##
**Exact Expression for the Lifting Condensation Level**

Romps, D., Lawrence Berkeley National Laboratory

Cloud Distributions/Characterizations

Warm Boundary Layer Processes

Romps D. 2017. "Exact expression for the lifting condensation level." *Journal of the Atmospheric Sciences*, 74(12), doi:10.1175/JAS-D-17-0102.1.

##### For surface air with a relative humidity of 50 percent, the heights of the lifting condensation level (LCL; where saturation with respect to liquid water occurs), the lifting deposition level (LDL; where saturation with respect to solid ice occurs), and the lifting freezing level (LFL; where aerosols freeze homogeneously).

## Science

Cloud base height is an important quantity for aviation and weather forecasting. For nearly 200 years, a number of approximate formulae have been used for the base height, but none of them have been exact.## Impact

The exact expression is derived in this work for the cloud base or, more accurately, for what is called the lifting condensation level. This expression can also be generalized to very cold conditions to give the height if ice-cloud bases.## Summary

The lifting condensation level (LCL) is the height at which a lifted parcel of air reaches saturation and forms a cloud. For nearly 200 years, many different expressions have been proposed for this height. Some of those expressions are analytic and some are complicated nonlinear equations that must be solved using iterative numerical methods. None of them, however, are exact or dependent in an obvious way on the fundamental parameters of the atmosphere.

Here, the exact, explicit, and analytic expression for the LCL is derived. This expression depends only on fundamental physical parameters of the atmosphere. This expression can be generalized to give the lifting deposition level (LDL; where the air parcel saturates with respect to ice). It can also be generalized to atmospheres on other planets with a condensable gas.

Here is a link to the cade that calculates the LCL: http://www.romps.berkeley.edu/pubs/pubs-2016-lcl.html#pubs-2016-lcl-code