On the prediction of ENSO: a study with a low-order Markov model

Abstract

linear model best fit to the Zebiak and Cane (1987) ENSO forecast model (ZC) is used to study the model’s prediction skill. Multivariate empirical orthogonal functions (MEOFs) obtained from the sea surface temperature anomaly, sea level and wind stress anomaly fields in a suite of 3-year forecast runs of ZC starting from the monthly initial conditions in the period January 1970 to December 1991, are used to construct a series of seasonally varying linear Markov models. It is found that the model with 18 MEOFs fits the original nonlinear model reasonably well and has comparable or better forecast skill. Assimilating the observed SST into the initial conditions further improves forecast skill at short lead times (> 9 months). The transient initial error growth in the model’s prediction is attributed to the non-self-adjoint property as in Farrell and Blumenthal. Initial error grows fastest starting from spring and slowest starting from late summer and is sensitive to the initial error structures. Two singular vectors (SVs) of the linear evolution operator have significant transient growth dominating the total error growth. Since the optimal perturbation (fastest SV) has mostly high MEOF components, the error growth tends to be larger when there are more high mode components in the initial error fields. This result suggests a way to filter the initial condition fields: the MEOFs higher than the 18th in the initial fields are mostly noise and removing them improves prediction skill. The forecasts starting from late summer have the best predictability because the fastest growth season (summer) is just avoided. The well known, very rapid decline in forecast skill in the boreal spring (the “spring barrier” ) is here attributed to the smallness of the signal to be forecast: the standard deviation of the NIN03 SST anomaly is smallest in spring.