PREDICTABILITY OF A COUPLED MODEL OF ENSO USING SINGULAR VECTOR ANALYSIS .2. OPTIMAL-GROWTH AND FORECAST SKILL

The fastest perturbation growth (optimal growth) in forecasts of Fl Ni no-Southern Oscillation (ENSO) with the Zebiak and Cane model is analy zed by singular value decomposition of forward tangent models along fo recast 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 v ector is found. Most of the variation of optimal growth, measured by t he largest singular value, for warm events and mean condition is seaso nal, attributable to the seasonal variations in the background states. For cold events the seasonal optimal growth is substantially suppress ed. The first singular vector is approximately white in EOF space, whi le its final pattern after a 6-month evolution is dominated by the fir st EOF The energy norm amplifies between 5- and 24-fold in 6 months. T his indicates that small-scale disturbances are able to draw energy ef ficiently from the mean seasonal background states and evolve into lar ge scales, characteristic of ENSO, in several months. The difference f ields between the initial conditions generated with the standard initi alization procedure and the more recent one of Chen et al. (referred t o as old and new ICs) are often so large that the optimal growth for t he 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 initia lization procedure indicates that the inherent ENSO predictability is only a secondary factor controlling current forecast skill; the imbala nces between the model and data discussed by Chen et al. are the prima ry 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 represen tative of the error fields of the old ICs, the initial error covarianc e is red under the energy norm. So a new norm that makes the initial e rror covariance white is used. The first singular vectors under the ne w norm are insensitive to initial time and optimization time, and are dominated by the first few EOFs. When the first singular vector compon ents of the initial error fields are removed from the old ICs, the for ecast skill is improved significantly. Thus the suppression of a singl e initial error structure accounts for most of the new scheme's improv ement in forecast skill.