Conservation of energy

A few days after my latest post, John Robson hadn't responded, so I asked on Twitter whether I'd persuaded him that CO2 traps heat. He replied:

In a jar, sure. Have I persuaded you the climate is a lot more complicated than a jar?

I was hoping for a little more than that, but if John's willing to say that CO2 in a jar traps heat, I suppose that's progress. It's pretty simple: CO2 is transparent to visible light, but blocks thermal radiation. This is a physical property of CO2 as a gas. It doesn't matter whether it's in a jar or in the earth's atmosphere (or Venus's atmosphere, or wherever), it's going to behave the same way.

Okay, let's move on to climate. What do we know about the earth's climate?

Thermal radiation and equilibrium temperature

Like the other planets in our solar system, the earth receives a continuous flow of energy from the sun, as visible light. Why doesn't the earth just keep heating up until it's as hot as the sun? Fourier asked and answered this question back in 1824: a warm object emits invisible (infrared) thermal radiation. The planet emits thermal radiation into space which is equal to the incoming solar energy, so the planet neither warms up nor cools down.

What happens if the incoming solar energy increases? The key principle is that a warmer object emits more thermal radiation. The planet will gradually warm up until the outgoing radiation balances the incoming solar energy again. Conversely, if the incoming solar energy decreases, the planet will gradually cool down, and its outgoing radiation will decrease.

For a given level of solar energy, we can calculate the equilibrium temperature at which the incoming and outgoing energy will balance. An example calculation. The key factors in the calculation are:

  • The temperature of the sun.
  • The distance from the sun to the earth.
  • The size of the earth.
  • The reflectiveness of the earth's surface ("albedo").

Finally, there's the composition of the earth's atmosphere. Without the atmosphere, the earth would be much colder than it actually is. Because the earth's atmosphere blocks some of the outgoing thermal radiation, the temperature where the earth emits enough thermal radiation to balance the incoming solar energy is higher than with no atmosphere (by about 33 degrees Celsius, assuming the earth reflects 30% of incoming light).

If these factors (including atmospheric composition) are stable, then the average temperature of the earth must also be stable. Heat can be redistributed within the system (for example, the oceans can absorb heat or release it, as in El Nino years), but because of the law of conservation of energy, we know that the overall amount of energy in the system can't change.

Changes in the energy balance

What can cause the energy balance to change?

  • Variations in the sun's output. For example, astronomers have monitored sunspots for a long time, so we know that there was a period from about 1645 to 1715 when sunspots (correlated with solar output) were very rare; it's called the Maunder Minimum. This was also the middle of the Little Ice Age. Now we use satellites to measure solar output, and we can see that there's a variation of about 0.1% in solar energy over an 11-year cycle.

  • Very slow and regular variations in the amount of solar energy reaching the earth's surface due to variations in the earth's orbit ("Milankovitch cycles"), over tens of thousands of years.

  • Changes in the reflectiveness of the earth's surface, e.g. as glacial ice sheets grow or melt over long periods of time. As ice sheets grow, the earth reflects more light back into space instead of absorbing it, causing cooling.

  • Changes in the composition of the atmosphere, which blocks outgoing thermal radiation. Volcanic activity releases CO2 from molten rock, raising the equilibrium temperature. (Volcanic eruptions also cause short- term cooling by injecting sulfates into the air.) This is balanced by a very slow process called rock weathering, which takes place over millions of years and turns CO2 into limestone.

Over very long periods of time in the past, we can see that these factors have resulted in dramatic changes in the earth's climate; this is the field of paleoclimate, and it's a fascinating story. (If you're interested, Spencer Weart describes the major discoveries. Lectures from the University of Michigan summarizing what we know about paleoclimate.)

But over the next century or so, a geologically short period of time, we're not going to see sudden changes caused by variations in the sun's output, or by Milankovitch cycles, or by changes in the reflectiveness of the earth's surface, because these factors aren't changing rapidly.

Of course, what is changing rapidly is the composition of the atmosphere. We're currently digging up and burning fossil fuels, releasing huge quantities of CO2 into the atmosphere, exactly as if we were a super-volcano. Since 1750, we've released over 300 billion metric tons of carbon into the atmosphere, and we're still going. We know that CO2 blocks outgoing thermal radiation (traps heat), and therefore the earth's temperature must rise in order to emit more thermal radiation. Until it reaches equilibrium again, there will be more energy coming in than going out.

For a given increase in the level of CO2, what will the equilibrium temperature be? Skeptical Science summarizes the multiple lines of evidence:

Climate sensitivity [the change in equilibrium temperature resulting from doubling CO2, or equivalently from increasing solar energy by 3.7 watts per square metre] can be calculated empirically by comparing past temperature change to natural forcings at the time. Various periods of Earth's past have been examined in this manner and find broad agreement of a climate sensitivity of around 3°C.

How stable is the earth's climate?

John argues at length that the earth's climate is not stable, and can change abruptly and unpredictably:

I have never said the climate is stable. On the contrary, in writing about global warming over more than a decade I have insisted that the climate is so remarkably unstable that it cannot be mathematically modeled at all. It is, technically, "non-linear" and in an age committed to the proposition that linear algebra can explain everything from chemistry (mostly true) to economics (wildly false) we generally assume without reflection that it can also explain climate.

Not so. And it is not me, but the alarmists with their “hockey stick” that shows a very stable global temperature until the 20th century, who would have you believe everything was orderly and harmonious until human wrongdoing expelled us from a temperate Eden into a lake of fire.


... [The alarmists] cannot even explain what has caused dramatic swings in the Earth’s climate in the past when increasing CO2 concentrations appear to be an effect not a cause. Nor can they explain why in the past once CO2 levels had risen we did not get a "greenhouse" effect instead of warming trends suddenly and unpredictably reversing and resuming despite the alarmists’ models suggesting bleak stability.


... look again at his chart of temperature changes over the past 400,000 years. Notice the endless abrupt changes.

What makes him think we're not just in one of those now? Again, it is not science to suggest that although the Earth’s climate has witnessed an uncountable number of sudden drops or rises in temperature for natural reasons, the one we're now in, if we are, cannot be of that sort and must be an entirely new kind where CO2 is suddenly and unaccountably driver not passenger.

My response is simple: no matter what we know or don't know about past changes in the earth's climate (and we actually know quite a lot), we know for certain that the earth's climate cannot violate the law of conservation of energy! We know that CO2 traps heat, so we know that there's more solar energy coming in than thermal radiation going out, and therefore there's more energy being trapped in the system as a whole.

That's why scientists were able to predict back in the late 1980s that temperatures would rise. And that's also why scientists are so alarmed about our inaction on global warming. This tweet summarizes it perfectly:

I don't expect my argument to convince John that global warming is a real problem, but I'm interested in seeing how he reconciles the law of conservation of energy with his belief that the earth's climate is unstable and unpredictable. (No matter how unstable and unpredictable it is, it can't destroy incoming energy!) If he responds, I'll add a link to his reply.

Next: How do we deal with the collective action problem? (As I've said before, fossil fuels are awesome; if they weren't, it'd be a lot easier to stop using them.) And if the scientists really do know what they're talking about, how bad do they think it's going to get?