Why John Dodds is Wrong

(c) 2007 by Barton Paul Levenson

John Dodds has a web site:

Arrhenius is Wrong!

In this web site, Mr. Dodds claims that carbon dioxide, and greenhouse gases in general, do not contribute to global warming. In fact, he claims that there is no such thing as the greenhouse effect, and thus that Svante Arrhenius's classic global warming paper of 1896 was wrong. (He doesn't appear to know that the idea of the greenhouse effect was first discussed by Jean-Joseph Fourier in 1824 and explained more rigorously by John Tyndall in 1859-1863.) What appears to be the key part of his reasoning runs as follows:

...the sun adds energy to the earth and dictates the ground and air temperature, the amount of energy that must be emitted to space, and the fluctuations. The GHGs simply act as a transfer agent for most of this energy from ground to space. The added GHGs do NOT absorb any more energy than what the sun previously dictated, because there is NO extra energy available to be absorbed. What comes in from the sun, already goes out, under equilibrium conditions. The added GHGs do not retain any extra energy because molecular collisions will return the energy to the air and equalize the GHG temperature with the air temperature/energy, depending on the air density and Gas Law. Changing the GHG concentration, with the associated minimal change to the air density, has virtually no impact (actually miniscule cooling) on the air temperature. Hence, greenhouse gases cannot cause global warming because they do not add energy to the air.

There are a number of things wrong here. One is that Mr. Dodds is confusing energy with temperature. Of course greenhouse gases don't create energy out of nowhere, but they don't have to. All they have to do is redirect it a bit. That's how the greenhouse effect works.

I'll explain it in stages.

1. Sunlight mostly passes through the atmosphere (some is absorbed by gases and clouds, but we can ignore this for now) and heats the ground.

2. The ground, being heated, radiates energy. The mean global annual average temperature of the Earth being about 288 degrees K, the energy radiated is mostly in the infrared range.

3. Greenhouse gases in the atmosphere absorb some of this infrared and are heated up.

4. The greenhouse gases radiate infrared energy of their own.

5. Some of this energy goes back down to the ground, heating it above the temperature it would have from only sunlight.

Now, Mr. Dodds would have us believe that greenhouse gases in step four would somehow be violating conservation of energy by radiating infrared back down to the ground. In his view, thermal energy can only come from the sun. But this just isn't true. Any hot body will radiate, including a gas. Some will radiate more than others. Carbon dioxide, a greenhouse gas, will radiate quite a lot. Nitrogen, not a greenhouse gas, will radiate very little.

Let's focus on part of Mr. Dodds's reasoning:

The added GHGs do not retain any extra energy because molecular collisions will return the energy to the air and equalize the GHG temperature with the air temperature/energy, depending on the air density and Gas Law.

Very true! Most of the energy absorbed by greenhouse gases will be lost to collisions with other molecules. But here is where Mr. Dodd violates conservation of energy. He seems to think the energy so transferred is lost, so that the process of transfer can only "equalize the GHG temperature with the air temperature." No, Mr. Dodds, it will raise the air temperature. Those molecular collisions will speed up the molecules collided with, on average, as shown by the science of statistical mechanics. And heat in a material body is simply faster molecular motion. There is an equation relating the two:

T = M V² / 3 R

where T is the temperature, M the mass of 1 kilomole of the substance in question (equivalent to the molecular weight), V the root-mean-square velocity of the molecules, and R the universal gas constant, for which the NIST CODATA figure is 8314.472 joules per kelvin per kilomole. Here's a numerical example for nitrogen. Let us take

M = 28.0134 AMU (28.0134 kilograms per kilomole).

V = 500.0 meters per second.

R = 8314.472 J K^-1 kmol^-1

We can then compute T = 280.77 degrees K.

So when greenhouse gases absorb infrared photons and lose the energy through molecular collisions, the mass of air in the vicinity increases its root-mean-square velocity and its temperature goes up. Most of the air is nitrogen and oxygen, which don't radiate very well, but they will transfer their kinetic energy to greenhouse gases every so often, and the temperature of the layer of air will be radiated away by those greenhouse gases -- the higher the temperature, the more the radiation, usually to the tune of the fourth-power law of the Stefan-Boltzmann relation, as modified for a non-gray radiator.

In short, greenhouse gases heat the air when they absorb infrared from the ground, and the air radiates, and some of that radiation goes back to the ground, and the ground heats up further. It isn't a question of energy being created out of nowhere. The amount of energy the Earth-atmosphere system gains from the sun must always be roughly matched by the amount the Earth system radiates, at the top of the atmosphere. But the amount surging around in the Earth system is higher the more greenhouse gases you have in the atmosphere.

It's like a tub with a hole in it being filled from a faucet. If the amount coming in from the faucet matches the amount being lost through the hole, the system is in equilibrium and mass is conserved. But the amount of water in the tub can still vary. You can have a lot or a little, and as a result the tub's "wetness" can vary, even though mass is still being conserved. Thus with thermal energy in the Earth-atmosphere system. And that's why Mr. Dodds is wrong and Arrhenius is right.