# The Limits of Atmospheric Carbon Dioxide Effects and Control

by Bryce Johnson

Abstract
[latexpage]
The interactions of the fossil-fuel source of carbon dioxide with the atmosphere as well as in the total biosphere are analyzed. The time dependence of resulting carbon levels and temperatures in all components of the biosphere are determined under a full range of possible insertion and depletion rates to and from the atmosphere as carbon dioxide. The three most significant findings follow:

1. There is no rate at which such man-produced carbon can be inserted into the atmosphere that will result in a harmful temperature rise before the total inventory of carbon in the world’s fossil-fuel reserves has been depleted, at which point CO2 and temperature increases cease.
1. Man’s efforts at reducing atmospheric carbon are ineffective. The same natural forces that inhibit increases in the atmosphere also inhibit decreases.  The total carbon content of the remainder of the biosphere and its exchange rate with the atmosphere overwhelm whatever man can do to alter the atmospheric level;
1. The natural temperature feedback from carbon dioxide increase in the atmosphere is predominantly negative (acting to diminish further increase). There is no possibility of an unstoppable runaway reaction.

The obvious conclusions from these findings are that there is no need to reduce man-made carbon dioxide in the atmosphere and such an attempted reduction would be completely futile even if there were a need.

• Abstract
• Introduction
• Overall Perspective on the Problem
• Analysis Method
• Major Findings
• CO2-Caused Temperature Rise
• Water Effects – pre-existing and feedback
• Time Dependence of Atmospheric CO2 and Temperature
• Evaluating of Carbon Reduction Scenarios
• APPENDIX A.  ATMOSPHERIC CARBON CYCLES
• APPENDIX B. USING MODTRAN
• APPENDIX C.  DRAFT UN REPORT ON IPCC TEMPERATURES
• REFERENCES
• ACKNOWLEDGEMENTS
• THE AUTHOR

#### Introduction

This essay addresses the role of carbon dioxide (CO2) in global warming (GW). Other factors that have a role in global warming are not addressed here. The reason for limiting the discussion to the effects of CO2 is that the International Panel on Climate Change has identified man-made atmospheric CO2 from fossil fuels as a major GW cause and man’s efforts to curb it are based on schemes for limiting or reducing such CO2 concentration in the atmosphere.

Overall Perspective on the Problem

Figure 1 depicts a fluid contained in four tanks representing the world’s reservoirs of accessible carbon: in fossil fuel, land/plants, atmosphere and ocean. The latter three comprise the biosphere. The blue content in each tank is proportional to the current carbon content in each world reservoir.

The atmospheric section is bounded on each side by permeable boundaries with its neighbors. The current exchange of the atmosphere with its neighbors is approximately equal for each and occurs simultaneously in each direction as CO2.

The total exchange is twenty times the rate at which it receives carbon from fossil fuels. But once carbon is liberated from fossil fuels, it cannot be put back. Man can insert or extract carbon from the biosphere only through the atmosphere but not at rates even approaching the biosphere exchange rate and extracting existing carbon permanently from the atmosphere is difficult. Man can minimally alter the exchange rate between the atmosphere and land/plants by reforestation and deforestation but has no control over exchange with the ocean.

Direct exchange between the land and ocean is negligible. Obviously, any attempt by man to alter the atmospheric carbon content is overwhelmed by the exchange between the atmosphere and the rest of the biosphere, a task that is comparable to attempting to fill or empty a 1-gallon sieve which is immersed in a 50-gallon-tank of water. When the fossil fuel is depleted the levels in the three biosphere components stabilize at a fractional-level increase equal to the ratio of the current total in fossil fuel to that total in the biosphere.

Analysis Method

The analysis is based on “limit analysis” and demonstrably conservative calculations, which mean that limits are designed that can be assured to bound the true answer and can be reliably and accurately calculated when the true exact answer may be elusive.  The advantage is that the limits so calculated provide valuable pieces of reliable information on which decisions can be made.

The primary example of this analysis is that it is easy to define an upper limit to the amount of CO2 that can ever be deposited in the atmosphere from man’s efforts as well as the temperature rise caused by this much deposition of CO2. Man’s upper limit is from transferring all the carbon in the world’s fossil-fuel reserves into the atmosphere. Such a limit would require an impossible instantaneous release because of leakage from the atmosphere.

Reliance has been placed on the ModTran computer code (1) described in Appendix B, which is an Air Force developed code that is available to the public to calculate the heat deposited in the atmosphere. It calculates infrared (IR) radiation transport including its absorption and emission.

World-wide average ModTran-calculated IR energy transmitted to outer space (approximately 240 watts per meter-squared) compares favorably with NOAA’s world-average measurements (233 w/m2) (2). ModTran also appropriately discriminates between those clouds which have negative feedback and those few that do not, as shown in Figure 5. And it appropriately accounts for saturation (defined below) as CO2 level increases.

From the atmospheric heat deposited, the CO2-generated temperature rise is determined by classical heat transfer equations. Time dependence of the levels within the three biosphere’s components and their transfer rates is governed by differential equations, solved by numerical means as described below.

Major Findings

Minor temperature increase. The increased temperatures predicted due to CO2 additions to the atmosphere show that the values predicted are roughly half those predicted by the International Panel on Climate Change (IPCC). Appendix C contains a draft report from the IPCC confirming that their temperature predictions have been consistently higher than actual temperatures.

Negative feedback. The effect of temperature change from increased CO2 (which comes mostly from increased water vapor) is preponderantly negative, to the extent that achieving the so-called “tipping point” where a “runaway” temperature rise is predicted is impossible. Pre-existing water in all three phases is demonstrated to significantly inhibit the ability of CO2 to raise temperatures. The small temperature rise from CO2-induced vaporization (feedback) in the atmosphere is overwhelmed by the strong negative impact as the “created” water becomes the “existing” water. The other negative feedback is from “saturation” (the absorption depletion of energy in the IR energy bands which diminishes the absorption effectiveness of added CO2 increments).

Short CO2 lifetime in atmosphere. There is no basis for the common claim that CO2 stays in the atmosphere for hundreds of years. Well-established figures for content and exchange rates show that its mean atmospheric dwell time is only approximately four years. The level of CO2 does stay constant when its net insertion rate becomes zero but the individual molecules continue to exchange with the remainder of the biosphere maintaining the short dwell time.

No short-term action required. The frequent assertion that there is a limited time to act in order to prevent an intolerable increase in temperature is not correct. At whatever increase in CO2 level can be achieved, the level and the associated temperature drop when input CO2 can no longer be maintained (due to depletion of fossil fuels). The drop rate is proportional to the level of CO2 attained. The final level to which CO2 and temperature drop is independent of the rate of CO2 insertion and its maximum level.  After the depletion of all fossil-fuel carbon, the stable temperature rise will be less than 0.5 oC.

CO2 elimination is ineffective. There is no basis for the claim that significant reduction in atmospheric CO2 can be achieved before the end of this century. It is fortunate that the CO2 temperature effect is limited to acceptable values, because once it is in the biosphere it is slow to be reduced in the atmosphere. The same factors that inhibit CO2 increase in the atmosphere also inhibit its decrease. Any permanent reduction requires reduction of the same fraction from the entire biosphere. The paltry effects of man’s elimination efforts are displayed in Figures 21 through 24.

CO2-Caused Temperature Rise

Figure 2 is the IPCC energy balance for the earth-atmosphere system.  It is very similar to other balances such as those by NASA (4) and the U. S, Weather Service (5). But since that of Figure 2 has become the standard, its values are chosen.

Using Figure 2 as a guide, the heat retained in the atmosphere is defined as

\label{eq:1}

H = IR_{in} +175 (IR_{in} / 396) – IR_{out}

Where H is the heat retained in the atmosphere at the particular CO2 level and 175 is the non-IR heat input from Figure 2. It is modified by the ratio $IR_{in} / 396$ to account for balances other than that indicated in Figure 2. It is assumed the $IR_{in}$ and whatever enters the atmosphere for non-IR sources maintain the same proportionality as that of Figure 2.

The ‘back radiation’ shown as 333 w/m^3 in Figure 2 is not part of the balance of the atmosphere because all that exits at the ground was created within the atmosphere for a net of zero for this component in the atmosphere balance. 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 Stefan- Boltzmann equation for radiative heat transfer:

\label{eq:2}

H_B = c_aT_B^4 – c_oT_o^4

\label{eq:3}

H_A = c_aT_A^4 – c_oT_o^4

Where subscripts a and o refer to atmosphere and outer space, respectively. $H_B, H_A$ are net heat rates into atmosphere before and after CO2 addition, respectively and c is a constant (Maxwell-Boltzmann constant times emissivity) $T_B, T_A$ are temperatures of the atmosphere before, after CO2 addition, respectively, in degrees Kelvin.

They are the temperatures within the atmosphere which would match the aggregate of all radiative transfers to outer space when used in the above equation. In this analysis they are assumed to be the maximum (at the earth’s surface) because that produces the maximum (most conservative) value.

Then

\label{eq:4}

\frac{H_A}{H_B} = \frac {c_aT_A^4 – c_oT_o^4}{c_aT_B^4 – c_oT_o^4}

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. Therefore, the second terms in both numerator and denominator on the right-hand side can be ignored without compromising accuracy. Then the constant term cancels out and this simplified equation results:

\label{eq:5}

T_A = (T_B) (\frac{H_A}{H_B})^{1/4}

Temperature rise due to added CO2 is the difference between $T_A$ and $T_B$.

Water Effects – pre-existing and feedback

Pre-existing water

There is no controversy about the negative feedback of saturation, but that due to water vapor is highly controversial. The main claimed source of feedback is from CO2-created water vapor, since that is also a greenhouse gas.  However existing water in any of its three phases has a predominantly negative effect on the ability of CO2 to increase atmospheric temperature. But existing water vapor is really a separate forcing function, and not feedback. Feedback is caused by the phenomenon itself and most of the water in the atmosphere is not caused by CO2. It is appropriate to separate existing water from that vapor created by CO2 addition as a true feedback in analyzing water’s effect on CO2 warming.

Figure 3 is a plot of the temperature results of using Equation 5, and ModTran calculation of IRin and IRout, to show the effects of varying water vapor on the temperature rise for increasing CO2. This figure shows the strong negative effect of existing water vapor on the ability of CO2 to increase atmospheric temperature. Figure 3 is for the U.S. Standard atmosphere, and a similar variation is shown for other climate regions available in ModTran. It may be unlikely that the four- and five-times levels could ever be achieved, but their effects can be calculated. The highest level of CO2, 5300 ppm in Figure 3, corresponds to that level that would be achieved if it were possible to put all of the world’s fossil-fuel carbon into the atmosphere.

Figure 4 is from the Climate Research Unit (CRU) at East Anglia University in Great Britain (6) and clearly shows the negative impact of low-level clouds on temperature. Clouds have competing effects on warming and cooling the atmosphere. Their white tops reflect the energy impinging on the earth from the visible rays of the sun and produce cooling, but their IR absorption retains heat that would otherwise escape. The predominant effect, however is cooling as indicated in Figure 4. Reference 6 reports that data on high-altitude clouds are insufficient for plotting but posits that they are likely positive rather than negative, but not sufficient to the counter that at low levels, so that cloud effect is negative overall.

Figure 4.  26-Year Record of World Temperature vs Cloud Cover (6)

However, Figure 5, below, does not support the East Anglia position (6) that most high-altitude clouds have positive temperature impact. It indicates that 2 of the 3 (high-altitude) cirrus-cloud models are lower than the curve for no rain or clouds, indicating that high-altitude clouds also have a net negative temperature impact.

The only one with a net positive impact is the sub-visual one. Its positive effect is much smaller than either of the two negative ones and caused by the fact that such clouds cannot reflect light to diminish the incoming heat from the sun (as visible clouds do) but they still absorb outgoing IR in the atmosphere for a positive-temperature greenhouse effect.

Sub-visual cirrus clouds have a small positive temperature impact in all the six climate regions available for modeling with ModTran. All the other 13 weather models have a significant negative impact on all the regions (compared to the one for no clouds or rain).

Reference 7 indicates that the high-altitude (cirrus-type) clouds occur much less frequently than lower level clouds which further augments the overall negative impact on temperature of atmospheric H2O.

Figure 5 through 6 are for ModTran’s “normal” water-vapor level but at climate conditions of rain and/or clouds. It is obvious from these curves that existing water in any phase (cirrus clouds shown are primarily ice crystals) strongly inhibits CO2’s ability to increase temperature.

Figures 3, 5, and 6 are all for the United States Standard climate. The trends shown are duplicated in the other five climate regions available in ModTran. The rain-and-clouds effect is not significantly diminished by calculations for the conditions of clouds without rain. However, since rain is always accompanied by clouds this fact does not affect the conclusion of this study.

All curves show a decreasing slope with increasing CO2 which is due to saturation effects described above.

Figures 7 and 8 compare the same weather conditions: clear sky, NOAA cirrus clouds, and most extreme rainfall, at winter time in the arctic regions and in the tropics. The three climate regions between these: midlatitude summer and winter and sub-arctic summer show very similar results. The negative impacts are duplicated for all weather conditions in all zones with the lone exception of sub-visual cirrus clouds, whose positive impact is much smaller than any one of the twelve negative impacts by the other weather conditions of rain or clouds.

Water from feedback

It is necessary to consider the feedback from the water vapor that the added CO2 creates in the atmosphere as a positive feedback from water’s greenhouse effect which adds to that temperature brought by the added CO2. That temperature addition, of course, creates more vapor and, again, more temperature rise for a continuing water-temperature feedback loop giving rise to the claim of a “tipping point” where an unstoppable runaway temperature will ensue.

Use is made of the method to derive a conservative upper limit to the amount of water vapor created by heat addition to the atmosphere developed by Calvin Wolff (8). Wolff assumes that the CO2 induced heat in the entire atmosphere is transferred uniformly into a finite depth of the ocean and calculates the resulting added fractional vapor pressure (from Tables such as that shown in Table 2).

In this study, Wolff’s calculation is then added to the previous vapor pressure for calculating a new temperature rise and second vapor addition causing another temperature increment over that by the original CO2 addition. Wolff’s calculation can then be repeated as many times as desired to model the possible continual increase. Figure 10 is a schematic of an actual temperature iteration process which damps out after a few iterations without achieving the so-called tipping point.

The key concern in using Wolff’s method is in determining an appropriate depth of water in which to deposit the added atmospheric heat. Fortunately there is help in the measured temperature gradients in the ocean. These all show a nearly constant temperature to a depth of 200 meters, as typified by Figure 9 from the National Weather Service. The constant value to that depth means that the ocean is thoroughly mixed to that depth and that whole depth can be considered to be the recipient of the CO2-induced heat to the atmosphere that increases the temperature uniformly throughout the depth of the region.

Figure 9. Ocean Temperature Profile ( 9)

The temperature rise is inversely proportional to the depth of the received heat. If the full 200-meter depth is used the temperature rise is too small to create enough added vapor pressure to be effectively resolved by ModTran. To accommodate ModTran’s resolution capability and also in keeping with the assurance of conservatism in the calculations, only ten percent of that depth, or 20 meters, is modeled as the depth of heating to a constant temperature from the atmosphere which, of course, exaggerates the true heating. With this assumption ModTran can calculate an effect and the parameters listed in Table 1 are applicable.

Table 2 is an excerpt from the thermodynamic properties of seawater that contains the U.S. Standard surface temperature (15.2 C) available with ModTran. The water vapor feedback was calculated for two other world atmospheres available through ModTran. These are those for the Tropics and for Midlatitude Winter, for which separate seawater tables were utilized. These choices provide a wide range of world climate conditions.

Table 2. Seawater Thermodynamic Properties (10)

Despite an initially positive feedback from added water vapor, that feedback damps out with only a small overall increase in atmospheric temperature depicted in Figures 10 and 11.  As shown in Figure11, that feedback-produced temperature increase diminishes with increasing existing water level.

Table 3 contains details of the calculation using both Equations 2, 3 and 5 to determine the increased heat rate to the atmosphere created by adding CO2 and the resulting temperature rise. Five levels of existing vapor (as input to ModTran) are calculated as multipliers of the normal water level required for the ModTran calculations (Appendix B).

Table 3 applies to the bottom curves of Figure 11 (for doubling CO2). IRin and IRout are those of Equation 1 and are calculated by ModTran.

“Capture” is the change in heat rate, H, to the atmosphere defined by Equation 1.

In the pairs of numbers in the “temp. inc.” column of Table 3, denote the first one as DT and the second of the pair as DT1. DT is the increase in going from 400 to 800 ppm in CO2 and DT1 is the increase from the CO2-produced water vapor, also computed with Equation 5. The ratio is DT1/DT, and the final column is defined by Equation 7.

It is not necessary to iterate more than once to determine a bound on the total temperature increase.  The temperature increments decrease with an increasing number of iterations and the total temperature increase is bounded by

\label{eq:6}

DT_{tot} = DT(1 + r + r^2 + r^3 + \dots + r^n)

as n approaches infinity, where DT is the initial temperature rise.

As long as r is less than 1, the infinite sum has a finite value of

\label{eq:7}

DT_{tot} = \frac{DT}{1-r}

Figure 10.  Perspective on  successive iterations for feedback temperature.

The r value is determined by the ratio, DT1/DT, where DT1 is the temperature rise of the first iterate.  Applying Equation 7 to the initial temperature increase plus that of the first iteration depicted in Figure 10 produces a final temperature increase of 0.77C compared to 0.76 C. from the six iterations shown.

There is no possibility of a runaway temperature increase from the feedback of CO2-produced water vapor, which is corroborated by the fact that no such event has even been known.

*U. S. Standard with NOAA cirrus clouds is indicated as “average” world climate in Appendix B

Figure 11 indicates a very limited positive feedback from CO2-produced water vapor and includes the maximum CO2 that can ever be transmitted to the atmosphere. Note that in all cases the feedback decreases with increasing existing water vapor—a negative feedback on the feedback. Given the considerably conservative assumptions used, including transferring all of heat imparted to the atmosphere (including that over land) to the ocean, these positive feedbacks are minor and not sufficient to overcome the strong negative effect of existing water content.

These calculations were also performed for the tropics and mid-latitude winter conditions to ensure that the limited feedback was universal and not due simply to the choice of climate. The results showed essentially the same results as for the average world climate and they show that the direct creation of water vapor by the added CO2 is insignificant.

Atmospheric water in any phase has a negative impact on CO2 temperature increase. This finding is significant because the IPCC claimed temperature increases depend on positive water feedback.

Time Dependence of Atmospheric CO2 and Temperature

The time dependence of CO2 level and temperature in the atmosphere requires knowledge of the world’ CO2 reservoirs and the flow rates between these. There are many reports on these available and examples are included in Appendix A. The reasons for the choices of initial values of reservoir content and outflow rates are also contained in Appendix A..

Four coupled simultaneous differential equations for the time-dependent concentration in each of the four CO2 reservoirs (atmosphere, land, ocean and fossil fuels—coal-oil-gas) are written as follows:

A’ (t) = Fa(t)*F(t) + La*L(t) + Ca*C(t) –Al*A(t) –Ac*A(t)

L’(t) = -La*L(t) +Al*A(t)

C’(t) = Ac*A(t) –Ca*C(t)

F’(t) = -Fa(t)*F(t)

Where ‘ indicates differentiation with respect to time, t. As indicated, all terms  are functions of time, t. A, L, C, and F are the CO2 quantities in the atmosphere, land, ocean and fossil fuels, respectively. The time dependent transfer rate from atmosphere to ocean is Ac; Ca is from ocean to atmosphere, etc.

The goal of these solutions is to determine CO2 concentration in the atmosphere for any CO2 insertion rate at any time. No guidance could be found in the literature on the transfer rates or concentration as functions of time. For this analysis it is assumed that the transfer rate out of a region is proportional to its concentration.

The only justification for this assumption is in its logic, but the choice does produce the appropriate ratios between the various reservoir contents when integration has continued long enough give stable levels in the reservoirs. Rates and concentrations at 0 time determine these values.

Therefore La(0)*L(t) = 100, and L(0) is 2000, so La = 0.05L(t). Similarly Al = Ac = 0.122*A(t) and Ca = 0.002451*c(T).

All these fractional rates are per year. The first 10 years of the excel integration of the case of a 0.005 fractional increase in the fossil rate is listed below and the associated entries for each year n+1 in terms of the entries for year n are as follows: For year 0, the current values of the carbon content are used.

\label{eq:8}

A_{n+1} = A_n(1- 0.244) + 0.05 L_n   + 0.002451 C_n   + 10(1 + 0.005n)

\label{eq:9}

L_{n+1}  = L_n(1-0.05) + 0.122 A_n

\label{eq:10}

C_{n+1}  = C_n(1-0.002451) + 0.122 A_n

\label{eq:11}

F_{n+1}  =F_n  – 10 (1+0.005n)

In the computations, only three regions were calculated and the fossil fuel addition rate was calculated for each nth year and the yearly quantity summed and the rate set to 0 after the total fossil region had been used up.

The following tabulation lists petagrams carbon content for each year as calculated by the above difference equations for the first ten years.

The following graphs are the results the numerical integrations for time dependent concentrations of CO2. Also included on the graphs are the associated temperatures computed with Equations 1 through 4.

It is instructive to plot all four CO2 input scenarios on the same graph to compare maxima and times to achieve the maximum as well as times to return to stable levels. Stability is regained faster for higher input levels.

In Figure 16 the solid curves are fractional CO2 increase and the dotted ones are temperature increase in degrees centigrade.  All these curves are extreme cases. The lowest input rate, 10 petagrams per year, exceeds the current rate, shown in Figure A-3 as 7.7.  But that curve is out of date.

The actual current rate is higher than 7.7, but lower than10. The 10 value was chosen for conservatism, and that rate requires 1000 years to deplete the fossil reserves.  CO2 in the atmosphere is increased by 30 percent in that time and the temperature rise is 0.3 C.

It requires 100 petagrams per year and 100 years to exceed a doubling with a temperature rise shown on the graph at slightly less than 0.8 C.  The temperatures on these four curves do not include that of the feedback calculated for Figure11 because of its negligibility.

A final input rate is calculated as the instantaneous release into the atmosphere as carbon dioxide, of all of the world’s fossil-fuel carbon shown in Figure 17.

Few would argue that such a value could ever be exceeded, yet the resulting maximum temperature barely reaches 3 degrees Celsius. Note that the CO2 level and temperature drop to that of a doubling CO2 situation (the so-called climate sensitivity) in less than 20 years.

Figures 13 through 17.indicate levels of CO2 only in the atmosphere. It is instructive to examine what is happening with the CO2 in the other reservoirs during that time. Figures 18 and 19 display these results.

All the curves up to this point have been for the extreme cases of continuing or increasing CO2 insertion. It is more realistic that they follow something like the Hubbert Curve or some symmetrical curve for time dependent oil production. A sine curve (a symmetric curve) has been chosen to illustrate such symmetry and  it is constructed to utilize all of the 10,000 petagrams of fossil carbon (i.e., the  area under the insertion rate vs. time curve integrates to 10,000).

The results are shown in Figure 20. In the Figure the atmosphere curve starts below zero because the zero point for carbon increase is at 160 years and not 0 years. The peak temperature level is well below that for the previous cases, as is expected.

#### Evaluating Carbon Reduction Scenarios

Sequestration, “cap-and-trade” and carbon taxes have been proposed and, to some degree, implemented in many parts of the world. The differential equation method derived here is effective in evaluating any method purported to reduce atmospheric carbon dioxide.

James Hansen of the Goddard Institute for Space Studies in a post to the Internet blog, the Integral Fast Reactor Group (IFRG), in September, 2012, noted that a combination of 6 percent annual reduction of the CO2 input to the atmosphere plus removing 2 gigatons per year from the atmosphere by reforestation would remove a significant fraction of CO2 from the atmosphere during this century.

He didn’t specify for how long these programs should last  and efforts to find this information have failed. In order to check these assumptions it was determined that the input reduction could never achieve a greater than 75-percent reduction and that reforestation at 2 gigatons/year could continue for no more than 100 years at which time ten percent of the current carbon content of the earth’s land and plants would be achieved and plants comprise only about one-fourth of that.

So such an increase would increase the plant contribution by 40 percent. These assumptions seem more than adequately conservative. Inserting these factors in the differential equations listed above produces the results shown in Figure 21.

The gross scale for carbon illustrates the ineffectiveness of the effort. There is no obvious effect whatever indicated by Figure 21. A finer vertical scale is required to check for actual effects. A plot of ratio of the time-dependent results to the 0-time results plotted in Figure 22 with a shortened time scale provides the needed perspective.

Figure 22 shows that the atmospheric effects are still extremely minor. Less than a one percent drop in content is observed and the temperature recovers rapidly. Such a small increment may even be below the resolution capability for ModTran to calculate a temperature difference. Since this is so small, an extreme carbon reduction scheme to test the limits of the capability to cope with the level of CO2 in the atmosphere has been calculated.

In Figure 23 the results for eliminating all man-made CO2 and adding reforestation for removing 10 gigatons per year for 100 years for (1000 gigatons total) are presented, which is considered a draconian measure.

One thousand gigatons is nearly twice as much as currently contained in the world’s plants. Doubling the carbon content of the world plants in one hundred years may be possible, but would surely be difficult. Plotting the “draconian” results as petagrams per reservoir still produces three very flat straight-lines. So the microscopic plotting scheme used for Figure 22 has been adopted for Figure 23.

This scheme shows a four percent drop. ModTran has adequate resolution to detect the temperature change but it would be small enough to be insignificant.

The curves show a recovery of the atmospheric level which is not shown in the curves of Figures 12 through 19 for cessation of carbon input due to depleting the fossil fuels. The difference is that 12 through 19 curves had no reforestation modeling in them, so that modeling was removed from the Figure 22 calculation to show the value in Figure 24, which indicates the disappearance of the recovery.

Even without recovery the calculations show the extreme effort at reducing atmospheric CO2 to be futile. Any successful effort would appear to require complete cessation of carbon input and sucking the existing carbon permanently out of the atmosphere. No such capability exists.

Reforestation is not a permanent isolation of CO2 from the biosphere. After the trees die and start to decay, they give it back. The rate at which the land/plants transfer CO2 to the atmosphere from Appendix A was based on the current situation which is an equilibrium between trees sucking CO2 out of the atmosphere and decaying to give it back, which depends on mostly mature trees as is the case with the world’s current trees, but freshly planted trees in reforestation cannot quickly start to give back by CO2 by dying and decaying, so the rate of CO2 recovery in Figures 22 and 23 is overestimated, but it does not contradict that fact that CO2 elimination is very minor.

APPENDIX A.  ATMOSPHERIC CARBON CYCLES

Cycles depicted in this Appendix are from Reference 11 and are typical of the many that are shown. All the depicted cycles are similar but show variation in the flows between reservoirs as well as the reservoir contents.

Most show two oceans (surface and deep ocean) and indicate a connection between the two but not all, as in A3, show the rate of flow between these. Some combine these oceans into one, but the one-ocean model does not differ from the two-ocean model in atmospheric effects when the exchange rates between the shallow ocean and the deep ocean match those rates between the atmosphere and the shallow ocean.

#### Figure A2.  University of New Hampshire World Carbon Cycle

Figure A3. Woods Hole World Carbon Cycle

APPENDIX B USING MODTRAN (Provided by Calvin M. Wolff)

MODTRAN (MODerate resolution atmospheric TRANsmission) is a computer program designed to model atmospheric propagation of electromagnetic radiation for the 100- 50,000 cm-1 (0.2 to 100 um) spectral range.

The most recently released version of the code, MODTRAN5, provides a spectral resolution of 0.2 cm-1 using its 0.1 cm-1 band model algorithm.

Some aspects of MODTRAN are patented by Spectral Sciences Inc. and the US Air Force, who have shared development responsibility for the code and related radiation transfer science collaboratively since 1987. The acronym MODTRAN was registered as a trademark of the US Government, represented by the US Air Force, in 2008.

All MODTRAN code development and maintenance is currently performed by Spectral Sciences while the Air Force handles code validation and verification. Software sublicenses are issued by Spectral Sciences Inc., while single-user licenses are administered through Spectral Sciences’ distributor, Ontar Corporation.

MODTRAN5 is written entirely in FORTRAN. It is operated using a formatted input file. Third parties, including Ontar, have developed graphical user interfaces to MODTRAN in order to facilitate user interaction and ease of use.

MODTRAN is accessible to the public at http://forecast.uchicago.edu/Projects/modtran.html.

When you access the url above, a menu will appear, as follows:

# Modtran IR in the Atmosphere

Where Iout is the infrared heat radiated outward from the earth at 70 km altitude.

On the graph, the smooth lines represent perfect blackbody radiation at the temperatures cited in the legend on the graph.  The red, jagged line is the earth’s actual infrared emission outward at 70 km altitude. The horizontal axis is in units of wavenumber, proportional to frequency and inversely proportional to wavelength. To convert wavenumbers to wavelength in microns, simply divide the wavenumber value into 10,000; i.e., 10,000 wavenumbers corresponds to a wavelength of 1 micron. The visible spectrum is from 0.8 to 0.4 microns.

Please note that the result is for the tropical latitudes, no clouds or rain, with the instrument or observer looking down to the earth.

To run simulations for the average earth, set “Locality” to “1976 U. S. Standard Atmosphere” and change “No clouds or rain” to “NOAA Cirrus Model (LOWTRAN 6 Model)”.

When you simulate at these conditions, you will see that the ground temperature changes from 299.7K to 288.2K, corresponding to the 15C that is usually taken as earth’s average surface temperature. The radiation emitted from earth, Io is 242.782 w/m^2.

To compare the heat loss from earth at various CO2 levels, use the 1976… and NOAA…. settings, leave all the rest the same, and set the CO2 ppm to 390, which is closer to the current amount.  Record Io (watts/m^2) for that simulation. Then change increase the CO2 amount to whatever you choose. Doubling atmospheric CO2 would be 2 x 390 ppm = 780 ppm. When you double CO2 (780 ppm), you will see that the new Io (heat lost to atmosphere) drops to 240.336. Therefore, using Modtran, the heat loss from the earth by doubling CO2 is 242.782 – 240.336 = 2.446 w/m^2,  which is the greenhouse effect of doubling CO2 (an estimate).

To study (estimate) the effects of changes in other atmospheric constituents (CH4, Ozone & water vapor) at any given, constant CO2 ppm, do as follows: multiply the default quantities (17 ppm CH4, 28 ppb O3, water vapor scale) by the 1 + the amount you want to change them. If you want a 20% increase, multiply by 1.2.

Modtran gives a good, but not the best estimate of radiative heat loss. Other programs, like SpectralCalcTM should give more accurate estimates. Remembering we are averaging over the entire earth over an entire year.

## APPENDIX C. Draft UN climate report shows 20 years of overestimated global warming, skeptics warn

By Maxim Lott, Charles Couger published January 28, 2013, FoxNews.com

In this graph from the U.N.’s IPCC, colored areas show temperature predictions, the black dots are actual observed temperatures. The black line (added by FoxNews.com) shows a linearized temperature trend.

A preliminary draft of the report by the IPCC was leaked to the public this month, and climate skeptics say it contains fresh evidence of 20 years of overstated global warming.

The report — which is not scheduled for publication until 2014 — was leaked by someone involved in the IPCC’s review process, and is available for download online. Bloggers combing through the report discovered a chart comparing the four temperature models the group has published since 1990. Each has overstated the rise in temperature that Earth actually experienced.

“Temperatures have not risen nearly as much as almost all of the climate models predicted,”

Roy Spencer, a climatologist at the University of Alabama at Huntsville, told FoxNews.com.

“Their predictions have largely failed, four times in a row… what that means is that it’s time for them to re-evaluate.”

—————————————————————————————

#### References

1. ModTran URL:http://forecast.uchicago.edu/Projects/modtran.html
2. http://www.climate4you.com/GlobalTemperature.htm, click tab on Outgoing Long-wave Radiation
3. Trenberth, Kevin E, et. al. “Earth’s Global Energy Budget,” BAMS, March, 2009. (IPCC. Report)
4. Internet search with: “NASA Global Energy Balance” (can be found under same subject as reference 5)
5. Internet search with subject: NWS JetStream Earth-Atmosphere Energy Balance Diagram”
6. Data sources: The International Satellite Cloud Climatology Project and University of East Anglia‘s Climatic Research Unit.  Last cloud data used: December 2009. Last figure update: 4 September 2011
7. http://www.climate4you.com/ , click on Clouds and Rain.
8. Private communication, Calvin M. Wolff, 2012:   http://calvin-m-wolff.com/H2O_Feedback.html
9. Internet Search with subject: “NWS JetStream Online School for Weather”  Table entry; “Ocean Layers”
10. Internet search with subject: “International Towing Tank Conference, Recommended Procedures, Revision 2, 2011”
11. Internet search with subject: “Images for global carbon budget”

Acknowledgements

The author gratefully acknowledges the following contributions to this effort.

To Calvin M. Wolff for many useful technical interactions, for comparing calculations, for providing useful methodology and references, and for contributing Appendix B.

To Neil Brown for much encouragement and for useful reviews of several drafts of the document.

To Ed Berry for early advice and encouragement and for posting prior versions and this one on his website for comments.

To William Happer for a critical review of the previous draft, for helpful suggestions, for encouragement and for lucid explanation of the physical processes involved.

Bryce Johnson is retired professional nuclear engineer in the state of California with a 45-year career in nuclear-reactor and nuclear-weapons research. His education includes BS (ME), University of Idaho; MS (NE), North Carolina State University and PhD (ME), Stanford University.

### 8 thoughts on “The Limits of Atmospheric Carbon Dioxide Effects and Control”

1. I may ask some questions later, but the main problem I see with this presentation is that it assumes cirrus clouds are a good average for the planet. The problem is that these very likely model very low humidity, so the 1.024 scale value still leaves you with almost negligible water in the atmosphere. Because of that, the first incremental temp increase is only .06, leading to overall low temp increase (after the infinite sum).

Not surprisingly, then, this low water feedback temp increase is way below the world-wide consensus and what complex computer models and much more basic models predict. Another clue that this humidity level is way too low is that if we look up from .001km using modtran, we observe 260-ish IR value rather than the Trenberth diagram 333 average global back radiation IR value.

In contrast, if we use any other cloud model except the cirrus ones we end up with back radiation around 360 (much more reasonable). Further, if we keep the cirrus but raise the water vapor scale to around 4 (400% of normal, rather than 1.024!), we then get close to the 333 back radiation level. It makes sense that the water humidity level (which is what causes a lot of the back radiation seen on the ground and the consequent higher temp) should be much higher on average world-wide than what cirrus provides. Even when it isn't cloudy, many places are humid, eg, in the tropics.

The 1976 US std atmosphere doesn't model humidity, and I'd wager the cirrus models have very low humidity values. Anyway, I'll re-calculate some of the key numbers (assuming most of the formulas are good enough for an estimate) and post again.

2. 1. I think we might use modtran (or better, hitran data) to calculate many different values around the planet with x and y percentages of various clouds and then we would integrate all of that data to get the actual global averages we want. To look at just one setting (of temp, cloud type, humidity, etc) is not modeling the planet, and I don't think can be made to match the relevant values from the Trenberth diagram.

However, we might try to do an estimate using the single set of modtran parameters used in this presentation (eg, Appendix B). That seems like a reasonable approach that might yield a ballpark result.

For example, let's make 2 estimates.

A) 1976 us std atmosphere, noaa cirrus model lowtran 6, ground temp=288.2K, water vapor scale=1.

i) 400ppm, 70km look down: 242.691
ii) 800ppm, 70km look down: 240.241

So, using (i) to fix the sun's effective intensity, we can adjust (offset) the ground temp at 800ppm so that when we look down we also get 242.691. An offset of +0.81 does the trick.

So by this estimate, a doubling of CO2 from today's level will lead to a .81 C increase in the ground temp when we ignore all water and other feedbacks.

B) 1976 us std atmosphere, cumulus cloud base .66km top 2.7km, ground temp=288.2K, water vapor scale=0.0001.

i) 400ppm, 70km look down: 242.031
ii) 800ppm, 70km look down: 240.116

So, using (i) to fix the sun's effective intensity, we can adjust (offset) the ground temp at 800ppm so that when we look down we also get 242.031. An offset of +0.64 does the trick.

So by this estimate, a doubling of CO2 from today's level will lead to a .64 C increase in the ground temp when we ignore all water and other feedbacks.

In conclusion, while there are more accurate procedures to use with modtran for estimating the no feedback 2x CO2 temp raise at ground and while there are more accurate tools to use than modtran itself, we still can get a rough idea of what 2x CO2 does using a one shot modtran calculation and a simple model like 1976 US std atmosphere model.

2. Is equation 1 useful? I don't think much.

Energy entering atmosphere – leaving atmosphere:

17 (thermal, contact from earth) +
80 (evaporation) +

[169 (radiation from air towards space) +
30 (radiation from clouds to space) +
333 (radiation from air and clouds towards ground)]
=
-1

So basically the atmosphere is close to equilibrium (since we also have rounding errors). If not it would be getting hotter (or colder) at a noticeably fast rate.

In contrast, equation 1 along with the calculated values of the various H suggests the atmosphere is gaining huge amounts of net radiation flux (energy per second per area) and thus makes no sense.

3. Later it's stated that using 200 meter ocean depth makes modtran useless. That could be a clue that the methodology might have problems. Instead the value 20 is used. Question, why not keep going and use just 1 meter or .001 meters? How would that impact the data? According to the logic employed, would that lead to a lot of heating? So why cherry-pick 20? [I am not sure because it wasn't clear to me how Table 1 was used, if at all.]

4. Putting aside the problems with equation 1 for a moment, Table 1 suggests that the "heat" in the atmosphere will be averaged into the ocean, but that doesn't make much sense since the sun is heating the oceans and the atmosphere at the same time. It isn't an either or proposition. What is Table 1 about?

5. How was humidity calculated and how does that translate to a water vapor scale value?

6. Measurements and theory suggests that water will result in a significant amount of temperature rise. This is inconsistent with the r result of .08. Instead a value of about 2/3 C is what leads to a 2 C rise beyond the 1 C anticipated for CO2 working by itself.

7.
(a1) "A, L, C, and F are the CO2 quantities in the atmosphere, land, ocean and fossil fuels, respectively. The time dependent transfer rate from atmosphere to ocean is Ac; Ca is from ocean to atmosphere, etc. …For this analysis it is assumed that the transfer rate out of a region is proportional to its concentration."

(a2) "La = 0.05L(t)"

(a3) Eqn 8: "A_n+1 = A_n*(1-0.244) + 0.05*L_n + 0.002451*C_n + 10*(1+0.005*n)"

(b1) "Therefore La(0)*L(t) = 100"

(b2) "A’ (t) = Fa(t)*F(t) + La(t)*L(t) + Ca(t) –Al(t)*A(t) –Ac(t)*A(t)*A(t)"

a1, a2, and a2 are consistent with each other. b1 and b2 are consistent with each other. a1, a2, a3 are inconsistent with b1, b2.

I'll assume b1, b2 were effectively typos and that a1, a2, a3 was intended.

For example, La(0) = 100 = .05*L(0).

3. Thanks to Jose for his thorough read of the document and his comments. I hope I can answer these to his satisfaction.

Response to paragraph 1 of Jose's first comment:

I quoted ModTran's writeup as NOAA cirrus clouds and U. S. Standard atmophere as being a world average (which was quoted in Appendix B). But I didn't base any conclusion or results on that particular climate region and weather condition. In fact, I tried to span the full range of weather conditions and climate regions. I sometimes used one example calculation to display typical results and I sometimes used what seem to be a reasonable number of calculations. If there was one specific example that did not fit the conclusions of the several calculations, it was noted and displayed. In fact the higher humidity samples had the lowest temperature increase. That can be seen in Figure 11. I will be glad to supply the results for any climate region, weather condition, or humidity condition of Jose's choosing. I DID NOT SHORT-CHANGE HUMIDITY IN THESE CALCULATIONS.

2nd Paragraph. If I had been in agreement what "world-wide consensus, and what complex computer models and much more basic models" predict, I would have had no reason to publish the paper. What an example of a much more basic model? I do't believe that a concatenation of multiple computer models with many guessed parameters adds up to precision. I, too noticed that greater or less than 333 back radiation could be generated with Modtran. I used Figure 2 to illustrate the components of atmospheric heat balance and to derive the second term of Equation 1, otherwise I relied on Modtran's ranges and parameters for temperature calculations.

3rd paragraph. See the last sentence on the first paragraph.

The 1976 U. S. Standard Model can be modeled with any humidity level you choose and you have 14 weather conditions to chose from in Modtran

Response to paragraphs of Jose's second set of comments.

1. I was not trying for an average of the planet and I was not trying to match Trenberth's figure. I was trying to do a broad enough sweep of all the world's available climate regions and weather conditions to ensure a valid conclusion of CO2's world-wide effect on temperature and on man's ability to control it. I I have left a major stone unturned in this quest, please inform me of what it was.

With your two estimates please note from my Figure 7 that your doubling of CO2 with NOAA cirrus clouds and with cumulus clouds and my results shown in Figure 7 are very close to the same. I don't really understand what point you are making. Your method may be better than mine but their divergence is minuscule.

In your method did you just do temperature increases by trial and error with the doubling until you matched the non-doubled exit radiation?

2. First, if my use of Equation 1 produced the same answer as your method did and you (I assume) consider your method to be correct, why is mine not much useful?

The reason for not including the back radiation as part of the atmospheric energy balance is difficult to grasp. I wrestled with that for some time myself. It doesn't permanently escape the atmosphere as those which exit to out space do. It comes right back again through the IR of the increased temperature of the earth. But that's not too satisfying either. But Modtran does not use it, otherwise there would be no escape of radiation to outer space and Modtran shows a lot of that. But the explanation I find most satisfying is that it is totally created within the atmosphere, so when the atmosphere loses that there is a net 0 in energy balance. In Figure 2, for all other energies into the atmosphere their source can be traced to outside the atmosphere. Back radiation's source cannot be traced to outside the atmosphere. I never found any way of using back radiation that gave anything but an irrational answer.

The atmosphere is, indeed, gaining huge amounts of net radiation flux. That is, after all, what global warming is all about. However, it is also losing a huge amount to outer space. The loss being proportional to absolute temperature to the 4th power, it doesn't required a large increase to get rid of a lot of energy. Global warming is a rather slow, steady process as more IR energy is dumped into the atmosphere, the hotter temperature quickly gets rid of it to outer space, but it has to have a higher temperature to do that.

3. I didn't say Modtran was useless. I just said it may be beyond its resolution capability. That, in itself is good information about its extremely small value.. Your question about why not keep going to 1 or .001 meters is a good one. Initially I was using ten meters then I discovered the curve shown as Figure 9 which indicated excellent mixing (i.e., constant temperature) down to 200 meters which means there is little error in using that full depth as the recipient of the atmospheric heat, Then I discovered the heat increase was maybe too small to calculated with Modtran and certainly too small to show up on a reasonable sized graph that showed the range needed. I opted for 20 as reasonable conservative, yet still demonstrable.

4. It doesn't matter than the sun is heating the oceans and the atmosphere at the same time. I can separately estimate that which is due solely to created water vapor and treat that as addition. I am only after the addition.
Table 1 is a tabulation of the results of the Clausius-Clapeyron equation. The last column in the table gives the fractional increase in vapor pressure per degree increase in water temperature. So multplying that fraction by the degrees of temperature rise of the water
gives the total fractional increase in vapor pressure. Modtran works on water vapor pressure, so that can be just added to the vapor pressure previously used for the modtran calculation. Vapor pressure of water doesn't depend on how much vapor is already above the water, it depends only on the water temperature and atmospheric pressure. Conveniently atmospheric pressure is given in atmospheres. I believe Modtran uses 1 atmosphere in all its calculations.

6.One of the three main goals of the paper was to refute your paragraph 6. The other two were to show that CO2 can never reach a harmful value and that man couldn't do anything about it if it did get that high.

7. I think your assumption is correct. I have checked my many excel calculations on this and they seem to be correct. Plus. their plots are good at displaying errors.

Thanks,

Bryce

4. I should make it clear that I am new to modtran use (through the free web service or otherwise) and also have not used any other similar tools. I try to research online and appeal to past discussions I have read on its use. Also, while I think point 7 is no big deal, I was a little harsh on earlier points as I best was able to understand the paper. Not only could I be wrong, but I can certainly not be recognizing the value of the analysis.

Further, while I am not a climate scientists and understand the field and topics in pieces, I think anyone getting significantly different results than most other experts in a field should take that as a warning and really try to make sure the logic and research are sound (and this is part of what I am trying to prod in this particular case). It seems also in order in time in order to establish a new set of significantly different results would be a critique of many key papers that have established a foundation of modern climate estimates of 2x CO2. The computer models from which temperatures may have slightly slipped off the edge (depending on interpretation of its assumptions made by the computer predictions) is not an automatic condemnation of the believed science but perhaps at most on its incompleteness, especially since the IPCC took pains to clarify that it presents the predictions from models that are known to be incomplete in a few important ways but offer our best estimates. Keep in mind the error bars cited are a confidence range of no more than 2 sigmas and have never claimed 100% absolute coverage (eg, as noted clearly in IPCC summary sections of their main reports). New papers attribute some of the lower temps than expected over this past decade to a large number of cyclical cooling la nina action. One way to attack the status quo would be from an analysis of the open source climate programs and/or from appealing for the non-open-source models to have their legitimacy knocked down a notch for their lack of full transparency. It's a tough job for any new player to analyze so much computer code, so it may help to promote open discussion forums for such an endeavor or to participate in any that might already exist. The models use more extensive physics (with many fewer approximations and greater appeal to fundamental physical equations), so it is easy to see why their results would carry extra weight in the minds of most experts. At the same time, there is greater room for error in greater complexity.

5. Bryce Johnson @3

>> In fact the higher humidity samples had the lowest temperature increase.

I noticed that as well after writing that first comment (and to my best understanding of what Modtran does).

>> The 1976 U. S. Standard Model can be modeled with any humidity level you choose and you have 14 weather conditions to chose from in Modtran

That was the assumption I made for comment #2. I am glad you agree since that increases the odds I am understanding how Modtran works.

>> I don’t really understand what point you are making.

I was implicitly agreeing that your .75 estimate of 2x CO2 seems as reasonable as anything I as able to pull from Modtran (if I understand that tool).

I was also emphasizing that these Modtran estimates are among a toolbox that includes more accurate techniques. [I guess you did use a larger sample size with more sensible statistics than I did. Again, I haven't spent all the time required to understand every part of your paper.]

This also means I was implicitly supporting your approach to use conservative boundaries.

So pt 1 agrees with this paper's general attitude and agrees with the ballpark of the 2x CO2 values calculated.

>> In your method did you just do temperature increases by trial and error with the doubling until you matched the non-doubled exit radiation?

Yes, and, partly because of that simple approach, I perhaps used fewer data trials than you did.

Again, my point 1 offers no real complaints except a note of caution that we are playing with estimates inferior to other approaches in using this tool to get these results.

>> First, if my use of Equation 1 produced the same answer as your method did and you (I assume) consider your method to be correct, why is mine not much useful?

In my mind, this paper's divergence with status quo results hinges significantly around the very low value obtained for the first iteration of the water (feedback) temp contribution. If we are to believe the status quo for a moment, that feedback iteration should be nearer to a 2/3rd C. You got around .06, which is only about 10% of what I think would be expected.

>> But Modtran does not use [back radiation], otherwise there would be no escape of radiation to outer space and Modtran shows a lot of that.

>> But the explanation I find most satisfying is that it is totally created within the atmosphere, so when the atmosphere loses that there is a net 0 in energy balance.

I agree that the back radiation is created within the atmosphere. My view of that is that it leads to a higher temp ("average energy") within that region. All forms of insulation create that effect, where the internal enclosed area resides at a much higher temp than the boundary. This is probably unintuitive at first sound (it certainly was for me), yet it doesn't seem you can prod the internal temps from the outside (at least not with a simple thermometer) but must infer it or otherwise place a thermometer inside. An oven or a sweater give only indirect clues of the temp inside. Note as well that the hottest point on the planet+atmosphere (statistical measurements and theory) is supposedly the surface, so I don't think there is any inconsistency with thermodynamic expectations. What we should remember is that the sun keeps adding more and more energy to the earth's ground level surface. Hypothetically, if the planet were to keep that energy that was added years and months back by the sun, that effectively today goes into space quickly (especially if the planet were to have no atmosphere, as is basically the case for the moon), instead fully accumulating within the earth's atmosphere by delaying its exit into space indefinitely (a fictional and boundary case, of course), then there is reason to expect that average temperatures in the atmosphere will rise "stratospherically" while a sensor looking from space to the planet would observe almost no energy coming out. Another example might be using mirrors (or something like a laser mechanism) to aggregate a lot of energy within a narrow enclosure in order to produce a very high temperature, rather than letting that energy (photons) continue along the path without mirrors and end up elsewhere. Energy that would otherwise be available to aliens quickly would instead be used at home.

>> The atmosphere is, indeed, gaining huge amounts of net radiation flux. That is, after all, what global warming is all about.

I would change "radiation flux" (the rate of energy movement) in that sentence to say "radiation energy". The latter allows for the accumulation of lots of total energy when looking at the entire planet, even if the rate is very small locally in time and space. The Trenberth values are the rates for an average second and meter square averaged over the entire planet's surface over an entire year, more or less. The average is over a large set of points in time and space, but it still represents the value of a single second and meter squared.

These things are not something I understood except after lots of online debate and thought.

>> Initially I was using ten meters then I discovered the curve shown as Figure 9… Then I discovered the heat increase [for 200 m] was maybe too small to calculated with Modtran and certainly too small to show up on a reasonable sized graph that showed the range needed. I opted for 20 as reasonable conservative, yet still demonstrable.

No disrespect wished, but that is why I used the word "cherry-pick". Your logic suggests that any value between 0 and 200 would do, so why not do the math when using 1 meter? If the method is robust, then you should get a result that still fits within the conclusions.

There are math steps missing in the paper related to the use of Table 1 that I have not yet figured out, so I can at most only perhaps suspect that if you use a value of .001 meter, that you might end up with a totally bogus result inconsistent with the conclusions of the paper.

>> 4.

I will read that more carefully later today/tonight, but try to see in particular if what I said above about "radiation flux" vs "radiation energy" makes sense.

6. >> I was implicitly agreeing that your .75 estimate of 2x CO2 seems as reasonable as anything

Oops, I should clarify that I am talking strictly about the non-feedback theoretical result. I think the traditional value is around 1 C, which is close to .75 C.

7. Any updates to this computer model in last 4 years given that the speed of climate science is constantly leaving most of us behind the curve?

8. I would also recommend that you incorporate the following Chapter 3 of a science textbook. It is titled "Absorption,emission,reflection and scattering".

After reading it and proofing it yourself for any errors, if you add that chapter or the equivalent info, to the above presentation, it will provide a more complete explanation of the whole absorption debate which you must agree is the crux of the matter in the false theory of AGM. This would be especially helpful to the non nuclear scientists like myself who found the explanation in your above presentation to be a tad skimpy. Thank you very much for helping to expose the AGM scandal.

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