Mirages are common occurrences, and are fairly well-understood. When light passes through a density gradient, it is refracted toward the greater density. It's just like a prism, except instead of there being a sharp density gradient at a gas-solid boundary, the gradient is entirely within the gas. In the Earth's atmosphere, if cooler, heavier air is at the bottom, light is refracted toward the Earth, creating what is known as a superior mirage. The same thing happens if there is a layer of hot air at the bottom, refracting light away from the Earth, in an inferior mirage. (See this for an example.)

The conditions most likely to create inferior mirages are:
  • a cloudless sky,
  • no wind,
  • low humidity,
  • relatively cool air temperatures above the ground (< 20 C),
  • perfectly flat terrain, and
  • poorly conducting soil.

As the Sun beats down on the soil, heating it to over 40 C, a layer of hot air (> 30 C) near the surface is created. The hotter air is less dense, and this sets up the gradient capable of refracting light. If the terrain is perfectly flat, light traveling near the surface is subjected to much more refraction, and the effect can accumulate to the point that it produces a noticeable mirage. In other words, light passing over a hill with a hot air layer will be refracted, but not perceptibly. Only if the light picks up a little bit of refraction over an extended distance does the effect become dramatic enough to see.

The curious thing about inferior mirages is that they require hot, low-density air at the bottom at the atmosphere. Normally, hot air rises. If we do a thermodynamic simulation, given a burner measuring 10 km2, and 20 C air above it, we don't get a perfectly stable layer of hot air on top of the burner. Rather, we get a series of Rayleigh-Benard convection cells, roughly 100 meters wide, and 50 meters tall. Air will pick up a couple of C traveling along the burner toward the central updraft in the nearest cell. Then the warmer air will rise to roughly 50 meters above the surface. The void left by the updraft will pull neighboring air downward, which will itself get heated as it travels along the surface. The result is a continuous recirculation of air, moving at roughly 1 m/s. Yet when an inferior mirage is present, Rayleigh-Benard convection cells are not (otherwise the heat would be well-distributed, and there would be no sharp density gradient to refract the light). This appears to be a violation of very simple principles of thermodynamics. Hot air rises, right? An extra 10 C represents a loss of several percent of density. Gravity is constant. The viscosity of air is low, and skin friction at a perfectly flat surface is slight. The air should flow quite freely in response to density differences of this magnitude. Clearly, we're missing something.

Buoyancy is a force. If it is not having its expected effect, then another force is present, which is counteracting the buoyancy. So what other forces are present?

Other than the thermodynamic factors already mentioned, there is only one other set of forces in the atmosphere: electromagnetism. Since the air is only infinitesimally responsive to the magnetic force, we should focus our attention on the possible effects of just the electric force.

Here it's significant to note that poorly conducting soils (such as sand in the desert) are better at creating inferior mirages. What would conductivity have to do with it?

It's possible that the sunlight ionizes the surface of the Earth. The loss of electrons leaves the Earth with a positive charge. A net positive charge would only be possible in poorly conducting soil. (With higher conductivity, lost electrons would be quickly replaced from the Earth's vast electron cloud.) Some of the electrons liberated from the soil will get captured by molecules in the air, producing negative ions. These molecules will then be attracted to the soil by the Coulomb force. Their presence in the boundary layer will make it more difficult for air to rise. In other words, if 1 molecule per million is a negative ion attracted to the ground, then hotter, less dense air heated by contact with the surface will encounter a drag force as it rises, coming from the embedded negative ions. This will result in a higher temperature near the surface than is predicted by thermodynamics alone.

If we explore the implications of another anomaly, we can increase the specificity of the model. Over the desert, the air is generally pretty dry, and this is one of the prerequisites for inferior mirages. Yet the diatomic molecules in dry air (N2 and O2) are really bad at absorbing infrared radiation. This begs the question of what heated the air to 10 C above ambient in the period of time in question. Yet even in the desert there is some water vapor in the air, where the primary source is evaporation from the ground. Water molecules are much better at accepting infrared wavelengths. The molecules then transmit the heat to neighboring molecules in collisions. Thus it's much easier to heat the air if water vapor is present. Interestingly, water molecules also make better negative ions that N2 and O2. Hence it's possible that as the sunlight heats the surface of the Earth, and water begins to evaporate, the sunlight also photo-ionizes the surface, and some of the liberated electrons are captured by water molecules. If so, the water vapor will be attracted to the Earth by the Coulomb force, and thus it will be the source of the drag force that results in an accumulation of hot air near the surface. The water vapor also absorbs infrared radiation from the Earth, and distributes the heat in molecular collisions, becoming the primary cause of hot air.

After poking around over a period of several years, I never succeed in finding any scientific data on the conditions that produce inferior mirages, with accurate numbers for the temperature and humidity gradients. And nobody has done a space charge study, according to the authorities I contacted. Therefore, the status of this model is that it is going to issue some predictions.

This model predicts that an inferior mirage is not possible unless the surface of the Earth has become positively ionized, where the lost electrons have been captured by water molecules. The space charge will then be at least 10-6 C/m3 (3 orders of magnitude greater than the charge density inside a thunderstorm) in the first 10 cm above the ground, and there will be an electric field of 10 kV/m (2 orders of magnitude greater than the fair weather field) between the air and the ground. The charge, temperature, and humidity gradients will be synchronized -- where the one is the greatest, the other two will be at their highest values also. And all of this should be concentrated in the first 10 cm above the ground. Greater than 1 meter above the ground, the charge, temperature, and humidity readings to be the same as 10 meters above the ground.