## North Pole Weather 9/23/13

The sun rose this morning at 7:38, and will set 12 hours, 8 minutes and 33 seconds later at 7:46 this evening. We’re still losing 6 minutes and 37 seconds a day.

Wait a minute. Yesterday at 12:44 pm was the Autumnal Equinox, the time when day and night are supposedly equal at 12 hours each. What are we doing with days still longer than 12 hours?

Actually, the 12 hour days on the equinox would be true if (a) the sun were a point source of light and (b) the earth had no atmosphere. Since neither is true, the days are still longer than 12 hours today and tomorrow. Why?

The sun actually has an apparent diameter of half a degree, and sunrise and sunset are defined as when the upper edge of the sun is just on the horizon. Further, the air is densest near the ground, which means that the light rays are to a certain extent bent around the Earth’s curvature. This last means that there is actually a day-to-day variation in the difference between the geometrical sunrise and the observed sunrise, so the times I give are only approximate. Specifically, they are taken from a website that calculates them based on a standard atmosphere (which is certainly not the case here in the winter!) To quote from the website I use:

### Sunrise and Sunset

The times for sunrise and sunset are based on the ideal situation, where no hills or mountains obscure the view and the flat horizon is at the same altitude as the observer. Sunrise is the time when the upper part of the Sun is visible, and sunset is when the last part of the Sun is about to disappear below the horizon (in clear weather conditions).

If the horizon in the direction of sunrise or sunset is at a higher altitude than that of the observer, the sunrise will be later and sunset earlier than listed (and the reverse: on a high mountain with the horizon below the observer, the sunrise will be earlier and sunset later than listed).

The Earth’s atmosphere refracts the incoming light in such a way that the Sun is visible longer than it would be without an atmosphere. The refraction depends on the atmospheric pressure and temperature. These calculations use the standard atmospheric pressure of 101.325 kilopascal and temperature of 15°C or 59°F. A higher atmospheric pressure or lower temperature than the standard means more refraction, and the sunrise will be earlier and sunset later. In most cases, however, this would affect the rising and setting times by less than a minute. Near the North and South Poles it could have greater impact because of low temperatures and the slow rate of the Sun’s rising and setting.

For locations north of 66°34′ N or south of 66°34′ S latitude, the Sun is above the horizon all day on some days during the summer and below the horizon all day on some days during the winter.

Technically, sunrise and sunset are calculated based on the true geocentric position of the Sun at 90°50′ from the zenith position (directly above the observer).

In case you’re wondering, my house is at 64° 33′ North latitude.

The photos above, by the way, were taken Friday. Saturday night and yesterday we had mixed snow and rain all day. I’ll add a current photo below as soon as it’s light enough to take one, but I fully expect an inch or so of snow.

This morning, 7:50 am

We broke 12 hours of daylight Friday, 2 days before the equinox. Why? And is this just due to my being close to 65 degrees North, or is it a more general anomaly?

There are two parts to this peculiarity. One is latitude combined with the finite diameter of the sun, which can be calculated. The other is the refraction of the atmosphere, which varies from day to day and can only be estimated.

Let’s take latitude first. Sunrise and sunset are defined as the time that the upper edge of the sun is just visible above a flat horizon. “Equal days and nights” (which is what equinox means) assumes the dividing line between day and night is the time when the center of the sun is on the horizon, assuming light moves in straight lines. If the sun rose vertically, as it does at the equator, it would rise at a rate of about 1 solar diameter a minute, and the calculated sunrise time based on the center of the sun would be only half a minute after the time the upper edge first showed.

At higher latitudes, however, the sun appears to rise at an angle and sunrise and sunset appear slower. At 65 degrees latitude the sun’s path at the equinox is 65 degrees from the vertical, and a little trigonometry stretches that half minute to about 1 minute 10 seconds, or twice that in day length. Latitude alone is still not enough to allow our days to be 12 hours 15 minutes long at the equinox. For that, the refraction of the atmosphere becomes important.

The apparent break in the spoon handle is due to refraction.

Everyone is familiar with refraction, though you may not know it by that name. The optical illusion of a broken spoon in water is caused by the fact that the speed of light in water is less than that in air. Yes, the speed of light in vacuum is constant, but in any other transparent medium it moves a little slower. When it crosses a boundary between two transparent media with different speeds of light, any light rays not moving at a right angle to the boundary are bent. Air is one of those transparent media, and while the speed of light in air is not a great deal slower than that in vacuum, there is enough of a difference that the bending affects what we can see.

The actual difference in speed depends on the density and moisture content of the air, which in turn depend on pressure, temperature and relative humidity. Air near the ground is almost always denser than that above it, and this is particularly true at sunrise. The change with height is gradual, and thus the light rays are not bent sharply, as in the water-air interface, but curved along the earth’s surface. Objects far away appear higher than they are, and this certainly applies to the sun at sunrise. The amount by which the sun appears higher in the sky than it really is will depend the atmospheric density and how it changes with height.

For practical purposes the time of sunrise is calculated assuming that the upper edge of the sun is visible when the center of the sun is 50 minutes of angle—almost a degree—below the horizon. This also means that the sun at the equinox will rise not quite due east, as it “rises” while it is still physically below the horizon and slightly north (in the northern hemisphere) of east. The difference, however, is slight.

Refraction is also responsible for the fact that the sun appears to flatten as it approaches the horizon when setting or just after rising. The part of the sun closest to the horizon is more strongly affected by atmospheric refraction than is the upper part of the sun, so the two appear pushed together and the sun appears flattened, rather than round. I’ve probably overused this in Tourist Trap.