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These data include the subset used by IPCC AR6 WGI authors of the datasets originally published in ESGF for 'CMIP6.HighResMIP.INM.INM-CM5-H.hist-1950' with the full Data Reference Syntax following the template 'mip_era.activity_id.institution_id.source_id.experiment_id.member_id.table_id.variable_id.grid_label.version'. The INM-CM5-H climate model, released in 2016, includes the following components: aerosol: INM-AER1, atmos: INM-AM5-H (0.67x0.5; 540 x 360 longitude/latitude; 73 levels; top level sigma = 0.0002), land: INM-LND1, ocean: INM-OM5-H (North Pole shifted to 60N, 90E. 0.167x0.125; 2160x1440 longitude/latitude; 40 levels; vertical sigma coordinate), seaIce: INM-ICE1. The model was run by the Institute for Numerical Mathematics, Russian Academy of Science, Moscow 119991, Russia (INM) in native nominal resolutions: aerosol: 50 km, atmos: 50 km, land: 50 km, ocean: 10 km, seaIce: 10 km.