How Do We Calculate Global Temps. Anyway?

Explanation? - 

1361 watts / m^2 incoming radiation hits outer Atmosphere and spreads out around the "half sphere" to deliver an "actual" 342 Watts/ m^2 to the Earth's atmosphere.  ( 1361 / 4 = 340). Conversion of flat disc to a sphere). Image below shows "reality" rays disperse over a 3 dimensional curving surface. 

The Sun doesn't Beam onto a Flat Surface
The Sun doesn't Beam onto a Flat Surface

Albedo effect - The Atmosphere reflects (dust, aerosols) or absorbs heat energy (ozone, water) and sends back 100 watts / m^2 to outer space (or a total of 393 watts "rejected" from the incoming 1361. (Assume this happens instantly). 

After sending back 100 watts / m^2 to space 242 watts / m^2 manages to make it to Earth's surface where it warms the air next to it to the "same" temperature. 

Each night the Earth has 12 hours to disperse 242 watts back to space to retain balance. 

Stephan Boltzman Formula says:

340 watts / m^2 is equivalent to a temperature of 288 degrees K. if there was no albedo / atmosphere. 

240 watts / m^2 is equivalent to a temperature of 255 degrees K.  =  Earth's Surface actual temp after filtering  incoming rays. 

Who cares about these numbers? - 1361 watts sent in, 393 watts sent back out, (242 watts/ m^2 times 4) = 968 watts night time out = balance. They don't really play into the / m^2 based calculations and end up confusing things.What other part of above doesn't make immediate sense?  -  The 393 number should really say "100" not "393". We've mixed watts with watts/ m^2 in the image above and it appears we haven't.  Very confusing. 

The IPCC considers the Earth to be a Black Body, and in doing so it uses the mathematics regarding radiative behaviour of black bodies that have existed for decades to describe Earth's relationship with the Sun and in particular, how the two bodies determine a thermostatically controlled average global temperature. As defined by the dictionary:

"Black Body Temperature of the Earth. - The temperature that the surface of a body (such as a planet, like the Earth) would be if it were not warmed by its own atmosphere. It can be calculated using the Stefan-Boltzmann equation. The black body temperature of the Earth is -15 °C, but the actual surface temperature is about 15°C. The difference (30°C) is the amount by which the planet is warmed by the absorption of radiation within its atmosphere, by the natural greenhouse effect."

I've modified (ie. simplified)  an excellent answer received off Quora from Brent Meeker, studied Physical Sciences & Computer Science at The University of Texas at Austin (1974) to explain why we use 15 degrees C as the gold plated standard to describe the ideal temperature of the Earth.

At our distance from the Sun the intensity of solar radiation is about 1361 w/m^2. Of this about 393 w/m^2 is reflected by clouds, etc. so the actual exposure is 968 watts / m^2. If the earth was a flat disc, this energy would be delivered over an area defined by the formula pi*R^2. But since it is actually shining on half of a sphere the actual exposed surface area of the Earth is 4*pi*R^2.  

This means the averaged energy received by Earth per actual unit area is (968 w/m^2) / 4 = 242w/m^2. This is also the amount of energy that the Earth must radiate back into space to remain at equilibrium. By looking at the chart below it can be seen that 242 watts calculates to a black body temperature of 258 deg. K  or - 15 deg. C.  Again, as a Black Body (which the Earth really isn't), this is the temperature that the Earth would have to be in order  to radiate all that energy back out to space again before it starts heating up again the next day. 

Remember - Earth's Avg. Flux is only Between 200 and 400 watts / sq. meter
Remember - Earth's Avg. Flux is only Between 200 and 400 watts / sq. meter

But remember that's the temperature at the top of the atmosphere where infrared radiation can go directly to space without any interference.  We're generally concerned with the temperature at the actual Earth's surface under a deep insulating blanket of gases about 12 km. in depth loosely called the atmosphere. That's what the 242w/m^2  passes through before it actually gets absorbed into the Earth's surfaces, and also what the night's heat must pass through to be conducted from the Earth's surface back up to the top of the atmosphere where it can be radiated out to space

This takes a temperature differential to make the energy flow up. So how hot the surface has to be at equilibrium depends on how much thermal resistance from atmospheric gases there is in transferring the energy up. This is where the resistance to heat flow and "pooling" of heat due to absorption and remission of IR by water vapour and CO2 become important. Calculating that is fairly complicated and has be done numerically in computers since the composition of the atmosphere, especially water content varies with altitude and temperature. This number is generally recognized to be 288 deg. K  or  15 deg. C. 

So the temperature differential would be equal to 30 degrees Celsius. It requires Earth to be + 15 C in order to drive its heat up to the -15 C edge of the atmosphere in the time given it before the Earth starts to heat up again (ie. the night). It can only go up through the mechanisms of conduction (minimal), convection (major) and radiation (moderate). 

Failure to penetrate the atmosphere in the time given before it starts heating again means that Earth will retain heat and the surface will warm higher than 15 C (ignoring any thermostatic responses by Earth's disposal mechanisms). Too open a sky (say by low humidities and cloud cover) means the actual surface will cool below 15 C as it keeps attempting to reach the edge of atmosphere black body temperature of - 15 C. 

So the trick of the atmosphere is to hold any heat given to it by conduction, convection and radiation only throughout the night until the next day when it begins to heat up again. If all runs well the day's heat will be lost by morning, a new "batch" of heat will be added during the next day, and then this will again be disposed of over the next night time. Balance achieved! The Earth is saved!

Inputs after reflection. Temps w/o and w/ atmospheres
Inputs after reflection. Temps w/o and w/ atmospheres


So, before the next section on atmospheric effects begins, let's do a quick review on the incoming radiation and generated  temperatures we've identified above;

1. Sun incoming at 1361 watts / m^2 becomes 968 watts / m^2 due to upper atmosphere reflection back to space. 

2. 968 watts / m^2 is spread over the exposed area (4*pi*R^2) of a sphere to give an average exposure equal to 242 watts / m^2.

3. Using Stephan Boltzman equation this exposure of 242 watts / m^2  on a black body would cause that black body to have a temperature of 258 deg. Absolute or - 15 degrees Celsius.

4. This would be true at the upper edge of the atmosphere at the edge of space or if the Earth had no atmosphere at all.  It is not true at Earth's surface which has an average (calculated) temperature of +15 degrees Celsius, not - 15 degrees Celsius because there is an insulating blanket of air holding heat back against the surface. 

5. How does atmosphere manage to hold heat, preventing it from escaping to space, and maintaining a steady average of +15 degrees Celsius on the Earth's environment?  That is the question and the debate. 

6. Statement (4) describes a form of Greenhouse Effect, the mechanism used by IPCC to credit C02 with warming the Earth. The question is - how significant, if any, is the C02 effect on creating this insulating blanket that keeps our surface temperatures so steady? 

Let's try to visualize things with a really simple "model". 

The Sun is really just a heat lamp that beams heat on to one side of  a gas ball with a hard core composed of water and earth. It warms this ball up for 12 hours a day ( 8 am to 8 pm) before being turned off as the hot side of the ball is turned away from it.  The ball, which has been heated up a sunset temperature of X, now has 12 hours to cool off, disposing of its heat to space and dropping its temperature down to a morning temperature of Y, when the heat lamp is turned on again and the exposed side rises in temperature from Y to a sunset temperature of X. 


1. The Earth does get hot - We know it's got heat in it because otherwise it would be frozen solid. 

2. We can see the light and feel the IR heat - we know the Sun's radiation is reaching ground level so we know the Sun is heating at least SOME of the Earth's surface.

3. We know if we dig into the core it gets hotter with depth, so mantle heat must have something to do with keeping the crust warm.

4. We know that the air can be cold and can also feel warm. We can measure it's temperature. So we know that the air can absorb and retain heat. Question is where does it come from - space or earth?

5. We know if we didn't have an atmosphere earth would be boiling hot during the day and freezing cold during the night. We know this is the effect of atmosphere. 

6. Putting aside "minor" furnaces such as core conduction, volcanoes and man made burning, we can reasonably assume that the overwhelmingly major heat source for Earth heat is the Sun. 

Sun comes from above. It must penetrate our atmosphere if it is to reach the Earth and physically warm the water and the crust. Again, does it heat the atmosphere and then the warm air heats the crust - or does it pass through, heat the crust and this warms the atmosphere?

The answer to this question - is most likely that the majority of the Sun's heat penetrates the atmosphere and reaches the surface of the Earth where it is absorbed, warming the waters and the crust. This heat must be lost overnight as the next day the crust will be subject to another wave of incoming radiant heat that will continue on and on until the temperatures would be ridiculously high. Heat leaving the Earth's crust by a variety of mechanisms warms the atmosphere. This affects our weather. Weather affects us.


1. Warm air rises - Heating at the top and all the way down to the surface of the Earth warms the mass of air molecules and increases their kinetic energy in a way that they air increases its vapour pressure in a closed system. This translates into a movement of the warmed molecules upwards in an open system such as the atmosphere. 

2. Cold air drops - when warm air is sent upwards away from the earth the air which replaces it is coldt er, not warmer. Cold air will encourage heat movement out of the crust and into the air not the other way around, according to the second law of thermodynamics.

3. What if warm air naturally dropped (and we absolutely know this is not so)  - we'd never get rid of it as it would never reach the fringes of outer space where its latent heat could be radiated away. The earth would overheat massively, not just a little. We get a glimpse of this when physically produced heat inversions occasionally occur, causing short term heat waves.

4. It must be the crust because lower elevations of the troposphere are warmer than upper areas. - heat moves from a region of high temperature to a region of low temperature. If the Earth heated the air the movement of heat would be in accordance with thermodynamics law #2 - from hot to cold. 

5. But there is some atmospheric heating  - We know there is heating in the upper atmospheres, particularly of water vapour, ozone (UV) and possibly of greenhouse gases such as C02 but again, the pull of outer space and the need to rise when warmed in any way keeps this entrapped heat away from the Earth's crust. It simply can't get down there in enough capacity to do any real damage.

6. This upward heat and upper absorbed heat appears to "collect" in the upper stratosphere which is warmer in the upper areas than in the lower areas. It's like there is a lower area of heat where the Earth is warming the air and an upper area where it all collects before radiating out to outer space.

7. But we know that air does heat the hard surfaces - warm air previously warmed can heat the cold earth by scrubbing in contact with it. Heat transfer can occur kinetically.  The question is, how did the air get heated in the first place. It's been previously warmed in some way such as contact with a section of hot earth, or warmed by combustion processes - not the Sun, for reasons stated above. 


So, what's the accepted version of heat absorption and disposal? See the Earth Energy Balance below. In summary we see:

1. Sun incoming radiation - set at arbitrary value of 100.

2. Total reflection straight back to space - 31 %

3. Absorption by ozone, water vapour and particulates, then up and back to space  - 24%

4. Heat reaching  and absorbed into surfaces of the Earth - 45%. 

The Earth Balance Chart above recognizes that Sun's heat is "diluted" by reflection in the sky and off the ground and by absorption of UV light by ozone and also by other gases (C02?) and dust. It also recognizes that this heat DOES NOT REACH THE GROUND but rather turns it skyward and sends it up to space. Of the 45% received by the ground, only 8% escapes directly to space without any interference. Evaporation of ground water carries away 19% and convected air 4% for a total of 31%. Then we come to C02 and Back Radiation.

Look at the orange box. 110 up (huh?) and 96 back down (huh?) for a net IR radiation through C02 of 14%. Talk about doublespeak!  WHERE DID 110 COME FROM WHEN WE ONLY STARTED WITH AND NEED TO LOSE A TOTAL OF 45 UNITS ABSORBED BY THE EARTH DURING THE DAYTIME.  HOW DID 96 OF THAT 110 MAKE IT BACK TO EARTH ANYWAY ? Makes no sense whatsoever. HAS SOMEONE CONTAMINATED THE DATA?

How about this? -  14% IR heat rises off the Earth's hot surface, encounters water vapour and carbon dioxide which are warmed up and  then convected up in the sky to the edge of space. Some energy transfer occurs along the way as collisional de-excitation occurs between the hot molecules particularly C02, and the more prolific (99.9%) neutral molecules - nitrogen N2 and Oxygen 02.  This spreads the heat out and encourages more mass to engage in the movement of air upwards (concept of thermals).  Forget about back radiation. It has been discussed elsewhere and does not occur as it violates basic laws of thermodynamics and common sense. 

The balance does eventually combine these mechanisms but unfortunately perpetuates the greenhouse concept along the way.


The anomaly pointed out in the section above is an example of a concept of radiative forcing. This claims that C02 can send IR back to the ground (disclaimed in several other blogs). In the chart above we deliver 14 units net and radiative balance was maintained. If we delivered less than that 14 units the balance would be upset, Earth would hold more heat than it gives up, and global warming would ensue. That is radiative forcing, caused by a phenomenon invented for the purpose and called "back radiation" that violates the 2nd law of thermodynamics. 

The images below show how charts have also been manipulated to show a picture far worse than it really is. 

Chart 1 - Shows the effect of the Sun on the Earth, as determined by the mechanisms described above:

Nothing seems amiss here. It shows carbon dioxide increasing from 280 to 400 ppm and says this has induced a situation of radiative forcing equivalent to 2 watts / square meter.

Chart 2 - next chart in the article translates this into temperature caused by radiative forcing, as per the IPCC predictions for our near future.

This chart says that when we reach the 400 ppm mark (we already have) the temperature will warm (only because of C02, not anything else) by 1.5 degrees Celsius. 

This is equal to . 5 to .75 degrees C / (watt / sq meter) depending on which curve you are reading in chart 2.

So, let's do the math using the Stephan-Boltzman calculator listed above (using pure Black Body as model).

Earth at an irradiance of 242 watts / sq. meter will have a temperature of :                   -17.556 C  

Earth at an irradiance of 244 watts / sq. meter will have a temperature of :                   -17.030 C

Difference in temperature due to 2 watts / sq. meter increase:                                         + .526 degrees Celsius

Rise in degrees Celsius per (watt / sq. meter) :   =                    + .525 deg. C / 2 =                             +. 2625 degrees Celsius.