Predictability of a Coupled Model of ENSO Using Singular Vector Analysis. Part II: Optimal Growth and Forecast Skill

Abstract

The fastest perturbation growth (optimal growth) in forecasts of El Niño?Southern Oscillation (ENSO) with the Zebiak and Cane model is analyzed by singular value decomposition of forward tangent models along forecast trajectories in a reduced EOF space. The authors study optimal growth in forecast runs using two different initialization procedures and discuss the relationship between optimal growth and forecast skill. Consistent with Part I of this work, one dominant growing singular vector is found. Most of the variation of optimal growth, measured by the largest singular value, for warm events and mean condition is seasonal, attributable to the seasonal variations in the background states. For cold events the seasonal optimal growth is substantially suppressed. The first singular vector is approximately white in EOF space, while its final pattern after a 6-month evolution is dominated by the first EOF. The energy norm amplifies between 5- and 24-fold in 6 months. This indicates that small-scale disturbances are able to draw energy efficiently from the mean seasonal background states and evolve into large scales, characteristic of ENSO, in several months. The difference fields between the initial conditions generated with the standard initialization procedure and the more recent one of Chen et al. (referred to as old and new ICs) are often so large that the optimal growth for the two sets of forecasts is very different. In such situations, linear growth is not an adequate measure of predictability of ENSO. That the present ZC forecast skill is significantly improved by the new initialization procedure indicates that the inherent ENSO predictability is only a secondary factor controlling current forecast skill; the imbalances between the model and data discussed by Chen et al. are the primary factor. Optimal growth describes dominant initial error growth only when initial error covariance is white under a choice of norm. If the difference fields between the old and new ICs are considered representative of the error fields of the old ICs, the initial error covariance is red under the energy norm. So a new norm that makes the initial error covariance white is used. The first singular vectors under the new norm are insensitive to initial time and optimization time, and are dominated by the first few EOFs. When the first singular vector components of the initial error fields are removed from the old ICs, the forecast skill is improved significantly. Thus the suppression of a single initial error structure accounts for most of the new scheme?s improvement in forecast skill.