•  Adv. Atmos. Sci.  2019, Vol. 36 Issue (3): 271-278    DOI: 10.1007/s00376-018-8123-5
 The Relationship between Deterministic and Ensemble Mean Forecast Errors Revealed by Global and Local Attractor Radii Jie FENG1, Jianping LI2, 3, *(), Jing ZHANG4, Deqiang LIU5, 6, Ruiqiang DING7, 8 1School of Meteorology, University of Oklahoma, Norman, OK 73072, USA2College of Global Change and Earth System Science (GCESS), Beijing Normal University, Beijing 100875, China3Laboratory for Regional Oceanography and Numerical Modeling, Qingdao National Laboratory for Marine Science and Technology, Qingdao 266237, China4Cooperative Institute for Research in the Atmosphere, GSD/ESRL/OAR/NOAA, Boulder, CO 80305, USA5Fujian Meteorological Observatory, Fuzhou 350001, China6Wuyishan National Park Meteorological Observatory, Wuyishan 354306, China7State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China8Plateau Atmosphere and Environment Key Laboratory of Sichuan Province, Chengdu University of Information Technology, Chengdu 610225, China
Abstract
Abstract

It has been demonstrated that ensemble mean forecasts, in the context of the sample mean, have higher forecasting skill than deterministic (or single) forecasts. However, few studies have focused on quantifying the relationship between their forecast errors, especially in individual prediction cases. Clarification of the characteristics of deterministic and ensemble mean forecasts from the perspective of attractors of dynamical systems has also rarely been involved. In this paper, two attractor statistics——namely, the global and local attractor radii (GAR and LAR, respectively)——are applied to reveal the relationship between deterministic and ensemble mean forecast errors. The practical forecast experiments are implemented in a perfect model scenario with the Lorenz96 model as the numerical results for verification. The sample mean errors of deterministic and ensemble mean forecasts can be expressed by GAR and LAR, respectively, and their ratio is found to approach $\sqrt{2}$ with lead time. Meanwhile, the LAR can provide the expected ratio of the ensemble mean and deterministic forecast errors in individual cases.

Corresponding Authors: Jianping LI
Just Accepted Date: 28 November 2018   Issue Date: 16 January 2019