Does the Tropopause Limit Carbon Dioxide Heat Trapping?

by Richard J. Petschauer, June 10, 2011, Revised June 29, 2011

[This revision adds non-standard atmospheric lapse rates to the calculations.]


Basic greenhouse theory shows that as the concentration of CO2 increases, a thinner atmosphere is required to allow the heat to radiate to outer space. This causes the typical emission altitude to increase that usually implies a lower temperature, thus causing a drop of the heat loss to space, forcing the atmosphere to warm and finally the surface below.

However as this paper shows at certain infrared wavelengths, CO2 is such a strong absorber that the present emission altitude is in a high region of the atmosphere, the tropopause, where temperature no longer drops with altitude and blends into the stratosphere where warming begins. So moving emissions at these wavelengths to higher altitudes does not increase warming, and under certain circumstances can cause some cooling.

This writer could not determine whether the past estimates of the heat unbalance expected from the common benchmark, namely a doubling of CO2, now widely reported at about 3.71 Wm-2 forcing, treated this correctly. The main motivation of this paper was to provide alternate estimates of the forcing by applying new, easy to use, computer tools that allow the characterization of a complete atmospheric path and the emissions leaving it.

1. Summary of results

We found the reduction of heat radiated to space caused by two times CO2 from the following sources (in Wm-2): the surface with clear skies at 3.38, low clouds at 2.71, medium clouds at 1.03 and high clouds at -0.30. The breakdown of each before and after CO2 doubling and the differences for various wavelength ranges is given in the appendix. The combined weighted average based on the relative occurrences of the clear sky and three cloudy conditions (also explained in the appendix) is 2.53 Wm-2. Note the value is negative from the high clouds at 10 km since this is near where the tropopause in the average atmosphere begins to warm with altitude, so a higher escape altitude means more, not less, heat radiated to space.

The value of 2.53 Wm-2 is considerably less than the presently accepted value of 3.71 Wm-2. This latter higher value is consistent with the widely cited paper by Myhre et al (1998) that provides an empirical equation to fit their estimates of CO2 forcing as 5.35 ln(C / C0). It is interesting that the ratio of all-sky/clear-sky forcing that we get of 2.53 / 3.38 or 0.749 compares closely to the Myhre et al value of 0.734, so this cannot explain the differences.

We used the widely accepted US standard atmosphere for this work. In some early comments received there was concern that the tropopause in the tropical atmosphere begins at a higher altitude than that of the standard atmosphere, about 17 km vs.11 km, so our premise may not be valid in that region. Because of this in the revised paper here we repeated the major parts of the estimates for the tropical, mid-latitude and polar regions and combined them based on weighting of the respective areas of the earth each covers. The results are covered in the appendix and are nearly identical to that of the standard atmosphere.

The use of the standard atmosphere is also validated since it shows the total radiation to space for clear-sky and all-sky (average cloud cover) cases of 266 and 235.4 Wm-2. These are in good agreement with measured satellite values of 265 and 235 Wm-2 as reported by Kiehl and Trenberth (1997). (During the time frame of these measurements, CO2 concentration was estimated at 353 ppm. The standard atmosphere used here has 330 ppm. We estimate that raising this value to 353 will reduce the values of 266 and 235.4 Wm-2 slightly to 265.1 and 234.9 Wm-2 respectively. We follow the normal assumption that considers any doubling of CO2 near its present value will produce the same surface temperature rise.

We also used atmospheric transmittance/absorption tools for altitudes 0 to 70 km in 70 path segments to verify the results and provide additional insight into the behavior of the physics involved, and these results are also presented. In one clear-sky test we eliminated the tropopause and let the atmosphere temperature drop with altitude at the normal lapse rate until it was 150 K at 22 km and then remain there. This increased the radiation forcing from doubling CO2 55% to nearly 5 Wm-2 and shows the significance of the atmosphere temperature at the higher altitudes.

A common method to estimate the surface temperature rise needed to offset a 1 Wm-2 loss of radiation to space uses the rate of change, dT/dW at an emission level of the combined outgoing radiation. For 235 Wm-2, this value, the temperature sensitivity factor, is 0.270 C/Wm-2.  Using the results here for 2 times CO2 gives a temperature increase at the surface before feedback of 2.53 x 0.270 or 0.68 C, significantly less than present estimates in the range of about 1 to 1.13 C.

Since feedback acts as a multiplying factor, if the temperature increase before feedback is reduced by a certain percentage, the increase after feedback will be reduced by the same percentage.

2.  Tools and methods available from Spectra

The tools used here are from the website, from Gats, Inc. Some are available at no charge. A full set requires an available subscription ($25 for a month, $65 for 3 months). These include properties of various atmospheres by latitude, including the US standard, or typical version of temperature, pressure and gas content vs. altitude, a blackbody emission calculator, and tools to calculate IR absorption, transmission and radiance (emission) for a user input of atmospheric properties and a path length of interest.  A number of databases are available. We used the HITRAN 2008 set. A recently added tool that was widely used for this paper is the radiance function for a complete atmospheric path from one altitude to another. The tool breaks the path into segments and automatically alters the temperature, pressure and greenhouse gas content with altitude for the final result.

Because of the large data required in the complete path solution, the wavelength band usually has to be limited to a few microns, with repeated runs for the band of interest. In using it for radiance, a background source is usually selected with a user-specified temperature and emissitivity. For example, for clear skies in an upward path, the surface temperature is used. For radiation from cloud tops, a temperature based on the cloud altitude is used. The radiance output is the sum of the background source that was transmitted through the atmosphere path involved plus what is emitted from the gas itself based on its temperature, pressure and gas content which the tool knows based on the path in question. The temperature of the path can be offset a selected amount by the user and each greenhouse gas concentration can altered by factors from their normal value.

The radiance tool was used for most of the estimates here including the change in outgoing radiation caused by a CO2 doubling and for the total top of the atmosphere outgoing radiation for various clear sky and cloudy conditions.

We also used the transmittance tool. It gives the probability, for each part of the band of wavelength selected, of a photon not being absorbed as it passes through a defined path. The path can be a portion of the atmosphere as described above or a segment with a fixed and uniform set of properties (temperature, pressure and gas content). Here a number of segments is usually needed for a path with properties for each segment altered based on its altitude.

The transmittance is the probability of transmission (of not being absorbed) for a given wavelength. For a path it is the combined product of the probabilities of all the segments for that wavelength. The purpose of the transmittance tool in this paper was to get insight into how the heat escape to space probability varies with altitude and/or greenhouse gas concentrations.

It can also be used to determine the radiance at any level and be compared with the path radiance tool. To do this, for each path segment, a transmittance, and its compliment the absorption, is determined for each wavelength. The output of a path segment is what is transmitted added to the emissions based on the temperature of the path segment. This is repeated through higher, less dense altitude levels until absorption is nearly zero for all the wavelengths of the band involved. At this point the transmittances at each segment are constant and the remaining heat continues and flows upward to outer space.

In our work for this we use 6000 discrete wavelengths for the range of 12 to 18 microns with 70 atmosphere segments, each 1 km thick. More details are provided in the appendix.

3.  Results from the transmittance / absorption tools

While the main results came from the Atmospheric Path Radiance tool, the transmittance calculations are very helpful to get an understanding of how transmittance and absorption vary with altitude, wavelength and greenhouse content, although this takes many more on-line computer runs. As shown later it can be used to check the radiance tool. Transmittance is the probability a photon, at a given spectral wavelength, will pass through a gas over some distance without being absorbed and giving up its energy to the gas. The probability of passing through of a series of these is the combined product of the individual values. The combined absorption probability is 1 minus the combined transmittance probability. While the radiance runs were done at 330 ppm as part of the standard atmosphere, all transmittance and absorption runs were done with CO2 at 350 or 700 ppm for the 2x value.

Figure 1 shows how absorption by CO2 for 1-km thick atmosphere layers varies with wavelength of the infrared heat and the altitude of the atmosphere layer. Nearly all the heat from the earth’s surface at 15C, the approximate global average, is in the range of 4 to 100 microns. Except for a small region from 4 to 5 microns, nearly all the action of CO2 is from 12 to 18 microns range, with a little up to 19 microns. But as can be seen, over this range it shows considerable variation with wavelength with strong absorption action centered around 15 microns. It can be seen that at 10 km, where atmospheric pressure and CO2 molecule density is about one-fourth of that at sea level, from 14 to 16 microns absorption probability is still mostly greater than 0.5.

This is in contrast to the response of water vapor that experiences a large drop in content at the reduced temperatures of the higher altitudes. Figure 2 shows this drop of absorption with altitude. Above about 10 km, water vapor greenhouse action can be ignored. This is not true for clouds that are made of liquid water droplets and act like solid bodies, absorbing and radiating over the complete IR wavelength range based on their temperatures.

Figure 3 shows the mean absorption probability over various wavelength bands with atmosphere containing both CO2 and H2O. In the important 14 to 16 micron region for CO2, the absorption is still quite strong at 10 km and higher which means that much of the final escape to outer space is delayed to higher altitudes.  This is important as can be seen from Figure 4 that shows the temperature stops falling at from about 11 to 20 km, the tropopause, and starts rising above this where the stratosphere begins. This means that the tropopause prevents increased CO2 content from increasing heat trapping in the important 14 to 15 micron range. (Figure A1 in the appendix shows data for both the standard and tropical atmospheres for comparison).

Figure 5 shows the combined results for CO2 and H2O over the entire 12 to 18 micron range for CO2 at 350 ppm and at 2 times or 700 ppm. There is significant absorption left to occur at altitudes above 11 km. Note also the shift to the right for the 700 ppm curve of about 2.5 to 3 km. From simple theory one would expect this to be about 5 km, the approximate distance that cuts the pressure in half needed to maintain a constant density of CO2 molecules with their ppm value doubled. However other factors come into play such as temperature changes with altitude.

4.  Using the transmittance tool to estimate the final heat leaving the planet

The radiance tool used over a complete atmospheric path is the quickest way to estimate how much heat that leaves the top of the atmosphere for a given set of greenhouse gas concentrations. The amount this changes for a doubling for CO2 gives the corresponding radiation forcing. However, the transmittance tool used over many layers of atmosphere can also be used. We did this to verify the radiance method and also to get a mental picture to help understand the mechanism of the way increased CO2 decreases heat leaving the atmosphere and hence the planet. We formed a single array of 6000 x 70 transmittance values for 6000 discrete spectral wavelengths over the 12 to 18 micron range for 70 ascending layers of atmosphere, each 1 km thick. A new array was made for a different CO2 concentration. The appendix describes in more detail the process used to build the arrays by using the transmittance tool.

Figure 6 shows the process for each of the layers of atmosphere. For the first layer, the “layer below” is the earth’s surface, or a cloud top for that situation. For the heat leaving the surface, the heat density in Wm-2 per micron wavelength is calculated using the Planck equation for the same set of 6000 wavelengths over the 12 to 18 micron range as used for the transmittances. For a 15 C surface the total from 12 to 18 microns is approximately 110.6 Wm-2, compared to about 390 over the complete spectrum. For the first layer, the 6000 heat density values from the surface are each multiplied by the corresponding transmittance to determine for that wavelength the fraction of heat that passes through that layer This is the transmitted portion, with the remaining part of heat density for each wavelength being absorbed.

The estimate of the amount radiated for each wavelength begins with the amount absorbed, which is then changed based on a “typical” temperature of the location of the emissions, which can be anywhere in the layer. For the temperature of the layer top and bottom we used the standard atmosphere values starting at 288 K at the surface that drops about 6.5 K / km until the tropopause at about 11 km where it is about 217 K (see Figure 4).

The transmitted and emitted parts of the heat leaving the layer are combined for each wavelength and this becomes the input for the next atmospheric layer. We can ignore the emitted radiation downward since its main role is to warm the layers below. But we already know their temperatures based on the average lapse rate implied in the standard atmosphere data. It can be seen that in the lower layers below 11 km each layer emits less than it absorbs because of the decreasing temperature with altitude. As the atmosphere thins at high altitudes, the absorption rate drops to near zero and the remaining heat finally leaves the planet to outer space. While Figure 6 shows the path length inside of a layer as equal to the layer thickness, we use a multiplying factor of 1.81 as recommended by SpectraCalc to represent an equivalent typical path length in the transmittance estimates. We varied this factor from 1 to 3, and the final emitted values changed only about plus, minus 6 percent.

We used three methods to estimate the typical location of the emissions within the each layer and hence their temperatures which determines their magnitudes. The results varied about 5% from their mean. For the following work described we selected the one that came closest to that of the radiance tool of the complete atmospheric path since the radiance method agreed well over the complete spectrum of the total longwave radiation leaving space based on Satellite measurements of 235 Wm-2.

Figure 7 shows the clear-sky atmosphere values with normal H2O and CO2 at 350 ppm out to 70 km where the process is essentially complete. The heat densities are multiplied by the width of each of the 6000 wavelengths and summed for each layer. The total is the input to each of the 1-km thick layers; the altitude shown is the top of the layer. The first layer’s input is the 110.6 Wm-2 leaving the surface in the 12 to 18 micron range that we use since this is where the majority of the CO2 absorption occurs. Over 80 Wm-2 is absorbed in the 1-km first layer, with only about 30 Wm-2 transmitted, mostly in the 12 to 14 micron and 16 to 18 micron ranges away from the strong CO2 absorption around 15 microns. The total drops because of the heat loss of the absorbed portions in each of the layers as they become colder with altitude. As the atmosphere thins, the absorbed fraction drops until the remaining of about 70 Wm-2 of the original 110 Wm-2 is transmitted to outer space.

Figure 8 shows the upward transmitted heat by altitude using the standard clear-sky atmosphere normal amount of H2O water vapor and CO2 concentrations of 350 and 700 ppm. The final heat leaving the atmosphere for 350 ppm is estimated to be 70.29 Wm-2. This compares with the radiance tool that provided 70.63 Wm-2. These compare with 110.6 Wm-2 that entered the atmosphere from the surface in same wavelength band of 12 to 18 microns.

Figure 9 shows the difference of the transmitted heat for the two CO2 concentrations by altitude. Note the drop with altitude after the peak showing the importance of continuing the analysis to a sufficiently high altitude. For the radiance tool we used 100 km as the observation point looking downward although there was little difference between 50 and 100 km.

The final difference for the transmittance method used to create Figure 9 is 3.18 Wm-2. The values from the radiance tool was 3.23 Wm-2 for the 12 to 18 micron range that increases to 3.38 when the bands of 4 to 5 and 18 to 19 microns are included. Since these values started from the surface, they correspond to the clear sky case. Radiance runs were also done starting from the various cloud tops that have lower temperatures and hence less initial heat entering the first layer, resulting in less total heat loss. These clear-sky and cloudy-sky cases were combined by weighting each by its estimated relative frequency of occurrence, with details provided in the appendix, to get a combined value of 2.53 Wm-2, substantially less than the widely reported and accepted value of 3.71 Wm-2 for CO2 doubling.

5.  Conclusions

The results here using modern tools indicate substantially less (about 32%) radiation forcing heat unbalance caused by increased CO2 content then the presently accepted values such as in cited in Myhre et al. This brings into question estimates often cited as being the “settled” values from many years ago and whether they should be redone by others with new tools and techniques. Of particular significance is the fact that the estimates from the radiance tools used here match closely with satellite data for both clear and cloudy sky conditions. We were disappointed in the excellent paper by Kiehl and Trenberth (1997), that we used for part of our work, that the authors, after estimating outward radiation that matched satellite data quite well for existing CO2 content, did not repeat it for double CO2 as we did here. They did attempt to assign the relative importance of existing greenhouse gases, but this is of little value in answering in the central question of climate sensitivity.


Kiehl, J. T., and K. E. Trenberth (1997): Earth’s Annual Global Mean Energy Budget. Bull. Amer. Meteorol. Soc., 78: 197-208

Myhre, G, et al: New estimates of radiative forcing due to well mixed greenhouse gases, Geophysical Research Letters. Vol. 25, No. 14, pages 2715-2718, July 15,1998.


A1.  Weighting of results from clear skies cloudy conditions

Estimates from Kiehl and Trenberth (1997) were used for cloud coverage. These are 49% at 1 to 2 km, 6% at 5 to 6 km and 20% at 10 to 11 km. The emissitivities were 1 for the low and medium heights and 0.6 for the high clouds. We handled this later case by reducing coverage from 20% to 12% and using an emissivity of 1. For cloud tops we used 2, 6 and 10 km. With cloud overlap, the clear sky probability is then (1– 0.49) x (1 – 0.06) x (1 – 0.12) or 0.422 that we rounded to 42%. For the low clouds we assumed half would be underneath medium clouds or high clouds, so the net percentage with clear sky above low clouds is 49 – 6/2 – 12/2 or 40%. We ignored overlap between the medium and high clouds, so the percentage with clear sky above medium clouds is 6% and high clouds 12%. So the percentages for weighting results for clear skies and the three levels of clouds is 42%, 40%, 6% and 12%.

A2.  CO2 forcing at the “Top of the Atmosphere” using the Radiance Tool

For each case of clear and cloudy skies, and for each bandwidth where CO2 is active, the outgoing radiation at 100 km from 1x and 2x CO2 were determined, and from that the decrease. Each run took about 2 to 3 minutes. The results are shown below in the four tables. Note the significant reduction for the cases from the cloud tops. And at 10 km, the heat loss increases slightly with 2x CO2 because the altitude’s increase with temperature at the higher attitudes.

Using the weighting described above, we get for the combined forcing for 2x CO2:

(A1)  F = 0.42 x (3.27 + 0.11) + 0.40 x (2.65 + 0.06) + 0.06 x 1.03 + 0.12 x (-0.30) = 2.53 Wm-2

A3.  Comparing the radiance estimates of total outgoing radiation with satellite data

The preceding work centered on the 12 to 18 micron range because this is the major band where CO2 plays a role. However we also used the radiance tool over the full range that virtually covers the complete longwave spectrum associated with the global average temperature. The results are shown in Table A5. The total leaving the top of the atmosphere under clear skies is estimated at 265.9 Wm-2, close to the satellite data of 265 Wm-2 as reported by Kiehl and Trenberth (1997).

Table A5 –Radiation leaving the surface and the atmosphere by wavelength (clear skies)When this was repeated for the three cloudy cases, the totals dropped from 265.9 to 240.2, 188.2 and 135.2 Wm-2. The combined total, using the weighting above, drops to 235.4 Wm-2, compared to 235 from Kiehl and Trenberth.

The agreement of the radiance tool with satellite data regarding outgoing radiation provides confidence in using it to estimate how it will change with increased CO2 concentrations.

A4.  More detail on how the transmittance tool was used

To perform the runs for the transmittance calculations that were described in the main body of this paper in the 12 to 18 micron range we wanted to cover 70 km of altitude above the surface broken down into 1-km thick segments for CO2, but for H2O we only had to use 10 segments since the water vapor content is virtually non-existent above this altitude because of the very low temperature there. So for water vapor (H2O) we did 10 runs with the temperature, pressure and H2O content set at the segment midpoints.

To reduce the number of runs for CO2 we did alternate segments out to 20 km. We then developed a curve fitted interpolation technique to set the transmittance for each wavelength for the in between layers. For altitudes from 20 to 70 km, we did runs every 5 km and developed a fitting equation for transmittance as a function of atmospheric pressure to generate the 1-km values from 20 to 70 km.

Some runs developed over 100,000 spectral point wavelengths, with higher values at low pressures. We sampled these down to a nearly common set of 6000 values. The spectral points are provided in microns but calculated in equally spaced “wavenumbers” (related to the inverse of the wavelength) so that the difference in the 6000 values in microns varied from the average value of 0.001 micron from about 0.0006 to 0.0013 micron. We used the same 6000-value set for both CO2 and H2O. Because we did not use the full set of spectral points, and since we ran CO2 and H2O separately, small errors are introduced when they are combined. However as shown in the paper, the values for the net radiation leaving the atmosphere and the change in it from a doubling of CO2 are quite close to those using the radiance tool.

While using the transmittance method requires more runs because of the large number of path segments, it has the advantage of providing simple ways find new transmittances caused by a change in the path length of a segment, combining greenhouse gases and changing the concentrations of each of the greenhouse gases involved. Since transmittance is a probability, simple probability rules apply,

For path length increase by a factor of K (for a decrease, K is less than 1)

(A2) Tnew = Told K (for each wavelength transmittance)

For PPM concentration increase by a factor of K (for a decrease, K is less than 1)

(A3) Tnew = Told K (for each wavelength transmittance)

Combining greenhouse gases G1, G2, and G3 with transmittances of T1, T2, and T3

(A4)  Tnew = T1T2T3 (for each wavelength transmittance)

For changes in absorption, a new transmittance must first be calculated, then

(A5) Anew = 1 – Tnew (for each wavelength transmittance)

Note: Mean transmittances and/or mean absorptions cannot combined.

A5. Comparing the standard atmosphere with a combination of other atmospheres types

Comments on the original paper questioned whether proper consideration was made of certain areas such as the warmer tropical latitudes where the tropopause starts at higher altitudes. The purpose of the following sections is to report on additional analysis that was done in response to these comments. In the foregoing we used the standard atmosphere values. Here we show results using five additional types: Tropical, mid latitude summer and winter and polar summer and winter. The data for these atmospheres was obtained from the website. As a benchmark we used the 12 to 18 micron band where nearly all of the absorption of CO2 occurs and used the clear-sky cases. It is shown here that these results agree closely with those using the standard atmosphere alone.

A6. Comparing the standard and tropical atmospheres

The tropopause in the tropical atmosphere starts at about 17 km compared to 11 km in the standard atmosphere that was used for all the analysis in the main body of the paper. Figure A1 shows how the atmospheric temperatures for these atmosphere types vary with altitude. It is a repeat of Figure 4 in the main body of the paper but with the values for the tropical atmosphere added. We treat the tropical atmosphere as covering the latitudes from S30 to N30 degrees. The standard atmosphere starts at the surface at 288 K, while the tropical atmosphere begins at 299 K. The value of 299 K or 26 C may seem low, but most of this is over the ocean with its moderating effect.

As can be seen with the tropical atmosphere the temperatures drop to lower values and the altitude of the minimum, the beginning of the tropopause, is about 17 km. Note the slopes, or lapse rates, are essentially equal up to about 11 km. Also the flat region in the standard atmosphere does not show up in the tropical atmosphere. Above 25 km there is less difference in the two temperatures. The starting altitudes of the tropopause for the mid latitude and polar atmospheres range from 9 to 13 km, being higher in the summer and dropping with higher latitudes.

Figure A2 shows how the water vapor varies with altitude. The higher tropical temperatures allow this atmosphere to hold significantly more water vapor than that of the standard type. The ratio varies from about 2:1 to 3.3:1 with an average of about 2.6:1. In both cases, water vapor content above 10 km is very low. An important result of higher water vapor content in the tropical atmosphere is the reduction of the effect of CO2 doubling because of the overlap or competition of water vapor with CO2. The result of this difference is covered later.

Figure A3 is a repeat of Figure 9 in the main body of the paper with the values for the tropical atmosphere added. It can be seen that the tropical atmosphere peaks and ends with higher values consistent with a higher surface temperature. But note that even with the higher tropopause, there is still significant drop in the transmitted heat with altitude after the peak as a result of the strength of CO2 absorption that continues out to about 50 km. Above 25 km, the temperatures of both atmosphere types is similar as can be seen in Figure A1.

A7. Comparing CO2 forcing using all five atmosphere types with the standard atmosphere

To run all the five additional atmosphere types we used the transmittance/absorption/emission method as described in Section 3. The reason is that is easy to change the program to vary the atmosphere temperature with altitude and the transmittance from water vapor content changes. For the water vapor for each atmosphere, we used the average of the values formed by dividing its ppm for each altitude by that of the standard atmosphere. For comparison purposes we ran only the clear-sky case.

Table A6 shows the results of the five individual atmosphere types with their water vapor factor compared to that of the standard atmosphere. Note the tropical atmosphere difference of 3.59 Wm-2 compared with 3.18 for the standard atmosphere. If we use the standard atmosphere water vapor content vs. altitude for the tropical atmosphere, the 3.59 Wm-2 value above increases to 4.11 Wm-2, showing the significance of the inhibiting action on CO2 changes caused by the higher water vapor at the warmer temperatures.

The five atmosphere types were combined by weighting based on the area of the Earth’s surface they cover. The tropical atmosphere is based on latitude of 15N, so we use it to represent an average from 30S to 30N; that is, 30 degrees on either side of the equator. For the mid-latitude we use 30 to 60 degrees from the equator and for the polar 60 to 90 degrees from the equator. Starting at the equator in three 30-degree latitude segments results in relative earth surface area values of 0.500, 0.366 and 0.134. Since the last four atmosphere types are for only 6 months, we divide their values by two. The final weighting values used are shown in Table A6.  Note the tropical atmosphere dominates with a weighting of 0.5.

The value of the final weighted mean heat outward for the two levels of CO2 are about 2% above those of the standard atmosphere, but the important values of their differences of 3.19 and 3.18 Wm-2 are nearly equal.  This demonstrates the use of the standard atmosphere only is sufficient to determine the radiation forcing for doubling CO2.

Table A6. Comparison of outward heat differences from CO2 doubling for different atmospheres.


Copyright (c) 2011 by Richard J. Petschauer


  1. Richard,
    The first point I want to make has to do with the curve in Figure 4. That curve shown is a crude straight-line segment approximation of the average temperature vs. altitude. In fact, the location of the Tropopause varies considerably with Latitude and season, and goes from a minimum of 9 km at the poles to a maximum about 18 km near the Equator (… )
    If you use an global average lapse rate, this variation results in a broad average region with the nearly linear dropping temperature in the lower Troposphere becomes progressively more non linear above 9 km, and reaches a minimum near 13 km, before the average temperature flattens then starts increasing again in the Stratosphere. However, in reality, there is a large local band near the equator that actually does not flatten until about 18 km. Thus using averages along with the radiation models may be badly deceptive. This means that moving the effective average altitude up for outgoing radiation from increasing CO2 will likely still have an effect as long as there is a significant decreasing temperature at the average altitudes of interest.

    The second point is that the amount of movement up of the radiation altitude due to doubling CO2 is fairly small. While the initial transient response would be to heat the atmosphere and surface of Earth, at steady state the temperature at the new altitude would increase some to obtain new radiation balance, and the surface would be 1C warmer. Note that the 1C warmer is due to the higher altitude for new balance. Since a warmer Earth also causes some increase in direct radiation to space, the new outgoing average CO2 radiation altitude would not be as warm as the previous level, but would be warmer than before the change. The temperature at the new altitude plus the integrated value of lapse rate times altitude would give the 1C surface increase.

    The small change in altitude needed to satisfy the required temperature change, along with the fact that much of the Tropopause extends significantly higher than 10 km (to as much as 18 km) may limit your basic argument that the Tropopause limits the CO2 greenhouse effect.

    I also want to point out it is not heat trapping that causes the atmospheric greenhouse effect, but partial radiation insulation in the presence of free convection (which raises the average location of outgoing radiation), combined with the adiabatic lapse rate, that causes the effect.

    In the end, the actual value of the ideal CO2 effect (which may or may not be smaller than 1C per doubling) and the actual feedbacks (which may reduce or increase the effect, but is not known) will determine the issue.

  2. Congratulations to Dr. ED for his success in Montana ,unfortunately this is just one battle in a major war. May there be many more wins we need them!!!!

  3. Berthold,
    You continue to misrepresent what is the atmospheric greenhouse gas effect. Back-radiation is real, but is a consequence of the effect, not the cause. Your "experiments" are poorly posed and would not prove anything. Just as yelling louder can't make someone that does not understand you understand more clearly, so restating your ideas more often does not make them more acceptable. It actually may be possible that "negative feedback" effects may greatly reduce CO2 increase effects (so that CO2 is a minor player), but this is not the same as the statement of no back-radiation. You need to understand that back-radiation is a consequence only of the fact that some gases (water vapor and CO2) absorb and also radiate IR in the range of interest, and this is a fact. However, the dominance of convection of absorbed solar energy on the ground and sea, and evaporation of water are the main transport means of surface energy up to altitudes, where radiation (from water vapor, clouds, CO2, and some direct from the surface) goes to space.

  4. 1.
    You continue to misrepresent what is the atmospheric greenhouse gas effect. Back-radiation is real, but is a consequence of the effect, not the cause. Your “experiments” are poorly posed and would not prove anything. Just as yelling louder can’t make someone that does not understand you understand more clearly, so restating your ideas more often does not make them more acceptable. It actually may be possible that “negative feedback” effects may greatly reduce CO2 increase effects (so that CO2 is a minor player), but this is not the same as the statement of no back-radiation. You need to understand that back-radiation is a consequence only of the fact that some gases (water vapor and CO2) absorb and also radiate IR in the range of interest, and this is a fact. However, the dominance of convection of absorbed solar energy on the ground and sea, and evaporation of water are the main transport means of surface energy up to altitudes, where radiation (from water vapor, clouds, CO2, and some direct from the surface) goes to space.
    Dr Leonard : lets examine my test piece by piece and note where I might agree with you and where the science does not.

    1. The IRags absorb the IR radiation and thus prevents it from escaping into space reducing the rate of atmospheric cool- it causes the air to be warmer.
    We agree that certain molecules absorb IR -CO2,Ch4, H20 and others.
    We agree that these same molecules radiate IR and I think we would agree that the IR is radiated in all directions -up, down to earth , tangential to the earth and upward to space and all degrees of directions in between. We do not agree that other molecules and atoms in the atmosphere do exactly the same thing.( See Alan Siddons -The Hidden flaw in Greenhouse Theory). Now the bases for this is Kirkoff's laws of Thermodynamics that all mater that is above absolute zero radiates IR proportional to its temperature. As all the molecules and atoms in a small volume of atmosphere can be assumed to be at the same temperature they will all be radiating IR at the same wave lengths.
    Now how can we tell if the IR of the same wave lengths is from the IRags or from other components of the atmosphere in this volume?

    2. The IRags will “back radiate” IR radiation to earth to cause increased heating of the surface.
    3. The IRags will heat up by the absorption of the IR radiation thus heating the air.
    4. The IRag’s have different levels of “back-forcing”. Having ask others how this is determined,( no answer yet) ,it is assumed that someone has reviewed the amount of IR that a particular molecule absorbs by a spectrophotometer analysis then comparing this to the absorption of CO2. (I have not seen any experimental data that the “back-forcing” relates to absorption).(an assumption based on The Bohr model however a time factor is needed)
    5. The higher the concentration of IRags the greater the amount of “back-radiation” the higher the “global atmospheric temperature will become.(were is the experimental data )

    Let's see if we agree so far.
    If you are confused by my experiment I also am confused by what you have stated in your response above. Bert
    I have used a different size font and color to differentiate from the copy of your response and the experiment.

  5. To Dr Leonard Weinstein and other followers of these postings: As Dr. Weinstein does not believe this experiment proves that the "greenhouse gas effect" does not exist, let's do a public "peer review" As this experiment has been posted on Judy Curry's Climate Etc. I'd hope that she jumps in as I believe some Of my E-mails to her help change her understanding on the subject.
    Check my math and any suggestions in text that will make it clearer would be welcome. Berthold Klein P.E.

    As I have been thinking about the experiment I would add two additional balloons to the group one with O2 and the other with N2. The purpose would be to demonstrate that I can take reading of the temperatures of these two balloons with an IR thermometer.( Gustav Kirchhoff. law of thermodynamics) As I see it they should show the same reading as any of the others that contain IRags. even when large amounts of IR passed through the balloons. They all should be at ambient air temperature.

  6. Response to Leonard Comment #1

    Thanks for your comments, Leonard.

    For several weeks I have not been able to add comments. It seems the problem was on my end and has now been fixed.

    I have revised the paper with the major change being running with 5 additional atmosphere types, including a tropical one following your comment. These are those available with the website. For this I used the transmission/absorption method since I can change parameters and do new runs much faster. I can use any temperature profile available. An added part of the Appendix contains the new results. These 5 atmospheres are weighted by the areas on the earth each covers with the tropical one weighted the highest. It shows a larger reduction of radiation to space with 2x CO2 than the US standard atmosphere, but when combining with the other atmosphere types, I get nearly the same value (3.19 Wm-2 vs. 3.18 Wm-2 for the clear sky case in the 12 to 18 micron range). See Table A6 in the revised version. The paper also shows that the water vapor content is about 2.6 times higher in the tropical atmosphere than that of the standard atmosphere. This increased competition of water vapor reduces the effect of CO2 substantially, about 15%. I ran it with both levels of water vapor. I also ran the standard atmosphere but with no tropopause, just a constant lapse rate of-6.5 K / km out to 22 km where it was 150 K and left it there. The drop in outgoing heat for 2x CO2 increased 55% showing the importance of the atmosphere temperature above 11 km (the standard atmosphere tropopause altitude).

    It is important to note that using the standard atmosphere, the results closely match that of global average outgoing longwave radiation from satellite data for both clear sky and cloudy sky conditions, namely 265 and 235 Wm-2 for CO2 content close to the period when the data was taken. If I match that with present CO2, it seems the estimates with 2x CO2 should be close. And they show the reduction of outgoing longwave reduced considerably less than 3.71 Wm-2 that I believe is required to produce the 1 C temperature you mention

    I assume your estimate of a 1 C rise comes from radiation forcing unbalance caused by 2x CO2, probably the one now accepted of 3.71 Wm-2. The point of my paper is questioning that value, not how it is converted to surface temperature, which is a separate issue. It seems only a few people did the estimates that arrived at the 3.71 Wm-2 or similar values, and they were done 10 to 20 years ago.

    I understand the process of warming due to CO2. In fact I thought you would appreciate my graphs that illustrated with values what you have been saying is the cause of warming from CO2. I only used the "trapping" in the title as being similar to absorption increases with more CO2 and a resulting reduction in outgoing radiation until temperatures rise to restore balance.

    I also understand that the affect of feedback has more uncertainty than the pre-feedback warming caused by CO2. But if the pre feedback value drops a certain factor, the final value with feedback will drop by the same factor.

    Finally, I hope you will read the entire revised paper. With these new computer tools available should the radiation forcing for 2X CO2 number (3.71 Wm-2) from the 1990s be redone?

  7. Are you considering cooling from anthropogenic aerosols? I didn't see it anywhere…. It's significant — its radiative forcing is about -1/2 of CO2's RF. If you're not including it, your calculation isn't going to return what you're claiming….

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