There could be no planetary atmosphere without gravity, but gravity also plays a fundamental role in the greenhouse effect thereby determining surface temperatures. To see why this is the case lets imagine that gravity has somehow been switched off and the atmosphere is held in place on the earth by an infinitely thin membrane at height d. Let’s also assume that the atmosphere is 100% composed of CO2 absorbing IR in the 15 micron band.
The atmosphere will behave as a perfect gas of temperature Ts. The pressure will be P = RTs/d and CO2 will absorb all 15 micron IR from the surface while emitting exactly the same amount to space at the membrane. Viewed from afar the IR spectrum will appear to be a perfect black body at temperature Ts. There is no greenhouse effect at all. Effectively the atmosphere can be viewed as part of the surface. There would be no net difference if the gas was replaced by Argon.
Conclusion: There can be no greenhouse effect without a gravitational field. CO2 has no greenhouse effect parallel to a gravitational field.
Now switch on gravity and remove the membrane. The atmosphere expands and a density/pressure gradient is setup as it quickly reaches hydrostatic equilibrium and the atmosphere extends upwards. The surface pressure equals the weight of the atmosphere per unit area – 15 psi or 101000 pascal falling exponentially with height approximately as
which assumes constant T, which as we will see is not exactly what occurs.
The density of CO2 molecules now diminishes exponentially with height. Therefore the IR radiative flux emitted by CO2 is no longer homogenous because gravity has broken the symmetry. Each layer has a different emissivity that depends on the density of CO2 molecules in that layer. Despite this radiative emission within a thin horizontal layer is still homogeneous in 2 dimensions and we call this ‘local thermodynamic equilibrium’ LTE for a given height h. However each height has a different emissivity ( or absorption) for 15 micron photons.
The net flux of radiation through the atmosphere from the surface at height h is then the integral of the (emission – absorption) from all lower levels minus the integral of the (emission – absorption) from all higher levels. There is no longer vertical thermodynamic equilibrium and temperature can vary with height.
How does the flow of radiative energy through the atmosphere change the energy balance? Since density falls exponentially there exists an effective emission height for each wavelength above which >50% of IR photons escape to space. I calculated this height for the 15 micron CO2 band using HITRAN cross-section data for 2 different concentrations of CO2 on earth..
Without convection the atmosphere would reach a radiative equilibrium whereby at all heights below this an equal flux of radiation would flow. This can only be achieved by the surface warming up significantly. Well before this can happen convection starts and stabilizes the temperature profile of the troposphere at the adiabatic lapse rate.
Here again gravity plays the crucial role because at the adiabatic lapse rate there is a perfect balance matching buoyancy against gravity. Such stable atmospheric condition are rare and this is what drives weather systems. Convection and the lapse rate both halt where the radiative transfer to thin upper layers stops and IR photons escape directly to space. This is the tropopause. Note that it is radiative transfer by GHGs through the troposphere that drives convection towards the lapse rate. The energy to power this atmospheric heat engine comes from the sun radiating energy directly onto the surface.
Conclusion: You need greenhouse gasses to generate a lapse rate. You need a lapse rate for greenhouse effect to work because radiation to space from higher altitudes reduces net upwelling IR. Gravity sets the scale of the lapse rate. (thanks tallbloke)
Blogger HockeySchtick and others (Stephen Wilde etc.) propose a purely gravitational/Mass theory of the atmospheric greenhouse effect seemingly independent of GHG. HockeySchtick writes :
The “effective radiating level” or ERL of planetary atmospheres is located at the approximate center of mass of the atmosphere where the temperature is equal to the equilibrium temperature with the Sun.
He then derives a formula for planetary temperature which works really quite well. However they all assume a pre-existing lapse rate generated only by gravity even in the absence of any greenhouse gasses. This is wrong because you need the sun’s energy plus both gravity and greenhouse gasses to power the convective heat engine maintaining the lapse rate. Radiative transfer of surface heat through the atmosphere tries to steepen the lapse rate towards radiative equilibrium. This instability drives convection (and evaporation on earth) resulting in the approximately observed adiabatic lapse rate. Gravity just defines the thermodynamic scale.
The centre of Mass of the atmosphere corresponds to a height with a pressure of half that of the surface pressure. This is also exactly where the number of CO2 molecules below and above are equal. Therefore you would expect this to approximately coincide with the effective emission height – but for a different reason. It is not the gravitational energy that is ‘warming’ lower levels due to compression – like in a bicycle pump . It is because above this level the IR ‘fog’ clears and photons can escape freely to space. Greenhouse warming is a subtle effect ’caused’ both by gravity and GHGs choking surface warming directly to space. You need both. A pure argon atmosphere would have no greenhouse effect and no real lapse rate.
How much warming results from CO2 on earth and how does that change with increased concentration? I previously calculated these emission spectra for different CO2 concentrations.
Resulting in a CO2 surface warming effect as follows
You can see how the surface temperature follows a . Direct CO2 forcing converges on a limiting GHE temperature at 100% concentration of about 11C for the 15 micron band. This is because the central lines saturate , and it is only the smaller side lines that continue to grow with concentration increase. So called ‘runaway greenhouse effects’ are not caused by CO2 but depend on assumptions about H2O feedbacks for hotter climates like that on Venus due to higher solar radiation.
The way the greenhouse effect on earth works is not obvious.
- There can be no greenhouse effect without gravity.
- Atmospheric pressure gradient is caused by gravity.
- The lapse rate scale is defined by gravity but is generated by convection.
- Convection is induced by Radiative transfer of heat through the atmosphere
- Radiative transfer is due to greenhouse gasses.
- There can be no greenhouse effect without greenhouse gases. Gravity alone will not work.