Guest essay by Richard J. Petschauer
A skeptic that believes in global warming? How can that be? We have been told that climate skeptics, sometime incorrectly called “deniers”, still believe the earth is flat and disagree with 97% of scientists. Well, first of all, most of us have seen a globe and know what it represents. Second, do you know on what these scientists agree? If not, don’t feel bad. Those making these claims, mostly politicians, probably don’t know either. Actually, a rather poor survey was done looking at a summary of many technical papers. If any one of many climate related points were made, they were put in the 97% camp. This article would probably have qualified too.
But the real question, not covered in the survey: How fast will the earth warm if we do nothing to curtail the growth of man made carbon dioxide emissions? And how much can we reduce the warming if we cut world emissions by some factor? The impact and costs of doing nothing or something will not be covered here, but it is obvious they would depend on how fast warming will occur. This we will discuss.
So what are the skeptics skeptical about? It is the amount and rate of the man made warming estimated by the United Nations Intergovernmental Panel on Climate Change (IPCC) and the claims of some spokespeople, many in government, who go much beyond what the IPCC says, like “the planet is having a fever” or “things are getting worse than expected”. But data shows global temperatures have increased much less than models predicted. In fact, unknown to many, accurate satellite data shows very little if any warming in the last 18 years.
Where there is general agreement
There are many areas where most skeptics and the “alarmists”, as they are called, agree. First is the idea of “climate sensitivity”, a useful benchmark for making estimates. It is the final average global temperature rise that would be caused by a doubling of the carbon dioxide (CO2) in the atmosphere, assuming there are no natural changes. Second, most agree on well established methods to estimate how greenhouse gases absorb and emit heat, and that doubling of CO2 will reduce the heat leaving the planet by a little more than 3.5 watts per square meter. This compares to both estimates and satellite measurements of the total now leaving of about 235 watts per square meter. If the value of 3.5 watts out of 235 seems low, it is because CO2 only absorbs the infrared wavelengths that involve about 20% of the heat leaving the surface, and in this region its action is partially saturated and the second doubling will reduce heat loss by about another 3.5, not 7 watts. A 1% change in energy from the sun or a 7% change in cloud cover would cause about the same change as doubling CO2. Third, there is general agreement on how much the average surface will warm to make up for this heat loss: about 1 C (1.8 F). But here is the rub: this estimate is before the atmosphere and the surface, including oceans, react to this temperature change.
Where there is not agreement
How the climate reacts to the initial warming is the main area where most skeptics have problems with the IPCC and others. These reactions are called “feedbacks”. Positive ones amplify any temperature change (warming or cooling from any cause, not just from CO2). Negative ones diminish a change. There are general agreements on the equations used to define the feedback strengths and how they are combined into one net temperature change multiplier that can be either greater or less than one. The major disagreements are the magnitudes of the feedback values and for clouds, even if it is positive or negative. The final IPCC warming estimates for doubling CO2 range from 1.5 to 4.5 C. The skeptics have no common voice, but their values range from about 0.5 to 1.2 C, a significant reduction. IPCC also uses a 1% annual growth of the CO2 content in the atmosphere, while data shows only about 0.55%. This increases CO2 doubling time from about 70 years to 140.
Two different approaches
One primary complaint is the IPCC and most government funding research have abandoned improving the simple energy balance model and the feedback concept and gone to complex climate models that try to estimate many conditions across the globe and layers in the atmosphere over many years and then a temperature change. Small errors can propagate into unknown large ones. There are over 100 of these models written by different teams and their results differ by a range to 3 to 1. And nearly all overestimate warming compared to observed data. This is settled science? No! And it is bad engineering practice, which some scientists apparently don’t understand, to try to solve such a complex problem without breaking it down into smaller steps that each can be verified and corrected. What is causing the errors in the climate models that cause them to overestimate global warming? How will any proposed correction be tested without waiting about 10 to 30 years?
Corrections to the complex computer models
We believe the complex computer models overestimation of warming is mostly based on a combinations of three factors: overestimating positive water vapor feedback, underestimating negative feedback from increased sea surface evaporation and treating cloud feedback as positive feedback while it is very likely negative. For water vapor (a major greenhouse gas) the climate models show it increases about 7% per degree C of warming. But extensive data over 30 years from 15,000 stations at many latitudes over land and sea show an increase of only about 5% at the surface, the atmosphere’s main water vapor source. (Dia, “Recent Climatology and Trends in Global Surface Humidity”, American Meteorological Society, August, 1997). Water vapor is also an absorber of incoming solar energy, reducing what reaches the surface. Reduced greenhouse action and increased solar absorption cut the computer models positive water vapor feedback in about half. Regarding the cooling effects of increased evaporation, mostly over the oceans, both data (Wentz, et al, “How Much More Rain Will Global Warming Bring?, Science, 13 July, 2007) and basic physics indicate an increase of about 6% per degree C of warming, over double what the climate models average. Finally, the models estimate a value of positive feedback for clouds only because this amount is needed to boost the initial 1 C prefeedback warming up to the models final average estimate. It is more likely that more evaporation and water vapor will increase cloud content, a net cooling effect. Using simple energy balance models with proven greenhouse gas absorption/radiation tools, the result of these changes indicates a warming from double CO2 in a range of 0.6 to 0.9 C, much less than IPCC’s value of 1.5 to 4.5 C. Note the uncertainty range drops by a factor of 10, from of 3 degrees C to 0.3 C, because of the elimination of unreliable complex computer models and their net positive feedback.
A skeptics summary
About 1 C warming in the next 140 years does not seem to be a problem. (It will actually take longer because the ocean heat storage will delay the warming). Furthermore, both simple models and data show that most of the warming will be in winter nights in the colder latitudes. Less water vapor here reduces its competition with CO2. An example is in Minneapolis, Minnesota at 45 degrees latitude. About half of July record highs were set in the 1930s, with only 3 since 2000. However 80% of the record January lows were from 1875 to 1950. This winter warming is a benefit. And what makes people think the climate around 1900 represents the ideal? In 2014 we just saw a very cold winter, typical of that era. Finally, warmer temperatures increase evaporation and precipitation and since CO2 is a plant food, food crop production will increase, contrary to some other estimates. And any climate model that estimates a small, slowly increasing temperature will “disrupt” the climate should be looked at with great skepticism.
Digging deeper – does carbon dioxide really trap heat?
We have heard that carbon dioxide “traps” heat high in the atmosphere somewhat like a blanket that covers everything and is getting thicker as emissions increase, trapping more heat. Well, it’s not so simple and fortunately not that bad. Let us explain what happens.
The above figure is taken from an often cited paper, including by the IPCC, titled “Earth’s Annual Global Energy Budget” by Kiehl and Trenberth from the Bulletin of the American Meteorological Society, 1997, with notations that we added. The top curve shows how the intensity of the average heat leaving the earth’s surface varies with infrared wavelength. The lower jagged curve is that leaving at the top of the atmosphere under average cloudy conditions. The area under a curve is its total heat in watts per square meter. Note the large downward notch leaving the atmosphere in the 12 to 18 microns range caused by CO2. It is such a strong absorber here that it cannot release its heat outward until the density of its molecules drops significantly at high altitudes where the temperature is about –60 F. Hence the low radiation rate. If the amount of CO2 increases, the escape altitude moves up causing both the temperature and heat loss to drop further. The area of the CO2 notch below the dashed line is about 22 watts per square meter and represents the impact of the total CO2 given the existing clouds and water vapor. Doubling CO2, taking over 100 years at the current growth rate, would move the notch downward and increase the area by about 3.5 watts per square meter, or 16%. When the heat loss drops, since the net heat from the sun remains at 235, the atmosphere gains heat and warms about 1 degree C until its emissions rise back to 235, restoring balance. A warmer atmosphere reduces the heat loss from the surface, and it also warms about 1 C. This is all that CO2 does. And very slowly. The feedback processes can increase or decrease this warming, as they do for any other temperature change.
Correction: The 140 years cited in two places as the time for CO2 doubling for the compound annual increase of 0.55 % of the last 20 years should be 126 years (1.0055 ^126.4 = 2.0003). The 140-year value is for 0.50 %, consistent with the last 35 years.
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The IPCC does the ‘ends justify the means’ science. The cart is before the horse. The goal is to control the planet and tax thin air as a tool of domination. It is NOT ‘science’. It is anti-science.
Petschauer like many skeptics and the PCC modelers makes his forecasts without regard to the natural 60 and more importantly 1000 year periodicities so obvious in the temperature record. This approach is simply a scientific disaster and lacks even average commonsense .It is exactly like taking the temperature trend from say Feb – July and projecting it ahead linearly for 20 years or so. The IPCC models are back tuned for less than 100 years when the relevant time scale is millennial. This is scientific malfeasance on a grand scale.
The temperature projections of the IPCC – UK Met office models and all the impact studies which derive from them have no solid foundation in empirical science being derived from inherently useless and specifically structurally flawed models. They provide no basis for the discussion of future climate trends and represent an enormous waste of time and money. As a foundation for Governmental climate and energy policy their forecasts are already seen to be grossly in error and are therefore worse than useless.
A new forecasting paradigm needs to be adopted.
For forecasts of the timing and extent of the coming cooling based on the natural solar activity cycles – most importantly the millennial cycle – and using the neutron count and 10Be record as the most useful proxy for solar activity check my blog-post at
http://climatesense-norpag.blogspot.com/2014/07/climate-forecasting-methods-and-cooling.html
The most important factor in climate forecasting is where earth is in regard to the quasi- millennial natural solar activity cycle which has a period in the 960 – 1020 year range. For evidence of this cycle see Figs 5-9. From Fig 9 it is obvious that the earth is just approaching ,just at or just past a peak in the millennial cycle.
I suggest that more likely than not the general trends from 1000- 2000 seen in Fig 9 will likely generally repeat from 2000-3000 with the depths of the next LIA at about 2650. The best proxy for solar activity is the neutron monitor count and 10 Be data. My view ,based on the Oulu neutron count – Fig 14 is that the solar activity millennial maximum peaked in Cycle 22 in about 1991. There is a varying lag between the change in the in solar activity and the change in the different temperature metrics. There is a 12 year delay between the neutron peak and the probable millennial cyclic temperature peak seen in the RSS data in 2003. http://www.woodfortrees.org/plot/rss/from:1980.1/plot/rss/from:1980.1/to:2003.6/trend/plot/rss/from:2003.6/trend
There has been a cooling temperature trend since then (Usually interpreted as a “pause”) There is likely to be a steepening of the cooling trend in 2017- 2018 corresponding to the very important Ap index break below all recent base values in 2005-6. Fig 13.
The Polar excursions of the last few winters in North America.are harbingers of even more extreme winters to come more frequently in the near
Quite true.
I keep saying, if anyone wishes to predict the future global climate, they must observe ice conditions in Hudson Bay most closely. This is literally the ‘bellwether’ of our planet in these Ice Age cycles.
I note that the warmists all focus on central Alaska and the edge of the Arctic Ocean there…the one place in the North American continent that never glaciated during Ice Ages except in the mountains along the southern coastline.
This is where the humans crossed from Siberia into North America on foot because there was little glaciation in this half of Siberia, too.
The choice of focusing only on the warmest parts of Alaska (during Ice Ages) is deliberate fraud designed to further the demand to tax CO2 (the air we exhale and plants ingest!) which is taxing thin air.
I did not make my estimates based on temperature records. Did you read the article? I only estimate what CO2 would do to the temperature, as I said “assuming there are no natural causes”. Using the superposition thorem, these changes would add to other natural causes. It is the IPCC, not I, that claims to know what part of recent warming is due to increased CO2, which is impossible. Please do not include me with them in this regard.
IPCC AR5 SPM RCP scenarios.
Scenario………GTC…….GTCO2……RCP ppm…..Anthro grams……..Anthro ppm……….%…………W/m2
RCP 2.6………..270…..….990…………421……….…9.90E17….………….86.8…………….21………..3.0
RCP 4.5………..780…….2860……….…538………….2.86E18……………250.6…………….47………..4.5
RCP 6.0………1060…….3885……….…670……….….3.89E18…..……….340.4……….……51……..…6.0
RCP 8.5………1685…….6180……….…936…….…….6.18E18……..…..…541.6………..….58……..…8.5
The RCPs are based on various assumptions and computer modeling.
GTC and GTCO2 are the projected/modeled amounts of man generated C/CO2 added to the atmosphere. RCP ppm is the projected/modeled atmospheric concentration of CO2.
Anthro grams is the amount of GTCO2 in grams with 45% remaining in the atmosphere.
Anthro ppm is the ppm increase compared to based on atmospheric weight.
% is the percentage of the RCP ppm due to anthropogenic sources of CO2 ppm.
W/m2 is the modeled radiative forcing due to RCP ppm.
Seems that not-man CO2 comprises half of the CO2 ppm & RF.
At least in the last moment we should realize that ocean is the main actor in the climate change process and that climate is the continuation of oceans by other means. I am sorry that we don’t pay more attention to the water and that in the past 150 years the only thing we did to the ocean was to fight naval wars. You can read on http://www.1ocean-1climate.com a collection of reasons for which today’s global warming is taking place.
Too bad increasing ice in Antarctica, Greenland and Canada are pointing in the opposite direction from ‘warming’.
Richard J. Petschauer,
You have stimulated a noteworthy discussion on this thread.
That said, I disagree with the context / theme of your post. I think using the concept of skeptic in a philosophical sense is problematic when also using the concept of belief in a philosophic sense.
So, arguably (in the history of philosophy) in a fundamental sense, the skeptical human would prima fascia not believe anything he/she is skeptical about. Believing is an un-skeptical position. Applied reasoning is the skeptical position
John
“Applied reasoning is the skeptical position”
It seems reasonable to believe a claim while still being skeptical of it; depending on various factors. If someone tells me I parked in an avalanche path and ought to move, I am willing to believe in the possibility absent proof simply by a Pascal’s Wager kind of thing.
Now if that person told me I had parked in an avalanche path and for a thousand dollars would be assured that the avalanche would not happen while parked there, of that I would be highly skeptical.
Michael 2
Ah, but we are told we must pay Big Government to bulldoze our house (destroy the world’s economic system and artificially raise energy prices, kill millions by starvation and illness) BECAUSE we might live in an avalanche zone … But our houses are in Florida, Alice Springs AU, Lubbock TX, Belgium, and Hudson Bay Canada.
Michael 2 on April 27, 2015 at 9:42 pm
– – – – – – – – –
Michael 2,
You seem to suggest that believing is a way to acquire scientific (and philosophy of science) knowledge. If that is your suggestion then I disagree. Applied reasoning is the only way to acquire scientific knowledge. Applied reasoning is not a process of believing.
John
John Whitman says “You seem to suggest that believing is a way to acquire scientific knowledge.”
That’s an interesting conclusion from my words. But you have a remarkable insight; for that is exactly correct. When you were a child, you were taught that 2+2=4 (and similar facts). Your choice is to believe it or disbelieve it (and substitute for some other result of 2+2). As you went through your schools, nearly every fact offered to you is to be believed or disbelieved. Such as you believe becomes part of what you know which is also exactly what you believe since there is no reason to not believe what you know (even though it does actually happen). “Belief” is emotional, right brain; “Know” is rational, left brain, but the same kind of thing. It is proper to both know and believe. When you know but don’t believe, or believe but don’t know, it creates tension in your mind.
Suppose you conduct a scientific experiment seeking knowledge. When you inspect the result, you will make a conclusion, and it is necessary and appropriate to believe your own conclusion as surely as you know it.
In the case of climate science, I see a great deal more belief than knowledge.
Consider the far side of the moon. IS there a far side? Have you personally seen it? Probably not. Yet you choose to believe the photographs made by satellites and astronauts, and from that you think you know about the far side.
“If that is your suggestion then I disagree.”
Of course you disagree. It wouldn’t be much of a discussion otherwise so I am grateful for your disagreement.
“Applied reasoning is the only way to acquire scientific knowledge.”
Now it is my turn to disagree. No amount of applied reasoning is going to reveal the far side of the moon. But it has its place especially in using deductive logic on bare facts.
Michael 2 said “That’s an interesting conclusion from my words. But you have a remarkable insight; for that is exactly correct. When you were a child, you were taught that 2+2=4 (and similar facts). Your choice is to believe it or disbelieve it (and substitute for some other result of 2+2). ”
Actually the whole 2+2 = 4 thing is a construct that we are all used to, but in junior high school, a half century ago, we were taught that computer language was base 2, i.e. just 0’s and 1’s or basically “on” or “off”. The concept of different bases was taught way back then, along with a lesson that we should understand that much of what we see and believe is a result of our upbringing and culture. If I remember my lessons, in base 3, 2+2 = 11 and in base 4 it would be 10.
Sometimes things that appear to self evident are not so clear from a different perspective. We all “assume” base 10 when we do numbers as that is what most of us are used to. The concept of different base systems can open your mind to different ways of looking at things in all areas of endeavour including climate.
Great thread but it sure clogged up my email. 😉
RACookPE1978 on April 28, 2015 at 3:42 am
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RACookPE1978,
Yes, ‘Michael 2’ is using analogy. Worthless are analogies in matters of applied reasoning in science, but in the non-scientific process called believing analogies like his might be the way to convey mythology.
John
Believing in “applied reasoning” as your Dog is also mythology.
To John Whitman. I used the terms because I am tired of the media referring to those who do not agree with the bad projections as “deniers”, tryng to make it a black or white issue. Plus the title was intended to attract attention. But it is not a question about philosophy, but one of getting the Physics right.
“I am a climate skeptic who believes in global warming”
Yeah, me too and I suspect that is so for just about everyone here.
I have a doubt it is all my fault, or that it is a doom, but the fact of warming since 1850 seems indisputable despite some major ups and downs along the way. That a potential path to danger exists seems hard to argue with; but then, many dangers exist quite a lot more certain and imminent; World War 3 being at the top of my list. If the world manages to avoid that; next up is simply running out of fuel.
The earth’s warming up since the end of the Little Ice Age has been declining since the 1930’s warm cycle. This latest warm cycle (these come along in 30-60 year waves) was definitely weaker than the previous one and this cycle is ending soon and we are already into a colder cycle in key areas such as Hudson Bay and both poles cooling down rapidly.
So global warming has been slowing down already for over 50 years and this has been ‘fixed’ by the ‘climatologists’ who believe in ‘the earth is heating up relentlessly’ by literally tampering with the data and making the 1930’s in particular, look colder.
It appear since 1930 the global sea level has rise by about 6 inches and most of that sea level rise is due to a slightly warmer ocean. It also seems to me that in next 85 years sea level will rise somewhere another 4 to 8 inches.
And such slow warming of the oceans over last century means to me the world in warming and since I think it will likely increase another 4 to 8 inches within a century, that I believe world continues to warm up from one coldest period of interglacial period- called the Little Ice Age.
As for air temperature, I think it’s largely related to oceanic cycles, and it seems we starting the cool phase, but over longer periods I expect air temperature to continue rise.
Global air temperature appears to be currently warming at rate of about 1 C per century, but it seems to me unlikely, though possible that in 100 years will add 1 C or more to global average temperature,
and more likely between .5 and 1 C by 2115.
And during this hundred year period, it seems unlikely sea levels will trend lower or air temperatures could lower as much as 1900, or that rising decadal trend in air temperatures which could exceeds the peak temperature of the 1998 Super El Nino temperature by 1 C
Reblogged this on Spin, strangeness, and charm and commented:
A pretty good summary on where CAGW skeptics (a.k.a. “climate realists”) agree with climate alarmists (more than you might think), and where they part company.
The conflict between the sceptics and alarmists is not the only conflict that currently rages. Another is the conflict between the legitimate scientists and the pseudoscientists. The pseudoscientists argue over the magnitude of the equilibrium climate sensitivity (TECS). The scientists point out that the magnitude is insusceptible to measurement thus TECS is a scientifically illegitimate concept.
TCR and ECS are common acronyms in the literature.
..
I have not found TECS anywhere.
Ollie:
The acronym usually used is ECS but this usage fails to capture the implication that this is property of Earth’s climate and a constant.
It’s me again, I’m going to take another shot at this.
After further investigation it appears that my ppm gram weight based method in an earlier post has some flaws. Let’s discuss ppm.
The IGSS site (Mass of atmos CO2 page) says ppm is volumetric based. I have seen other sources that refer to ppm as volumetric based including references to Mauna Loa. ppmv
My approach posted earlier suggested that ppm is gram weight based. ppmgw
World Bank 4C report says ppm is mole based. See earlier post in this thread. ppmmol
Which is it? Which one did IPCC use? Why don’t they specify?
Since the specific volume of CO2 is less than that of air, the anthro CO2 ppm volumetric or mole basis will be even less than the gram weight based. All of these cases use the residual 45% atmospheric component.
IPCC AR5
Year……ppm
1750……278
2011……390.5
Diff…….112.5
Additional CO2 due to man…….555 PgC (As noted in my earlier thread this C is carbon dioxide. If this C were carbon one would have to multiply by 3.67 and the result would be more than the ppm & mass difference.)
ppm gram weight based=(grams CO2 added)/(atmospheric grams)
(5.55E+17/ 5.14E+21)*.45 = 48.6 ppm or about 50% of the 112.5 ppm CO2 increase between 1750 and 2011.
ppm volumetric based=((grams CO2 added)/((1.842 grams CO2)/m^3 ))/((grams air)/((1.205 grams air)/m^3 ))
(5.55E+17 * 1.205)/ (5.14E+21 * 1.842)*.45 = 35.4 ppm or about 30% of the 112.5 ppm CO2 increase between 1750 and 2011.
ppm mole based=((grams CO2 added)/((44.01 grams CO2)/mole))/((grams air)/((28.97 grams air)/mole))
(5.55E+17 * 28.97)/ (5.14E+21 * 44.01)*.45 = 35.6 ppm or about 30% of the 112.5 ppm CO2 increase between 1750 and 2011.
What it all boils down to is: 1) mankind’s CO2 output contributed about 30% of the CO2 increase between 1750 and 2011 and 2) evaporating water vapor absorbs the increased RF from CO2 without increasing the global temperatures.
You are mistaken about the cumulative total emissions of CO2, the figure of 555 PgC is of Carbon not CO2 so needs to be multiplied by the factor of 3.67.
Total cumulative emissions from 1870 to 2013 were 390±20 GtC from fossil fuels and cement, and 145± 50 from land use change. The total of 535±55GtC was partitioned among the atmosphere (225±5 GtC), ocean (150±20 GtC), and the land (155±60 GtC).
http://www.globalcarbonproject.org/carbonbudget/14/hl-full.htm
Some Generall Comments
This article was intended for the general audience, to be short and hopefully simple. I have other much more complicated and detailed ones, some available on the Internet. For example see
Major errors apparent in climate model evaporation estimates at:
http://wattsupwiththat.com/2014/04/15/major-errors-apparent-in-climate-model- evaporation-estimates/
Where we show the reason climate modelers use to explain why their evaporation increase with warming rates are so low, i.e., “Not enough energy to support more evaporation” is based on bad physics. The energy for evaporation derives from the temperature of the water only impeded by the humidity of the air. We suspect their estimates are low because they have relative humidity increase with temperature, not remain constant.
Improved simple climate sensitivity model at:
http://edberry.com/blog/climate-clash/g90-climate-sensitivity/improved-simple-climate-sensitivity-model/
where we define equations for a three level global energy balance model. This gets around the present simple model serious limitation that only considers energy balance at the planet level, looking down from the top of the atmosphere. The new model adds the requirements of balance at the surface and the atmosphere as a separate entity. This allows forcing at all three levels. This is the best way to handle latent heat transfer from the surface the atmosphere, a major negative feedback now being ignored except for an attempt to include it with lapse rate feedback. For the expected 6% change C in evaporation per C, the model gives a negative feedback factor of -0.739 C / C. The IPCC value for the lapse rate is only –0.2625 C / C. These compare to the IPCC value for water vapor of 1.8 Wm-2 / C x 0.3125 C / Wm-2 or +0.5625 C / C.
The new model also allows a better estimate of feedback from changes in cloud cover. Changes in clouds effect four parameters in the model. The model also handles changes in atmospheric solar absorption from clouds and things such increased water vapor, now neglected as a feedback factor. Later versions of the paper have been completed, but not published or posted.
A Closer Look at Carbon Dioxide Radiation Forcing at the Top of the Atmosphere
Does the Tropopause Limit Carbon Dioxide Warming?
at
http://edberry.com/blog/climate/climate-physics/climate-sensitivity/does-the-tropopause-limit-carbon-dioxide-heat-trapping/#more-18372
which goes into much detail how heat transfers layer by layer in the atmosphere.
It also uses results from many detailed runs using SpectralCalc’s spectral calculation tools for atmospheric paths using the Hitran 2008 database. It is similar to the free version of Modtran, but with many more features while also more time consuming to use. Because of this I do not respond much to all the opinions on how CO2 absorbs and omits radiation. It showed rather that 3.5 Wm-2 for doubling CO2, only 2.53 under a combination of clear and different cloud conditions. (Modtran gives results less than 3 looking down at 70 km as pointed out by others). However, not realized by many, this does not include the increased downwelling radiation with the emission level being moved to lower, warmer levels in the atmosphere. Later I did this and found looking up from the surface increased downwelling 3.21 and 0.716 Wm-2 for clear and cloudy conditions, with a weighted average of 1.99 Wm-2. However to convert this to an equivalent at the top of the atmosphere the ratios of downward and outward radiations must be used, so we end up with 1.99 x (195)/(324) or 1.20 Wm-2, where 195 and 324 are the total radiations leaving the top and bottom of the atmosphere including clouds. Adding this to the 2.53 we get a total of 3.73, very close to 5.35 log (2) or 3.71 the value many including IPCC which I rounded down to 3.5 for simplicity. However using 3.73 and that rate of change of outward radiation with temperature, one gets a final surface temperature rise of 3.73 x 3.73 or 1.01 C compared with IPCC value of 3.7 x 0.3125 or 1.16 C. Incidentally IPCC’s value of 0.3125 is close to an earlier simple one of 0.3047 that merely takes the rate of change of radiation with temperature at the surface times the “greenhouse multiplier” or 390/235, the ratio of the radiations from the surface and the atmosphere. However, the radiation of the atmosphere increases with temperature at a faster rate than the surface, and 0.27 Wm-2 / C is a closer value. The more accurate three level model described above that can handle changes in downwelling directly without referring to the TOA gives 0.9819 for 2x CO2, a little higher than 1.01 above.
There seems to be a lot of misunderstanding about CO2 climate sensitivity and observed temperature changes and whether their historical trends are accurate. Since we can’t measure CO2 climate sensitivity that does not mean we should try to estimate it with basic physics. This is where I think the simple energy balance model extended down to the surface and including feedbacks is much more reliable method than the complex computer models.
Some comments that I read that I do not think are true or have any significant meaning
(1) “If we can’t measure warming from CO2 it cannot be science”
That reminds me of the question, “If a tree fell in the forest and no one heard or saw it, did it really happen?”
But it is seems that with so many natural changes in global temperature, many still unknown, we will never be able to measure climate sensitivity directly. But that does not mean it does not exist. Can we “prove” it exists? No. But we can’t prove it does not exist either. On the other hand statements such as the IPCC claims that there is high confidence that the majority of warming since some date is caused by CO2 or anything else is mere speculation and not based on science.
But with more time we might be able to put some estimated bounds on CO2 climate sensitivity. In fact with the recent 18+ years with little or no warming, whatever exists is being cancelled by net natural cooling. And we have seen no natural cooling as large as the warming rate that the IPCC estimates, so CO2 climate sensitivity must be much less.