3. Dynamic modes
We run the coupled model with various initial conditions. The initial disturbances always disperse into two sets of mode, one is symmetric and the other anti-symmetric, much like those schematics in Fig. 2. The symmetric mode is the familiar ENSO mode due to the Bjerknes feedback. It is strongly trapped by the equator. The other mode is the dipole, with interhemispheric differences in SST and wind reinforcing each other. So this demonstrates that it is dynamically consistent to think of tropical SST variability in terms of equatorial and dipole modes. Our dynamic model formulation has a further advantage of allowing us to compute the dispersion relations for the first time in a unified Bjerknes-WES model.
The dispersion curves for the ENSO and dipole modes are shown in Fig. 3. The frequencies of two modes are well separated: the equatorial mode is interannual whereas the dipole has lower frequencies. The growth rate curves are most interesting. Because the Bjerknes feedback is an interaction in the zonal direction, the growth rate of the equatorial mode is small at wavenumber zero, peaks at some wavelength and then decreases toward the shortwave limit. The WES mode, on the other hand, is a north-south mode. So its growth rate is maximum at k=0 and monotonously decreases with the wavenumber. The wavenumber is normalized by the zonal size of the Atlantic so the Atlantic is at k=1. In an ocean like the Atlantic, disturbances of zonal wavenumbers zero and one are both possible. Because the k=0 dipole mode and the k=1 equatorial mode have comparable growth rates, we will see both ENS0-like mode and a dipole oscillation in the Atlantic. And because k=0 has the maximum growth rate, we expect the dipole oscillation to be mostly zonally uniform, which is consistent with observations. The Pacific is about three times as large, so its wavenumber one corresponds to k=1/3, at which the growth rate of the equatorial mode is much larger than other possible modes. So we only see ENSO in the Pacific1.
Consistent with observations (Fig. 1), the equatorial mode has a much broader meridional scale in the Atlantic than in the Pacific (Fig. 4). This is because of the lower growth rate in the Atlantic that allows the mean Ekman flow to advect farther poleward the SST anomalies generated in the equatorial upwelling zone.
4. Simulation of cross-equatorial SST gradient
The interhemispheric SST gradient (ISG) in the Atlantic Ocean is highly correlated with the variability in the latitude of the ITCZ and hence in precipitation over northeastern Brazil (e.g. Mehta 1998). Both ISG and northeastern Brazil precipitation display pronounced quasi-decadal periodicity. Some have argued that the quasi-regularity in ISG variability is simply a fortuitous coincidence between independently varying northern and southern tropics. Here we suggest the otherwise and show it can be simulated by including the dipole-generating WES mechanism in a coupled model.
For this purpose, we remove the thermocline dynamics from our model so that the WES is the only positive feedback that remains. We force the model with observed extratropical COADS wind anomalies confined poleward of 20N and 20S. We leave the tropics within 20N and 20S free of forcing so the ISG must be internally generated.
1 Yukimoto et al.'s (1998; also in this volume) coupled GCM apparently has a dipole mode in the tropical Pacific, with the WES feedback at work. It is thus interesting to see if such a dipole mode still exists when the ocean GCM is replaced with a thermodynamic mixed layer (Kitoh et al., 1998; also in this volume).
