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Water in its three ambient phases plays the central thermodynamic role in the terrestrial climate system. Clouds control Earth's radiation balance, atmospheric water vapour is the strongest "greenhouse" gas, and non-equilibrium relative humidity at the air-sea interface drives evaporation and latent heat export from the ocean. On climatic time scales, melting ice caps and regional deviations of the hydrological cycle result in changes of seawater salinity, which in turn may modify the global circulation of the oceans and their ability to store heat and to buffer anthropogenically produced carbon dioxide. In this paper, together with three companion articles, we examine the climatologically relevant quantities ocean salinity, seawater pH and atmospheric relative humidity, noting fundamental deficiencies in the definitions of those key observables, and their lack of secure foundation on the International System of Units, the SI. The metrological histories of those three quantities are reviewed, problems with their current definitions and measurement practices are analysed, and options for future improvements are discussed in conjunction with the recent seawater standard TEOS-10. It is concluded that the International Bureau of Weights and Measures, BIPM, in cooperation with the International Association for the Properties of Water and Steam, IAPWS, along with other international organisations and institutions, can make significant contributions by developing and recommending state-of-the-art solutions for these long standing metrological problems in climatology.