Theoretical and Applied Climatology

, Volume 138, Issue 3–4, pp 1435–1444 | Cite as

Toward practical approaches for ergodicity analysis

  • Hongrui Wang
  • Cheng WangEmail author
  • Yan Zhao
  • Xin Lin
Original Paper


It is of importance to perform hydrological forecast using a finite hydrological time series. Most time series analysis approaches presume a data series to be ergodic without justifying this assumption. To our knowledge, there are no methods available for test of ergodicity to date. This paper presents a practical approach to analyze the mean ergodic property of hydrological processes by means of augmented Dickey Fuller test, Mann-Kendall trend test, a radial basis function neural network, and the assessment methods derived from the definition of ergodicity. The mean ergodicity of precipitation processes at Newberry, MI, USA, is analyzed using the proposed approach. The results indicate that the precipitations of January, May, and July in Newberry are highly likely to have ergodic property, the precipitations of February, and October through December have tendency toward mean ergodicity, and the precipitations of all the other months are non-ergodic.



The authors thank Dr. N. Suciu for the constructive comments and corrections which enable us to greatly improve the quality of this manuscript. This study was supported by the National Key Research and Development Program of China (2018YFC0407900), National Natural Science Foundation of China (Grant No. 51879010, 51479003), and the 111 Project (Grant No. B18006). Argonne National Laboratory’s work was supported under U.S. Department of Energy contract DE-AC02-06CH11357.


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Copyright information

© UChicago Argonne, LLC, Operator of Argonne National Laboratory 2019

Authors and Affiliations

  1. 1.Beijing Key Laboratory of Urban Hydrological Cycle and Sponge City Technology, College of Water ScienceBeijing Normal UniversityBeijingChina
  2. 2.Environmental Science Division, Argonne National LaboratoryLemontUSA
  3. 3.Information Technology DivisionIndustrial Bank CO., LTD.FuzhouChina
  4. 4.School of Mathematical SciencesBeijing Normal UniversityBeijingChina

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