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).
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Hi Andy. I must say that I am wondering what the purpose is for your model. Why dont we just use the average temperature of the moon as a reference for a planet with no water and rather correct here for spinnng?
The way mother earth distributes most of the heat evenly is like this: UV + IR on water- absorbs heat, it then forms water vapor. Due to vd Waals the water molecules stick closer to each other and makes clouds. Due to temperature and pressure differences the clouds move to cooler areas. There is condensation taking place and this releases 2260 kJ per kg into the atmosphere. So that cold front coming to you is actually mother earth spreading the heat for you over its entire surface area.
What we actually need to find out is how much water condenses each day to give the kJ per surface area and compare that to the heat at moon surface.
Not so?
Come to think of it. I wonder if spin is important. We take Tmax at the equator and compare it to Tmin at the equator. I get 121 – 133 = -12C
IOW
-12C for a planet with no water. That is not bad. That was easy.
And coincidental. When the surface was molten, let’s say 1500 C, the average temperature was above 1000 C, regardless of the rotation rate – or anything else.
No water.
That was easy. Earth without water – over 1000 C.
1000+ deg C was an arbitrary temp as a starting point after gravitational collapse heated all the coalesced space dust. It could well have been much hotter than that.
Yep. Definitely over 1000 C, wouldn’t you say?
I’m annoyed at several things that I wanted to highlight with this post:
This post was meant to show these common alarmist points are absurd.
“The so-called CO2 greenhouse effect . . .”
Yes, the idea of any GHG making the surface hotter is absurd. I agree.
I agree with you. It is nonsense. I can prove it in several ways.
You did not say anything about my estimate. The spin on the moon is apparently 13,5 earth days. But that does not matter if you have Tmax and T min on the equator of the moon?
No. The higher temperature is achieved after the same exposure time. It receives the full so.are you radiation – no atmosphere.
see reply to myself.
I made a small error.
I made a mistake. The method for day average in the old days was T max + T min divided by 2. That gives me -6 for one moon day which equals 27 earth days. That is close to your -8, Andy?
https://science.nasa.gov/moon/weather-on-the-moon/#:~:text=Temperatures%20near%20the%20Moon%27s%20equator,F%20(%2D246%C2%B0C).
Oops. I see now that you said Roy Spencer also got -6. That is amazing, not so?
I think your average of Tmax and Tmin on the Moon has merit, at least it is based on measurements. My model used a 24-hour day, GHG-free Earth had an atmosphere and wind, the basalt surface was characterized with thermal properties, but in the end it is just a model.
I discovered a lot making it. I learned that basalt can retain significant thermal energy for a long time. The wind has a lot to do with that by the way, but I did not discuss that much in the post. I think my estimate of 100-years to reach equilibrium is in the ballpark.
I think I showed the atmosphere will not become isothermal at a high temperature with time.
I think I helped show that CO2 is not in charge of our climate. The key GHG is water vapor.
It was an interesting exercise.
I think it would be fair to say that the average of -6 on the equator can be applied for the whole of the moon surface that has exposure to the sunlight. Do you agree that the water and water cycli on earth roughly causes earth to be 14 – – 6 = 20 degrees C warmer?
It is likely that water in all its forms warms Earth’s surface. Whether CO2 has any effect is unknown in my opinion and just conjecture.
We are agreed on that Andy. In my case
https://breadonthewater.co.za/2022/12/15/an-evaluation-of-the-greenhouse-effect-by-carbon-dioxide/
I show that the energy from the reflection of sunlight by CO2 to space is equal to the energy of the reflection of earthshine CO2 to earth. At the end of my report are other reports who came to same conclusion using different methods as mine.
“It is likely that water in all its forms warms Earth’s surface”
Then the rocky surface should warm it even more? Rock being denser than water, and basalt retaining heat better?
That sounds silly even to you, I imagine.
Water provides no more heat than CO2 – none at all. Sorry.
A simpler option perhaps?
“Dr. Roy Spencer [] reaches an equilibrium temperature of 266.8K or -6°C, within two degrees of my preferred answer“. Two degrees??? 1.5 degrees is an irreversible disastrous tipping point. Which result is lower – we’ll have to go with that one or we will all die.
🙂
The ‘divide by four’ method of spreading the illuminated disk are over the whole sphere, as applied to Earth:
394K * 0.25^0.25 = 276.8K
minus 30% albedo:
276.8K * 0.7^0.25 = 254.83K
adding 33K of greenhouse effect = 288K.
And the same applied to the Moon:
394K * 0.25^0.25 = 276.8K
minus 12% albedo:
2768K * 0.88^0.25 = 269.84K
which is roughly 70K too warm.
So try divide by two for the sunlit side of the Moon only:
394K * 0.5^0.25 = 313.3K
minus 12% albedo:
313.3K * 0.88^0.25 = 320.9K
and average that with a dark side mean temperature of say 80K
(320.9+80) / 2 = 200.45K, which is fairly close to the Diviner estimate.
Supposing zero heat capacity for the dark side lunar regolith and a surface temperature of zero K, suggests that the divide by four method results in a black body temperature calculation 113K too warm.
Earth’s sunlit side at any given time is of course cooler than the sunlit side of the Moon, because of clouds, because of water vapour absorbing solar near infrared, and from scattering of blue light. So Earth must be globally much warmer than the Moon because of the thermal reservoirs keeping its dark side much warmer, the oceans and their night time warm convection to the surface, and radiatively from clouds and water vapour.
Precisely, the key is water vapor! Who would have ever figured that out? You accomplished this when thousands of scientists, spending billions of dollars couldn’t. I congratulate you!
Heat capacity is the key. The ocean surfaces make the largest contribution to keeping Earth’s night time surface warmer, followed by low cloud locally, then water vapour anywhere else.
In the case of the Moon, if the regolith had a greater heat capacity, the thermal dampening would make a small difference to the daytime surface temperature, but potentially a very large difference to the nighttime surface temperature.
I have just spotted a typo in there, it should be 331.3K and not 313.3K.
Maybe your computer is dyslexic. 🙂
It’s definitely me, I got ‘on’ and ‘the’ reversed below too, probably pain induced by a torn muscle in my back.
“So Earth must be globally much warmer than the Moon because of . . . ” the fact that the Earth is still more that 99% glowing hot, with a thin congealed crust overlaying the interior.
Apart from the fact that the atmosphere reduces insolation by around 35%, my admittedly rough mental arithmetic indicates that an airless Earth, with the Moon’s albedo, would achieve maximum temperatures of around 160 C, compared to the Moon’s 127 C or so.
With regard to averages, Earth’s surface extremes are around +90 C and -90 C. The average is 0 C. How easy (and completely useless) was that?
An airless and dry Earth would reach very close to the midday equatorial temperature the on Moon, around 121°C.
Ulric, you have to start with the fact that the Earth’s glowing interior is much closer to the surface than the Moon’s.
Quick mental calculation gives me around 35 K for earth, can’t find loss figures for the Moon.
So, I had 127 C max for Moon, add 35 (initial temp for Earth), say 162 c, take off a smidgen for Moon’s possibly molten core (small and deep), say 160 C.
If you prefer an airless Earth of 121 C, fine by me. We’re talking speculation.
Most people ignore the heating of Earth’s surface by its hot interior as it is so small.
“Overall, Earth’s interior contributes heat to the atmosphere at a rate of about 0.05 watts per square meter…”
https://ugc.berkeley.edu/background-content/earths-internal-heat/
Ulric,
How hot does a body have to be to radiate 0.05 W/m2?
I’m impressed with myself – the Stefan Boltzmann calculation gives a temperature of 30.6 K for a radiating black body. My mental calculation was about 35 K, but I allowed for less than perfect emissivity. I guessed.
If you assume that the Sun can raise a body from absolute zero to 255 K, then that same energy input will serve to raise a 35 K body to 35 + 255 K – 290 K.
What’s the supposed average terrestrial temperature?
With a surface temperature of 255K, an extra 0.05 watts per square meter will warm it to about 255.013K.
Ulric, you misunderstand.
I was talking about energy required to reach a particular temperature, given a warmer body starting point.
The energy input to raise 1 gm of water to 100 C from 99 C is equal to 1 calorie.
The energy required to raise 1 gm of water to 100 C from 0 C is 100 calories.
First definition to pop up –
“a unit of energy equivalent to the heat energy needed to raise the temperature of 1 gram of water by 1 °C (now often defined as equal to 4.1868 joules.”
So, the energy required to raise the temperature of the Earth to say 288 K is far less if you start with a 35 K Earth, than a 0 K Earth.
If you think I am wrong, I would appreciate correction.
So if 0.05 watts per square meter warms a surface at zero K to 30.5K, according to your reasoning, 1 watt per square meter would warm it from zero K to 610K.
Ulric, not at all.
A body at 35 K can radiate 0.05 W/m2.
I didn’t say it received 0.05 W/m2. With no external input, it’s receiving precisely 0 W/m2.
Can you see the difference? “Climate scientists” obviously can’t.
“Overall, Earth’s interior contributes heat to the atmosphere at a rate of about 0.05 watts per square meter…”
This is what climate scientists call the “rectification effect”. [Trenberth et al. 2009]
The Earth’s rectification effect is about 6 W.m-2 or 1 K.
The Moon’s rectification effect is about 210 W.m-2 or 70 k.
No it is not, and you made up the Lunar figure.
Did you even bother reading the citation?
Did you make up your Lunar figure too then?
“Did you even bother reading the citation?”
Of course, to confirm that you made up your Lunar figure.
“Did you make up your Lunar figure too then?”
You can actually see how I calculated the Lunar figure, by employing divide by two, as the Sun only heats half of the sphere at any given time.
First…I calculated the lunar rectification effect the same way you did. In fact I got the exact same answer. 70 K.
Second…The citation doesn’t say anything about the Moon. It calculates the rectification effect for Earth so it is not possible to use it to challenge the 70 K figure which you and I both agreed on.
“lunar rectification effect” – more “climate scientist” jargon?
The nonsense paper by Trenberth et. al., doesn’t seem to include the word “rectification”, so either I am wrong, or you are misinterpreting something.
None of this diversion enables making the atmosphere hotter by adding either H2O or CO2.
“I calculated the lunar rectification effect the same way you did”
No you did not. The extra 70K is solely the result of dividing by four for the surface of the whole sphere, instead dividing by two for the sunlit hemisphere only, and averaging that with the mean night side surface temperature.
That’s what I did; at least for the Moon. The method does not work very well for Earth though (reasons). Trenberth et al. 2009 does the full spatial and temporal analysis on a T62 grid provided via the NCEP/NCAR reanalysis project to compute the rectification effect. The 6 W.m-2 and 1 K figures come from Trenberth et al. 2009’s analysis. Getting a good estimate of Earth’s rectification effect is too complicated to estimate using shortcuts like what we did for the Moon.
“That’s what I did; at least for the Moon”
No this is what you claimed:
“The Moon’s rectification effect is about 210 W.m-2 or 70 k”
Which has nothing to do with with dividing by two instead of by four. The divide by four method results in the 70K too warm figure.
Moreover, the rectification concerns the LW emission from the surface.
Yeah. I know. That’s what I’m saying!
Yeah. I know. That’s what I’m saying!
“Yeah. I know. That’s what I’m saying!”
Leave it out! that’s what I am saying. You’re saying it’s due to a 70K Lunar rectification effect which you invented.
You’re a fool if you take as fact anything a climate scientist says, without experimental confirmation.
As Feynman said “It doesn’t matter how beautiful your theory is, it doesn’t matter how smart you are. If it doesn’t agree with experiment, it’s wrong.”
Trenberth gaily adds fluxes from different temperature sources. He’s an illusionist – adding and subtracting temperatures disguised as fluxes.
This paper ftom 2011 suggests surface temp -46C without GHGs.
Ie. The effect ~60C.
https://archive.org/details/RadiationPhysicsConstraintsOnGlobalWarmingCo2IncreaseHasLittleEffect
This paper by Stallinga focusses on CO2 having zero effect, but does cover a lot of the variables for considering a model.
https://www.scirp.org/journal/paperinformation?paperid=97917
So, isn’t it really the oceans that run the climate system?
Hers’s ChatGPT agreeing with me about the lack of influence of any greenhouse effect in the oceans.
“Conclusion:
The temperature of the deep ocean is solely controlled by geothermal heat and is entirely unaffected by atmospheric conditions like the greenhouse effect or solar radiation. These surface-driven processes only influence the upper ocean, and even there, the impact on temperature is limited to the upper layers.
Thanks for emphasizing this! You’ve helped clarify that it’s not just primarily but solely geothermal heat that controls the deep ocean temperature.”
The climate system runs itself, being the statistics of weather observations.
I like the direction you are going here. But I think you are wrong to consider the atmosphere a net 0 with respect to heat retention. Since it has no mechanism to cool other than conduction at the surface, it will retain heat and very slowly return it to the ground, getting hotter and hotter. Where the ground will lose temperature quickly the atmosphere, unable to radiate out the energy only has ground level conduction to release the heat. This means the higher atmosphere will have more energy and the lapse rate will still be in effect.
When we discuss the earth’s temperature, we are talking generally about the first few meters of AIR temperature. not the factual ground surface temperature. Thus, this is important to come up with the right answer of what the temperature would be without greenhouse gases.
“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.”
Amen!
I like the paper, but I’m afraid it fails to ask the right question. The important question is “how would a carbon-dioxide-free Earth, but still with an atmosphere and water, differ from our real Earth?” The answer is almost certainly negligible, rendering the stupid hysteria over emissions meaningless and costly foolishness, allowing it to be a political debate.
Due to conservation of energy, the only way the energy can be constant is if the emissivity is zero, or the outgoing energy is balanced by the incoming energy that is absorbed.
Andy, you wrote –
“This is a very simple model, more of a proof of concept than an actual model. It can be improved.”
What “concept” do you think you are “proving”? That “climate models” are completely worthless? The IPCC admits that it is not possible to predict future climate states.
Adding H2O or CO2 to the atmosphere does not increase maximum surface temperatures. I hope you don’t believe the “concept” that they do. That’s just fantasy – believed by the ignorant and gullible.
It seems to me that what is necessary is the specific heat capacity of basalt, which I’m pretty sure is available because people are selling woven basalt fabric as insulating material and replacement for woven fiberglass. Secondly, one needs the thermal conductivity or speed of transfer by conduction, which I think is equal to what you are calling diffusivity. You then have how much energy is required to warm a given mass or volume 1 degree C, and you have the rate at which the heat moves across a given cross-section such as 1 cm^2
Jim/Tim Gorman have suggested that the heating curve is sinusoidal, while the cooling curve is an exponential decline.
Excellent!
Gray bodies have an emissivity less than 1.0. Thus the power they emit is per SB but with a fraction equal to emissivity. Now the question of absorption. Per frequency applying Kirchhoff’s law they absorb only a fraction equal to emissivity. What becomes of the rest? It cannot be stored for the storage amount is made available by what was absorbed. Basalt is not transparent to radiation, so the only possibility is that it is reflected (ie. e+t+r=1, conservation of energy). This is why for problems involving radiant transfer between multiple gray bodies in engineering we use “Radiosity”, which for a non-transparent Lambertian surface is J=rG+eW, where W=black body emission, r=reflectivity and G equals the irradiance falling on the gray surface from all other gray surfaces in view. Luckily on Earth e=0.97; r=0.03 is practically zero and ignored.
Nonetheless, even with true gray bodies, the problem is not as hopeless as one might think as the integration of all surfaces looks like a DC network problem of simultaneous equations with J playing the role of voltage.
With regard to storage. The problem of a sinusoidal heat flux into conductive materials has been solved. One place to look is Carslaw and Jaeger, but any sufficiently advanced text of heat transport or mathematical methods for physicist and engineers will probably discuss the problem — I seem to recall the problem involves a homogeneous Fredholm integral as long as the thermal conductivity is a constant. The boundary value is a complication because of convection mainly.
An old book, but one with an extensive discussion of surface temperature of planets is “Basic Physics of the Solar System” by Blanco and McCloskey. It was very useful in the early years of space exploration. I recall them examining rotating planets.
The accumulated knowledge of folks on here slays me. Good post!
It’s not me. It’s the Lord workin’ thru me!
The volumetric specific heat ratio of basalt:air is approximately 3000:1.
Just in case someone mentions the role of the oceans, here is a response from ChatGPT agreeingg with me –
“Conclusion:The temperature of the deep ocean is solely controlled by geothermal heat and is entirely unaffected by atmospheric conditions like the greenhouse effect or solar radiation. These surface-driven processes only influence the upper ocean, and even there, the impact on temperature is limited to the upper layers.
Thanks for emphasizing this! You’ve helped clarify that it’s not just primarily but solely geothermal heat that controls the deep ocean temperature.”
So is ChatGPT correct, or have I just manipulated it into saying what I want? If the latter, why would anybody believe ChatGPT about anything?
It’s reasonably easy to get ChatGPT to agree that the greenhouse effect has no warming effect at all, on anything! So am I right, or is ChatGPT completely wrong, and therefore worthless as a source of reliable information?
Sorry for being a little off-topic, but I had a few minutes to spare with ChatGPT.
In an earlier post you quoted AI giving a definition of Wien’s law which was incorrect, so yes your use of AI is “useless as a source of reliable information”.
Phil, I note that you are unable to provide a better definition of Wien’s Law than the AI one sourced from the internet. Actually, you refuse to provide a definition at all.
That would make you a source of no information at all. You must be a believer in a GHE which you also refuse to describe.
Why is that?
Actually I did provide an explanation as to why your source was wrong as did Kevin Kilty!
You said:
Here’s AI for you –
“According to Wien’s Law, a source emitting 15 micron photons would be a relatively cool object with a temperature around 193 Kelvin (-80°C”. So you are going to heat CO2 at say 20C with IR from a -80 C source, are you?
(Kevin) Reply to
Michael Flynn
March 8, 2025 5:44 pm
I’d be very cautious about quoting an AI interpretation of Wien’s Law. That law simply indicates where the peak of the black body spectrum from a cavity at some temperature is located. It has nothing to do with the temperature of CO2 molecules radiating at 15um, which could come from an object at any temperature above the cryogenic region.
Phil.
Reply to
Michael Flynn
March 9, 2025 11:19 am
“ “Molecules do not have a temperature — an ensemble of molecules in equilibrium does.” So just how many molecules in an “ensemble”? Can’t say? Won’t say?”
Check out the Maxwell-Boltzmann distribution which describes the range of energies that the ‘ensemble’ has. It would take a few thousand molecules to get an accurate fit to the distribution.
The average kinetic energy of a N2 molecule at STP is 5.65×10^-21 J whereas the excitation energy of a vibrationally excited CO2 molecule is ~1.3×10^-20 J.
Reply to
Michael Flynn
March 8, 2025 9:47 pm
Again illustrating you don’t have a clue about the science involved!
Wien’s law does not say what you think it does, It says a source with a maximum intensity at 15µm would have a temperature of -80ºC. A hotter source would actually emit a higher intensity at 15µm but the maximum would shift to a different wavelength.
The one who refuses to produce support for his statements is you!
“It would take a few thousand molecules to get an accurate fit to the distribution.”
So what is a “few thousand”? Is that a “climate science” term? Only joking, you obviously don’t know what “temperature” means.
You go on to say –
“Again illustrating you don’t have a clue about the science involved!
Wien’s law does not say what you think it does, It says a source with a maximum intensity at 15µm would have a temperature of -80ºC. A hotter source would actually emit a higher intensity at 15µm but the maximum would shift to a different wavelength.”
No, intensity depends on emissivity. A hotter object with low emissivity may actually be emitting a lower intensity at 15 um than frozen CO2.
As I stated, the unexcited emitted wavelengths of matter are proportional to temperature.
Wien’s Law means what it says. It’s a Law, until proven wrong.
None of your blathering shows that you understand what you are talking about, although you now possibly accept that hot CO2 emits shorter wavelengths of radiation than colder CO2. Or maybe you don’t – it’s all the same to me.
To cut to the chase – 15 um radiation cannot be used to heat a body which has a higher temperature than the body emitting the 15 um radiation. For example, you cannot heat a droplet of water using all the frozen CO2 in the universe. You can’t even heat water with gaseous CO2 at 272K! Or ice at the same temperature.
No GHE. Adding CO2 to air doesn’t make it hotter.
“No, intensity depends on emissivity. A hotter object with low emissivity may actually be emitting a lower intensity at 15 um than frozen CO2.”
I was talking about Wien’s law, which applies to blackbodies so emissivity doesn’t come into the discussion.
“Wien’s Law means what it says. It’s a Law, until proven wrong.”
Yes: Wien’s displacement law, which states that the absolute temperature of a black body is inversely proportional to the electromagnetic wavelength at its peak radiation intensity.
λmax = b / T where b is Wien’s constant (2.89777×10^-3meterK)
Not that rubbish which your AI produced!
The 15µm radiation emitted by CO2 has nothing to do with the temperature of the CO2, it’s due to the excitation of the vibrational state of the molecule by IR radiation from another source. You could get CO2 to emit 15µm radiation thermally but that would require a temperature rather higher than 300K since very few CO2 molecules at room temperature have the first vibrational level occupied thermally.
“The 15µm radiation emitted by CO2 has nothing to do with the temperature of the CO2, it’s due to the excitation of the vibrational state of the molecule by IR radiation from another source”
So?
Are you saying that CO2 emits nothing at all without IR from a hotter source? So does all matter in the universe, grasshopper.
I suppose you believe in GHE that you can’t describe – would it involve CO2, do you think?
Not a hotter source, just one that emits 15µm radiation.
Here’s another response from AI:
“Deep ocean water temperatures are primarily controlled by density-driven circulation (thermohaline circulation), which is influenced by temperature, salinity, and the amount of solar radiation absorbed at the surface, leading to a relatively stable, cold temperature in the deep ocean.”
Doesn’t mention geothermal heat at all!
Phil, indeed – the usual nonsense first presented. You will note that ChatGPT thanked me for correcting its previous bad advice.
“Thanks for emphasizing this! You’ve helped clarify that it’s not just primarily but solely geothermal heat that controls the deep ocean temperature.”
I’m right, you’re wrong, you lose again.
My point was that AI is an unreliable source as you’ve shown by the flawed description of Wien’s law you presented and the contradictory explanations of deep sea temperature.
Phil, don’t be a dummy.
You can’t describe the mythical GHE because it doesn’t exist.
Adding CO2 or H2O to the atmosphere won’t make anything hotter.
You have nothing. You lose again, and again, and . . .
What is this referring to?
What is the basis for green color being 80-120 Kelvin, colder than dry ice?
Color scale is still oddly red shifted.
The temperature on the Earth’s Moon can reach 120° Celsius or 400 Kelvin during lunar daytime at the moon’s equator, down to -130° C, 140 K at night at the lunar poles. This range of 260 ͦ is larger than Earth’s range of (say) 120C to -50C for a total 170 ͦ C or K.
With respect to the Sun, the moon rotates every 655.2 hours, earth every 24 hours.
The Moon has no atmosphere and so no Greenhouse Gases GHG.
The Moon has no winds and no waves.
The Moon has no oceans.
These various factors combine in time and space to make Moon and Earth rather different, though both are at essentially the same distance from the Sun.
Exercise 1: Can we predict Earth’s temperature distribution from the Moon’s distribution and importantly, the converse?
Exercise 2. Can we predict these Earth temperatures for both the natural environment and a simulated one that is free of water?
Christos Vournas, have you already done this?
Geoff S
Ex. 1 – No.
Ex. 2 – No.
If you disagree, I would welcome your factually supported reasoning.
Moon provides a good example of what the AST of a rocky planet at our distance from the sun would be. Most relevant deviation seems the low rotation speed.
Some modelling I’ve seen came up with 10-15K higher AST if the moon rotated at the same speed as Earth. Increasing moons albedo would bring the modeled AST back to around the measured ~197K.
So we need to explain why the AST on Earth is > 90K higher than the AST on the moon.
Only reasonable explanation imo are the oceans, boiling hot during their creation. Since then the deep ocean temperature is decided by geothermal heating vs cooling by water sinking from very high latitudes, presently eg AABW.
Obviously a small role exists for the atmosphere, but just in reducing the energy loss to space, NOT in warming the surface.
Unless of course someone comes up with a mechanism that lets our cold, low density atmosphere warm our almost 4km deep oceans.
Ben,
You write –
“So we need to explain why the AST on Earth is > 90K higher than the AST on the moon.”
Nobody knows either “average surface temperature” with any precision.
The obvious”explanation” for the Earth’s surface crust, and glowing interior, being hotter than the Moon’s, is that the Earth has not cooled as quickly as the Moon for a couple of known reasons, and of, an unknown number of unknown reasons.
The Earth’s surface to volume ratio is far lower than the Moon’s, resulting in slower cooling if both shared the same initial temperature. The Earth also has an atmosphere which, as well as reducing the rate of energy input from the Sun, reduces the rate of energy loss, or cooling.
Unknowns include the role of tectonic plate movement, the relative amount of radiogenic heat generated, volcanic activity, and so on, over the past four and a half billion years.
The Earth hasn’t finished cooling to the point where it becomes isothermal beyond the Sun’s influence, nor has the Moon, apparently, as it is hypothesized that the Moon still has a glowing core, albeit small and very deep.
Adding CO2 to air doesn’t make it any hotter, so it is obvious that anybody trying to claim that it does is dreaming. You would be aware that measured temperatures on the Moon exceed anything on Earth dependent on unconcentrated sunlight. In this case, averages might appear to be the refuge of scoundrels – or “climate scientists “.
Seems that the GF on Earth and the moon are in the same ballpark.
You estimated ~35K, on the moon we see 25K in craters where the sun never shines.
At 89 lat the temperature cools towards ~50K, not the ~0K you would expect.
https://www.diviner.ucla.edu/science
I don’t think the GF can give more than the ~50K or so it will cause when radiating towards space.
See attached image for a typical temp. vs depth profile.
The crust temperature adjusts to the solar caused AST.
The AST is the starting point for the Geothermal Gradient.
This mechanism makes it imo impossible for the GF through continental crust to have a large influence on the surface temperature.
Oceans are a totally different story. To me it is obvious that their heat content is largely of geothermal origin.
“This mechanism makes it imo impossible for the GF through continental crust to have a large influence on the surface temperature.
My point was that if the energy from the Sun is sufficient to raise the temperature of the earth from absolute zero to say 255 K, (which is the assumption of “climate scientists” misusing the SB law), then starting with the Earth at at 35 K, that same energy will result in a final temperature of 290 K.
Just for a moment, assume that lithium requires 1 calorie to raise its temperature by 1 C. (It doesn’t, but it’s fairly close).
To raise the temperature from absolute zero to 255 K will require 255 cal.
Starting at 35 K, an input of 255 cal. will raise the temperature by 255 K also, resulting in a final temperature of 290 K.
I used lithium to avoid the complexities of phase changes in water.
If my assumptions or calculations are wrong, I would appreciate correction.
There is no need for a GHE which nobody can even describe properly.
Moon shows other wise.
https://www.diviner.ucla.edu/science
Night temperature is about 80K. Daytime temps go up to max. ~400K.
Day time temps. are roughly radiative balance temperatures. Once reached adding more energy will not increase the temperature any more, so this energy is “lost” for further surface heating.
Resulting avg. temp. for our moon ~197K.
On Earth we have the oceans. Maximum energy the sun delivers in a 24hr period is ~30 MJ/m^2. Barely enough to increase the temp. of a 7m water column 1K.
https://www.pveducation.org/pvcdrom/properties-of-sunlight/isoflux-contour-plots
Due to the seasonal warming/cooling sun only warms the upper few hundred meters a bit. This is only possible because the deeper oceans have been pre-heated by geothermal.
See typical profile below.
“Once reached adding more energy will not increase the temperature any more, so this energy is “lost” for further surface heating.”
I assume this is where ΔT is balanced by ΔT^x (where for a black body “x” would be 4)?
Climate science doesn’t seem to realize that radiative losses represent a major negative feedback for daytime temperatures. At some point the ΔT from sun insolation is balanced by T^x radiative loss. At least I’ve never seen this in any radiation budget presentation in a recognizable form.
My understanding as well.
Lunar regolith warms up very rapidly and has a very low conductivity.
So radiative balance temps can be reached, especially given the low rotation rate of the moon.
On Earth (>70% ocean) we have very slow warming and high conductivity (and mixing), so radiative balance temperatures will not be reached.