Sunset Measurements

One thing that we could be getting a lot more out of is sunsets and sunrises. This is particularly true for amateur meteorologists.

One day, just as a mental exercise, I tried to think of a way to calculate the height of a cloud in the sky. First, I considered measuring the cloud's shadow and then measuring it's angular diameter in the sky. But this method would surely be very cumbersome and prone to error.

Then, I thought of a better way. Wait until sunset and position yourself so that you have an unobstructed view of the western horizon. As soon as you see the sun dip below the horizon, start a timer. Then look up at the cloud. Since it is high up, the sun will still be shining on it when the sun is no longer visible to you on the ground. Stop the timer when you see the cloud start to turn orange, since this means that the sun has dipped below the horizon from the cloud's point of view and it is only lit by orange refracted light from the sun.

Now, we know how fast the earth is rotating. Since we know that your location rotates 360 degrees in 24 hours, we can easily tell how many degrees the earth rotated while you were waiting for the sun to fade from the cloud. All we have to do is divide 24 hours by the time measurement you took. Then divide 360 degrees by that. The earth rotates an angular degree every four minutes.

After you use your measurement of the time it took for the cloud to begin the orange phase after the sun dipped below the horizon, find the angle that the earth rotated during this time, which is one degree for every four minutes.

Find the cosine of that angle, you should get a number just below 1.

Now find the reciprocal of that cosine so that you get a number just above 1.

Now subtract 1 from your answer so that you get a very small number we will call x.

Next, multiply the radius of the earth (4,000 miles) by the cosine of your latitude.

Now, multiply that number by x.

The result will be the altitude of the cloud in whatever unit you expressed the radius of the earth.

You can also use the sunset to measure the angle at which the earth's atmosphere refracts light relative to empty space. You can see the refraction of light by putting an object at the bottom of a bowl of water. When you reach in for the object, you can see that it is not quite where it appears to be because water refracts light at an angle relative to air. It is easy to see that the atmosphere refracts light and that it refracts blue light more than red by watching the reddish tinge to the earth's shadow on the moon during a lunar eclipse.

To measure the atmosphere's angle of refraction, watch the cloud and begin measuring when the eastward point on it enters the orange phase. This means that it is lit by the sun's refracted, rather than direct light. The light is orange because the atmosphere refracts blue light more than the light at the red-orange end of the spectrum and the sun's bluish light is refracted away into space and the orange-red remains. If you look at images of earth from space, you can sometimes see a bluish tinge along the line where night meets day.

Stop the timer when the cloud begins to turn purplish. This means that it is lit only by the sun's scattered light and not by either it's direct or refracted light. You do not need an unobstructed view of the western horizon to measure how much the atmosphere is refracting light.

Divide 24 hours by the time that the cloud is in the orange phase.

Then divide 360 degrees by that.

The result will be the angle at which the earth's atmosphere is refracting light. As with the cloud altitude, it will be one degree for each four minutes.

I wonder if the angle of refraction varies under different circumstances, such as how much pollutants or dust are in the air. I would think that clean air would have a lower angle of refraction because such particles will reflect light.

As another mental exercise one day, I tried to think of a way to find my position if I found myself somewhere on the earth's surface with a map of the earth but no idea where I was.

Many types of cloud, such as those fluffy cumulus clouds, usually form around the same altitude, about 4,000 feet, anywhere in the world. We can find our approximate latitude on the earth's surface by using the cloud altitude measurement in reverse. A sighting on the altitude of the north star above the horizon can also tell you your latitude but this cloud method can be used when the northern horizon is obstructed.

The earth rotates in 24 hours. But since it's circumference is greatest at the equator, a point on the equator is travelling faster than elsewhere. This means that a cloud of given altitude will exit the sun's light following sunset faster near the equator than nearer the poles. Measure how long it takes a cumulus cloud to enter the orange phase after the sun dips below the western horizon from your perspective. Divide 24 hours by that reading and then divide 360 degrees by that.

You will get the angle that the earth rotated before the orange phase began. It will be one degree for every four minutes.

Find the cosine of that angle.

Then find the reciprocal of the cosine.

Then subtract 1.

Divide the height of the cloud by that small number.

Then divide that answer by the radius of the earth. The result will be the cosine of your latitude.

When measuring a cloud's altitude, do not try for great accuracy. First of all, a cloud is a somewhat nebulous object. Second, the ground is rarely perfectly level. The same type of cloud may not all be at near the same level.

If you cannot easily get an unobstructed view of the western horizon, most ideally over a body of water, you can look at the sun's reflected light on a high object. I live near a tall brick smokestack which I used for this purpose.

You should watch a few sunsets and the resulting light changes on clouds to familiarize yourself before trying these measurements. Familiarize yourself with the types of cloud and their usual altitudes and make sure your answer makes sense. Cumulus clouds average right around 4,000 feet while high wispy cirrus clouds are maybe five miles in altitude. Clouds with an alto- prefix such as altocumulus and altostratus are in between. If the sky is overcast or you have those low layer stratus clouds, obviously this method will not work.

Sunset measurements or sunset geometry is not an entirely new idea. But few people of heard of it and I believe that we could be getting much more out of it. Obviously these techniques can also be used at sunrise in reverse, you would look for signs of direct sunlight on a cloud above and then time how long from then it took for the sun to become visible above the horizon.