E-mail from the South Pole

Here is an e-mail sent by NOAA to workers at the South Pole as they guess when the sun will actually set down there.


Subject: (A few too many words about the question:) When will the sun actually disappear?

Hi all,
 
 With the equinox coming up shortly, I think we're all starting to look forward to the disappearance of the sun.  Predicting the time of sunset at South Pole is essentially impossible, but there are a few parameters, and then past experience, that let one make at least an estimate of the last time we might see some direct sunlight. 

The start of any reckoning is the moment of the equinox, which is:

1732 UTC 20 March 2010
0632 NZDT 21 March 2010 (aka South Pole local time) 21 March 2010
 
This is the moment when, absent any atmospheric impact, and presuming a perfectly spherical earth, and presuming that you are looking from right at the surface of that perfect earth (ie you have no height or elevation), the sun would be exactly halfway below the horizon as viewed from either Pole.
 
Of course, sunSET is when the last of the sun vanishes below the horizon, not when the sun is split by the horizon.  The sun is a little over 30 arc-minutes (about half a degree) wide, and at the equinoxes it's moving north or south at a little less than one arc-minute per hour, so figure about 16 hours for it to go from split to gone.
 
The atmosphere bends any light that passes through it, and the more atmosphere the light has to pass through, the more the light is bent.  By the time an object *appears* to be on the horizon, it is in fact well below.  The amount of this "lifting" that a well-mixed atmosphere does depends on the density of the air, which in turn can be expressed as a function of the temperature and pressure  of the air.  Curiously enough, in theory the coldness of the air at South Pole almost exactly cancels out the thinness due to the elevation, and the refractive impact is about the same as for a normal temperate sea-level site, which, for an object apparently on the horizon, is approximately 34 arc-minutes.  Again, figuring that the sun is moving slightly under one arc-minute per hour, this refractive lifting might produce a delay of about 36 hours. 


The final semi-predictable factor in the disappearance of the sun is the height of the observer.  A person viewing from six feet up commands a horizon that is about three miles distant; from 35 feet (say, standing in galley) you can see about seven miles.  Each mile that you can push the apparent horizon to the north allows you to see objects in the sky that are just under an arc-minute further north, and again with the sun's speed, this means that each mile is worth about an hour's delay in losing the solar image.   Unfortunately (for the purposes of this exercise), although at a glance it sure looks flat out there, it turns out that it's not: within a ten mile radius of station there are places that are as many as 30-50 feet higher or lower than station.  Since it's impossible to predict accurately enough in which direction the sun will be when it vanishes, it's impossible to determine if this topographic variation will delay or accelerate the sunset.  If the sun sets behind a low point, there might be another few hours of delay; if it goes down beyond a high point, then the delay gained by gaining elevation here will be pretty much cancelled.  So this is a wild card, ranging from maybe 0 to 10 hours of extra delay.
 
So that gives us a sum estimated total of 52-62 hours after the equinox for the solar disc to vanish.  As an example, here's an image from 2003 taken approximately 30 hours BEFORE the September equinox.  This is a bit deceptive, as it looks like the sun is well clear of the horizon, but in fact only the top 1/6 to 1/4 of the disc is actually visible here, with the rest lost in the ground haze.  >From the scalloped shape of the top edges of the sun, it's also clear that there are non-standard refractive effects in play here (reed on), but this at least confirms that we're in the right ballpark on the estimate outlined above; from this image, and ignoring the possibility of non-standard effects, one might guess that the true "sunrise" happened about 30 hours before the photo was taken, or 60 hours before equinox.
 
 
 
The entire previous discussion and estimate presumes refraction provided by a "standard" atmosphere, one in which temperature decreases smoothly, predictable, and nearly linearly as you go up through it.  Unfortunately, as far as these calculations go, but fortunately for what we might see, the atmosphere at South Pole is typically anything but standard.  Due to a strong mismatch between the amount of energy being radiated away by the snow surface and the amount of energy being provided by the sun (a mismatch that's obviously particularly strong in low- and no- sun conditions, when the energy input is negligible), we frequently experience a condition known as thermal inversion here, where, for a while at least, as you go up into the atmosphere the temperature actually increases, instead of decreasing as a standard atmosphere would predict.  The optical results of thermal inversions and other non-standard atmospheric temperature profiles are very complicated, and depend greatly on the specifics of the profile and, particularly, the observer's position relative to (above, within, or below) the thermal oddity.  For those interested in an amazingly detailed and truly fascinating web site on the matter, check out:
 
http://mintaka.sdsu.edu/GF/explain/explain.html
 
and all its related links.  For the rest of you, suffice it to say that pretty much all the specificity of the timing detailed above can be thrown out the window.  As (potential) compensation for that loss, one of the effects that is often produced at sunset by the odd temperature profile at Pole is the famous "green flash".  For (lots of) details on what it is and why we see it, check out the link above, but here's a little example, taken by Rodney Marks at sunset in 2000.  Here the flash is actually blue, which is also common at the  South Pole since our atmosphere is thinner and "cleaner" (fewer particulates) than in most other locations around the world, so the blue light isn't scattered away as efficiently as elsewhere.
 
 
 
In most locations, the rapid vertical motion of the setting or rising sun means that the green flash is a phenomenon whose duration is measured in fractions of a second, but because the sun here is sinking so slowly, the flashes often linger on and on, forming, changing color, dissipating and reforming for periods of hours and hours.
 
Finally, to give an example of just how delayed the final viewing of the sun can be, here are some images from sunset 2003, taken 108 hours (four and a half days) after the equinox.  These are likely to be the result of particularly strong and layered thermal inversions called ducts, and for further information I again refer you to the link included above.  In other seasons there have been reports of sunlight as long as a week after equinox, which could be the result of any of amazingly strong ducts, reflection off distant clouds, or exaggeration on the part of the viewers :-).

In any event, in the case of a Pole sunset, it's certainly true that it ain't over 'til it's over, so keep a sharp eye out, and please do all-call if you see anything really spectacular (include your location, too, since elevation plays such an important role in what is seen).
 

By: "NOAA Winter Over"
 
PS.  All offers null and void in the case of bad weather, including but not limited to complete overcast or just a crappily obscured horizon.