Wednesday, September 24, 2008

An Explanation of Global Warming, Part I

During the last century, we averaged .07 degrees C warmer per decade (which lept to .13 degrees in the last 50 years). This is from the Intergovernmental Panel on Climate Change, 2007. Our concern should be that even a little bit of warming exacerbates the problem. This is because CO2 does not function in water the same way most molecules do. Most molecules are more soluble in warmer water, but CO2 is less soluble in warm water. This means that by even increasing the temperature a little bit, we are reducing the ability of our oceans to hold CO2. This creates a positive feedback situation with our atmosphere that begins a self-perpetuating cycle in which the C02 not absorbed by our oceans helps our atmosphere to trap more heat, which causes the oceans to be able to hold less C02, so on and sof orth. The figures atop this paragraph represent that little bit of warming that will catalyze an exponential increase in temperature in the troposphere (where we live).

For more on this, read here.

Here are the relevant graphs:

The consistent warming of the troposphere is a fact. Period.

So, how much are we contributing to this? First, see this graph.

That is how much we are augmenting the problem. Remember, even a little increase creates an exponential increase, and it's clear that such an increase is precisely what we have. We can cross reference the above research through a variety of methods such as examining the C02 inferred from polar ice cores.

They all point to the exact same conclusion. We can also measure the ppm (parts per million) of C02 in the atmosphere, and we have gone from a pre-industrial average of 280 ppm to 385 now (and this trend is continuing). The only way you could shrug this off is if that addition 105 average ppm didn't make a difference, which I've already established for you it does.

Now, onward to basic physics.

Blackbody radiation:

Suffice for now that a blackbody is a perfect radiator, and thus absorbs energy at all wavelengths and thus reflects none.

You'll also need to have an elementary understanding of Planck's Law, which deals with emission vs. wavelength at a particular temperature. There are several forms of this law, but the one most relevant here deals with wavelength in terms of microns (the reason will become apparent later).

I'll also be using the Wien Displacement Law (the 1st derivative of Planck's Law), which provides us with the peak emission for a specified temperature.

Lastly, you'll also need to be marginally familiar with the Stefan-Boltzman Law (the integral of Planck's Law), which gives us our total emission intensity for a specified temperature.

So, let's start with Solar Irradiance. The surface of the sun runs at about 5,780K - this all must get distributed to our planet somehow. We determine this by using Planck's Law:

(5.67 * 10^-8 Js^-1 m^-2 K^-4)(5,780K)^4
= 6.3 * 10^7 Js^-1 M^-2
= 63 MW per M^2

We can also find the peak wavelength we receive from the sun via the Wien Displacement Law:

Wavelength (in um [microns]) = 2,898um * K/5,780k = .501um = 501nm

These numbers will come in handy shortly. I'll take a moment to point out that it should be clear in this case that we cannot make science say whatever we want. Science points directly, and unequivocally, to very specific conclusions. I say this because I am composing this primarily as a response to somebody who asserted that we could, in fact, make science say whatever we want.

Now, the total amount of energy reaching our outer atmosphere is 1,370 Wm^2. From this, we derive two different figures.

1. The energy delivered to our cross section (pi * r^2)
2. Total amount dispersed over Earth's surface area (4 * pi * r^2)

The total of 1 divided by the total of 2 should give us the average energy reaching our outer atmosphere. This comes out to 342 Wm^2.

Now, go back to blackbody radiation - this is how the Earth works. If the Earth had no atmosphere, it would absorb 342 Wm^2. What temperature would this predict, that would radiate that same amount of power?

342W/m^2 = (5.67 * 10^-8 * w/m^2K^4)T^4
T = 279K or about 6 degrees celsius.

This is pretty damn cold, so something must be missing.

What's missing is the Earth's Albedo. This encompasses what solar irradiance gets reflected from things like clouds, ice caps, water bodies, light colored land, etc. For the Earth, our Albedo is about 30% of solar irradiance.

Figuring out how much energy reaches our surface is pretty easy after we have our Albedo. It's Solar irradiance * (1 - a), with "a" being our Albedo, which comes out to about 240 Wm^-2. So, to attain a stable temperature, we need to balance incoming energy with emitted energy. The 240 Wm-2 in, must be balanced by 240 Wm^-2 out via blackbody radiation of the Earth's surface.

We can use the Stefan-Boltzman Law to determine what surface temperature we would expect to find in this case.

T ={ [240 Wm^-2] / [5.67 * 10^-8 Wm^-2 * K^-4]}^-1/4 which comes out to be 255K (or -18 degrees C).

So, the 255K represents -18C, but we observe the average temperature of the Earth to be about 15C. This predicts 390Wm^-2. How can this be?

It's because about 150Wm^-2 never escapes back into space. It gets absorbed by the atmosphere and re-emitted to the surface. The primary variable in this is greenhouse gasses.

Before I go on, I'll stop to say that I hope you're getting a feel now for how science is not simply a matter of guesses. It is a very precise process of using what we know to wrest our circumstances from a mute nature.

Additionally, before we go forward, it's really not important that you understand any of this (or that I understand all of it which, allow me to assure you, I do not). All that is important is that the experts do understand it. They have dedicated their lives to this, and understand it better than anybody else on the planet. That is why they are in consensus, and it is the reason that people like John Coleman, non-scientists masquerading as experts, are not present in peer-review - their arguments would simply never survive it.

Part II will be coming shortly.


Anonymous said...

"CO2 is less soluble in warm water"
That explains why the historical graphs have the temperature rising BEFORE the CO2 levels go up.

JT Eberhard said...

The planet, as a result of a number of variables, goes through heating and warming cycles. Currently, we are warming faster than the normal cycle (and should be cooling).

What graphs are these? Link me and I'll take a peek at them.