Impact of perturbation schemes on the ensemble prediction in a coupled Lorenz model

Abstract: Based on a simple coupled Lorenz model, we investigate how to consider 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: 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 a very short period of lead time in a fast subsystem, but after a relatively long period of time in a slow subsystem. As a result of coupled dynamic processes, whether adding perturbations to fast variables or to slow variables can contribute to an improvement in the forecasting skill for fast variables and slow variables. When it comes to the initial perturbation approaches, the NLLVs show higher forecasting skill than BVs or RPs overall. NLLVs and ETKFs had nearly equivalent prediction skill, and NLLVs won by a narrow margin. In particular, when adding perturbations to slow variables, independent perturbations (NLLVs and ETKFs) perform much better in the ensemble prediction. These results are simply implied in a real coupled air–sea model. For the prediction of oceanic variables, independent perturbations (NLLVs) and adding perturbations to oceanic variables will be expected to perform better in the ensemble prediction.

Keywords:
• skill score,
• applied meteorology,
• forecast score