The importance of such averaging can be easily demonstrated using linear interpolation. From Fig. 1 we see that the pool extends roughly to 8｡? and 8｡?. Taking into account that the migration speed reduces to zero at these latitudes, and that the averaging was done from 4｡? to 4｡?, we find (by linear interpolation) that the averaging gives a value that is about 25% less than the maximum speed along the equator. This is roughly the same as the difference between our upper bound and the quoted values for the observed drift, indicating that there may not be any difference at all between our predicted speed and the observed speed along the equator.
A similar comparison of the model to data can be made with the 1997 El Nino but, unfortunately, as of this writing, this El Nino has been only partially analyzed. A simple comparison can, nevertheless, be made. To do so we first note that the FSU tropical Pacific wind stress analysis (Center for Ocean-Atmospheric Prediction Studies 1998), averaged over a rectangle bounded by 160E-170W and 4N-4S, show that during March, April and May of 1997 the winds almost completely relaxed as required by our model. Second, we can see from the SST analysis presented by BMRC (Bureau of Meteorology Research Centre 1996) that, for the same period, the position of the 28℃ isotherm (averaged from 2°N to 2°S) propagates eastward at an average rate of 40-60km day-1. As pointed out earlier regarding the 1982 El Nino, this propagation rate is roughly equal to our calculated upper bound.
A comment should also be made regarding the observed speed under the pool. According to Kuroda and McPhaden (1993), the water immediately under the pool drifts westward at roughly the same speed as the pool's eastward migration [10-20cm s-1, see (their) Fig. 7c], in agreement with our general scenario of an eastward moving pool and a compensating westward flow immediately underneath. This agreement between the theory and the observations is important as such westward motions under the pool cannot be explained by a simple Kelvin wave.
Finally, an additional comment should be made regarding our use of the no-recirculation assumption. As we saw, without recirculation, the zonal eastward pressure gradient is balanced by form-drag exerted on the pool by the intermediate water that is diving undemeath the eastward propagating pool. With anticyclonic recirculation, part of this zonal pressure gradient would be balanced by the equatorward meridional flow near the “nose” of the pool and, consequently, the pressure gradient available to drive the pool forward would be reduced. This is consistent with the familiar idea that moving fronts are generated and maintained by ageostrophic and not geostorphic motions (see e.g., Hoskins and Bretherton 1972, Nof 1979). It means that the recirculation would slow the pool's migration rate down so that its neglect for the purpose of computing our upper bound limit is certainly adequate.
SUMMARY
Before listing our conclusions it is appropriate to mention again that, although our two-and-a-half-layer model (Fig. 3) is fully nonlinear, it neglects the effects of energy loss and friction. It also neglects the drag that is usually exerted on the pool by the trade winds implying that the model results are applicable only to those situations when the winds completely relax (e.g., the 1982 and 1997 El Ninos). The results can be summarized as follows:
1. By considering a control volume that extends a few deformation radii away from the pool's nose in the east-west direction and an infinitesimal distance ε in the north-south direction (Fig. 3), considering the corresponding flow-force, energy, mass, and potential vorticity conservation, assuming that there is no recirculation, and then taking the limit asε→ 0, we show that an infinitesimal band of water in the immediate vicinity of the equator moves steadily eastward.
2. When the above limit is taken, all the terms involving the Coriolis parameter drop out of the problem demonstrating that, under such conditions, a narrow band in the immediate vicinity of the equator is not directly affected by the earth's rotation.
