This essentially results from the symmetry of the problem (relative to the equator) which implies no crossequatorial flow within the head of the pool and no east-west Coriolis force. The above limit gives an upper bound for the migration speed because the thickness of the pool decreases gradually away from the equator [implying that the forward propagation rate (which is proportional to the thickness) also decreases away from the equator].
3. For a given pool's thickness (and intermediate layer thickness ahead of the pool) and a given density difference between the pool and the intermediate water below, there is one propagation rate (Figs. 5 and 6), one thickness under the pool and one density difference ratio (i. e., one ratio of the density difference between the pool and the intermediate water and the density difference between the intermediate water and the deep water underneath).
4. The calculated upper bound for the eastward migration of the pool's nose is [2g(Δρ1/ρ)H]1/2 (H2/H1), where Δρ1 is the density difference between the pool and the water underneath H, H1 and H2 are the pool thickness, the intermediate water thickness ahead of the pool and the intermediate water thickness under the pool. The above formula is simple to use but it does not contain all the information that the model provides. Specifically, according to (6) there is a particular ratio between H and H1 for any given pool so that, from a theoretical point of view, the migration speed should be written in terms of only three variables, e. g., C=[2g(Δρ1/ρ)H1]1/2 (1-H2/H1)3/2.
There are three aspects of the model that agree with the observations. First, it turns out that the combined pool and intermediate layer depth under the pool (H + H2) is always smaller than the intermediate layer depth ahead of the pool, H1, so that the modeled interface rises under the pool. This is supported by Kuroda and McPhaden's (1993) observation of the pool (see Fig. 2) even though the winds did not completely collapse during the year that the observations were made (1990). Furthermore, all the measured density differences and depths are also in good agreement with the theoretical predictions. Apparently, the drag induced by the trade winds prevented a continuous free eastward movement but did not alter the density field significantly. Second, and most important, a comparison of the predicted and observed migration speeds during the 1982 El Nino shows that our predicted nonlinear upper bound is about 25% higher than the averaged observed speed, and about 40% higher than the speed predicted by both the Gent and Cane model and the earlier linear model. The difference between our upper bound and the observed values is either due to our neglect of friction, breaking waves and recirculation (which would reduce the computed speed) or due to the averaging of the pool's observed speed over an 8ﾟ band (that “hides” the actual speed along the equator which is expected to be greater than the off-equatorial speed) or both. Third, a comparison between the modeled speed under the pool to the observed speed under the pool show that, as required, both speeds reverse direction with depth (i.e., both display a westward speed underneath the pool).
As of this writing the analysis of the 1997 El Nino has not been completed to a degree that a detailed satisfactory comparison to the data can be made. A simple comparison is nevertheless possible and gives very reasonable values.
ACKNOWLEDGMENTS
This study was supported by the National Science Foundation (NSF) under grants OCE 9102025 and OCE 9503816, National Aeronautics and Space Administration (NASA) grants NAGW-4883 and NAG5-4813, and Office of Naval Research (ONR) grant N00014-96-1-0541. Conversations with A. Clarke and correspondence with M. McPhaden and W. Kessler were very helpful. We thank T. Delcroix for providing us with his unfiltered data for the observations and numerical values shown in Fig. 4.
