The complex nonlinear and non-stationary features exhibited in hydrologic sequences make hydrological analysis and forecasting difficult. Currently, some hydrologists employ the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method, a new time-frequency analysis method based on the empirical mode decomposition (EMD) algorithm, to decompose non-stationary raw data in order to obtain relatively stationary components for further study. However, the endpoint effect in CEEMDAN is often neglected, which can lead to decomposition errors that reduce the accuracy of the research results. In this study, we processed an original runoff sequence using the radial basis function neural network (RBFNN) technique to obtain the extension sequence before utilizing CEEMDAN decomposition. Then, we compared the decomposition results of the original sequence, RBFNN extension sequence, and standard sequence to investigate the influence of the endpoint effect and RBFNN extension on the CEEMDAN method. The results indicated that the RBFNN extension technique effectively reduced the error of medium and low frequency components caused by the endpoint effect. At both ends of the components, the extension sequence more accurately reflected the true fluctuation characteristics and variation trends. These advances are of great significance to the subsequent study of hydrology. Therefore, the CEEMDAN method, combined with an appropriate extension of the original runoff series, can more precisely determine multi-time scale characteristics, and provide a credible basis for the analysis of hydrologic time series and hydrological forecasting. KEYWORDSComplete ensemble empirical mode decomposition with adaptive noise; data extension; radial basis function neural network; multi-time scales; runoff

This study investigated the influence of data extension on the decomposition and prediction accuracy of runoff data series. To this end, an original data series was constructed using annual runoff data from a hydrological station in China (Tang Naihai) for the period 1956–2013, and radial basis function neural network (RBFNN) extension was applied to the original data series. Complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) was then applied to both data series, and their decomposition and prediction results were compared. The decomposition results indicate that the end effect significantly lowers the accuracy of low–middle frequency components. Nevertheless, the end effect could be effectively suppressed and decomposition error could be reduced by applying RBFNN extension. At the end points, the extension data series could more accurately reflect the real fluctuation characteristics of components and subsequent variation trends. Regarding component prediction, the prediction results followed the variation trend of the components themselves, with a rather large gap in the prediction results of low-frequency components between the two groups of data series. The final prediction results obtained from the reconstruction of the component prediction results suggest that the extension sequence has a clearly superior prediction accuracy than the original data series. Hence, when using the CEEMDAN method to process non-stationary hydrological data, multi-time-scale information of the data series can be obtained through reasonable extension after decomposition of the original data series. The acquired information provides evidence for the analysis and prediction of the evolution law of hydrological elements.