Moving correlation coefficient-based method for the identification of periodicities in hydrologic time series

Abstract

Accurate identification of periodicities is an important issue for understanding the hydrological variability, medium- to long-term hydrologic simulation and forecasting, as well as water security assessment. Many methods have been developed presently for handling the issue, including the simple partial wave method (SPWM), harmonic analysis method (HAM), power spectrum method (PSM) and maximum entropy spectral analysis (MESA). However, the results of periodic identification are not good as expected due to the complexity of hydrological variability and defects of methods. In this article, a new moving correlation coefficient-based method is proposed for the identification of periodicities in hydrological time series. The specific steps of periodicity identification by the proposed methods is described as follows: (1) Generate a simulated periodic series by using the sinusoidal function; (2) use the correlation coefficient as an index to evaluate the fitting accuracy between the simulated periodic series and the original series, which generally includes the periodic components and stochastic components; (3) change the periodic value and the initial phase of the sinusoidal function, and repeat the above steps to calculate the correlation coefficient values; and (4) find the maximum magnitude of the correlation coefficient, and its corresponding simulated periodic series is regarded as the expected periodic component, and its significance is evaluated by doing hypothesis test. Theoretical analysis and formula derivation demonstrate that the index of correlation coefficient can reflect the significant degree of periodic variability of the original hydrological time series. Bigger correlation coefficient value corresponds to more significant periodic variability. Results of Monte-Carlo experiments confirm the advantages of the proposed method compared with other conventional methods such as HAM, PSM and MESA. The former has high identification efficiency and can keep its stability, even if encountering the influences of some advance factors, including the sample length, mean value, coefficient of variation, the semi amplitude, period length and initial phase. By applying the proposed method to analyze the annual precipitation series at 21 meteorological stations in the Lancang River Basin, results indicate that the annual precipitation presents periodic variations at multi-time scales; comparatively, annual precipitation series in the northern and central parts of the basin mainly presents a 2- to 5-year periodic variability, versus the 5- to 10-year periodic variability in the south part.