The Characterization of Rainfall Data Set Using Persistence Diagram and Its Relation to Extreme Events: Case Study of Three Locations in Kemaman, Terengganu

Floods are recurring phenomena at certain locations because of excessive rainfall, resulting in the overflow of lakes, drains, and rivers. In this work, we employ Persistence Homology (PH) to investigate the relationship between rainfall and flood that occurred from 1997 to 2018. Three stations in Kemaman, Terengganu, have been chosen to study this relationship. Persistence Diagram (PD) is one of the most powerful tools available under the umbrella of PH for detecting topological signatures in high dimension points cloud. In this paper, we use the rainfall time series dataset and express it in higher dimensions by selecting the embedded dimension, \(M = 5\), , and manipulating the time delay τ to obtain the maximum persistence. Then, we compared with past flood events which are labelled based on water level and PD’s max score to identify its suitability for flood identification. The area under the curve of receiver operation characteristics (ROC) have been used to measure the performance with three different thresholds for station 4131001, 4232002, and 4332001. The results clearly show PD’s significance to characterize the rainfall dataset as normal and flood events. The employed maximum persistence is robust despite missing data values.