Advertisement

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

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. 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.

Notes

Acknowledgements

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.

References

  1. Alp M, Cigizoglu H (2007) Suspended sediment load simulation by two artificial neural network methods using hydrometeorological data. Environ Model Softw 22:2–13.  https://doi.org/10.1016/j.envsoft.2005.09.009 CrossRefGoogle Scholar
  2. Chen H, Rao A (2002) Testing hydrologic time series for stationarity. J Hydraul Eng 7:129–136Google Scholar
  3. Chick S, Shortle J, Van Gelder P, Mendel MB (1996) A model for the frequency of extreme river levels based on river dynamics. Struct Saf 18:261–276.  https://doi.org/10.1016/S0167-4730(96)00020-3 CrossRefGoogle Scholar
  4. Davis A, Marshak A, Wiscombe W, Cahalan R (1994) Multifractal characterizations of nonstationarity and intermittency in geophysical fields: observed, retrieved, or simulated. J Geophys Res Atmos 99:8055–8072CrossRefGoogle Scholar
  5. Ding J, Deng Y (1988) Stochastic hydrology. Press of Chengdu Technology University, Chengdu, ChinaGoogle Scholar
  6. Domowitz I, El-Gamal MA (2001) A consistent nonparametric test of ergodicity for time series with applications. J Econ 102:365–398.  https://doi.org/10.1016/S0304-4076(01)00058-6 CrossRefGoogle Scholar
  7. Duan J, Goldys B (2001) Ergodicity of stochastically forced large scale geophysical flows. Int J Math Math Sci 28:313–320.  https://doi.org/10.1155/S0161171201012443 CrossRefGoogle Scholar
  8. Fiori A, Janković I (2005) Can we determine the transverse macrodispersivity by using the method of moments? Adv Water Resour 28:589–599.  https://doi.org/10.1016/j.advwatres.2004.09.009 CrossRefGoogle Scholar
  9. Hsu KC (2003) The influence of the log-conductivity autocovariance structure on macrodispersion coefficients. J Contam Hydrol 65:65–77.  https://doi.org/10.1016/S0169-7722(02)00231-0 CrossRefGoogle Scholar
  10. Jiang G-P, Zheng WX (2005) A simple method of chaos control for a class of chaotic discrete-time systems. Chaos, Solitons Fractals 23:843–849.  https://doi.org/10.1016/j.chaos.2004.05.025 CrossRefGoogle Scholar
  11. Koutsoyiannis D (2005) Stochastic simulation of hydrosystems. In: Lehr JH, Keeley J (eds) Stochastic simulation of hydrosystems: surface water hydrology. Wiley, New York, pp 421–430Google Scholar
  12. Liu C (1998) Some problems of water interaction. In: Liu C, Ren H (eds) The experiment of water interaction and compute analysis. Science Press, Beijing, p 341Google Scholar
  13. Mitosek HT (2000) On stochastic properties of daily river flow processes. J Hydrol 228:188–205.  https://doi.org/10.1016/S0022-1694(00)00150-5 CrossRefGoogle Scholar
  14. Morvai G, Weiss B (2005) Forward estimation for ergodic time series. Ann l’Institut Henri Poincare Probab Stat 41:859–870.  https://doi.org/10.1016/j.anihpb.2004.07.002 CrossRefGoogle Scholar
  15. Nørgaard M (1997) Neural network based system identification toolbox Version 1.1. LyngbyGoogle Scholar
  16. Oliveira TF, Cunha FR, Bobenrieth RFM (2006) A stochastic analysis of a nonlinear flow response. Probabilistic Eng Mech 21:377–383.  https://doi.org/10.1016/j.probengmech.2005.11.010 CrossRefGoogle Scholar
  17. Shahin M, Oorschot HJL, Lange SJ (1993) Statistical analysis in water resources engineering. Aa Balkema, The NetherlandsGoogle Scholar
  18. Suciu N (2014) Diffusion in random velocity fields with applications to contaminant transport in groundwater. Adv Water Resour 69:114–133.  https://doi.org/10.1016/j.advwatres.2014.04.002 CrossRefGoogle Scholar
  19. Vamos C, Craciun M (2012) Automatic trend estimation, 2013 Editi. Springer NetherlandsGoogle Scholar
  20. Veneziano D, Tabaei A (2004) Nonlinear spectral analysis of flow through porous media with isotropic lognormal hydraulic conductivity. J Hydrol 294:4–17.  https://doi.org/10.1016/j.jhydrol.2003.10.025 CrossRefGoogle Scholar
  21. Wang H, Feng Q, Lin X, Zeng W (2009) Development and application of ergodicity model with FRCM and FLAR for hydrological process. Sci China, Ser E Technol Sci 52:379–386.  https://doi.org/10.1007/s11431-008-0191-9 CrossRefGoogle Scholar
  22. Wang H, Song Y, Liu C, Chen J (2004) Application and issues of chaos theory in hydroscience. Adv Water Sci 15:400–407Google Scholar
  23. Xia L (2005) Prediction of plum rain intensity based on index weighted Markov chain. J Hydraul Eng 36:988–993Google Scholar
  24. Yaglom AM (1987) Correlation theory of stationary and related random functions. Volume I: basic results. Springer-Verlag, New YorkCrossRefGoogle Scholar
  25. Zhou PL, Tao XL, Fu ZQ et al (2001) Precipitation prediction based on improved radial basis function neural networks. J Chinese Comput Syst 22:244–246Google Scholar

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

Personalised recommendations