Wednesday, October 04, 2017

Physics in the Autumn Sunrise

The sun is an hour over the horizon. It's the first week of October in Maryland, and there's something uniquely enchanting in how the light catches the tips of the trees. What is it that makes this morning sunlight so spectacularly yellow-gold? As with most things, the answer—at some level—comes down to physics.

And, because I know someone in the comments is going to get on my case for trying to turn a rational eye to the sublime beauty of nature, let me preempt that with words from someone who's addressed that concern far more eloquently than I ever could.

It is sometimes said that scientists are unromantic, that their passion to figure out robs the world of beauty and mystery. But is it not stirring to understand how the world actually works—that white light is made of colors, that color is the way we perceive the wavelengths of light, that transparent air reflects light, that in so doing it discriminates among the waves, and that the sky is blue for the same reason that the sunset is red? It does no harm to the romance of the sunset to know a little bit about it.
—Carl Sagan
Sunlight is a mixture of the entire visible spectrum—often partitioned into seven colors, but obviously existing as a continuum in reality. It's not an even mix of all these colors, though, and by the time direct rays of sunlight reach Earth's surface, they're usually dominated by the lower-energy end of the visible spectrum—as Sagan mentioned, blue wavelengths are more easily scattered in the higher atmosphere.

This figure shows the intensity of the sun's light at various wavelengths—the yellow curve is the radiation spectrum at the top of the atmosphere, while the red curve is what it looks like at sea level. Attenuation by scattering of shorter wavelengths shapes the red curve, with sharp dips created by absorption bands of atmospheric molecules.
Image Credit: Wiki user Nick84 (CC BY-SA 3.0)
One of the main variables that affects the quality of light is its spread. When you shine a flashlight straight down onto the ground, the photons coming from it all land in a small circle. But tilt that flashlight so that the light it shines spreads out across a wider region, and the intensity within the illuminated area drops. The further from the equator you get, the more the planet's surface curves away—effectively angling the ground that the light is landing on, spreading out the sunlight and reducing its intensity as shown below.

Thanks to Earth's curvature, the same number of parallel photons will spread out over a larger area, creating cooler, dimmer light.
Image Credit: Peter Halasz (CC BY-SA 3.0)
The other main factor influencing the quality of light, which has greater influence over the color than the intensity, is the amount of air that a sunbeam has to travel through. This, in turn, depends on four main factors—time of year, latitude, time of day, and elevation. The reason for that last one is hopefully obvious, but the others might not be; all of them have to do with the relative orientations of the sun and the earth.

The first two, time of year and latitude, can be bundled up together, and tie into spread. As you can see in the diagram above, light reaching locations further from the equator have to travel through more atmosphere to reach the ground. Additionally, as the planet's axis tilts over the course of a year, the part of Earth closest to the sun—and therefore receiving the least-spread-out sunlight, migrates north and south.

This also affects the amount of atmosphere between the ground and the sun, though. At high latitudes, the shift from summer to winter means a shift to longer, lower-energy wavelengths as more light is diffused by the atmosphere—giving October sunbeams their yellow-gold hue and creating pale skies saturated with scattered light.

Time of day, of course, is the most significant of all these factors—as anyone who's seen a lava-red sunrise can attest. 

When on the horizon, the sun is passing through the greatest possible amount of atmosphere before reaching the ground. At midday, that amount is at its minimum.
Image Credit: Stephen Skolnick (CC BY-SA 3.0)
The geometry at work here is similar to the seasonal case, except on the east-west axis, instead of north-south. The atmosphere, being a spherical "shell" a (roughly) fixed distance from Earth's surface, is thinnest when viewed top-down, rather than from an oblique angle. Spread is at work here, too—which is part of why it's fine to look at a sunset or sunrise, but the midday sun will give you eye damage pretty quickly.

Physics is a useful tool, but just as importantly it can be a source of understanding and awe—and there's wonder in this: two photographs of the exact same scene, taken on different days, will have variations in which colors are most strongly pronounced, in how sharp the shadows are. Although the sun never changes, each day it rises slightly different than the last. At every latitude, every elevation, every time of day and every day of the year, there's a unique spectrum of light—unlike the day before, unlike even the minute before, unlike the view from a hundred miles north or south. Temperature variations, air pressure, and atmospheric pollutants, too, give rise to changes that are at once subliminal and sublime, letting us see each day in a new light. 

Stephen Skolnick

For more on light, scattering, and the atmosphere, check out our post: Blue Smoke, Red Sun.

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