Posted by: John Nicklin | July 15, 2007

More fun with graphs

Today, I’d like to continue a little exploration using the graph from yesterday with CO2 superimposed and ask a few questions.

hadcrut3-co2.png

We are told, by Al Gore and others, that the connection between CO2 and temperature is very complex, but that when there is more CO2 the temperature goes up. Well Al is right, the relationship is complex and there would appear to be an increase in CO2 accompnying the increase in temperature. The graph above shows this quite nicely. However, one has to ask, if CO2 is such a driver of temperature, why did it take 27% of the total CO2 increase to produce 60% of the warming and the remaining 73% increase in CO2 only caused 40% additional warming?

The link between CO2 and temperature is complex. CO2 as a greenhouse gas is logarythmic agent, not linear. Lets say that the CO2 levels have risen 100 ppm since preindustrial times, and that 100ppm has produced 0.6 degrees of warming. The next 100 ppm will not provide another .6 degrees. You have to go to 200ppm additional (300ppm total) to get the next 0.6 degrees. Then 400ppm (700ppm total) for the following 0.6 degrees, and so on. In this scenario, it would take a total increase of 700 ppm to raise temperatures by 1.8 degrees C. To get to Al Gore’s 11 degrees F or about 6 degrees C, would take a staggering 51,200 ppm additional CO2 for a total of 102,580 ppm atmospheric CO2. Somewhere around 4,000 ppm CO2, the air becomes toxic to humans and most other mammals. It is doubtful that there is enough carbon sequestered in all known reserves of fossil fuels worldwide to get us to an additional 51,200 ppm CO2, even if we burned it in one giant orgy of SUV driving and jet setting.  This is compounded by the sinking of CO2 in oceans and plants.

Is it possible for the global temperature to rise by another 5 or 6 degrees? Yes, historical reconstructions tell us so, despite Mann’s Hockey Stick, but not using CO2 as a driver, we would have to consider other, natural, sources, like the Sun or water vapour or some factor that we just don’t know about right now.

Posted in CO2, Global Warming

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Responses

You have seriously miscalculated the logarithmic dependence of CO2 forcing on earth’s climate.

You say, “Lets say that the CO2 levels have risen 100 ppm since preindustrial times, and that 100ppm has produced 0.6 degrees of warming. The next 100 ppm will not provide another .6 degrees. You have to go to 200ppm additional (300ppm total) to get the next 0.6 degrees.”

From pre-industrial times to the present, CO2 concentration has risen from 280 to 380 ppm. The ratio is 380/280 = 1.357. Taking the logarithm to base 2, we get 0.44, so this represents (logarithmically) 44% of a doubling of pre-industrial levels.

Also, earth has not yet experienced all the warming due to this CO2 alone. The actual warming due to this 44% of a doubling is estimated at 1.3 deg.C, but due to the massive thermal inertia of the oceans, it will take some time for the remaining warming to be felt. It is “in the pipeline,” and will be experienced even if we hold atmospheric greenhouse gases at their present level.

The best estimate is that each doubling of CO2 concentration leads to 2.9 deg.C warming. From pre-industrial 280 to 560 will be 2.9 deg.C, from 560 to 1120 will be another 2.9 deg.C, etc.

Furthermore, the imminent melting of the polar ice cap will lead to “ice-albedo feedback” which will cause further warming, and melting of the permafrost will release massive amounts of CO2 and methane which will cause more warming still.

Considering that the global average temperature difference between full glacial and interglacial conditions (during ice ages) is only 5 deg.C, a “mere” 3 deg.C warming will be extremely dangerous, and double that will be disastrous.

By: tamino on July 15, 2007
at 12:40 pm

Thanks for the explanation. If part of the heat delta of 1.3 degrees is not seen due to inertia in the system, which is not in question, why are we currently experiencing no increase in temperatures over the last 9 years since 1998? Other factors, besides CO2, are in play.

Your example deals with a doubling of preindustrial CO2 levels. Mine deals with doubling the delta CO2 since then. If we took a pristine planet with no CO2 and added 100 ppm and observed 0.6 degrees rise over 100 years, then would we not expect to see another 0.6 degrees rise if we added an additional 200 ppm CO2?

My point is, and always has been, that CO2 is not the primary driver of observed temperature. As you have pointed out, there are many other factors that need considering. I think that we give too much credit to CO2 and the current global mania over chasing CO2 is folly, there are just too many other things going on.

Even though there is inertia in the system, we are talking about 100 years here. In the grand scheme of things that may be nothing or a lot.

By: John Nicklin on July 15, 2007
at 12:59 pm

If we took a pristine planet with no CO2 and added 100 ppm and observed 0.6 degrees rise over 100 years, then would we not expect to see another 0.6 degrees rise if we added an additional 200 ppm CO2?

No. When first adding CO2 to a planetary atmosphere, the absorption bands of the CO2 molecule absorb infrared radiation from the planet proportional to the concentration of CO2. This is the linear region of the absorption-vs-concentration graph.

When the absorption bands of CO2 begin to saturate (so that in the very center of the absorption bands, nearly all the radiation is absorbed), the “saturation region” of the spectrum widens, and the effectiveness of CO2 as an infrared absorber goes roughly as the square root of the CO2 concentration.

When the absorption bands are nearly saturated, two effects remain. First, the very edges of the absorption band are still unsaturated, so increased CO2 still leads to increased infrared absorption. Second, as CO2 concentration increases, the infrared radiation which actually escapes to space (which is how planets cool themselves) comes from higher and higher altitudes. Because all planetary atmospheres exhibit a lapse rate (decrease of temperature with altitude in their lower layers), as the primary emitting region gets to higher altitude, the temperature at the base of the atmosphere (which is “emitting temperature” + “lapse rate” x “altitude”) gets higher. This is the logarithmic region, in which surface temperature increase is roughly proportional to the logarithm of the greenhouse-gas concentration.

Earth’s present atmosphere is squarely in the logarithmic region with respect to CO2 concentration.

… there are are many other factors that need considering. I think that we give too much credit to CO2 and the current global mania over chasing CO2 is folly, there are just too many other things going on.

Indeed there are many factors which influence global temperature, which is why there is considerable year-to-year natural variation. The strong el Nino of 1998 made it the warmest (according to HadCRU) or 2nd-warmest (according to NASA GISS) year ever, while the explosion of the Mt. Pinatubo volcano caused about two years of global cooling in 1992. But the natural variation factors go up and go down; what they give, they also take away, over long time scales the average temperature change is zero. Reconstructions of past global temperature for the last few thousand years testify to the stability of global temperature on millenial timescales.

… we are talking about 100 years here. In the grand scheme of things that may be nothing or a lot.

The time scale for the remaining warming which is “in the pipeline” due to CO2 we’ve already emitted is not 100 years, but more like 30. The reason scientific reports focus on longer timescales is that CO2 will not remain at present levels; it’ll continue to increase (currently at about 2 ppm/yr) until we stop dumping it into our atmosphere.

You should also be aware that the 5 deg.C warming from full glacial to interglacial conditions (during ice ages) typically takes 5000 years or more. The sustained rate of global warming is about 0.001 deg.C/yr, or 1 deg.C every 1000 years. We are now warming the planet at a rate of about 0.02 deg.C/yr, or 2 deg.C every 100 years — twenty times faster than a rapid deglaciation.

By: tamino on July 15, 2007
at 1:39 pm

How do you arrive at an increase of 2 ppm/year? NOAA pegs the long term average at 1.5ppm/year.

By: John Nicklin on July 15, 2007
at 2:01 pm

The long-term average refers to the entire period from 1958 (when Charles Keeling began making accurate measurements of atmospheric concentration) to the present. However, the rate of increase has itself increased over the years. This is examined in this post.

By: tamino on July 15, 2007
at 2:39 pm

NOAA also mentioned that CO2 levels had increased by 2.3 ppm for two years, but that the increase had fallen back to the long term average subsequently. Short terms deviatons do not indicate long term trends.

according to David Hofmann, director of the NOAA Climate Monitoring and Diagnostics Laboratory in Boulder, Colo., the rate of carbon-dioxide increase returned to the long-term average level of about 1.5 ppm per year in 2004, indicating that the temporary fluctuation was probably due to changes in the natural processes that remove CO2 from the atmosphere.

By: John Nicklin on July 15, 2007
at 3:51 pm

I believe Dr. Hofmann is referring to the return to about 1.5 ppm/yr as the “temporary fluctuation.” If he believes the present trend is at a rate of 1.5 ppm/yr (which I doubt), then he’s mistaken. But then, he’s not a specialist in the statistical analysis of time series; I am.

But don’t take my word for it. At this page you’ll see (on the right-hand side) the actual NOAA data for “Annual Mean Growth Rate” of atmospheric CO2 (from Mauna Loa atmospheric observatory). Copy and paste it into ExCel, and have fun with another graph.

By: tamino on July 15, 2007
at 4:27 pm

Tamino; the NOAA article clearly says, A spike in the amount of carbon dioxide released into the atmosphere between 2001 and 2003 appears to be a temporary phenomenon and apparently does not indicate a quickening build-up of the gas in the atmosphere, according to an analysis by NOAA climate experts.

As measured in air samples collected from more than 60 sites in the NOAA Global Cooperative Observing Network, the amount of CO2 in the atmosphere increased by nearly 5 parts per million (ppm) between 2001 and 2003. The increase in 2002 was 2.43 ppm; the increase in 2003 was 2.30 ppm. In other words, more than two additional carbon-dioxide molecules were added to each million molecules of air each year during that period. The annual increase was higher than the long-term average annual CO2 increase of approximately 1.5 ppm.

I looked at the link you provided and did import the raw numbers into excel. The average CO2 increase per year over 48 years is 1.40 ppmv/year. There are anomalies in certain years up and down. A rough long term average of 1.5 ppm/year would seem reasonable.

By: John Nicklin on July 15, 2007
at 5:27 pm

The NOAA press release gives the impression that the current rate of increase is 1.5 ppm/yr, but that notion is definitely mistaken. I’m a mathematician, my specialty is the statistical analysis of time series, so I know what I’m talking about.

But again, don’t take my word for it. Now that you have the data in Excel, add a trend line to that data. You’ll note that the trend is increasing, that the increase is statistically significant, and that the present value of the trend line is 2 ppm/yr. You’ll also note that the increase rate has been above 1.5 ppm for the last 7 years, and 9 of the last 10 years.

By: tamino on July 15, 2007
at 5:59 pm

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