Carbon dioxide: a radiation absorber as well as emitter

The most crucial issue in current AGW debate is of course the greenhouse warming effect of CO₂ gas.  Laboratory and satellite spectra show CO₂ gas has three main absorption bands at wavelengths of 2.7, 4.3 and 15 µm, respectively.  The 15 µm absorption band absorbs significant amount of thermal radiation emitted from the earth ground surface.  We all know that absorption of radiation waves leads to warming up of an object.  Water vapor and CO₂ molecules absorb, N₂ and O₂ do not.  It thus appears logical and straightforward to label water vapor and CO₂ greenhouse gases that warm up the atmosphere.  While the warming effect of absorption has been well addressed, the cooling effect of emission for CO₂ has not. 

There are two simple physical laws: one is the absorption law describing how much

energy, I, an object absorbs; the other is the Stefan-Boltzmann law expressing how much energy, J, the same object with surface temperature, T, emits per unit area and unit time.

(1)          I = aI₀                                           

(2)          J = ε σT⁴         

                                                                                    

where, α and ε are surface absorptivity and emissivity of the object, σ is the Stefan-Boltzmann constant equal to 5.670373 x 10^-8 (W/m²K⁴), and I₀ represents the radiation source.  I is the energy in, and J is the energy out of the object.  If I > J, the object gains heat resulting in warming; if I < J, the object loses heat leading to cooling.  When I = J, the object reaches its radiative equilibrium.  For a given radiation source, I₀, there is a corresponding radiative equilibrium temperature, T, for an object.

Absorptivity and emissivity are the intrinsic material properties of an object.  According to the Kirchhoff’s law, an object with absorptivity α = 0 (or α = 1), emissivity of the object must be equal to ε = 0 (or ε = 1).  Visa verse, if α ¹ 0 (or α ¹ 1), there must be ε ¹ 0 (or ε ¹ 1).  Put it in words: an object that absorbs emits, or an object that emits absorbs.  Indeed, absorption and emission are two inseparable equivalent identities of the same physical essence.

An important message from Eqs (1) and (2) is that absorption of heat energy relies on and only on EXTERNAL factor - radiation source, I₀, whilst emission is determined by and only by INTERNAL factor - surface temperature, T, of the object. 

Bearing these concepts in mind, we are now ready for a thought experiment:

1) Cover the Earth with literally white cloth so that there is no radiation wave for CO₂ molecules to absorb.  The temperature of CO₂ molecules shall approach 0 K (-273.15°C).  This is because:

If I₀ = 0, there must be I = 0 according to Eq. (1);

But J > 0 because T > 0 according to Eq. (2); therefore CO₂ keeps losing heat and dropping its temperature until T = 0.

Figure 1.  What will be the CO₂ temperature if the Earth ground surface is covered with literally white cloth.

2) Remove the white cloth to expose CO₂ molecules to the earth ground surface radiation, I₀, which will raise the temperature of CO₂ molecules at lowest altitude from -273.15°C to -78°C (math omitted here) because I₀ is not strong enough.  CO₂ temperatures at higher altitude would be even lower because of damped intensities of the radiation waves. 

3) Now take heat transfer by molecular collision into account.  One may argue that CO₂ will not be frozen to 0 K in 1) or -78°C in 2) because of constant heat transfer due to molecular collisions with neighboring N₂ and O₂ molecules.  In fact, CO₂ will be only slightly cooler or even in the practically same temperature as N₂ and O₂ depending on how fast heat transfer by molecular collisions as compared with radiative emission. 

When CO₂ is warmer than its radiative equilibrium temperature, it emits more heat energy than that it absorbs.  In other words, CO₂ emits not only the heat energy gained from absorption, but also the heat energy gained from N₂ and O₂ by molecular collisions.  A heat transfer route is shown below:

N₂ and O₂ do not emit heat but pass heat to CO₂ by molecular collisions;

CO₂ dissipates heat by thermal radiation to space.

With this alternative interpretation, we have a better explanation of the temperature-altitude profile in the thermosphere.  A CO₂ molecule is heavier than N₂ and O₂ due to higher molecular weight; so is water vapour but due to aggregation of molecular clusters.  Neither water vapour nor CO₂ reaches the high altitude thermosphere.  Even if there are still residual greenhouse gas molecules in the thermosphere, there would be no effective heat transfer by molecular collisions any more because of extremely low air pressure.  The temperature in the thermosphere is well above 100°C, increases steadily and exceeds 1000°K with increasing altitude.  Without so-called greenhouse gases in the thermosphere, N₂ and O₂ have no mechanism for heat dissipation.

As long as T > 0, CO₂ emits, regardless whether its heat is gained by absorption of radiation or molecular collisions.  The downward radiation waves emitted by CO₂ are absorbed by the earth’s ground surface, resulting in a small temperature increase so that the outgoing radiation blocked by CO₂ goes to space via other wavelength bands.  CO₂ functions as a half-mirror hanging on the sky to the earth’s ground surface.  This theme, however, will be addressed in a separate article. 

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It is true that absorption of radiation waves leads to an object warmer than otherwise.  The key question is: what is the temperature of the GHGs without absorption of radiation waves?  It shall not be difficult to find that we have counted, without knowing, twice or more of the warming effect of CO₂ absorption.  This perhaps is the most important underlying conceptual issue that must be resolved to advance climate science. 

(Dr Jinan Cao)