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 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.

摘 要

本文基于一个简单的耦合 Lorenz 模型, 探讨了多尺度模式的集合预报初始扰动构造相关问题. 集合预报试验使用了四种初始扰动方法：随机扰动 (RP)、 繁殖向量 (BV)、 集合变换卡尔曼滤波 (ETKF) 和非线性局部 Lyapunov 向量 (NLLV) 方法. 结果表明, 无论使用哪种方法, 预报的初始阶段, 集合**均与控制预报相**. 耦合 Lorenz 模型由慢系统和快系统耦合而成. 由于误差在不同时间尺度系统呈现不同的增长模态, 快系统经过较短的一段时间后, 集合**均的结果开始优于控制预报, 然而, 慢系统经过相对较长的时间后, 集合预报才开始起作用. 此外, 由于不同尺度之间的相互反馈过程, 无论是对快变量还是对慢变量叠加扰动, 都有助于提高慢系统和快系统的预报技巧. 对不同初始集合扰动生成方法进行比较, 发现 NLLVs 总体上优于 BVs 和 RPs, NLLVs 和 ETKFs 的预报能力几乎相当. 当向慢变量叠加扰动时, 独立扰动 (NLLVs 和 ETKFs) 在集合预报中表现出更好的预报技巧. 将简单模型的结果引申到真实的海气耦合模式. 我们推测, 对于海洋变量的预报, 使用独立扰动 (NLLVs) 并且在海洋变量叠加扰动, 会取得更好的集合预报效果.