Global Warming: Leave CO2 Alone!

I find it confusing when I see groups with strong positions in direct opposition to each other. Somewhere between the two extremes is some version of the truth, and I wish more than anything to discover the truth. With Global Warming I think I'm getting closer to the truth.

First, I think I should disclose that I have sympathized more with the Global Warming deniers. This comes partially from distrust and discomfort with phrases like "the debate is over", "everyone knows", "if we don't do something now...", etc. However, I decided that in my quest for truth, I needed to be willing to accept the truth, whatever it might be. I have therefore put on my objectivity hat making myself willing to accept the truth.

I've tried to make my analysis as simple as possible, since global climate is extremely complicated. My focus is on the question: Are humans increasing the emissions of Carbon Dioxide (CO2) and are CO2 emissions causing the planet to warm up?

To save you time from reading this whole posting, I'll give you my conclusions up front, with the analysis after. I found some surprises.

Global Warming Conclusions:

1. CO2 levels have been rising for the last 50 years.
2. Humans may be responsible for CO2 rising (CO2 growth appears to match population growth).
3. CO2 DOES act as a greenhouse gas with a warming effect (this was a surprise to me).
4. The CO2 warming effect is much weaker than reported by the media.

Besides CO2, I think that humans are affecting the environment and we should be serious about monitoring what we are doing. Still, draconian measures are not yet justified.

CO2 levels have been rising for the last 50 years

The primary support for this are the CO2 measurements at Mauna Loa Observatory in Hawaii [1] [2] These show a steady rise in CO2. Although this might be expected near an active volcano, other data from around the world show the same trend [3]. The data before 1959 are not as reliable, but an interesting study has been done by Beck [4].

Man may be responsible for CO2 rising

This required a little more analysis. I tried to find reliable data for CO2 from fossil fuel emissions and finally settled on data from the CDIAC [5]. The fluctuations in the fossil fuel data don't show up in the atmospheric CO2 data. The atmospheric CO2 data does look suspiciously like an exponential growth curve. The world population also follows a exponential growth, so this is included as well. It's reported that people exhale about 1 kg of CO2 per day (by my calculations, people breathing produces about 30% as much as fossil fuel use).
This chart (click to enlarge) shows the CO2 from fossil fuels, atmospheric CO2 concentration above 265 ppm (since we are talking about an increase over some supposed baseline), and world population. Both CO2 levels are scaled (normalized) to the 1959 population data. I purposely picked a 265 ppm baseline since it shows how closely atmospheric CO2 and population growth are correlated. The most important note is the fluctuations in fossil fuel consumption are not reflected in the atmospheric CO2 concentrations.

This chart of the Carbon Cycle [5] also shows that CO2 from fossil fuels is only a small part of the overall carbon cycle (Though there is no reference to where the numbers come from).

The chart below shows the fluctuations of CO2 concentrations derived from ice core data for the last 400,000 years. It would be interesting to know what caused these fluctuations (volcanoes, natural climate change cycles, etc.). These numbers are used to show that we are currently at the highest levels in 400,000 years, although it is disputed whether or not the ice core data accurately show peaks in CO2 occuring, this site attempts to dispel this as a myth [6].

CO2 acts as a greenhouse gas with a warming effect

Much of the "proof" that CO2 is a hazardous greenhouse gas comes from complex computer models of the climate. While I don't have the expertise to critique these models, I do have enough experience to be suspicious of the claim that CO2 is a problem.

I use a simple model. Consider a sphere just slightly larger than the earth and its atmosphere. If more energy goes into the sphere than comes out, the inside heats up. The energy going in is solar radiation and the energy coming out is reflected solar radiation and thermal (infrared) radiation from the earth. CO2 doesn't absorb the solar energy but it does absorb some of the infrared energy. See my post on Black Body Radiation for more info.

My suspicion comes for the fact that CO2 absorbs 100% of that thermal radiation (energy) over a short distance and increasing CO2 shouldn't result in more absorption.

An analogy for this is a car parked in direct sunlight. The car gets hot inside since the sunlight goes through the window and heats up the interior. The thermal or infrared radiation from the interior is then blocked by the window glass (glass is opaque in the infrared). Making the glass in your windshield slightly thicker is similar to increasing CO2 levels and unlikely make your car hotter.

Luckily we don't have to depend on my hunches or an analogy to show whether CO2 acts as a greenhouse gas. There is a computer model (MODTRAN) that has been well verified for computing the transmission of radiation through the atmosphere. MODTRAN can be run using a simple web interface that allows setting atmospheric CO2 concentration and surface temperature of the earth [7]. This is much better than many of the crude calculations I've seen on the Internet [8][9] The chart below shows the MODTRAN output for a Mid-Latitude Summer Day, 375 ppm CO2. The red line is the energy leaving the earth's atmosphere. The big dip in the middle (between wave numbers 600 and 800) is due to CO2 absorption.
The next chart is the same results with no atmospheric CO2. You can see the dip is missing, which means with no CO2, the energy is escaping the earth's atmosphere.
The next chart shows the difference in radiation leaving the earth for 375 ppm and with CO2 doubled at 750 ppm.
The total area under the blue curve is the radiant energy at 375 ppm. The red curve (mostly overlayed by the blue) is for 750 ppm. There are small differences at the edges of the CO2 absorption band. Though small, this does show that CO2 acts as a greenhouse gas, blocking some radiant energy.

The CO2 warming effect is much weaker than reported by the media.

Two questions need to be answered:
1. How much energy is trapped due to the CO2 greenhouse effect?
2. What is the effect on temperature?

Update Jan. 20, 2010: The IPCC refers to this as "radiative forcing" or "the change in net (down minus up) irradiance (solar plus long-wave; in Wm^-2) at the tropopause AFTER allowing for stratospheric temperatures to readjust to radiative equilibrium, but with surface and tropo-spheric temperatures and state held fixed at the unperturbed values".IPCC definition of "Radiative Forcing"

I will show that the IPCC definition is flawed, since allowing the surface temperature to change significantly offsets the green house effect.

MODTRAN can be used easily to demonstrate this. The next step is to balance the radiative forcing (solar in, thermal out) while assuming solar irradiance is constant. As the earth heats up from the green house gas, it emits more thermal radiation, which is only partially absorbed by CO2. So the earth only needs to heat up slightly to create a balance.

The table below shows calculations for various CO2 concentrations. The Radiant Intensity is how much energy (Watts) is leaving the surface of the earth per square meter (300 Watts is the same as three 100 Watt light bulbs). The surface temperature was determined by running MODTRAN with various surface temperatures until the radiant intensity matched the baseline. As you can see, the temperature changes are not as severe as those predicted by the experts [10].

	Atmospheric CO2 (ppm)	Radiant Intensity (W/m2)	Surface Temperature (Kelvin)	MODTRAN Predicted Temperature Change due to CO2 (C)	Measured and Predicted (p) Temperature Change (C)
Baseline	265	281.093	290	-0.21	-0.25 (m)
1959	316	280.371	290.21	0	0 (m)
2007	375	279.648	290.41	0.20	0.35 (m)
Double	750	276.791	291.27	1.06	2.5-3.5 (p)
Worst Estimate of CO2 in 2100	1000	275.598	291.64	1.43	4.4 (p)

Notes

• My analysis does not address the hypothesis for the potential magnifying effects of CO2 (i.e., slight CO2 warming causes more water vapor in the atmosphere. The water vapor acts as a stronger greenhouse gas than CO2.). See The Climate Effects of Water Vapour
• Besides energy transfer outside the earth's atmosphere, there is also transfer at the earth's surface (land and oceans). There are many potential processes here (geothermal, ocean warming/cooling, etc). The only human activity that I could think of was mining/drilling and then burning fossil fuels (converting chemical energy into thermal energy). I calculated this effect to be less than 1% of the greenhouse effect.
• Melting glaciers and polar ice caps cools the atmosphere (Most likely by a very small amount).
  
• Water (clouds and humidity) have a much greater greenhouse effect than CO2
• Other gases (Methane, etc.) from human activities were not included in my analysis. If they are the real problem, than I think we should stop talking about CO2 and focus on emissions of these other gases.
  
• Climate change addresses local variations, global warming addresses thermal energy being added to the whole system.

Cosmic rays the real cause of Global Warming?
Update Jan. 16, 2010: Climate experts divided on implications of brutal cold spells
Evidence of Arctic Warming
Update Dec. 2, 2011: The climate may not be as sensitive to carbon dioxide as previously believed
Update Oct. 14, 2012: Global warming stopped 16 years ago
Update Oct. 17, 2012: No, Global Warming Hasn't Stopped
More info at the Petition Project
Update Jan. 20, 2018: Worst case global warming scenarios not credible study