Tuesday, June 4, 2013

How we know global warming is because of CO2: Part 2

After Joseph Fourier deduced the existence of the greenhouse effect in the 1820s, it took until 1861 before John Tyndall identified the first components of the greenhouse effect as water vapor and CO2 (Tyndall 1861).  One hundred fifty-two years of research later, we know far more about the absorptive properties of CO2 and other greenhouse gases, including water vapor, including how they affect Earth's infrared spectrum.


Taken from Jacob 1999, Chapter 7, page 121


Note that CO2 absorbs strongest right where Earth's infrared spectrum would peak and also has the deepest valley.  Water vapor has the broadest portion of the spectrum it absorbs.  As a result, CO2 is directly responsible for about 1/3 of the greenhouse effect, the rest is due mostly to water vapor. (Kiehl and Trenberth 1997Pierrehumbert 2011).

Only 35 years after Tyndall identified the first greenhouse gases, the absorptive properties of carbon dioxide were known well enough for Svante Arrhenius to propose the theory of anthropogenic climate change (Arrhenius 1896).  Arrhenius calculated that a doubling of CO2 would raise global temperatures by 3 to 4ºC, which is within the range for the best estimate of climate sensitivity today (2.5 to 4ºC, Knutti and Hegerl 2008Paleosens 2013).

Beyond Arrhenius' calculations and laboratory measurements of absorptive properties, we have direct satellite measurements showing that increasing levels of CO2 and CH4 are the primary gases trapping more heat in the atmosphere, with minor contributions from other greenhouse gases such as CFCs, ozone, and N2O (Harries et al. 2001; Anderson et al. 2004Griggs and Harries 2007; Chapman et al. 2013).  So if CH4 is also rising and most of the greenhouse effect is due to water vapor, why the focus on CO2?

First, water vapor cannot cause a warming trend by itself.  The amount of water vapor in the atmosphere is controlled by air temperature, not the other way around.  The relationship between water vapor and air temperature is given by the Clausius-Clapeyron relation:

where
es = saturation water vapor pressure
T = Temperature
Rv = water vapor gas constant and 
Lv = Latent heat of evaporation

Since Lv is also dependent on temperature, the August-Roche-Magnus formula is often used to approximate the relationship:

where
T = Temperature (ºC)

The August-Roche-Magnus formula shows that the amount of water vapor in the atmosphere rises exponentially with temperature.  So what is the role of water vapor?  Positive feedback.  As air temperature rises, the amount of water vapor also rises, reinforcing and magnifying that rise in air temperature.  The converse is also true: As air temperature falls, water vapor precipitates out of the atmosphere, magnifying the drop in air temperature.  Without the backstop provided by CO2, once temperature started falling, water vapor would magnify that drop until there was no more water vapor left to precipitate out, lowering global average temperature by 21ºC to an average surface temperature of -6ºC (21.2ºF) (Lacis et al. 2010).

The water vapor positive feedback effect has already been measured in the atmosphere.  In the wake of Mount Pinatubo's 1991 eruption, a drop in water vapor magnified the cooling effect from sulfate aerosols temporarily increasing Earth's albedo (Soden et al. 2002).  The long-term trend, however, is for water vapor to increase as the atmosphere warms.  For instance, water vapor increased over the oceans at an average rate of 0.41 kg/m2 per decade between 1988 and 2006 (Santer et al. 2007) as the atmospheric temperature increased by 0.206ºC per decade during that time period (rate calculated using UAH temperature data).

As for methane, while it is a powerful greenhouse gas with a global warming potential 25x greater than CO2, its current concentration is 1.874 ppmv (CDIAC 2013).  The average concentration for carbon dioxide for the last 12 months is 393.82 ppmv, more than 210x greater.  We can also calculate the amount of warming expected from changes in each gas once equilibrium is reached using the Equilibrium Climate Sensitivity equation:

ΔT = λΔF
where
ΔT = change in global temperature (ºC)
λ = Climate sensitivity (best current estimate: 0.809ºC/W/m2) and 
ΔF = change in radiative forcing (W/m2).

According to Myhre et al. (1998), for CO2, ΔF can be calculated as
where
C = target CO2 concentration (ppmv) and 
C0 = reference CO2 concentration (ppmv), usually set at the pre-industrial value of 280 ppmv.

The corresponding equation for CH4 is
where
M = target CH4 concentration (ppbv) and 
M0 = reference CH4 concentration (ppbv), usually set at the pre-industrial value of 700 ppbv.

Plugging in the current concentration of CO2 and CH4 into their respective formulas gives us

ΔT (CO2) = 0.809ºC/W/m2 * [5.35 W/m2 * ln(393.82 ppmv / 280 ppmv)] 
                 = 0.809ºC/W/m2 * 1.82 W/m2
                  = 1.47ºC

ΔT (CH4) = 0.809ºC/W/m2 * [0.036 W/m2 * (√1874 ppbv - √700 ppbv)
                 = 0.809ºC/W/m2 * 0.606 W/m2
                 = 0.49ºC

While CH4 may be the more potent gas on a molecule by molecule basis, changes in CO2 concentrations are currently causing 3x the amount of temperature change.  

So why the focus on CO2?  Simple.  It's currently the main gas behind the increase in global temperatures.

4 comments:

  1. This is excellent. Would you have anything further on the persistence of CH4 in the atmosphere?

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    Replies
    1. Oops. Sorry I missed this question for 4 months. Methane only persists in the atmosphere for 9.6 years before it breaks down into water and carbon dioxide.

      http://www.epa.gov/methane/pdfs/Methane-and-Nitrous-Oxide-Emissions-From-Natural-Sources.pdf

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  2. Jim, hi,

    Just stumbled on your site, and I must say, it is an excellent resource. I'm am EE, so can follow the math, but the way you go through it in detail makes it accessible for those with even modest algebra skills.

    BTW, you might be interested to know where I landed here from. It's from an Oz-based blog called Hot Whopper and... oh, I see you have her on your blog roll too.

    Anyway, I've bookmarked this section of your blog as a handy AGW resource. Great stuff.

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    Replies
    1. Thank you for reading and for your kind words. I appreciate them. If you ever find an error on this site, let me know and I'll do my best to correct it.

      BTW, I admire Sou for her willingness to draw attention to and to debunk the silliness on WUWT. It's a thankless task she's set for herself but one I think is as necessary as sites (like my own) setting forth the actual science.

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