5. Summary and discussions

A series of experiments have been performed with a simplified GCM (General Circulation Model) to examine the effect of vertical profile of radiative cooling on the space-time distribution of equatorial precipitation activities and the circulation structures associated with them in aqua-planet experiments. The role of present study is to extend those classic researches on aqua-planet experiments such as HS86 and Numaguti and Hayashi, 1991; we realize a parameter study and presented movie representations (subsection 3.3 and subsection 4.3 which was difficult to persue at those classic ages. We have utilized two types of cumulus parameterizations, namely, the Kuo scheme and mosit adjustment scheme, which are the similar level of those used in the classic researches and are quite simple compared to those used in the present-day sophisticated GCMs. The aim is to present some basic information for considering behaviors of equatorial precipitation activity by perfoming a parameter study with a rather simplified GCM whose system complexity is located between the equations of geophsical fluid dynamics, especially equatorial dynamics, the system of present-day GCMs.

The behavior of the precipitation activity represented by our simplified GCM with the resolution of 128x64x16 follows those obtained by the previous studies; precipitation occurs in the form of eastward or westward sequences of grid-scale precipitation events (see Appendix C as to the difference from the results of previous studies). It is shown that the preference depends on the profile of radiative cooling; for the upper level cooling experiment, where condensation heating is larger in the upper levels, eastward sequences become more evident than westward. This is consistent with the expectation given by the wave-CISK theory.

The dependence on the radiative cooling profile is more clear in the experiment with Kuo scheme. Composite analysis demonstrate, that the circulation structure associated with eastward precipitation events is consistent with that expected by the wave-CISK theory with equatorial Kelvin waves, as was presented by Numaguti and Hayashi (1991). The difference of responses between utilized cumulus parameterization schemes also suggest that the eastward structure associated with grid-scale precipitation events is related to that of the wave-CISK theory. Kuo scheme is a parameterization which represents condensation heating directory by horizontal convergence, namely, upward motion of the atmospheric motion, and hence is quite close to the formulation of the wave-CISK theory. On the other hand, moist convective adjustment is a parameterization where generation and signature of condensation heating heavily depends on atmospheric local conditions such as humidity and stratification. Consequently condensation heating varies vitally independent of the motion associated atmospheric waves. Especially, in the grid-scale phenomena, the relationship between atmospheric motion and condensation is expected to be stochastic, which enable us to imagine that the discrepancy from the expectation by the wave-CISK as a simple linear theory becomes large.

As for the westward sequences of grid-scale convective events, the westward speed is close to the easterly wind speed of the lower atmosphere. Moreover, the locations of precipitation coincide with the locations where humidity is high in the lower atmosphere. These results suggest that the westward motion of precipitation activity can be explained by the advection of high humidity anomaly by the background low level wind.

In addition to those two grid-scale features, we find three more components of equatorial precipitation activity which correspond to dispersion relation of equatorial wave. The first is an eastward moving structure with long wavelengths such as wavenumber one, as mentioned in the previous works (e.g., HS86). The reason of the existence of the eastward propagating large scale disturbances is still unclear. The results of present study show that their phase speeds are roughly the same as the eastward motion of grid-scale precipitation events, but they appears more clearly in the lower level cooling experiments, and they show no westward phase tilt. These indicate that the eastward propagating large scale disturbances are not related to the propagating unstable solution of wave-CISK. The structure seems to be that of neutral equatorial Kelvin waves which have a decreased phase speed owing to the effect of cumulus heating, i.e., so called moist Kelvin waves (Gill, 1982). Moreover, emergence of long wave cannot be explained by the wave-CISK linear theory, since it predicts the smaller growth rate for the longer wavelength disturbance. There still remain other possible mechanisms to be pursued; for instance, WISHE (wind induced surface heat exchange) as discussed by Numaguti and Hayashi (1991) and self-organized moisture redistribution as discussed by Lindzen (2003). The second is a westward propagating structure with long wavelengths and low frequencies. The disturbances of this category seem to correspond equatorial Rossby waves with a small value of equivalent depth. The third one is a eastward or westward propagating structure with long wavelengths but high frequencies. The disturbances of this category seem to correspond equatorial inertio-gravity waves. These two types of structures might also be explained as a result of interaction between waves and cumulus activities. However, in the present study, we could not perform systematic analysis since the corresponding signals are noisy and are hard to extract.

In this study, we have demonstrated several new clues additional to those discussed Numaguti and Hayashi (1991) as for the eastward propagating grid-scale disturbances. However, the argument we have presented here on the relationship with the wave-CISK theory (propagating unstable waves) and moist Kelvin waves (propagating neutral waves) are still conjectural. These are within the range of simple linear theory, and are far from desired theory which can describe non-linear phenomena like those motions driven by moisture advection and its condensation heating. A simplified GCM is yet complicated enough to understand; it seems that, as is emphasized by Held (2005), we still need to develop models of intermediate levels and continue trials to understand those phenomena.