Without Delay

In reel-to-reel tape decks, there is a record head and a play head and they are separated by a small gap. The play head comes after the record head, and the record and playback circuitry are separate, so it's possible to monitor a tape recording more or less as its being recorded, albeit with a small delay.

The small delay was often used to produce an "echo effect" on recordings and in the studio. For the echo effect, the tape output was mixed with the line in and patched back into the tape input. Depending on the tape speed, the echo delay could be controlled, and the gain between output and input controlled the echo strength. A gain of greater than 1 produced the "infinite echo" that rapidly became a sound pulsation with its frequency centered at the maximum frequency response of the system.

One practical joke that was often played at radio stations was to hook up a tape deck to generate a delay, then feed the announcer's voice back to him with a fraction of a second delay. I was once trying to get an echo effect on my voice and I found that I'd practical joked myself; I had to remove my headphones in order to continue. The delay makes it almost impossible to speak. It's hard to explain why, but the experience is compelling.

In a course, Voice and Image Processing, that I took at RPI there was a similar demonstration with video. A ball was placed behind a small barrier, and a video camera showed the ball on a TV screen. Normally, you could just watch the monitor and reach behind the wall to pick up the ball. But with a half-second time delay, such a seemingly ordinary task became almost impossible. You soon found yourself reaching for the ball, overshooting, then overcorrecting, then overshooting, etc.

Such a thing is called a 'limit cycle' in systems control theory, but it's pretty eerie to be a part of a limit cycle and unable to break out of it. Eventually, you just stop moving entirely, then veeeeerrrrrrrryyyyyy slowly move your hand to get the ball. It could literally take 30 seconds or more to do that simple task.

There's a bunch of mathematics in systems theory that deals with time delay and "controllability." The upshot is that if you add enough time delay into a control system, it becomes uncontrollable. Your ability to affect events is slower than those events. Imagine trying to pick up the ball behind the wall if it is moving erratically.

One of my favorite jokes is about the economics professor walking through the Quad with his students. One of his students says, 'Look, there's a ten dollar bill on the ground.' The professor replies, 'Can't be. If it were, someone would have picked it up already.'

For a long time, economics was dominated by what are called "equilibrium calculations," models of an economy under steady state conditions, no shortages, prices in equilibrium, all the usual assumptions. Those are the simplest conditions to model and to easy calculate, so they were the first results. Evolutionary biology tended toward the same simplifications, for the same reasons. The advent of the computer, and the growing access to massive amounts of computing power changed the landscape, but it took a while for theoretical models to catch up to the improved tools. In fact, the catch-up is still going on.

I had lunch with a colleague a while ago, and he asked my opinion about global warming/climate change/greenhouse gases. I told him that it was pretty obvious that the signal was out of the noise, the whole process was clearly underway, and was he surprised at this answer? He noted my well-known contrarian streak. I observed that James Hansen hadn't made a wrong prediction since 1988, and I wasn't going to challenge that sort of success.

In truth, I was a little late to the global warming party, partly because of that contrarian streak, but also because I was focusing on the science and not the policy. I was also perhaps yielding too much to my own libertarian leanings. So let's review why I should have been convinced sooner than I was, at least on the policy issues.

From the standpoint of political philosophy, one fact should be paramount: if we do not have a right to the air we breathe, then human rights, including property rights, are meaningless. And that should include the right to have that air remain unaltered. You shouldn't have to prove that harm is being done to you, any more than you should have to prove that people are harming you in order to not want a stream of trespassers walking across your lawn.

Now any given individual has no real impact on the contents of the entire atmosphere, although it's certainly possible for an individual to affect your current breathable air, and you generally have recourse. If someone smokes in your house and you don't like it, you can throw them out. If the neighbor's barbecue is noxious, you can usually complain to some agency, and I, for one, do not consider that to be an infringement on your neighbor's rights, though your neighbor may disagree.

But group behavior can, and does, affect urban, regional, and global resources. The industrial world's propensity for fossil fuels has had an undeniable effect on the concentration of some important trace gases in the atmosphere. Regulating group behavior is not the same as regulating individual behavior. Regulating corporations or national economies is not the same as regulating individuals, and giving free license to groups and organizations reduces individual freedom.

In the case of global climate change, regulating group behavior is essential. Actually, of course, group behavior is regulated. It just happens that it is regulated by those who rule, manage, control, and lead those organizations, the corporate boards, the CEOs, the congresses, presidents, agency heads, judges, and lawyers whose fingers are entwined with the strings of authority.

But authority and control are meaningless if the system is uncontrollable. The global climate system takes decades, if not centuries to equilibrate to any given greenhouse gas level. Glaciers take even longer to melt or rebuild. And the human political process likewise has major delays built into it.

There is a thin straw to clutch at, called feedforward in control theory. Using feedforward, you attempt to compensate for feedback delays by anticipating the system response. But feedforward control is seriously limited by your understanding of the underlying system. Without that understanding, feedforward is useless.

In regulatory policy, science is the feedforward control signal. Science, however, is currently under political attack from numerous quarters. And big money is being spent to target climate research in one part of that attack.

We're going to lose south Florida, and, my colleague suggests, most of Louisiana and Mississippi. California will acquire a new inland sea. Much of Bangladesh will vanish, as will plenty of islands in the Pacific and Indian Oceans. The fact that these things are going to happen long after you and I are dead does not make the future more palatable. It makes it more inevitable.

Meanwhile...

Meanwhile, deep in the heart of the Ural Mountains, the secret Great Communist Conspiracy powers up their iinsidious Tesla Coil to send another burst of Dark Chaos at the heart of the One Nation Under God. The conspirators had already achieved their first purpose, of lulling the Western Powers into believing that Communism was dead, by pretending to relinquish control over the vast Soviet Empire. But the wiley Commies were never interested in mere empire; they required world domination. So they banked their fires in Mother Russia, and intensified their efforts to put across the Greatest Hoax of All: the Global Warming Conspiracy.

Now their plans were accelerating. Dark Prince Gore, having failed to acquire the job of President of the U.S. (only the heroic efforts of the Godly men--and woman--of the Supreme Court had managed to thwart that scheme!), forged a new alliance with Soros, that Elder of Zion, first to create a propaganda masterpiece of a movie, and then, through their Swedish dupes to steal a Nobel Prize.

Now the Tesla Coil was turned to the task of igniting fires on the West Coast of the United States. Significantly, the surreptitious heat ray was aimed at parts of the State of California that understood that the Communist Conspiracy was not dead, that its goal was to wreck the U.S. economy by a combination of air quality regulations and socialized medicine, because once those were under its insidious control, the Nation itself would soon fall....

A Brief Primer on Global Warming

Global warming skeptics hide behind the notion that the effects of greenhouse gases are “very complicated,” which is true, but that shouldn’t stop anyone from knowing the easy parts.

The first easy part has to do what’s called radiative equilibrium, which may be expressed with a Firesign Theater reference to Teslacles’ Deviant to Fudd’s Law: “It goes in; it must come out.” In other words, the energy input to the Earth from the Sun must be re-radiated, otherwise the Earth would continue getting hotter without bound, and that would violate the Second Law of Thermodynamics.

In fact, the Earth, along with most other planets, radiates slightly more energy than it gets from the Sun, because the Earth has a natural, internal heat source, caused by radioactive decay. But that’s a small correction for the Earth (Jupiter’s excess heat is much greater, but Jupiter has more than just radioactive sources for its internal heat source).

Now the first thing that happens to light hitting a planet is that some of it gets reflected immediately. That’s called albedo, and it’s not a small effect. The albedo of the Earth is about 37%, which is pretty high compared to the other inner planets. Only Venus, at 65% is higher, whereas Mercury’s reflectivity is only 11%, the Moon’s is 12% and Mars’ 15%. These are averages, of course, although Venus is pretty uniform, because of the constant clouds.

The Gas Giants (Jupiter, Saturn, etc.) hover around 50%; some icy moon’s (I’m looking at you, Enceladus!) have very high albedos, despite not having atmospheres.

But it’s atmospheres that boost albedo, no real surprise there, because molecular scattering of light by gases (Raleigh scattering) is pretty efficient. Then there are those spiffy sulfuric acid droplets in the atmosphere of Venus.

Venus is particularly instructive, because its atmosphere is both thick and reflective. The result is that, by one measure, the place is surprisingly cool. That measure is the temperature at 55 km above the surface, where you have about one-half Earth’s atmospheric pressure and a temperature of a balmy 80 F. Up the O2 in your air supply a bit, and you could live there quite comfortably (in my story “Aphrodite’s Children,” I have it a bit cooler, owing to a reduction in the planetary greenhouse, but that just means that people can live further down). If Venus had a lower albedo, you wouldn’t be able to do that, because even at that height it would have to be much hotter to get rid of all the absorbed sunlight.

But the surface of Venus is hundreds of degree hotter, because increasing pressure heats things up. This is called the adiabatic lapse rate, and it’s a simple consequence of Boyle’s Law. Put some more pressure on a quantity of gas and its volume gets smaller, and its temperature increases.

So what does this have to do with the Earth’s greenhouse effect?

Well, first, Earth’s atmosphere is mostly transparent. Oxygen photodissociates in the hard ultraviolet (below about 280 nm, as I recall), and ozone is produced in the upper atmosphere. Ozone, in turn, absorbs certain wavelengths of infrared, so the stratosphere warms, and because there’s a lot of ozone in the stratosphere, it’s warm enough to stratify, i.e. form a thermal inversion.

Other gases absorb some IR, most notably water vapor. Water vapor is mostly confined to the lower atmosphere, because it gets colder as you go up (adiabatic lapse rate/Boyle’s law again), and the water rains and freezes out.

The Sun puts out a fair approximation of black body radiation, and at the temperature at the surface of the Sun, most of the energy is in the visible and near IR region. So the atmosphere is mostly transparent to sunlight. Some of it does get scattered (“Why is the sky blue, Daddy?”) and that has a lot to do with the Earth’s relatively high albedo. And some gets reflected away by clouds, more on that in a bit.

Most sunlight reaches the surface of the Earth, and most of it is absorbed. So the surface warms. Then what?

The surface of the Earth only gets up to, at most, a bit over three hundred Kelvin; a hundred degrees F is mighty hot for an Earth surface temperature, and most of the surface is way below that. At those temperatures, the radiation emitted is in the microwave, very long IR region. A lot of gases have absorption bands in that region; these are the so-called “greenhouse gases,” water vapor, CO2, methane, ozone, etc.

So when the Earth emits radiation, a good bit of it is absorbed by the air above it.

Also, and this is very important, air is warmed by contact with the Earth. So again, air near the ground gets warmed by the Earth.

Warm air rises, and as it rises, it cools. Eventually, it reaches the same temperature as the air whose level it has risen to. But there are some things that interfere with the idea of a “dry adiabat,” as it’s called. For one thing, the air probably contains some water vapor. As the air cools, it loses the capacity to hold water, and so you get water or ice formation (and precipitation). The condensation of the water vapor emits heat, so the air gets some extra “oomph” as it rises.

Then there is the matter of the air continuing to emit thermal radiation. The atmosphere is transparent to some of the bands in the radiation that the air is emitting, so that energy escapes rapidly into space. That cools the air more quickly than you would expect. Eventually, the cooling air begins to descend; usually it has moved toward higher latitudes when it does this, because of the large scale circulation patterns in the atmosphere.

If you add more greenhouse gases to the atmosphere, that radiative cooling phenomenon that I just mentioned happens at a higher altitude than if the GHGs weren’t there. The “optical thickness” of the atmosphere is greater to IR, so the rate of radiative loss is less at any given height. So the air stays warmer longer—and goes higher.

But Boyle’s Law still applies, and when the air begins to sink again, by the time it reaches the ground, it’s a bit warmer. That’s the “Greenhouse Effect” in a nutshell.

Now if that were all there was to it, estimates of global warming would be about half of what they currently are at. So current models of GW have a positive feedback term in them. That positive feedback term is water vapor. Warm air hold more water vapor.

Back in the 1980s, before the GW signal was really clear in the statistics, I thought that the water vapor effect was a loophole. In fact, I thought that increased water vapor would mean increased clouds, and that would result in a negative feedback term, so GW estimates might be high by as much as a factor of four.

Then came Pinatubo.

The eruption of Pinatubo put huge amounts of sulfuric acid droplets into the stratosphere, increasing Earth’s albedo by an easily measured amount. And the standard Global Climate Models just nailed the effect. The water vapor/clouds effect isn’t a long time constant effect. If it were a loophole, it would have shown up after Pinatubo. It didn’t; water vapor is a positive feedback effect, end of story.

Actual scientists (as opposed to political operatives, who are thick on the ground with corporate money from the carbon lobby) have been searching for negative feedback effects to offset GW for many years now. One was the notion that more water vapor meant increased precipitation at higher latitudes, more snow and ice, and that would have an effect on albedo. Nope, glaciers have been in retreat. Others think that added CO2 will cause greater plant growth, and this will somehow do something, but CO2 just keeps going up.

In fact, only about half of emitted CO2 stays in the atmosphere; most think the rest goes into the ocean. Heaven help us if that negative feedback loop goes positive.

And there have been some negative loops that have flipped. Sometime in the 1980s, the Arctic tundra went from being a net sink to a net source of greenhouse gases.

As things continue to heat up, the GW denialists are looking more and more like a faith-based initiative. The science just keeps looking more and more certain, while the denials get more and more strident. It’s already ugly. It’s going to get worse.