The Sub-Duct Green Flash

Introduction

When the observer is just below a duct, a very large, long-lasting green flash is visible. They are the most spectacular of all direct green flashes. This page shows what they look like, and how they're formed.

As sub-duct flashes are a little more complicated than the flashes due to the better-known inferior and mock mirages, a little more explanation is required. That means this page will be a bit more technical than the ones dealing with those other flashes. 15K inversion between 200 and 250m; profile to 300m

Let's begin with the model. To show the features of this flash well, I've used a temperature inversion of some 15 degrees. That's a lot, but it's typical of the strongest inversions formed off the California coast during Santa Ana conditions, when hot air at 35 or even 40°C flows out over the ocean, where the water temperature is only 20 or 25°C. Usually, this temperature difference is split among several weaker inversions; but on rare occasions, we get the whole difference across a relatively thin layer.

As the one sub-duct flash I've seen was from a height of about 100 m, I've put the model inversion well above that, with its base at 200 m, and its top at 250 m height. Those numbers were chosen rather arbitrarily; they put the base of the duct a little above 130 m, which is 70 m below the base of the inversion. That's a little higher than where I was standing; but that difference only makes a little more of the sunset visible below the astronomical horizon: the dip of the sea horizon is about 20 minutes of arc, instead of the 16 or 17′ that I usually see from 100 m.

You can see from the figure how oversimplified this is. Above the inversion, the profile is just the Standard Atmosphere; below it, the standard lapse rate of 6.5°/km is used. That's not very realistic; but it's enough to capture the main features of sub-duct flashes.

The corners of the profile have been smoothed to capture features that appear when the eye is just at the edge of the duct. Remember that the local zenith distance of a ray is the same at the top and bottom of a duct; so when the observer is at the bottom, the line of sight at the astronomical horizon becomes tangent to the upper edge of the duct, at the top of the inversion.

Before we leave the profile, notice how far the bottom of the duct is (at about 133 m; not drawn on the figure) below the bottom of the inversion (at 200 m). The observer is in a region of perfectly ordinary lapse rate; there's no hint in the local temperature gradient of the duct immediately overhead.

Transfer curves

You can see where the bottom of the duct is at different wavelengths by looking at the transfer curves for a few heights just above 130 m. transfer curve at 133m

 

First, here are transfer curves for an observer at 133 m. You can see we're below the duct at every wavelength here. And the broad minima show that a large green flash will be visible.

Notice that the minima fall very nearly at the astronomical horizon (the zero-point on the scale of apparent altitude, at the bottom of the figure).
transfer curve at 134m

 

Just a meter higher, we see that we're in the duct at the shortest wavelengths, but not in green light: the blue and violet curves become vertical, marking the edges of Wegener's blank strip. (Note that the blank strip is symmetrical about the astronomical horizon.)

The greater depth of the green and cyan minima mean that the flash will last longer here than at 133 m. (Remember that the vertical coordinate of the transfer curve is true altitude, which is nearly a linear function of time at sunset.)
transfer curve at 135m

 

Another meter higher, at 135 m, we're in the duct at green, but not at the longest wavelengths (red, orange, and yellow). We can have a yellow or orange flash, but not a green one.
transfer curve at 136m

 

Finally, at 136 m, we're in the duct at all visible wavelengths. But the width of the blank strip varies greatly with wavelength: it's wide in the blue, and narrow in red light. These circumstances produce some peculiar appearances, but not a green flash.

What a remarkable change in just 3 meters (10 feet) of vertical distance! What you see at the base of a duct is very sensitive to your height. And this is for a pretty big duct, too; with a smaller one, these changes would span an even smaller interval of height.

Now, let's move on to the actual sunset images, below. There's the usual problem with dynamic range: the computer monitor can't show the range of brightness in a typical sunset image. So I'll put in a lot of low-lying aerosol to suppress the brighter parts of the Sun's disk below the flash. That may make the extinction so big at the sea horizon that you can't actually see the horizon line. This is a little artificial, but only a little; some real sunsets look like that, too.

You can see from the transfer curves that the interesting flashes are confined to the region around 133 or 134 meters above sea level. Perhaps the best example is the view from 133 m, so we'll start there.

 


Sorry to have this sudden change in appearance; we need a black background in the next section, so that details in the darker parts of the sunset images can be seen. A white background drowns them out.

 

The sub-duct sunset seen at 133 meters

It's worth going through the whole sunset here, not only because there are interesting phenomena, but also because there are precursors that can alert you to the imminent appearance of the great sub-duct green flash. Sun at -40' from 133m

Here's the first indication that something unusual is about to happen. The Sun's center is 40′ below the true horizon, but none of it appears below the astronomical one yet. The refraction is clearly larger than normal; and the most obvious sign of that is the unusually large flattening of the disk.

Also, if you look closely, you'll see that the red rim on the lower limb is much wider than usual.

By the way, the little white ticks at the left and right sides of the figure (just below the lower limb here) mark the astronomical horizon. I've left in the full amount of sky between it and the apparent horizon, which is 50 pixels up from the bottom of the image, to emphasize how high in the sky the features of this sunset appear.
Sun at -44' from 133m

About 20 seconds of time later, the Sun's center is at −44′, and a big, bulbous red flash has sprouted from the lower limb. → Sun at -45' from 133m

 

← Four or five seconds later, the Sun is a minute of arc lower, and the bulb has grown rapidly. This big red flash is the first really striking feature of this sunset.

Notice that the neck between the flattened upper part and the bulbous lower part is almost exactly at the astronomical horizon (tick marks).
Sun at -59' from 133m

At −59′, the sides are almost vertical. →

The lower limb fades out into the haze at the apparent horizon, here.
Sun at -70' from 133m

← At −70′, we start to see some green around the edges of the upper limb. The Sun is now 20′ lower than the depression used to calculate nominal sunset times in the Astronomical Almanac, but we still see a considerable arc of the strongly-flattened upper limb above the astronomical horizon.

Sun at -74' from 133m

 

At −74′, the green edges are wide enough to be seen with the naked eye. These are clearly much wider than the usual green rim. →

The neck now rapidly narrows down, pinching off the part at the astronomical horizon.
Sun at -75.5' from 133m

← At −75.5′, the pinching has produced an orange triangle with a broad green border.

Sun at -76' from 133m

 

At −76′, the orange has shrunk to nothing, leaving a big green flash. The triangular shape is very characteristic of the sub-duct flash. →
Sun at -76.5' from 133m

← At −76.5′, the green triangle is shrinking. But it has already been visible for two seconds (if seen near the equator) or three seconds (at about 50° latitude) — that's already longer than a normal green-rim flash, such as an inferior-mirage flash or a mock-mirage flash. And we still have a way to go.

Sun at -77' from 133m

 

At −77′, the flash is fading, but still visible — and it's already been visible for about three times the duration of a normal flash. Even at this stage, it's larger than the average flash of the commoner kinds. →

Notice that the flash faded from the bottom up, leaving a green ellipse at the astronomical horizon. At this stage, it's easily mistaken for a mock-mirage flash. But look how much higher in the sky it is than a mock mirage. Once you see the differences, you can tell them apart.
Sun at -77.5' from 133m

How long can we follow this slowly fading flash?

← Here's an enhanced image (in effect, overexposed to show faint details) at −77.5′. There's still a pale elliptical wisp visible at the astronomical horizon, if you look closely. This is bluish in color; it would require extremely clear air to be seen.


Variations with height of eye

The appearance of the sub-duct flash varies rapidly with height of the eye, as you'd expect from the dramatic changes in the transfer curves with height. If the observer is too low, the transfer curves have no minimum; there's an extended green rim, but not a proper flash at all. Sun at -75' from 131m

← For example, here's what an observer 131 meters above sea level sees when the Sun's center is 75′ below the horizontal. (Colors in the bright orange part of the disk are distorted by clipping the brightest reds to make the green plainly visible.)

Sub-duct GF from 132m

 

But at 132 m, the eye is close enough to the bottom of the duct to have a proper green flash. →

Notice that there's a bulge at the top of the green area, even though it isn't separated from the orange disk below it. The neck below the bulge is an inverted image of part of the upper limb — due to a mirage: Wegener's Nachspiegelung.

In this and the following pictures, the “green flash” stage is arbitrarily chosen to be the moment when the wavelength of 580 nm has just disappeared from view in the middle of the flash. That is, we draw a horizontal tangent to the bottom of the dip in the 580-nm transfer curve, and place the Sun's upper limb at that true altitude.
Sub-duct GF from 133m

← At 133 m, the flash is entirely separated from the orange disk below it, and triangular in shape. This is very nearly the same as the sub-duct flash image shown in the main sunset sequence above for a true zenith distance of −76′. However, this version has been brightened to show the green area better, while (as mentioned before) losing color fidelity in the overexposed orange disk. Also, the altitude of the Sun's center is now −76.0937 minutes instead of −76 exactly, so as to show the appearance when the last bit of 580-nm light has disappeared.

You can see a faint remnant of the stalk that connected the green flash to the disk below it in the previous picture; it's the dim green glow just above the orange disk.
Sub-duct GF from 134m

At 134 m, the flash has flattened out; it's wider in the horizontal direction, but thinner in the vertical. The solar depression is now 77.4134′, which moves the orange disk down into the haze more, reducing the dynamic-range problem; so the disk colors are only a little distorted. (The colors in the flash, as in all the above images, are correct — or, at least, as correct as the limitations of computer displays allow.) →

It isn't obvious here, but we're already starting to run into the duct itself at the shorter wavelengths. That is, there's a narrow blank strip at blue wavelengths, right at the astronomical horizon. But the blue light is so attenuated by atmospheric extinction that it contributes next to nothing to the image, and you don't see anything peculiar at the astronomical horizon. However, the width of the blank strip is proportional to the square root of distance above the bottom of the duct; so just a few centimeters more will suffice to produce an apparent defect through the middle of the flash. Sub-duct GF from 134.5m

← So we can't even get a proper flash at 135 meters, because the transfer curves become so strange that our rule for picking a green-flash altitude gives a very odd result. You can see the problem developing here at 134.5 meters, where the Sun's depression is 78.593′ at the flash.

There's still a minimum in the yellow-green transfer curve; but some of the green is interrupted by a blank strip, whose width increases as wavelength decreases. The changes are so rapid with wavelength that we're beginning to have visible artifacts due to the limitations of my method of interpolating between tabulated refraction data.

Of course the trend toward flatter flashes with increasing height of the eye has continued. We now have a flash whose width, left to right, is about 3/4 the diameter of the Sun. Because the orange disk is now deep in the haze at the horizon, the dynamic-range problem has disappeared: the relative brightnesses and colors in this image have not been adjusted.

Beyond this point, the effects of the duct edge are so strong that I can't generate satisfactory simulations. I'll have to give up here, for the time being.

Discussion

The sub-duct flash can certainly be huge. If the duct and the observer were moved down about 120 meters, the orange disk would lie completely below the sea horizon when the sub-duct flash appears. Then it would seem that the whole Sun had turned green; and, with no orange light available to light up the boundary-layer aerosol, we'd probably have enough green illumination to make green crepuscular rays in the aureole of the flash. I suspect that's how the various kinds of “green ray” displays are produced.

 

Copyright © 2005 – 2012, 2013 Andrew T. Young


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