From Glossary of Meteorology
For dry air, κ = 0.2854. For moist air,
where Rd and cpd are the gas constant and specific heat of dry air, ε is the ratio of the gas constants of water vapor and dry air, cpv is the specific heat of water vapor, and rv is the water vapor mixing ratio. The Poisson constant appears in the Poisson equation and in the definition of potential temperature.