Teaching Wet-Bulb Temperature With the One-Third Rule: Theory and Applications

Wet-bulb temperature is one of the less fully understood meteorological quantities that students encounter in atmospheric thermodynamics classes.  After the requisite demonstration using a sling psychrometer is performed, then the questions arise: how do you relate the wet-bulb to air temperature, or dewpoint, or both?  The graphical answer of Normand's Rule appeals to visual learners, but there is still a nagging sense among at least some students and some instructors that there should be a straightforward relationship between the wet-bulb temperature and other, more commonly used meteorological variables such as temperature and dewpoint.  However, as one commonly used thermodynamics textbook states, "Unfortunately, there is no simple mathematical formula for dewpoint as a function of the wet-bulb and dry-bulb temperatures."

In this presentation, we demonstrate that there is, in fact, a simple approximate formula--the "One-Third Rule"--that relates the three variables of wet-bulb, dry-bulb, and dewpoint temperatures that is quite accurate for wet-bulb temperatures in the general vicinity of the melting point of water.  This is fortunate, because several important applications of the wet-bulb temperature are made for conditions near zero degrees Celsius, including precipitation type forecasts in synoptic meteorology and protection from frost damage in agriculture.  We first present the empirical roots of the One-Third Rule, then justify it for near-freezing temperatures, illustrate its accuracy using real-world data and examples, and close with suggestions for how to teach this in the atmospheric thermodynamics classroom. 

We propose that this work partly fills a small but frustrating gap in atmospheric thermodynamics pedagogy, and hope that it becomes incorporated in future textbooks on the subject.