Toward practical approaches for ergodicity analysis
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.
- Chen H, Rao A (2002) Testing hydrologic time series for stationarity. J Hydraul Eng 7:129–136Google Scholar
- Ding J, Deng Y (1988) Stochastic hydrology. Press of Chengdu Technology University, Chengdu, ChinaGoogle Scholar
- 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
- 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
- Nørgaard M (1997) Neural network based system identification toolbox Version 1.1. LyngbyGoogle Scholar
- Shahin M, Oorschot HJL, Lange SJ (1993) Statistical analysis in water resources engineering. Aa Balkema, The NetherlandsGoogle Scholar
- Vamos C, Craciun M (2012) Automatic trend estimation, 2013 Editi. Springer NetherlandsGoogle Scholar
- Wang H, Song Y, Liu C, Chen J (2004) Application and issues of chaos theory in hydroscience. Adv Water Sci 15:400–407Google Scholar
- Xia L (2005) Prediction of plum rain intensity based on index weighted Markov chain. J Hydraul Eng 36:988–993Google Scholar
- 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