The singular vectors of a coupled ocean-atmosphere model of ENSO. I: Thermodynamics, energetics and error growth

The singular vectors of a dynamical system are the most rapidly growing perturbations that can exist in the system before nonlinearity becomes important. We have studied the singular vectors of an intermediate coupled ocean-atmosphere model of El Niño/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 how the singular vectors of the observed seasonal cycle are influenced by various thermodynamic processes which operate in the upper-ocean mixed-layer, and which affect sea-surface temperature (SST). These processes include vertical movements of the main thermocline, zonal advection and vertical upwelling. The main findings are: • the singular vector spectrum is dominated by the fastest growing member, regardless of which thermodynamic processes are active; • the growth factors of the singular vectors exhibit a strong seasonal dependence; • the western and central parts of the Pacific Ocean are the areas most often favoured for growth by the singular vectors, and the general criteria that must be met for singular-vector growth have been determined; • at a given time of year, the growth factors of the singular vectors are sensitive to different combinations of thermodynamic processes, although the configuration of the dominant singular-vector wind field after optimal growth has been achieved is very similar in all cases. This suggests that in the tropics, the coupled system has a preferred response that the ocean thermodynamics controlling SST conspire to produce, regardless of which processes are operating in the mixed layer; • the observed ENSO cycle is likely to influence singular-vector growth significantly. These results and ideas have important ramifications for the growth of errors and uncertainties in models during ENSO forecasts, and for the way this influences the predictability of ENSO. They also have important ramifications for the way perturbations grow in the real coupled ocean-atmosphere system.