Using persistent homology as preprocessing of early warning signals for critical transition in flood.

Flood early warning systems (FLEWSs) contribute remarkably to reducing economic and life losses during a flood. The theory of critical slowing down (CSD) has been successfully used as a generic indicator of early warning signals in various fields. A new tool called persistent homology (PH) was recently introduced for data analysis. PH employs a qualitative approach to assess a data set and provide new information on the topological features of the data set. In the present paper, we propose the use of PH as a preprocessing step to achieve a FLEWS through CSD. We test our proposal on water level data of the Kelantan River, which tends to flood nearly every year. The results suggest that the new information obtained by PH exhibits CSD and, therefore, can be used as a signal for a FLEWS. Further analysis of the signal, we manage to establish an early warning signal for ten of the twelve flood events recorded in the river; the two other events are detected on the first day of the flood. Finally, we compare our results with those of a FLEWS constructed directly from water level data and find that FLEWS via PH creates fewer false alarms than the conventional technique.