Sunday, March 1, 2009

Physics of Global Warming

The temperature of the earth is governed by physics, namely the Stefan-Boltzmann law which states that the amount of energy radiated is proportional to the fourth power of its temperature.

ERad = SB * Temp^4.

Or Temp = (ERad/SB)^0.25

ERad is the amount of energy radiated to outer space in watts/meter^2
SB is the Stefan-Boltzmann constant is 5.670 x 10-8 Watt/meter^2 Kelvin^2
Temp is the absolute temperature (kelvin) at which the radiation is emitted.

For Earth at equilibrium, the amount of energy radiated should equal the amount of energy received from the sun. However, the Earth is not at equilibrium and is actually receiving slightly more energy that it is emitting. This is why the earth is warming. If the earth were in equilibrium, then the amount of energy being radiated would equal the amount received from the sun. That is ERad would be a constant and a function of average Total Solar Irradiance (TSI) and albedo (a).

ERad = TSI*(1- a)/4

TSI is 1365.5 Watts/meter^2
a is albedo which is 0.3 for Earth

So, ERad is approximately 237 Watts/meter^2.

Putting this altogether yields an Earth Temperature of 254°K (-18°C or -1°F). This temperature corresponds to the atmospheres temperature at about 5 kilometers above the surface (16,000ft). It is at this elevation where the earth's atmosphere can radiate to outer space approximately the same amount of energy it receives from the sun. Temperatures at lower elevations are generally much warmer due to the greenhouse effect, which makes it difficult for the atmosphere to radiate infrared energy at lower elevations.

Greenhouse gases inhibit radiation to such an extent, that convection of heat is the dominate mechanism for transporting energy from the surface to elevations where it can be effectively radiated to outer space. The earth radiates primarly in the infrared which is the predominate wavelength at 254°K and nfrared is invisible to humans.

If there were no greenhouse gases, then earths surface temperature would become so cold that the oceans would freeze. This in turn would raise the earths albedo and reflect more energy directly to outer space. In turn the Stefan-Boltzmann law would drive the temperature even colder and we would end up living on a giant snowball.However, the earths atmosphere does have greenhouse gases. In particular CO2, which warms the atmosphere enough so that water can exist as a vapor. Since water vapor is also a greenhouse gas, together these greenhouse gases have warmed earths surface to about 287°K (14°C or 57°F).

While CO2 may comprise just a small fraction of the atmosphere, it behaves like a dye in that it absorbs infrared energy very well.Finally, the earths temperature is not in equilibrium. The earth is absorbing about 1.5 watt/meter^2 more energy than it is emitting. This in turn is warming the atmosphere, oceans, land, snow and ice. By far, most of the extra heat is going into the oceans. The oceans have a tremendous capacity for storing heat and it will take a long time before they reach equilibrium. When equilibrium is eventually reached, there will be more evaporation of water and the atmosphere will become thicker from increased amount of water vapor. This will result in warmer surface temperatures and a higher elevation at which the earth can radiate to outer space.

I’m not the first person to figure this all out. In fact, an intergovernmental panel of climate change scientist (IPCC) have been studying this subject intently for well over 20 years. The IPCC has carefully reviewed many scientific studies and have published their latest assessment here:

What has been concluded (TS.4.5 on page 64) is that the earths temperature is sensitive to changes of CO2 concentration. In particular, equilibrium change is likely to be in the range 2°C to 4.5°C per doubling of CO2, with a best estimate value of about 3°C.


  1. Label me a skeptic, but didn't Arhenius state that a doubling of CO2 would result in an increase of 1.6 degrees Celsius? According to what I've read, our current contribution to the total CO2 level is about 3%. Assuming natural levels remain unchanged (we can't change them), wouldn't our contribution have to climb over 33 times their current level to equate to a doubling (wholly man-made) of CO2?

    I've noticed the IPCC downplay the role of naturally produced CO2, trying to show the importance to man-made CO2. What is the physical difference between the two? If there is a difference, why were the temperatures swinging wildly before man's existence?

    I noticed the quote "The oceans have a tremendous capacity for storing heat and it will take a long time before they reach equilibrium." Define: "long time" in terms of years.

    Given all this, why is there any form of hysteria regarding global warming?

  2. The Stefan-Boltzmann law is only good for ideal black bodies and is not 100% accurate for bodies with filtered light - ie colored objects like the Earth. Please run a search for "0707.1161v4.pdf" for more details on the physics.