Encroachment method

From Glossary of Meteorology

encroachment method

A technique used in boundary layer meteorology to denote a type of mixed layer growth rate that is proportional to the rate of warming of the mixed layer divided by the ambient lapse rate immediately above the top of the mixed layer.

In other words, heating from the surface causes the depth of the mixed layer to increase. Also known as the thermodynamic method, the mixed-layer top can be found by finding the area under the early morning sounding (between the sounding and an adiabat for warmer air) that is equal to the area under a plot of the surface heat flux versus time up to the time of interest.
Compare energetics method.