Rainfall dynamics in an ecologically vulnerable area using applied algebraic topology methods

Applied algebraic topology is employed in this work to shed new light on the rainfall dynamics in the Pernambuco state, Brazil. Historical data from the NASA’s Tropical Rainfall Measuring Mission (TRMM) precipitation processing system, for the period 1998 to 2020 with a spatial resolution of 0.25° and temporal resolution of 3 h is used to construct correlation matrices in different time frames. Matrices are then analyzed in terms of topological constructs of network theory to yield novel insights into this highly complex phenomenon in this semiarid, ecologically vulnerable area. The outcomes of the algebraic topological analysis reveal clustering patterns of areas and are related to natural climate phenomena. Together with the generality of the applied methodology, the results suggest a broad scope of future applications for the extraction of patterns in datasets related to the changes in the climate system.