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This report documents the program and the outcomes of Dagstuhl Seminar 23342 "Computational Geometry of Earth System Analysis". This seminar brought together experts of algorithms and the Earth sciences to foster collaborations that can tackle algorithmic problems in the Earth system by the crossover of expertise in these different areas. The Earth sciences include a manifold of disciplines that deal with atmospheric, oceanic and terrestrial observations to further our understanding of climate processes. New generations of observation systems that are being developed right now provide novel data about the atmospheric and surface conditions at increasing spatial and temporal resolution. This provides unique information to improve weather and climate prediction but cannot always be handled by traditional numerical models. Computational Geometry is rooted in a strong tradition of algorithm and complexity analysis applied to practical geometric problems. Efficient algorithmic methods developed in this field are often tailored to the low-dimensional geometric settings that arise in a multitude of application areas, but have until recently not been applied to problems arising in the Earth system sciences - and in particular not in meteorology.