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Hindawi Publishing Corporation Advances in Meteorology Volume 2011, Article ID 296914, 34 pages doi:10.1155/2011/296914 Research Article Toward an Understanding of the Madden-Julian Oscillation: With a Mesoscale-Convection-Resolving Model of 0.2 Degree Grid Masanori Yamasaki Research Institute for Global Change, Japan Agency for Marine-Earth Science and Technology, 3173-25 Showa-machi, Kanazawa-ku, Yokohama 236-0001, Japan Correspondence should be addressed to Masanori Yamasaki, firstname.lastname@example.org Received 29 March 2011; Revised 29 July 2011; Accepted 3 August 2011 Academic Editor: Hann-Ming Henry Juang Copyright © 2011 Masanori Yamasaki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper describes results from numerical experiments which have been performed as the author’s ﬁrst step toward a better understanding of the Madden-Julian oscillation (MJO). This study uses the author’s mesoscale-convection-resolving model that was developed in the 1980s to improve parametrization schemes of moist convection. Results from numerical experiments by changing the SST anomaly in the warm pool area indicate that the period of the MJO does not monotonously change with increasing SST anomaly. Between the two extreme cases (no anomaly and strong anomaly), there is a regime in which the period varies in a wide range from 20 to 60 days. In the case of no warm pool, eastward-propagating Kelvin waves are dominant, whereas in the case of a strong warm pool, it produces a quasi-stationary convective system (with pronounced time variation). In a certain regime between the two extreme cases, convective activities with two diﬀerent properties are strongly interacted, and the period of oscillations becomes complicated. The properties and behaviors of large-scale convective system (LCS), synoptic-scale convective system (SCS), mesoscale convective system (MCS), and mesoscale convection (MC), which constitute the hierarchical structure of the MJO, are also examined. It is also shown that cloud clusters, which constitute the SCS (such as super cloud cluster SCC), consist of a few MCS, and a new MCS forms to the west of the existing MCS. The northwesterly and southwesterly low-level ﬂows contribute to this feature. In view of recent emphasis of the importance of the relative humidity above the boundary layer, it is shown that the model can simulate convective processes that moisten the atmosphere, and the importance of latent instability (positive CAPE), which is a necessary condition for the wave-CISK, is emphasized. 1. Introduction very often used by many researchers. Although the period of this intraseasonal oscillation certainly takes a wide range This paper describes results from a study which is made from about 30 days to 60 days, the author prefers to refer as the author’s ﬁrst step toward a better understanding of to the oscillation as a 40–50 day oscillation and intends to the Madden-Julian oscillation (MJO) with a mesocale-con- understand why the period is about 40–50 days rather than vection-resolving model. As is well known, the MJO was dis- 30 days. The former period was still used in a review paper covered in the early 1970s by Madden and Julian [1, 2], and by Madden and Julian . its understanding has been advanced by a number of obser- The second problem in which the author is interested is vational, theoretical and numerical studies in these 40 years. the so-called super cloud cluster (or super cluster), which is The author intends to better understand the following a synoptic-scale (2,000–4,0000 km) cloud system observed in three problems at the early phase in a series of his studies. the MJO. In this paper, the two terms super cloud cluster The ﬁrst is the period (or time scale) of the MJO. The period (SCC) and super cluster (SC) are used as having the same meaning (used interchangeably). The term super cluster (SC) was ﬁrst identiﬁed as 40–50 day by Madden and Julian [1, 2]. In the 1980s, a period of 30–50 day was preferably used by wasﬁrstusedbyHayashi andSumi in their numerical Krishnamurti and Subrahmanyam , and 30–60 day by study. Observational evidence of SC was given by Hayashi and Nakazawa , andanextensive studyofSCwas made by Nakazawa [4, 5]. In these 25 years, the latter period has been 2 Advances in Meteorology Nakazawa , referred to as N88. The SCs moved eastward, the term MCS has been usually used for an isolated mesoscale −1 and its phase speed was about 15 m s in the numerical system, it can be used as indicating one component of the −1 modelofHayashi andSumi, and 5–15 m s in the hierarchical structure of SCS. The author is interested in observational study of N88, which used the GMS IR data. In each of the behaviors of these ﬁve classes of convection that the observational study by Sui and Lau , the phase speeds constitute the hierarchical structure of the MJO, particularly −1 of two observed SCCs were 4–6 m s in the western Paciﬁc in the behaviors of SCS, MCS and MC. area. They indicated that the SCCs tend to slow down and This paper describes results from numerical experiments intensify when they approach the warm pool in the western that have been performed with an intention of understand- Paciﬁc. Subsequent studies have conﬁrmed this feature of ing the three problems listed above. Before describing the SCC. The recognition of this feature was an important basis results, a review is necessary concerning theoretical and of a numerical study of Oouchi and Yamasaki , referred numerical studies in the past. to as OY01. The present study is made along this line. Intensive theoretical and numerical studies on the MJO The second problem is closely related to the ﬁrst problem. started in the middle of the 1980s by Hayashi and Sumi  In the case of the OLR data used by Lau and Chan , the and Lau and Peng . It was suggested that the MJO should propagation speed of the most dominant mode of tropical be essentially excited and maintained by the mechanism convection (associated with the 40–50 day oscillation) was of the so-called wave-CISK (conditional instability of the −1 4-5 m s over the equatorial Indian/western Paciﬁc Ocean. second kind), and it appears that many subsequent studies Using nine year data of Northern Hemisphere summer, have supported this. Knutson et al.  showed that the phase speeds of the The concept of wave-CISK dates back to the late 1960s −1 OLR and the upper-level zonal wind were 4–6 m s in just before the MJO was discovered. Before this concept −1 the eastern hemisphere and the latter was 15 m s in the emerged, a concept of CISK was proposed in the early 1960s western hemisphere. Hendon and Salby  also indicated by Ooyama  and Charney and Eliassen  in their stud- that the phase speeds of the OLR anomaly in the eastern and ies of tropical cyclones (TCs). One of linear stability analyses −1 −1 western hemispheres were 5 m s and 10 m s ,respectively. for the problem of TCs was made by Syono and Yamasaki It has been increasingly recognized that the warm pool in . After nonlinear numerical experiments of TCs by the Indian/western Paciﬁc Ocean plays an important role not Yamasaki [23–25], the linear stability analysis was applied only in the propagation speed of SCC but also in the period to wave disturbances in the tropical atmosphere (Yamasaki of the MJO. The important role of the warm pool is one of , referred to as Y69) with an intention of understanding the major concerns of the present study. easterly waves in the troposphere and a westward propagat- The third problem of the author’s interest is how con- ing large-scale wave in the stratosphere, which was discov- vection behaves in the MJO. Convection associated with the ered by Yanai and Maruyama  and was later identiﬁed MJO circulation was referred to as “large-scale convection” as the mixed Rossby-gravity wave studied by Matsuno . by Madden and Julian . The observational evidence that In Y69, a two-dimensional model was used as the ﬁrst step, synoptic-scale convection (such as SC) is identiﬁed in the and it was suggested that three types of unstable waves might MJO was given by Hayashi and Nakazawa , as mentioned exist, depending on the vertical proﬁle of the parameterized above. Furthermore, N88 showed that SC, which propagates convective heating, the so-called beta-eﬀect, vertical shear of eastward, consists of several mesoscale cloud clusters which the environmental wind, and surface friction. The instability move westward. (It was later shown by Lau et al.  that of thistype, whichisdiﬀerent from CISK applied to TCs, was there are other two types in the combination of the moving later referred to as wave-CISK by Lindzen . directions of SC and cloud cluster.) The time scale of the The two-dimensional linear analysis of Y69 was extended cloud cluster is about 2 days (N88; ), and that of SCC to the three-dimensional (Hayashi , referred to as H70; is 10–15 days . It is equally important to remark that Yamasaki , Y71). In the absence of vertical shear of cloud clusters in the tropical atmosphere consist of mesoscale the environmental wind and surface friction, separation convective cells. It is also important to remark that the basic of variables can be made in a set of linearized equations mode of moist convection has been referred to as cumulus (unless the parameterized heating parameter depends on the convection. The present author [17, 18] recognized a basic latitude). In this case, the vertical structure equation, which organized form of cumulus convection in his numerical determines the properties of the instability, takes the same studies of tropical cyclones and tropical convection, and form as that in the two-dimensional model. Therefore, the referred to it as mesoscale convection (MC). With the term parameterized heating condition for instability is also the MC, a cloud cluster can be considered as an ensemble of MC same. The three-dimensional model provides us with the in many cases. diﬀerent properties for various types of equatorial waves Thus, the hierarchical structure of the MJO can be de- such as Kelvin wave, mixed Rossby-gravity wave and other scribed in terms of the large-scale convection (LSC), synop- waves through the horizontal structure equation. The major tic-scale convection (SSC), mesoscale cloud cluster (MSCC), concern of Y69, H70 and Y71 was directed to a planetary- mesoscale convection (MC), and cumulus convection. Con- scale stratospheric wave corresponding to the mixed Rossby- vective systems corresponding to LSC, SSC, and MSCC can gravity wave, but not to Kelvin wave, although Kelvin wave in be referred to as large-scale convective system (LCS), syno- the stratosphere had been observed . The MJO, which is a ptic-scale convective system (SCS), and mesoscale convective tropospheric phenomena and should be an interesting target system (MCS), respectively. SCC belongs to SCS. Although of wave-CISK studies, was discovered just after that time. Advances in Meteorology 3 As described in H70, gravity waves are most preferred, (as well as unconditional heating) was used. (The terms and the growth rate increases with decreasing horizontal “conditional” and “unconditional” were also used in Lau scale under the parameterized heating used by Y69. The et al.  and others.) Conditional heating (positive-only instability of gravity waves and the preference of small-scale heating) assumption alters the vertical motion ﬁeld such that gravity waves were ﬁrst noted in a numerical experiment ascending motion area (convective area) is conﬁned to a of TCs by Syono and Matsuno (unpublished) and later relatively small area and descending motion occurs in a much examined by linear stability analysis of Syono and Yamasaki wider area. This contrast of the features for conditional and . The unstable gravity waves were interpreted as unreal- unconditional heating cases is quite similar to that of moist istic modes that arose from inappropriate parameterization convection in the conditionally unstable atmosphere and dry of moist convection. This interpretation was an important convection in the absolutely unstable atmosphere. Keeping basis for studies of Y69 and Y71, and it was considered this diﬀerence in mind, the stability analyses of Y69 and Y71 that only the linear stability analysis of Rossby wave and were made only for the unconditional heating case because mixed Rossby-gravity wave which have low frequency should the essence of the stability properties can be understood be informative. As for Kelvin wave, the author felt that from this case. One of important results obtained from the preference of small-scale Kelvin wave (H70) was also a numerical experiments by Lau and Peng  is that the result of inappropriate parameterization because Kelvin wave eastward propagating mode is much more enhanced than the is essentially similar to gravity waves with respect to the westward, as also seen in Hayashi and Sumi . However, stability property, as evident from the vertical structure in the only a single ascending area (convective area) with a longitude-height cross section. As for planetary-scale (and “relatively small” horizontal scale was obtained. (In the gen- large-scale) Kelvin waves with low frequency, the problem eral case, ascending motion is not necessarily conﬁned to a remained to be studied. single area.) It is unlikely that the LSC associated with the In addition to the problem of the unrealistic gravity MJO can be simulated by the parameterization used. In waves, it was strongly recognized in Y69 and Y71 that addition, the description of SCC may not be realistic, as in the vertical proﬁle of the parameterized heating is one Hayashi and Sumi , because of the coarse resolution (R15, of the very important factors to determine the stability rhomboidal truncation at wavenumber 15) and the parame- properties of various waves and their structure. Recognizing terization scheme used. these important problems (including TCs) and intending The dominance of Kelvin waves with wavenumber 1 to get a basis for an appropriate parameterization of moist was also found in a GCM of Geophysical Fluid Dynamics convection, the author started his studies, in the 1970s, with Laboratory (GFDL) that included realistic land, orography the use of a cumulus-convection-resolving model with a and some other physical processes. N. C. Lau and K. M. Lau horizontal grid size of 500 m–1 km (e.g., [17, 18, 39–42]  showed this feature from a GCM with R15 although Based on the results from such studies, the author developed SCC was not simulated because of the coarse resolution used. aTCmodel [43, 44], whichisreferredtoasmesoscale- Hayashi and Golder  showed that a clear peak of the convection-resolving model (abbreviated as MCRM). This space-time power spectrum is also found at wavenumber 1 model was developed to study not only TCs but also other in a GCM with higher resolution of R30. Since these studies phenomena in which moist convection plays an important used GCMs that have zonally inhomogeneous sea surface role. The development of the MCRM in the 1980s is one of temperature (SST) and land-sea distribution, it was not clear the important basis for the present study. that the dominance of wavenumber 1 is realized without Now we will return to the review on the numerical zonal inhomogeneity. Other GCM studies with zonal homo- studies of the MJO in the 1980s. Hayashi and Sumi  geneity such as N. C. Lau et al. , Swinbank et al. , and performed numerical experiments using the aqua-planet Hayashi and Golder  have strongly suggested that the (and zonally homogeneous sea surface temperature) version Kelvin wave with wavenumber 1 should be one of the most of a general circulation model (GCM). The most important preferred modes that arise from the wave-CISK mechanism result is that synoptic-scale convection (such as SC) which and that this mechanism should explain the essence of moves eastward, and Kelvin-like wave with wavenumber 1 the MJO. are simulated by the model. The latter means that planetary- Now, we proceed to a review in connection with the scale Kelvin wave is obtained as one of the most preferred ﬁrst and second problems of the author’s interest mentioned modes, which was not predicted from the wave-CISK studies above. It is well known that the period of the MJO has been in the early 1970s. On the other hand, the calculated SC underestimated in most of theories and numerical experi- may not be necessarily realistic in view of the coarse grid ments in the past. For example, the period of the eastward size (T42, triangular truncation at wavenumber 42) and the propagating Kelvin wave was about 30 days rather than 40–50 parameterization scheme used. days in Hayashi and Sumi . Although the period probably Lau and Peng  performed numerical experiments depends on many factors, some researchers considered a pos- with parameterized heating which is similar to that used sibility that the shorter period should be due to the param- in the previous wave-CISK studies but without cooling eterization scheme of moist convection. When Hayashi and in regions of low-level divergence, positive-only heating Sumi’s  result emerged, the author considered that the sta- parameterization in their terminology. This assumption was bility analysis of Syono and Yamasaki  for gravity waves previously used in the stability analysis for TCs by Syono was informative, because the Kelvin wave is quite similar and Yamasaki  in which the term conditional heating to the gravity wave with respect to the stability property. 4 Advances in Meteorology According to the analysis, the phase velocity of the unstable The MCRM, which was developed in the middle of gravity wave is very sensitive to parameterized heating 1980s, has been used for studies of TC structure [43, 44, 58], rates (nondimensional parameter used in Y69) in the lower TC formation [59–63], TC motion , and for studies of troposphere, particularly, in a layer of 900–800 hPa (or 900– cloud clusters associated with Baiu-Meiyu fronts [65–68]. 700 hPa). As the low-level heating rates increase, the phase An application of the MCRM to Kelvin wave-CISK was also velocity decreases. (When the rates exceed critical values, made. Because of computer restrictions, its application to a gravity wave becomes a stationary unstable wave (CIFK) the MJO, however, was not made until recently. except for longer waves in which inertial stability is impor- Instead, the author started his study of the synoptic- tant.) A similar stability analysis was made by Takahashi , scale and large-scale gravity wave-CISK (as a basis for Kelvin and the conditional heating case of Syono and Yamasaki  wave-CISK) with the use of a two-dimensional CCRM in the was studied by Miyahara . On the other hand, Lau and middle of the 1990s . These studies, which were made Peng , Sui and Lau , and Lau et al.  suggested that as extensions of Yamasaki [17, 18], included discussions of the propagation speed is sensitive to the level of maximum the important role of the cold pool and gravity waves (of heating. Tokioka et al.  also referred to the level of max- the small-scale and mesoscale) in the successive formation of imum heating. However, the author has recognized that it is MC and cloud clusters, as in CISK of TCs and easterly waves. much more appropriate to understand this problem in terms ThesestudieswereextendedbyOouchi. of the low-level heating rather than the level of maximum It should be mentioned here that the ﬁrst study of the heating. gravity wave-CISK with a CCRM was made by Nakajima Although the period of the MJO can be simulated by . Although the author  studied another type of wave- artiﬁcial modiﬁcation of the vertical distribution of the CISK (corresponding to the easterly wave in the tropical parameterized heating, what is important is how the vertical troposphere), whether or not gravity wave-CISK could be distribution is realized in nature. As mentioned already, the simulated by a CCRM remained to be studied. Nakajima author’s study with a cumulus-convection-resolving model  was the ﬁrst to show that the gravity wave-CISK is (CCRM) in the 1970s and 1980s was a step toward a better simulated by a two-dimensional CCRM although corre- understanding of this problem, and the development of the spondence to observed phenomena was not discussed. One MCRM by the author [43, 44] in the 1980s was based on of the important concerns of these studies [33, 70]with such a study. Some details of the signiﬁcance and intention CCRMs was the successive formation of new cloud clusters of the MCRM development are described in these papers to the east of the existing clusters, as observed in SCC and Yamasaki [54–56], and it is not repeated here. However, studied by N88. In the absence of vertical shear of the the following remark is important in connection with the environmental wind and low-level wind, both eastward and parameterized heating used in the wave-CISK studies in the westward propagations of an envelope of cloud clusters late 1960s–1980s. In the MCRM, it is intended to resolve MC, are obtained in the two-dimensional model, whereas an which is the basic organized form of cumulus convection, eastward propagation is much more enhanced when the and the eﬀects of cumulus convection are incorporated as westerly shear  or low-level easterly ﬂow  exist. the subgrid-scale (or parameterized). The heating rate due In the latter case, the west-east asymmetry of the wind- to cumulus convection is assumed to be of the same form induced surface heat exchange (WISHE) is one of the as that used in TC studies of Ooyama [20, 57]and wave- important factors, as pointed out by Emanuel and CISK studies of Y69, Y71, and many others (except for the use Neelin et al. . It should be again emphasized that the cold of the conditional heating). The values of unknown heating pool and gravity waves (of the small-scale and mesoscale) parameters are determined so that MC may be realistically play important roles in successive formation of cloud simulated. An important point in this respect is that realistic clusters. simulation of MC completely prevents unrealistic growth of The successive formation of cloud clusters to the east of gravity waves, which was the most serious diﬃculty in the the existing clusters was also simulated by Chao and Lin  wave-CISK studies (as well as TC studies). In the MCRM, with a two-dimensional model that included the parameter- TCs and other phenomena (sush as wave disturbances) ized heating in a coarse-grid model. They emphasized the can be simulated through description of many ensembles importance of simulating cloud clusters for successful simu- of MC. One of the typical examples of the ensemble of lation of SCC and the MJO. Needless to say, the model results MC is a rainband in TCs. In the case of the MJO, an were very sensitive to the parameterization schemes used. ensemble of MC is manifested as a cloud cluster, which is a They succeeded in simulating not only successive formation constituent of SCC (SCS in general). It should be emphasized of cloud clusters, but also the slow eastward phase speed of that the development of the MCRM was based on the SCC in the presence of the low-level easterly ﬂow. However, recognition of the importance of describing MCS (cloud description of MCs that constitute each cloud cluster, as done clusters or mesoscale cloud systems including rainbands) in the MCRM, was beyond the scope of that study partly through resolving MC. One of the author’s major concerns because the horizontal grid size was taken to be large (about in this study is whether or not the MCRM can simulate 100 km). Although the author’s numerical experiments with the observed period of the MJO and the phase velocity of the MCRM at that time simulated successive formation of SCC. Another concern, which is the central topic of the third cloud clusters, the results were not submitted for publication, problem, is how MC and cloud clusters behave in SCCs and studies with a CCRM started, as mentioned above. The described by the MCRM. basic study of Yamasaki  and the subsequent study of Advances in Meteorology 5 Oouchi  led the ﬁrst attempt to study the MJO-like wave make research much more eﬃcient. A number of numerical with a CCRM by OY01 . experiments for TCs and tropical disturbances, which have The present study is made as an extention of OY01  been performed in these 25 years, have suggested that use in which a two-dimensional CCRM was used. In this study, of such a coarse grid is, to a fair degree, justiﬁed for better a three-dimensional MCRM is used. Although a review of understanding of various phenomena. studies in these 10 years since OY01  may be desirable The original version of the MCRM was developed in the here, this will be described in the following sections when it middle of the 1980s [43, 44], as mentioned already. A revised is necessary, to avoid a lengthy introduction. version was developed later  with two major improve- However, the following remark concerning the deﬁnition ments. One is that the subgrid-scale cloud water was treated of the term MJO may be necessary to avoid some readers’ with a diagnostic equation in the original version, as in the misunderstanding of the descriptions in this paper. Some most parameterization schemes, whereas it is treated with researchers have used this term as implying convective a prognostic equation. This modiﬁcation has improved the activity that occurs primarily over the warm pool area, cloud water ﬁeld to a considerable extent. Another modiﬁca- and a circulation associated with it. Lin et al. deﬁnes tion is that the fraction of parameterized (implicitly treated) the MJO as the eastward-propagating mode with periods clouds (cumulus-scale ascending area) is not assumed to be 30–70 days and zonal wavenumbers 1–6, based on the suﬃciently small compared to unity, as done in the past observational study of Wheeler and Kiladis inwhich parameterization schemes, but assumed to take ﬁnite values the MJO is distinguished from convectively coupled Kelvin (such as 0.2). This is because the horizontal grid size in the waves (nondispersive) in view of the dispersion relation. MCRM is taken to be so small that mesoscale motions such The author deﬁnes the MJO essentially as an eastward- as MC can be simulated. In addition to these two improve- propagating Kelvin wave whose phase speed is relatively ments, the determination of the condensation rate in the small over the Indian/western Paciﬁc warm pool area and cumulus-scale ascending area (implicitly treated cloud area) large in the western hemisphere, based on Madden and Julian is modiﬁed in Yamasaki  although its eﬀect is not large.  and many studies in the 1980s and 1990s. The author These MCRMs are hydrostatic models, because most has also recognized that many convectively coupled Kelvin of TC models, GCMs, and numerical weather prediction waves may be dispersive, in contrast to the nondispersive (NWP) models in the 1980s when the original MCRM property of the convectively coupled Kelvin waves described was developed were hydrostatic models. Very recently, a by Takayabu , Wheeler and Kiladis , and Wheeler nonhydrostatic version has been developed . The ice et al. , and neutral Kelvin waves discussed by Matsuno phase has not been taken into account in the hydrostatic . This recognition is based on a study of Oouchi and MCRM yet, whereas it is incorporated in the nonhydrostatic Yamasaki  and the results (described later) from the MCRM. In the present study, we use the hydrostatic MCRM author’s recent numerical experiments with the MCRM. of Yamasaki , because essential discussions of the MJO In Section 2, brief descriptions of the model used and can be made by the hydrostatic MCRM and because the experimental design are given. In Section 3, the period of the hydrostatic MCRM is much more eﬃcient (much less Kelvin waves (MJO) obtained from numerical experiments computer time) than the nonhydrostatic MCRM. and the hierarchical structure of convection are discussed. In The model behavior (or performance) of the hydrostatic Section 4, additional discussions concerning wave-CISK and MCRM of Yamasaki  has been described in Yamasaki [58, other problems are given. Concluding remarks are given in 62, 63, 66–68] for studies of TCs and cloud clusters associated Section 5. with Baiu-Meiyu fronts. Results from its application to mesosale cloud systems over a large island in the equatorial area show a more realistic diurnal variation of rainfalls 2. Model (presented at the spring meeting of the Meteorological 2.1. A Brief Description of the MCRM. In the MCRM, it is Society of Japan in 2007). The author believes that even the intended that MC is resolved by the grid of a numerical original version of the MCRM gave better results for TCs model, and the eﬀects of cumulus convection are included [33, 43, 44, 59–61, 64] than other models. as the subgrid scale (or parameterized), as mentioned in One of the important model features that contribute to signiﬁcant improvements is that cloud water and rainwater Section 1. The horizontal grid size for properly describing MC is, ideally speaking, about 1–5 km. However, it is mixing ratios are included as prognostic variables despite considered that use of the MCRM is most eﬃcient when the the fact that it is a hydrostatic model, and the subgrid- grid size is taken to be 5–20 km. Although a 20-km grid is scale rainwater is also predicted. The prediction of cloud somewhat too large to describe MC with smaller horizontal water and rainwater, which had not been made in other scales, MC with large horizontal scales can be described to hydrostatic models (hydrostatic TC models and GCMs and some extent, and qualitative simulation and understanding NWP models) before the middle of the 1980s, was based of MCS and SCS can be made with this grid size. In this on recognition that rainwater evaporation and the resulting cold pool play important roles in successive formation of study, a 0.2 degree grid is used for the equatorial region in the spherical coordinate model. When a larger computer MC and MCS and, thereby, more realistic behavior of larger- becomes available, it can be expected that a 0.1 degree grid scale disturbances such as TCs. This recognition is just what was obtained from the studies with a CCRM in the will be easily used. Although it is possible to use the latter grid even at the present time, use of the former grid enables us to 1970s and 1980s. Although the importance of rainwater 6 Advances in Meteorology Table 1: Values of σ at 11-levels where vertical σ-velocities are predicted, the corresponding basic state pressure P , basic state temperatures T , relative humidity at the center of a moist area R , maximum values of the basic state zonal velocity in the middle latitudes, and those of B H0 the zonal velocity of a wave given at the initial time. σP T R U U B B H0 max K max −1 −1 (hPa) (K) (%) (m s)(ms ) 0.0 100 200 50 (125) 16 3 0.055 150 206 50 (175) 28 7 0.110 200 219 55 (240) 28 10 0.198 280 237 60 (340) 25 6 0.330 400 256 65 (475) 20 3 0.495 550 271 70 (625) 12 0 0.695 700 282 75 (760) 7 −3 0.791 820 289 80 (860) 4 −6 0.879 900 293 85 (927) 2 −10 0.940 955 296 83 (982) 1 −8 1.0 1010 300 80 evaporation and the cold pool has been recognized from 30 layers are used for the troposphere. On the contrary, observational studies, this had not been taken into account qualitatively correct numerical solutions can be obtained for in the hydrostatic models before Yamasaki [43, 44]. Charney-Phillips grid even when a ten-layer model is used. The values of σ at 11 levels at which the vertical σ-velocities Theimportanceofconvectivemomentumtransport are predicted, and the corresponding basic state pressure P was emphasized by Grabowski and Moncrieﬀ . In are shown in Table 1. the MCRM, the momentum transport by subgrid-scale convection is not taken into account, because a large portion of the momentum transport is accomplished by MC. 2.2. Experimental Design. The goal of a series of this study is The hydrostatic MCRM uses sigma (σ) as the vertical to understand the MJO under the most realistic conditions coordinate. A ten-layer model has been used since Yamasaki as observed in the real atmosphere. That is, the land-sea , because the author has believed that qualitative simu- distribution, orography, the diurnal and seasonal changes lation and understanding have been successfully made with of solar insolation, seasonal changes of SST as well as the only ten layers. It should be mentioned in this respect that ground temperature, and other factors have to be taken the author has used Charney-Phillips grid with respect to into account at the ﬁnal stage of this study. In this paper, the vertical arrangement of the predicted variables. This is results from numerical experiments under the most idealized based on the author’s recognition that a very small vertical and simpliﬁed conditions are presented. Since the behavior grid size (such as 20m or 2hPa) is required for Lorenz and mechanism of the observed MJO are aﬀected by many grid when we study CISK problems with the use of a factors as mentioned above, it is a reasonable ﬁrst step numerical model that includes parameterization of moist toward a satisfactory understanding to examine the MJO-like convection. The author recognized this in the 1960s when he phenomena obtained under simpliﬁed conditions. Because performed numerical experiments of TCs with a multiple- of many factors that are not included in the model used layer model . Although the required vertical grid size as the ﬁrst step, it is anticipated that there should be many should be increased by the eﬀects of nonlinear advection diﬀerences (or discrepancies) between the calculated MJO and eddy diﬀusion processes, it should be still very small. and the observed MJO. The primary objective of this ﬁrst- There is a possibility that numerical solutions should be step study is to understand what occurs under simpliﬁed largely distorted (owing to computational modes) even if conditions. Advances in Meteorology 7 Table 2: Sea surface temperature (SST) of the basic state. The SST (or 120 deg) and Δϕ = 20 deg. The location of the center of is linearly interpolated between two latitudes shown. It is taken to the warm pool is taken to be (120E, equator); λ = 120 deg T0 be symmetric with respect to the equator. and ϕ = 0. Although a cold pool exists around or just to T0 the south of the equator in the eastern Paciﬁc, it is not taken Latitude 0 5 15 25 30 35 40 45 55 70 into account in this study. SST 301 301 300 299 298 294 288 283 280 280 The initial condition is given by the sum of the basic state which does not depend on longitude and the perturbation. The basic state westerly ﬂow (westerly jet) in the middle As is well known, the most important factors for the latidudes in the northern hemisphere is given by MJO are the latitudinal variation of SST and the warm pool in the Indian/western Paciﬁc Ocean. In this study, an U ϕ, p acqua-planet model (only covered with the sea) is used. ⎡ ⎤ Although the latitude of the maximum SST shows seasonal ⎪ π ϕ−ϕ / ϕ −ϕ C N ⎪ C ⎣ ⎦ ϕ >ϕ>ϕ U p cos max N S change in nature, we consider the situation such that SST = 2 is constant with respect to time and a maximum of SST ⎪ 0 (otherwise), is located at the equator. The north-south gradient of SST (2) in the middle latitudes is also taken into account. This means that baroclinic instability occurs in the model. The where ϕ is the latitude of the center of the westerly jet subtropical highs are produced, and the easterlies exist in and ϕ and ϕ are latitudes of the northern and southern N S the equatorial sides of the subtropical highs. Although this boundaries of the westerly ﬂow, respectively. In this study, easterly ﬂow does not control the MJO directly, it should we take ϕ = 48 N, ϕ = 35 N,and ϕ = 22 N. In the N C S have some indirect eﬀects. The most important eﬀects of southern hemisphere, the same westerly ﬂow is given at the the easterly ﬂow are to enhance convective activity (through same latitudes (symmetric with respect to the equator). Since the sensible and latent heat ﬂux at the sea surface) and to the SST gradient is imposed, the westerly ﬂow is produced producestrongervorticesand TCsinthisarea. Therelation after a long time even if it is not imposed at the initial of the MJO and TC formation, which has been one of the time. The speciﬁcation of the westerly ﬂow at the initial time interesting subjects in MJO studies, will be discussed at shortens the necessary integration time. the later stage of this series of studies. The easterly ﬂow The geopotential, surface pressure and temperature ﬁelds also contributes to westward movement of vortices and at the basic state are determined so that the geostrophic TCs. Under the existence of the subtropical high, TCs tend and hydrostatic balances may be satisﬁed. The values of to move into the middle latitudes, and TCs are removed U (p) as well as the basic state temperatures T (p) used max B from the subtropical and equatorial areas eﬀectively. The in this study are given in Table 1. Since the westerly ﬂow easterly ﬂow also contributes to frictional convergence in changes with time so that it may adjust with the imposed SST, the equatorial area, which provides a favorable condition for speciﬁcation of more appropriate values of U (p)given at max convective activity in this area. the initial time is not very important. The latitudinal distribution of SST used in this study is The initial relative humidities R are given in the shown in Table 2. It is taken to be symmetric with respect following form: to the equator. The magnitudes of the latitudinal gradient of SST in the equatorial area and in the middle latitudes are πr C + (1−C )cos R p (r< 1) RH RH H0 important. If results obtained in this study are qualitatively R = modiﬁed by the use of more realistic distributions of SST, ( ) C R p r> 1 , RH H0 it is worthy to discuss such cases. In this paper, only results ⎡ ⎤ 1/2 obtained from the SST in Table 2 are presented. 2 ϕ − ϕ R0 ⎣ ⎦ A warm pool corresponding to the Indian/western Paciﬁc r = ((λ − λ )Δλ ) + . R0 R Δϕ Ocean is imposed in the following form: (3) πr T cos (r< 1) warm The relative humidity at each level takes a maximum R (p) H0 T = sea at (λ , ϕ ). The values of R (p) are shown in Table 1, ⎩ R0 R0 H0 0 (r> 1), and λ and ϕ are taken to be 180E and 0 (equator), R0 R0 (1) ⎡ ⎤ 1/2 respectively. The width and shape of the moist area are given λ − λ ϕ − ϕ T0 T0 by Δλ and Δϕ .Wetake Δλ = 50 deg and Δϕ = 20 deg. ⎣ ⎦ R R R R r = + , Δλ Δϕ A parameter C indicates the ratio of the relative humidity T T RH outside the moist area to that at its center. In this study, C RH where λ is longitude (deg), ϕ is latitude, T is the SST is taken to be 0.8. sea anomaly, and T is a model parameter, which is taken It should be mentioned in connection with Table 1 that warm to be 0, 1.0, 1.5, and 2.0 K in this study. When T is 0, the basic state pressures of the lowest and uppermost layers warm SST is uniform in the longitudinal direction. The horizontal where the potential temperature and mixing ratios of water width and shape of the warm pool area are given by two vapor, cloud water, and rainwater are predicted are taken to parameters Δλ and Δϕ . In this study, we take Δλ = 80 deg be 982–1,010 hPa, and 100–125 hPa, respectively. T T T 8 Advances in Meteorology In order that large-scale convection may be initiated in Table 3: Speciﬁcation of ﬁve numerical experiments which are performed to examine the eﬀects of the warm pool. the model tropics, a perturbation (zonal-vertical circulation) similar to Kelvin wave is imposed at the initial time. The Δλ Integration Case T (K) Initial zonal velocity is given in the following form: warm (deg) period (day) ⎛ ⎞ 2 2 Case (N) 0 0–320 βa ϕ kπ(λ − λ ) ⎝ ⎠ U λ, ϕ, p = U p exp − cos , K K max Case (S) 1.0 80 80 Day of case (N) 80–560 2C Case (M) 1.5 80 160 Day of case (S) 160–640 (4) Case (L) 2.0 80 240 Day of case (M) 240–800 where U (p) is the maximum zonal velocity associated K max Case (W) 2.0 120 320 Day of case (L) 320–800 with the wave. The values of U (p)are givenin Table 1. K max The maximum westerly at upper levels and the maximum easterly at low levels are imposed at 0E (λ = 0deg). In the ﬁrst portion of the next section, results from ﬁve Other notations are a: the radius of the earth, β: Rossby numerical experiments are presented. The speciﬁcations of −11 −1 −1 parameter(2 × 10 s m ), C : phase speed of the wave, the ﬁve experiments are given in Table 3. The SST anomaly and k:wavenumber. In thisstudy,wetake k = 1and C = corresponding to the warm pool is changed to examine its −1 10 m s . impact. Other several experiments have also been performed The surface pressure and geopotential and potential to understand the dependency of the model behavior on temperature ﬁelds are determined so that the geostrophic some parameters used in the model. Results from two balance may be satisﬁed with respect to the latitudinal direc- numerical experiments among them are presented in this tion (in addition to the hydrostatic balance). As for the lon- paper. gitudinal direction, the structure of the wave is similar to that of the eastward-propagating gravity wave. The amplitude of the surface pressure and temperature at 700 hPa corre- 3. Results sponding to the imposed U are about 1.0 hPa and 1.0 K, K max respectively. The center of the initial low-level convergence is 3.1. ThePeriodofCalculatedKelvinWaves. As mentioned located at 90W. The temperature in the lower layer is lowest in Section 1, the author’s ﬁrst interest is to understand the at 180E, which corresponds to the surface high centered at period of the MJO. At ﬁrst, results from case (N) in which this longitude. The buoyancy of air rising from the boundary SST is uniform in the longitudinal direction are shown. The layer is positive (latently unstable) around this area. It can longitude-time sections (Hovmol ¨ lor diagrams) for rainwater be inferred that two centers of induced convection are found mixing ratio at the lowest level (or surface rainfall intensity), at 90W (initiated by low-level large-scale convergence) and surface pressure, and zonal wind speed at 925 hPa are shown 180E (latent instability) at the very early stage of the time in Figure 1. These physical quantities are those averaged from integration. Although the behaviors of convection and other 5S to 5N. For the ﬁrst 15 days, two eastward-propagating ﬁelds which are caused by the initial condition are also inter- peaks of low surface pressure, easterly ﬂow and rainfall can esting, the primary objective of this study is to understand be seen. The western peak (located at 0–90E) is associated the behaviors of these ﬁelds at the later stage when the eﬀect with the initially given planetary-scale convergence, which is of the artiﬁcial initial condition becomes small. Long-time centered at 90W. The eastern peak is produced by convective integrations (about 500 days) are made in this study. activity due to the initial latent instability (positive buoyancy Thehorizontalgridsizeofthe numericalmodel is taken of rising air) and gravity waves that are excited after the to be 0.2 deg in the equatorial region (about 20 km), as initial time. The maxima of the easterly ﬂows are located mentioned already. This grid size covers only an area of 20S– slightly to the east of the low-pressure centers in these two 20N. A grid size of 0.6 deg is used for other regions. The systems. This feature indicates the structure of an eastward- northern and southern boundaries are placed at 70N and propagating Kelvin wave which is ampliﬁed or maintained 70S, respectively, because inclusion of the polar areas is not against frictional dissipation. necessary although the MCRM is designed so that the polar Our major interest is directed to the model behavior at areas can be included. The number of grid points is 1, 800 × the stage (after 30 days) when the eﬀects of the artiﬁcial initial 201 in the equatorial region and 600× 81 in each of other two condition become small. The most important result from regions. A time increment for the time integration is taken to Figure 1 is that the period of the eastward-propagating wave be 15 sec. The values of other model parameters are taken (with wavenumber 1), which is Kelvin wave, is about 30 days. −1 to be the same as those used in Yamasaki [54, 65]exceptfor The phase speed is about 15 m s . This period (phase speed) the Newtonian cooling rate. The coeﬃcient Q is taken is (or happens to be) very similar to that obtained by Hayashi RADN −1 to be somewhat large (0.3 day ) in the ﬁrst series of the andSumi. Although it is important to understand this −1 numerical experiments. The value of 0.2 day is also used. period obtained by their model and the present model, it As mentioned by Bony and Emanuel , theoretical models remains to be studied (not clariﬁed in this study). of the tropical atmosphere had long represented radiative Oneofotherpronouncedfeaturesseenin Figure 1 is a processes as a Newtonian cooling. A model that includes westward-propagating mode (referred to as WPM) whose −1 cloud-radiation interaction should be used at the later stage phase speed is about 1-2 m s (200 deg/100–200 days). of this series of studies in the future. The WPM modulates convective activity associated with Advances in Meteorology 9 No warm pool Case (N) 5S–5N Surface rainfall Surface pressure Zonal velocity (925 hPa) 0 60 120E 180 120 60 0 0 60 120E 180 120 60 0 0 60 120E 180 120 60 0 −6 −4 −20 2 −12 −8−4 0 48 12 0.02 0.07 0.13 0.25 (g/kg) (hPa) (m/s) Figure 1: Longitude-time sections (Hovmollor ¨ diagrams) of rainwater mixing ratio at the low level (the lowest level of the model, P = 996 hPa), surface pressure, and zonal velocity at P = 925 hPa in case (N). Values averaged for 5S–5N are shown. the Kelvin wave. The surface pressure and the zonal wind Figure 2 shows the longitude-time sections of surface rainfall are also modulated by WPM and the modulated convective intensity, surface pressure, and zonal wind speed at 925 hPa. activity. An example of rainfall systems modulated by WPM The deviations of the surface pressure and zonal velocity is indicated by red ellipses (left panel). from their time averaged values are also shown. The SST The eastward propagation of the Kelvin wave is nearly anomaly is imposed after 80 days of case (N) with an abrupt continuous until about 150 days. Afterwards, new peaks of increase of the SST. Comparison of the uppermost portion of the easterly wind speed are produced to the east of the the left panel of Figure 2 with the middle portion of the left existing one. The rainfall systems that contribute to the panel of Figure 1 indicates that the eﬀects of the SST anomaly formation of the new peaks are indicated by two blue ellipses. can be clearly seen after several days and long-lasting rainfalls The formation of these two rainfall systems is closely related associated with the warm pool appear, as indicated by the to the westward-propagating, low-level westerly and easterly uppermost red ellipse. Somewhat, long-lasting rainfalls are ﬂows (white ellipses) which were excited by convective also seen in the warm pool area in a period of 180–310 days. activity 20–30 days before. Although the phase speed of The patterns of the rainfall and the zonal wind after 320 −1 the Kelvin wave after 120 days is close to 10 m s , the days are signiﬁcantly diﬀerent from those before that time. formation of these convective systems shortens the period of The time when the maximum easterly ﬂow is located at 0E the oscillation; about 30 days (not 40 days) is also seen after is indicated by the red arrows. The period is about 25 days 120 days. in a period of 160–240 days, and afterwards, it takes 50–60 In addition to the WPM, eastward-propagating modes days. In the latter period, the Kelvin wave does not propagate (with similar phase speeds) are also seen (particularly, continuously around the globe, but a new peak of the easterly after 240–360 days, although it is not shown). No physical wind speed is produced around 180E (indicated by three blue interpretation for the westward- and eastward-propagating arrows). The corresponding rainfalls are indicated by three modes can be made in this study, although it is certain that red ellipses in the lower portion of the left panel. The phase cooling due to rainwater evaporation in the subcloud layer speed of many eastward-propagating convective systems is −1 plays an important role. about 15 m s , which is similar to that in case (N), but the The second numerical experiment, case (S) is performed above-mentioned feature (formation of eastward propagat- with inclusion of some eﬀect of the warm pool, but the ing cloud systems and resulting Kelvin wave) is responsible maximum of the SST anomaly is taken to be only 1.0 K. This for the longer periods of 50–60 days. The termination (or choice is made with an intention of better understanding weakening) of the eastward-propagating, strong easterly ﬂow the results for the case with realistically large anomaly. is closely related to strong westerly ﬂow (indicated by white (day) 10 Advances in Meteorology Weak warm pool (centered at 120E) Case (S) Surface rainfall Surface pressure Zonal velocity (925 hPa) 0 90 180 90 0 0 90 180 90 0 90 180 90 0 0 90 180 90 0 0 90 180 90 0 (hPa) (hPa) (m/s) (m/s) (g/kg) Figure 2: Same as Figure 1 but for case (S). Deviations from time-averaged values are also shown for surface pressure and zonal velocity. circles), which was produced by strong convective activity in are given by numerals. It is important to note that the time the warm pool area 15–20 days before. Since new convective interval of the anomaly peaks in case (M) takes a wide range clouds are formed just to the east of the warm pool area, from 20 days to 60 days. The propagation of Kelvin wave is the period is 25–30 days in the western hemisphere, which is most irregular among the four cases (N), (S), (M), and (L) contrasted with that (50–60 days) in the eastern hemisphere despite the intensity of the SST anomaly is between those to the west of about 150E. Although it is of interest to see in case (S) and in case (L), which will be shown in the what happens after 560 days, the time integration has been following. terminated, because it can be considered that the major Figure 4 shows results from case (L) in which the maxi- objective of the numerical experiment has been achieved; it is mum of the SST anomaly is taken to be 2.0 K after 240 days suggested that two types of rainfall patterns may occur in case of case (M). As expected, convection in the warm pool area is of the weak warm pool, as indicated by those in the upper very active and long-lasting. The longitudinal scale of rainfall and lower portions of the ﬁgure. is also larger. The anomaly of the surface pressure is very pronounced. The strong convective activity produces more Results for case (M) are shown in Figure 3. Since the SST anomaly (1.5 K) is taken to be larger than in case (S), convec- notable Kelvin wave, as seen in the zonal wind speed. It may tive activity in the warm pool area is stronger and more long- be important to remark again that the amplitude of Kelvin lasting, whereas it is much weaker in the western hemisphere. wave is smallest in case (M) among the four cases. In case The eastward propagation of convection, surface pressure (N), Kelvin wave is maintained by convective activity which is fairly uniform in the longitudinally uniform SST ﬁeld. In and low-level wind is not so clear as in case (S); that is, the amplitude of Kelvin wave is much smaller than in case (S) case (L), Kelvin wave is enhanced by convective activity in although more distinct anomaly of the surface pressure can the warm pool area, and somewhat maintained by convective activity to the east of about 150E. The eastward-propagating be seen in the warm pool area in case (M). The low-pressure peaks are indicated by the red arrows, and the time intervals convection is stronger in case (L) than in case (M) owing (day) 0.02 0.07 0.13 0.25 −6 −4 −2 −2 −1 −8 −4 −4 −2 6 Advances in Meteorology 11 Moderate warm pool (centered at 120E) Case (M) Surface rainfall Surface pressure Zonal velocity (925 hPa) 0 90 180 90 0 0 90 180 90 0 90 180 90 0 0 90 180 90 0 90 180 90 0 Figure 3: Same as Figure 2 but for case (M). to stronger convection in the warm pool area and resulting speeds in this area are very small. The small phase speeds stronger vertical circulation. of the low-level easterly anomaly are closely related to the Peaks of negative anomaly of the surface pressure are persistence of the low-level westerly ﬂow that contributes to indicated by the red arrows. The time intervals are 50–60 long-lasting convection in the warm pool area. The smallest −1 days and about 80 days. (Inclusion of a weak peak at 430 phase speed is about 2-3 m s ,which canproduce along days indicates addition of 30 and 50 days instead of 80 days.) period of even 80 days. The phase speed of eastward-propagating easterly anomaly Probably it is correct to say that the phase speed of the −1 in the western hemisphere ranges from about 15 m s to Kelvin wave (in terms of the easterly peak) become small −1 22 m s . The faster phase speed appears to be related to by the eﬀects of strong convective activity in the warm stronger convection in the warm pool area and resulting pool area, and therefore, the period becomes longer. Some weaker convection in the western hemisphere. researchers may argue that the long period in case (L) is In order to understand the time interval of the negative not related to Kelvin wave, but it is primarily determined anomaly peaks mentioned above, the deviations of the by strong convective activity associated with the warm pool. surface pressure and the low-level zonal wind speed from However, as seen in Figure 4, the amplitude of the eastward- their time averages are also shown in Figure 4 (as well as propagating Kelvin wave is still large even just to the west in Figures 2 and 3). Since the time averaged ﬁeld indicates of the warm pool area. This suggests the importance of the the stationary component of disturbances produced by the role of the Kelvin wave in determining the period. Only warm pool (stationary vertical circulation similar to Walker the concept of the standing oscillation induced by strong circulation), the subtraction of the time averaged value from convective heating does not appear to be appropriate. the total value makes the propagating component more Westward propagations of cloud clusters can be seen in distinct. As for the propagating easterly anomaly in the the rainfall pattern. However, the eastward propagation of western hemisphere, the phase speeds are nearly the same SCS, which is an ensemble of cloud clusters, is very slow. as those mentioned above. On the other hand, propagations The long period of Kelvein wave, persistence of convection, in an area of 0–120E can also be seen clearly, but the phase and the slow eastward propagation of the SCS in the warm (day) 12 Advances in Meteorology Strong warm pool (centeredat120E) Case (L) Surface rainfall Surface pressure Zonal velocity (925 hPa) 0 90 180 90 0 0 90 180 90 0 90 180 90 0 0 90 180 90 0 90 180 90 0 440 80 Figure 4: Same as Figure 2 but for case (L). pool area suggest that it is of interest to perform another The value of Q ,acoeﬃcient concerning Newtonian RADN −1 numerical experiment by changing the longitudinal scale cooling is taken to be 0.2 day .Thiscaseisreferredtoas Δλ of the warm pool. case (R), which should be compared with case (W). Results Figure 5 shows results from case (W) in which Δλ is in case (R) are shown in Figure 6. Qualitatively, the three taken to be larger (120 deg) after 320 days of case (L). It is ﬁelds of the surface rainfall, surface pressure, and low-level more important to remark that the longitudinal gradient of zonal wind in case (R) are similar to those in case (W). The SST is smaller in case (W) than in case (L). It appears that the time intervals of the MJO-scale in case (R) are 40–45 days in magnitude of the gradient is more important than the hori- many cases and 25–35 days and 60–65 days in some cases. zontal scale of the warm pool area, although the maximum The average time interval is about 40 days, which is shorter anomaly of SST is also very important. As clearly seen from than that (about 50 days) in case (W). A more notable comparison of Figure 5 with Figure 4, strong convections in diﬀerence between the two cases is that small-amplitude the warm pool area in case (W) are separated into two or oscillations with shorter time intervals (10–30 days), which three groups in the longitudinal direction. This feature is the are seen in case (W), are much suppressed in case (R). This most notable result in case (W) compared with other cases diﬀerence can be understood because stronger Newtonian (L) and (M). Another signiﬁcant diﬀerence can be found in cooling in case (W) acts to suppress convective activity and to the period of the oscillation, which is slightly shorter in case produce more unstable stratiﬁcation in a shorter time, which (W). The period is 50–70 days (50–80 days in case (L)) before leads to shorter time scales of convective activity. Although 560 days, and it is about 50 days (50–60 days in case (L)) after Newtonian cooling is probably assumed to be somewhat too that time. As expected, the amplitude of the surface pressure strong in the ﬁve cases, it can be inferred that the above- in the warm pool area is weaker in case (W) than in case (L). mentioned results concerning the eﬀects of the intensity In the above, the results from the ﬁve cases listed in and the size of the warm pool area are not qualitatively Table 1 have been described to show the eﬀects of the modiﬁed for a reasonable value of Newtonian cooling. A intensity and the size of the warm pool (centered on 120E). more reasonable result should be obtained for a realistic An additional numerical experiment has been performed. formulation of radiative cooling. The eﬀects of radiation (day) Advances in Meteorology 13 Wide warm pool (smaller gradient of SST) Case (W) Surface rainfall Surface pressure Zonal velocity (925 hPa) 0 90 180 90 0 0 90 180 90 0 90 180 90 0 0 90 180 90 0 90 180 90 0 Figure 5: Same as Figure 2 but for case (W). interacting with moisture (water vapor and clouds), as (10–30 days) of the eastward-propagating systems is also studied by Grabowski and Moncrieﬀ and Bony and longer than that of the observed SCC. The phase speed of the −1 Emanuel  for the organization of convection, remain to eastward propagation is about 2 m s , which is signiﬁcantly −1 be studied with the MCRM after better understanding of smaller than that of the observed SCC (about 5 m s ) the model MJO under realistic conditions (such as land-sea although it seems to the author that some envelopes of low distribution). OLR studied by Weickmann and Khalsa  move eastward −1 at speeds of less than 4 m s . Physical quantities used in the model and experimental conditions which cause these two 3.2. Convective Activity in the Warm Pool Area. This sub- features (diﬀerences from observations) will be examined in section describes results concerning the second and third future studies. In this respect, a remark is given here. In a problems among the three listed in Section 1 although the −1 two-dimensional CCRM of OY01  with a 1-km grid, the observed phase speed (about 5 m s ) of super cloud cluster −1 eastward speed of the SCCs is about 1-2 m s .The physical (SCC) is not well simulated. As mentioned in Section 1,SCC signiﬁcance of this similarity should be examined in future belongs to synoptic-scale convective system (SCS). More def- studies with an attempt to simulate the observed speed. initely, SCC is deﬁned as a slow-moving system in the warm In addition to the westward-moving cloud clusters, two pool area in this paper, as in many other papers. As an exam- cloud clusters that move eastward are seen in Figure 7. ple, results from case (R) are presented. At ﬁrst, Hovmol ¨ lor These clusters have the property of the squall-line in that its diagram for the surface rainfall intensity (Figure 6)is propagation direction is diﬀerent (opposite) from that of the reproduced in Figure 7, but only for 480–640 days to make low-level wind. These are referred to as S1 and S2. the rainfall pattern much clearer. It can be seen from the ﬁgure that most of the eastward-propagating rainfall systems Now, we will see horizontal distributions of the mixing (named A–K), which are somewhat similar to SCC, consist ratio of rainwater at the lowest level of the model (surface of several westward-propagating rainfall systems which cor- rainfall intensity). Figures 8(a) and 8(d) show rainwater respond to the mesoscale cloud cluster. The clusters form at ﬁelds from 578 day 12 h to 602 day 00 h at a time interval a time interval of about 2–4 days, which is somewhat longer of 12 hours. These ﬁgures describe the behaviors (time than the observed interval of about 2 days. The lifetime evolution) of SCC G and H, and squall clusters S1 and S2. (day) 14 Advances in Meteorology QRADN = 0.2 Case (R) Surface rainfall Surface pressure Zonal velocity (925 hPa) 090 180 90 0 90 180 90 0 0 90 180 90 0 90 180 90 0 0 90 180 90 0 Figure 6: Same as Figure 2 but for case (R). Mesoscale cloud clusters that constitute G and H are named possibilities: the eﬀects of the SST distribution and the land- G1, G2, G3, H1, H2, H3, and H4. The westward movement sea distribution. The diurnal variation over the land has a of these seven clusters and the eastward movement of S1 strong eﬀect of producing convective systems with a period and S2 are clearly seen although S1 begins to move westward of 2 days. In the author’s idealized numerical experiments of after 583 day. An unrealistic feature seen in the ﬁgure is that the diurnal variation of rainfall over a large island over the the lifetime of the cloud clusters is too long. It takes a range equatorial area, the model could simulate not only realistic from 5daysto10days(even more). As seen in Figure 7, the phase of maximum rainfall (most intense rainfall time in lifetimes of cloud clusters in SCC C, E, K, and J are not so LST) in the diurnal variation but also convective activity with long as those in SCC G and H. The lifetimes of the former a period of 2 days (presented at a meeting of the MSJ in are 2–5 days. 2007). This feature is closely related to consumption of water Although several important features seen in SCC and vapor due to strong convection and its slow recovery due to mesoscale clusters are simulated qualitatively, it has an the surface ﬂux. This has also been discussed by some other important problem quantitatively, as mentioned above. The authors. It can be argued that the long lifetimes of SCC and large grid size of about 20 km is certainly responsible for cloud clusters obtained in this study are not necessarily due this problem. If a smaller grid size is used, a cloud cluster to shortcomings of the model although it is certain that the can be easily replaced by a new cluster that forms in its large grid size is partly responsible for the too long time scale. vicinity. In this case, the time interval of the formation of It can also be expected that the results described in this paper new clusters and the lifetime of the clusters will be shorter will be useful for better understanding as a basic research and than those shown in Figures 7 and 8. It appears that the further studies under observed conditions. formulations of the model and the values of the parameters Since Figure 8 covers a large area, and it is somewhat hard used are also responsible for these problems. However, it to see details of the behavior of each cloud cluster, a smaller should be remarked that the model (MCRM) has an ability area is shown for cloud cluster H1 in Figure 9.Compared of simulating realistic time scale of cloud clusters (rainbands with Figure 8, details of the rainwater distributions are in the case of TC), as has been seen in these many years. much more clearly seen although ﬁner resolution in creating As the next step of this study, the author will seek for other Figure 8 would represent clearer distributions. The rainwater (day) Advances in Meteorology 15 Surface rainfall intensity Case (R) 060 120 180 120 60 0 560 D S1 S2 Figure 7: Longitude-time section (Hovmollor ¨ diagrams) of the low-level rainwater mixing ratio in case (R). It is reproduced from Figure 6, but only a period from 480 to 640 days is shown. Each of synoptic-scale convective systems is labeled by A–K (except I). Squall-line systems are labeled by S1 and S2. distributions in Figure 9 are shown at a time interval of 2 of MC behavior is not made in this paper. An important hours from 588 day 02 h (588 : 02) to 590 day 00 h (599 : 00). question is whether the unsatisfactory property of the The zonal scale of cluster H1 is 800–1500 km, which is much calculated MC greatly aﬀects the behavior of cloud clusters larger than that of isolated mesoscale clusters ordinarily (MCSs) and SCC. This problem will be studied in the future observed in the tropics. Although the author describes the when a ﬁner resolution can be used. It should be added that hierarchical structure of the MJO in terms of LCS, SCS, the model has an ability of simulating the time scale of MC MCS (corresponding to the mesoscale cluster), MC, and for a 20-km grid to some extent in cases of TCs and Baiu- cumulus convection in Section 1, Figure 9 shows that cluster Meiyu fronts, as was shown in the author’s previous studies. H1 consists of some MCSs. At 588 : 02, it can be considered Numerical experiments with other experimental conditions that cluster H1 consists of MCS H1A and H1B. MCS H1A as well as ﬁner resolution may answer the present problem. moves eastward, and does not constitute H1 after 589 : 00. A The second example of the behavior of cloud clusters is small cluster, which is referred to as MCS H1C, is located to shown in Figure 10 for cluster G3. This cluster consists of the west of H1 at 588 : 06, moves eastward and joins cluster three MCSs G3A, G3B, and G3C at 587 : 02. MCS G3A joins H1. MCS H1D forms around the western edge of H1 and G3B and decays in the eastern portion of G3. MCS G3C joins MCS H1E, which is located to the west of H1 at the early joins G3B after 588 : 06 and decays (or lose its identity) in the stage, moves eastward, and constitutes the western portion western portion of G3. Cluster G3 is a single system of MCS of cluster H1. After 589 : 14, cluster H1 consists of two MCSs G3B after 588 : 10∼16. It takes a nearly circular shape rather H1B and H1E, and a large cluster with a zonal scale of more than a band shape after 588 : 16, and its horizontal scale is than 1,000 km is seen at this stage. about 400 km at this stage. As mentioned in Section 1, MCS is an organized form of Figure 11 shows the result for cluster G1 at a time MC. Rainwater mixing ratio peaks of calculated MC corres- interval of 4 hours. The areas shown in the left and right pond to peakswhich canbeseenin Figure 9. Although the of Figure 11(b) are diﬀerent, and also diﬀerent from that MCRM can be eﬃciently used for horizontal grid sizes of in Figure 11(a). A small MCS G1A at 579 : 04 grows while 5–20 km, the grid size of 20 km used in this study is some- it moves southward. It is matured in a period of 580 : 04– what too large to properly describe MC. (The most desirable 580 : 16, and afterwards decays rapidly. This MCS constitutes grid size for simulation of MC is 1 km or so.) The lifetime of the eastern portion of cluster G1. MCS G1B, which forms the calculated MC is too long. Therefore, further discussion around 579 : 20, begins to lose its identity after 581 : 00. MCS (day) 16 Advances in Meteorology Case (R) 578 : 12 581 : 12 5N EQ G2 F4 G1 H1 5S F4 S1 S1 579 : 00 582 : 00 5N EQ G2 F4 H1 G1 5S S1 S1 579 : 12 582 : 12 5N G1 EQ F4 G2 H1 5S G1 S1 S1 00 583 : 00 580 : 5N G1 EQ H1 G2 F4 G1 5S S1 S1 583 : 12 580:12 5N EQ G1 G2 F4 G1 5S H1 S1 S1 581 : 00 584 : 00 5N EQ G2 G1 F4 G1 5S H1 S1 S1 90 100 110 120 130 140 15090 100 110 120 130 140 150 Longitude Longitude (g/kg) 0.06 0.22 0.76 1.4 2.6 14 16 32 64 () mm/h (a) Case (R) 584 : 12 587 : 12 5N H2 EQ G2 H2 G3 G2 S1 H1 H1 5S 585 : 00 588 : 00 5N EQ S1 H2 H2 H1 G2 G2 G3 5S H1 585 : 12 588 : 12 5N H2 EQ H2 G2 G2 G3 H1 5S H1 586 : 00 589 : 00 5N EQ H2 G2 G3 G2 G3 H2 H1 5S H1 586 : 12 589 : 12 5N EQ H2 G3 H2 G3 5S G2 H1 H1 587 : 00 590 : 00 5N EQ H2 G3 G2 G3 H2 H1 5S H1 100 110 120 130 150 160100 110 120 130 140 150 160 Longitude Longitude () b Figure 8: Continued. Latitude Latitude Latitude Latitude Latitude Latitude Latitude Latitude Latitude Latitude Latitude Latitude Advances in Meteorology 17 Case (R) 590 : 12 593 : 12 5N EQ G3 5S H1 H2 H1 H2 H3 591 : 00 594 : 00 5N EQ G3 H3 5S H1 H2 H2 S2 591 : 12 594 : 12 5N EQ H2 H3 5S H1 S2 H2 592 : 00 595 : 00 5N EQ H2 H3 5S H2 S2 H1 592 : 12 595 : 12 5N EQ H3 H1 H2 H2 5S S2 596 : 00 593 : 00 5N EQ H2 H3 S2 H1 H2 5S 100 110 120 130 140 150 160 100 110 120 130 140 150 160 Longitude Longitude () c Case (R) 596 : 12 599 : 12 5N EQ H3 H3 H4 5S H2 S2 S2 597 : 00 600 : 00 5N EQ H3 S2 H3 H4 H2 S2 5S 597 : 12 600 : 12 5N EQ H4 H2 H3 S2 S2 5S 601:00 598:00 5N EQ S2 H4 S2 H3 5S H2 601 : 12 598 : 12 5N EQ S2 H3 H4 5S S2 602 : 00 599 : 00 5N EQ S2 H3 H4 5S S2 160 160 110 120 130 140 150 110 120 130 140 150 10 7 10 7 Longitude Longitude () d −1 −1 Figure 8: Horizontal distribution of the low-level rainwater mixing ratio (g kg ) or surface rainfall intensity (mm h ) in case (R) at a time interval of 12 hours: (a) from 578 day 12 hour to 584 day 00 hour, (b) 584 day 12 hour–590 day 00 hour, (c) 590 day 12 hour–596 day 00 hour, and (d) 596 day 12 hour–602 day 00 hour. Each of cloud clusters, which constitute the synoptic-scale convective system, is labeled by F4, G1, G2,..., and H4. Squall line clusters are labeled by S1 and S2. The ordinate ranges from 8S to 8N. Latitude Latitude Latitude Latitude Latitude Latitude Latitude Latitude Latitude Latitude Latitude Latitude 18 Advances in Meteorology 588 : 14 588 : 02 3N H1C EQ G3 H1B H1A H1E H1B H1A 3S 588 : 16 588 : 04 3N H1C EQ H1B H1A H1E H1B H1A 3S 588 : 18 588 : 06 3N H1C EQ H1C H1A H1B H1E H1B H1A 3S 588 : 08 588 : 20 3N H1C EQ H1A H1B H1C H1E H1D H1B H1A 3S 588 : 10 588 : 22 3N H1C EQ H1E H1A H1B H1D H1B H1C H1E H1A 3S 588 : 12 589 : 00 3N EQ H1E H1C H1B H1A H1E H1D H1B H1A 3S 120 125 130 135 140 120 125 130 135 140 (a) rain water 589 : 02 589 : 14 3N EQ H1E H1D H1B H1A H1E H1B 3S 589 : 04 589 : 16 3N EQ H1D H1E H1B H1E H1B 3S 589 : 06 589 : 18 3N EQ H1E H1D H1E H1B H1B 3S 589 : 20 589 : 08 3N EQ H1E H1D H1E H1B H1B 3S 589 : 22 589 : 10 3N H1D EQ H1E H1E H1B H1B 3S 589 : 12 590 : 00 3N EQ H1E H1B H1E H1B 3S 120 125 130 135 140 120 125 130 135 140 (b) Figure 9: Horizontal distribution of the low-level rainwater mixing ratio in case (R) at a time interval of 2 hours: (a) from 588 day 02 hour to 589 day 00 hour and (b) 589 day 02 hour–590 day 00 hour. Each of mesoscale convective systems, which constitute cloud cluster H1, is labeled by H1A, H1B,...,and H1E. Advances in Meteorology 19 587:14 587 : 02 5N G3C G3C EQ G3B G3B G3A G3A 587 : 04 587:16 5N G3C G3C G3A EQ G3B G3B G3A 587 : 06 587:18 5N G3C G3C EQ G3B G3A G3B G3A 587 : 08 587:20 5N G3C G3C G3B G3B G3A EQ G3A 587 : 10 587:22 5N G3C G3C G3B G3B EQ G3A G3A 587 : 12 588:00 5N G3C G3C G3B EQ G3B G3A G3A 110 115 120 125 130 110 115 120 125 130 (a) rain water 588:02 588 : 14 5N G3C G3B G3A G3B EQ 588:04 588 : 16 5N G3C G3A G3B G3B EQ 588:06 588 : 18 5N G3C G3B G3B EQ G3A 588:08 588 : 20 5N EQ G3B G3B G3A 588:10 588 : 22 5N G3B EQ G3B 588:12 589 : 00 5N G3B EQ G3B 110 115 120 125 130 110 115 120 125 130 (b) Figure 10: Horizontal distribution of the low-level rainwater mixing ratio in case (R) at a time interval of 2 hours; (a) from 587 day 02 hour to 588 day 00 hour, and (b) 588 day 02 hour–589 day 00 hour. Each of mesoscale convective systems, which constitute cloud cluster G3, is labeled by G3A, G3B, and G3C. The ordinate ranges from 1S to 5N. 20 Advances in Meteorology 579:04 580 : 04 7N G1A 4N G1A G1B 1N 579:08 580 : 08 7N G1A 4N G1A G1B 1N 579:12 580 : 12 7N G1A 4N G1A G1B 1N 579:16 580 : 16 7N G1A 4N G1A G1C G1B 1N 580 : 20 579:20 7N G1A 4N G1B G1A G1B G1C 1N 580:00 581 : 00 7N 4N G1A G1B G1B G1A G1C 1N 110 115 120 125 130 110 115 120 125 130 (a) rain water 581:04 582:04 6N G1D 3N G1C G1B G1C EQ 581:08 582:08 6N G1D 3N G1B G1C G1C EQ 581:12 582:12 6N G1D 3N G1D G1C G1B EQ 581:16 582:16 6N G1D 3N G1D G1C EQ 581:20 582:20 6N G1D 3N G1D G1C EQ 582:00 583:00 6N G1D 3N G1D G1C EQ 105 110 115 120 125 95 100 105 110 115 (b) Figure 11: Horizontal distribution of the low-level rainwater mixing ratio in case (R) at a time interval of 4 hours; (a) from 579 day 04 hour to 581 day 00 hour, and (b) 581 day 04 hour–583 day 00 hour. Each of mesoscale convective systems, which constitute cloud cluster G1, is labeled by G1A, G1B, G1C, and G1D. Advances in Meteorology 21 0.1 0.5 1234 (g/kg) Qc (200) , V (200) 580 day 13N 10N EQ 7S (a) 0.06 0.22 0.76 1.4 2.6 4.8 Qr (sfc) , V (980) (g/kg) 13N 10N G1 F4 S1 EQ 7S 90 100 110 120 130 140 (b) Figure 12: Horizontal distribution of the low-level rainwater mixing ratio (lower panel), and the upper-level (200 hPa) cloud water mixing ratio (upper panel) at 580 day in case (R). Wind vectors are also shown. Cloud clusters F4, G1, and S1 are labeled. G1C begins to grow just before 580 : 16. MCS G1D forms mixing ratio near the surface at 580 day is shown in the lower at almost the same time as G1C to its west (around 107E, portion of Figure 12. Clusters F4, G1, and S1 are seen. This outside the area shown). It is a single MCS that constitutes rainwater ﬁeld corresponds to that shown for a smaller area cluster G1 after 582 : 12. The horizontal scale is about 400 km in the left of Figures 8(a) and 11(a). At this stage, cluster G1 at this stage. This case shown in Figure 11 is one of the most consists of MCS G1A and G1B. It can be seen that westerly, typical examples that new MCS forms to the west of the old northwesterly, and southwesterly ﬂows contribute to cluster one. G1. The vertical shear in the lower troposphere is easterly The author has considered that a typical organized form shear (vertical proﬁle: not shown), and this contributes to of MC is MCS that has horizontal scales of 200–500 km, the formation and growth of new convection to the west of which correspond to the smaller portion of the so-called existing convection, which has been known in these many meso-α-scale. This has been increasing recognized in the years (since the 1970s). The air of the northwesterly ﬂow author’s studies of TCs, and cloud clusters associated with comes, in many cases, from the northern area where easterly tropical disturbances and Baiu-Meiyu fronts. As in TCs ﬂow prevails. and other tropical disturbances, the present numerical The upper portion of Figure 12 shows the cloud water experiments indicate that two or more MCSs very often (cloud ice in nature) mixing ratio and the wind ﬁeld at constitute a large (larger portion of the meso-α-scale) cloud 200 hPa. As a matter of course, cloud water produced by con- cluster in the case of SCC (generally, SCS). vection is advected by the upper-level outﬂow. In this ﬁgure, Our next concern is why new MCS tends to form and southwesterly∼westerly and northeasterly∼northerly ﬂows grow to the west of old MCS in the case of cloud clusters are pronounced. which constitute SCC although a new cloud cluster tends to Another example is shown in Figure 13. The selected form to the east of old one (eastward propagation of SCC as time is 588 day when four clusters G2, G3, H1, and H2 exist. an envelope of cloud clusters). In order to understand this The rainwater ﬁeld corresponds to that shown in the right problem, the low-level wind ﬁeld as well as the rainwater of Figure 8(b). Cluster H1 consists of MCS H1A and H1B 22 Advances in Meteorology 0.1 0.5 1 2 3 4 (g/kg) Qc (200) , V (200) 588 day 13N 10N EQ 7S (a) 0.06 0.22 0.76 1.4 2.6 4.8 Qr (sfc) , V (980) (g/kg) 13N H2 10N G2 G3 H1 EQ 7S 100 110 120 130 140 150 (b) Figure 13: Same as Figure 12 but at 588 day. Cloud clusters G2, G3, H1, and H2 are labeled. (uppermost left of Figure 9(a); nearly the same time), and at the early 1970s in some respects and signiﬁcantly diﬀerent cluster G3 consists of MCS G3A, G3B, and G3C (lowest from that in other respects. As Ooyama  stated, one right of Figure 10(a)). In the lower panel of Figure 13 for should view wave-CISK (CISK in general) in terms of the low-level ﬁeld, it can be clearly seen that the air in the the conceptual content that has grown and matured with northern area has easterly component, it turns its direction, advances in research. and it has northwesterly component when it enters cluster The discharge-recharge mechanism was proposed by H1. As in other cases, southwesterly ﬂow from the southern Blade and Hartmann . This mechanism appears to cor- hemisphere also contributes to cluster H1 (also, G2 and G3). respond to consumption (due to convection) and recovery In the upper troposphere, outﬂow is seen with pronounced (due to the ﬂux at the sea surface) of water vapor, which southerly and northerly components, and the zonal ﬂow have been considered essential to wave-CISK. For instance, does not have pronounced westerly and easterly components the problem of the recovery of water vapor and its time scale in most of the area shown in this ﬁgure. was discussed by Ooyama . Kemball-Cook and Weare  discussed the importance of building and discharge of the low-level moist static energy in determining the period 4. Additional Discussion of the MJO. (However, they also mentioned that it is not 4.1. Wave-CISK. As mentioned in Section 1, the author has necessary to invoke large-scale wave motions to explain the considered the term wave-CISK as an instability imply- observed oscillation of convection.) Benedict and Randall ing cooperative interaction between moist convection (of  discussed the importance of this mechanism in terms various types) and a large-scale (including synoptic-scale of low-level moistening and heating by shallow convection. As mentioned above, the mechanism included in these dis- and planetary-scale) wave. It appears that inappropriate descriptions concerning wave-CISK, which might lead to cussions can be considered as one of important components misunderstanding, have often been made. depending on of wave-CISK. The time evolution of the vertical proﬁles of how one deﬁnes it (e.g., Chao ). The author’s present the moisture and heating, which should be one of interesting understanding of wave-CISK is common with that envisaged results, is not shown in this paper but remains to be reported. Advances in Meteorology 23 The WISHE mechanism was proposed by Emanuel  are embedded. Without surface friction, the ﬂow is very and Neelin et al. , as mentioned in Section 1. Hayashi diﬀerent from that obtained in the numerical experiments. and Golder  argued that intraseasonal oscillations are Only the direct eﬀects of surface friction on Kelvin waves maintained primarily through the evaporation-wind feed- have to be extracted, keeping the environmental ﬂow. back (EWF: similar to WISHE) mechanism. The present Only idealized numerical experiments have been performed, author has considered that the dependence of surface heat without environmental ﬂow, for various zonal domains and moisture ﬂuxes on the wind speed is one of the with the cyclic condition. The numerical experiments have important components of CISK (including wave-CISK). This conﬁrmed the dispersive property of Kelvin waves which has been important basis for TC studies since the 1960s. was suggested by Oouchi and Yamasaki . That is, in the −1 This was clearly shown by Ooyama . More surface ﬂuxes case when the speed of the eastward propagation is 22 m s −1 in stronger wind areas, which are the general property of for a zonal wavelength of 40,000 km, the speeds are 9 m s −1 the turbulent process in the boundary layer, are favorable and 6 m s for zonal wavelengths of 10,000 km and 5,000 km, or important to CISK in that water vapor consumed by respectively. Although these speeds are modiﬁed according convective activity can be compensated by more surface to experimental conditions, it can be suggested that the ﬂuxes due to stronger wind that has been produced by dispersive property would not be changed. Only this role of convective activity. surface friction is what the author can suggest at the present Another aspect of WISHE eﬀects is that a wave due to stage. It is certain that surface friction plays a signiﬁcant wave-CISK tends to propagate eastward (westward) in the (favorable) role in convective activity in the equatorial area presence of the environmental, low-level easterly (westerly) through frictional convergence because subtropical easterlies ﬂow because of the west-east contrast of the surface ﬂux are usually present. However, direct eﬀects (other than dis- as a result of superposition of the environmental ﬂow and persive property) of surface friction on Kelvin waves remain the ﬂow associated with the wave, as was suggested by to be studied in the future. Emanuel  and Neelin et al. . A study of OY01  The vertical proﬁle of convective heating is very impor- with a two-dimensional CCRM was based on this eﬀect of tant, particularly in the case of models in which the heating WISHE. However, in the case when the Coriolis parameter directly controls the planetary-scale (or synoptic-scale) wave, depends on latitude, as in nature and also in the present as mentioned in Section 1. In this connection, our concern study, the eastward propagation of the planetary-scale wave is to what extent the heating in the upper stratiform clouds is primarily caused by this eﬀect, as manifested as Kelvin (stratiform heating) and cooling associated with stratiform waves (dominance of Kelvin waves in the usual case). The precipitation play important roles in Kelvin wave-CISK. WISHE may play a signiﬁcant role but not important to wave The author has not recognized yet the importance of the propagation. stratiform precipitation that may produce the top-heavy Another problem related to wave-CISK is the role of heating proﬁle (e.g., Lin et al. ) as far as the instability surface friction (friction between the atmosphere and the sea (not structure) of Kelvin waves is concerned. In addition, surface). An instability that arises when surface friction is the author has not understood that stratiform instability included in a model has often been referred to as frictional Mapes  and moisture-stratiform instability Kuang  wave-CISK. The instability of this type was found in linear play important roles in the MJO. analysis made in a TC study of Syono and Yamasaki , which showed the instability of gravity waves of two types 4.2. Tropospheric Humidity and Latent Instability. Wave- with and without surface friction. The Kelvin-wave CISK as CISK can occur only in the presence of latent instability, well as gravity wave-CISK was studied by Hayashi , and which is characterized by positive CAPE (convective available laterbyWang and others (e.g., Wang and Rui ; Xie potential energy). In recent years, some researchers have and Kubokawa ; Wang and Li ; Salby et al. ; discussed the importance of moistening above the boundary Wang and Schlesinger ; Kemball-Cook and Weare ). layer in the MJO (e.g., Maloney and Hartmann ; This problem was also discussed by Oouchi and Yamasaki Maloney ; Bony and Emanuel ). The sensitivity of . One of the most important results from the latter is that moist convection to mid-tropospheric humidity was also Kelvin wave induced by convective heating in the presence of discussed (e.g., Derbyshire et al., ). The importance surface friction is dispersive, whereas neutral Kelvin wave is of the humidity in convective activity and rainfall was nondispersive Matsuno . studied using observational data (e.g., Bretherton et al., . Although the role of surface friction in wave-CISK Zhu et al.  suggested that precipitation is stronger as may be understood to a fairly degree as far as the results the column integrated relative humidity increases and that from linear stability analyses are concerned, our important it should be an exponentially increasing function of the question should be directed to the role of surface friction column saturation fraction to better simulate the MJO. The in a nonlinear model (and in nature). The author has importance of the humidity in convective activity has been tried to understand this problem to some extent. However, no deﬁnite answer has been obtained. In the case of the well known, at least, since the 1960s. What is important in the discussion of wave-CISK (CISK in general) is how numerical experiments in this study, surface friction strongly aﬀects the environmental ﬂow such as not only subtropical the tropospheric relative humidity behaves as a result of easterlies associated with mid-latitude baroclinic waves but interaction of moist convection and larger-scale motions. In also the ﬂow in the equatorial area in which Kelvin waves numerical models with a coarse-grid, it depends on how 24 Advances in Meteorology the eﬀects of moist convection are treated (or parame- portion (around 925 hPa) of the boundary layer and lower terized). Some studies have imposed a relative humidity temperature air at 700 hPa contribute to positive B(700). The threshold for parameterized convection in GCMs to get right panel of Figure 14(c) shows the temperature anomaly better results (e.g., Wang and Schlesinger ; Zhang and at 980 hPa. The importance of the cold pool associated with Mu ). Thayer-Calder and Randall  suggested the active convection can be conﬁrmed. importance of convective moistening; that is, a model has to Raymond and Fuchs [102, 103] explored the hypothesis realistically represent convective processes that moisten the that the MJO is driven by “moisture mode” instability. This entire atmosphere in order to simulate the MJO. term was derived from their view on numerical studies with In the MCRM of Yamasaki [43, 54], active convective the past parameterization schemes that did not incorporate region is more humid as a result of the combined eﬀects of the eﬀects of moist convection appropriately. It seems to the mesoscale (and large-scale) ascending motion and con- the author that this is not a new type of instability, but it vective activity. The author has seen such a feature in tropical corresponds to part of CISK (such as stationary CISK and cyclones and Baiu-Meiyu fronts computed with the MCRM slowly moving Kelvin wave-CISK). Some of their results and in these 25 years. This is also true for the present numerical the present results concerning the behavior of the MJO over experiments of the MJO. the warm pool area appear to have some common properties The right panels of Figures 14(a) and 14(b) show the although the models used and the terms for instability are Hovmol ¨ lor diagrams of the relative humidity at 700 hPa and diﬀerent. at 900 hPa in the same period as that shown in Figure 7. Although some authors have not mentioned the impor- The mixing ratio of cloud water (cloud ice in nature) at tance of latent instability (positive CAPE) but rather empha- 200 hPa is shown in the left panel of Figure 14(a). These sized the importance of relative humidity in recent years, the quantities are those averaged for 3S–3N (not 5S–5N). The present author has considered that it is most important to mixing ratio of low-level rainwater, which corresponds to discuss wave-CISK problems in terms of latent instability. Figure 7, is shown in the left of Figures 14(c) (averaged for Latent instability is the most important and necessary 3S–3N). For convenience, the surface pressure and the zonal condition for wave-CISK. The author has emphasized it in velocity at 925 hPa (Figure 14(d)) are reproduced from part his previous papers. In the MCRM, not relative humidity of Figure 6 (averaged for 5S–5N). but the positive buoyancy of the air that rises from the It can be seen from these ﬁgures that active convective boundary layer is one of the most important quantities for and rainfall areas are generally more humid than other areas. subgrid-scale convective heating although relative humidity The upper troposphere is also more humid (not shown). signiﬁcantly aﬀects the buoyancy of the rising air. This result means that the MCRM satisﬁes the suggestion by Thayer-Calder and Randall . As mentioned above, this 4.3. Other Problems. One of the important concerns in the feature has been a general property of the moisture ﬁeld from MJO is the relative dominance of eastward-propagating the MCRM in these 25 years. Kelvin waves and quasi-stationary component that may Another important feature is that the area to the east usually behave like a localized standing oscillation in the of the warm pool area is more humid than the warm pool warm pool area. It can be argued that the former is enhanced area at 900 hPa, whereas the former is drier than the latter or excited by the latter although the latter is strongly aﬀected at 700 hPa although it is somewhat too dry in the model. by the former (more speciﬁcally, by the low-level wind This feature means that downward motion associated with associated with the former). Some features of the localized planetary-scale circulation makes the atmosphere drier at standing oscillation and the relative dominance were 700 hPa outside the warm pool area and that more shallow described by Zhang and Hendon . As also shown in clouds exist to the east of the warm pool area (not shown). the present numerical experiments, the relative dominance The warm pool area at 900 hPa is less humid than the area is determined primarily by the SST anomaly and its gradient outside it because of compensating downward motion due (Figures 1–6). It appears that the stationary component (or to strong convection in the warm pool area. standing oscillation) is too pronounced in cases (L) and (W) The left panel of Figure 14(b) shows the Hovmol ¨ lor in which the maximum SST anomaly is 2 K. One example diagram of B(700), a measure of the buoyancy which the air that the intraseasonal oscillation is dominated by strong rising from the boundary layer acquires at 700 hPa. Although stationary oscillation was shown by Hsu et al. . They the vertical proﬁle of the buoyancy is also important, the also showed that the upper tropospheric circulation did author has presented this quantity in his papers when not complete the cycle around the globe. This is diﬀerent only one ﬁgure concerning the buoyancy is shown. This is from the result of many other studies (e.g., Knutson and because he has considered that this quantity should be most Weickmann ). It is remarked that the dominance of the important. In other words, the author has not considered standing oscillation may indicate that the zero wavenumber CAPE as the most important quantity. The formulation is dominant. The latter is not pronounced in the wind ﬁeld of the eﬀects of subgrid-scale cumulus convection in the but the pressure (geopotential) and temperature ﬁelds, as MCRM is based on this consideration (Yamasaki [43, was mentioned by Itoh and Nishi . The temperature 54]). Since latent instability (positive CAPE) is one of the (not shown) and surface pressure ﬁelds in cases (L), (W), necessary conditions for convection, B(700) is positive in and (R) clearly show this feature. almost all areas of rainfall in the mesoscale sence, as seen Closely related to the above problem, it is also our in the ﬁgures. Needless to say, more humid air in the upper important concern to clarify whether eastward-propagating Advances in Meteorology 25 Case (R) R (700) QC (200) H 060 120 180 120 60 0 0 60 120 180 120 60 0 0.01 0.02 0.05 0.1 0.2 0.3 20 30 40 50 60 70 80 (g/kg) (%) (a) B (700) RH (900) −12 −9 −6 −35 0 1 2 3 4 6 50 60 70 80 85 90 95 99 (%) (K) (b) Qr (980) T (980) Case (R) 060 120 180 120 60 0 0 60 120 180 120 60 0 0.03 0.11 0.2 0.38 −1 02 1 3 (g/kg) (K) (c) Figure 14: Continued. (day) (day) (day) 26 Advances in Meteorology Ps. U (925) −6 −4 −20 2 −80 −4 4 8 12 (hPa) (m/s) (d) Figure 14: (a) Longitude-time sections of the upper-level (200 hPa) cloud water mixing ratio, and relative humidity at 700 hPa, (b) a measure of buoyancy (in unit of temperature) which the air rising from the boundary layer (about 750 m height) acquires at 700 hPa, and relative humidity at 900 hPa, (c) the low-level rainwater mixing ratio, and temperature anomaly at the lowest level of the model (P = 996 hPa), and (d) surface pressure and the zonal velocity at 925 hPa in case (R). The period corresponds to that in Figure 7, but the values are averaged for 3S-3N. Kelvin waves strongly aﬀect the standing oscillation in are essentially similar although upper-level clouds are more the warm pool area. Hu and Randall  argued that widely spread, as is well known. An eastward-propagation −1 dynamically induced convection is not needed to explain speed of about 5 m s is clearly seen in both ﬁelds (averaged the observed oscillation and that it is a side eﬀect. They for 3S–3N). This is not clear in Figure 7 (averaged for 5S– also suggested that the long time scale of radiative cooling 5N). This speed corresponds to the observed phase speed is an important factor for the low-frequency oscillation. The of SCS (including SCC) which many authors have obtained present author considers that the time scale of recovery of from satellite data. Since the present author considers that water vapor ﬁeld due to surface ﬂux which compensates low-level rainwater ﬁeld is much more important than the consumed water vapor is much more important than that upper-level cloud water for better understanding of wave- of radiative cooling and that the eastward-propagating wave CISK, it is hoped that much more observational data of low- (as well as surface ﬂux) plays an important role to determine level rainwater will be obtained in the future. It is important the time scale of the oscillation in the warm pool area. In to clarify which aspects of the results obtained in this study order to answer this problem clearly, it may be the best way will be validated or invalidated from such observations. to perform numerical experiments by adopting a suﬃciently The ﬁnal numerical experiment presented in this paper wide zonal area instead of about 40,000 km, or a condition in is performed with a maximum SST anomaly of 1.5 K, which which convection outside the warm pool area is suppressed. is the same as that in case (M). Other conditions are taken to A remark is made for the relation between low-level be the same as those in case (R). The longitude-time sections rainwater (surface rainfall) and upper-level cloud water corresponding to Figures 3 (case M) and 6 (case R) are shown ﬁelds. The author has usually examined (or has been in Figure 15(a), but the zonal velocity at 175 hPa is shown interested in) the low-level rainwater ﬁeld at ﬁrst when a instead of the surface pressure deviation. The variability of numerical experiment is performed, because he has consid- the time interval of the minimum surface pressure is notable, ered that description of low-level rainwater is much more as in case (M). The time interval takes a range from 20 days important for better understanding (not for comparison to 55 days. On the other hand, the low-level zonal velocity with observations) than that of the upper-level cloud water has only six major propagations in the eastward direction. (cloud ice in nature) in many problems. However, we are also This is somewhat in contrast to more propagations (shorter concerned with the upper-level cloud water ﬁeld, particularly time scales) in cases (M) and (R). This is primarily due because most of observational studies have described results to the combined eﬀects of smaller gradient of the SST and from satellite data, and because better simulation of the weaker anomaly. As is well known, the upper-level zonal ﬂow upper-level cloud water ﬁeld is important to the radiation is nearly out of phase with the low-level ﬂow. Very strong −1 budget in future studies. Our concern here is whether any westerly ﬂow exceeding 20 m s canbeseenatthe upper- important diﬀerence between distributions and behaviors level. The low-level westerly ﬂow and the upper-level easterly of low-level rainwater and upper-level cloud water exists. ﬂow prevail over the active convection and rainfall in the Comparison of the Hovmol ¨ lor diagrams of the two ﬁelds warm pool area, as has been usually observed. Relatively (left panels of Figures 14(a) and 14(c)) indicate that these slow propagation of the zonal wind speed around the warm (day) Advances in Meteorology 27 SST = 1.5 Case (MWR) 5S–5N Surface rainfall U (925) U (925) U (175) Ps. 090 180 90 0 0 90 180 90 0 0 90 180 90 0 90 180 90 0 090 180 90 40 8 0 80 4 (m/s) (m/s) (hPa) (g/kg) (m/s) (a) Case (MWR) SST = 1.5 5S–5N QC (200) R (700) R (900) T (980) B (700) H H 090 180 90 0 0 90 180 90 0 090 180 90 0 0 90 180 90 0 90 180 90 0 40 8 80 4 (%) (%) (0.1 g/kg) (K) (0.1 K) (b) Figure 15: Continued. (day) (day) 0.02 0.1 0.2 0.07 0.5 0.13 0.25 −12 −6 −6 0 −4 −2 −8 −4 −4 −2 −20 −10 −10 −5 40 28 Advances in Meteorology Case (MWR) Meridional wind V (175) 5S–5N 10N–15N V (925) 5S–5N 10N–15N 090 180 90 090 180 90 0 0 90180 90 0 90180 90 0 40 8 80 4 −12 −60 6 12 −4 −20 2 4 (m/s) (m/s) (c) Figure 15: (a) Same as Figure 2 but for case (MWR). The zonal velocity at 175 hPa is shown instead of the surface pressure deviation, (b) upper-level cloud water, a measure of buoyancy (in unit of temperature) at 700 hPa, relative humidity at 700 hPa and 900 hPa, and temperature anomaly at the lowest level of the model (P = 996 hPa), and (c) the upper-level and low-level meridional velocities averaged for 5S–5N and 10N–15N are shown. pool area and the relatively fast propagation in the western to the west of southerly ﬂow. At the upper-level, nearly hemisphere can also be seen, as in other two cases. The stationary modes prevail. The phase speed of eastward surface pressure ﬁeld, which has large amplitude of zero- propagations to the east of the warm pool area is only about −1 wavenumber, exhibits much faster eastward propagation. 1ms . The physical mechanism remains to be studied. This Figure 15(b) shows the upper-level cloud water, a mea- ﬁnal experiment is a step toward numerical experiments sure of latent instability B(700 hPa), and relative humidities under more realistic (observed) conditions, which will be at 700 hPa and 900 hPa, corresponding to Figures 14(a) and reported in the future. 14(b). The descriptions made for case (R) are also valid in this case qualitatively. The major convection area over the 5. Concluding Remarks warm pool is more humid at 700 hPa (also in the upper troposphere, not shown). At 900 hPa, it is more humid to the This paper describes the results from numerical experiments east of the warm pool area. The temperature near the surface which have been performed as the author’s ﬁrst step toward (right panel) is lower in active convective area owing to a better understanding of the MJO. One of the main features evaporative cooling, and higher in the cloud-free area, where of this study is that it uses the author’s mesoscale-convection- adiabatic compression due to downward motions occurs, as resolving model (MCRM) which has been used, in these 25 also seen in Figure 14(c). years, for his studies on several phenomena such as tropical Figure 15(c) shows the meridional component of the cyclones (including the formation process) and cloud clus- wind at the low and upper levels. The two diﬀerent values ters associated with Baiu-Meiyu fronts. A somewhat large averaged for 5S–5N and 10N–15N are shown. The most grid size of about 20 km is used for more eﬃcient research, pronounced feature seen in these ﬁgures is that the synoptic- although a grid size of 10 km or 5 km is more desirable. One scale waves propagate westward at the low level. Superim- of the primary objectives of this study was to examine to what posed on this, eastward propagations of the envelope of degree the MCRM can describe the properties (behavior) westward propagating and somewhat stagnant modes can of the observed MJO (and large-scale convective system), also be seen. These propagation speeds are signiﬁcantly slow SCS (synoptic-scale convective system including SCC), and compared with that of the zonal wind. At 10–15N, strong MCS (mesoscale convective system) and MC (mesoscale vortices (TCs) are often seen (not shown), as suggested from convection; a basic organized form of cumulus convection). strong (even for the 10–15N average) northerly ﬂow just Another feature of this study is that the author intends to (day) Advances in Meteorology 29 understand the observed MJO by considering simpliﬁed and  stated that SCC does not appear to be a salient feature idealized experimental conditions as the ﬁrst step. Therefore, of the MJO and that the role of SCC in the excitation good simulation of the MJO is somewhat beyond the scope and propagation in the MJO is questioned. As suggested of this study. The most important points in this study are from observations and model results in these many years, to understand what happens in the model and to infer what it appears that SCC is a natural consequence of convective conditions are important to the observed MJO. This study organization in the warm pool area of the Indian/western suggests that numerical experiments should be performed by Paciﬁc Ocean and that it plays an important role in the MJO taking account of the land-ocean distribution as the next step as its component. of this study. Inclusion of the land-sea distribution in the future One of the results which the author had not necessarily study will also modify other aspects of convective activity. expected (or inferred) before performing the numerical It has been pointed out that convective activity is weaker experiments is that the period of the MJO does not over the Maritime Continent, for example, [104, 112, 113]. monotonously change with increasing SST anomaly in the Convective activities over the America and Africa Continents warm pool area. Between the two extreme cases (uniform have to be simulated. A more realistic SST distribution (such SST in the longitudinal direction and large SST anomaly as inclusion of the cold pool around and to the south of corresponding to the Indian/western Paciﬁc Ocean), there is the equator in the eastern Paciﬁc) is also important. It is a regime in which the period varies in a wide range from 20 to our strong concern to see how the MJO and various types 60 days. In the case of longitudinally uniform SST, eastward- of convective systems behave in the model under realistic propagating Kelvin waves are dominant, whereas in the case conditions. of a strong warm pool, a quasi-stationary convective system As mentioned in Section 2, the baroclinic instability (with a pronounced time variation; standing oscillation) is occurs in the middle latitudes in the numerical experiments. formed in the warm pool area, and it strongly enhances The behaviors of the model MJO and convective systems Kelvin waves that propagate eastward around the globe. In should be indirectly aﬀected by what occurs in the middle a certain regime between the two extreme cases, convective latitudes and more strongly aﬀected by the behavior of the activities with two diﬀerent properties coexist, and these subtropical highs, which are closely associated with the baro- are strongly interacted. Therefore, the period of oscillations clinic instability. As for the extratropical forcing that may becomes complicated. contribute to the initial excitation of convection in the Indian Another notable result from the numerical experiments Ocean (or onset of the MJO), some authors have discussed is that mesoscale cloud clusters, which constitute SCS (in- the role of subtropical Rossby wave train (e.g., Hsu et al. cluding SCC), very often consists of two or three meso-scale ). The importance of midlatitude baroclinic eddies in convective systems (MCSs), each of which has the meso-α- the excitation of the equatorial CISK mode was pointed out scale of the smaller portion, and that a new MCS tends to in a discharge-recharge theory of Blade and Hartmann ). form to the west of the existing MCS. The northwes-terly These problems are also interesting, but are beyond the scope and southwesterly low-level ﬂows of the air, the origin of of this study. The problem of tropical cyclones associated which is the air in the easterlies on the equatorial side of the with the MJO also remains to be reported in the future. subtropical highs, contribute to this feature. It may be useful to refer to the cloud resolving convec- The most notable diﬀerence of the model results from tion parameterization (CRCP, Grabowski ). An early observations is that the lifetimes of many MCSs, cloud attempt to study the MJO with the CRCP was made by clusters, and SCCs are too long. Whether this is inevitable in Grabowski . Some recent GCMs (SP-CAM) have used the case of a 20-km grid and whether the experimental condi- super parameterization (SP: the same as CRCP) for studies tions used in this study are responsible remain to be studied. including the MJO e.g., [101, 116–118]). Since a coarse As mentioned in Section 3, the author’s idealized numerical horizontal resolution (such as T42) has been used, the experiments of the diurnal variation of rainfall over a large objectives of their studies with the SP-CAM and the present island over the equatorial area showed that the MCRM could study with the MCRM should be diﬀerent in some respects. simulate convective activity with a period of 2 days. Some The author’s interest is how the SP-GCM will behave when authors have also shown that the diurnal variation over the the resolution becomes ﬁne in the future. land has a strong eﬀect of producing convective activity with As often mentioned in the author’s previous papers, the a period of 2 days. Inclusion of the land-sea distribution as MCRM was developed in the 1980s to study various phe- the next step of this study will be important, particularly with nomena in which moist convection plays an important role, respect to the lifetimes of MCSs, cloud clusters, and SCCs (in with an intention of improving existing parameterization addition to distributions of tropical cyclones). schemes of moist convection. Recent studies of the global In this connection, a remark is made here. Although warming eﬀect on tropical cyclones still uses parameteriza- some authors (e.g., [109, 110]) interpreted the 2-day period tion schemes which are essentially similar to those in the cloud cluster in SCC as a westward-propagating inertio- 1980s. In the near future when a ﬁner grid (such as a 20 km gravity wave, the author has interpreted the cloud cluster grid) can be used, the author expects that the MCRM will be as an organized form of MCs, although gravity waves (of small scale and mesoscale) contribute to the organization of useful for studies of the global warming eﬀect. Also, for this purpose, further studies of the MJO with the MCRM should convection; the cluster is not an inertio-gravity wave. As for the importance of SCC in the MJO, Hendon and Liebmann be important. 30 Advances in Meteorology As mentioned in Section 1, the MCRM used in this study tion as “CISK-type parameterization”. However, this is a hydrostatic model. In recent years, studies of the MJO term is not appropriate because other parameteriza- and/or SCC have been made with a nonhydrostatic model tion schemes have also been (and should also be) used e.g., [119–121]. Although the horizontal grid size used is not for studies of CISK. ﬁne enough to resolve cumulus convection, the eﬀects of the 3. In Y69 and Y71, the easterly wave in the troposphere subgrid-scale convection have not been taken into account. was also one of the major concerns. The author’s interest is to understand to what degree the model can properly treat the MJO and various types of 4. The author has used the term wave-CISK as indicating convective systems. Comparison of results from the MCRM an instability due to cooperative interaction between a and the coarse-grid nonhydrostatic model will answer this wave and moist convection, as mentioned in Yamasaki problem. Numerical experiments under the same conditions [18, 33], and OY01 . Some researchers (e.g., Chao and grid size have not been performed, however. ) have used it as implying the instability of the There is no doubt that a nonhydrostatic global model type discussed in the 1970s and 1980s (including the with a ﬁne grid (such as a 1 km grid) will be (easily) used instability of unrealistic, small-scale Kelvin waves and to study many problems in the near future. Even in that situ- gravity waves). The author’s deﬁnition is also diﬀerent ation, a coarse-grid, hydrostatic and nonhydrostatic models from that of Chao and Lin  in which it is stated will be still useful for eﬃcient research. A nonhydrostatic that wave-CISk is responsible for the growth of a cloud MCRM has also been developed for this purpose (Yamasaki cluster. The author has considered that it is appropriate ). Since the hydrostatic MCRM is much more eﬃcient to use the term wave-CISK as instabilities of Kelvin than the nonhydrostatic MCRM, the former is used in this wave, and SCC that is an ensemble of cloud clusters. In study. However, the latter has diﬀerent merits, and it will the case of TCs, what has been called CISK phenomenon be more useful for other objectives of research. Compar- is not a rainband (corresponding to a cloud cluster) ison of three results from hydrostatic and nonhydrostatic but a TC that is an ensemble of rainbands and various- MCRMs, and a coarse-grid nonhydrostatic model without shaped convective systems including an eyewall. subgrid-scale eﬀects will help us better understand observed 5. The instability of gravity waves is a result of the inter- phenomena, and thereby, improve these models. Under action between two vertical modes, as was suggested some restricted conditions, a cumulus-convection-resolving by Syono and Yamasaki . It was also shown that (global) model (with a grid size of 1 km or less) will be used, a stationary wave occurs when parameterized heating and it should also be important for better understanding of rates exceed critical values in the lower troposphere. observed phenomena and improvement of the two MCRMs. This instability, which corresponds to conditional Needless to say, interactions among researchers are very instability of the ﬁrst kind (CIFK), is also due to inap- important. Although this study is by no means satisfactory propriate parameterization of moist convection because in understanding the MJO and related convective systems, the parameterization used intended to avoid CIFK. and a number of necessary studies (modeling studies as well These instabilities were later discussed by Chang and as observational studies) remain to be made, it is hoped that Lim  with the equatorial beta-plane model. When this study will be useful for interactions among researchers surface friction is taken into account, another type of in this research ﬁeld and that it will contribute to advances an unstable gravity wave is obtained (e.g., Syono and in meteorology through this open access Journal “Advances Yamasaki ; Wang ; Oouchi and Yamasaki ). in Meteorology”. 6. Cumulus-convection-resolving model (CCRM) corre- sponds to the cloud resolving model (CRM) that is Acknowledgments used for a horizontal grid size of 1 km–100 m. Some The numerical experiments have been performed with researchers have used the term CRM for a larger grid size the use of the NEC SX-8R super computer in the Japan such as 5 km. It should also be mentioned that the term Agency for Marine-Earth Science and Technology. As for cloud resolving is rather a general term that can be used drafting ﬁgures, the author thanks Dr. Y. Wakazuki for his for a wide range of clouds. The model used in this study arrangements for the community PC of the research team. (MCRM) also belongs to CRM in this sense. Therefore, the author has used the term CCRM instead of CRM. This is also based on the recognition that it is important Endnotes to resolve cumulus convection which is the basic mode −1 of moist convection, unless the eﬀects of cumulus 1. The phase speed is described as 10–15 m s in N88, and −1 convection are taken into account (or parameterized). SCCs with slower phase speeds (5–10 m s )inN88 are referred to by Lau et al. . 7. Some researchers have argued that the unconditional 2. It was assumed that the heating rate was proportional heating case is unrealistic. However, the discussion from to the vertical velocity at the top of the boundary layer, this case was very important as the ﬁrst step because the as was proposed by Ooyama inhis TC study. In essence of the stability properties was obtained from the this respect, a remark is necessary. 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