Using Heat Transport Powers of the NASA Earth Energy Budget to Prove that Carbon Dioxide has an Insignificant Effect on Surface Temperatures

In my recent post A Summary of Some of the Physics Errors of the NASA Earth Energy Budget, I discussed a number of problems with the energy budget shown below in which heat transport powers are given as a percentage of the solar insolation at the top of the atmosphere. I demonstrated in that post or referred to earlier posts that demonstrated that the following NASA heat transport power values were very wrong:

1) Back radiation of 100%, which is fictitious when the atmosphere is cooler than the surface

2) Surface Infrared Emission of 117%, which is hugely exaggerated

3) The Surface Absorbed Solar Radiation minus Surface Convection Loss minus Water Evaporation Surface Cooling = 48% - 5% - 25% = 18% in this energy budget. If those values are correct then this sum is also equal to the Surface Infrared Emission. However, I went on to show that this 18% value is too high and/or the 12% of the Earth’s surface radiation emitted through the atmospheric window into space is too low, because it implies that even if the atmosphere were a black body absorber, its temperature would have to be lower than any temperature found in the atmosphere to absorb such a large fraction of the surface emitted infrared radiation.

In conclusion there is virtually no heat transport power in the NASA Earth Energy Budget which is correct. However, given the stridency with which the so-called settled science of the catastrophic man-made global warming hypothesis is said to be unquestionable, let us run through an exercise using some of their own heat transport powers to prove that carbon dioxide at its present atmospheric concentration has a negligible effect on surface temperatures and that increases in that concentration will also have negligible effects on the surface temperature. Remember that this calculation that I will be doing is based on the values provided as an integral and essential part of the so-called consensus science which also is often claimed to be the settled science.

I am going to ask the question what would the surface temperature be if there were no infrared-active gases in the atmosphere, these being the gases commonly called greenhouse gases.  When we have removed all such infra-red active gases from the atmosphere, including carbon dioxide and water vapor and the clouds that result from water vapor, we will calculate an equilibrium average surface temperature.  There will be no surprise in that result.  We will then add carbon dioxide back into the atmosphere and recalculate the surface temperature.  The change in temperature will be the temperature effect of the current carbon dioxide atmospheric concentration on the surface temperature.  This is where the surprise relative to the effect prescribed by the advocates of catastrophic man-made global warming will be seen.  In fact, this result will also surprise the lukewarmers as well.

In order to remove the infra-red active or greenhouse gases, we need to look at another somewhat earlier NASA schematic diagram of heat transport in the atmosphere so that we can separate out the solar insolation reflected from the atmosphere and that part reflected from clouds. We must also be able to use NASA values to separate the portions of the solar insolation absorbed by the atmosphere from that part absorbed by clouds. Of course we expect this alternative NASA Energy Budget to agree with the one above because when the energy budget was promulgated it was already being claimed that the science was settled.

           

Note that 51% is absorbed by the surface instead of 48%, that the sum of the solar insolation reflected from clouds and the atmosphere is 26% instead of 23%, that 19% of solar insolation is absorbed by the atmosphere or by clouds rather than 23%, that solar insolation reflected from the surface is 4% instead of 7%, that conduction is 7% instead of 5%, that water evaporation is 23% instead of 25%, that the surface radiation emitted through the atmospheric window into space is 6% rather than 12%, and that the surface infrared radiation absorbed by the atmosphere is 15% instead of 105%. The second schematic was the viewpoint before that of the first schematic. One has to wonder what the claimed consensus does agree upon and how that agreement is deemed sufficient to make the scientific issues so settled.

If one removes water vapor from the atmosphere, there are no clouds and the mechanism of putting water vapor into the atmosphere has to be removed, namely the evaporation of water. Some solar insolation will still be reflected from the atmosphere or scattered from it with little loss of energy, but most of the reflection is from clouds. The second energy budget tells us that 6%/26% = 0.23 is the fraction of atmospheric reflection not by clouds. The total reflection of both clouds and the atmosphere in the first energy budget is 23%, so the percentage still reflected by the atmosphere with no clouds is (0.23)(23%) = 5.3%. Thus the portion of the solar insolation no longer reflected by clouds is 23% - 5.3% = 17.7%. The fraction of the atmosphere plus clouds absorption of solar insolation which is absorbed by the clouds is 3%/19% = 0.158. The portion of the solar insolation absorbed by clouds is then (0.158)(23%) = 3.6%. Thus the portion of the solar insolation still absorbed with no clouds is 23% - 3.6% = 19.4%.

The removal of the infrared-active gases from the atmosphere also requires us to remove the absorption of incoming solar radiation in the atmosphere by the infrared-active gases. We need additional information to estimate the fraction of the solar insolation absorbed by the infrared absorbing gases. Let us consider these two graphics:

It appears that of the total absorption of solar insolation by the atmosphere, about one-third is absorbed by the infrared-absorbing gases. We just determined that the atmosphere absorbs about 19.4% of solar insolation when we remove clouds, but still have water vapor and other infrared-active gases in the atmosphere. One-third of this is about 6.5%.

Now let us add up the solar insolation power incident upon the surface, P_SI, based on the power values of the first NASA Earth Energy Budget:

P_SI = 55% + 17.7% + 3.6% + 6.5% = 82.8%,

so the solar insolation incident upon the surface when water vapor, clouds, and all infrared-active gases are removed is much increased relative to the current 55% with them present.

At present, 7%/55% is reflected according to the first NASA energy budget above. Let us assume this fraction of reflected solar incident radiation is unchanged, so that the power of solar insolation now absorbed by the surface, P_ABS, is:

P_ABS = (1 - {7%/55%})(82.8%) = 72.3%

This power absorbed by the surface is now going to be dissipated by convection and by radiation. In the NASA Earth Energy Budget, 5% is dissipated by convection. Given that water evaporation is not now occurring, it would be reasonable to think the energy dissipation rate by means of convection might go up, but let us do the calculation with a 5% value. The power radiated by the surface to space, P_SRS, is then

P_SRS = 72.3% - 5% = 67.3%

Now apply the Stefan-Boltzmann Law with an emissivity of 0.95 for the surface and we have

P_SRS = (0.673)(340 W/m²) = (0.95) σ T_S⁴,

where T_S is the surface temperature with no clouds and no greenhouse gases. Solving for T_S,

T_S = 255.30 K

Which is the effective radiation temperature of the Earth today with clouds and infrared-active gases in the atmosphere. So, if the NASA power numbers we used from the NASA Earth Energy Budget are right, then water vapor and clouds and other infrared active gases cause the Earth to be 33K warmer than it would be without them. This is consistent with a common claim of the so-called settled science.

Now I will put carbon dioxide back into our atmosphere and observe the effect of doing so.

Nearly all of the absorption of solar insolation by the atmosphere in the infrared spectrum is due to water vapor. How much is absorbed by carbon dioxide is little addressed by the settled science beyond a determination to ignore this cooling effect. To eye-ball the last figure above, it appears that the absorption by CO₂, is about one-fifteenth that by water vapor. Since the total infrared absorption of solar insolation by the atmosphere was estimated above to be 6.5%, the part due to carbon dioxide is then about one-sixteenth of that or 0.41%.  However, about 7/55 of this is reflected and not absorbed by the surface, leaving about 0.36% less surface absorption.

In the first NASA Earth Energy Budget above, the infrared radiation from the surface absorbed by the atmosphere is given by (117% - 100%) - 12% = 5%, where the difference of the first two powers in parentheses is the real surface infrared emission and 12% is lost through the atmospheric window into space. Most of the 5% of the atmospheric absorption of the surface infrared emission is due to water vapor. It is also important here to only add in that part of the surface emission absorption that carbon dioxide adds to that absorption normally done by water vapor if we would find the relevant net effect of carbon dioxide. From the figure immediately above, this additional CO₂ absorption effect relative to that of water vapor is about one-eighth.  The fraction of the 5% of surface emission absorbed by the atmosphere is then one-ninth of 5% or 0.56%.

I am looking to modify the calculation for the surface temperature that we did above after removing water vapor, clouds, and carbon dioxide from the atmosphere to accommodate the return of carbon dioxide to the atmosphere to see how the surface temperature changes. It is clear that one needs to subtract the insolation power lost to surface absorption due to CO₂ absorbing it in the atmosphere and one wants to add some power due to some additional absorption in the atmosphere of the longwave radiation emitted from the Earth’s surface. Using the full value of the atmospheric absorption of the Earth's infrared emission is actually going to make the warming effect on the surface temperature larger than it is. Most of the heating in the atmosphere stays in the atmosphere and does not cause the surface heat supply to change. It is also likely that the cooling effect on the surface operates at a greater efficiency than does the warming effect.  Consequently, what we will be calculating here is an exaggerated, upper limit on the magnitude of the effect of having CO₂ in the atmosphere and may even have the wrong sign.

Upon subtracting the insolation power lost by CO₂ absorption and adding the power of surface infrared emission absorbed by the atmosphere, we get

P_SRS = (0.673 - 0.0036 + 0.0056)(340 W/m²) = (0.95) σ T_S⁴,

and we must observe that each of the cooling and warming effects of carbon dioxide are already the equivalent of mere rounding errors and the difference between them is still more piddling. Nonetheless, let us carry out the calculation to obtain what is surely an upper limit on the surface temperature:

P_SRS = (0.675)(340 W/m²) = (0.95) σ T_S⁴,

T_S = 255.49 K,

making the total warming effect of carbon dioxide all of about 0.19 K at most at its present concentration. This implies that a doubling of the present CO₂ concentration in the atmosphere will produce a temperature increase much smaller than 0.19 K due to the logarithmic decrease of absorption with increased concentration.  Even at this upper limit of a 0.19 K temperature increase due to the present levels of CO2 in the atmosphere, the fraction of the greenhouse gas warming due to carbon dioxide is only about

0.19 K / (288.15 K - 255.30 K) = 0.0058 or 0.58%

Meaning that the so-called greenhouse effect is about 99.4% attributable to water vapor and the clouds that result from water vapor.

What is more, in the real world in which there is water vapor, there is a negative, not a positive, feedback response by water vapor which would erase a portion of the fraction of 0.19 K that a doubling of the carbon dioxide concentration in the atmosphere would produce according to these approximations using NASA Earth Energy Budget values.

 As I have maintained since 2010, the net effect of carbon dioxide on the surface temperature is entirely negligible. Great increases in the carbon dioxide concentration in the atmosphere will have no significant effect on the surface temperature of the Earth. For all intents and purposes, only water vapor has significant effects on the surface temperature of the Earth and most of its effect is due to clouds and the water evaporation-condensation cycle.  There is no real reason for alarm about the effects of using fossil fuels based on added emissions of CO₂.

It is unfathomable that after governments around the world have spent well over $100 billion on the catastrophic man-made global warming hypothesis that relatively few scientists are pointing out the errors and contradictions that riddle the so-called settled science. It would appear that government funding of science corrupts science absolutely and/or makes scientists incompetent. It is an interesting parallel to what government power does to government employees.

Updated 2 July 2018.