Abstract
Linear prediction models applicable to a basic nonlinear two-level quasi-geostrophic model and extended range forecasting are described. One prediction model is linearized around the nonlinear model baroclinic climatological state and solved via an expansion in normal modes. The skill of these predictions are superior to persistence forecasts of daily events for at least 20 days and time averages for at least 90 days. As might be expected, initial states that project strongly onto the linear baroclinic model slow modes provide skillful forecasts at long forecast lags (seasons), which thus provides a prediction of the quality of the prediction and a possible explanation as to why persistence and forecast skill have been found to be correlated at long lags.
An equivalent method for partitioning extended range forecast quality is provided via an EOF expansion. Initial states strongly projecting onto the first and dominant EOF mode are predicted best by the linear baroclinic model. This dominant EOF mode is very similar to the first eigenmode calculated from the linear baroclinic climatological operator.
An alternative linear prediction method is to construct an empirical linear operator from the anomalies. This latter empirical method provides the greatest forecast skill for both dependent and independent datasets. Moreover, the dominant empirical linear prediction mode is again similar to the dominant mode calculated from the EOF expansion and the linear baroclinic model.
