Stable stratification

Introduction

When the surface is colder than the overlying air — a situation that is common at night, or when warm air is advected over cold water — a thermal inversion is produced. Weak inversions seem to be treatable by Monin-Obukhov similarity theory. But the strong inversions responsible for good superior-mirage and Fata Morgana displays are not well understood. I hope that the study of these mirages will help clarify this problem.

In the meantime, there are some informative videos available on the Web that display the characteristics of these very stable layers. Simon Christen's time-lapse movies of the evolution of capping inversions are beautiful, and very informative:

Christen's time-lapse movie The Unseen Sea

There is a nice display of crepuscular rays between 0:15 and 0:20 in this video. From 1:06 to 1:17, the clouds in the capping inversion partly evaporate as the inversion passes over a depression in the landscape a little to the right of center — and then re-condense as the air climbs back out of this hole, nearly in the middle of the images.

(Also, notice the progressive flattening of the Moon by differential refraction from 2:30 to 2:43 as it approaches the horizon.)

Similar effects of evaporation of the capping cloud as the air flows downhill are shown in the next video, especially from 1:20 to 1:26 :

Christen's time-lapse movie Adrift

Another set of time-lapse movies of extremely stable layers, seen at close range, is available at submeso.org. These, too, are extremely informative. They show the “sheet and layer” structure that is now known to be ubiquitous in the atmosphere.

Radiative heating and cooling

Why is it warm in the daytime and cooler at night? If the sky is clear, it's obvious that sunshine warms things up by day. But it's not so obvious what gets warmed up — the ground or the air?

Diurnal heating

In fact, air absorbs very little energy from sunshine. It's mostly the surface of the Earth that is warmed by sunlight; then the surface heats the adjacent air. Air expands as it warms; about an hour after sunrise, the surface air is less dense than air a little above it. The warm surface air is displaced by denser air from above, rising and mixing with the cooler overlying layers. A convective pattern of rising warm air and descending cooler air develops.

The temperature gradient is steepest near the ground, because the presence of a solid surface inhibits convection. This makes inferior mirages visible over smooth surfaces. Even when the sky is overcast, enough sunlight reaches the ground to produce a shallow convective layer. Weak inferior mirages have even been detected when rain was falling.

The convection is strongest in the middle of the day, when the sun is highest in the sky, sending about a kilowatt per square meter to the surface at temperate latitudes. By the end of the afternoon, the thickness of the convectively heated region is usually a few hundred meters.

Losses

An hour or so before sunset, solar heating is too weak to overcome heat losses. Some sensible heat is conducted into the ground, and latent heat is lost by evaporation of water from damp surfaces and plants.

Heat is also radiated to the cold space beyond the atmosphere. This radiation is mostly at middle infrared wavelengths, between the strong carbon dioxide bands near 15 microns wavelength and the 6-micron band of water vapor. Most of the radiated heat is from the ground, because the overlying air is generally cooler than the ground. Convection ceases, and the surface (and the adjacent air) begins to cool.

Nocturnal cooling

After sunset, the ground surface cools rapidly by radiation to cold space. The cold surface cools the adjacent air, and the daytime pattern of cooler air above a warm surface is reversed. However, this “inverted lapse rate” is dynamically stable, unlike the unstable (convective) daytime air. Stable layers decouple the air from the surface, and the complex pattern of “sheets and layers” develops. This nocturnal inversion picture is normal whenever the sky is clear enough to see the stars.

These nocturnal inversions were discovered in the 19th Century. Brandes mentioned them in 1806; but they were more widely puiblicized by Glaisher's popular book “Travels in the Air” (1871), where he wrote: “The differences have been immense; even with a clear sky, the most favourable for establishing a mean, the figures vary very greatly---that is to say, within 100 feet near to the earth we now know there may be a decline of temperature of several degrees during the mid-hours of the day, and that during the mid-hours of the night there may be, and generally is, an increase of several degrees.”

Lapse rates

Obviously, the lapse rates in the few hundred meters of air that swing back and forth between diurnal solar heating and nocturnal radiative cooling undergo large variations every day. These variations are not taken into account in the various "Standard Atmosphere" models. What can we reasonably expect?

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