Diatribes of Jay

This is a blog of essays on public policy. It shuns ideology and applies facts, logic and math to economic, social and political problems. It has a subject-matter index, a list of recent posts, and permalinks at the ends of posts. Comments are moderated and may take time to appear. Note: Profile updated 4/7/12

15 March 2013

Positive Global-Warming Feedback

What is feedback?
Common examples of positive feedback
Positive feedback in global warming Conclusion
Coda: the President’s NEPA order

One of the most important scientific and engineering concepts that policymakers and the public must understand is feedback. That concept holds the key to our future as a species. Positive feedback, which leads to runaway instability, could destroy us. Negative feedback, whether natural or contrived, could save us.

What is feedback?

Simply defined, feedback is the property of any system to change its own behavior automatically, without human intervention. If the feedback is negative, the automatic changes tend to counter random or accidental ones and make the system stable. If the feedback is positive, small human-made or accidental changes can magnify themselves and make the system unstable. This can happen very quickly.

Examples of positive feedback in our mostly artificial world are relatively rare today. Why? Because the engineers who design our products and systems go to great pains to make sure that feedback is negative, so that systems stay stable and under our control. Nevertheless, there are still stark examples of positive feedback with which most of us are familiar.

Common examples of positive feedback

One of the most common examples of positive feedback is amplifier screech. It happens when you have a microphone connected to an amplifier and speakers. If you put the microphone too close to the speakers, any small sound gets amplified through the speakers, fed back into the microphone, and amplified again.

This is a classic case of positive feedback. It maxes out the sound system, producing a horrible, ear-splitting screech, which occurs instantaneously. The screech continues until the operator is smart enough to move the microphone away from the speakers, cut the amplifier’s volume, or kill the power.

Nowadays, clever solid-state circuitry reduces this sort of positive feedback by sensing amplifier overload and reducing the gain electronically and automatically. In other words, engineers have partially solved this problem with artificial circuitry that converts positive feedback into negative feedback.

Positive feedback is not limited to electronic systems. It can happen with mechanical systems, too. It happened to me when I was learning to drive.

In those days, there were no seat belts. Thinking me a bright boy, my mother decided to save money and teach me to drive herself. We took our big, heavy 1950s-vintage car onto a quiet residential street. After I conquered my initial fear, I started to drive the car too fast, and my mother told me to stop.

Being obedient, I hit the brakes quickly and a bit too hard. That car had good brakes, so it slowed down immediately. Without a seat belt, my body did not. The inertia of my body’s forward motion caused my foot to stomp even harder on the brakes than I had intended. The quick stop became a panic stop.

All this happened in an instant. The tires squealed. My torso hit the steering wheel, and my mother’s head hit the windshield. She decided that she was not such a good driving instructor after all, so she sent me to a commercial driving school. If I remember correctly, its cars had seat belts, even though they were not then required by law.

This was another example of positive feedback, and one of the many reasons for wearing seat belts. If we had been in traffic, my unintended panic stop might have caused a car behind me to hit mine, producing another kind of positive feedback—the kind that causes multi-car pile-ups in fog and rain.

Positive feedback can affect financial systems, too. The so-called Flash Crash of May 2010 was such an event. Apparently mistaken orders caused an instability in our automated electronic trading systems. Those systems had (and still have) multiple connected trading algorithms, each trying automatically to gain an advantage over the others. In mere milliseconds, the electronic market went into a tailspin. During the next hour, Dow dropped about a thousand points, and some stocks lost over 90% of their value.

That was a classic example of positive feedback, but the result was hardly positive. The screeching of traders and brokers was nearly as instantaneous as the screech from a runaway amplifier. What stopped the process from becoming a serious financial panic was the cutoff rules earlier established by regulators and the ability of regulators and market makers to unwind the bizarre transactions, slowly and carefully, after the fact.

Positive feedback in global warming

Now that we recall what positive feedback is—and how quickly it can cause disaster—we can explore the two big sources of positive feedback in global warming.

The first is the melting of our ice, including the polar ice caps and our glaciers. Melting ice feeds back positively to cause further global warming in two ways. First, ice is a big heat sink. It take a lot of energy (in the form of heat) to melt ice. When the ice has melted, the heat sink is gone, and warming accelerates. The other big cause of feedback is the release of methane, a greenhouse gas ten times more potent than carbon dioxide. Both the melting of permafrost and the breakdown of methane hydrates add to this effect. Let’s examine each of these causes of positive feedback in turn.

    Melting of ice
Readers who remember their high-school physics might recall two key numbers. The first is the definition of a calorie of energy. That’s the amount of heat it takes to raise the temperature of a cubic centimeter of water one degree Centigrade. At room temperature, a cubic centimeter of water masses one gram, also by definition. The Centigrade scale, as its name implies, divides the temperature “distance” between the melting point of ice and the boiling point of water (at normal atmospheric pressure) into 100 degrees.

The second number to remember is the melting heat of ice. The melting temperature of ice is 0 degrees Centigrade or 32 degrees Fahrenheit. But once ice is at that temperature, it takes 80 calories of energy to melt each gram (or cubic centimeter, which is the same thing), without raising its temperature at all. This quantity—80 calories—is called the latent heat of melting.

Together, what do these two facts mean? They mean that the same quantity of heat—of energy—needed to melt a gram of ice would raise the resulting water to 80 degrees Centigrade, i.e., four-fifths the way to boiling.

That’s why ice is such a great heat sink. It takes a lot of energy to melt it. But once it’s melted, the same quantity of energy that melted it raises its temperature nearly to boiling.

Fortunately for our species, the vast majority of water on our planet is liquid, not ice. If it were ice, and that ice all melted, we would self-extinguish as a species in about the same time after our planetary ice melted as global warming took to do the melting. No human can survive at 80 degrees Centigrade, and the century or so it would take our Earth to get there is far too short for evolution to make survival possible.

Even so, our ice caps and glaciers hold a lot of frozen water in the form of ice. After they melt, the same global warming that caused their melting will feed back into warming our oceans. The loss of ice’s great heat sink will cause positive feedback in global warming.

The second reason why melting ice causes positive feedback in global warming is reflection. Ice is white, smooth, and highly reflective. Water is blue, wavy and much less so. Soil and rock, with their various topographic guises and floral ground cover, are still less so. (Where there are plants, their photosynthetic green absorbs light.)

So ice reflects a far larger proportion of the Sun’s electromagnetic energy back into space than does water or land. When glaciers over land melt, the effect is even more pronounced, because land reflects even less than water.

Scientists call the reflectivity of a planet “albedo.” As our ice melts, the albedo of our planet decreases. More electromagnetic energy gets absorbed, and less gets reflected. The temperature of our planet goes up because it absorbs more energy from the Sun. All this is simple physics.

These two effects of melting ice—loss of our heat sink and decreased albedo—are noncontroversial and well known. What is not known is how quickly the positive global-warming feedback they cause will act.

The Earth is a very complex place. Its albedo will be highly variable geographically, even after the ice melts. We also don’t know whether the loss of our ice heat sink will affect global atmospheric temperature immediately, or only through a process of slow diffusion, from the polar regions to the rest of our planet.

Our atmospheric temperature is the result of incredibly complex processes of atmospheric diffusion, convection, water-vapor formation and transport, ocean currents, ocean layering and weather. Scientists are still trying hard to model the impossibly complex system with useful reliability and accuracy.

But what we do know is that ice melting is occurring faster than anyone predicted. In just the 34 years since reliable satellite measurements began, our summer Arctic sea ice has decreased nearly 30% in extent.

    Release of methane
The second cause of positive feedback in global warming is even more dangerous and less understood than melting ice. It’s methane release.

Methane is a so-called “greenhouse” gas. When released into our atmosphere, it causes global warming just like the carbon dioxide that we generate by burning fossil fuels.

But methane is a much more powerful greenhouse gas than carbon dioxide. Gram for gram and molecule or molecule, it causes ten times as much global warming as carbon dioxide.

Here is where positive feedback gets really scary. Our planet contains enormous amounts of natural methane, left over from the decay of ancient vegetation. Much of it is right near the surface, frozen in the “permafrost” of Arctic and Siberian tundra. As global warming melts the permafrost, it will release enormous quantities of this potent greenhouse gas into our atmosphere.

There is little we can do about this melting process. Global warming is already baked into our climate, a result of the carbon dioxide our industry has spewed into the atmosphere over two centuries. We can’t exactly cover Alaska, most of Canada and Siberia and (once its ice cap melts) Greenland with plastic sheeting.

As the permafrost melts, it will spew methane into our atmosphere in huge quantities. It will so do in years or decades, not centuries. And remember, each gram of methane has ten times the warming effect of the carbon dioxide that we know is causing warming now.

Because of the factor-of-ten increase in the greenhouse effect and the enormous quantity of methane trapped in frozen soil so near our planet’s surface, the effect of that soil’s melting is likely to be infinitely more rapid and destructive than the relatively slow increase of carbon dioxide from human industrialization. The release of methane frozen into our soil is the positive-feedback “wild card” that could literally decimate our global population.

And that’s not all. There is also an enormous amount of methane locked in methane hydrates under our seas. These compounds are basically methane held in a cage of frozen water molecules. Recently, they have been the subject of intense interest as an energy source, as Japan and India begin work to unlock the methane and use it as a fuel like natural gas (which is mostly methane and propane).

Unfortunately, methane hydrates are also a potent source of positive feedback in global warming. This is so for two reasons. First, global warming may release the methane in methane hydrates entirely apart from their commercial exploitation.

We don’t fully understand what keeps the methane locked in its cage of water molecules far below the oceans’ surface. Undoubtedly the massive pressures in deep seas are part of the answer. But temperature may be, too. As deep-ocean temperatures rise with global warming, it is possible that methane hydrates might release their methane into the atmosphere just as melting permafrost releases its raw methane.

The evidence we have suggests that rapid global warming as a result of methane release may have helped end the last Ice Age 15,000 years ago. Here is a summary of the key conclusions, taken from a report of a meeting at the Department of Energy on the subject of “Catastrophic Methane Hydrate Release Mitigation”:
[T]he example of a 1 GtC release . . . . represents 0.01% of the total methane hydrates in the ocean. The quantity degassed to the atmosphere 15,000 years ago, at the end of the last ice age is now believed to be around 4 GtC as methane or 0.04%. The average temperature of the Earth increased from 30°F to 60°F within a few decades. The radiative forcing from the methane alone would have been insufficient to cause more than a 3°F increase. It is thought that feedback effects from additional methane released from melting permafrost, carbon dioxide and water vapor contributed to the rest of the warming. But the initial methane hydrate release from the ocean may have been the catalyst.
In other words, the warming effect of a methane release from hydrates might have triggered further release of methane from melting permafrost. Together, the cascade of methane releases might have produced catastrophic acceleration of global warming through two kinds of positive feedback. The result: an increase in average temperatures of between 30 and 60 degrees Fahrenheit, or between 16.6 and 33 degrees Centigrade “within a few decades.” Our agriculture and civilization, let alone our coastal areas, would be unlikely to survive such a precipitous rise in global temperature in so short a time.

The second source of methane-related positive feedback is likely to be smaller but is almost certain to happen. As we humans exploit methane hydrates as a new energy source, we could accidentally release disastrous amounts of methane into the atmosphere.

If we could recover 100% of the methane from methane hydrates and burn it all, we would make a vast improvement over coal. In fact, we would cut our carbon dioxide emissions per unit of energy (from burning fossil fuels to generate electricity) by about 50%. At the same time, we would vastly reduce pollution, for burning methane produces none of the sulfur dioxide (acid rain), mercury pollution, or disease-causing particulate smog that burning coal does.

But unfortunately, we fallible human beings seldom do anything with 100% success. If we let just 5% of the methane from hydrates escape into the atmosphere in the process of mining or extracting them, we will nullify their global-warming advantage over coal. (Methane’s tenfold increase in greenhouse effect over carbon dioxide, multiplied by 5%, cancels the presumed 50% greenhouse advantage of burning pure methane over coal.) If we let as much as 15% of the methane escape, we will double the greenhouse effect of our energy operations, and thereby double the acceleration of global warming now, even with coal.

Here we run up against a basic law of economics and indeed nature generally. There is no such thing as a free lunch. Unless we do it with the 100% care for which our species is not generally noted, an energy “gold rush” toward methane hydrates could create a powerful additional positive feedback mechanism, massively accelerating global warming.


Positive feedback is inherently nonlinear and counterintuitive. “Common sense” simply does’t work with it. “Common sense” tells you—counterfactually—that amplifiers don’t screech unless you turn the volume control up too high. But if you put the microphone too close to the speakers, the screech will come anyway.

In order to understand positive feedback, let alone control it, you have to know and use math. That’s why we have scientists. (As a scientist/engineer, I once used this sort of math to design a negative feedback system for stabilizing the temperature of a small experimental apparatus.)

Positive feedback happens fast, and it happens hard. That’s why a screeching amplifier hurts your ears far more quickly than you can raise you hands to cover them. That’s why I hit the steering wheel and my mother’s head hit the windshield. That’s why securities regulators are still worried (and rightly so!) about another “flash crash,” which might create a real financial panic, just as did the sudden mortgage-backed-securities meltdown in 2008.

We don’t know enough about the detailed structure and the physics our of huge, complex planet now to make accurate predictions of positive feedback. But that’s precisely the point. Once positive feedback begins, tiny changes in our global climate system can drive it into catastrophic instability in impossibly short times. Those changes and that instability are difficult or impossible to predict reliably. They are impossible to stop. That’s the nature of nonlinear systems and nonlinear math.

So by the time it starts to happen, it will be far too late to stop. Already we have warning signals. The Arctic summer ice pack has dwindled by about 30% in 34 years. No one, not even the most fervent climate alarmists, expected that.

We still have the Antarctic ice pack, which is much bigger and melting more slowly. But Arctic and near-Arctic average temperatures are rising rapidly, far more than average temperatures in the rest of the globe. And there is little or no permafrost in the Southern Hemisphere, because our Antarctic continent is surrounded by a wide ocean.

All our frozen tundra is in the Northern Hemisphere, right near the Arctic, where rapidly rising temperatures threaten to release its methane from melting permafrost. This is a gigantic positive feedback loop waiting to go unstable.

There may not be much we can do now. After two centuries of burning fossil fuels, we’ve already baked in (pardon the expression) a certain amount of global warming. Atmospheric carbon dioxide takes decades or centuries to be net absorbed. It may be that all that methane is destined to erupt, and there’s nothing we can do to stop it. It would be ironic if, after barely avoiding species self-extinction by nuclear fire in 1962, we approached the same result by a slower and more “innocent” path in this century.

We have no way of taking carbon dioxide or methane out of our atmosphere. All we can do now is slow the acceleration of global warming and not make things much worse. Even doing that will take more understanding and political will, more universally held, that we have ever demonstrated as a species. But if we don’t act, our fate will be sealed. The Earth on which we evolved will change in a way that will make it much harder for our present, let alone future, population to survive. Positive feedback threatens to make that happen far more quickly than anyone now expects.

All is not yet lost, however. We can still act. During the 1960s, we became aware that atmospheric testing of nuclear weapons was poisoning our air and putting radioactive isotopes in our children’s milk. We managed to forge—and to obey—a treaty banning above-ground nuclear weapons testing. We did so at the height of the Cold War, when mutual distrust and suspicion had reached the level of paranoia. Maybe, with that positive example in mind, we can avoid the disaster of positive global-warming feedback.

That sort of feedback would be “positive” only in a mathematical sense. In its effect on our lives and longevity, “positive” global-warming feedback would be a catastrophe.

Footnote: The abbreviation “GtC” stands for “[metric] gigaton of carbon,” or a billion thousand kilograms of carbon. Since methane (CH4) consists of four hydrogen atoms and one carbon atom, and since the atomic-mass ratio of carbon to hydrogen is about 12, the corresponding mass of methane would be about 16/12, or a factor of 1.33, higher. The 33% difference between the two masses is inconsequential because of the approximate nature and huge magnitude of the numbers discussed.

Coda: The President’s NEPA Order

Once again, readers may consider me prescient. I’m posting the foregoing essay on the same day that President Obama is ordering federal agencies to use the Nixon-era National Environmental Policy Act (NEPA) to fight global warming.

But no, I’m neither an insider nor clairvoyant. I’ve been working on this essay for several days. News of the President’s action motivated me to publish it earlier than I had planned.

The President, of course, has much better information than I do. Unlike others, he does not engage in wishful thinking or kill messengers. He no doubt has been briefed about the threat of disastrous positive climate-change feedback since well before the election.

That’s why he mentioned energy and climate change so prominently in his second inaugural address. But he had to get re-elected before he could do anything about either. Now he is making good on his promise as a rational leader, using all the power at his disposal to do what he can.

NEPA doesn’t stop any project. By itself, it won’t even delay positive feedback, let alone stop it. All it does is require federal agencies to consider relevant information in making decisions on projects “significantly affecting the quality of the human environment[.]” By virtue of the President’s order, that information now must include likely effects on global warming, as well as local pollution.

Henceforth all federal agencies with power over projects that might accelerate positive climate-change feedback must consider that possibility in deciding whether to approve them. And if they don’t, NEPA will give injured parties a chance to ask the courts to require the agencies to take a second look. That’s the least we could and should do to avert potentially devastating climate surprises.



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