Impact of Perturbation Schemes on the Ensemble Prediction in a Coupled Lorenz Model

Based on a simple coupled Lorenz model, we investigate how to assess a suitable initial perturbation scheme for ensemble forecasting in a multiscale system involving slow dynamics and fast dynamics. Four initial perturbation approaches are used in the ensemble forecasting experiments: the random perturbation (RP), the bred vector (BV), the ensemble transform Kalman filter (ETKF), and the nonlinear local Lyapunov vector (NLLV) methods. Results show that, regardless of the method used, the ensemble averages behave indistinguishably from the control forecasts during the first few time steps. Due to different error growth in different time-scale systems, the ensemble averages perform better than the control forecast after very short lead times in a fast subsystem but after a relatively long period of time in a slow subsystem. Due to the coupled dynamic processes, the addition of perturbations to fast variables or to slow variables can contribute to an improvement in the forecasting skill for fast variables and slow variables. Regarding the initial perturbation approaches, the NLLVs show higher forecasting skill than the BVs or RPs overall. The NLLVs and ETKFs had nearly equivalent prediction skill, but NLLVs performed best by a narrow margin. In particular, when adding perturbations to slow variables, the independent perturbations (NLLVs and ETKFs) perform much better in ensemble prediction. These results are simply implied in a real coupled air–sea model. For the prediction of oceanic variables, using independent perturbations (NLLVs) and adding perturbations to oceanic variables are expected to result in better performance in the ensemble prediction.