Monday, December 14, 2009

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
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 1.062.5-3.5 (p)
Worst Estimate of CO2 in 2100 1000 275.598 291.64 1.43 4.4 (p)


  • 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


Spencer said...

Nice try, Ron, but by leaving out the amplification due to the increase of water vapor in the atmosphere, you are leaving out the most important effect of adding CO2. This is not a calculation performed by "Al Gore and friends" but by actual scientists, beginning more than a hundred years ago... Arrhenius didn't have a computer, he did it with pencil and paper and got substantial warming, because he did include H2O. Of course his calculation was still far from good, leaving out lots of things... which you, too, overlook.

It must be nice to believe that in a few weeks you can figure out stuff that thousands of really smart people who have devoted their lives to the subject just somehow don't understand...

Ron said...

Spencer, I have a hard time believing that I've found something that 1000s of smart people should already know. That's why I've published this, hoping that someone could help me find the science that includes increased radiative cooling due to raising global temperatures. Please share. BTW, this insight was not solely from a few weeks but from over a decade of work with radiative exchange models.

Ex-PFC Wintergreen said...

As someone who is NOT a physicist, but is a fairly decent aerospace engineer with a couple of fluid mechanics classes under my belt, and a lot of experience with physical modeling of complex systems, my biggest problem with AGW is the uncertainty: are there models, calibrated to the data for, say, 1860 to 1960, that can reasonably accurately reproduce the filtered global temperature anomaly (let's use a filter time constant of, say, 3 to 5 years) from 1961 to the present day? Can that same model predict backwards past the terminus of its calibration data? If so, then that would be something worth looking at. I don't know if such a model exists or not; I haven't seen one, but that doesn't mean it doesn't exist.

Also, I understand that projecting into the past is tricky, because you have to calibrate your proxy data (modern thermometer was invented in 1724) such that you can use it. Once again, I would like to see an actual calibration of a physics-based model for said proxy data; a purely statistical method such as regression using principle component analysis doesn't cut it. Again, maybe this exists, but I haven't seen it.

If a physical model, with genuine predictive power as outlined above, says that we are in trouble with the current anthropogenically-caused CO2 changes, then I'll take notice. Otherwise, I'll tend to agree with Freeman Dyson, Bjorn Lomborg, etc.

Finally, cheap and abundant power that does not rely on burning fossil fuels would be the game-changer that we're looking for, because it would remove both the worry about the potential effects of AGW, and provide the means to improve the world's standard of living. I'm beginning to believe that 4th gen nuclear power, in particular the Liquid Floride Thorium Reactor (see for more details) could bring that about.

Mike G said...

I don't have the science credentials of the author or the commentors (I am a graduate engineer but got a "D" in Fluid Dynamics). What bothers me most about all of this is the leap to draconian action without a fair cost/benefit analysis - even given the worst predictions of those "thousands of really smart people who have dedicated their lives to AGW" - who by the way are looking pretty dumb right now.

There is a signifiant cost of being wrong and since weather and climate are really chaos phenomena, I don't believe anyone sould bet their house on what any model says.

Furthermore, if you model the system in its entirety - taking into account the abilities of mankind to adapt and the high correlation between the wealth of a community and its ability to achieve harmony with nature - I see scant reason to empower governments and organizations like the UN to further abuse the people of the world over this issue.

Anonymous said...

Ron, please permit me to pick a nit. (It is just a nit because it doesn't affect your main points, which are excellent.)

You wrote, "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."

But that isn't correct.

The reason your car heats up in the sun is not mainly because the windows block IR. It would heat up nearly as much if they did not block any IR at all. It heats up almost entirely because the windows block air movement.

The main thing that cools the interior of your car when the windows are down is air movement, due to convection & wind. Radiative emission of IR is a very minor factor.

That's why greenhouses made with plastic windows work just as well as those with glass windows, and also why the terms "greenhouse effect" and "greenhouse gas" are misnomers.

Also, it turns out that window glass is actually transparent to quite a bit of the IR spectrum, roughly from the red end of the visible range (~700 nm) to ~2750 nm. However, this is a minor nit because the IR emitted by your car's hot upholstery is almost all in the far-IR, outside this range: