THE SINGULAR VECTORS OF A COUPLED OCEAN-ATMOSPHERE MODEL OF ENSO .1. THERMODYNAMICS, ENERGETICS AND ERROR GROWTH

The singular vectors of a dynamical system are the most rapidly growin g perturbations that can exist in the system before nonlinearity becom es important. We have studied the singular vectors of an intermediate coupled ocean-atmosphere model of El Nino/Southern Oscillation (ENSO) in an effort to understand the dynamics responsible for the growth of small perturbations in the tropics. In particular, we have examined ho w the singular vectors of the observed seasonal cycle are influenced b y various thermodynamic processes which operate in the upper-ocean mix ed-layer, and which affect sea-surface temperature (SST). These proces ses include vertical movements of the main thermocline, zonal advectio n and vertical upwelling. The main findings are: the singular vector s pectrum is dominated by the fastest growing member, regardless of whic h thermodynamic processes are active; the growth factors of the singul ar vectors exhibit a strong seasonal dependence; the western and centr al parts of the Pacific Ocean are the areas most often favoured for gr owth by the singular vectors, and the general criteria that must be me t for singular-vector growth have been determined; at a given time of year, the growth factors of the singular vectors are sensitive to diff erent combinations of thermodynamic processes, although the configurat ion of the dominant singular-vector wind field after optimal growth ha s been achieved is very similar in all cases. This suggests that in th e tropics, the coupled system has a preferred response that the ocean thermodynamics controlling SST conspire to produce, regardless of whic h processes are operating in the mixed layer; the observed ENSO cycle is likely to influence singular-vector growth significantly. These res ults and ideas have important ramifications for the growth of errors a nd uncertainties in models during ENSO forecasts, and for the way this influences the predictability of ENSO. They also have important ramif ications for the way perturbations grow in the real coupled ocean-atmo sphere system.