Exact Expression for the Lifting Condensation Level

Abstract

AbstractMany analytic, but approximate, expressions have been proposed for the height of the lifting condensation level (LCL), including the popular expressions by Espy, Bolton, and Lawrence. Here, the exact, explicit, analytic expression is derived for an air parcel?s LCL as a function of its temperature and relative humidity. Unlike previous analytic expressions, some of which can have errors as high as hundreds or thousands of meters, this exact expression is accurate to within the uncertainty of empirical vapor pressure measurements: this translates into an uncertainty of around 5 m for all temperatures and relative humidities. An exact, explicit, analytic expression for the lifting deposition level (LDL) is also derived, and its behavior is compared to the LCL. At sufficiently cold temperatures, aerosols freeze homogeneously below the LCL; an approximate, implicit, analytic expression is given for this lifting freezing level (LFL). By comparing the LCL, LDL, and LFL, it is found that a well-mixed boundary layer can have an ice-supersaturated layer that is no thicker than 400 m.