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Other than knowing which direction is east and which direction is west, or observing for a sufficient timespan (to determine the direction of motion), is there any way of telling whether what one is seeing is a sunset or a sunrise? A priori it seems not but I was wondering if there are some subtler effects beyond Rayleigh.

Note. I just came across an article that mentions that the green flash can occur only at sunset, and provides additional references:

Broer, Henk W. Near-horizon celestial phenomena, a study in geometric optics. Acta Appl. Math. 137 (2015), 17–39.

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    $\begingroup$ It depends. From the point of view of physics, the answer is no - the two are symmetrical. But human activity (e.g. pollutants) can break that symmetry. $\endgroup$ – lemon May 29 '16 at 8:41
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    $\begingroup$ Can't you just wait a few minutes and see if the sun's position relative to the horizon has gone up or down? $\endgroup$ – fibonatic May 29 '16 at 10:25
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    $\begingroup$ @fibonatic, let me put it another way: can one detect whether this is a sunrise or a sunset from a very precise and detailed photograph? $\endgroup$ – Mikhail Katz May 29 '16 at 12:39
  • $\begingroup$ If there is a green flash, I think that only happens at sunset, but it's too rare to be useful. $\endgroup$ – Todd Wilcox May 29 '16 at 17:01
  • $\begingroup$ After clarifying that your question relates to a picture, the answer is an emphatic NO. There is no way a person would be able to tell if the picture is of a sunrise or sunset. $\endgroup$ – Guill May 31 '16 at 20:14
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In real life: A sunset is "redder" than a sunrise which makes people feel more romantic.

It's mostly because the atmosphere is warmer in the evening (no pollution here, lemon, the Earth is warmer in the evening because it was naturally warmed up during the day). However, there's also a very small contribution of the Doppler shift, one that you could in principle measure accurately. When you're looking to the East, your point on the Earth is moving towards the Sun at speed up to 1,500 km/h or so (on the equator). This small velocity still exceeds the radial component of the velocity around the Earth, I think, so if you measure the Doppler shift accurately, you may learn something about the motion.

You may also watch where the Sun is moving. If it is setting (dropping, approaching the horizon), it is a sunset, and if it is rising, it is a sunrise. ;-)

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    $\begingroup$ Why does warmer make it redder? $\endgroup$ – Mikhail Katz May 29 '16 at 8:47
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    $\begingroup$ @MikhailKatz This is a good question. I think the answer is because, with typical atmospheric temperature profiles at the end of the day there is much stronger refraction than at dawn, so the sunlight is passing through much more air (when you see sunset the Sun is often actually already below the horizon), and there is then more scattering of blue light. $\endgroup$ – tfb May 29 '16 at 10:23
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    $\begingroup$ @PeterDiehr, if it is the dust particles that enhance the red then the reason is not temperature but rather pollution, as someone noted above. Is it temperature or pollution? $\endgroup$ – Mikhail Katz May 29 '16 at 12:47
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    $\begingroup$ @MikhailKatz: dust is a natural phenomenon, and increases on dry days, but is brought lower in the sky with increasing humidity. So one cannot simplify weather to (a) or (b); these are complex systems. Minaert's "Light and Colore in the Outdoors" goes into the details for the various cases. For the sailor's ditty, see (loc.gov/rr/scitech/mysteries/weather-sailor.html) $\endgroup$ – Peter Diehr May 29 '16 at 13:39
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    $\begingroup$ Since at least some sunrises are redder than some sunsets, I don't see how this helps. Personally, as an observer of many sunrises and sunsets in the mid-Atlantic US, I haven't noticed sunrises being less red. At least the difference in redness has not been enough that I have noticed it. $\endgroup$ – Todd Wilcox May 29 '16 at 16:57
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I don't know if this is kind of answer you're looking for, but you could measure the temperature difference between the air and the open ground (as dark as possible). Over the course of a day they should diverge because the ground absorbs so much more radiant energy than the air. By sunset they will have equalized some, but by the following sunrise they will have equalized even more, because at night there's almost no radiation to make up for the heat the ground loses to the air and sky.

Of course weather might frustrate this test.

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You got other answers explaining that there are physical reasons in the atmosphere for a sunset to be slightly different from a sunrise. But the problem is that the variations from one day to the other in atmospheric vertical profile (temperature and water vapour) because of meteorological effects are IMHO much greater than the difference caused by the day heating. So if you have only a visible photography, the signal/noise ratio will not allow you to certainly determinate. You would need more informations to deduce the vertical atmospheric profile and from there the moment in the day

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It's not something you can directly see, but various amateur radio propagation modes turn on around dawn and turn off around dusk. Read up on the ionosphere and solar ionization.

I imagine this could lead to spectral voids in setting sunlight, but I expect the effect to be too small to see (maybe not too small to measure).

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