DPS Theory

June 20, 2008

Thermodynamics for Climate Change Denialists

Filed under: Math, Politics, Science — Peter @ 7:00 pm

Let’s take a look at the latest ideas in global warming denialism (with a screencap, in case the original source ever gets embarrassed by this). It goes something like this:

Greenhouse gasses can’t increase the temperature of the Earth: they don’t add heat to the climate (causing global warming), they just trap what heat is already there, slowing down any cooling. Those are two different things.

It’s a nonsense argument, so trying to really understand it is impossible, but I think that’s a decent approximation. My first reaction was similar to PZ’s, that it’s true as far as it goes, but omits the effects of any external source of heat.* But really, it’s not even true if you forget about the sun (but remember anything else about the climate). If you slow the cooling of the Earth at evenings and during the transition from summer into winter, you will increase the average temperature of the Earth without increasing the maximum temperature of the Earth. Therefore, the globe will warm.

But let’s see what happens when we don’t forget that big hot yellow Sun that’s heating us up. Generally, as you pour more energy (sunlight, and to a much lesser extent these days geothermal energy) into a system, the system heats up, temperature rising. As the temperature rises, the body (the planet Earth) emits radiation, shedding heat into its surroundings (in the case of the Earth, the radiation is primarily infrared, although atmosphere evaporating into space would count, too). The rate that heat is radiated off is proportional to the temperature of the Earth. The rate that heat is trapped is proportional to the reflectance r (albedo) or absorbance A = 1- r of the object, as well as surface area, and maybe some other things that will be constant here. The temperature T equation looks like this:

CdT/dt = AP0 – kBT

with C the heat capacity, heat per unit temperature, of the Earth, P0 = the (constant) rate of energy flow into the system, from the sun (Isun•σ), geothermal sources, cosmic rays, whatever, and kB the constant describing the rate of heat loss per unit temperature due to radiation (and other sources, such as evaporating atmosphere or maybe chemical reactions, which are mostly constant-”conduction” and “convection” wouldn’t really apply to the planet Earth as a whole). Roughly speaking, to determine the temperature of the Earth, you solve this equation for dT/dt = 0, the thermal equilibrium condition where heat flow in is equal to heat flow out. Increasing the absorbance of the Earth by increasing greenhouse gas concentrations increases the equilibrium temperature, which we’ll interpret as an increase in extreme temperatures of the climate, as well as increased average temperature.

Of course, the fine details of weather and climate are MUCH MUCH MUCH more complicated than this–but they’re much more complicated that you’d expect to see on a children’s climate website, too, and they’re more complicated than Kate and Hans Schreuder seem to realize, too.

*It’s amazing to me that they have made fundamentally the same mistake that some people make when they claim that evolution violates the 2nd law of thermodynamics, i. e. they forget that there is a Sun.

Alright, here goes: the atmosphere looks like a thin film, with light shining down, with no transmission through the surface of the earth, some absorption, some reflection; some of the reflected sunlight is reflected by greenhouse gases back to the Earth’s surface, and either absorbed or re-reflected back to the atmosphere to be re-re-reflected, and so on. With each reflection back to the surface, a bit more gets absorbed; each reflection back to the atmosphere a little more gets back out to space; and also, there is a bit perpetually trapped reflecting back and forth between surface and atmosphere (which helps keep us from dropping to near 0 kelvins at nights). Turn the Sun off, and that trapped bit will decay exponentially, but the Sun isn’t going anywhere anytime soon.

Chemical reactions and some other things are technically additional degrees of freedom, and change the heat capacity C of the system. More chemical reactions, for example, would slow down temperature rise, but not necessarily the rate of heat gain or loss.

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