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A flow-following finite-volume icosahedral model (FIM) over the global domain has been developed. The model is based on hybrid isentropic-sigma layers and an icosahedral geodesic grid. Equations are discretized with conservative finite-volume operators. The flow-following isentropic-sigma vertical coordinate is an improved version of the re-gridding and re-mapping scheme which has been successfully used in atmospheric and ocean models such as RUC (Rapid Update Cycle) and HYCOM (HYbrid Coordinate Ocean Model). The icosahedral geodesic grid consisting of hexagonal grid cells with 12 pentagons provides a quasi-uniform coverage of the sphere and allows hierarchical refinement of grid spacing. Tendency terms in the prognostic equations are approximated by the explicit 3rd order Adam-Bashforth time differencing scheme. Monotonicity in the transport scheme is achieved by extending the …