Toward a practical approach for ergodicity analysis

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.