Non-modal growth in ENSO and its interdecadal change

A Markov model is constructed in a reduced multivariate empirical orthogonal function (MEOF) space of observed sea surface temperature (SST), wind stress and sea level analysis. The Markov model trained in 1980-95 has a competitive skill in the independent 1964-79 period, and has successfully predicted the 1997-98 El Nino and the 1998-99 La Nina.

The non-modal growth of the Markov model is calculated using singular vector analysis. We found that only the first singular vector grows, and the first singular vector component of the initial conditions accounts for most of the ENSO growth in the Markov model. For a nine month integration, the optimal growth rate (first singular value) is largest for initial months in early spring, and smallest for initial months in summer. The optimal growing pattern (first singular vector) is not sensitive to integration times and initial seasons. We found that the correlation between the optimal growing pattern, composed of three variables, and the initial conditions during early spring season is indicative of ENSO development. The correlation in sea level leads the correlations in SST and wind stress, suggesting that sea level contains the precursor for ENSO. The optimal growing pattern with a sea level anomaly within the range of 3-4 cm at the basin scales of the tropical Pacific can evolve into a moderate ENSO event in nine months, suggesting that we need to represent such pattern within that accuracy in the initial conditions for ENSO forecast models.

To study the interdecadal change of the non-modal growth, two Markov models are constructed using observed SST, wind stress and sea level simulation forced with observed winds --- one for 1964-76 and another for 1977-89. The model-observation correlation shows a strong spring barrier for the period before 1976 and little spring barrier after 1976. This is a result of ENSO being phase-locked to annual cycle before 1976 and little phase-locked to annual cycle after 1976.

For the two Markov models, the first singular vector component of the initial conditions accounts for most of the ENSO growth, and the optimal growth rate is a function of initial seasons. The seasonality of the optimal growth rate for 1964-79 is much larger than that for 1977-89. The optimal growing patterns for the two periods have similar sea level and wind stress structures, but different SST. The final patterns of the optimal growing patterns after a nine month integration resemble a mature phase of ENSO. The evolution of optimal growing patterns describes the westward propagation of SST before 1976 and the eastward propagation of SST after 1976. It is proposed that the interdecadal change of seasonal growth rate and optimal growing patterns is related to the changes in the mean and annual cycle in the two periods.