By Andy May
The overall greenhouse effect (GHE) is often defined as the difference between Earth’s average global temperature without greenhouse gases (GHGs) and with them. Greenhouse gases are all the gases that absorb some portion of the thermal energy emitted by Earth’s surface. The most important of these gases is water vapor, but there are minor GHGs like CO2, ozone, and methane.
The calculation of Earth’s temperature without GHGs is usually done by unwrapping the planetary sphere and placing it in space at the average distance of the Earth from the Sun and having the whole of Earth’s surface illuminated by the Sun with one-fourth of the Sun’s power to account for the spherical Earth and the fact that half of Earth is always dark. This imaginary flat Earth does not rotate, and no part of it is ever dark. A description of the calculation can be read in Benestad, 2017. The global average temperature calculated with this scenario is around 255K (-18°C) and since this is about 33°C less than the current global average temperature of 15°C, the overall greenhouse effect is assumed to be about 33°C. Further discussion of this definition can be seen here.
In this post I will first list the problems with this “flat Earth” GHE model, then provide a model of a new GHG-free spherical rotating Earth. After this, I will list the assumptions used to create the spherical Earth model, the problems with it, and finally discuss what we learned making the model. Computer models are learning tools, they never give you a correct answer, but they do help you learn about the problems they were designed to investigate.
Problems with the flat Earth model
The flat-Earth no-GHG model ignores the fact that the Earth is a rotating sphere and that half of it is always in the dark. The dark side is always emitting energy, but receiving none, this is very different than the model in which the Sun is always shining directly overhead 24 hours a day with the same intensity everywhere. The proponents of the flat Earth model justify it because the satellite GHG emission temperature of the Earth is also 255K (Benestad, 2017), which using an average temperature vs height table (the U.S. or International standard atmosphere), works out to an average emission height of around five km. There is little discussion about how the energy gets from the surface, where most solar energy is absorbed to five km. But the transport is mostly done through convection and most of the GHG-emitted energy is carried to five km inside water vapor as latent heat. Above 5 km it is mostly emitted to outer space as the water vapor condenses to water droplets in the colder middle to upper troposphere.
By dealing only with averages, that is the average atmospheric temperature profile, the average surface temperature, the average emission height, the average emission intensity spectrum, etc. the flat Earth model can seem accurate and consistent with reality. But GHG emissions to space originate in a tropospheric layer from about two km to ten km, depending upon atmospheric and cloud conditions. Further, there is no consistent relationship between surface temperature and the temperature in the atmospheric GHG emission layer, it varies with weather conditions, cloudiness, season, and time of day. The surface operates mostly independently of the emission layer, they are separated by convection and weather.
In astronomy, the emission frequency and intensity of a planet is often assumed to be the planet’s “blackbody” frequency spectrum, which according to the Stefan-Boltzmann law defines a blackbody temperature. This is not the planet’s actual surface temperature; it is only a ballpark estimate. Planets are not perfect blackbodies. They are “gray bodies.” A black body emits all the energy that it absorbs, and since it has a constant temperature by definition, it emits all incident energy with a frequency spectrum that is determined by its temperature. Most importantly, a black body has no energy storage capacity or its total energy storage is constant and never changes.
Gray bodies on the other hand do not emit all the energy they absorb; they store some of it and emit the rest. Earth’s oceans have an enormous heat capacity and they store more energy than exists on the surface of Venus, but while Venus’ surface has a temperature of 464°C, Earth’s surface temperature is only about 15°C. This is because Earth’s oceans have a heat capacity of 5.4 x 1024 Joules/K and Venus has no oceans. The lack of oceans and atmospheric water vapor combined with thick sulfuric acid cloud cover and a very dense atmosphere forces Venus to have a high surface temperature.
A GHG-free spherical, rotating Earth model
The goal of the flat-Earth model is to compute the greenhouse gas effect on Earth’s surface temperature. This requires an estimate of the surface temperature with no greenhouse gases. This is difficult, because it means no water, clouds, or water vapor and these are defining characteristics of Earth. The classic flat-Earth model assumes the planet retains its current albedo (reflectivity) of 0.3, meaning 30% of the incoming solar energy is reflected. But half or more of that albedo is due to clouds. Without water, there would be no clouds and Earth’s albedo would be more like the Moon’s, which has an albedo of 12%. We investigate both albedo estimates with the model.
Another important consideration is that GHGs emit energy to space, if there are no GHGs in the atmosphere it will emit little energy to space and act as an insulator. However, while GHGs capture surface emitted radiation in our atmosphere, the no-GHG atmosphere is transparent and all surface emissions will travel straight to space, Earth only retains the solar energy absorbed by the rocky surface.
The most common rock on Earth’s surface is basalt. On our Earth we have a lot of water that chemically transforms basalt to mud or dirt. On GHG-free Earth there is no water, so I assumed the surface is bare basalt. It will broken up a bit by meteorites, but we will ignore that for this model. Rocks have a higher thermal inertia than dirt or mud and they retain absorbed heat longer.
Like most rocks, basalt is a pretty good insulator, but it does have a thermal diffusivity, which is the speed it transfers heat through its interior. Thermal diffusivity has units of m2/second. Anyone who has been in an old medieval church on a warm day knows that the thermal diffusivity of rock is low. Thus, when sunlight strikes basalt and warms it, some of the heat will penetrate into the basalt where it will be stored for a time, and the basalt will emit the rest of the solar energy through the GHG-free, transparent atmosphere to space. My GHG-free model explicitly takes thermal diffusivity into account.
In addition, the warm basalt will also pass some heat to the atmosphere through conduction. The atmosphere is GHG free and as a result it emits very little energy directly to space, so little we can ignore it for our model. However, the dayside of the rotating planet is around 170°C warmer than the night side, so winds will appear to transport excess thermal energy as sensible heat from the dayside to the nightside or from the tropics to the poles, these winds are likely to be quite fierce in the absence of water vapor which helps stabilize the weather on our planet due to its high heat capacity. For example, wind speeds in the water-free atmosphere of Venus reach 700 km/hour (430 mph). The winds carry excess heat from the hotter areas to the cooler areas and then some of the heat will be conducted down to the surface to be emitted to space or absorbed. For this reason, warming of the atmosphere in our GHG-free planet is assumed to be exactly counterbalanced by warming of the surface from the atmosphere.
The model assumes that the atmosphere is completely transparent to incoming sunlight and all the energy is absorbed by the basalt surface which warms according to the sunlight incident angle on the daytime half of the spherical surface. While some sunlight will be scattered by the atmosphere, this effect is ignored in the model. Figure 1 shows the temperature after one day of the GHG-free Earth according to the model. The east-west locations are arbitrarily centered on the equator at zero longitude and are meaningless due to GHG-Earth’s constant rotation. The north-south locations are meaningful and are representative of an Earth with no axial tilt. The lack of an axial tilt means that GHG-free Earth has no seasons.
Figure 1 illustrates that the surface warms in direct proportion to the radiation it receives, and the maximum radiation is received when the sun is directly overhead. The maximum insolation, after correcting for the lunar albedo of 12% is 1198 W/m2 and occurs for a few minutes along the equator at the local noon. In figure 1 this is at longitude=0 and latitude= 0, that is the equator directly south of Greenwich England where the temperature reaches 381K (108°C) at noon. Earth rotates from west to east, which is why the temperature on the nightside is higher on the eastern end of the night side (right of figure 1) than on the western side (left of figure 1).
Because the thermal diffusivity of basalt is very low, about 9 x 10-7 m2/sec (Robertson, 1988), it takes a while to warm the upper layers of the rock surface and reach a sort of equilibrium global average basalt temperature in this model. The day side both absorbs solar radiation and emits thermal energy. However, the night side receives nothing but still emits radiation due to its stored thermal energy. The night side emits less energy than the dayside due to its lower surface temperature.
Exactly how much is stored in the basalt in the daytime, versus emitted later in the day when the surface temperature is cooler, is unknown, but can be estimated using basalt’s thermal diffusivity. Diffusivity varies with temperature roughly according to the function plotted in figure 2.
Even though the diffusivity is lower at higher temperatures, the basalt initially stores more energy during the day than it releases at night. The model tells us that more total energy is emitted on the daytime side than on the nighttime side, but this is due to the higher daytime surface temperature. Thus, the model tells us that some of the energy that is diffused into the basalt during the daytime is taken to the nightside, the rest is emitted during the day at lower daytime temperatures encountered nearer to the edges of the dayside as the planet rotates.
On the nightside some of the daytime stored energy rises to warm the surface and is emitted to space. There are two opposing forces at work on the night side. The thermal diffusivity of basalt increases at lower temperatures, but the lower nighttime temperatures cause lower emissions of energy to space. Thus, there is a mismatch between daytime storage and nighttime emissions. This does not mean that the surface cools to absolute zero, that will not happen because the thermal inertia of basalt is too high and because the diffusivity is too low, but it does mean that a stable surface temperature takes a while to reach. I ran this model for 36,500 iterations or about 100 years. The global average surface temperature evolved as shown in figure 3.
As shown in figure 3, using the assumptions built into my model, the average surface temperature eventually stabilizes to a surface temperature cooler than today’s temperature. This result uses the lunar albedo, which would be similar to Earth’s albedo in the absence of water or water vapor. It also assumes a fudge factor for thermal inertia of 0.1. I tried various estimates of thermal inertia, including thermal effusivity (Sabol, Gillespie, McDonald, & Danillina, 2006) and the “R” insulation factor, and none of them worked well for various reasons. There are a lot of ways heat can be transferred, conduction, convection, and radiation and these vary with the local circumstances, so there is no general definition of thermal inertia. However, all reasonable assumptions show a high value of thermal inertia in the basalt which causes the temperature to decline after model initialization.
Although different assumptions do change the ultimate equilibrium global average temperature, all reasonable values for thermal inertia result in a lower global average surface temperature than we have today. Figure 4 compares some of the scenarios I examined after 100-year runs. The model was run both with the lunar albedo of .12 and Earth’s current albedo (including the non-existent clouds) of 0.3. Without GHGs Earth would not retain its current albedo, but this is the traditional value used, so I ran it for comparison purposes. The two discussed thermal inertia values (0.1 and 0.15) are reasonable assumptions, since the actual thermal inertia of basalt is quite high, but even these values may be a little high. Higher values of this factor imply a lower inertia and lower values a higher inertia. Other values of inertia were investigated, but considered unlikely.
Thermal inertia is the resistance of a material to change its temperature. There is no formal or general way to describe thermal inertia, since it is very situation specific. Newton’s Law of Cooling works for small temperature differences but breaks down in situations like I’ve modeled here. Thermal effusivity, also called thermal responsivity, which is the square root of the product of thermal conductivity, density, and specific heat capacity didn’t work either. My final attempt was to use the “R” insulation factor, but it was another failure.
My analysis of these various inertia factors is attached as a spreadsheet, a link to download it is at the bottom of the post. Some sort of new measure of thermal resistance (inertia) will need to be developed for the situation I modeled. For now, I have created an assumed factor that is the proportion of thermal energy stored in the basalt that can make it to the surface in 12 hours and is free to be emitted as radiation. In the model this is called “inertia_f.” The values, 0.1 and 0.15, are reasonable considering the established values of thermal conductivity, density, and specific heat capacity of an average basalt.
Notice that all the temperatures calculated after 100 years are less than the current global temperature. Given the large uncertainty in the model, values that are greater than the current global temperature are possible, but values larger than 300K are thought to be extremely unlikely. In addition, the temperature difference between the dayside of the GHG-free rotating Earth and the nightside will never disappear, it is shown after 100 years in figure 5.
The assumptions used in the model
The model assumes that the only meaningful losses of energy are from the surface, although the atmosphere will emit a small amount of energy to space. These atmospheric emissions are ignored in the model.
The model assumes no axial tilt.
The model assumes a circular orbit.
The model does not consider convection, except to assume that it is net zero with regard to emissions to space. This is reasonable since we also assume the atmosphere is transparent to surface emissions.
The model assumes that any topography (mountains, valleys, etc.) do not affect heat transport by the atmosphere on a net basis.
The model assumes that the thermal diffusivity of the surface basalt follows a function of temperature as described in Robertson, 1988. The function is plotted in figure 2. Thermal diffusivity (α) follows the formula in equation 1:
Equation 1:
Where: k= thermal conductivity, ρ=density, and cp is the specific heat capacity.
Thermal diffusivity increases at lower temperatures consistent with decreasing rock specific heat capacity and increasing thermal conductivity, see the attached spreadsheet for the details and units. The data available for thermal conductivity and specific heat capacity of basalt does not extend to the low temperatures encountered on the night side, so the values used in the model had to be extrapolated.
The thermal diffusivity of dry air is from 6 to 38 times higher than for basalt at the temperatures seen in this model. Thus, the surface heat flux will normally be from the basalt to the air if the temperatures are similar. But the lower value of six occurs at lower nighttime temperatures and if the overlying air is sufficiently warmer than the basalt there will be a flow from the air to the basalt. Thus, the expected high winds from the dayside to the nightside will matter and transport thermal energy to the nightside basalt to be radiated to space.
The most important assumption in the model is the assumed thermal inertia, which plays an important role in the temperature of the nightside. My calculation of retained heat carried from the dayside to the nightside is reasonable and justifiable, but the speed at which it is emitted to space on the nightside is somewhat speculative.
The problems with the model
The calculated absorption of thermal energy by the surface on the dayside is very crude. I did use the thermal diffusivity of basalt in the calculation and assumed the remainder of the energy was emitted to space.
A uniform and smooth rocky surface was assumed for simplicity, which is unlikely. Without oceans, a rugged topography is likely, and it will guide the expected very high velocity winds in an atmosphere without water vapor. This will cause a more complicated and non-uniform surface temperature than shown in figures one and five. However, regardless of the complexity of the convection, it is reasonable to assume that net atmospheric transport of thermal energy is close to zero. The energy into the atmosphere comes from the basalt and the energy out of the atmosphere goes into the basalt. The real Earth has more control, by using energy storage in water and water vapor it has some control on both emissions and insolation by varying cloud cover, total atmospheric water vapor, and ocean storage, but this does not apply to a GHG-free Earth.
Discussion of what I learned
In my opinion, the GHG-free model has a fairly narrow range of plausible outcomes. Some model runs (not all runs are shown) result in global average temperatures a little above freezing, but global average surface temperatures higher than today are considered unlikely. Temperatures much lower than 235K (albedo=0.3 and Inertia_f=0.05) are also unlikely. Using this model, the total overall greenhouse gas effect is likely between 15 and 53°C. Thus, the flat Earth overall greenhouse effect is within the plausible range seen using this rotating spherical Earth model. While the influence of water vapor, ice, and water on the climate of Earth is readily seen, the influence of the other greenhouse gases is harder to detect.
The flat Earth greenhouse effect model is designed to simply compute the difference between the apparent blackbody temperature of the Earth as seen from space from the current global average surface temperature. Yet, Earth is clearly not a blackbody and the blackbody temperature as seen from space is not a surface temperature. The GHG radiation detected from space is emitted mostly by water vapor from 2 to 10 km in the atmosphere (see figure 4 here), plus some minor emissions from other greenhouse gases from various other altitudes. Surface radiation in the GHG frequencies cannot make it all the way to space from the surface. At sea level, a greenhouse gas is 50,000 times more likely to dissipate the energy from an absorbed photon via collisions with other molecules as re-emit it, so convection must first transport the thermal energy from the surface to an altitude where it can be radiated to space.
The rotating spherical Earth GHG-free model described in this post is more realistic than the flat Earth model, but it still has problems. As George Box famously wrote in 1976, “all models are wrong.” The model is not definitive, but my preferred model run has an albedo of 0.12 and an inertia_f of 0.1, the result of this run is shown in figure 3. It results in a GHG-free surface temperature of 265K (-8°C) which is smaller than the flat Earth model and shows a smaller overall greenhouse gas effect. However, this result is still uncertain. The main uncertainty in the model is in the thermal properties of the rocks on the surface, in particular the poorly defined “thermal inertia,” which was assumed.
Future
This is a very simple model, more of a proof of concept than an actual model. It can be improved. Adding an axial tilt so GHG-free Earth has seasons might be interesting, so would adding some orbital eccentricity. But the most significant add would be a well-defined and appropriate function for basalt thermal inertia. Perhaps some petrophysicist out there has an idea of how to do that? We can only hope. Comments on the appropriateness of assuming the atmosphere is thermally net neutral would be interesting to read. In any case this is certainly an improvement on simply subtracting the average satellite measured black body temperature from the current average surface temperature to compute a possible greenhouse gas effect.
One additional point, I dislike the tendency of climate modelers to ignore surface thermal properties when modeling Earth’s climate. The surface, whether it is an ocean or land or a combination, is not a thermally static “slab.” In the real Earth, the surface, both the ocean and the land, have a large store of thermal energy and that storage changes with time (May & Crok, 2024) & (Crok & May, 2023), it definitely plays a role in long-term climate and should be taken into account.
Update: After I finished this post, I found out that Dr. Roy Spencer had done a similar calculation in 2016 (see here). Using an albedo of 0.1, an assumed IR emissivity of 0.98, and iterating for 47 days, Spencer reaches an equilibrium temperature of 266.8K or -6°C, within two degrees of my preferred answer using the thermal diffusivity of basalt.
To download the model, which is written in R, click here.
To download the thermal diffusivity spreadsheet click here.
Bibliography
Benestad, R. E. (2017, May). A mental picture of the greenhouse effect. Theoretical and Applied Climatology, 128, 679-688. Retrieved from https://link.springer.com/article/10.1007/s00704-016-1732-y
Box, G. E. (1976). Science and Statistics. Journal of the American Statistical Association, 71(356), 791-799. Retrieved from http://www-sop.inria.fr/members/Ian.Jermyn/philosophy/writings/Boxonmaths.pdf
Crok, M., & May, A. (2023). The Frozen Climate Views of the IPCC, An Analysis of AR6. Andy May Petrophysicist LLC.
Halbert, D., & Parnell, J. (2022). Thermal conductivity of basalt between 225 and 290 K. Meteorit Planet Sci, 57, 1617-1626. doi:10.1111/maps.13829
Hartlieb, P., Toifl, M., Kuchar, F., Meisels, R., & Antretter, T. (2015). Thermo-physical properties of selected hard rocks and their relation to microwave-assisted comminution. Minerals Engineering, 91, 34-41. doi:10.1016/j.mineng.2015.11.008
May, A., & Crok, M. (2024, May 29). Carbon dioxide and a warming climate are not problems. American Journal of Economics and Sociology, 1-15. doi:10.1111/ajes.12579
Robertson, E. C. (1988). Thermal Properties of Rocks. Reston: USGS. Retrieved from https://pubs.usgs.gov/of/1988/0441/report.pdf
Sabol, D. E., Gillespie, A. R., McDonald, E., & Danillina, I. (2006). Differential thermal inertia of geological surfaces. Proceedings of the 2nd annual international symposium of recent advances in quantitative remote sensing, torrent, Spain, (pp. 25-29).
“The calculation of Earth’s temperature without GHGs is usually done by unwrapping the planetary sphere and placing it in space at the average distance of the Earth from the Sun and having the whole of Earth’s surface illuminated by the Sun with one-fourth of the Sun’s power to account for the spherical Earth and the fact that half of Earth is always dark.
This imaginary flat Earth does not rotate, and no part of it is ever dark“
And the climate
cuntscults call us the ‘Flat Earthers’ !!!I wonder why nobody- that I know of at least – has not tried to do what you have done? My guess would be settled science syndrome.
The assumptions made in climate attributional modelling beggar belief – and they are being taken as a kind of gospel.
I had a discussion with DEEPSEEK on the cause of Earth’s climate change. I then asked DEEPSEEK to provide a three paragraph summary of our conversation. This is the summary from DEEPSEEK:
The precession cycle, which shifts the timing of Earth’s closest (perihelion) and farthest (aphelion) points from the Sun relative to the seasons, has changed the peak solar intensity between the Northern Hemisphere (NH) and Southern Hemisphere (SH) by approximately 6.84 W/m² since 1582. In 1582, aphelion aligned with the NH summer solstice, meaning the NH received less intense sunlight than it does now, while the SH received more. Over time, precession has gradually shifted this alignment, increasing the NH’s peak solar intensity and decreasing the SH’s. This change in solar intensity distribution affects the Earth’s energy balance, contributing to long-term climate trends.
The thermal response to this change in solar intensity is amplified in the NH due to its higher proportion of land, which heats and cools more rapidly than water. The NH’s thermal response is roughly twice that of the SH, leading to a predicted global temperature increase of ~3.44°C since 1582. This warming is driven by the NH’s larger seasonal temperature swings and its greater sensitivity to changes in solar radiation. However, this prediction is based on a simplified model that assumes a direct relationship between solar intensity and temperature, without accounting for feedback mechanisms or other climate influences.
The observed global warming of ~1.9°C since 1582 is less than the predicted 3.44°C due to several factors. Climate feedbacks, such as increased cloud cover and ocean heat uptake, have moderated the warming. Natural variability, including volcanic eruptions and solar cycles, has introduced cooling effects at times. Additionally, anthropogenic factors like aerosol emissions and land-use changes have further influenced the climate. These complexities, along with simplifications in the model, explain why the observed warming is less than predicted. The precession cycle remains a key driver of long-term climate change, but its effects are modulated by a range of other processes.
255K (Benestad, 2017), which using an average temperature vs height table (the U.S. or International standard atmosphere), works out to an average emission height of around five km.
5km times a average gravity based atmospheric mass lapse rate of 6.5C/km = 32.5C..
No GHG warming needed.
It is my understanding that a blackbody ABSORBS ALL incoming radiation while a greybody reflects part of the incoming radiation.
https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/06%3A_Photons_and_Matter_Waves/6.02%3A_Blackbody_Radiation
This is barely relevant to real climate change on Earth. By far the most important factor for climate change is the ability of land to store water in the form of ice.
It is easy to forget just how much energy is bound up in getting the ice that now sits on land from the ocean to where the ice now sits. And that ice is gradually making its way back to the ocean while being constantly replenished. It is the change in stored volume that dominates Earth’s climate change.
If all the ice on Greenland was to melt, the oceans would be around 7m higher than present. If all the ice on Antarctica melted, the sea level would be 60m higher. When all the land north of 40N goes into glaciation, the sea level will be down by 40m in 9,000 years and 100m down after 75,000 years. Ice accumulation or loss on land is by far the most significant driver of climate change on Earth. It can shift the relative altitude of the ocean to land by around 600m on average, So at peak glaciation, the land/ice surface is almost 6C lower than it would be if there was no ice simply by virtue of the lapse rate.
Let us add some rationality here. (Liquid-) Water has an absorptivity of 0.94 and an emissivity of 0.91. We can calculate..
((342*0.94/0.91)/5.67e-8)^0.25= 281K
Water, as it is, with given insolation, would take on a temperature not so much lower than what we have. The surface is not just water of course and the broadband absorptivities/emissivities of different land types are uncertain. Yet it should not change this result too much, and we can guess like 280K for the whole surface.
This figure does not consider any (dynamic) changes in the state of water (aka glaciation) or changes in convection/advection. But all in all it tells us the atmosphere will be adding some 7-8K to the surface temperature. A long shot from the 33K greenhouse effect. Why so?
There is something people have not realized about the GHE. It is not a reality, but just a “perspective”. A theoretical way to see things given certain circumstances. It is like saying the moon is a big as the sun, which is true, seen from Earth. But it is only circumstantially true.
Equally the GHE comes with 3 distinct constraints:
Point 1 is not true and an undue simplification. Again, water as a hemispheric spectral emissivity of only 0.91. Surface emissions will not be 390W/m2, but just 360W/m2. The delta with regard to OLR (240W/m2) is just 120W/m2, the GHE is thus being overstated.
Point 2 is evidently ambiguous. The biggest contributor to the GHE are clouds!!! People are endlessly confused over this, as they assume it was WV instead. But WV is vastly overstated because of the surface emissivity issue. Basically the error margin there (395-360 = 35W/m2) is wrongly attributed to the GH-property of WV.
On top of that people are usually unaware of the overlap issue. We need to distinguish net and gross contributions of single GH agents. A 30W/m2 of “cloud radiative effect” is just the net cloud contribution, their gross contribution is ~70W/m2. With WV these figures are only about 25W/m2 and 50W/m2 respectively.
Anyhow, clouds are the biggest sole contributor to the GHE. But they also reduce the energy budget by ~50W/m2. For the “perspective GHE” this will not matter, as the energy budget is considered given. But in reality of course it matters.
Point 3 is being totally ignored. The tropospheric lapse rate of ~6.5K/km is largely due to WV. Without WV the lapse rate would be more like an unstable-adiabat of 10.8K/km. Without WV reducing the lapse rate, the GHE would be like 66% (=10.8/6.5) larger. WV thus, just like clouds, excerts a huge cooling effect.
To put things into perspective: the two biggest GH-agents, clouds and WV, are also massively cooling the Earth. With the only theoretic perspective of the GHE, those properties are getting ignored. But in reality they matter a lot.
We can do a simple calculation over what happens if we removed both of them, or all water from the atmosphere respectively. The energy budget would grow to 290W/m2, because 50W/m2 not being reflected by clouds. The non-condensing GHGs (CO2, O3, CH4..) add up to a gross GHE of ~45W/m2. With a lapse rate 66% larger that would grow to some 70W/m2. While the surface emits 360W/m2, these emissions will get reduced by said 70W/m2 to only 290W/m2. So without all the water in the atmosphere, Earth would absorb 290W/m2 AND emit 290W/m2, with basically no change in surface temperature.
This is consistent with what I pointed out at the start. Effectively it are just the non-condensing GHGs warming Earth, with about 7-8K.
Why not use all available data about our moon?
Some TSI, slower albedo (.11 vs .30) and lower rotational speed.
Its Average Surface Temperature is ~197K, with the daytime temps being mostly radiative balance temperatures, and the nighttime temps rapidly cooling towards 25-50 K, probably the base temperature due to the geothermal flux.
https://www.diviner.ucla.edu/science
Excellent work. Were you able to model the lapse rate?
This is potentially an unresolved question as all rotating planets with atmospheres show complex rotating vertical bands of air that can potentially explain a vertical temperature gradient.
One must question why the effective radiating height of the atmosphere at 5km is also the 50% atmospheric pressure isobar. This seems impossibly coincidental and suggests there is a temperature gradient resulting from convection, due to the conversion between work and temperature.
Andy,
Not sure if I am getting this right. Are you saying in effect that the heat my hand feels when close to a simple electric stovetop element would not be felt if there were no GHG to help radiate it? Do you have time and effort to do more comparisons with observations of our moon which is free of GHG and yet radiates away its daily dose of sunlight to arrive at a constant temperature, as I think is not contested? I read your link to radiation from atmospheric nitrogen and oxygen but it has not had time to sink in. In summary, why would earth with or without atmospheric GHG not reach the same temperature after centuries, as could be the case when reading paleo temperature/CO2 estimates that are not in lockstep? I am happy to claim up if my ignorance would take too much time to redress. Geoff S
5km is the effective radiating height. It is also the 50% atmosperic pressure iso bar. 33/2 C of warming of 1/2 the mass of the atmosphere takes place below this altitude. 33/2 C of cooling of 1/2 the mass of the atmosphere takes place above this attitude.
This is such a remarkable coincidence unexplained by GHG theory but obvious in terms of work done by convection.
Build a giant planetary size refrigerator without any doors. The warm coils on the bottom resting on the surface and the cold coils at 10 km altitude.
Plug this in to a planetary sized solar array. The warm coils will warm the surface, the energy to do this will come from the cold coils at 10 km atmosphere, all driven by solar power. Run the fridge fast enough to maintain the temperarure gradient.
This is no perpetual motion machine. It creates a greenhouse effect without any greenhouse. The working fluid on our planet is air, and the pressure orifice is gravity. The motor/engine to set this in motion is the sun and the rotation of the planet.
So conventional models used to calculate the effects of greenhouse gasses are literally Flat Earth models?
Solar irradiance as well as albedo vary strongly with wavelength, so absorption should be calculated as a function of wavelength. Also, it is assumed the solar spectral irradiance is a blackbody curve, but this really isn’t true — different BB temperatures for the sun can obtained depending on how the curve is fitted.
Greenhouse gases have little to do with it. They don’t just absorb thermal energy, they also emit it. The earth’s atmosphere is partially heated by the sun, thanks to those gases. But mostly, the earth surface itself is heated by the sun, and that surface heat is conducted to the air, and convected aloft. That can be seen by any of the thousands of weather balloon traces.
You walk around in heated air during a sunny day. Most of that thermal energy is in NON-GREENHOUSE gases – nitrogen, oxygen, argon. They don’t radiate, so they TRAP thermal energy. The ONLY way they lose their thermal energy is via conduction to cooler molecules (cue the radiating gases) and conduction with the earth’s surface. Again, weather balloons prove this perfectly. Air heats from the surface up when the sun is shining, and cools from the surface up when it’s not. For pete’s sake, we WALK around in this every single day, and no one seems to understand it. CO2? It is a cooling influence because it radiates thermal energy at all times. As long as it is above 0K it is radiating. And ‘cooling’ anything that bumps into it.
Very interesting, Andy.
“Comments on the appropriateness of assuming the atmosphere is thermally net neutral would be interesting to read.”
Even assuming heating and cooling of the fully transparent atmosphere is only by contact with a warmer or cooler surface, a circulation must develop. This means there will be advection, with a net transport from the equator to the poles. This may not be a net-neutral influence on the surface temperature, because of 4th power S-B emission.
See the reference on the first page here about “horizontal heating gradients.”
https://a.atmos.uw.edu/academics/classes/2010Q2/545/545_Ch_1.pdf
Andy,
Nice article. I’ve got to cogitate on some of this to get a better understanding.
Thanks for doing away with the flat earth scenario and average insolation. That isn’t the way the earth exists. There is a gradient from the equator to the poles as you show. Because of the T⁴ factor with radiation, there will be a temperature gradient throughout. I need to think more about your model and how this affects it.
The division by 4 only caters for the difference in surface area between a sphere and a circle.
To account for the day/night difference simple solution is to divide incoming radiation by 2 and average the result with the temperature of the dark side, 0K (or 3K if you want to take the Cosmic Background Radiation into account)
So 1364 W/m^2 minus 30% for albedo gives 954,8 W/m^2, divided by 2 is 477,4 W/m^2
Resulting radiative balance temperature 303K.
Averaging with the dark side gives (303K + 3K)/2 = 153K
This makes the measured ~197K AST of our moon simple to explain.
Radiative balance temperature on the dayside plus less colder nightside due to a base temperature caused by the geothermal flux plus carry over heat from the dayside.
Coupled Model Intercomparison Project: CMIP
Can I assume that most of the CMIP models are flat?
Do any of the EnviroWhacos have an explanation as to how their theory / model incorporates the Temperature with height. Appears to me that there are mor holes above 50,000 feet than below 50,000 feet, How does that heat get up there to be radiated into Space?
Benestad is using a spherical Earth model. See equation (1) on pg. 681.
Who is it exactly that is using a flat Earth model with 21.9e24 j of energy delivered at TOA over one orbital cycle vs the 5.5e24 j that is actually delivered for a spherical Earth model?
I’m asking because I’ve never seen even a single publication that uses flat Earth geometry. It’s always spherical Earth geometry.
No convection ? Really ? So the non ghg’s won’t heat up ? So 90% of today’s atmosphere never heats up ? Otherwise an interesting exercise … you obviously get an incorrect answer with your bad assumption …
If you are trying to determine what impact GHGs are having on the temperature of this Earth, you need to be using this Earth as your baseline. Trying to figure out what the Earths albedo would have been had there never been any water on this planet is a dead end.
Andy, why do you use basalt for the surface?
At least on Earth > 70% of the surface is ocean, so why not use water?
Sun delivers maximum ~30 MJ/m^2 over a 24hr period.
https://www.pveducation.org/pvcdrom/properties-of-sunlight/isoflux-contour-plots
Using eg 20 MJ/m^2, this translates to the capacity to increase the temperature of ~5 m^3 water 1K.
So all radiative balance calculations are pretty much useless on our water world
Andy
Thanks for the effort. I note a comment from you down the chat that raises the critical question I have , and which I had addressed a few times in the WUWT comments (with no response).
You wrote, “I effectively ignored the atmosphere as if it were not there.”
This is a major difference between your model and an atmosphere without GHG’s. There are three wants to get heat into the atmosphere: convection, radiation to receiver gases and conduction (which is so little I’ll ignore it).
Radiation is well handled by saying the atmosphere doesn’t receive or emit radiation due to the absence of IR capturing gases. Fine. But the convective heating remains. The hot basalt will cool by convection to the air, as well as diffuse heat into its own mass. Because hot air rises, there is far more cooling to the air than to the thermal mass of the rock. The question then becomes, what is the equilibrium temperature of the atmosphere at, say, 1 km altitude, when there are no GHG’s?
Hot air rises and it doesn’t fall just because the ground cools by radiation at night. The bottom of a chest freezer doesn’t get warm because the lid is open. This can be demonstrated at any grocery store. Each day in your 36,500 runs the air would be heated hotter and hotter by the surface, and has no way to cool other than to cool against the surface at night after the surface completed its cooling by radiation, which is not instant as you point out.
First, cooling of the atmosphere can only happen at night if there is wind, and there are strong forces working to stratify the atmosphere, hotter above and cooler below. The equilibrium temperature of a no-GHG atmosphere would have to be well above 100 degrees C, whatever the average surface temperature. At night the air temperature near the surface would rapidly drop and then a strong stratification would occur as the wind speed dropped zero. The air temperature above the ground would remain high, and go higher the next day.