Study on a mother wavelet optimization framework based on change-point detection of hydrological time series

Hydrological time series (HTS) are the key basis of waterconservancy project planning and construction. However, under the influenceof climate change, human activities and other factors, the consistency ofHTS has been destroyed and cannot meet the requirements of mathematicalstatistics. Series division and wavelet transform are effective methods toreuse and analyse HTS. However, they are limited by the change-pointdetection and mother wavelet (MWT) selection and are difficult to apply andpromote in practice. To address these issues, we constructed a potentialchange-point set based on a cumulative anomaly method, the Mann-Kendall test andwavelet change-point detection. Then, the degree of change before and afterthe potential change point was calculated with the Kolmogorov-Smirnov test,and the change-point detection criteria were proposed. Finally, theoptimization framework was proposed according to the detection accuracy ofMWT, and continuous wavelet transform was used to analyse HTS evolution. Weused Pingshan station and Yichang station on the Yangtze River as studycases. The results show that (1) change-point detection criteria can quicklylocate potential change points, determine the change trajectory and completethe division of HTS and that (2) MWT optimal framework can select the MWT thatconforms to HTS characteristics and ensure the accuracy and uniqueness ofthe transformation. This study analyses the HTS evolution and provides abetter basis for hydrological and hydraulic calculation, which will improvedesign flood estimation and operation scheme preparation.