On a clear night on a mountain, the sky is open in two places. One of them you can see. The other was found by a telephone engineer, listening to static.
Chapter 9 · Beyond the visible
Windows in the Sky
The Sun above the air, and the Sun at the ground. What three millimetres of ozone does, why sunburn needs a high Sun, and where the sky is open.
Look first
The Sun, above the air and at the ground
The outline is sunlight as it arrives at the top of the atmosphere. The filled curve is what is left of the direct beam at the ground, through a standard clear sky with the Sun about 42° up. Most of the light gets through, but not evenly.
Look at the gaps. Near 760 nm a narrow notch is cut by oxygen. Further out, water vapour takes whole bands: a dip at 940 nm, a deeper one at 1130, and at 1400 and 1900 nm nothing at all. These are the places where chapter 7’s ideal Sun was too ideal. Then look at the far left. The curve at the ground stops short of the curve above the air, as if cut with a knife.
Power per nanometre, in W m−2 nm−1. The standard spectra are computed from measured atmospheric properties, and checked against measured sunlight.
Commit to a prediction
Three millimetres
The knife is ozone. It is spread thinly through the air, mostly between 15 and 35 km up. If you could gather all the ozone above you and bring it down to the ground, at the pressure and temperature of a cold day at sea level, it would make a layer about three millimetres thick. That is how ozone is measured: 300 Dobson units means three millimetres.
Ozone absorbs ultraviolet light most strongly near 255 nm.
With the Sun overhead, how much of the Sun’s 255 nm light gets through those three millimetres?
Fraction of light that passes 300 Dobson units of ozone, Sun overhead. The vertical scale is logarithmic: each gridline is ten billion times smaller than the one above.
Why the first guesses made sense
Thin is not the same as weak
If you chose most of it, or half, you were judging by thickness, and for most materials in daily life thickness is a fair guide. Three millimetres of window glass passes nearly all visible light. But how much a layer absorbs depends on two things multiplied together: how many molecules the light meets, and how likely each one is to take it. At 255 nm an ozone molecule is an extraordinarily good absorber.
If you chose a part in a thousand, you were right that the absorption is strong, and missed how strong exponential can be. Split the layer into thin slices. Each slice passes the same fraction of what reaches it. At 255 nm the three millimetres behave like ninety slices that each pass about 37%. Ninety factors of 0.37 make a number with about forty zeros after the decimal point.
The same multiplication explains the knife edge. Ozone’s absorbing power falls smoothly with wavelength, about thirty times between 255 and 300 nm. But a smooth change in the number of slices becomes a cliff in what gets through: ninety slices pass nothing, three slices pass a few percent, and a quarter of a slice passes most of the light. The edge of the Sun’s spectrum at the ground is that cliff.
The bench
Move the Sun, thin the ozone
Below is the ultraviolet end of sunlight, from 280 to 400 nm: above the air as an outline, and the direct beam at the ground filled. The red tint shows the light weighted by how strongly each wavelength burns skin. Lower the Sun and its light crosses more air. Thin the ozone and the edge moves the other way.
Ultraviolet at the ground
A case you have not seen
Seattle in December
At noon on the longest day of the year, the Sun over Seattle stands 66° above the horizon. At noon on the shortest day it stands 19° up, and its light crosses about three times as much air.
In the direct beam, green light at 550 nm drops to about four-fifths of its midsummer value. Now take ultraviolet at 300 nm, among the wavelengths that burn skin and that skin uses to make vitamin D.
In the direct beam, how much of its midsummer value is left at midwinter noon?
Three times the air does not divide the light by three. It cubes the fraction that gets through. Green light passes nine-tenths of the air overhead, and nine-tenths cubed is still most of it. Ultraviolet at 300 nm passes about a hundredth, and a hundredth cubed is a millionth. A small transmission raised to a power is the most unforgiving number in this exhibition.
The sky softens it. Blue sky is sunlight scattered sideways, and it scatters ultraviolet best of all, so on a winter day much of the ultraviolet that reaches you comes from the whole sky rather than the Sun’s disc. Even so, through most of a Seattle winter the noon Sun is too low for skin to make much vitamin D, and it is very hard to get sunburnt. Researchers call it vitamin D winter.
What you can now say
The air is open in two windows, one for light and one for radio. A few millimetres of ozone close the ultraviolet at about 300 nm, and because absorption multiplies, the edge is a cliff that moves with the height of the Sun.
Everywhere else the air is a wall: atoms high up stop X-rays and gamma rays, water vapour and carbon dioxide fill most of the infrared, and above a few tens of metres, radio waves are turned back by the charged layers of the upper air.
For the determined reader: the model, the data, and where it stops
The direct beam
T(λ) = exp( −m [ τR(λ) + NO3σ(λ) ] )
τR is the Rayleigh optical depth of the whole atmosphere at sea level, 0.008569 λ−4(1 + 0.0113 λ−2 + 0.00013 λ−4) with λ in micrometres: 0.097 at 550 nm, 1.21 at 300 nm. NO3 is the ozone column, 2.6867 × 1016 molecules cm−2 per Dobson unit. σ(λ) is ozone’s absorption cross-section, measured by Serdyuchenko and colleagues (2014): 1.12 × 10−17 cm2 at 255 nm, 3.9 × 10−19 at 300 nm. The air mass m is the path through the atmosphere relative to the path straight up, from Kasten and Young’s formula, which allows for the curvature of the Earth and the bending of light near the horizon.
| Wavelength | τ of 300 DU ozone | Through ozone alone, Sun overhead |
|---|---|---|
| 255 nm | ||
| 290 nm | ||
| 300 nm | ||
| 310 nm | ||
| 320 nm |
Sunburn weighting
The red tint uses the CIE erythemal action spectrum (McKinlay and Diffey, 1987): weight 1 up to 298 nm, 100.094(298−λ) to 328 nm, 100.015(140−λ) to 400 nm. The UV index you see in weather forecasts is this weighted irradiance, from the whole sky, multiplied by 40 m2 W−1.
Where this stops
Only the direct beam is modelled. The sky’s scattered light, which matters most in the ultraviolet and when the Sun is low, is left out, and so are clouds and haze. The cross-sections are measured at 20 °C, while stratospheric ozone is near −50 °C, where it absorbs a little less between 310 and 340 nm. The full-spectrum strip at the top of the chapter is a schematic of typical clear air at sea level: between 280 and 4000 nm it is drawn from the ASTM data, and elsewhere from textbook values. Real windows move with altitude, humidity, season and, for radio, with the Sun’s effect on the upper air from day to night.
The edge that moved
In 1879 the French physicist Alfred Cornu photographed the ultraviolet end of the Sun’s spectrum and found that it stopped abruptly, near 300 nm. Over the course of a day the edge moved: when the Sun was low, the spectrum ended sooner. The cut-off was not in the Sun. It was in the air, and it grew with the length of the path. Two years later Walter Hartley, measuring ozone in the laboratory, found that it absorbed exactly that part of the spectrum, and proposed that ozone in the upper air was the knife. In the 1910s and 1920s Charles Fabry and Henri Buisson, and then Gordon Dobson, measured how much ozone there is. The answer was a layer a few millimetres thick, and Dobson’s name became its unit.
The second window was found by someone looking for something else: in 1932, a telephone engineer chasing the static on transatlantic calls. That story is the next chapter.
Where this explanation stops
Two openings
Until the middle of the twentieth century, every picture anyone had of the universe came through two narrow openings in the air. The optical window gave us the stars and the planets, and everything in the first room of this exhibition. The radio window gave us the hiss of the galaxy. The rest of the sky, in X-rays, in the far infrared, in gamma rays, had to wait for balloons, rockets and satellites to carry instruments above the wall.
Clear air at sea level, Sun overhead. Brightness shows how much of the light reaches the ground.
We built our picture of the universe through two narrow openings in the air. What would the sky look like through all the others?
End of chapter 9
Added to your notebook
The air is open in two windows, light and radio. A few millimetres of ozone close the ultraviolet at about 300 nm, and the edge moves with the height of the Sun.
Who found the second window, and what was hissing in it?
Chapter 10 · The Size of a Dish