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.

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Relative humidity (RH) is a quantity widely used in various fields such as metrology, meteorology, climatology or engineering. However, RH is neither uniformly defined, nor do some definitions properly account for deviations from ideal-gas properties, nor is the application range of interest fully covered. In this paper, a new full-range definition of RH is proposed that is based on the thermodynamics of activities in order to include deviations from ideal-gas behaviour. Below the critical point of pure water, at pressures p < 22.064 MPa and temperatures T < 647.096 K, RH is rigorously defined as the relative activity (or relative fugacity) of water in humid air. For this purpose, reference states of the relative activity are specified appropriately. Asymptotically, the ideal-gas limit of the new definition is consistent with de-facto standard RH definitions published previously and recommended internationally. Virial approximations are reported for estimating small corrections to the ideal-gas equations.

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. In this paper, we examine the climatologically relevant atmospheric relative humidity, noting fundamental deficiencies in the definition of this key observable. The metrological history of this quantity is reviewed, problems with its current definition and measurement practice 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 this long standing metrological problem, such as are suggested here.

A wide variety of empirical equations are used in measurement science in which the equation parameters are determined through some form of interpolation or least squares fit. When the equation is a good model of the system and the fitting process is accompanied by a full uncertainty analysis, the equation parameters summarize all the input data and associated uncertainty. Often, however, only the uncertainty in the equation result is reported and that information may be insufficient to carry out a full uncertainty analysis when the equation is used. In particular, the lack of information about correlation is an issue for many humidity calculations which require the empirical enhancement factor and vapour pressure formulations to be evaluated twice, once directly (i.e. in the forward direction) and once in the inverse direction. For these calculations it is clear that uncertainties in the two evaluations are correlated and that for sufficiently close values, error associated with use of the formulations should cancel. However, apart from the special case where the evaluations in each direction are at the same vapour pressure, the error and hence the autocorrelation is unknown. When the full equation parameter covariance is known, the ‘parameter covariance’ method (PCM) presented here does give the reduction in uncertainty expected for autocorrelation within the formulation.