In order to determine what portion of the unfiltered climatological variation is explained by TIW variation, the ratio of the seasonal variability of TIWs to the seasonal variability necessary of unfiltered data was computed (data not shown). From this calculation, the ratio of an intraseasonal cycle, like TIWs, to the seasonal cycle can be estimated. About 10�C20% of the temperature and more than 80% of the meridional current climatological variations are explained by the TIW variability around the equator between 110��C150��W. However, unlike temperature and meridional current, TIW variability occupies a very small portion of climatological variation in the zonal current. This is because zonal current has a stronger seasonal cycle than meridional current [29, 30], and the seasonal variability of an unfiltered zonal current is much larger than the seasonal variability of an unfiltered meridional current.
Therefore, zonal current has a very low ratio of TIW variation in climatological variation, while a meridional current that has a weak seasonal cycle shows a very high ratio. Especially near the equator, the variation of TIWs in the meridional current is responsible for over 90% of the seasonal variability. Although the seasonal cycle of temperature is strong and its intraseasonal cycle is also strong, it is different from the zonal current. On the whole, TIWs in the temperature and the meridional current contribute significantly to climatological variation. As seen in Figure 3(c), 20% of the total variability of TIWs can be explained by its seasonal variability.
In order to clarify the seasonal locking of TIW variability, the mechanisms underlying the generation of TIWs were investigated. It is known that TIWs are generated through barotropic instability caused by the shear of zonal currents, and also baroclinic instability associated with the temperature gradient [4�C6]. Two instability mechanisms were estimated from the eddy kinetic energy (EKE) equation [31, 32]. The EKE equation can be derived directly from the momentum equations. The EKE equation is given by(EKE)t=?v???(EKE)?v��??(EKE)????v��??P��?+Bt+Bc?��,(1)where Bt=-��0(u��u��-u-x+u��v��-(u-y+v-x)+v��v��-v-y), Bc=-�ѡ�gw��-. In (1), EKE indicates ��0(u��2+v��2+w��2)-/2, where the overbars denote the monthly mean, primes denote the TIW components that have been applied to a 50-day high-pass-filter, and ��0 is the constant value for the density of water, 1000kgm?3. In (1), Bt represents the kinetic energy conversion between mean and eddy flows. If Bt is positive, then energy is transferred from mean kinetic energy to eddy Carfilzomib kinetic energy through barotropic instability.