Singular vectors and the predictability of weather and climate

The local instability properties of a chaotic system are determined by the singular vectors and singular values of the dynamical evolution operator, linearized about a finite trajectory portion of the integral curves of the nonlinear equations. Knowledge of these quantities allows an assessment of the reliability of a finite-time forecast from a chaotic system. After a brief study of the Lorenz model, singular vector analysis is applied to study three predictability issues in atmosphere-ocean dynamics. The first concerns the predictability of weather forecasts of a few days, and singular vector calculations are made from a large-dimensional numerical weather prediction model using an interative Lanczos algorithm. The second concerns the predictability of El Nino on seasonal to interannual timescales. Here singular vector calculations are made using a coupled ocean-atmosphere model of the tropical Pacific region. Finally we show results from a multi-decadal integration of a medium-resolution quasi-geostrophic model, and discuss the possible relevance of singular vector analysis for the problem of climate change.