Climate II

[Schneibster]

Time for another physics lesson.

I've gone over this in detail, but I may have been at too high a level for some folks here. Let's begin with light, because that's where the story starts.

Light from the Sun is all colors mixed together. This is because the Sun is a very good approximation of a blackbody. A blackbody is a theoretical abstraction, which nineteenth and twentieth century physicists invented to mathematically study the absorption and emission of energy. It is "black" because tests showed that black objects both absorb and emit heat the most efficiently. You mustn't think of it as ordinary black like black paint, certainly not gloss black; the perfect object would be flat black, of a blackness so complete you could not see a highlight on a sphere made of it in bright sunlight. You wouldn't be able to tell whether it was a circle or a sphere without walking around it to see its shape from all sides.

This is why the insides of thermoses are silvered. Thermoses also use another trick. Now, remember that this is the study of radiated energy; that is, we are talking about only one way that energy moves, radiation. We are not discussing conduction or convection. Those are the three ways energy moves: radiation, convection, and conduction. The thermos' other trick is to use a two-walled flask, with the space between the walls evacuated of all matter. This is called a "vacuum" and as a result thermoses are also called "vacuum flasks," and are used to keep hot things hot and cold things cold for extended periods, far longer than they would stay hot or cold otherwise.

So the perfect blackbody is not only an absolute black that absorbs all energy, but is also in space so that it cannot be affected by convection or conduction (both of which require direct contact with a gas or liquid).

Physicists were actually able to approximate a blackbody by making a furnace that had a very, very rough interior so that any light that went in would never make it back out, but would reflect within until it were absorbed. This seems like a trick of some sort, but it actually works, and in fact when the furnace is heated to various temperatures, not only its color, but much of its spectrum (and all of its visible spectrum, to a difference too small for nineteenth century science to measure) was eventually found to correspond to a true blackbody spectrum.

Now, one of the members of the British Royal Society, William Thompson, did foundational work in thermodynamics, including finding the value of absolute zero. For this he was knighted, and eventually raised to the peerage as Lord Kelvin. But at one pursuit he was stymied: explaining the spectrum of the blackbody. Remember, by this time they could measure it, approximately, and as the technology improved and they got alloys to make their furnaces out of that could take higher and higher temperatures, they found that the basic logic Kelvin had applied to try to calculate it in fact did not agree with the reality. And even Kelvin was never happy with it; Kelvin's logic insisted that the emission of any given frequency was a matter of pure chance, and thus (since there are exponentially more high frequencies than low) all the energy should be radiated away immediately at the highest available frequency, blinding irradiating and killing everyone in sight of it. Kelvin self-deprecatingly dubbed this obviously incredibly wrong result the "ultraviolet catastrophe." He never seriously maintained it.

It was therefore obvious to physicists that something made the emission of higher and higher frequencies less and less likely. Exponentially less likely, in fact, because the mere existence of so many more higher frequencies made it exponentially more likely, so whatever was quashing it must be even more powerful yet.

Planck, of course, resolved the dilemma of the "ultraviolet catastrophe." He did so by proposing the quantum. Planck says that light must always be emitted as quanta (the plural of quantum). The size of a quantum depends upon how much energy is emitted; given that, the wavelength and frequency are known, related to the energy by Planck's Constant. And the thing about quanta is, as long as there is enough energy to make one there is a nonzero chance it will be emitted; and this chance increases with time. So here is the explanation: almost all quanta emitted haven't time to build up enough energy to amount to a really high frequency; they're emitted with a lot less energy because the temperature isn't hot enough for them to build enough before the molecules that contain them emit them. Thus, the higher the frequency the more unlikely a quantum is to be created with it, and precisely enough to offset the "ultraviolet catastrophe" and result in the observed spectra of blackbodies.

Next, I'll show that quanta are absorbed as whole quanta by materials, just as they are emitted by them. This will prove that this model of the emission and absorption of energy is not merely an abstraction but a good description of reality.

[Schneibster]

There will be another physics lesson tomorrow; this one will concern how materials absorb these brand-new "quanta" Planck had proposed.

Teaser: Einstein won the Nobel Prize for this, not for Relativity. And it's especially ironic that... but read tomorrow.

[Schneibster]

So now we have Max Planck's Quantum Theory. But so far, it's only been used to explain emission, not absorption. Most physicists are treating it as a rule of thumb; it appears to work in some circumstances but they've no notion it describes the real state of affairs; they're still using the same old absorption equations they were, it's only emission they're using Planck's new theory for.

Basically, the idea is, molecules in a heated object become more likely to emit radiation the more they are heated. They spontaneously dissipate their energy whenever they can. However, when they emit radiation, they emit it as individual quanta; and the amount of energy they were able to accumulate before the spontaneous emission determines the size of the quantum they emit. The more energy there is around, the more energy they're likely to accumulate before spontaneous emission occurs. In other words, the hotter an object, the brighter and higher frequency its radiation is. This eliminates the "ultraviolet catastrophe" by making higher and higher frequencies less and less likely to be emitted. Yet, as the temperature of the radiator rises, the peak of its radiation goes up and up; just not exponentially like the naive probability based on the number of frequencies available predicts.

Enter Albert Einstein. Albert was having a great year. In this year, 1905, he would publish three scientific papers, all the work of genius, and two of which arguably form the basis of modern physics: Special Relativity, and the theory I am about to speak of: the photoelectric effect. The third one explained Brownian motion, and arguably proved the atomic theory by direct observation. These three monuments of science have firmly established Albert as one of the greatest physicists who has ever lived, with Newton and Galileo and Archimedes and Leonardo.

This particular little puzzle was first discovered by Heinrich Hertz, who noted that sparks were far more easily drawn, and capable of leaping much farther, if all the metal were doused with ultraviolet light. We're talking about what the '60s drug culture called "black lights." Most folks these days have seen them as pet urine detectors, or used in police-procedural forensics thrillers on TV. Hertz experimented with variations, of course, like all curious physicists do, and discovered that there were some very curious properties involved.

Most importantly, by increasing the intensity of the UV light, Hertz was able to increase the size of the spark, but he could not increase the distance over which it would strike. So the intensity of the light could increase the amount of electric fluid that moved, but couldn't increase its electromotive force, or the urgency with which it desired to cross a gap. But when he began to vary the frequency of the light rather than its intensity, he found that the higher the frequency, the longer the spark would strike, even if the UV light intensity was low so the spark was small.

This was discovered in the late 1880s, in between Maxwell's theory of electromagnetics and Planck's quantum theory. When the quantum theory came, many physicists tried to reconcile it with Hertz' observations, and many replicated his experiments, but none could explain it until Einstein.

Einstein pointed out that if Planck were correct then energy could only be absorbed as whole quanta. The quanta of higher frequency were more energetic; thus, the electrons they knocked out of the metals could strike farther, having greater energy. Now electrical theorists had a definition for voltage: it was the average energy of electrons' charges, just as kinetic energy was for their momentum. But that wasn't all. The intensity, no matter how high, couldn't make higher energy electrons, therefore of a higher voltage; it could only make more electrons which would make a higher current.

For this theoretical work, Albert received his only Nobel Prize in Physics.

[Schneibster]

Tomorrow I will explain why this quantum theory implies global warming.

[Schneibster]

So now, we've established that energy is both absorbed and emitted as quanta.

And furthermore, we've established that the electromagnetic spectrum extends as a single entity all the way from radio waves hundreds of thousands of kilometers long, to gamma rays smaller than a micron. They're all the same thing, they're all the same kind of quanta, so physicists decided to call them "photons," that is "ones of light."

Now to us, these types of radiation appear enormously different. The ones lower than infrared we cannot detect without special equipment; and also the ones above ultraviolet, though they will kill us if we get too much. Ultraviolet gives us sunburn; infrared will burn us if we get too much, and it's less than the amount of light that will; infrared is more efficient, but visible light will still do it too, if it's bright enough. In between them is the narrow spectrum of visible light. This is only a very small portion, barely an octave, of the electromagnetic spectrum; but it is where all the Sun's energy is concentrated. That's why our eyes evolved to be most sensitive around this radiation peak in the green.

So over the entire sunlit half of the Earth, solar radiation is constantly being absorbed. It's really important to understand that absorbing radiation of no matter what wavelength is absorbing energy; and eventually absorbed energy becomes mechanical heat, that is, an increase in the average velocity, and therefore the average kinetic energy, of the atoms and molecules making up a substance. And when I say eventually I mean within a few milliseconds; this is a very long time on the quantum scale.

Once the substance of the Earth has increased in its average kinetic energy, it also radiates; but its radiation is governed by its temperature, not that of the Sun. The Sun no longer has anything to do with it; its energy has been absorbed and randomized and turned from photons into mechanical vibrations. Only the Earth's temperature matters any more to what happens to the heat.

We have already discussed that a blackbody of a given temperature has a radiation peak related to that temperature by Planck's equation. And the higher the temperature, the higher the peak. What does the graph of these peaks, against various types of stars, look like?

Well, stars are graded by their surface temperature into spectral classes. These classes are established based on the stars' spectral peaks, as described above. Our Sun is near the middle of these, and not as a mere arbitrary choice; it actually is of middle temperature and spectral class, class G0. The G is the wide class, and the 0 is the top of that class. 9 is the bottom. The wide classes are

(W) O B A F G K M (R N) S (I)

where the ones in parentheses are disputed.

In addition, stars are classified by their absolute magnitude, that is, the magnitude they would present at ten parsecs. These two characteristics are plotted against one another, and form the "Hertzsprung-Russell," or "HR" diagram that is characteristic of all stars even in remote galaxies. There are exceptions, called "giants" the most common of which are "red," and "dwarfs" the most common of which are "white," but most stars appear somewhere on the "main sequence," in which stars of higher spectral class generally have higher absolute magnitudes. Big Os and Bs are short-lived, bright, extremely active stars, lasting less than a billion years and exploding with extraordinary violence; tiny Ms may live for tens or even hundreds of billions of years, slowly guttering down into quiescent darkness.

There are no M stars close enough to be within direct human vision; the closest is Wolf-396, which can be seen with a decent 8" telescope. It's deep red and visible in Leo on summer nights in the Northern Hemisphere.

Most stars fall along a curve shaped like an "S" on its side, called the "main sequence," and of those, most fall in the center of the "S" in the AFGK section. As make too much ultraviolet for life like ours; but we can expect to find life around Fs Gs and Ks, in the liquid water zone, on rocky planets. A recent survey has estimated that there are over a billion planets in the liquid water zones of F, G, and K stars, in the Milky Way. Remembering that life is spontaneous, we can expect nearly half of these to support oxygen-breathing, carbon-based, water-using life like ours. How much of it is smart remains to be seen.

In any case, here we are in the middle of the HR diagram, with a nice stable star that can be expected to be quiet for a few billion years.

Its spectrum peaks at the frequency associated with 5600K, which is why photographers recognize that setting on their cameras. (5400K is the temperature of diffused sunlight, because of the color temperature of the sky, which dissipates some of the blue, cooling the Sun's color temperature.) This light is between 350nm, or 0.350 µm, and 750nm. Meanwhile, the Earth's color temperature is deep in the infrared, at nearly 10µm, far below the ability of human eyes to see.

Climate deniers therefore look in the "transparent" sky and say, how can the heat not get out if it came in?

And the answer is, at the Earth's temperature the sky is not transparent. But it is at the Sun's. So the Sun's energy gets through, but the Earth's doesn't.

[Schneibster]

And what's the primary obscuring agent?

Well, it's CO2.

A not uncommon gas among the solar nebulae of forming G-class stars, along with water, ammonia, and methane.

But see the thing is it's only obscuring at Earth's temperature, not at the Sun's. So the heat keeps coming in, but more and more can't get out.

That's global warming.

It will happen anytime the heat coming from the Sun exceeds the heat escaping from the Earth. Which is precisely what satellites measure happening.

[Schneibster]

If you want to see really bad global warming look at Venus.

Luckily, we're farther from the Sun than that, and we have less CO2 than that. We could never have our global warming run away like that.

But that's not to say there's not a lot of room for us to have a lot more global warming than we have now without running away. And it's happened before when animal life was too profligate, near the end of the Cambrian. Two of the largest extinctions ever occurred then, almost certainly due to extreme CO2 poisoning; the Edicaran and Botomian Extinctions. The only larger is the Great Dying at the end of the Permian/beginning of the Triassic.

[Schneibster]

So the point of all this is,

energy can come and go at different frequencies; but which ones it comes and goes at are dictated by temperature, and radiation peaks.

Heat can manifest either as radiation, or as molecular kinetic energy. Where the boundary is depends on the temperature, which governs the peak frequency.

All heat not absorbed is reflected; and measured as output.

Therefore, either heat absorbed == heat emitted, or the object is getting hotter (heat absorbed > heat emitted) or cooler (heat emitted > heat absorbed).

Satellites can measure heat absorbed from the Sun per square meter and thus the total heat absorbed by Earth can be calculated without question.

Satellites can measure heat emitted by the Earth per square meter and thus the total heat emitted by Earth can be calculated without question.

When these things are done the amount absorbed is greater than the amount emitted, and the ground measurement of the temperature change, along with the latest measurement of the increase of heat in the middle depths of the ocean, accounts for the difference.

Consilience, you see. The ground measurements confirm the sea measurements confirm the satellite measurements. It's really quite straightforward. Denying it is really quite stupid.

[Schneibster]

Was doing a bit of research on a post on another site and came across this; it's a pretty good aggregation of the available satellite data into a continuous record of the solar constant since the late 1970s.



I'll keep it handy for after I fetch the graph of satellite measurements of the temperatures at the radiating top of the atmosphere.

[Stubby]

The current Arctic ice data is mainly from satellite observation dating from 1979.
An arctic researcher has discovered a way to reach further back in to time (646 years) by checking growth rings in crystalline algae.

This is a work in progress by so far but their findings this far were published last week in PNAS.

http://www.pnas.org/content/early/2013/ ... 966e41e7b8

Abstract

Northern Hemisphere sea ice has been declining sharply over the past decades and 2012 exhibited the lowest Arctic summer sea-ice cover in historic times. Whereas ongoing changes are closely monitored through satellite observations, we have only limited data of past Arctic sea-ice cover derived from short historical records, indirect terrestrial proxies, and low-resolution marine sediment cores. A multicentury time series from extremely long-lived annual increment-forming crustose coralline algal buildups now provides the first high-resolution in situ marine proxy for sea-ice cover. Growth and Mg/Ca ratios of these Arctic-wide occurring calcified algae are sensitive to changes in both temperature and solar radiation. Growth sharply declines with increasing sea-ice blockage of light from the benthic algal habitat. The 646-y multisite record from the Canadian Arctic indicates that during the Little Ice Age, sea ice was extensive but highly variable on subdecadal time scales and coincided with an expansion of ice-dependent Thule/Labrador Inuit sea mammal hunters in the region. The past 150 y instead have been characterized by sea ice exhibiting multidecadal variability with a long-term decline distinctly steeper than at any time since the 14th century.

My emphasis. Will be interesting to see if other N/S transects show the same results.