Modification of Vapor-Pressure Reference Functions to Include Parameter Covariance

Abstract

The reference functions for the saturation water vapor pressure and the water vapor-pressure enhancement factor for moist air used by the humidity community are approximate, and the uncertainty contributions from their use are characterized by simple functions or tables. Many humidity calculations, such as for the determination of the dew point of moist air following a change in pressure, require two evaluations each of these functions and errors in the functions will tend to cancel. It has been shown that if the reference function uncertainty is represented using parameter covariance, the expected reduction in error is reflected in a corresponding reduction in the uncertainty of the calculation result. Here, two major vapor-pressure reference functions are modified to encapsulate the published uncertainty as parameter covariance, by refitting the equations or modified forms to “input data” generated by the original equations. It is shown that the form of the uncertainty function is influenced by the degree of correlation in the input data and that there is greater uncertainty reduction with greater input data correlation. In all cases the reduction in uncertainty is significant and indicates that conventional uncertainty analysis for many humidity calculations overestimates the uncertainty deriving from the reference functions.