Correcting the Kiehl Trenberth Energy Budget



Here we see the classic energy budget analysis supporting the hypothesis that the surface of the Earth is warmer than the S-B equation would predict due to 324 Wm2 of ‘Back Radiation’ from the atmosphere to the surface.

It is proposed that it is Back Radiation that lifts the surface temperature from 255K, as predicted by S-B, to the 288K actually observed because the 324 Back Radiation exceeds the surface radiation to the air of 222 Wm2 ( 390 Wm2 less 168 Wm2) by 102 Wm2. It is suggested that there is a net radiative flow from atmosphere to surface of 102 Wm2.

I now discuss an alternative possibility.

The portions I wish to focus on are:

i) 390 Wm2 Surface Radiation to atmosphere

ii) 78 Wm2 Evapo-transpiration surface to atmosphere

iii) 24 Thermals surface to atmosphere

iv) 324 Back Radiation atmosphere to surface

The budget needs to be amended as follows:

The 78 Wm2 needs to be corrected to zero because the moist adiabatic lapse rate during ascent is less than the dry lapse rate on adiabatic descent which ensures that after the first convective cycle there is as much energy back at the surface as before Evapo-transpiration began.

The 24 Wm2 for thermals needs to be corrected to zero because dry air that rises in thermals then warms back up to the original temperature on descent.

Therefore neither ii) nor iii) should be included in the radiative budget at all. They involve purely non radiative means of energy transfer and have no place in the radiative budget since, being net zero, they do not cool the surface.  AGW theory and the Trenberth diagram incorrectly include them as a net surface cooling influence.

Furthermore, they cannot reduce Earth’s surface temperature below 255K because both conduction and convection are slower methods of energy transmission than radiation. To reduce the surface temperature below 255K they would have to work faster than radiation which is obviously not so.

They can only raise a surface temperature above the S-B expectation and for Earth that is 33K.

Once the first convective overturning cycle has been completed neither Thermals nor Evapo-transpiration can have any additional warming effect at the surface provided mass, gravity and insolation remain constant.

As regards iv) the correct figure for the radiative flux from atmosphere to surface should be 222 Wm2 because items ii) and iii) should not have been included.

That also leaves the surface to atmosphere radiative flux at 222 Wm2 which taken with the 168 Wm2 absorbed directly by the surface comes to the 390 Wm2 required for radiation from the surface.

The rest of the energy budget diagram appears to be correct.

So, how to decide whether my interpretation is accurate?

I think it is generally accepted that the lapse rate slope marks the points in the atmosphere where there is energy balance within molecules that are at the correct height for their temperature.

Since the lapse rate slope intersects with the surface it follows that DWIR equals UWIR for a zero net radiative balance if a molecule at the surface is at the correct temperature for its height. If it is not at the correct surface temperature it will simply move towards the correct height by virtue of density variations in the horizontal plane (convection).

Thus, 222 UWIR at the surface should equal 222 DWIR at the surface AND 222 plus 168 should add up to 390 and, of course, it does.

AGW theory erroneously assumes that Thermals and Evapo-transpiration have a net cooling effect on the surface and so they have to uplift the radiative exchange at the surface from 222 Wm2 to 324 Wm2 and additionally they assume that the extra 102 Wm2 is attributable to a net radiative flux towards the surface from the atmosphere.

The truth is that there is no net flow of radiation in any direction at the surface once the air at the surface is at its correct temperature for its height, which is 288K and not 255K. The lapse rate intersecting at the surface tells us that there can be no net radiative flux at the surface when surface temperature is at 288K.

A rise in surface temperature above the S-B prediction is inevitable for an atmosphere capable of conducting and convection because those two processes introduce a delay in the transmission of radiative energy through the system. Conduction and convection are a function of mass held within a gravity field.

Energy being used to hold up the weight of an atmosphere via conduction and convection is no longer available for radiation to space since energy cannot be in two places at once.

The greenhouse effect is therefore a product of atmospheric mass rather than radiative characteristics of constituent molecules as is clearly seen when the Trenberth diagram is corrected and the lapse rate considered.

Since one can never have more than 390 Wm2 at the surface without increasing conduction and convection via changes in mass, gravity or insolation a change in the quantity of GHGs cannot make any difference. All they can do is redistribute energy within the atmosphere.

There is a climate effect from the air circulation changes but, due to the tiny proportion of Earth’s atmospheric mass comprised of GHGs, too small to measure compared to natural variability.

 What Happens When Radiative Gases Increase Or Decrease?

Applying the above correction to the Trenberth figures we can now see that 222 Wm2 radiation from the surface to the atmosphere is simply balanced by 222 Wm2 radiation from the atmosphere to the surface. That is the energy being constantly expended by the surface via conduction and convection to keep the weight of the atmosphere off the surface. We must ignore it for the purpose of energy transmission to space since the same energy cannot be in two places at once.

We then have 168 Wm2 left over at the surface which represents energy absorbed by the surface after 30 Wm2 has been reflected from the surface , 77 Wm2 has been reflected by the atmosphere and 67 Wm2 has been absorbed by the atmosphere before it reaches the surface.

That 168 Wm2 is then transferred to the atmosphere by conduction and convection leaving a total of 235 Wm2 in the atmosphere (168 plus 67).

It is that 235 Wm2 that must escape to space if radiative balance is to be maintained.

Now, remember that the lapse rate slope represents the positions in the atmosphere where molecules are at their correct temperature for their height.

At any given moment convection arranges that half the mass of the atmosphere is too warm for its height and half the mass is too cold for its height.

The reason for that is that the convective process runs out of energy to lift the atmosphere any higher against gravity when the two halves equalise.

It must follow that at any given time half of the GHGs must be too warm for their height and the other half too cold for their height.

That results in density differentials that cause the warm molecules to rise and the cold molecules to fall.

If a GHG molecule is too warm for its height then DWIR back to the surface dominates but the molecule rises away from the surface and cools until DWIR again equals UWIR.

If a GHG molecule is too cold for its height then UWIR to space dominates but the molecule then falls until DWIR again equals UWIR.

The net effect is that any potential for GHGs to warm or cool the surface is negated by the height changes relative to the slope of the adiabatic lapse rate.

Let’s now look at how that outgoing 235 Wm2 is dealt with if radiative gas concentrations change.

It is recognised that radiative gases tend to reduce the size of the Atmospheric Window (40 Wm2) so we will assume a reduction from 40 Wm2 to 35 Wm2 by way of example.

If that happens then DWIR for molecules that are too warm for their height will increase but the subsequent rise in height will cause the molecule to rise above its correct position along the lapse rate slope with UWIR to space increasing at the expense of DWIR back to the surface and rising will only stop when DWIR again equals UWIR.

Since UWIR to space increases to compensate for the shrinking of the atmospheric window (from 40 Wm2 to 35 Wm2) the figure for radiative emission from the atmosphere will increase from 165 to 170 which keeps the system in balance with 235 Wm2 still outgoing.

If the atmosphere had no radiative capability at all then radiative emission from the atmosphere would be zero but the Atmospheric Window would release 235 Wm2 from the surface.

If the atmosphere were 100% radiative then the Atmospheric Window from the surface would be zero and the atmosphere would radiate the entire 235 Wm2.


Published by Stephen Wilde April 6, 2014

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