By Philip Mulholland
1. Introduction.
The following image shows the Earth’s outgoing longwave radiation recorded by the CERES (Clouds and the Earth’s Radiant Energy System) Instrument onboard the NASA Aqua Satellite (Damadeo and Hanson, 2017). This image is compiled from measurements made on March 18 2011, near the time of the Vernal Equinox.
Image credit: NASA
The colour table legend records the energy flux of the outgoing radiation. This flux ranges from a minimum value of 150 W/m2 displayed as white, to a maximum flux of 350 W/m2, displayed as yellow. Using the Stefan-Boltzmann law of radiative emission these energy flux values can be converted to emission temperatures using the following equation: –
Where T is the thermodynamic temperature in Kelvin.
j* is the black body radiant emittance in Watts per square metre.
σ is the Stefan-Boltzmann constant of proportionality.
(Sigma has a value of 5.670373 * 10-8 W m-2 K-4)
Using equation 1 we can determine that the emission temperatures recorded by the Ceres instrument range from a minimum value of 226.8 Kelvin (-46.2oC) for the 150 W/m2 low-end flux, to a maximum value of 280.3 Kelvin (7.3oC) for the 350 W/m2 high-end flux.
2. Calibrating the CERES image
The CERES image is a single snapshot of the Earth’s thermal radiant emission to space. This image contains a significant amount of information, however to understand this in its global context we must first calibrate the image against known measurements of the major components of the Earth’s atmospheric system.
The Earth’s atmosphere is a dynamic system composed of three separate types of interlocking cells, symmetrically distributed in each hemisphere. These cells consist of two thermal cells and one mechanical cell, they are: –
1. The tropical thermal Hadley cell located between the equator and latitude 30 degrees.
2. The temperate mechanical Ferrel cell located between latitude 30 degrees and latitude 66.56 degrees.
3. The frigid thermal Polar cell located around each pole and defined by the Arctic and Antarctic circles.
The global areal distribution of each cell is as follows: –
1. The Hadley cells occupy 50% of the surface area of the globe, and in total intercept 60.9% of the sun’s insolation.
2. The Ferrel cells occupy 41.75% of the surface area of the globe, and in total intercept 36.29% of the sun’s insolation.
3. The Polar cells occupy 8.25% of the surface area of the globe, and in total intercept only 2.81% of the sun’s insolation.
The high concentration of insolation intercepted by the tropical Hadley cells, compared to the low insolation intercepted by the Polar cells, is the fundamental reason for the low surface temperatures found in the polar regions of our planet.
Visual inspection of the CERES image shows the presence of cloud tops associated with the convective storms of the equatorial intertropical convergence zone (ITCZ) or doldrums. These storms are radiating at 150 W/m2 and have an emission temperature of 227 Kelvin (-46.2oC). In order to determine the elevation of this emission, we need to establish three atmospheric parameters for the Hadley, Ferrel and Polar cells, which are: –
1. The height of the tropopause.
2. The temperature of the tropopause.
3. The environmental lapse rate of the atmospheric cell.
Using these three metrics we can then calculate the temperature elevation profile that relates to the given emission rate for each of the three atmospheric circulation cells. Published information for the temperature of the tropopause is not easy to establish, however using various sources the values used in this analysis were obtained and are recorded in Table 1.
| Cells | Hadley | Ferrel | Polar |
| Tropopause Height (km) | 17 | 13 | 9 |
| Tropopause Temperature (Celsius) | -83 | -78 | -78.5 |
| Environmental Lapse Rate (K/km) | -6.5 | -6.5 | -6.5 |
| Information Source | Environmental Lapse Rate |
Table 1: Atmospheric Cell Parameters.
Using the values established in Table 1 we can now determine the top down temperature profile for each of the three atmospheric cells. The calculations for the Hadley cell show that to maintain a 17 km tropopause with a temperature of 190 Kelvin (-83oC) and a lapse rate of -6.5 K/km, then the average surface temperature of the tropical zone must be 301 Kelvin (27.9oC).
Table 2: Hadley Cell – CERES Image Emissions Calibration Table.
Converting this average surface temperature of ~28oC into a radiant energy emission flux, by using the Stefan-Boltzmann equation, we can establish that the tropical surface energy flux is 465 W/m2. This value is 115 W/m2 higher than the maximum observed flux of 350 W/m2 in the Ceres image, and so we have established that this image does not record direct sea level surface radiant emission. Rather, with this image we are observing the atmospheric temperatures at elevations of 3,160 m (10,370 ft) and above. Consequently, all high elevation land surfaces in the latitude zone of 30oS to 30oN, such as the Tibetan plateau at 4,500m (14,750 ft), will be capable of directly emitting thermal radiant energy to space through the overlying atmosphere.
The calculations for the Ferrel cell show that to maintain a 13 km tropopause with a temperature of 195 Kelvin (-78oC) and a lapse rate of -6.5 K/km, then the average annual surface temperature of the temperate zone will be 280 Kelvin (6.5oC).
Table 3: Ferrel Cell – CERES Image Emissions Calibration Table.
Converting this average surface temperature of 6.5oC into a radiant energy emission flux, by using the Stefan-Boltzmann equation, we can now establish that the temperate zone surface energy flux is 346 W/m2. This value is 46 W/m2 higher than the maximum observed flux in the Ceres image of 300 W/m2 for the temperate zone as seen from space. Once again, although this image does not record direct sea level surface radiant emission, all land surfaces with an elevation above 1,500 m (4,920 ft) will be capable of directly emitting thermal radiant energy to space through the overlying atmosphere.
The calculations for the Polar cell show that to maintain an 9 km tropopause with a temperature of 194.5 Kelvin (-78.5oC) and a lapse rate of -6.5 K/km, then the average annual surface temperature of the polar zone will be 253 Kelvin (-20oC).
Table 4: Polar Cell – CERES Image Emissions Calibration Table.
Converting this average surface temperature of -20oC into a radiant energy emission flux, by using the Stefan-Boltzmann equation, we can now establish that the polar zone surface energy flux is 232 W/m2. This value is just 7 W/m2 higher than the maximum observed flux in the Ceres image of 225 W/m2 for the region of the Southern Ocean, south of the Antarctic circle. This calculation demonstrates that all parts of the polar regions above 310 m (1,020 ft) elevation, and in particular the high elevation ice domes, will be capable of directly emitting thermal radiant energy to space through the overlying atmosphere.
3. Conclusion
Using the average surface temperature values calculated for each cell (Tables 2, 3 & 4), combined with the percentage of the global areal distribution of each cell (Table 5)
Table 5: Calculating the Global Areal Distribution of the Atmospheric Cells.
we can now compute the average annual surface temperature of the Earth (Table 6).
Table 6: Calculating the Global Average Temperature of the Earth.
The average temperature of the Earth determined by this calculation method is 288 Kelvin, which is the currently accepted value of 15oC used by climate science.
4. Discussion
The process of establishing the average temperature of the surface of the Earth presented here, relies on the following atmospheric measurements and fundamental planetary parameters.
These are: –
1. The height of the tropopause for each atmospheric cell.
2. The temperature of its tropopause.
3. The environmental lapse rate of each atmospheric cell.
4. The relative proportion of the Earth’s surface occupied by each cell.
With these measurements established, the global average temperature of the Earth is simply the arithmetical sum of the relative proportion surface temperatures for the three atmospheric cells.
Perhaps the most interesting part of this analysis is the apparent coincidence between the maximum surface elevation of the Antarctic Icecap at Dome A (4093m) and the maximum elevation of supercooled water (Moore and Molinero, 2011) in the atmospheric profile of the Polar Cell (Rubin, 1953). It would appear that the vertical elevation of continental ice caps is limited by atmospheric processes, however it is equally clear that no such vertical constraint occurs with solid rock land surface elevation. Because mountain ranges can reach vertical elevations that lie within the radiant transmission zone to space for each atmospheric cell, it appears that these topographic features can form leak zones that emit radiant energy to space independently of the transmission properties of the overlying atmosphere.
References
Beal, A. 2011. The Surface Area of a Sphere Between Parallel Planes. Online Blog
Damadeo, K. and Hanson, H. 2017. CERES Clouds and the Earth’s Radiant Energy System. NASA 9pp.
Moore, E.B. and Molinero, V. 2011. Structural transformation in supercooled water controls the crystallization rate of ice. Nature, 479, 506-508.
Rubin, M.J., 1953. Seasonal variations of the Antarctic tropopause. Journal of Meteorology, 10(2), pp.127-134.
Excel spread sheet containing the source tables for the essay.
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I like the way Kristian deals with the CERES data in relation to global warming theory. As he states:
Three Tests for GHG Warming in the Sky
The null hypothesis in this case would claim or predict that, if there is NO strengthening “greenhouse mechanism” at work in the Earth system, we would observe:
1. The general evolution (beyond short-term, non-thermal noise (like ENSO-related humidity and cloud anomalies or volcanic aerosol anomalies))* of the All-Sky OLR flux at the ToA to track that of Ttropo (e.g. TLT) over time;
2. The general evolution of the All-Sky DWLWIR at the surface to track that of Ttropo (Ts + Ttropo, really) over time;
3. The general evolution of the All-Sky OLR at the ToA and the All-Sky DWLWIR at the surface to track each other over time, barring short-term, non-thermal noise.
The post at okulaer is https://okulaer.wordpress.com/2018/11/11/how-the-ceres-ebaf-ed4-data-disconfirms-agw-in-3-different-ways/
My synopsis is https://rclutz.wordpress.com/2018/12/12/no-ghg-warming-fingerprints-in-the-sky/
My interpretation is that, whatever internal system changes occur, the average surface temperature stays the same for the same insolation and atmospheric mass but the energy distribution across the surface changes.
If it were not so then the existence of atmospheric convective cells would not continue indefinitely.
The convective cells must change in size, shape or vigour in order to neutralise internal system imbalances otherwise the atmosphere would either be lost to space or fall to the ground.
That scenario is implicit in the author’s four relevant parameters.
The only question then is to what extent do the air circulation patterns change in response to GHGs.
Given the size of natural variability it must be indiscernible.
Stefan-Boltzmann is invalid in this context, as would be Kirchhoff’s Law. Neither Earth nor its atmosphere, nor any part of the atmosphere is a black-body. To be valid, these “laws” require a genuine black-body, as in soot black.
THX1138
I’m asking how long this ridiculous black-body manipulation will persist among the ‘skeptic’s.
The one and only difference between a black-body and the rest (the so called gray-bodies) is that while a black body absorbs all incoming radiation, the others reemit a part of it.
The rest is pure, unscientific invention.
Actually, the unscientific invention is the notion that a planet whose principal means of heat transfer to its gravitationally-bound atmosphere is via evaporation constitutes a thermodynamic”gray” body.
1sky1
Sorry: writing a highly educated prose does not exempt a proof.
I guess the more important take away from this picture is, whether you think it supports the IPCC position according to which clouds reduce emissions by 31W/m2 (or even less), or whether it is (much) more. Nothing less than the GH theory is at stake.
Leitwolf
I don’t think that there has ever been any doubt that clouds block surface emission to space. We know that on clear winter nights a ground frost occurs as radiation passes out to space through the atmospheric window. Whereas on cloudy nights the temperature does not fall as low because the clouds block surface radiative cooling.
The real question is what is going on where there are no clouds? Have a look at India, its shape can easily be identified coloured in bright yellow on the 18Mar2011 CERES image. This is pre-monsoon season and India appears to be like the Atacama Desert in Chile. The humidity in the Atacama Desert, is between 5 to 10% all year round. Here is a link to the nullschool Total Precipitable Water (TPW) data for 18 Mar 2014 (the 2011 data is not available).
https://earth.nullschool.net/#2014/03/18/0000Z/wind/surface/level/overlay=total_precipitable_water/winkel3=174.48,-0.32,332/loc=-68.246,-24.300
Move the green cursor ring from Chile (3.217 kg/m3) to pre-monsoon India (click on the map) and notice that the TWP values there are up to 9 times those of the Atacama.
https://earth.nullschool.net/#2014/03/18/0000Z/wind/surface/level/overlay=total_precipitable_water/winkel3=174.48,-0.32,332/loc=75.156,17.506
Nice article.
What is the relation between Earth rotation speed, aka angular momentum of air mass on equator, aka Coriolis force and size of Hadley cell?
Earth rotation is significantly slowing down in scope of hundreds million years.
My feeling is that higher the Earth rotation speed, the stronger and stable jet streams and Hadley/Ferrel cells.
Thus greater difference in temperature between tropic, moderate and polar zones.
Thanks Peter.
Planetary rotation rate is a big issue. The speed of daily rotation is one of the fundamental controls on planetary climate. We can divide the terrestrial bodies that have a gaseous atmosphere into two groups, slow rotators, such as the planet Venus and the Saturn moon Titan, and rapid rotators such as Earth and Mars. Slowly rotating Venus does not have an equatorial bulge, this is in contrast with rapidly rotating planets, such as Earth and Mars, that do.
On Earth the rapid daily rotation limits the latitudinal reach of the Hadley cell, it creates forced descent of upper atmospheric air in the mid-latitudes and directly accounts for the existence of the Ferrel cell. The Ferrel cell is a mechanical cell that acts as a cog between the tropical thermal Hadley cell of solar heating and energy surplus, and the thermal Polar cell of surface radiant cooling and energy deficit.
The impact of the forced descent of Hadley cell air in the mid-latitudes can clearly be seen in the CERES image. This descent creates a zone of high surface pressure and reduced moist convection that allows for significant planetary thermal loss to space over continental land areas, such as the Sahara Desert of North Africa. Over the adjacent mid-Atlantic and Indian Oceans, the same latitudinal zone of forced air descent allows for clear skies and deep penetration of solar insolation that leads to energy capture and retention by the marine waters below.
Slowly rotating Venus does not have a Ferrel Cell. On Venus the Hadley cell extends from the equator to the pole, and only at the Venusian poles can deep atmospheric release of thermal energy to space occur. As a direct consequence of mid-latitude forced air descent on Earth there is a significantly larger planetary area that can produce solid surface thermal loss to space, thereby acting as one of the controls of planetary temperature.
Have a look at these two papers that deal with the issue of planetary rotation rate: –
Hunt, B.G. 1979: The Influence of the Earth’s Rotation Rate on the General Circulation of the Atmosphere. Journal of the Atmospheric Sciences, Vol. 36 (8), 1392-1408.
Del Genio, A.D. & R. J. Suozzo 1987: A Comparative Study of Rapidly and Slowly Rotating Dynamical Regimes in a Terrestrial General Circulation Model. Journal of the Atmospheric Sciences, Vol. 44 (6), 973-986.
Excellent document.
From this is clear that Hadley cell is increasing while rotation speed decreases, eventually Hadley cell will reach poles.
It is far future, whole world having average average temperature of 15C.
Closer future is about disappearing polar cell, merging with Ferrel cell and increasing size of Hadley cell. That means tropics will be bigger, very slightly colder. But moderate area on Earth will suffer from merge with polar, temperature falling rapidly.
My guess here is: moderate area shrinking from 41.75% to 31.75%, merging with 8.25% polar area.
Temperature in moderate area will be around 1K colder 278.5K, because of losing 10% of warmest part.
This is giving weighted average temperature: (31.75%x278.5K+8.25%x253K)/40%=10929.6/40=273,24K
Whole moderate area from 40 degrees north/south to pole will have average temperature around 0C!!!
Question is how far this state is. It is even possible that it already started, polar cell merging with Ferrel. My guess is that first symptoms are meandering of jet stream dividing polar area from moderate. And this is already happening.
Peter,
Interesting new application of the Wighted Area technique, with a troubling result.
Welcome to my world. 😉
I am not a scientist but we don’t live in a moisture free world with the same -6.5 degree lapse rate and top of troposphere temperatures of -78.5 to -83 degrees celsius. I got lost right there when you somehow decided the whole world had a constant moisture free lapse rate all the way to the top of the troposphere. The top of the troposphere is supposed to be about -56.5 C per the source link you provided for your lapse rate. The reason there does not appear to be a green house gas effect is because you used a moisture free lapse rate for the whole world and bogus temperatures for the top of the tropopause based on that. I have often questioned why CO2 is not included in the lapse rate if it really has a significant impact on temperature but I thought everyone understood why humidity was included in the lapse rate.
James,
As I mentioned in my essay, finding accurate temperature data for the tropopause is not easy. This is not least because the tropopause is a dynamic zone and subject to daily and seasonal variations, as well as latitudinal differences both within and between the main atmospheric circulation cells.
That said I am a great admirer of the philosophy of science practised by Richard P. Feynman in particular this quote:-
“Study hard what interests you the most in the most undisciplined, irreverent and original manner possible.”
There are two basic issues with ideas in Science ; –
1. The idea is wrong, but the data are correct.
2. The idea is correct, but the data are wrongly applied.
Clearly, we aim to achieve the optimum position of: –
The idea is correct and the data are correct.
My motivation for this study was to try and establish if, from a long-term geological perspective, land surface elevation is a factor in reducing global average temperatures over the last 65 million years. The mechanism I am exploring is if the presence of high elevation land surfaces, such as the Tibetan plateau, provide a persistent energy leak point that allows radiant energy to pass more easily through the atmosphere and out to space.
Calibrating the CERES image is one way to achieve this. My numbers may be wrong in absolute terms, but I believe that the concept is valid, and while capable of refinement with more accurate data, it has not been disproved by my analysis.
Looking now in detail at the specifics of your criticism regarding the role of humidity in the lapse rate. Firstly, the great bulk of the Earth’s atmosphere is composed of the three non-condensing gases Nitrogen, Oxygen and Argon. So, to a first approximation the atmosphere is dry.
Next the atmosphere is a vertical drying machine. Moist air at the base when lifted dries out through the process of rainfall that leaves air lifted aloft drier than that of the surface.
The process of latent heat release by the water in the rising air as it first condenses from vapour to liquid, and then crystallises to solid ice ensures that upper atmosphere air possesses a large Potential Temperature.
Cold low-pressure stratospheric air needs to be cooled when it is brought inside the pressurised cabin of a jet airliner because of it large potential temperature, something that is well understood by aircraft engineers. Similarly forced descent of dry upper air in the vertical overturn of the tropospheric Hadley cell returns air to the surface in high pressure anticyclones. Air that undergoes heating at the dry adiabatic lapse rate as it descends.
1. It seems that ‘potential temperature’ is just another way of looking at lapse rate.
2. In the article you state:
Most of the energy ‘release’ at height in the convective cells such as Hadley Cells, is the release of latent heat on change of state of water – say from liquid to ice.
Latent heat does not follow Stefan Boltzmann – it is a set number of 334 Kj/Kg liquid to ice and 2264.7 Kj/Kg vapor to liquid. In some of the extreme convective updrafts in the Hadley cells water can still be vapor and liquid at 30,000ft, so the phase changes can happen at that height.
Is the use of Stefan/Boltzman to back calculate atmospheric temperature correct?
“In some of the extreme convective updrafts in the Hadley cells water can still be vapor and liquid at 30,000ft, so the phase changes can happen at that height.”
Ian,
You have spotted what I consider to be one of the flaws in the Energy Budget diagram, namely Latent Heat transport is a mass motion process and not a radiation process. It is impossible to vector latent heat without also convecting water. Then there is the issue of descending mass in a gravity field. All mass that has been lifted aloft, be it air or water, must convert potential energy back into kinetic energy as it descends. Witness the effect on solar panels of descending hail stones. The issue is one of quantity of energy being transported. As a hill walker I am very familiar with the effect on clouds as moist air descends over a Scottish ridge. The evaporation of the cloud moisture as it descends is another example of latent heat transport, but this time in a descending air parcel.
“Is the use of Stefan/Boltzmann to back calculate atmospheric temperature correct?
Probably not, but I am just trying to apply the pre-set rules as best I can. YMMV
Emissive power at 15 C is 392 W/m^2 of which 80 W/m^2 is absorbed by the spectral bands of CO2, am I correct in observing this from the above tables derived from the CERES data.