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This study presents a global classification of storm structures derived from satellite observations, using Self-Organising Maps (SOM) as an unsupervised learning method. The analysis is based on the Global Precipitation Measurement (GPM) mission, which extends the Tropical Rainfall Measuring Mission (TRMM) with broader latitudinal coverage and improved sensitivity to various precipitation types. The Dual-frequency Precipitation Radar (DPR) onboard the GPM Core Observatory provides vertical reflectivity profiles that are well-suited for studying storm dynamics. A custom database of storm features was constructed from the GPM-DPR measurements. The SOM was trained on physically meaningful descriptors to identify recurrent storm morphologies. The resulting clusters revealed distinct gradients of storm structure, ranging from compact, intense convective cores to large, stratiform-dominated systems. They showed strong correspondence with established convective system categories defined by Houze, including Deep Convective Cores (DCC), Wide Convective Cores (WCC), and Broad Stratiform Regions (BSR). Analysis of cluster distribution across seasons and climate zones (via Köppen-Geiger classification) revealed meaningful geographic and climatological patterns. Overall, this work demonstrates the value of combining satellite-based observations and unsupervised learning to characterise the diversity of global precipitation systems and extend existing classification frameworks.