From the temperature point at the ground, we go up dry adiabatically (the
atmosphere in the mixed layer is usually neutral) until we hit the inversion
layer aloft. Parcels of air starting at the ground at higher temperatures do
not hit the environmental temperature profile and lose their positive buoyancy
until they reach a higher altitude. Thus, summer mixing
heights tend to be larger than winter mixing heights, and afternoon mixing
heights are larger than morning mixing heights.
The significance of the mixing height variation is that from box model concepts, the pollution concentration is higher when the mixing height is smaller, because the mixing height is proportional to the volume of air in which pollution can disperse.
This can also be applied to temperature variations during the course of a day. The morning ground temperatures are less than the afternoon temperatures, so the morning mixing height tends to be smaller than the afternoon mixing height. On a day-to-day basis, there is a general relationship that as the ground temperature increases, the mixing height increases.
Unfortunately, the real-world case in the Los Angeles area is more complicated
than this. It turns out that often, our warm days occur when subsidence is strong
(regional or large-scale) because that is what suppresses cloud formation and
allows the sun to heat the ground, plus the sea breeze (which keeps the region
cool) is somewhat suppressed by the strong subsidence. Thus, hot days around
L.A. may actually be associated with relatively low mixing heights and poor
air quality.