aty.sdsu.edu - The Omega Sunset (and Sunrise)

home - domains - aty.sdsu.edu

sunset horizon Daruma sun inferior mirage Omega sun cause explanation refraction mirage

Goto Site

https://aty.sdsu.edu/explain/simulations/inf-mir/Omega.html

Site Description

Omega sunset: photographs and explanation

Example Site Content

The Omega Sunset (and Sunrise) The Omega Sunset (and Sunrise) Introduction As there seems to be considerable interest in the Ω shape produced by inferior mirages over water, I thought it would be useful to provide more information about this phenomenon. (I already have a page devoted to George Kaplan's photos of it, which compares theoretical models with the observed shapes; see also Laurent Laveder's time-series showing the development of the Omega, and Bob Harrison's photos of an Omega sunrise.) The picture at the right shows the relation between the Omega and the inferior-mirage green flash: the flash occurs at the fold line, where the “feet” join the body of the Omega. Explanation The explanation of the shape is very simple: the “feet” of the Ω are just inverted images of the parts of the Sun directly above them — remember that refraction only moves images vertically, not horizontally. The inverted part of the image, below the fold line, is an inferior mirage. However, this inferior mirage over warm water is often very inconspicuous. Why is it occasionally so spectacular? The answer begins with the temperature profile that produces inferior mirages. The temperature profile above a heated surface has been studied by the boundary-layer meteorologists. When you calculate refraction for that profile, you certainly get something close to what's observed. And the simulations of these inferior mirages show what kinds of alterations you get by changing the parameters of the profile. Here's the lowest 30 meters of the temperature profile I've used to make most of the inferior-mirage simulations. At the upper left, it becomes a straight line, with the adiabatic lapse rate. More important is the curved part near the sea surface: notice that the temperature increases more and more rapidly, the closer you get to that surface. The most obvious parameter is the temperature difference between the warm water and the cool air. But just where should one measure these temperatures? There's a continuous change in temperature through several meters of air above the surface of the water (and, in fact, a similar change in the water just below the surface). So you really need to measure the change in temperature gradient with height. Fortunately, there's a parameter in the standard form for this profile that describes this. A less-obvious parameter is the height of the waves. If the waves are high, you don't see very close to the water (except just at the wave crests). In fact, the waves cut off your view of the best part of the inferior mirage. So the lower the waves, the more of the mirage you get to see. That's a big ingredient in the showiness of the Omega right there: low waves make big feet. Finally, there's the height of the eye. The mirage is produced by the curvature of the temperature profile in just the lowest few meters of the air. But if you're standing at the shoreline, your eye is only a little above those layers: the place where the rays are horizontal is not far from you, and the mirage subtends a large angle at your eye. If you're higher up, the horizon is farther away, so the mirage-producing layer subtends a small angle. Nearly the same part of the Sun is miraged, and nearly the same few meters of air are involved, regardless of eye height, because all the action takes place in the very lowest layers. So the inverted part of the image is squashed down into a very thin line at the horizon if the eye is high up, but makes big fat feet on the Omega if you're close to sea level. I'll take these items in turn — starting with eye height, because that doesn't require generating variants of the model atmosphere. Eye Height Other things being equal, we expect the distance to the horizon to be proportional to the square root of the eye height. The angular height of the feet on the Omega is roughly inversely proportional to this; so fairly large changes in height are required to make a big difference in the appearance of the feet. ← For example, here's the Omega seen from a height of 1.5 meters. The feet are big and fat. (This is roughly what's seen by a person standing at the water's edge.) But if we move up to a height of 30 meters, we see much thinner feet. → ← And if we go up to 450 meters, the height from which the Vatican Observatory pictures were taken, we find the feet reduced to just a thin line at the apparent horizon. And, sure enough, the Vatican photos show only a very thin line in their Omegas.   There is another way to think about the shrinkage of the feet as the height of the eye increases. As you can see, the angular height of the feet is larger than the narrow zone around the fold line, where the vertical magnification is large. That means that nearly all of the inferior mirage can be regarded as a reflection — indeed, it's that very property of mirages that fools the casual observer into thinking that they are pools of w

Websites with similar content