An Efficient and Accurate Method for Computing the Wet-Bulb Temperature along Pseudoadiabats

Abstract

A new technique for computing the wet-bulb potential temperature of a parcel and its temperature after pseudoadiabatic ascent or descent to a new pressure level is presented. It is based on inverting Bolton’s most accurate formula for equivalent potential temperature θE to obtain the adiabatic wet-bulb temperature Tw on a given pseudoadiabat at a given pressure by an iterative technique. It is found that Tw is a linear function of equivalent temperature raised to the −1/κd (i.e., −3.504) power, where κd is the Poisson constant for dry air, in a significant region of a thermodynamic diagram. Consequently, Bolton’s formula is raised to the −1/κd power prior to the solving. A good “initial-guess” formula for Tw is devised. In the pressure range 100 ≤ p ≤ 1050 mb, this guess is within 0.34 K of the converged solution for wet-bulb potential temperatures θw ≤ 40°C. Just one iteration reduces this relative error to less than 0.002 K for −20° ≤ θw ≤ 40°C. The upper bound on the overall error in the computed Tw after one iteration is 0.2 K owing to an inherent uncertainty in Bolton’s formula. With a few changes, the method also works for finding the temperature on water- or ice-saturation reversible adiabats. The new technique is far more accurate and efficient than the Wobus method, which, although little known, is widely used in a software package. It is shown that, although the Wobus function, on which the Wobus method is based, is supposedly only a function of temperature, it has in fact a slight pressure dependence, which results in errors of up to 1.2 K in the temperature of a lifted parcel. This intrinsic inaccuracy makes the Wobus method far inferior to a new algorithm presented herein.