A new formulation for the critical temperature for contrail formation

Abstract

A new formulation of the equations describing the conditions necessary for aircraft exhaust contrail formation is derived from the fundamental necessary condition. First, the original solution of Appleman is derived from the necessary condition to illustrate the continuity of the new formulation. Then the new formulation offers an analytic solution for the critical temperature Tc expressed in terms of water vapor mixing ratio and atmospheric pressure, rather than in terms of relative humidity and pressure, thus avoiding potential forecast errors associated with the temperature sensitivity inherent in relative humidity. A variety of results is presented, including a comparison with the seminal results of Appleman, a comparison of the sensitivity of Tc to perturbations in relative humidity versus perturbations in mixing ratio, and some typical results for actual atmospheric conditions. The clear superiority of a formulation based on mixing ratio rather than relative humidity is seen in the reduced sensitivity of Tc to errors or uncertainties in the input atmospheric variables.