ESTIMATION OF TROPICAL SEA-LEVEL ANOMALY BY AN IMPROVED KALMAN FILTER

Kalman filler theory and autoregressive time series are used to map se a level height anomalies in the tropical Pacific. Our Kalman filters a re implemented with a linear state space model consisting of evolution equations for the amplitudes of baroclinic Kelvin and Rossby waves an d data from the Pacific tide gauge network. Ln this study, three versi ons of the Kalman filter are evaluated through examination of the inno vation sequences, that is, the time series of differences between the observations and the model predictions before updating. In a properly tuned Kalman filter, one expects the innovation sequence to be white ( uncorrelated, with zero mean). A white innovation sequence can thus be taken as an indication that there is no further information to be ext racted from the sequence of observations. This is the basis for the fr equent use of whiteness, that is, lack of autocorrelation, in the inno vation sequence as a performance diagnostic for the Kalman filter. Our long-wave model embodies the conceptual basis of current understandin g of the large-scale behavior of the tropical ocean. When the Kalman f ilter was used to assimilate sea level anomaly data, we found the resu lting innovation sequence to be temporally correlated, that is, nonwhi te and well fitted by an autoregressive process with a lag of one mont h. A simple modification of the way in which sea level height anomaly is represented in terms of the state vector for comparison to observat ion results in a slight reduction in the temporal correlation of the i nnovation sequences and closer fits of the model to the observations, but significant autoregressive structure remains in the innovation seq uence. This autoregressive structure represents either a deficiency in the model or some source of inconsistency in the data. When an explic it first-order autoregressive model of the innovation sequence is inco rporated into the filter, the new innovation sequence is white. In an experiment with the modified filter in which some data were held back from the assimilation process, the sequences of residuals at the withh eld stations were also white. To our knowledge, this has not been achi eved before in an ocean data assimilation scheme with real data. Impli cations of our results for improved estimates of model error statistic s and evaluation of adequacy of models are discussed in detail.