Forecast of tropical Pacific SST and Sea Level using Markov models

A series of linear statistical models (Markov models) is constructed in a reduced multivariate empirical orthogonal function (MEOF) space of sea surface temperature (SST), sea level and wind stress. The Markov models are trained in the 1980-95 period and verified in the independent 1964-79 period. It is found that the Markov models which include seasonality fit to the data better in the training period and have a substantially higher skill in the independent period than the models without seasonality. We conclude that seasonality is an important component of the dynamical ENSO system.

The impact of each variable on the prediction skill of Markov models is investigated by varying the weightings among the three variables in the MEOF space. For the training period the Markov models which include sea level information fit to the data better than the models without sea level information. For the independent period, the Markov models which include sea level information have a much higher skill than the Markov models without sea level information. We conclude that sea level contains the most information for predictability of ENSO.

The appropriate number of retained MEOFs for the Markov models is three. The Markov model with three retained MEOFs has competitive skill in both the training and independent periods, and has successfully predicted the 1997-98 El Nino and the 1998-99 La Nina. We propose that ENSO can be approximately described as a low order linear system with a dimension of three.

The reliability of the forecasts by the Markov model is estimated. The forecast skill is measured by the averaged spatial correlations and root mean square differences (RMSD) between predicted and observed SST anomalies over a 12-month forecast period. It is found that the spatial correlation skill correlates significantly with the amplitude of the ENSO POP (Principal Oscillation Pattern) in the initial conditions, while the RMSD skill does not. This result suggests that the phase of ENSO is better forecast than the amplitude of ENSO, and the stronger the POP cycle is the more reliable the forecast is. This result is consistent with the fact that most of the ENSO forecast models perform poorly during 1993-96 when the ENSO POP is weak, and recover their skill after 1997 when the ENSO POP becomes strong.

The same Markov model is used to forecast the tropical Pacific sea level anomalies. Preliminary results show that predictability of sea level is higher than that of SST, and the most predictable regions are the equatorial central Pacific and the north-western Pacific around 10 latitude.