Detecting the Indian Monsoon using Topological Data Analysis

A monsoon is a wind system that seasonally reverses its direction, accompanied by corresponding changes in precipitation. The Indian monsoon is the most prominent monsoon system, primarily affecting India's rainy season and its surrounding lands and water bodies. Every year, the onset and withdrawal of this monsoon happens sometime in May-June and September-October, respectively. Since monsoons are very complex systems governed by various weather factors with random noise, the yearly variability in the dates is significant. Despite the best efforts by the India Meteorological Department (IMD) and the South Asia Climate Outlook Forum (SCOF), forecasting the exact dates of onset and withdrawal, even within a week, is still an elusive problem in climate science. We interpret the onset and withdrawal of the Indian monsoon as abrupt regime shifts into and out of chaos. During these transitions, topological signatures (e.g., persistence diagrams) show rapid fluctuations, indicative of chaotic behavior. To detect these shifts, we reconstruct the phase space using Takens' embedding of the Indian monsoon index and apply topological data analysis (TDA) to track the birth and death of $k$-dimensional features. Applying this approach to historical monsoon index data (1948-2015) suggests a promising framework for more accurate detection of monsoon onset and withdrawal.