Concerning the Response of the Atmosphere to a Tropical Sea Surface Temperature Anomaly

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Abstract
The appropriateness of using simplified versions of the equations of motion to explain the response of the atmosphere to external forcing, such as that associated with the 1982/83 El Niño, is considered. In particular, the terms in the baroclinic equations linearized about a zonal basic state or about the three-dimensional mean climatic state are evaluated, and the appropriateness of the linearization is considered with reference to the results from both the observations and a simulation with a general circulation model. A similar analysis is undertaken of the terms of the barotropic vorticity equation at 200 mb. Considerations of the specification or parameterization of the source/sink term in the simplified equations are also discussed. Generally it is found that the equations which arise when linearizing about a zonal basic state are clearly unsuitable in this case. The neglected terms are of the same order as those retained and the balances of energy and vorticity which occur in the general circulation model and the observations are not those of the linearized equations. The linearization about the three-dimensional mean state in the case of the baroclinic equations is considerably less in error. The linearization can be carried out successfully in the tropical region of direct response to the El Niño forcing but it is not successful in the case of the remote extratropical response to the tropical forcing. In the extratropics, the nonlinear transient terms cannot be neglected compared to the linear terms even when the linearizations are about the three-dimensional mean state. For the barotropic vorticity equation, linearization is generally unsuccessful and here the nonlinear mean as well as the non-linear transient terms cannot be neglected. Finally, the correct specification of the sources and sinks for the simplified equations is an area of difficulty since, in the case of the response to the El Niño, both localized anomalous source and sink regions are found while the usual approach is to specify or parameterize a localized source but a distributed sink. Apparently an “anomaly” physics would be required in which both localized sources and sinks of energy and vorticity would be specified or parameterized.

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