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Please forgive me if this is a dumb question, or if my understanding of basic physics is wrong. Please feel free to correct me.

As I understand it, if the Earth didn't have any atmosphere, then the time of sunrise would be the point when the Sun's rays approached your position at a tangent. For example, imagine that the Earth is a perfect sphere, with you standing on top, and the (apparent) motion of the Sun was it travelling clockwise as follows (scales completely wrong, but hopefully the concept is correct)...

No atmosphere

Now, assume for simplicity that the Earth's atmosphere is of constant destiny, and starts at a defined height above the planet's surface, then (if I understand correctly), the Sun's rays would be refracted as they entered the atmosphere, meaning that you would see the sun slightly earlier (exaggerated)...

With atmosphere

Obviously, this is very simplified, not least because the atmosphere is a gas, and therefore of variable density, presumably being less dense the higher you went. I imagine that the variation in density would mean that the rays appeared to curve, rather than take a sudden turn as shown above.

My question is, how much difference does the air temperature make to the amount of diffraction, which in turn affects the time at which you would see the sunrise? My feeling is that if it were cold across the Earth, then the air would be more dense, resulting in a greater degree of refraction, and so an earlier sunrise. By contrast, a higher temperature would mean lower density, less refraction and a later sunrise.

Anyone able to give me some estimates of how much difference you would expect to see between a warm summer's day and a cold winter's day, assuming normal parameters for "cold" and "warm" for our planet?

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    $\begingroup$ Not much, BUT, atmospheric refraction is actually a very important source of temperature measurements for the daily weather forecast! See GPS Radio Occultation. From variations in the time a GPS signal takes to reach a receiver at a constant (known) location, we can measure atmospheric temperature; by doing it again and again until the satellite has set, we can measure an entire temperature profile. However, this works with microwave radiation, not with visible. I'm not aware of visible refraction (as opposed to absorption) being used for remote sensing. $\endgroup$ – gerrit Jan 23 at 15:41
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The biggest cause of refraction is the change in density of the atmosphere with altitude, not changes caused weather conditions at the surface.

There are formulas to calculate this effect assuming standard values of temperature and pressure at ground level. The apparent change in position of the sun in those conditions is about the same as the sun's visible diameter.

The time difference this causes depends on the angle at which the sun rises above the horizon, which depends where you are on the earth and what time of the year it is. If the sun rises vertically, the time difference is about 2 minutes, but if it rises at a shallow angle to the horizon it may be much longer.

Changes in air temperature and pressure also have an effect, which is easy to observe (from the known position of the stars, not just by observing the sun) but difficult to predict in a useful way. As a consequence of this, it is not very useful to predict sunrise and sunset times to more accuracy than the nearest minute.

See https://en.wikipedia.org/wiki/Atmospheric_refraction

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  • $\begingroup$ Changes in the vertical distribution of potential temperature are going to affect the vertical change in density and influence the time of sunrise... but whether this is by milliseconds or microseconds, I don't know. $\endgroup$ – gerrit Jan 23 at 15:31
  • $\begingroup$ "The apparent change in position of the sun in those conditions is about the same as the sun's visible diameter." Wow, that's quite a lot! $\endgroup$ – David Jan 23 at 15:49
  • $\begingroup$ @alephzero Wow, what a great answer! Thanks very much. Re your first sentence, does that mean that the change in density of the air as you go from the Earth's surface upwards doesn't change much with the temperature on the ground? I assumed (quite possibly incorrectly) that as the sun's rays passed through the atmosphere, warming the surface, they would also warm the air, lowering the density higher up as well. Sounds like that might not be right. $\endgroup$ – Avrohom Yisroel Jan 23 at 16:30

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