Two Simple and Accurate Approximations for Wet-Bulb Temperature in Moist Conditions, with Forecasting Applications

Abstract

Abstract The wet-bulb temperature is a widely used moist thermodynamic variable. The relationship between the wet-bulb temperature, the dry-bulb temperature, and the dewpoint temperature is nonlinear. Most atmospheric thermodynamics textbooks indicate or imply that no simple and accurate approximation relating these three meteorological variables exists. This article provides theoretical justifications for, and real-life applications of, two different simple linear approximations for the wet-bulb temperature. These two approximations are 1) an arithmetic mean of dry-bulb and dewpoint temperatures and 2) a weighted mean of dry-bulb and dewpoint temperatures known as the “one-third rule.” These approximations are highly accurate in two contiguous temperature and moisture regimes: the arithmetic-mean rule outperforms other approximations for relatively moist (average relative humidity = 61%) situations with dry-bulb temperatures bracketing 13°C, and the one-third rule outperforms other approximations for relatively moist (average relative humidity = 50%) situations with dry-bulb temperatures bracketing 4°C. The one-third rule is especially useful because its domain of maximum accuracy includes the phase change for water from solid to liquid and vice versa. Examples of the application of the one-third rule to precipitation-type forecasting and to agricultural practices to prevent frost damage are presented.