Predicting Regime Changes in the Lorenz Model with Ensemble Spread

The Lorenz model produces chaotic solutions with the Lorenz (1963) equations, and is a foundation for predictability of extreme events. Evans et al. (2004) showed that strong bred vector growth is an accurate predictor of regime change taking place in the following orbit, and that the duration of this growth is also an accurate predictor of the duration of the next regime. Palmer (2002) illustrated that the spread of an ensemble depends heavily on the location of the initial ensemble center. Lynch et al. (2016) computed bred vectors from a single time series data using time-delay embedding and nearest neighbor breeding, and found that this provided a new way to model and predict sudden transitions in systems represented by time series data alone. In the present study we initialized ensembles with 10 members on the Lorenz model, tracked them over 8 time steps and measured their spread. The growth of spread was found to predict the change of regime at least as accurately as the growth of bred vectors, and the number of time steps with a growth of spread larger than 6.4% also was a good predictor of the duration of the next regime.