Variable-Sized Cluster Analysis for 3D Pattern Characterization of Trends in Precipitation and Change-Point Detection

Abstract

A novel analysis procedure, referred to as variable-sized cluster analysis (VSCA), was developed to identify trends and change points in precipitation time series data set. The procedure involved station-scale rainfall data of 100 years from seven districts (Saharanpur, Bareilly, Agra, Jhansi, Lucknow, Varanasi, and Gorakhpur) of the state of Uttar Pradesh (UP), India. In contrast with the traditional Mann-Kendall (MK) test that yields a monotonic trend for the whole span of time, VSCA enables one to detect multiple change points while characterizing the pattern of precipitation trends over the historical time period. The Pettitt-Mann-Whitney (PMW) test was also modified to graphically represent the multiple change points, which confirmed the results of VSCA. Thus, VSCA demonstrated the unified strength of MK and PMW tests. The three-dimensional (3D) figures drawn for visualizing the changing trend of precipitation utilized 100-year-long time series data set with the minimum size of data cluster as 10, which resulted in the right triangular shape of the graphs due to the repeated application of the MK test to variable-sized data clusters. Application of VSCA showed a decreasing trend of precipitation over Lucknow, Gorakhpur, and Varanasi around 1990 onward, with major changes in the decades of 1970–1980. Saharanpur and Agra contrarily displayed an increasing trend until 1940 and no trend thereafter; however, Bareilly and Jhansi showed reducing trends in precipitation.