Predictability of Ensemble Forecasting Estimated Using the Kullback–Leibler Divergence in the Lorenz Model  

作　　者：Ruiqiang DING Baojia LIU Bin GU Jianping LI Xuan LI 

机构地区：[1]State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics,Institute of Atmospheric Physics,Chinese Academy of Sciences,Beijing 100029,China [2]College of Earth Sciences,University of Chinese Academy of Sciences,Beijing 100049,China [3]Institute of Space Weather,School of Math and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China [4]College of Physics and Optoelectronic Engineering,Nanjing University of Information Science and Technology,Nanjing 210044,China [5]College of Global Change and Earth System Sciences,Beijing Normal University,Beijing 100875,China

出　　处：《Advances in Atmospheric Sciences》2019年第8期837-846,共10页大气科学进展（英文版）

基　　金：supported by the National Key Research and Development Program of China (Grant No. 2018YFC1506402);the National Program on Global Change and Air–Sea Interaction (Grant Nos. GASI-IPOVAI-03 and GASIIPOVAI-06);the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (Grant No. 2015BAC03B07)

摘　　要：A new method to quantify the predictability limit of ensemble forecasting is presented using the Kullback–Leibler(KL)divergence(also called the relative entropy), which provides a measure of the difference between the probability distributions of ensemble forecasts and local reference(true) states. The KL divergence is applicable to a non-normal distribution of ensemble forecasts, which is a substantial improvement over the previous method using the ensemble spread. An example from the three-variable Lorenz model illustrates the effectiveness of the KL divergence, which can effectively quantify the predictability limit of ensemble forecasting. On this basis, the KL divergence is used to investigate the dependence of the predictability limit of ensemble forecasting on the initial states and the magnitude of initial errors. The local predictability limit of ensemble forecasting varies considerably with the initial states, as well as with the magnitude of initial errors. Further research is needed to examine the real-world applications of the KL divergence in measuring the predictability of ensemble weather forecasts.A new method to quantify the predictability limit of ensemble forecasting is presented using the Kullback–Leibler(KL)divergence(also called the relative entropy), which provides a measure of the difference between the probability distributions of ensemble forecasts and local reference(true) states. The KL divergence is applicable to a non-normal distribution of ensemble forecasts, which is a substantial improvement over the previous method using the ensemble spread. An example from the three-variable Lorenz model illustrates the effectiveness of the KL divergence, which can effectively quantify the predictability limit of ensemble forecasting. On this basis, the KL divergence is used to investigate the dependence of the predictability limit of ensemble forecasting on the initial states and the magnitude of initial errors. The local predictability limit of ensemble forecasting varies considerably with the initial states, as well as with the magnitude of initial errors. Further research is needed to examine the real-world applications of the KL divergence in measuring the predictability of ensemble weather forecasts.

关 键 词：PREDICTABILITY ENSEMBLE forecasting Kullback–Leibler DIVERGENCE 

分 类 号：P456[天文地球—大气科学及气象学]