciences 65, 4; 10.1175/2007JAS2395.1
Equatorial sections of (a) water vapor content (×10−3 kg kg−1) in the SCC mode, (b) OLR (W m−2), (c) horizontal moisture convergence (×10−4 kg m−2 s−1), and moisture flux from the sea surface (×10−4 kg m−2 s−1) along (d) the equator and (e) 5°N/S. Gray lines in (c)–(e) indicate the sum of all zonal wavenumber components (deviations from the zonal means, with a 1200-km running average). Broken (solid) lines in (c) represent zonal (meridional) components, with thick (thin) lines indicating total column (below 1.5 km) integrated values.
Citation: Journal of the Atmospheric Sciences 65, 4; 10.1175/2007JAS2395.1
As in Fig. 12 but for the 40 000-km mode.
Citation: Journal of the Atmospheric Sciences 65, 4; 10.1175/2007JAS2395.1
Major terms of the meridional momentum equations at z = (top) 1500 and (bottom) 35 m for the (left) SCC and (right) 40 000-km modes along 1°N/S; shown are the rotational effects (dashed–dotted, ×10−5 m s−2), pressure gradient (dashed–dotted–dotted, ×10−5 m s−2), advection (thick dashed, ×10−5 m s−2), sum of the above three (solid, ×10−5