A Kalman Filter Analysis of Sea Level Height in the Tropical Pacific

Abstract

The Kalman filter is implemented and tested for a simple model of sea level anomalies in the tropical Pacific, using tide gauge data from six selected island stations to update the model. The Kalman filter requires detailed statistical assumptions about the errors in the model and the data. In this study, it is assumed that the model errors are dominated by the errors in the wind stress analysis. The error model is a simple covariance function with parameters fit from the observed differences between the tide gauge data and the model output. The fitted parameters are consistent with independent estimates of the errors in the wind stress analysis. The calibrated error model is used in a Kalman filtering scheme to generate monthly sea level height anomaly maps for the tropical Pacific. The filtered maps, i.e., those which result from data assimilation, exhibit fine structure that is absent from the unfiltered model output, even in regions removed from the data insertion points. Error estimates, an important byproduct of the scheme, suggest that the filter reduces the error in the equatorial wave guide by about 1 cm. The few independent verification points available are consistent with this estimate. Given that only six data points participate in the data assimilation, the results are encouraging, but it is obvious that model errors cannot be substantially reduced without more data.