Wednesday, September 26, 2012

New analysis finds man-made CO2 will have an inconsequential effect on world temperature

A new post today at at Dr. Ed's Climate Clash explains why 

  • Consumption of all the world’s fossil fuels at any credible rate will not achieve a doubling of the current CO2 level and will increase world temperature by barely one-half degree Celsius.
  • Increased carbon dioxide from the burning of fossil fuels causes an inconsequential impact on world temperature. 
  • The most significant conclusion, however, is that increased moisture, the presumed cause of feedback, causes a decrease in the warming effect of CO2 (negative feedback).

The limits of carbon dioxide’s influence on world temperature

[Excerpts below, emphasis added, full post here]

Abstract: Consumption of all the world’s fossil fuels at any credible rate will not achieve a doubling of the current CO2 level and will increase world temperature by barely one-half degree Celsius. The achievable level of atmospheric CO2 is proportional to its release rate because its dilution by exchange with the land and ocean takes time.  An instantaneous release is the worst case and if the entire world’s CO2 from fossil fuels were so released (impossible, of course) it represents an extreme upper bound to the CO2 level. And even that would achieve an increase of less than 3 degrees Celsius. Most significant, however, is the strong evidence that feedback from increased CO2 is negative.

The Modtran computer code (4) developed by the Air Force and considered the standard for computing radiation transport in the atmosphere is used to solve the increase in IR energy absorption as a function of increase in CO2 concentration. Modtran is described in Appendix B.
This analysis assumes that Modtran uses sufficiently accurate calculation and atmospheric parameters to produce reliable results. The analysis includes feedback to the extent that results are compared with very different moisture conditions in the atmosphere, and the basis for claimed feedback is the additional atmospheric moisture caused by increased atmospheric CO2.
The elevated temperatures claimed by AGW proponents depend on positive feedback. Water vapor’s greenhouse effect frequently increases more in a day than CO2 can increase in decades.  Thus, if positive feedback were possible the world cataclysm that AGW proponents predict would have occurred centuries ago due to water alone.  And nature’s feedbacks are predominantly negative.  Both history and physics are aligned against the assumption of positive feedback.
Figure 4 shows the Modtran computed IR flux in watts per square meter across the atmosphere in both the upward and downward direction.  Upward flow stabilizes and downward flow disappears beyond about 30 km altitude because IR interactions are effectively zero due to the extremely low density of the atmosphere. Where the slope of the deposition is downward in the direction of the radiation, IR is being absorbed faster than it is being generated (by the heated molecules) and the opposite is true for an upward slope. 
The “thermals” and “latent heat” shown in Figure 5 entering from the earth’s surface are not IR.  That absorbed directly from sun into the atmosphere is radiation, but very little in the IR range. Its frequency degrades in the atmosphere to the IR energy range where it is absorbed as heat.  These non-IR components, 17, 80 and 78 watts/m2, respectively sum to 175 and must be added to the IR input value in order to derive a heat balance.
Figure 5. Energy Balance by IPCC (5)
Figure 5 values are similar to other heat balances, such as that by the weather service (6) and NASA (7).  But only the IPCC balance of Figure 5 indicates a net heat absorption into the earth, whose existence is highly controversial. The IR exiting the atmosphere to outer space is the only heat loss mechanism of the earth-atmosphere system.  Modtran is used to calculate input and output IR energy for all the other levels of CO2 of concern which are indicated in Table 1.
Figure 6 illustrates the baseline case of 400 ppm, the approximate current level of atmospheric CO2.
The heat rate to the atmosphere, H, for each CO2 level is determined with the following calculation:
H = IRin +175 – IRout                                                                     
Where H is the heat retained in the atmosphere at the particular CO2 level and 175 is the non-IR heat input, This equation forms the basis for calculating temperature rise. To maintain at least a short-term steady state the heat added must be removed and the only mechanism whereby the earth-atmosphere system can remove heat is by radiation to outer space, according to the Maxwell-Boltzmann equation for radiative heat transfer:
H =  caTa4 – coTo4
Where subscripts a and o refer to atmosphere and outer space, respectively;
H is heat rate into the atmosphere,
T is temperature in degrees Kelvin.
Ta is the temperature within the atmosphere which would match the aggregate of all radiative transfers to outer space when used in the above equation. In this analysis it is assumed to be the maximum (at the earth’s surface) because that produces the maximum (most conservative) value.
c is a constant (Maxwell-Boltmann constant times emissivity).
Outer space temperature is a factor of 100 lower than the characteristic atmospheric temperature, so that its 4th power is a factor of nearly a billion smaller and the second term on the RHS can be ignored without compromising accuracy. Subscripts b and g refer to conditions before and after the CO2 addition, respectively.  Dividing the Hg equation by that for Hb, the constant term cancels out and this simplified equation results:
Tg =  Ta*(Hg/Hb)1/4                                                (1)
Temperature rise due to added CO2 is the difference between Tg and Ta.
Figure 6 is a plot of the temperature rise in the atmosphere as a function of CO2 content and Table 1 summarizes the inputs and results of the computation.
A long period for burning the fossil fuel assures a relatively small maximum CO2 level because of the extra time available for mixing with land and ocean.  Under the scenario of maintaining the Figure-1 level of 10 petagrams per year to the atmosphere, the complete depletion of the fossil-fuel carbon occurs at 1000 years.
These scenarios depend on fossil fuels ending abruptly with no diminishing over time. Such scenarios are unrealistic but they ensure that maximum atmospheric CO2 content is not underestimated. The value of 0.5-percent-per-year increase of the fossil input rate to the atmosphere matches the current rate at which CO2 level is increasing in the atmosphere according to Figure 3.  A 1.5- percent-per-year value is the maximum increase indicated for carbon insertion of Figure 2.
These small temperature numbers of Table 1 are not likely to be underestimates.  It does not appear conceivable that either a half degree C temperature rise or a doubling of current CO2 level could be achieved.  Even if all that CO2 could be dumped in instantaneously, less than a 3 oC temperature rise would be seen. The maximum CO2 level and associated temperature rise is proportional to the rate of CO2 input.
In Figure 6, 400 ppm is assumed to be the current CO2 level in the atmosphere and all increases are from the temperature at that level.  Figure 6 shows the declining effect of increased CO2, but the most significant result is the dramatic decline in temperature rise caused by increasing atmospheric moisture. The Modtran code description, Appendix B, indicates that the middle curve best represents world average conditions.  Top-curve values are those in Table 1 because these are the most conservative.
Figures 7 through 10 show the time-dependent atmospheric CO2 content (as a ratio to the current content) and the resulting temperature rise above the current value as a result of the atmospheric carbon insertion rates indicated in Table 1.
The results show that increased carbon dioxide from the burning of fossil fuels causes an inconsequential impact on world temperature. The most significant conclusion, however, is that increased moisture, the presumed cause of feedback, causes a decrease in the warming effect of CO2 (negative feedback).
  1. “Understanding The Global Carbon Cycle,” Richard Houghton, WoodsHoleResearchCenter, 2007
  2. Fossil Fuel – Wikipedia,  Global Fossil Carbon Emission by Fuel Type from 1800 through 2007.
  3. CO2 Now.Org, CO2 Now | Home, Global Carbon Budget 2010
  4. Modtran Infrared Atmospheric Radiation Code,
  5. Trenberth, Kevin E., et al “Earth’s Global Energy Budget,” BAMS, March, 2009. This is by the Intergovernmental Panel on Climate Change (IPCC)
  6. http//
  7. budget
The Author
Bryce Johnson is a retired professional nuclear engineer in the State of California.  His career spanned 45 years work in nuclear power and nuclear weapons research.  His education includes:  BS(ME), University of Idaho, MS(NE) North Carolina State University and PhD(ME), Stanford University.

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