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 1997; Pierrehumbert 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 2008; Paleosens 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. 2004; Griggs and Harries 2007; Chapman et al. 2013, Gastineau et al. 2014).  Gastineau et al. (2014) also found that the total greenhouse effect had increased by 0.80 ± 0.13 W/m² per decade between 1982 and 2004. 

So if CH₄ is also rising and most of the greenhouse effect is due to water vapor, why the focus on CO₂?  There are two reasons.

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

e_s = saturation water vapor pressure

T = Temperature

R_v = water vapor gas constant and 

L_v = Latent heat of evaporation

Since L_v 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. 

Relationship between water vapor pressure and air temperture

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.