Topological Features with Persistent Homology for Improved Detection, Classification, and Early Warning of Precipitation Extremes and Temperature Anomalies in Ghana

Ghana faces escalating climate extremes: severe floods, prolonged droughts, and intensifying heatwaves that demand improved detection, classification, and early warning capabilities beyond those offered by conventional statistical approaches. This study applies Topological Data Analysis (TDA), and specifically persistent homology, to 65 years (1950–2014) of monthly precipitation and temperature records for Ghana, demonstrating for the first time the utility of topological features in characterizing climate extremes in a West African context. Time-delay embeddings of climate time series are constructed using Takens' theorem and subjected to Vietoris–Rips filtrations, yielding persistence diagrams and Total Persistence summary statistics that quantify the multi-scale geometric complexity of the climate attractor. Sliding-window analysis reveals that topological complexity co-varies systematically with the occurrence of extreme events: Welch t-tests confirm significant differences in Total Persistence between normal and extreme-wet months (p < 0.05), while persistence under extreme-dry conditions is significantly lower than normal (p < 0.05). A 6-month rolling-window classification framework comparing logistic regression with classical statistical features against TDA-augmented models yields cross-validated AUC scores of 0.870–0.923. The near-equivalent performance of classical and TDA-augmented classifiers at this spatial and temporal resolution is interpreted in light of the theoretical relationship between H0 persistence and classical dispersion statistics, and the pathway to larger TDA gains via H1 homology on gridded spatial data is clearly delineated. Power spectral analysis, extreme value, and Mann–Kendall analyses characterise the broader statistical structure of Ghana's climate over the instrumental record.