# 11.6: The Story of Diurnal Boundary Layer Growth Told in Vertical Profiles of Virtual Potential Temperature

Recall the concept of virtual potential temperature, which was introduced in Lesson 2. The virtual potential temperature is found by replacing the temperature in the formula for virtual temperature with the potential temperature:

$T_{v}=T(1+0.61 q)$

$\theta=T\left(\frac{p_{o}}{p}\right)^{0.286}$

$\theta_{v}=\theta(1+0.61 q),$ for unsaturated air

θv is the virtual potential temperature. It is a useful quantity because it takes the moisture into account as well as temperature when considering buoyancy and stability. Thus, adiabatic ascent or descent in moist air follows the constant virtual potential temperature line all the way up to the lifting condensation level (LCL), where the potential temperature increases. So let’s look at the evolution of the profile of virtual potential temperature in a cloud-free boundary layer.

Start with the late afternoon (S1 above). Surface heating causes the air near the surface to have a higher virtual potential temperature than the air just above it, so that the air is superadiabatic. Thus, air parcels of this warm moist air rise all the way up to the point in the free atmosphere where the virtual potential temperature is as great or greater than the air parcel’s value. At this point the air parcel likely mixes with the surrounding air and therefore contributes to raising the mixed layer’s temperature. As convection of air parcels continues, the slightly cooler air from the upper boundary layer sinks around the rising air parcels and continues the mixing process as the air parcels going up encounter air coming back down. The result is a well-mixed boundary layer.

Just after sunset (S2 above), the surface cools by infrared radiation and the air near the surface becomes stable with a virtual potential temperature (and thus temperature) inversion that prevents air from the surface to rise. As a result, the nocturnal boundary layer becomes quite stable, and as the surface continues to cool, the boundary layer becomes even more stable during the night (S3 above). Note also that the stable boundary layer grows, not by convective mixing, but by shear mixing.

Just after sunrise (S4 above), the surface is warmed by the sun, and as it continues to get warmed throughout the morning (S5 above), convection begins to mix warm air up first throughout the stable boundary layer and then into the mixed layer. Any trace atmospheric constituents left in the residual layer from the day before are now mixed back into the boundary layer as it grows higher. Finally, the residual layer is entirely mixed into the growing boundary layer (S6 above), and the boundary layer returns to its condition of the previous afternoon (S1 above).

Think about morning and evening rush hours. During morning rush hour, which is near sunrise, the vehicle emissions mix into a shallow boundary layer and hence the mixing ratios of the pollutants can be quite substantial. This situation leads to the photochemistry that makes pollution, including ozone. In the evening, the rush hour traffic also emits the same amounts of pollutants into the boundary layer, but because the boundary layer height is so much greater in the early evening than in the morning, the pollutant mixing ratios are less because the same level of emissions are being mixed into a larger volume of air. Thus the effects of evening emissions are not as severe as the effects of morning emissions. In addition, modeling the planetary boundary layer height correctly is essential for accurate air quality modeling.

The diurnal variation of the planetary boundary layer height is more than just a curiosity - it has influence on our daily lives and health because we live, work, and breathe mostly in the atmospheric planetary boundary layer. Thus it is important that meteorologists and atmospheric scientists gain a better understanding of the atmospheric motions and energy budget of the planetary boundary layer. Gaining this understanding means learning something about atmospheric turbulence, which is the small-scale chaotic winds that are a significant factor in the planetary boundary layer.