Defining relative humidity in terms of water activity: III. Relations to dew-point and frost-point temperatures. (1st August 2022) - Feistel, Rainer; Hellmuth, Olaf; Lovell-Smith, Jeremy
Abstract: Relative humidity (RH) is a fundamental quantity used in many fields of engineering and science, and in particular in meteorology and climate research. Relative fugacity (RF) and, equivalently, relative activity of water vapour in humid air have recently been proposed as a physically well-founded, unambiguous common metrological reference quantity for several conventional but mutually inconsistent definitions of RH. The RF definition is valid is valid under real-gas conditions and above boiling and sublimation temperatures. While differences between RH and RF mostly remain within uncertainties of typical present-day RH measurements, such systematic discrepancies are expected to be of substantial climatological relevance. Consequently, interdisciplinary harmonisation of RH definitions is overdue within the SI framework. Dew-point and frost-point temperatures are preferred measurands in humidity metrology using, for example, chilled-mirror hygrometers. Here, relations are presented for estimating RF from those temperatures, based on equations of state of the 2011 IUGG 6 standard TEOS-10, the 'international thermodynamic equation of seawater—2010'. Recommendations are given for numerically computing RF using the open-source TEOS-10 SIA library 6 . The asymptotic limiting laws of RF for nearly saturated humid air exhibit the familiar form of Clausius–Clapeyron-like equations, despite departing from ideal-gas assumptions. Under various practical conditions, these simple equations may cover the full humidity range with only minor residuals compared to the full numerical TEOS-10 solution for RF.