Application of a Reduced-Order Kalman Filter to Initialize a Coupled Atmosphere–Ocean Model: Impact on the Prediction of El Niño

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Abstract
A reduced-order Kalman filter is used to assimilate observed fields of the surface wind stress, sea surface temperature, and sea level into the coupled ocean–atmosphere model of Zebiak and Cane. The method projects the Kalman filter equations onto a subspace defined by the eigenvalue decomposition of the error forecast matrix, allowing its application to high-dimensional systems. The Zebiak and Cane model couples a linear, reduced-gravity ocean model with a single, vertical-mode atmospheric model. The compatibility between the simplified physics of the model and each observed variable is studied separately and together. The results show the ability of the empirical orthogonal functions (EOFs) of the model to represent the simultaneous value of the wind stress, SST, and sea level, when the fields are limited to the latitude band 10°S–10°N, and when the number of EOFs is greater than the number of statistically significant modes. In this first application of the Kalman filter to a coupled ocean–atmosphere prediction model, the sea level fields are assimilated in terms of the Kelvin and Rossby modes of the thermocline depth anomaly. An estimation of the error of these modes is derived from the projection of an estimation of the sea level error over such modes. The ability of the method to reconstruct the state of the equatorial Pacific and to predict its time evolution is shown. The method is quite robust for predictions up to 6 months, and able to predict the onset of the 1997 warm event 15 months before its occurrence.

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