UC Berkeley

Abstract The algorithms currently in use for calculating the wet-bulb temperature from pressure, relative humidity, and air temperature have errors of a degree or more. Here, the equation for the thermodynamic wet-bulb temperature is derived using the Rankine–Kirchhoff approximations, which are highly accurate for meteorological and climatological applications. Likewise, equations are derived for the thermodynamic ice-bulb temperature and for the psychrometric wet-bulb and ice-bulb temperatures. The equations are fast to solve, requiring only a microsecond on a current laptop computer, and the results match empirical data to within hundredths of a degree. Furthermore, the equations reveal the existence of air temperatures and humidities that generate bistability: Evaporating liquid water is stable at a liquid temperature above freezing and, simultaneously, sublimating ice is stable at an ice temperature below freezing.