Refer, also to the sub-page: 'The Greenhouse Effect - Technical References & Backup'
Describing how the Greenhouse effect works for laypersons, the following describes how the Schwarzschild’s radiative transfer equation is applied. As a technically complex issue, the following description refers the interested reader to the section: "The Greenhouse effect: Technical References and Backup" by references (*X) referring to section 'X'.
The first half of this description is for 'Clear Skies' conditions that the reader will find covered by many other sources. It is a description where there is no cloud - a condition that occurs about one third of the time.
The second half looks at the impact of clouds and 'Reaal Skies' conditions.
The warm surface of the Earth emits heat as infrared radiation. This is a flux of photons (*1).
This upward flux of photons leaves the warm surface of the Earth headed for the cold of space. Along the way some of the photons encounter Greenhouse gas molecules (GHGM *2) with which they interact.
Eventually the reduced photon flux leaves the Top of the Atmosphere (TOA *3) and heads for space.
This whole process from the surface to space occurs almost instantaneously to human observers.
The Greenhouse effect cannot be observed directly.
Different GHGMs absorb different wavelength photons. An individual absorption peak is known as a spectral band and has a bell-like shape (4). The spectra of H₂O and CO₂ are very complex containing hundreds of individual peaks. A clear skies spectrum may be observed from space (5).
The fundamental physics and chemistry of GHGM infrared absorption as the surface heat photon flux passes through the atmosphere on its way to space is captured in Schwarzschild’s radiative transfer equation (*6).
The detail of what happens as the photon flux passes through the atmosphere on its way to space is described below as a layman’s version of the Schwarzschild’s radiative transfer equation.
On emission from the Earth’s surface the photon flux soon encounters GHGMs. If a photon is the right frequency (*7) to match the vibrational energy frequency of a GHGM, the encounter may result in absorption of the photon by the molecule. This causes the GHGM’s energy to increase and hence its temperature.
Where the effective density (*8) of GHGMs is high, encounters will be successful.
Where the effective density (8) of GHGMs is negligible, photons will not see any GHGMs and will continue up, unabsorbed, to be emitted to space through ‘the window’ (9).
When a GHGM has absorbed a suitable photon, it becomes ‘excited’ and is less likely to absorb another one. Within a short time – it either passes the extra energy to other molecules through collision (average time between collisions is 5/10000000000ths of a second) or could remain ‘excited’ or emit a photon similar to the one just absorbed or possibly absorb another photon to become 'super-excited'.
The absorption of photons is balanced by emissions. Any GHGM may spontaneously emit a photon and move from an ‘excited’ state to a ‘less-excited’ state. A ‘hotter’ (more excited) molecule is more likely to emit than a ‘cooler’ molecule.
The probability of emission follow the Planck Black body relationship (*10).
Within the first layer of the atmosphere where the flux of photons is of high intensity and the density of GHGMs is high, GHGMs will have many successful absorption encounters nearly, but not quite, balanced by emissions.
Summarising:
• The ‘window’ photons sail through. • A net absorption of photons by GHGMs in the atmospheric layer leads to a tiny increment in temperature for the whole layer (<<< 0.01⁰C in a short period of, say, one second) if ‘excited’ molecules can pass their extra energy to other non-GHGMs before emitting a photon. • For a 10-metre-thick atmospheric layer, the upper surface will remain about 0.1 ⁰C cooler than the lower surface • The ‘upward’ flux of photons is diminished slightly by the net absorption as total emissions of photons is less than the total absorption – the balance of the photon’s energy going into raising the temperature of the layer. • Where the effective density of GHGMs (8) is high, the upward flux of photons leaving the layer will have the Planck Black body characteristics of the surface at the temperature of the upper surface of the layer (10).
The two processes: absorption and emission, occur simultaneously so it appears to an observer that the photons have, largely, ‘passed through’ the atmospheric layer leaving some of the heat in the atmospheric layer.
The next layer of atmosphere receives a photon flux slightly reduced by the heat absorbed in the first layer.
Where the effective density of GHGMs (*8) remains high, encounters will be successful and the probability of absorption (and hence re-emission) is only reduced by the tiny reduction in flux intensity.
The result in the next layer is similar to the first layer and similarly for successive higher layers.
As altitude increases, the drop in pressure reduces the effective density of GHGMs (*8). Some, like carbon dioxide, where the concentration (but not density) is constant with altitude experience only pressure reduction.
Others, like water vapour experience rapid concentration drop-off with altitude.
There comes an altitude where the effective density of GHGMs (*8) no longer guarantees capture of upcoming photons and some escape through ‘the window’.
This escaping effect gets more exaggerated with altitude so there comes a point where the effective density (*8) has fallen to be nearly negligible.
This tailing-off is gradual but can be characterised by an Effective Emission Altitude (EEA *11) somewhere near the middle of the middle of this tail-off zone.
This EEA concept is important as it is critical to understanding how any increment to the total Greenhouse effect is brought about by increased atmospheric levels of GHGMs. Into the Stratosphere
The temperature falls off at a fairly steady rate with altitude in the Troposphere until the Stratosphere is reached at around 10 kilometres (*12).
The idealised temperature for the next 10 kilometres of the lower Stratosphere is one of constant temperature.
In a constant temperature profile, the thermodynamic element of Schwarzschild’s equation (*6) kicks in so absorption of photons is exactly balanced by emissions. In effect, whatever photon flux reaches the start of the Stratosphere is the same as emitted 10 kilometres higher.
However, the Stratosphere is not a completely static, homogeneous temperature layer. Local temperature gradients will favour further heat absorption (and emission) – particularly by carbon dioxide which is the only GHGM of any appreciable effective density (*8) in the lower Stratosphere.
At around 20 kilometres altitude the Stratosphere begins to warm up. By around 50 kilometres altitude it has warmed by as much as 60⁰C.
If the effective density of all GHGMs (8) remained as high as at sea-level for the warmest Stratospheric level at 50 kilometres, then TOA (3) emissions would have the signature of about 0⁰C - the Planck Black body temperature (*10).
As it happens, the effective density of GHGMs tails off to insignificance by 50 kilometres.
Only two GHGMs have non-trivial effective densities (*8) in the upper (warming) Stratosphere: carbon dioxide and ozone.
The emissions from the diminished but still non-negligible effective density (8) in these warmer parts of the Stratosphere are clearly observed by satellite (5).
There are two extreme situations for different frequencies of photons under ‘Clear Skies Greenhouse Effect’ conditions:
These photons escape to space (TOA *3 emission) with the same intensity as they had when they embarked on their journey.
that absorption and transmission continue all the way to the static temperature profile of the stratosphere (with some augmentation from the warmer layers of the Stratosphere). The TOA (*3) emission is determined by the temperature of the stratosphere.
The Greenhouse absorption for this ‘saturation’ element is determined, quite simply, by the two temperatures: at the Earth's surface and at the start of the Stratosphere. Any increase of, say atmospheric CO2, has no effect on the GHGM absorption in this ‘saturation’ zone.
is the intermediate case where absorption gradually tails-off with altitude but can be characterised by an Effective Emission Altitude (EEA *11).
Increased GHGM concentrations in this zone leads to an increment of the effective density (*8) of GHGMs.
Although the concentration of carbon dioxide is almost constant throughout the Troposphere, the concentration of the significantly overlapping GHGM – water – is extremely variable. Building water’s variability into the calculation is extremely complex as random, non-linear adjustments are difficult to tie-down.
In effect, the theoretical calculations relating to increased carbon dioxide concentrations which are the cornerstone of ‘Climate Change dogma’ are attempting to estimate the tiny decrement (or increments) of EEA (*11) in this overlap and broadening zone.
Using the technique of ‘Spectral Analysis’ (13), the Climate Change modellers estimate an Arrhenius form equation (14) linking surface temperature – for the ‘All Skies’ case – to GHGM concentration increments.
There is no accepted comprehensive theoretical basis for how clouds affect the outgoing infrared radiation into space. Satellite data on cloud cover is available from sources like the Copernicus Climate Data Store.
For infrared radiative heat - the photon flux - from the Earth’s warm surface the meeting with the base of a cloud layer is complex.
The size of cloud water droplets is typically between 5 and 50 microns (average close to the peak 15-micron wavelength of carbon dioxide’s main absorption band).
Typically, cloud droplets are widely spaced with average distances between droplets one or two orders of magnitude greater than average droplet size.
Upcoming radiation is not reflected in the same way as the incoming sun’s radiation reflection from the top of the cloud layer. It is not mirror-like reflection but diffraction.
Diffraction is the spreading out of waves as they pass through a gap or around the edge of an obstacle. This phenomenon occurs when the size of the aperture or obstacle is similar to the wavelength of the wave.
The extent of the spreading depends on the relationship between the gap width and the wavelength, with the effect being most pronounced when they are comparable in size.
The author’s 1960s laboratory specialised in this aspect of the problem studying refraction / reflection, transmission and absorption. This was with continuous liquid phase rather than cloud droplets.
Even with a 'simple' continuous liquid phase the experimental observations are difficult to set up and interpret. As a result, the laboraatory only issued one (relevant?) paper on the arcane issue of the ‘Reflection Phase-shift Dispersion Relation’.
That some upcoming photon flux is absorbed within clouds is beyond question – but how much and by which mechanism is unclear.
The situation within clouds is further confused by the heating effect of condensation. Water evaporated from the surface of the Earth passes upwards and cools (or super-cools) and condenses with the evolution of heat.
W. A. van Wijngaarden and W. Happer’s 2024 paper (*15) goes someway to putting a theoretical basis behind the effect of clouds.
This implies the incident, upcoming, heat is ‘absorbed’ by the surface. This heat addition may be transmitted upwards through the cloud by physical transport, conduction, convection mixing and radiation. The emissions from the top of the cloud are then the expected emissions from a surface with the temperature of the top of the cloud (*10).
where the radiation is scattered in all directions increasing residence time in the cloud layer with the outgoing radiation spread in all directions. Any Greenhouse gas absorption is essentially determined (as elsewhere in the atmosphere) by the difference in temperature between the incoming layer’s interface and the outgoing interface, for clouds these interfaces are ‘fuzzy’. The water droplets will also absorb some radiation in their passage of multiple reflections from the droplet’s surface. This, as studied in the author’s 1960s laboratory is not simple to estimate as it is difficcult to theoretically calculate for one droplet and varies with frequency and droplet size.
The closest clouds get to the ‘classical liquid ensemble’ is for very dense and massive thunder clouds stretching into the stratosphere. This cloud, where the upper surface is at Stratospheric temperature, has, theoretically, the ‘heat signature’ of lower stratosphere temperature (*10).
This has been confirmed to be the situation by satellite observation.
For very dense low cloud where there is little infrared radiation transmitted upwards through the cloud layer, the top of the cloud layer will exhibit the ‘heat signature’ of its top layer (*10). Theoretically, satellite observation of the spectrum from space will show the ‘Clear Skies’ spectrum from a surface the temperature of the cloud’s top layer.
However, the top layers of clouds are ‘fuzzy’ with different emitting surfaces at different temperatures – a nightmare for a theoretical modeller.
For very light cloud, barely unimpeded transmission upwards will be the infrared signature observed by satellite.
Only ‘window’ photons are reflected back to the Earth’s surface.
The reflected ‘saturation zone’ photons join the upcoming photon flux to be transmitted upwards. Reflected photons in the ‘Overlap and broadening zone’ add to the complexity of estimating what goes on should the EEA (*11) be below the lower cloud layer altitude – which has a low probability of occurring.
The regional effect of clouds varies. For tropical ocean areas average surface temperatures and humidity are greater than Global averages which means that a large part of Greenhouse warming takes part in tropical areas. The impact of variability in tropical clouds impact the Tropical total Greenhouse effect variability which the largest geographic contributor to Global Greenhouse effect variability.
Polar regions, on the other hand, contribute little to the total Global Greenhouse effect so variations in cloud cover over polar regios have relatively little impact.
Variations in cloud cover affect warming from the sun and help explain why large variations in local and regional surface temperature occur.
Of the two thirds of the sky that is cloudy there is a mixture of 'Clear Skies', thin cloud effects and some thick cloud effects. The 'Clear Skies' element added to the one third of the sky that is cloudless at any moment indicate the 'Clear Skies' situation is applicable for up to about 50% of the time.
Any modeller attempting to incorporate the effect of clouds is faced with an impossible task. Some modellers choose to ignore the effect of clouds; some treat the effect as a constant while some assume simplifying assumptions to make a stab at incorporate cloud effects.
That the calculations of Anointed modellers, particularly in respect of the ‘Direct Greenhouse Effect’, are presented with spurious accuracy should not fool laypersons that they are absolute ‘facts’. They have not been verified by observation or experiment.
The preceding sections, although simplified, highlight the complexity of theoretically calculating the incremental warming effect on the Earth’s surface from any enhanced total Greenhouse effect caused by increased concentrations of GHGMs.
Most might classify the subject as ‘too difficult’.
The ‘acceptable’ contribution calculation (acceptable only to the Climate Change Anointed’) start their calculation at the finishing line of ‘Anthropogenic emission cause Global Warming’. This renders them as fine examples of circular reasoning or confirmation bias ‘research’ and disqualifies them from serious consideration in any proper scientific debate.