Comparative study of Lorenz model based ensemble forecasting and single forecasting
Authors: Liang Ding  , Gu Bin  , Ding Rui-Qiang  , Li Jian-Ping  , Zhong Quan-Jia  ,   Institute of Space Weather Research, Nanjing University of Information Science and Technology, Nanjing 210044, China;,   State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics(LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China;,   College of Physics and Optoelectronic Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China;,   College of Global Change and Earth System Science(GCESS, Beijing Normal University, Beijing 100875, China
Published: December 2020

In the past two decades,the ensemble forecasting has gained considerable attention.The atmosphere is a chaotic system,and a small error in the initial conditions will result in an enormous forecast uncertainty with time.It is impossible to precisely predict the future state of the atmosphere by a single (or control) forecasting.The ensemble forecasting is a feasible method to reduce the forecast uncertainty and to provide the reliability information about forecast.Many studies showed that because of the nonlinear filtering effect,the ensemble forecasting is more skillful than the single forecasting according to the statistical average over a large number of numerical experimental cases. However,the forecast skill can vary widely from day to day according to the specific synoptic events.The dependence of the ensemble forecasting on specific event has not been fully addressed in previous studies.Therefore,the performances of the ensemble forecasting in specific experimental cases should be further studied,which is important for improving the forecast skill in weather and climate events.In this paper,the nonlinear local Lyapunov vectors (NLLVs),which indicate orthogonal directions in phase space with different perturbation growth rates,are introduced to generate the initial perturbations for the ensemble forecasting.The NLLVs span the fast-growing perturbation subspace efficiently, and thus may grasp more components in analysis errors than other ensemble methods.Meanwhile,the bred growing mode (BGM) method,which indicates the fastest growing perturbation mode,is also used for the ensemble forecasting. Based on the NLLV and BGM methods,the forecast performances of the ensemble forecasting and single forecasting are compared in the Lorenz63 and Lorenz96 models for specific experimental cases.Additionally,two practical measures, namely the root mean square error (RMSE) and pattern anomaly correlation (PAC),are used to assess the performances of the ensemble forecasting.The results indicate that each ensemble mean forecasting is more skillful than its single forecasting in terms of RMSE and PAC.For each experimental case,the proportion of the ensemble forecasting better than single forecasting gradually increases with time in Lorenz63(Lorenz96) model by both NLLV and BGM methods, respectively.In addition,the variation of probability distribution of the ensemble mean states might be the reason why the forecast error of ensemble forecasting is less than that of the single forecast.The results based on simple model could provide a new perspective to understand ensemble forecasting and may be conducive to the weather and climate prediction.