CO2 The Miracle Molecule - Addendum Synopsis When presenting any theory in respect of global warming and climate change one is always aware that the results can be dismissed simply by reference to the numerous complications associated with how the atmosphere reacts to infra-red radiation from the earth. After all there are dozens of climate models and even if one can understand their complexities you can’t satisfy them all. Once engulfed in this mire it becomes very difficult to extricate the arguments. This problem can perhaps be overcome by using the calculations of atmospheric absorptivity from HITRAN data as a basis for calculation of equilibrium earth temperature. Indeed ,this is what the paper, CO2 The Miracle Molecule attempts to do. However, in writing the paper a number of assumptions were made, which allow it to be justifiably questioned. This addendum is an attempt to overcome the problems associated with assumptions by calculating climate sensitivities in a manner which takes into account all possible atmospheric models and theories and in doing so shows that climate sensitivities, defined as the increase in temperatures due to a doubling of atmospheric CO2 values, are naturally constrained to a narrow band with a maximum value of 0.65degC, suggesting very strongly that CO2 is not a driver of climate change.

Introduction In the results reported in the paper “CO2 The Miracle Molecule” a number of assumptions have been made which can cast doubt on the veracity of the conclusions. Let us list some of these assumptions and see how their impacts can be evaluated. 1 The mean atmospheric concentrations of H2O and CO2 2 The atmospheric thickness which affects the degree of absorption. 3 The impact of varying temperature and pressure with increasing altitude. 4 The assumption of a 50/50 split of absorbed radiation being transmitted through to space or redirected back towards earth. 5 No consideration of atmospheric thermodynamics, including convection effects. Each one of these issues and others not even mentioned is open to debate with no definitive answers from the proliferation of climate models and the variances between them. How then to proceed towards an acceptable conclusion? Radiation Balance The equilibrium temperature of the earth is governed by the radiation balance at the extremity of the atmosphere. Incident short wavelength radiation from the sun I0 is balanced by the emission of long wavelength radiation from the earth. That is it, no ifs, no buts. The radiation R from the earth is governed by its temperature. R = sT4 W/m2 Some of this radiation is absorbed by “greenhouse gases” principally CO2 and H2O, particularly H2O. Let us identify this absorption by “a”. The radiation transmitted through the atmosphere is thus (1 – a).R W/m2

The key question, which must be answered, is “how much of that absorbed radiative energy is actually retained by the earth/atmosphere system”. Let us attribute the identifier “n” to this fraction. Thus, absorbed energy retained by the atmosphere/earth = n.a.R W/m2 And the fraction of this absorbed energy that is ultimately lost to space

= (1 – n).a.R W/m2 This makes the total radiative losses to space = (1 – a).R + (1 – n).a.R W/m2 = (1 – n.a).R W/m2 This makes the radiation balance at the “top” of the atmosphere I0. pr2 = s T4 .(1 – n.a) x 4pr2

So that equilibrium temperature T = ( I0/4s)1/4/(1 – n.a)1/4 = 255/(1 – n.a)1/4 Kelvin The problem of global warming thus boils down to this simple equation, which has only two variables, “a” atmospheric absorptivity and “n” the fraction of the absorbed energy that is retained in the earth/atmosphere system. Atmospheric Absorptivity Let’s begin with something that can be calculated with some precision. The atmospheric absorptivity for a range of concentrations of H2O and CO2 is calculable with a high degree of precision thanks to the HITRAN database of molecular infra-red absorption spectroscopy. This provides a solid platform for further calculations. There are changes in the spectra due to variations in temperature and pressure, but these are small for the temperature and pressure ranges experienced in the bulk of the climate and are readily identified in HITRAN. The table and graph reproduced here from the original paper, show the results of calculations of atmospheric absorption for a range of H2O and CO2 concentrations. Table 1

%H2O 0.0 0.1 0.25 0.5 1.0 2.0 4.0ppm CO2 Absorption

0 0.000 0.544 0.613 0.662 0.711 0.761 0.81010 0.082 0.595 0.649 0.688 0.727 0.769 0.83220 0.101 0.605 0.656 0.693 0.730 0.771 0.83350 0.126 0.619 0.666 0.700 0.735 0.774 0.834

100 0.144 0.631 0.674 0.706 0.740 0.777 0.836200 0.163 0.642 0.683 0.713 0.745 0.781 0.839300 0.174 0.649 0.688 0.717 0.748 0.784 0.841400 0.182 0.653 0.692 0.720 0.751 0.786 0.842500 0.188 0.657 0.695 0.723 0.753 0.787 0.843600 0.192 0.660 0.697 0.725 0.755 0.789 0.844

1000 0.206 0.668 0.705 0.731 0.760 0.793 0.8483000 0.241 0.692 0.725 0.749 0.776 0.807 0.859

These results do not depend on any assumptions about what happens to the absorbed radiation and they cover a range of gas concentrations larger than any perceived atmospheric variations and estimations, thus overcoming uncertainties in assumptions about concentration and atmospheric optical path thickness. Calculation of Equilibrium Earth temperature To calculate the equilibrium earth temperature, we need to know the value of “n”. For a given value of “a”, the fraction “n” becomes the only variable. However, “n” is dependent on every possible atmospheric variable, and its correct value is the holy grail of atmospheric physics. To predict a value for this variable which cannot be argued against would be impossible. What we do know is that “n” will have a value between 0 and 1, these being the limiting conditions. 0 is the condition where all the absorbed energy is transmitted through to space. This becomes the zero-atmosphere condition where no absorption takes place and the equilibrium earth temperature is 255K. The value of 1 would be the case where all the absorbed radiation remains within the atmosphere/earth system and would give maximum possible warming. Since we do not know the true value for “n” we must allow for all possible values for it and therefore cover every possible model and theory for CO2 induced global warming. From the values of absorption calculated in Table 1 we can predict the earth temperature for any given H2O and CO2 content for values of “n” varying from 0 to 1, using the radiation balance equation above. The results are shown in the series of tables in 2.0 through 2.10. This produces values for the equilibrium earth temperatures ranging from 255K, when n = 0 to the extreme of 416K when n = 1.

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FIGURE 1 Atmospheric IR Absorptivity

0%H2O 0.1%H2O 0.25%H2O 0.5%H2O 1.0%H2O 2.0%H2O 4.0%H2O

n Table 2.00.0 %H2O 0 0.1 0.25 0.5 1 2 4

ppm CO2 Temperature K0 255.0 255.0 255.0 255.0 255.0 255.0 255.0

10 255.0 255.0 255.0 255.0 255.0 255.0 255.020 255.0 255.0 255.0 255.0 255.0 255.0 255.050 255.0 255.0 255.0 255.0 255.0 255.0 255.0

100 255.0 255.0 255.0 255.0 255.0 255.0 255.0200 255.0 255.0 255.0 255.0 255.0 255.0 255.0300 255.0 255.0 255.0 255.0 255.0 255.0 255.0400 255.0 255.0 255.0 255.0 255.0 255.0 255.0500 255.0 255.0 255.0 255.0 255.0 255.0 255.0600 255.0 255.0 255.0 255.0 255.0 255.0 255.0

1000 255.0 255.0 255.0 255.0 255.0 255.0 255.03000 255.0 255.0 255.0 255.0 255.0 255.0 255.0

n Table 2.10.1 %H2O 0 0.1 0.25 0.5 1 2 4

ppm CO2 Temperature K0 255.0 258.6 259.1 259.4 259.7 260.1 260.4

10 255.5 258.9 259.3 259.6 259.9 260.2 260.620 255.6 259.0 259.4 259.6 259.9 260.2 260.650 255.8 259.1 259.4 259.7 259.9 260.2 260.6

100 255.9 259.2 259.5 259.7 259.9 260.2 260.6200 256.0 259.3 259.6 259.8 260.0 260.2 260.6300 256.1 259.3 259.6 259.8 260.0 260.3 260.7400 256.2 259.3 259.6 259.8 260.0 260.3 260.7500 256.2 259.4 259.6 259.8 260.0 260.3 260.7600 256.2 259.4 259.6 259.8 260.1 260.3 260.7

1000 256.3 259.4 259.7 259.9 260.1 260.3 260.73000 256.6 259.6 259.8 260.0 260.2 260.4 260.8

n Table 2.20.2 %H2O 0 0.1 0.25 0.5 1 2 4

ppm CO2 Temperature K0 255.0 262.5 263.5 264.2 265.0 265.7 266.5

10 256.1 263.2 264.0 264.6 265.2 265.9 266.920 256.3 263.4 264.1 264.7 265.3 265.9 266.950 256.6 263.6 264.3 264.8 265.3 266.0 266.9

100 256.9 263.7 264.4 264.9 265.4 266.0 266.9200 257.1 263.9 264.5 265.0 265.5 266.1 267.0300 257.3 264.0 264.6 265.1 265.5 266.1 267.0400 257.4 264.1 264.7 265.1 265.6 266.1 267.0500 257.4 264.1 264.7 265.1 265.6 266.2 267.1600 257.5 264.2 264.8 265.2 265.6 266.2 267.1

1000 257.7 264.3 264.9 265.3 265.7 266.2 267.13000 258.2 264.7 265.2 265.6 266.0 266.5 267.3

n Table 2.30.3 %H2O 0 0.1 0.25 0.5 1 2 4

ppm CO2 Temperature K0 255.0 266.6 268.3 269.5 270.8 272.1 273.4

10 256.6 267.8 269.2 270.2 271.2 272.3 274.020 257.0 268.1 269.4 270.3 271.3 272.3 274.050 257.5 268.4 269.6 270.5 271.4 272.4 274.0

100 257.8 268.7 269.8 270.6 271.5 272.5 274.1200 258.2 269.0 270.0 270.8 271.6 272.6 274.2300 258.4 269.2 270.2 270.9 271.7 272.7 274.2400 258.6 269.3 270.3 271.0 271.8 272.7 274.3500 258.7 269.4 270.3 271.1 271.9 272.8 274.3600 258.8 269.5 270.4 271.1 271.9 272.8 274.3

1000 259.1 269.7 270.6 271.3 272.0 272.9 274.43000 259.8 270.3 271.1 271.8 272.5 273.3 274.7

n Table 2.40.4 %H2O 0 0.1 0.25 0.5 1 2 4

ppm CO2 Temperature K0 255.0 271.1 273.6 275.4 277.3 279.2 281.2

10 257.1 272.9 274.9 276.4 277.9 279.6 282.120 257.6 273.3 275.2 276.5 278.0 279.6 282.250 258.3 273.8 275.5 276.8 278.2 279.8 282.2

100 258.8 274.2 275.9 277.1 278.4 279.9 282.3200 259.3 274.6 276.2 277.3 278.6 280.0 282.4300 259.6 274.9 276.4 277.5 278.7 280.1 282.5400 259.9 275.1 276.5 277.6 278.8 280.2 282.6500 260.0 275.2 276.6 277.7 278.9 280.3 282.6600 260.2 275.3 276.7 277.8 279.0 280.3 282.7

1000 260.6 275.6 277.0 278.0 279.2 280.5 282.83000 261.6 276.5 277.8 278.8 279.8 281.1 283.3

n Table 2.50.5 %H2O 0 0.1 0.25 0.5 1 2 4

ppm CO2 Temperature K0 255.0 276.1 279.4 282.0 284.6 287.4 290.4

10 257.7 278.5 281.3 283.3 285.5 287.9 291.720 258.3 279.0 281.7 283.6 285.7 288.0 291.750 259.2 279.8 282.2 284.0 286.0 288.2 291.8

100 259.8 280.3 282.6 284.3 286.2 288.4 292.0200 260.5 280.9 283.1 284.7 286.5 288.6 292.1300 260.9 281.3 283.4 284.9 286.7 288.8 292.2400 261.1 281.5 283.6 285.1 286.8 288.9 292.3500 261.4 281.7 283.7 285.2 287.0 289.0 292.4600 261.5 281.8 283.8 285.4 287.1 289.1 292.5

1000 262.0 282.3 284.2 285.7 287.4 289.3 292.73000 263.3 283.6 285.4 286.8 288.3 290.2 293.4

n Table 2.60.6 %H2O 0 0.1 0.25 0.5 1 2 4

ppm CO2 Temperature K0 255.0 281.5 286.0 289.4 293.1 297.0 301.2

10 258.2 284.7 288.5 291.3 294.3 297.7 303.120 259.0 285.5 289.0 291.7 294.5 297.8 303.250 260.0 286.4 289.7 292.2 294.9 298.1 303.3

100 260.8 287.2 290.3 292.7 295.3 298.4 303.5200 261.6 288.0 290.9 293.2 295.7 298.7 303.7300 262.1 288.4 291.3 293.5 296.0 298.9 303.9400 262.5 288.8 291.6 293.7 296.2 299.1 304.0500 262.7 289.0 291.8 293.9 296.3 299.2 304.2600 262.9 289.2 292.0 294.1 296.5 299.3 304.2

1000 263.6 289.9 292.5 294.6 296.9 299.7 304.63000 265.2 291.6 294.1 296.0 298.3 300.9 305.6

n Table 2.70.7 %H2O 0 0.1 0.25 0.5 1 2 4

ppm CO2 Temperature K0 255.0 287.5 293.4 298.0 302.9 308.4 314.4

10 258.8 291.7 296.7 300.5 304.6 309.4 317.120 259.7 292.7 297.4 301.0 305.0 309.6 317.350 260.9 293.9 298.4 301.7 305.5 310.0 317.5

100 261.9 295.0 299.2 302.4 306.0 310.3 317.8200 262.8 296.0 300.0 303.1 306.6 310.8 318.1300 263.4 296.7 300.5 303.5 307.0 311.1 318.4400 263.8 297.1 300.9 303.9 307.2 311.3 318.6500 264.1 297.4 301.2 304.1 307.5 311.5 318.7600 264.4 297.7 301.5 304.4 307.7 311.7 318.9

1000 265.1 298.6 302.2 305.0 308.3 312.2 319.33000 267.1 300.9 304.4 307.1 310.2 314.0 320.9

n Table 2.80.8 %H2O 0 0.1 0.25 0.5 1 2 4

ppm CO2 Temperature K0 255.0 294.2 301.8 307.9 314.7 322.4 331.1

10 259.4 299.7 306.2 311.4 317.1 323.8 335.220 260.4 300.9 307.2 312.1 317.6 324.1 335.450 261.8 302.6 308.5 313.1 318.3 324.6 335.8

100 262.9 303.9 309.6 314.0 319.0 325.2 336.2200 264.1 305.3 310.7 314.9 319.8 325.8 336.7300 264.7 306.2 311.4 315.6 320.4 326.3 337.1400 265.2 306.8 312.0 316.0 320.8 326.6 337.4500 265.6 307.2 312.4 316.4 321.1 326.9 337.6600 265.9 307.6 312.7 316.7 321.4 327.1 337.8

1000 266.8 308.8 313.7 317.6 322.2 327.9 338.53000 269.1 311.9 316.8 320.5 325.0 330.5 340.9

As expected, there is a huge variation in calculated equilibrium earth temperatures varying from 255K to 416K, covering all possible atmospheric models and scenarios. Figure 2 shows a graph of calculated temperatures v “n” factor for varying levels of CO2, all at 1%H2O content. What is immediately striking is the relatively small impact that a wide range of CO2 levels have on the equilibrium temperatures.

n Table 2.90.9 %H2O 0 0.1 0.25 0.5 1 2 4

ppm CO2 Temperature K0 255.0 301.7 311.6 319.9 329.3 340.3 353.5

10 259.9 308.8 317.6 324.6 332.6 342.4 360.020 261.1 310.4 318.8 325.5 333.3 342.9 360.450 262.8 312.6 320.6 326.9 334.4 343.6 360.9

100 264.0 314.5 322.1 328.2 335.4 344.4 361.6200 265.3 316.3 323.7 329.5 336.6 345.4 362.4300 266.1 317.5 324.7 330.4 337.3 346.1 363.0400 266.6 318.3 325.4 331.1 337.9 346.6 363.5500 267.1 318.9 325.9 331.6 338.4 347.0 363.9600 267.4 319.4 326.4 332.0 338.8 347.4 364.3

1000 268.4 321.0 327.9 333.4 340.1 348.6 365.43000 271.1 325.4 332.1 337.6 344.1 352.5 369.4

n Table 2.101.0 %H2O 0 0.1 0.25 0.5 1 2 4

ppm CO2 Temperature K0 255.0 310.3 323.3 334.5 347.9 364.7 386.3

10 260.5 319.6 331.3 341.1 352.9 367.9 398.020 261.9 321.7 333.0 342.5 353.9 368.7 398.650 263.7 324.7 335.5 344.5 355.5 369.9 399.7

100 265.1 327.1 337.6 346.3 357.0 371.2 400.9200 266.6 329.7 339.9 348.3 358.8 372.8 402.4300 267.5 331.2 341.3 349.6 360.0 373.9 403.6400 268.1 332.3 342.3 350.6 360.9 374.7 404.5500 268.6 333.2 343.1 351.3 361.6 375.4 405.2600 269.0 333.9 343.8 352.0 362.3 376.1 405.9

1000 270.2 336.0 345.9 354.0 364.3 378.0 408.23000 273.2 342.3 352.1 360.4 370.7 384.6 416.0

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Figure 2 Equilibrium Temperature v "n" factor for 1% H2O

0 CO2 10ppmCO2 20ppmCO2 50ppmCO2 100ppmCO2 200ppmCO2

300ppmCO2 400ppmCO2 500ppmCO2 600ppmCO2 1000ppmCO2 3000ppmCO2

Climate Sensitivity We are now in a position to determine climate sensitivities to CO2 concentration for all values of H2O and CO2 concentrations over a range of “n” values from 0 to 1, therefore covering all climate scenarios. These results are shown in tables 3.0 through to 3.10

Table 3.0 Climate Sensitivity n = 0%H2O 0.0 0.5 1.0 2.0 4.0CO2 doubling ppm Temperature Increase K10 to 20 0.00 0.00 0.00 0.00 0.0050 to 100 0.00 0.00 0.00 0.00 0.00100 to 200 0.00 0.00 0.00 0.00 0.00200 to 400 0.00 0.00 0.00 0.00 0.00300 to 600 0.00 0.00 0.00 0.00 0.00500 to 1000 0.00 0.00 0.00 0.00 0.00

Table 3.1 Climate Sensitivity n = 0.1%H2O 0.0 0.5 1.0 2.0 4.0CO2 doubling ppm Temperature Increase K10 to 20 0.12 0.03 0.02 0.01 0.0150 to 100 0.12 0.04 0.03 0.02 0.01100 to 200 0.12 0.05 0.04 0.03 0.02200 to 400 0.12 0.05 0.04 0.03 0.02300 to 600 0.12 0.05 0.04 0.03 0.03500 to 1000 0.12 0.06 0.05 0.04 0.03

Table 3.2 Climate Sensitivity n = 0.2%H2O 0.0 0.5 1.0 2.0 4.0CO2 doubling ppm Temperature Increase K10 to 20 0.24 0.08 0.05 0.03 0.0250 to 100 0.25 0.10 0.07 0.05 0.03100 to 200 0.25 0.10 0.08 0.06 0.04200 to 400 0.25 0.11 0.09 0.07 0.05300 to 600 0.25 0.12 0.10 0.08 0.06500 to 1000 0.25 0.13 0.11 0.09 0.07

Table 3.3 Climate Sensitivity n = 0.3%H2O 0.0 0.5 1.0 2.0 4.0CO2 doubling ppm Temperature Increase K10 to 20 0.37 0.13 0.08 0.05 0.0350 to 100 0.38 0.16 0.12 0.08 0.05100 to 200 0.38 0.17 0.14 0.10 0.07200 to 400 0.38 0.19 0.15 0.12 0.09300 to 600 0.38 0.20 0.16 0.13 0.10500 to 1000 0.39 0.22 0.19 0.16 0.12

Table 3.4 Climate Sensitivity n = 0.4%H2O 0.0 0.5 1.0 2.0 4.0CO2 doubling ppm Temperature Increase K10 to 20 0.50 0.19 0.13 0.07 0.0450 to 100 0.51 0.24 0.18 0.13 0.08100 to 200 0.52 0.26 0.21 0.15 0.11200 to 400 0.52 0.28 0.23 0.18 0.14300 to 600 0.52 0.30 0.25 0.20 0.16500 to 1000 0.53 0.33 0.28 0.24 0.19

Table 3.5 Climate Sensitivity n = 0.5%H2O 0.0 0.5 1.0 2.0 4.0CO2 doubling ppm Temperature Increase K10 to 20 0.63 0.27 0.18 0.11 0.0650 to 100 0.65 0.34 0.25 0.18 0.12100 to 200 0.66 0.37 0.29 0.22 0.16200 to 400 0.67 0.40 0.33 0.27 0.20300 to 600 0.67 0.42 0.36 0.29 0.23500 to 1000 0.68 0.47 0.41 0.35 0.28

Table 3.6 Climate Sensitivity n = 0.6%H2O 0.0 0.5 1.0 2.0 4.0CO2 doubling ppm Temperature Increase K10 to 20 0.76 0.37 0.25 0.15 0.0950 to 100 0.80 0.47 0.36 0.26 0.18100 to 200 0.81 0.52 0.41 0.32 0.23200 to 400 0.82 0.56 0.47 0.38 0.29300 to 600 0.82 0.59 0.51 0.42 0.34500 to 1000 0.84 0.65 0.58 0.49 0.41

Table 3.7 Climate Sensitivity n = 0.7%H2O 0.0 0.5 1.0 2.0 4.0CO2 doubling ppm Temperature Increase K10 to 20 0.90 0.51 0.35 0.22 0.1350 to 100 0.95 0.64 0.50 0.37 0.26100 to 200 0.96 0.71 0.58 0.45 0.34200 to 400 0.98 0.77 0.66 0.54 0.43300 to 600 0.98 0.82 0.71 0.60 0.50500 to 1000 1.01 0.90 0.81 0.71 0.61

Table 3.8 Climate Sensitivity n = 0.8%H2O 0.0 0.5 1.0 2.0 4.0CO2 doubling ppm Temperature Increase K10 to 20 1.04 0.70 0.49 0.31 0.1950 to 100 1.10 0.88 0.70 0.53 0.40100 to 200 1.12 0.98 0.81 0.66 0.52200 to 400 1.15 1.08 0.93 0.78 0.66300 to 600 1.15 1.13 1.01 0.87 0.76500 to 1000 1.18 1.26 1.15 1.03 0.93

Table 3.9 Climate Sensitivity n = 0.9%H2O 0.0 0.5 1.0 2.0 4.0CO2 doubling ppm Temperature Increase K10 to 20 1.19 0.97 0.70 0.47 0.3150 to 100 1.27 1.24 1.00 0.79 0.64100 to 200 1.29 1.38 1.18 0.99 0.84200 to 400 1.32 1.52 1.35 1.18 1.07300 to 600 1.33 1.61 1.47 1.32 1.24500 to 1000 1.37 1.80 1.69 1.57 1.53

Table 3.10 Climate Sensitivity n = 1.0%H2O 0.0 0.5 1.0 2.0 4.0CO2 doubling ppm Temperature Increase K10 to 20 1.34 1.38 1.04 0.74 0.5850 to 100 1.43 1.79 1.52 1.28 1.19100 to 200 1.47 2.02 1.80 1.60 1.58200 to 400 1.51 2.24 2.08 1.94 2.02300 to 600 1.52 2.39 2.27 2.17 2.35500 to 1000 1.57 2.69 2.63 2.60 2.93

Interestingly, as you might imagine, the climate sensitivity increases as “n” increases as is clearly seen in Figure 3. Even more interesting is that the highest climate sensitivity is only 2.9degC in the extreme condition when “n” = 1 and temperature is 416K. It should, of course, be possible to narrow down the range of “n” values because the derived equilibrium temperature must be in the region of current earth temperatures of 288K. If we select an acceptable range of +/- 10K ( 278 to 298K) this restricts the values of “n” to be within the range of 0.4 to 0.6. (See Figures 2.4, 2.5 and 2.6) for H2O levels in the range 0.5 to 2% and CO2 between 200 and 600ppm. While this still covers a wide variation in atmospheric thermodynamic considerations, the calculations suggests very strongly that climate sensitivity must be within the range 0.25degC to 0.5degC for current atmospheric concentrations of 400ppm CO2 and 1% H2O. Conclusions Without making any assumptions about atmospheric thermodynamics, other than that equilibrium earth temperatures are a function of the radiation balance at the extreme of the atmosphere, we can calculate these temperatures for the complete set of possible thermodynamic conditions and processes within the atmosphere. This is achieved by introducing into the radiation balance equation, a parameter “n”, which is defined as the fraction of outgoing radiation energy absorbed by the atmosphere that is retained by the earth/atmosphere system and has a value between 0 and 1. This covers all possible atmospheric thermodynamic models. This, not unexpectedly, results in an unlikely range of possible earth temperatures between 255K and over 400K as “n” varies from 0 to 1. It also shows that climate sensitivity increases with increasing temperature and has an upper limit of 2.9degC at the extreme temperature of 416K. By narrowing down the calculated temperatures to a reasonable range of +/-10K (278 to 298K) comparable with current global mean temperatures, we can constrain the variable “n” to a value between 0.4 and 0.6, still a very wide range.

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Figure 3 Climate Sensitivity v "n" factor for 400ppmCO2 & 1%H2O

Within this range for “n” we can see that climate sensitivity increases with increasing CO2 content, but reduces with increasing H2O content, somewhat at odds with the claims of a positive feedback due to increasing H2O values. We can also note that climate sensitivity remains below 0.65degC under all conditions up to 1000ppm CO2 and for H2O above 0.5% concentration. In producing these results no assumptions have been made about the mechanisms of heat transfer within the atmosphere, other than the fraction of absorbed outgoing IR radiation that remains with the earth/atmosphere lies between 0.4 and 0.6. Values outside this range result in unreasonable equilibrium earth temperatures. These results are totally at odds with the IPCC version of climate sensitivity ranging between 1.5 and 5degC and suggest quite clearly that CO2 is not, repeat not, a significant driver of global warming and climate change.