Forecast of Tropical Pacific SST Using a Markov Model

contributed by Yan Xue and Ming Ji

Environmental Modeling Center, National Centers for Environmental Prediction, NOAA, Camp Springs, Maryland

Forecasts of the tropical Pacific SST anomaly are presented here using a linear statistical model (Markov model). The Markov model is constructed in a reduced multivariate EOF space of observed sea surface temperature (SST), surface winds and sea level analysis (Xue and Leetmaa 1997). The SST from 1964 to 1981 is the reconstruction of historical SST by Smith et al. (1996) and the SST from 1982 to present is the SST analysis by Reynolds and Smith (1994); the surface winds from 1964 to present is the FSU pseudo windstress (Goldenberg and O'Brien 1981); the sea level from 1964 to 1979 is from a model simulation which uses the GFDL MOM1 model forced by the FSU winds and the sea level from 1980 to present is from the ocean analysis at NCEP (Behringer et al. 1997). All the data are monthly values and cover the tropical Pacific region within 20^O of the equator.

The training period is from 1980 to 1995 and the annual cycle for this period is removed from the data. The model is built in a combined EOF space with 3 retained EOFs where the anomalous fields of SST, winds and sea level are equally weighted. The model contains 12 monthly transition matrices as that of Xue et al. 1994. The skill of the model is tested for the training period with a cross-validation method (one year is held out at a time). Fig. 1. shows that the skill with a cross-validation is lower than that without a cross-validation, but is significantly higher than the skill of persistence forecasts. The skill of the model is also tested using an independent period from 1964 to 1979. The hindcast skill of the model is much higher than that of persistence forecasts (Fig. 2).

The confidence in the prediction skill of the Markov model is estimated. A useful relationship between prediction skill and signal to noise (S/N) ratio is identified. Signal is defined as the fraction of the total field spanned by the 3 EOFs and noise is the difference between the total field and the signal. A S/N ratio is defined as the ratio of the standard deviations of the signal and noise fields. We found that the S/N ratios for SST, winds and sea level are highly correlated in time. The amplitudes of the S/N ratios for SST and sea level are comparable, but the amplitude of the S/N ratio for winds is about 1/3 of those for SST and sea level. An averaged S/N ratio is calculated as

represent the S/N ratios for SST, sea level and winds. Prediction skill is measured by a spatial correlation between the observed and forecast SST averaged for the first 6 months of forecast lead time. Shown in Fig. 3 is the scatter plot of prediction skill vs. S/N ratio. It indicates that when S/N ratio is high prediction skill tends to be high. Thus the S/N ratio can be used to estimate confidence in the prediction skill of the Markov model. Due to the small sample size this relationship between prediction skill and S/N ratio may not be well defined. Caution should be used when this relationship is used to estimate confidence in the prediction skill of the Markov model in real time forecasts.

The model has predicted the 1997/98 warm event and the 1998/99 cold event (Fig. 4). The S/N ratio shown in the bottom panel of.Fig 4 is a measure of confidence in the prediction skill of the Markov model. Confidence in the prediction skill increases in the spring season of 1997 when S/N ratio increases. The predictions initiated from the early spring of 1997 underestimated the peak phase of the warm event, but the predictions initiated later improve with shorter lead months. For the decay phase of the event the predictions of the model are very consistent. The model predicted the warm anomaly would dissipate quickly in spring, return to a neutral condition in summer and develop into a moderate cold event by the end of 1998. However the forecast NINO3.4 anomalies by the model initiated from the latest three months (May-July 1998) are less consistent. The forecast NINO3.4 anomalies for the winter of 1998 varies from -1^OC to -2^OC.

The forecast SST anomalies for seasonal means by the model initiated from July 1998 are shown in Fig. 5. The forecast indicates that a cold SST anomaly will develop quickly in the central-eastern Pacific in fall and reach an amplitude of 2.5^OC by the end of 1998. Considering this model is a linear statistical model and nonlinearity is important for cold events, we believe that this latest forecast probably overestimates the amplitude of the event.

References:

Behringer, D. W., M. Ji and A. Leetmaa, 1997: An improved coupled model for ENSO prediction and implications for ocean initialization. Part I: The ocean data assimilation system. J. Climate, in press.

Goldenberg, S. B. and O'Brien, J. J., 1981: Time and space variability of tropical Pacific wind stress. Mon. Wea. Rev., 109, 1190-1207.

Reynolds, R. W., and T. M. Smith, 1994: Improved global sea surface temperature analyses using optimum interpolation. J. Climate, 7, 929-948.

Smith, T. M., R. W. Reynolds, R. E. Livezey, and D. C. Stokes, 1996: Reconstruction of historical sea surface temperatures using empirical orthogonal functions. J.Climate, 9, 1403-1420.

Xue, Y., M. A. Cane, S. E. Zebiak and M. B. Blumenthal, 1994: On the prediction of ENSO: a study with a low-order Markov model. Tellus, 46A, 512-528.

Xue, Y. and A. Leetmaa, 1997: Predictability of ENSO: a study with Markov models. Proceedings of the twenty-second annual climate diagnostics and prediction workshop, Berkeley, Ca, Oct. 6-10, 1997.