On Formulas for Equivalent Potential Temperature

Several new formulas for pseudoadiabatic equivalent potential temperature (EPT) are devised and compared to previous ones. The maximum errors of all the formulas are determined from calculations on a dense grid of points in the region of a thermodynamic diagram defined by wet-bulb potential temperature ≤32°C (EPT ≤ 400 K) and pressure between 100 and 1050 mb. One of the new formulas has an accuracy of 0.015 K in the specified region. Finding the imitation first law of thermodynamics that they satisfy approximately reveals how the formulas work.