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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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doi:10.5194/npgd-2-1425-2015
© Author(s) 2015. This work is distributed
under the Creative Commons Attribution 3.0 License.
Research article
21 Sep 2015
Review status
This discussion paper has been under review for the journal Nonlinear Processes in Geophysics (NPG). The revised manuscript was not accepted.
Toward a practical approach for ergodicity analysis
H. Wang1, C. Wang1,a, Y. Zhao1, X. Lin2, and C. Yu1 1College of Water Sciences, Beijing Normal University – Key Laboratory for Water and Sediment Sciences, Ministry of Education, Beijing, 100875, China
2School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China
acurrently at: Environmental Science Division, Argonne National Laboratory, Lemont, IL 60439, USA
Abstract. 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. This paper presents a practical approach to analyze the mean ergodic property of hydrological processes by means of autocorrelation function evaluation and Augmented Dickey Fuller test, a radial basis function neural network, and the definition of mean ergodicity. The mean ergodicity of precipitation processes at the Lanzhou Rain Gauge Station in the Yellow River basin, the Ankang Rain Gauge Station in Han River, both in China, and at Newberry, MI, USA are analyzed using the proposed approach. The results indicate that the precipitations of March, July, and August in Lanzhou, and of May, June, and August in Ankang have mean ergodicity, whereas, the precipitation of any other calendar month in these two rain gauge stations do not have mean ergodicity. The precipitation of February, May, July, and December in Newberry show ergodic property, although the precipitation of each month shows a clear increasing or decreasing trend.

Citation: Wang, H., Wang, C., Zhao, Y., Lin, X., and Yu, C.: Toward a practical approach for ergodicity analysis, Nonlin. Processes Geophys. Discuss., 2, 1425-1446, doi:10.5194/npgd-2-1425-2015, 2015.
H. Wang et al.
H. Wang et al.

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Short summary
Ergodic properties are commonly assumed in practice which allow researchers to determine the statistical properties of a process from a single realization. With an attempt to justify the erodicity assumption, this paper presents a practical approach to analyze the mean ergodic property of montly preciptation by means of autocorrelation function evaluation and Augmented Dickey Fuller test, a radial basis function neural network, and the definition of mean ergodicity.
Ergodic properties are commonly assumed in practice which allow researchers to determine the...
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