# The Mathematics of Carbon Dioxide, Part 1

This is a guest essay by Mike Jonas, part 1 of 4

Introduction

The aim of this article is to provide simple mathematical formulae that can be used to calculate the carbon dioxide (CO2) contribution to global temperature change, as represented in the computer climate models.

This article is the first in a series of four articles. Its purpose is to establish and verify the formulae, so unfortunately it is quite long and there’s a fair amount of maths in it. Parts 2 and 3 simply apply the formulae established in Part 1, and hopefully will be a lot easier to follow. Part 4 enters into further discussion. All workings and data are supplied in spreadsheets. In fact one aim is to allow users to play with the formulae in the spreadsheets.

Please note : In this article, all temperatures referred to are deg C anomalies unless otherwise stated.

Global Temperature Prediction

The climate model predictions of global temperature show on average a very slightly accelerating increase between +2 and +5 deg C by 2100:

We can be confident that all of this predicted temperature increase in the models is caused by CO2, because Skeptical Science (SkS) [6], following a discussion of CO2 radiative forcing, says :

Humans cause numerous other radiative forcings, both positive (e.g. other greenhouse gases) and negative (e.g. sulfate aerosols which block sunlight). Fortunately, the negative and positive forcings are roughly equal and cancel each other out, and the natural forcings over the past half century have also been approximately zero (Meehl 2004), so the radiative forcing from CO2 alone gives us a good estimate as to how much we expect to see the Earth’s surface temperature change.

[my emphasis]

So, if we can identify how much of the global temperature change over the years from 1850 to present was contributed by CO2, then we can deduce how much of the temperature change was not. ie,

T = Tc + Tn

where

T is temperature.

Tc is the cumulative net contribution to temperature from CO2. “CO2” refers to all CO2, there is no distinction between man-made and natural CO2.

Tn is the non-CO2 temperature contribution.

Obviously, all feedbacks to CO2 warming (changes which occur because the CO2 warmed) must be included in Tc.

CO2 Data

The Denning Research Group [4] helpfully provide an emissions calculator, which shows CO2 levels and the estimated future temperature change that it causes under “Business as usual” (zero emission cuts) :

Cross-checking the future warming in this graph against Figure 1, the CO2 warming from 2020-2100 is just under 3.5 deg C compared with about 3.25 deg C model average in Figure 1. That seems close enough for reliable use here. But data going back to at least 1850 is still needed.

There is World Resources Institute (WRI) CO2 data from 1750 to present [3], and CO2 data measured at Mauna Loa from 1960 to present [5]. Together with the Denning “Business as usual” CO2 predictions above, the CO2 concentration from 1750 to 2100 is as follows :

For dates covered by more than one series, the Mauna Loa measured data will be preferred, then the WRI data.

Because the “pre-industrial” CO2 is put at 280ppm [6], and the data points in the above graph before 1800 are all very close to 280ppm, a constant level of 280ppm will be assumed before 1800.

CO2 Contribution

The only information still needed is the CO2-caused warming before about 1990.

A method for calculating the temperature contribution by CO2 is given by SkS in [6] :

dF = 5.35 ln(C/Co)

Where ‘dF’ is the radiative forcing in Watts per square meter, ‘C’ is the concentration of atmospheric CO2, and ‘Co’ is the reference CO2 concentration. Normally the value of Co is chosen at the pre-industrial concentration of 280 ppmv.

dT = λ*dF

Where ‘dT’ is the change in the Earth’s average surface temperature, ‘λ’ is the climate sensitivity, usually with units in Kelvin or degrees Celsius per Watts per square meter (°C/[W/m2]), and ‘dF’ is the radiative forcing.

So now to calculate the change in temperature, we just need to know the climate sensitivity. Studies have given a possible range of values of 2-4.5°C warming for a doubling of CO2 (IPCC 2007). Using these values it’s a simple task to put the climate sensitivity into the units we need, using the formulas above:

λ = dT/dF = dT/(5.35 * ln[2])= [2 to 4.5°C]/3.7 = 0.54 to 1.2°C/(W/m2)

Using this range of possible climate sensitivity values, we can plug λ into the formulas above and calculate the expected temperature change. The atmospheric CO2 concentration as of 2010 is about 390 ppmv. This gives us the value for ‘C’, and for ‘Co’ we’ll use the pre-industrial value of 280 ppmv.

dT = λ*dF = λ * 5.35 * ln(390/280) = 1.8 * λ

Plugging in our possible climate sensitivity values, this gives us an expected surface temperature change of about 1–2.2°C of global warming, with a most likely value of 1.4°C. However, this tells us the equilibrium temperature. In reality it takes a long time to heat up the oceans due to their thermal inertia. For this reason there is currently a planetary energy imbalance, and the surface has only warmed about 0.8°C. In other words, even if we were to immediately stop adding CO2 to the atmosphere, the planet would warm another ~0.6°C until it reached this new equilibrium state (confirmed by Hansen 2005). This is referred to as the ‘warming in the pipeline’.

Unfortunately, not enough exact parameters are given to allow the temperature contribution by CO2 to be calculated completely, because the effect of ocean thermal inertia has not been fully quantified. But it should be reasonable to derive the actual CO2 contribution by fitting the above formulae to the known data and to the climate model predictions.

The net radiation caused by CO2 is the downward infra-red radiation (IR) as described by SkS, less the upward IR from the CO2 warming already in the system (CWIS). This upward IR will be proportional to the fourth power of the absolute (deg K) value of CWIS [9]. The net effect of CO2 on IR is therefore given by :

Rcy = 5.35 * ln(Cy/C0) – j * ((T0+Tcy-1)^4 – T0^4)

where

Rcy is the net downward IR from CO2 in year y.

Cy is the ppm CO2 concentration (C) in year y.

C0 is the pre-industrial CO2 concentration, ie. 280ppm.

j is a factor to be determined.

T0 is the base temperature (deg K) associated with C0.

Tcy is the cumulative CO2 contribution to temperature (Tc) at end year y, ie, CWIS.

SkS [6] says “it takes a long time to heat up the oceans due to their thermal inertia”. On this basis, CWIS is presumably in some ocean upper layer.

For a doubling of CO2, in the absence of other natural factors, the equilibrium temperature increase using the SkS formula is 5.35 * ln(2) * λ where λ = 3.2/3.7 (assuming a mid-range equilibrium climate sensitivity (ECS) of 3.2).

At equilibrium, Rc = 0. For ECS = 3.2, j can therefore be determined from

0 = 5.35 * ln(2) – j * ((T0+3.2)^4 – T0^4)

hence

j = (5.35 * ln(2)) / ((T0+3.2)^4 – T0^4)

Because “the natural forcings over the past half century have also been approximately zero” [6], the SST should be a reasonably good guide to CWIS. The global average SST 1981 to 2006 was 291.76 deg K [8]. Subtracting the year 1993 Tc of 0.7 (from the Denning data [4]) gives T0=291 deg K. Hence j = (5.35 * ln(2)) / ((291+3.2)^4 – 291^4) = 1.16E-8 (ie. 1.16 * 10^-8, or 0.0000000116).

Using the formula

δTcy = k * Rcy

where

δTcy is the increase (deg C) in CWIS in year y.

k is the one-year impact on temperature per unit of net downward IR.

the value of k can be found which gives a future temperature increase matching that of the climate models, ie. 3.25 deg C from 2020 to 2100. A reasonability check is that the result should closely match but be slightly lower than the Denning warming calculation in Figure 2 (lower graph) (slightly lower because target is 3.25 deg C not 3.5) …..

….. it does, for k = 0.02611 (the graph for 3.5 deg C is also shown in [7]). [Note that the calculated warming is “anchored” at 1750 T=0, and that the shape is determined only by the formula so there is no guarantee that the 2020 and 2100 temperatures will be close to the Denning temperatures. ie, this is a genuine test.].

Note: At this rate, global temperature takes 52 years to get 80% of the way to equilibrium (as in “equilibrium climate sensitivity”), 75 years to reach 90%, 97 years to reach 95%, 148 years to reach 99%.

The above formula can therefore reliably be used for CO2’s contribution to global temperature since 1750.

1850 to 2100

The above formulae can now be applied to the period 1850 – 2100, to see how much has been and will be contributed to temperature by CO2.

For temperature data 1850 to present, Hadcrut4 global temperature [1] is used. For future temperatures, the formula warming (as in Figure 4) is used.

Applying the above formulae shows the contributions to temperature by CO2 and by other factors :

As expected,

· the dominant contribution is from CO2,

· other factors contribute the inter-annual “wiggles” and virtually nothing else.

Note : The contribution to global temperature by CO2 is only man-made to the extent that the CO2 is man-made. As stated earlier, no distinction is made between man-made CO2 and natural CO2. Obviously, all pre-industrial CO2 was in fact natural. Similarly, for the non-CO2 contribution, no distinction is made between natural factors and non-CO2 man-made factors (such as land-clearing, for example), but the non-CO2 factors are thought to be predominantly natural. The feedbacks from the CO2 warming as claimed by the IPCC (eg. water vapour, clouds) are included in the CO2 contribution above.

Conclusion

The picture of global temperature and its drivers as presented by the IPCC and the computer models is one in which CO2 has been the dominant factor since the start of the industrial age, and natural factors have had minimal impact.

This picture is endorsed by organisations such as SkS and Denning. Using formulae derived from SkS, Denning and normal physics, this picture is now represented here using simple mathematical formulae that can be incorporated into a normal spreadsheet.

Anyone with access to a spreadsheet will be able to work with these formulae. It has been demonstrated above that the picture they paint is a reasonable representation of the CO2 calculations in the computer models.

The next articles in this series will look at applications of these formulae.

Footnote

It is important to recognise that the formulae used here represent the internal workings of the climate models. There is no “climate denial” here, because the whole series of articles is based on the premise that the climate computer models are correct, using the mid-range ECS of 3.2.

See spreadsheet “Part1” [7] for the above calculations.

Mike Jonas (MA Maths Oxford UK) retired some years ago after nearly 40 years in I.T.

References

[2] Climate model predictions from http://upload.wikimedia.org/wikipedia/commons/a/aa/Global_Warming_Predictions.png (Downloaded 20/5/2015) Note: Wikipedia is an unreliable source for contentious issues, but for factual information such as the output of computer models, and in the context for which it is being used here, it should be OK.

[3] CO2 data from 1750 to date is from World Resources Institute http://powerpoints.wri.org/climate/sld001.htm (Downloaded 20/5/2015. Digitised using xyExtract v5.1 (2011) by Wilton P Silva)

[4] Emissions calculator from Denning Research Group at Colorado State University http://biocycle.atmos.colostate.edu/shiny/emissions/ using no emissions cuts, ie, “Business as usual”. (Downloaded 20/5/2015. Digitised using xyExtract v5.1 (2011) by Wilton P Silva)

[6] Skeptical Science 3 Sep 2010 http://www.skepticalscience.com/Quantifying-the-human-contribution-to-global-warming.html (As accessed 20/5/2012).

[7] Spreadsheet “Part1” with all data and workings Part1 (Excel .xlsx spreadsheet)

[9] Stefan-Boltzmann law. See http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html

Abbreviations

AR4 – (Fourth IPCC report)

AR5 – (Fifth IPCC report)

CO2 – Carbon Dioxide

CWIS – CO2 warming already in the system

ECS – Equilibrium Climate Sensitivity

IPCC – Intergovernmental Panel on Climate Change

LIA – Little Ice Age

MWP – Medieval Warming Period

SKS – Skeptical Science (skepticalscience.com)

WRI – World Resources Institute

Article Rating
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Steven Mosher(@stevemosher)
July 25, 2015 10:08 am

“We can be confident that all of this predicted temperature increase in the models is caused by CO2, because Skeptical Science (SkS) [6], following a discussion of CO2 radiative forcing, says :
Wrong.
You are looking at both history and future projections.
If you want to know what FORCINGS drove the model, you cannot and should not rely on SKs
GO TO THE SOURCE.
The forcing files are available for all CMIP experiements.. THAT is the proper source. not Sks.
science 101.. Primary sources. USE THEM.

Mike Jonas(@egrey1)
Editor
July 25, 2015 3:29 pm

Hi Steven – Everything cross-checks. The mid-range models exactly match the predictions from the mid-range ECS on their own. Bar a few small wiggles, the past 150 years of actual temperatures exactly match the application of the mid-range ECS on its own (Figure 6). In other words, the past and the future both match exactly the supposed effects of CO2, assuming the mid-range ECS, plus nothing else. The forcings you talk about are all built into this process, IOW they are all built into the ECS. By using the ECS, I am in fact using them.

don t drink the koolaid
July 25, 2015 8:06 pm

Which means these effects (presumed to be anthropogenic in origin) fall within natural variability …as best as one can calculate.

Frank
July 26, 2015 2:08 am

Mike: FWIW, I don’t trust SKS to accurately report consensus climate science, so it will be difficult to trust your derivative work. I agree with Mosher, go to the original sources.

looncraz
July 26, 2015 6:39 am

You are using a formula with values derived from the assumption that all observed warming is from CO2. That means the results will absolutely match all data that went into the calculation of that value.
It is similar to tricks used to compress image data in a “lossy” manner.
Depending on when you calculated the ECS value you can get different expected curves that will fit the past data and, due to the dependence of future temps on current and past temps, be reasonably assured of a trend that will appear to fit for at least a couple of decades.
I’m also not convinced that there aren’t naturally sources of warming. 20th century solar activity, alone, was quite different than from the 19th century, and no one really agrees on what the effects would have been (more/less cloud nucleation? more/less wind? altered wind/ocean currents? etc…).
And, of course, the other data assumption is the CO2 levels themselves, but there is little we can do about that.

Steven Mosher(@stevemosher)
July 27, 2015 2:08 pm

[snip]
[ Until you start providing links and description, you don’t get to simply yell WRONG here anymore. Step up – Anthony]

July 25, 2015 3:43 pm

It depends on what the author’s purpose is, which we do not yet know (at least I don’t, since make no clairvoyancy claims). Lewis and Curry (2014) used central AR5 values (even though several have since been ‘improved’ ) to show that the likeliest ECS must be at the low end of the stated AR5 range. A rather nice ‘Perry Mason’ paper sticking it to AR5, yet also criticized for not using the newest estimates–which would have defeated the purpose. Maybe this is similar, in which case your point is not just irrelevant, but also wrong. Why not have the patience to find out what the purpose here is?

July 28, 2015 12:16 pm

Sketchy Science is what the shill site “Skeptical science” does. It poses as realist, but is actually designed to twist the real science that disproves the Global Warming Claims and make it look stupid or impotent. Find the real thing at WattsUpWith That.com

Bruce Cobb
July 25, 2015 10:22 am

So many assumptions, so little time. In the end, reality shows it is wrong.

fonzarelli
July 25, 2015 1:46 pm

Yeah, Bruce, i don’t spend too much time here at watts, but i must say this is the most delusional posting that i’ve seen here in a long while. I do wish anthony would be more careful about what’s being posted here…

July 25, 2015 3:44 pm

Guys, get a grip. This is establishing what the SkS models say. It’s not saying those models are right.

July 26, 2015 3:06 am

Agreed, the physics of a specific glibal ti Co2 interaction aught to be well understood by now, its what is not well understood which intrigues the most. There could be dozens of interactions which are not well understood driving climate in spite of C02 forcing. And we may have physics revise the math behind the radiative properties of C02 before long.

July 25, 2015 10:23 am

Well done looking forward to the series.

TRM
July 25, 2015 10:28 am

So the question becomes what is ECS value? If doubling CO2 will give us 1-1.7 C increase in temperature how do they get to 3.2? Feedbacks? Which ones and where is the data?
Thanks for the article. I’m looking forward to the next 3 parts.

July 25, 2015 10:35 am

I have strong objections on labeling the RCP8.5 scenario as “business as usual”. RCP8.5 is a worst case scenario similar to SRES A1FI. Using the real busines as usual model SRES A1B with a climate sentitivity of 1.3 yields this:
With this temperature calculation:
So only a one degree rise after 1990

Mike M.
July 25, 2015 11:17 am

Hans Erren,
You are absolutely right. RCP8.5 is a fantasy. The path we are on will take us somewhere between RCP4.5 and RCP6, unless there are breakthroughs in non-fossil energy (as, of course, there will be).

HAS
July 25, 2015 1:24 pm

RCP8.5 isn’t a fantasy, it is a scenario based on clear assumptions, no more no less. It doesn’t claim to forecast what might or mightn’t happen, it is a projection that “corresponds to a high greenhouse gas emissions pathway compared to the scenario literature .., and hence also to the upper bound of the RCPs”.

July 25, 2015 2:09 pm

HAS, all scenarios are science fiction the underlying assumption of A2 is increasing poverty combined with extreme population growth. That’s not business as usual for India nor China.

HAS
July 25, 2015 3:39 pm

Hans
You miss my point.
The scenarios are no more than the product of their assumptions. Discuss the assumptions and the ways they have been projected into the future by all means, but don’t expect them to give a realistic view of the future unless the assumptions align with what is happening and the methods of projection valid (which as you note they don’t).
The point of criticism is the people that take the scenario and ascribe to it more meaning than it has – claiming for it a realistic view of the future usually under cover of calling RCP8.5 “business as usual”.
I should add that that follows through to the GCMs that are again basically complex projections rather than forecasts, and the RCPs are just one of the assumptions made to form those projections.
GCMs only become problematic when people start saying that their output is the way the world will be (and suggesting their range of outputs are “likely” for example as AR5 WG1 did).

Chris Edwards
July 25, 2015 8:50 pm

But as you know CO2 can’t produce warming can it! And most of the CO2 came from warming oceans and that has stopped!

The Ghost Of Big Jim Cooley
July 25, 2015 10:37 am
JimS
Reply to  The Ghost Of Big Jim Cooley
July 25, 2015 10:45 am

And yet, the alarmists are known to continually accuse “climate deniers” of adhering to conspiracy theories.

Reply to  The Ghost Of Big Jim Cooley
July 25, 2015 11:05 am

Micheal Mann’s depression deepened on reading this. He especially felt low about the report on the lady who was in the house when that one guy fell down the stairs claiming that homicide was preposterous. But back to the math at hand!

Old'un
July 25, 2015 12:46 pm

Also in The Times today, there is an article on the NOAA claim that this is the going to be the hottest year on record, referencing Mann’s latest paper in which he claims we are all going to hell in a hand cart, even with a two degree temperature rise. At that temperature, Mann et al claim a sea level rise of 10ft in 50 years. They also state that CO2 is a ‘tight control knob on global climate’, but they are not claiming that Big Oil is trying to assassinate them, so I guess that they haven’t totally flipped (yet).

Mark from the Midwest
Reply to  The Ghost Of Big Jim Cooley
July 25, 2015 12:30 pm

I’m dealing with second hand information, so it’s hard to tell how accurate, but according to accounts Giles ran into a small delivery truck, the truck did not run into her. Laxon fell down a flight of stairs at a New Years party and died of a brain hemorrhage.
If this was murder then this is the most clever and skilled assassin in history to have multiple cases where the victim initiates the final sequence leading to death.

Reply to  Mark from the Midwest
July 25, 2015 1:34 pm

They are super ninja turbo charged oil fed murdering assassins that use vulcan mind meld to steer their victims to their demise! They throw Neon bright spinney star like thoughts of death right out of their foreheads!

Graham
Reply to  Mark from the Midwest
July 28, 2015 12:06 pm

Easy. Just spike the drinks with heavily magnetized rare earth metals. Person runs into truck because its largely metal. Person falls down stairs because a strange delivery consisting of a blob of metal was left at the bottom of steep stairs. Man struck by lightning because of the metal inside him. I totally buy this (sarc).

M Courtney
Reply to  The Ghost Of Big Jim Cooley
July 25, 2015 12:37 pm

In fairness he has a point.
Nobody ever has an accident on a bicycle without there being nefarious causes.
Motorway bumps are unheard of ever. And he probably would have died if he hadn’t had that covert advanced automobile training with MI6 (shh).
And the guy who was hit by lightning was clearly attacked with a CIA/Exxon space Tesla Ray.
Lewandowsky can explain why you’re being irrational in doubting the great scientist.

katherine009
Reply to  The Ghost Of Big Jim Cooley
July 25, 2015 1:05 pm

Arranging for someone to be struck by lightning is a neat trick. Who would ever suspect it was murder?

MikeB
July 26, 2015 4:18 am

It just shows that the conspiracy goes right to the top.

Reply to  The Ghost Of Big Jim Cooley
July 25, 2015 2:11 pm

Interesting, but unlikely to be a coincidence.
There may be an important common element, which I am very familiar with.
I often come across something in a data file, and however unlikely when it confirms my expectations, I wander down the road oblivious of the surroundings, unable to get it out of my head until I can glimpse some kind of resolution.
These scientists died in early months of 2013, while Arctic Sea ice extent in the late 2012 hit new low.
http://ocean.dmi.dk/arctic/plots/icecover/icecover_current_new.png
All three were very intelligent highly educated people, I suspect they knew perfectly well that this could not have been consequence of the CO2; but what is it and why?
Lack of concentration while riding a bike even for few seconds in London traffic, or coming down stairs (I did it once, had bruised ‘lower back’ for months, my wife see only funny side of it). Going to a UK hospital on Sunday, let alone New Years day with a life threatening injury, a very slim chance of recovery. In the third case could be simply carelessness and ignorance of the elements by walking in a thunderstorm while the mind is preoccupied by some other matter.
Professor Peter Wadhams you are wrong, not succession of assassinations, as your own case confirms. Of course you wouldn’t be also loosing concentration while driving and daydreaming about “ that the North Pole will be exposed (no ice) this summer – it’s not happened before” as you claimed some years ago, or some other nonsense, but for some reason a crazy lorry driver didn’t like your climate politics.

Janice the Elder(@janicetheelder)
July 25, 2015 10:41 am

It is entertaining to see so much math, when some of the underlying initial assumptions are completely fabricated. I have seen nothing which would indicate that carbon dioxide was a specific steady-state level from 1750 to about 1900. The published numbers from that time were all over the place, depending on where the air samples were taken. The numbers being used here are taken from the lowest readings, and are not even an average from known readings in a general area. This would be interesting if it was based upon some real numbers as a starting point.

July 25, 2015 10:56 am

Janice,
The old (chemical) measurements were more or less reliable (+/- 10 ppmv with good skills), the places where they were taken were not: midst of towns, under, in between and over growing crops, midst of forests, etc… Completely unreliable for “background” CO2 levels.
The 280 ppmv is mainly taken from the most uncontaminated places (over the oceans, coastal with wind from the sea) and are around the ice core data which have a resolution of around 20 years over the past 1,000 years.

John
July 25, 2015 10:43 am

Looking forward to part 4 but stopped reading whe you quoted the Skeptical Science rag. Please find more credible sources to establish the math.
Also, the assumption that co2 alone will cause a linear change in the climate system is nonsense and the reason the models are so flawed/inaccurate.

Peter Sable
July 25, 2015 11:56 am

Looking forward to part 4 but stopped reading whe you quoted the Skeptical Science rag
Patience young Paduan, the purpose is likely to hoist them on their own petard.

old engineer
July 25, 2015 2:11 pm

exactly my thought. Let’s wait to see where he takes this before commenting.

July 25, 2015 6:33 pm

Peter,
I think you are correct in your prediction.
Sorry to be pedantic, but I believe it would be “to hoist them [with/by] their own petard”. I believe a petard is a bomb, in medieval times affixed to a gate to blow a hole for getting into a fortification. The quote comes from Shakespeare (Hamlet) and I believe means “blown up by one’s own bomb”.

Zipperfish
July 27, 2015 3:34 pm

Exactly. Once we confirm he’s on our side, we’ll be able to accept the science. Otherwise, it will be summarily dismissed.

fonzarelli
July 25, 2015 12:55 pm

Yeah, John, this is really a bit bizarre of jonas… The warming of a hundred years ago is thought to be largely natural as well as up to half of recent warming (if that’s even to be believed). So nearly three quarters of the warming is due to nature alone. Maybe i’m not understanding the point that jonas is trying to make (?)…

Mike Jonas(@egrey1)
Editor
July 25, 2015 3:35 pm

John. Sorry if I didn’t make it clear – I’m establishing the maths used in the climate models, and to do that I’m uncritically using the logic behind the climate models. I then apply the maths later in the series.

John
July 26, 2015 10:20 am

Hi Mike,
IMO, SKs is not nor is it ever likely to be considered a credible source. Its credibility has been undermined by the antics of its principals. I was simply pointing out my reaction.
Looking forward to Part 4.

July 25, 2015 10:45 am

“It is important to recognise that the formulae used here represent the internal workings of the climate models. There is no “climate denial” here, because the whole series of articles is based on the premise that the climate computer models are correct, using the mid-range ECS of 3.2.”
Well, unfortunately “the premise that the climate computer models are correct” is false for many reasons, thus rendering the remainder of this article incorrect. Reasons include, but are not limited to,
1. An artificially fixed tropospheric lapse rate of 6.5K/km, which does not adjust to perturbations in the atmosphere. This false assumption artificially limits negative lapse rate feedback convection. Using physically correct assumptions, Kimoto (link below) finds the climate sensitivity to doubled CO2 to be a negligible 0.1-0.2C.
2. Mathematical error in the calculation of the Planck response parameter λ, due to a false assumption of fixed emissivity, an error which continues to be promulgated by the IPCC (explained in section 3 of this Kimoto paper):
http://hockeyschtick.blogspot.com/2015/07/collapse-of-agw-theory-of-ipcc-most.html
3. Positive feedback from water vapor (whereas millions of radiosonde & satellite observations demonstrate water vapor has a net negative-feedback cooling effect)
4. Fixed relative humidity (contradicted by observations showing a decline of mid-troposphere relative and specific humidity) (A new paper also finds specific humidity is the most non-linear and non-Gaussian variable in weather models, also implying relative humidity is non-linear, and borne out by observations)
5. Neglect of the < 15 micron ocean penetration depth of GHG IR radiation, which greatly limits potential greenhouse gas warming of the top ocean layer.
6. Incorrect assumption that line-emitters CO2 and H2O are blackbodies for which Planck's, Kirchhoff's, & Stefan-Boltzmann laws apply [your equation [9] above]. Neither are blackbodies, don't have a Planck curve, and their emissivity decreases with temperature, *opposite* to a true blackbody.
7. False assumption that CO2 can absorb/emit at an equivalent blackbody temperature of anywhere from 200K-330K (but is limited to ~15 micron line-emission emitting temperature of 193K maximum by basic physical chemistry & quantum theory).
et al

July 25, 2015 10:48 am

Clarification above on #6: “…their emissivity decreases with increased temperature, *opposite* to a true blackbody.”

Crispin in Waterloo
July 25, 2015 1:02 pm

Hockeyschtick
The emissivity of a blackbody is 1.00. I cannot, by definition, increase with temperature. It is already a perfect emitter.
Did you mean something else?
The emissivity of most things is surprisingly constant with temperature provided it doesn’t start burning.

July 25, 2015 1:37 pm

“The emissivity of a blackbody is 1.00”
Correct, but the points I was trying to make are that CO2 and H2O are mere line-emitters and not true blackbodies, emissivity is always less than a true blackbody, i.e. 193K.

July 25, 2015 1:44 pm

For some reason, the remainder of my reply got cut off:
CO2 & H2O are mere line-emitters and not true blackbodies for which emissivity = 1. GHGs have emissivities 193K.

July 25, 2015 1:48 pm

GHGs CO2 & H2O are mere line-emitters and not true blackbodies for which emissivity = 1. GHGs have emissivities 193K.

July 25, 2015 1:51 pm

Mod: for some reason your system has repeatedly cut off the remainder of my comment I’ve tried to post 4 times – I think I discovered problem using a less than sign w/o a space… Trying one more time:
GHGs CO2 & H2O are mere line-emitters and not true blackbodies for which emissivity = 1. GHGs have emissivities less than 1 like true blackbodies and which decline further with temperature as proven by observations:
The reason why is basic physical chem & quantum theory. For example, for CO2 ~15 micron line-emission, the maximum possible emitting temperature is 193K by Planck’s/Wein’s Laws. 193K CO2 photons cannot transfer heat or be thermalized/warm any body at more than 193K.
http://hockeyschtick.blogspot.com/search?q=kirchhoff+planck

Mike M.
July 25, 2015 11:23 am

hockeyschtick ,
There is much to criticize in climate models, but these claims are bogus. No more than two of 1, 3, and 4 can be true. And none of this claims are consistent with what is actually done in climate models.

Peter Sable
July 25, 2015 12:01 pm

There is much to criticize in climate models, but these claims are bogus. No more than two of 1, 3, and 4 can be true.
It only takes one being true to falsify the models. I think taking a shotgun approach and then eliminating the incorrect ones by scientific method is a reasonable approach. Thanks for suggesting which candidates to target first.

July 25, 2015 12:09 pm

“but these claims are bogus… And none of this claims are consistent with what is actually done in climate models”
Absolutely false. If you had bothered to read and understand the Kimoto papers
http://hockeyschtick.blogspot.com/2015/07/collapse-of-agw-theory-of-ipcc-most.html
you will find the literature citations which show the Hansen/NASA/GISS & IPCC models do in fact make these false assumptions. The 1976 US Std Atmosphere also proves many of these same false assumptions, and did not use one single radiative transfer calculation in their mathematical model of the temperature profile from 0-100km.
Arguments solely from the authority of “Mike M.” are worthless without out any specifics or references/mathematics/links/etc to back them up.

Nick Stokes(@bilby)
July 25, 2015 2:33 pm

Kimoto’s paper is bad. But if you had bothered to read it, you would find that he isn’t talking about modern climate computer models at all in your linked ms, “:Collapse of the Anthropogenic Warming Theory of the IPCC”. He is talking about the early 1D models. He cites Manabe and Strickler, 1964, Manabe and Weatherald 1967, Hansen 1981. What he calls 1D RCM models. His only reference to modern GCMs is a claim that they have followed a Cess method (which he says is wrong) for Planck feedback. But GCM’s do not use such a method. They have no need to. They calculate radiative transport using a full transport model.
As Mike M says, none of that has anything to do with what GCM’s do. And for the most part, Kimoto doesn’t claim that it does.

July 25, 2015 2:53 pm

Nick Stokes claims “Kimoto’s paper is bad. But if you had bothered to read it, you would find that he isn’t talking about modern climate computer models at all in your linked ms, “:Collapse of the Anthropogenic Warming Theory of the IPCC”. He is talking about the early 1D models. He cites Manabe and Strickler, 1964, Manabe and Weatherald 1967, Hansen 1981. What he calls 1D RCM models. His only reference to modern GCMs is a claim that they have followed a Cess method (which he says is wrong) for Planck feedback”
No it is not “bad,” and if you had bothered to read my introduction to Kimoto’s papers you would find “top” climate scientists saying Manabe et al was the “first physically sound climate model allowing accurate predictions of climate change.” The paper’s findings have stood the test of time amazingly well, Forster says.
“Its results are still valid today. Often when I’ve think I’ve done a new bit of work, I found that it had already been included in this paper.” “[The paper was] the first proper computation of global warming…” etc.
And guess what, those early Manabe/Hansen/ et al models came up with essentially the same alleged climate sensitivities back then as your super-sophisticated models do now, using the same false assumptions.
Kimoto is correct that GCMs assume or calculate a Planck feedback response of 1.2K, which is a mathematical error based on the false assumption that emissivity is a constant. This is not true for non-blackbodies like GHGs, for which the absolute maximum possible emitting temperature is fixed due to quantum theory/physical chem. For example, max possible emitting temp of ~15um CO2 emission is ~193K, but Manabe et al models assume CO2 can emit at any potential temp up to 300K+. This is physically impossible.
In addition, this new paper using “state-of-the-art” radiative code shows GHGs are increasing LWIR cooling at Earth temps < 295K (current 288K):
http://hockeyschtick.blogspot.com/2015/07/new-paper-finds-greenhouse-gases.html

Nick Stokes(@bilby)
July 25, 2015 4:25 pm

“Kimoto is correct that GCMs assume or calculate a Planck feedback response of 1.2K, which is a mathematical error based on the false assumption that emissivity is a constant.”
So says HS. Anything to back it up? It makes no sense to anyone who knows anything about GCM’s. For a start, emissivity is not constant in any GCM. Obviously, gas emissivity depends on GHG concentration, and GCMs do a spectral breakdown.
Yes, Manabe et al did pretty well with simplifying assumptions. So what? It doesn’t mean they are still used.

July 25, 2015 6:19 pm

Nick Stokes makes the absurd claim “Obviously, gas emissivity depends on GHG concentration”
Uhh no, emissivity of CO2 has nothing to do with its concentration. Whether were are talking about one molecule of CO2 or one million, the peak emissivity by Wein’s/Planck’s laws at 15um is limited to that of a 193K blackbody. As I’ve already pointed out several times, quantum theory limits the 15um CO2 emission to a maximum of 193K IF CO2 was a true blackbody. It is not, and its emissivity goes DOWN with temperature.
“So says HS. Anything to back it up?”
Of course, observations from Hottel et al show that CO2 & H2O are not blackbodies and emissivity goes down with temperature:
http://1.bp.blogspot.com/-UWg2eWMGU2A/U2vvgvyMnpI/AAAAAAAAF-w/9AJ44NLDsX4/s1600/photo.PNG
http://3.bp.blogspot.com/-Nb4poOlIaco/U2vys448_PI/AAAAAAAAF_c/6NNWzpHJQoE/s1600/water+vapor+emissivity.jpg
“Yes, Manabe et al did pretty well with simplifying assumptions. So what? It doesn’t mean they are still used.”
Uh no, he absolutely did not “do pretty well” with his unphysical false assumptions, and Kimoto shows multiple reasons why the models run way too hot as a direct result of these false assumptions. Manabe shows in his paper that CO2 emits radiation at an emitting temperature of up to 300K. This is absolutely false Fizzikx contradicted by basic physical chemistry & quantum theory.
In addition, the mathematical model of the 1976 US Std Atm was published 9 years after Manabe’s “most influential climate paper of all time” and completely discards CO2 from the model, and doesn’t do one single radiative transfer calculation. How come?
I see you’ve also carefully avoided mentioning my link to the new paper which uses 2 state-of-the-art radiative codes and shows GHGs are causing LWIR COOLING at the present Earth T=288K. Why do you think that is?

Trick
July 26, 2015 7:41 pm

I looked up the Hottel experimental curve your 6:19pm in another text, took only a few minutes in this age. The left most curve temperature is about 300K, 400K dipping down, then 800K double the distance from 400K all the way to upwards of 2800K bottom right all at the same total P 1bar. This curve is from a family of curves looking through a layer with various curves of various (H2O partial pressure * layer depth) in units of mbar-m. The left scale goes down several orders of magnitude starting from 2 ! thus the log. Note this 2 measured is well above even common emissivity of BB 1.0. You know, like the IR opacity of Venus atm. looking up from the surface.
A well known ideal law says the density of the gas in these curves is decreasing rapidly, all at constant P and increasing T. Appears what you are seeing is the effects of the gas becoming rarefied so your conclusion is not well founded. Because the optical depth of an atm. does depend on density (mixing ratio) of the constituents.
For earth atm. the emissivity of CO2 with H2O pp is all off the scale to the left, there are other experiments you will need to consider. Hottel found these tests needed in industry & performed them – way before modern RTM accuracy made the experimental work unnecessary. Industry uses RTM these days, it is more accurate than even your Std. Atm.

MikeB
July 27, 2015 1:27 am

Dahlquist
July 25, 2015 11:34 am

Perhaps the author intends to make a point about exactly what you have brought up. To demonstrate just how screwed up the models are and the screwed up outcomes, using their flawed data or means.
Maybe. Just a thought.

July 25, 2015 11:50 am

@ hockeyschtick
Good points. All of them. Thanks for taking the time to outline these “stubborn facts”.

Phil.
July 25, 2015 5:09 pm

hockeyschtick July 25, 2015 at 10:45 am
7. False assumption that CO2 can absorb/emit at an equivalent blackbody temperature of anywhere from 200K-330K (but is limited to ~15 micron line-emission emitting temperature of 193K maximum by basic physical chemistry & quantum theory).

Absolute nonsense, the 193K temperature is the temperature of a blackbody which has a peak radiance at 15 microns, it has nothing to do with the absorption/emission of CO2.
CO2 absorbs at 15micron because the separation between the ground state energy level and the first excited state corresponds to a 15 micron photon. Any 15 micron photon can be absorbed regardless of the temperature of its origin. An excited CO2 molecule will emit a photon of the same wavelength as long as it not first collisionally deactivated.

July 25, 2015 6:31 pm

Phil claims “Absolute nonsense, the 193K temperature is the temperature of a blackbody which has a peak radiance at 15 microns, it has nothing to do with the absorption/emission of CO2.”
Wrong, by Kirchhoff’s law (assuming CO2 is a true blackbody, which it is not), CO2 emits and absorbs at the same 15um LWIR wavelength. Obviously CO2 has other absorption/emission lines, but for the purposes of discussing a radiative GHE, I am discussing the peak CO2 line emissions centered at ~15um. By Wein’s/Planck’s laws the maximum possible emitting temp of CO2 (also falsely assuming CO2 is a true blackbody) is 193K. In reality, GHGs are not true blackbodies and emit/absorb less than true blackbodies.
You also falsely state “Any 15 micron photon can be absorbed regardless of the temperature of its origin.” indicating you don’t understand the fixed quantum relationship between emitting temperature and wavelength.
“An excited CO2 molecule will emit a photon of the same wavelength as long as it not first collisionally deactivated.”
Ahh, CO2 in the troposphere does preferentially transfer heat energy to the remaining 99.9% atmosphere via collisions, which INCREASES negative-feedback cooling convection. Convection and non-radiative heat transfer dominates ~92% of heat transfer in the troposphere, and easily overcomes any alleged (false) radiative forcing from 193K CO2 photons.

Phil.
July 25, 2015 9:31 pm

By Wein’s/Planck’s laws the maximum possible emitting temp of CO2 (also falsely assuming CO2 is a true blackbody) is 193K.
The source of your errors is this misunderstanding of Wien’s Law, it does not define “the maximum possible emitting temp of CO2′. Wien’s Law states that the black body radiation curve for different temperatures peaks at a wavelength inversely proportional to the temperature. Here’s a good illustration of it:
The dashed line shows the position of the maximum as defined by Wien’s law, the curves illustrate Planck’s law for different temperatures, showing quite clearly that there is not a fixed relationship between temperature and wavelength. In fact as the envelope of the curve increases at all wavelengths with temperature it shows that a black body at 300K will emit more 15micron light than one at 193K.
You also falsely state “Any 15 micron photon can be absorbed regardless of the temperature of its origin.” indicating you don’t understand the fixed quantum relationship between emitting temperature and wavelength.
As shown above there is no such ‘fixed relationship’.

July 25, 2015 10:10 pm

Phil. incorrectly claims “there is not a fixed relationship between temperature and wavelength” for blackbodies.
False. Please read up on Wein’s Displacement Law here, & “the wavelength of the peak of the blackbody radiation curve gives a measure of temperature” via Wein’s Law, which is derived from Planck’s Law:
http://hyperphysics.phy-astr.gsu.edu/hbase/wien.html
Try the calculator there: Type in 193K for the temperature and lo and behold it calculates 15um peak BB emission.
“In fact as the envelope of the curve increases at all wavelengths with temperature it shows that a black body at 300K will emit more 15micron light than one at 193K.”
That is true for TRUE blackbodies, but even though climate scientists assume GHGs are blackbodies, observations clearly show they are not. They are mere fixed-quantum-E line-emitters, and each line has a corresponding peak blackbody emission temperature for a given wavelength. GHGs emissivity is less than a true BB and decreases with temperature due to the fixed emitting temp at particular wavelengths.

July 26, 2015 4:20 am

As Phil says, an elementary misunderstanding. You can see this looking at the colorful diagram in this comment below. The dark blue curve at 210K does indeed have a maximum at about 14μ. But that doesn’t mean that at 210K 14μis the max possible emitting temperature. Just look at the next curve, 220K (light blue). There is higher intensity at 14μ. It just isn’t the max any more, at that temp.

Phil.
July 26, 2015 9:16 am

hockeyschtick July 25, 2015 at 10:10 pm
Phil. incorrectly claims “there is not a fixed relationship between temperature and wavelength” for blackbodies.

There is not, Planck’s Law says that there is a distribution of wavelengths emitted at any temperature. It also says that for a black body there will be more photons of any given wavelength emitted by a hotter bb. Therefore a 300K object will emit more 15 micron photons than one at 193K. Contrary to your assertion that “For example, for CO2 ~15 micron line-emission, the maximum possible emitting temperature is 193K by Planck’s/Wein’s Laws”, Planck’s law says that a bb of any temperature will emit a 15 micron photon. Wien’s law says nothing about it at all.
False. Please read up on Wein’s Displacement Law here, & “the wavelength of the peak of the blackbody radiation curve gives a measure of temperature” via Wein’s Law, which is derived from Planck’s Law:
I have and I have taught the subject at graduate level for decades, Wien’s law just defines the peak of the Planck distribution, it does not say what you claimed: “For example, for CO2 ~15 micron line-emission, the maximum possible emitting temperature is 193K by Planck’s/Wein’s Laws”
That is true for TRUE blackbodies, but even though climate scientists assume GHGs are blackbodies, observations clearly show they are not.
Not true, no-one makes that assumption.
They are mere fixed-quantum-E line-emitters, and each line has a corresponding peak blackbody emission temperature for a given wavelength.
Again not true, depending on conditions each line has either a Lorenzian, Gaussian or Voigt profile:
The envelope of all the lines has an upper bound corresponding to the bb emission distribution for that temperature, i.e. no individual line can exceed the emission at that wavelength of a bb at that temperature.
GHGs emissivity is less than a true BB and decreases with temperature due to the fixed emitting temp at particular wavelengths.
The bolded part is totally false, there is no such thing.
Please stop posting such nonsense, you clearly don’t understand the subject, as anyone who picks up a undergraduate text on Physical Chemistry or Spectroscopy will quickly find out.

July 26, 2015 9:59 am

Both Nick Stokes and Phil. continue to conflate molecular-line-emitters with TRUE blackbodies.
GHGs are not TRUE blackbodies, they are molecular-line-emitters without a Planck BB curve, although climate science incorrectly assumes that they are true blackbodies and have emissivity = 1 regardless of T, and which does not decrease with temperature as observations (I posted above and others) clearly show.
Energy of TRUE BB of temperature T (in kelvins) is calculated using this equation: E=kT where k is Boltzmann’s constant. Energy of a light with frequency f is calculated using this equation: E=hf where h is Planck’s constant. So spectral radiance of emitted light with frequency f from BB with temperature T is calculated using β(T)=((2hf^3)/(c^2))*(1/(e^(hf/kT)−1)) via Planck’s law.
Please provide a published reference stating CO2 can have an emitting temperature of 330K (like Manabe shows in his model) and thus have peak emission at 8.8 micron wavelength IR. Impossible.
Furthermore, as shown on page 1061 of Kimoto’s published paper, the assumption that Cess (and state-of-the-art models) make that εeff of the atmosphere is a constant is incorrect:
According to the annual global mean energy budget [Kiehl et al., 1997], OLR can be expressed as follows.
OLR = Fs,r + Fs,e + Fs,t + Fsun − Fb (14)
Fs,e: surface evaporation 78W/m2
Fs,t: surface thermal conduction 24W/m2
Fsun: short waves absorbed by the atmosphere 67W/m2
OLR: outgoing long wave radiation 235W/m2
From Eq. (9) and (14), the following equations are obtained.
εeffσTs**4 = εeffFs,r = Fs,r + Fs,e + Fs,t + Fsun − Fb (15)
εeff = 1 + (Fs,e + Fs,t)/Fs,r + (Fsun − Fb)/Fs,r (16)
Therefore, εeff is not a constant but a complicated function of Ts and the internal variables Ij, which can not furnish the differentiation of Eq. (9) to obtain Eq. (10):
λo = −∂OLR/∂Ts = −4εeffσTs**3 = −4OLR/Ts (10)
i.e. the Planck feedback parameter, and basis of climate sensitivity calculations running way too hot.
Still waiting after 3 requests for Nick Stokes to address why this new paper containing 2 of the state-of-the-art radiative codes, including that used by IPCC modelers, finds LWIR from all GHGs is causing surface COOLING at the present Earth Ts=288K…
http://hockeyschtick.blogspot.com/2015/07/new-paper-finds-greenhouse-gases.html
And why the 1976 US Std Atm mathematical model completely discards CO2 from the 50 pages of theoretical calculations, and does not use one single radiative transfer calculation whatsoever. Why not?

July 26, 2015 11:04 am

In reply to “though climate scientists assume GHGs are blackbodies, observations clearly show they are not.”
Phil. says “Not true, no-one makes that assumption.”
Phil. there are many thousands of references, lectures, texts, papers, etc. which do in fact apply Kirchhoff’s, Planck’s and most commonly the Stefan-Boltzmann Laws for blackbodies to GHG line-emitters with emissivity a constant of 1 at all temperatures. Observations clearly show GHG line-emitters do not behave as BBs and emissivity decreases with T. Therefore, the false assumption emissivity =1 at any T for GHGs is false and is one of the reasons that leads to an exaggerated Planck feedback parameter, as explained in Kimoto’s published paper, which also addresses the additional reasons why e(eff) is not a constant as commonly assumed in calculating the (exaggerated) Planck feedback.
Phil. says “The envelope of all the lines has an upper bound corresponding to the bb emission distribution for that temperature, i.e. no individual line can exceed the emission at that wavelength of a bb at that temperature.”
Exactly, that has been my point all along! Thus, the maximum emitting temperature of a TRUE BB with peak ~15um radiation is ~193K. CO2 is not a true BB, thus the max emitting temperature of the fixed ~15um band CO2 photons is ~193K and cannot exceed that of a true BB having a peak emission at ~15um.

July 26, 2015 11:54 am

Frank, Ian, Phil. et al:
Here’s an easy proof that a pure N2 atmosphere without any IR-active gases would establish a greenhouse effect/tropospheric temperature gradient even a bit warmer at the surface than our present atmosphere:
http://hockeyschtick.blogspot.com/2014/11/why-greenhouse-gases-dont-affect.html

Frank
July 26, 2015 4:11 pm

Hockeystick wrote: “Here’s an easy proof that a pure N2 atmosphere without any IR-active gases would establish a greenhouse effect/tropospheric temperature gradient even a bit warmer at the surface than our present atmosphere:”
Your proof requires some mechanism to move gas from one altitude to another. On earth, that normally happens by convection of heat absorbed by the surface to the thinner upper atmosphere, where it can escape to space as radiation. An atmosphere with no GHG’s can’t radiatively cool, so there will be no convection to move large amounts of gas from one location to another (though some people discuss the Coriolis Force and other mechanisms). The only way heat can escape from an atmosphere with no GHGs would be through collisions with the surface. IF you eliminate radiation, buoyancy-driven convection and other forms of bulk motion, then the only mechanism of heat transfer is conduction (molecular collisions). If you consult Chapter 40 Vol 1 of the online Feynman lectures on physics, you might find that Feynman expects an isothermal atmosphere (and I think he is right). However, the situation is so complicated that a long debate would not be useful – I’m only commenting to alert you to complications and another point of view.
http://www.feynmanlectures.caltech.edu/I_40.html

July 26, 2015 5:00 pm

Thank you Frank for that Feynman reference which I was previously unaware of! At first glance, it confirms the exact same gravito-thermal GHE/temperature gradient as first described by Maxwell in his 1872 book Theory of Heat, and the same barometric formulae used as the basis of the US Std Atmosphere & HS ‘greenhouse equation’
I find no mention at first glance in Feynman’s reference of radiative calculations, radiative forcing, greenhouse gases, CO2, Arrhenius, “greenhouse effect,” etc., etc., nor any mention that our atmosphere would be isothermal w/o GHGs. What makes you think that Feynman was suggesting that?
“Your proof requires some mechanism to move gas from one altitude to another. On earth, that normally happens by convection of heat absorbed by the surface to the thinner upper atmosphere, where it can escape to space as radiation. An atmosphere with no GHG’s can’t radiatively cool, so there will be no convection to move large amounts of gas from one location to another (though some people discuss the Coriolis Force and other mechanisms). The only way heat can escape from an atmosphere with no GHGs would be through collisions with the surface. IF you eliminate radiation, buoyancy-driven convection and other forms of bulk motion, then the only mechanism of heat transfer is conduction (molecular collisions).”
Frank, a column of pure N2 with a heating element at the bottom would definitely have convection and thus a temperature gradient. Why would you think not? In actuality, GHGs increase convection through collisions with N2/O2 in the troposphere up to P ~= 0.1 atm, which enhances convective “*cooling* of the surface. That is why a pure N2 atmosphere would be warmer than our current atmosphere, due to less convection and less radiative surface area from GHGs which act like a heat sink to increase radiative cooling to space.

Frank
July 26, 2015 8:51 pm

Hockeyschtick wrote: “I find no mention at first glance in Feynman’s reference of radiative calculations, radiative forcing, greenhouse gases, CO2, Arrhenius, “greenhouse effect,” etc., etc., nor any mention that our atmosphere would be isothermal w/o GHGs. What makes you think that Feynman was suggesting that?
Feynman: “Let us begin with an example: the distribution of the molecules in an atmosphere like our own, but without the winds and other kinds of disturbance. Suppose that we have a column of gas extending to a great height, and at thermal equilibrium—unlike our atmosphere, which as we know gets colder as we go up. We could remark that if the temperature differed at different heights, we could demonstrate lack of equilibrium by connecting a rod to some balls at the bottom (Fig. 40–1), where they would pick up 12kT from the molecules there and would shake, via the rod, the balls at the top and those would shake the molecules at the top. So, ultimately, of course, the temperature becomes the same at all heights in a gravitational field.”
RGB and DeWitt have made similar arguments: Since one can extract work from any temperature difference, if a temperature gradient develops spontaneously, you have a perpetual source of energy. Some other work I have done agrees.
Hockeyschtick also wrote: “a column of pure N2 with a heating element at the bottom would definitely have convection and thus a temperature gradient.”
Absolutely. However, the sun is not a heating element. The surface of a planet without GHGs would be in radiative equilibrium with the sun. Conduction will occur as long as a temperature gradient exists, so the atmosphere and the surface will eventually come into equilibrium by conduction. Since the atmosphere can’t radiate, it can only lose or gain energy from the surface – whose temperature is controlled by radiative equilibrium.
Now, if you want to say the poles will receive less radiation than the equator and produce bulk mixing, the problem becomes too complicated for me to be sure what will happen. I’m discussing the simpler – but still complicated – situation similar to Feynman’s column with no bulk motion.

July 27, 2015 9:55 am

Frank, Feynman goes on to explain why an N2/O2 atmosphere is not isothermal due to gravity/mass/density/pressure:
“If the temperature is the same at all heights, the problem is to discover by what law the atmosphere becomes tenuous as we go up. If N is the total number of molecules in a volume V of gas at pressure P, then we know PV=NkT, or P=nkT, where n=N/V is the number of molecules per unit volume. In other words, if we know the number of molecules per unit volume, we know the pressure, and vice versa: they are proportional to each other, since the temperature is constant in this problem. But the pressure is not constant, it must increase as the altitude is reduced, because it has to hold, so to speak, the weight of all the gas above it. That is the clue by which we may determine how the pressure changes with height. If we take a unit area at height h, then the vertical force from below, on this unit area, is the pressure P. The vertical force per unit area pushing down at a height h+dh would be the same, in the absence of gravity, but here it is not, because the force from below must exceed the force from above by the weight of gas in the section between h and h+dh. Now mg is the force of gravity on each molecule, where g is the acceleration due to gravity, and ndh is the total number of molecules in the unit section. So this gives us the differential equation Ph+dh−Ph= dP= −mgndh. Since P=nkT, and T is constant, we can eliminate either P or n, say P, and get
dndh=−mgkTn
for the differential equation, which tells us how the density goes down as we go up in energy.
We thus have an equation for the particle density n, which varies with height, but which has a derivative which is proportional to itself. Now a function which has a derivative proportional to itself is an exponential, and the solution of this differential equation is
n=n0e−mgh/kT.(40.1)
Here the constant of integration, n0, is obviously the density at h=0 (which can be chosen anywhere), and the density goes down exponentially with height.
Fig. 40–2.The normalized density as a function of height in the earth’s gravitational field for oxygen and for hydrogen, at constant temperature.
Note that if we have different kinds of molecules with different masses, they go down with different exponentials. The ones which were heavier would decrease with altitude faster than the light ones. Therefore we would expect that because oxygen is heavier than nitrogen, as we go higher and higher in an atmosphere with nitrogen and oxygen the proportion of nitrogen would increase. This does not really happen in our own atmosphere, at least at reasonable heights, because there is so much agitation which mixes the gases back together again. It is not an isothermal atmosphere.”
This IS the gravito-thermal GHE/temperature gradient as first described by Maxwell in ~1872

Chic Bowdrie
July 27, 2015 10:13 am

Frank,
Re: Feyhman’s argument for an isothermal atmosphere which based on hockeyschtick’s last comment is preliminary(?), there would be no perpetual motion. In his thought experiment, the initial energy from the lower more energetic “balls” would readily establish a new* equilibrium with distribution up the column determined by -g/Cp*.
On the second matter you raised, the surface of the planet never gets in radiative equilibrium with the sun, so convection would be a daily occurance on an N2 planet just like our own.

Joe Born(@jhborn)
July 29, 2015 5:12 am

RGB and DeWitt have made similar arguments: Since one can extract work from any temperature difference, if a temperature gradient develops spontaneously, you have a perpetual source of energy. Some other work I have done agrees.

—Frank
That’s an example of why critical thinkers mistrust scientists.
It is trivial to show that an isolated single molecule bouncing around in a gravitational field exhibits a kinetic-energy gradient of mg. It’s slightly less trivial to show that the gradient is less for two molecules, but it can probably be done if you put your mind to it. More arduous is Velasco et al.’s demonstration that for 10^23 molecules it is much, much less. The gradient is so small that even in principle it would probably take on the order of a lifetime to measure: it certainly is much less than the adiabatic lapse rate, for which hockeyschtick argues.
But it is not zero, so the proofs to which Frank refers are flawed; they are based on the proposition that any gradient at all, no matter how small, can be made to drive perpetual motion. They make a qualitative argument: any gradient at all is impossible because it could drive perpetual motion. But that’s just not true. Just as the single-molecule system exhibiting the mg gradient could not drive perpetual motion, the mole-sized system exhibiting the Velasco-derived non-zero gradient couldn’t, either.
The proper argument is quantitative: it shows what the equilibrium gradient is and that it is therefore much less than the adiabatic lapse rate.
DeWitt Payne has tried to wriggle out of that dilemma by playing with the definition of temperature, but in attempting to show that there’s no need to rely on Velasco et al. he unwittingly does use Velasco et al.’s result.
Unfortunately, the various flavors of that perpetual-motion proof are such a farrago of latent ambiguities, unfounded assumptions, and, occasionally, just bad physics that dealing with it thoroughly would probably take a dozen pages. So that bad penny will continue to turn up.

Frank
July 26, 2015 12:42 am

Hockystick, Crispin and Mike: The concept of blackbody radiation only applies to radiation that has come into equilibrium with matter. (The original derivation of Planck’s Law postulates radiation in equilibrium with quantized oscillators. The early experiments with black cavities with a pin hole were designed to produce such an equilibrium.) Radiation of some wavelengths comes into equilibrium with some GHGs in the lower atmosphere, but the atmosphere is often not in equilibrium with the radiation passing through it. When equilibrium isn’t present, the Schwarzschild eqn is needed:
change in radiation = emission – absorption
dI/ds = n*o*B(lamba,T) – n*o*I_0
where dI is the incremental change in radiation intensity of wavelength lambda as it passes an incremental distance, ds, through a medium with a density n of absorbing/emitting molecules (GHGs), o is the absorption cross-section of wavelength lambda, I_0 is the intensity of radiation entering the ds increment, B(lambda,T) is the Planck function, and T is the local temperature. In the laboratory, I_0 comes from a filament at several thousand degrees, so the emission term is negligible and Beer’s Law for absorption results. If equilibrium is present, dI/ds is 0 and I_0 = B(lambda,T), producing blackbody radiation.
Radiative transfer calculations (in climate models, MODTRAN and elsewhere) use the Schwarzschild equation, typically integrating along a path from the surface to space (OLR) or space to the surface (DLR). Since n, T and I_0 vary with altitude, numerical integration is required. Integration of the Planck function over all wavelengths gives the Stefan-Boltzmann equation. Integration of the Schwarzschild equation over all wavelengths takes into account variations in absorption cross-section (line strength) with wavelength. As long as temperature drops with altitude, B(lambda,T) will be less than I_0 and dI/ds will increase with n – producing a GHE.
So emission from GHGs varies with n*o*B(lambda,T). Sometimes people say the the emissivity of a gas is proportional to the amount of GHG it contains, but this isn’t strictly correct. When the gas is dense or “optically thick”, emission approaches blackbody intensity. When the gas is less dense or “optically thin”, emission is proportional to the quantity of GHG it contains. These are limiting cases, not generalizations.

Ian Macdonald
July 26, 2015 3:26 am

It seems to be unsettled as to whether there is any interchange of energy between random thermal collisions of bulk gas molecules, and CO2 molecular vibration. Do you have any suggestions on that aspect?
Though, such interactions aside, infrared fluorescence is a very different mechanism from black body radiation. One depends on infrared flux in a relatively narrow band as its energy source and only emits in the same narrow band; the other depends on bulk temperature as its energy source, and has an output spectrum which changes with temperature.
The fact that a bulk N2/CO2/H2O gas mix is not a black body is easily proven by the observation that a stoichiometric blowtorch flame does not significantly heat objects to its side, but strongly heats objects in its convection path. In this case the gas has a higher than normal amount of CO2 from the combustion process, of course, yet its infrared radiation is still minimal, certainly way below that of a lump of iron at the same temperature.
Dial down the air/oxy and you then have a bright white flame and significant IR emission to the sides. This is because the flame now contains solid carbon particles which act as black bodies. Or, a candle shows the same effect.
I realise that the very short photon path length in the flame example makes it nonrepresentative of miles of atmosphere, but it does provide food for thought.

Phil.
July 26, 2015 9:22 am

Ian Macdonald July 26, 2015 at 3:26 am
It seems to be unsettled as to whether there is any interchange of energy between random thermal collisions of bulk gas molecules, and CO2 molecular vibration. Do you have any suggestions on that aspect?

It’s not unsettled, in fact in the lower atmosphere such collisions are the major mode of energy transfer from a vibrationally excited CO2 molecule, at higher altitudes the loss by emission becomes more likely.

July 26, 2015 10:40 am

“As long as temperature drops with altitude, B(lambda,T) will be less than I_0 and dI/ds will increase with n – producing a GHE.”
Got your cause mixed up with the effect:
Lapse rate dT/dh = -g/Cp
Temperature drop with altitude is a function of gravity and *inversely* related to heat capacity at constant pressure Cp.
GHGs increase heat capacity Cp, inversely related to temperature change.
In addition, GHGs preferentially transfer heat by collisions with N2/O2, thereby accelerating negative-feedback convection/surface & atmospheric cooling.
The 68K tropospheric temperature gradient [gravito-thermal GHE] is a consequence of the Maxwell/Clausius/Carnot atmospheric mass/gravity/pressure/density GHE, and low-energy photons at < 220K emission temperatures from GHGs is the effect, not the cause, of the GHE. (Proven by the 1976 US Std Atm, the HS greenhouse equation, Chilingar, Kimoto, Maxwell, Clausius, Carnot, et al)

July 26, 2015 1:15 pm

Very good points Ian re “Though, such interactions aside, infrared fluorescence is a very different mechanism from black body radiation. One depends on infrared flux in a relatively narrow band as its energy source and only emits in the same narrow band; the other depends on bulk temperature as its energy source, and has an output spectrum which changes with temperature. The fact that a bulk N2/CO2/H2O gas mix is not a black body is easily proven by the observation that a stoichiometric blowtorch flame does not significantly heat objects to its side, but strongly heats objects in its convection path. In this case the gas has a higher than normal amount of CO2 from the combustion process, of course, yet its infrared radiation is still minimal, certainly way below that of a lump of iron at the same temperature.”
Exactly! And climate science since Manabe, Cess, Hansen, et al up to the present have falsely assumed that GHGs are true blackbodies that obey physical laws for blackbodies including a constant emissivity of 1.0 that doesn’t change with temperature. The false assumption of constant εeff (and others) has led to an exaggeration of the critical Planck feedback parameter. The whole CAGW hysteria is due to these math errors and unphysical, false assumptions.

Frank
July 26, 2015 3:46 pm

Ian MacDonald wrote: “It seems to be unsettled as to whether there is any interchange of energy between random thermal collisions of bulk gas molecules, and CO2 molecular vibration. Do you have any suggestions on that aspect?”
There are a fair number of mis-informed people who don’t realize that GHGs are excited and relaxed (“de-excited” or “thermalized”) by collisions with other molecules. Excitation usually involves the lowest excited vibrational state and/or many rotational states. Excitation and relaxation also occurs by absorption and emission of a photon. The collisional and radiative processes COMPETE with each other. The rate of excitation by absorption depends on the intensity of the local radiation, while excitation by collision depends on temperature and density/altitude. The rate of relaxation by photon emission depends on temperature (B(lambda,T)), while relaxation by collision depends temperature and density/altitude.
In the lower and middle atmosphere (troposphere and stratosphere), collisions DOMINATE excitation and relaxation. The fraction of molecules in an excited state(s) therefore depends ONLY on temperature – not absorption of photons. This is called Local Thermodynamics Equilibrium or LTE, a term that is widely misinterpreted. (The upper atmosphere is not in LTE, but the upper atmosphere doesn’t effect our climate and can be ignored. For more info, see Grant Petty’s text, “A First Course in Atmospheric Radiation” p126-127. (The book has nothing to do with climate change and is worth the \$40 is costs.)
To put it rudely, anyone who talks about “RE-EMISSION” of absorbed photons in the troposphere is MISLEADING you. 99% of the excited GHG molecules there were excited by a collision and 99% will be relaxed by a collision before they can emit a photon. Anyone talking about black- or gray-body radiation – with emission proportional to T^4 – by definition is discussion an emitter in LTE. Re-emission is important in lasers, fluorescent lights, the upper atmosphere, and a negligible fraction of relaxations in the troposphere.
Finally, you can WATCH collisional excitation of gas molecules at the website below, which simulates the behavior of a two-dimensional gas. Choose the diatomic “Preset”, which clearly shows interconversion of rotational and translational energy by collisions. To unambiguously see translational energy being converted to vibrational energy, you need to select a smaller box, fewer molecules (you need to manually add bonds), higher temperature and slow down the action (time step and steps per frame).
http://physics.weber.edu/schroeder/md/InteractiveMD.html

The other Phil
July 25, 2015 11:06 am

You said
“Humans cause numerous other radiative forcings, both positive (e.g. other greenhouse gases) and negative (e.g. sulfate aerosols which block sunlight). Fortunately, the negative and positive forcings are roughly equal and cancel each other out, and the natural forcings over the past half century have also been approximately zero”
Presumably you meant “negative and positive forcing other than CO2”

Willis Eschenbach(@weschenbach)
Editor
July 25, 2015 11:15 am

Thanks, Mike, this is interesting. However, you need to be clear about your assumptions. You are ASSUMING that the climate does not respond or react to a change in forcing in any but the most mechanical of manners. In particular you are assuming that tropical clouds do not change despite a temperature change, which to me is a totally untenable claim, as it has been demonstrated by myself and others that the tropical clouds increase with increasing temperatures.
As a result, I fear that you are not describing the real world. Instead, you are investigating the math of Modelworld, which is an interesting world to be sure but which only intersects very occasionally with the real world. So I fear that your quest will ultimately be somewhat fruitless, as your conclusions will NOT apply to the real world.
This is not to say that they won’t be interesting, they already are. And it is not to say that they won’t reveal things about Modelworld, they may do that.
It’s just that the way you’ve set it up, your conclusions won’t tell us anything about the real world ….
w.

AndyZ
July 25, 2015 11:28 am

What need is there for the real world when you have models though…

Mike Smith
July 25, 2015 11:33 am

Maybe. Let’s wait and see what Mike has to say in parts II through IV 🙂

richardscourtney
July 25, 2015 12:55 pm

Willis Eschenbach:
You say to Mike Jonas

As a result, I fear that you are not describing the real world. Instead, you are investigating the math of Modelworld, which is an interesting world to be sure but which only intersects very occasionally with the real world. So I fear that your quest will ultimately be somewhat fruitless, as your conclusions will NOT apply to the real world.
This is not to say that they won’t be interesting, they already are. And it is not to say that they won’t reveal things about Modelworld, they may do that.
It’s just that the way you’ve set it up, your conclusions won’t tell us anything about the real world ….

The climate models are part of the “real world”, and their projections are being touted as useful indications of future climate.
Hence, consideration of the performance of climate models can provide very important conclusions concerning the part of the “real world” which you call “Modelworld”.
Richard

Mike Jonas(@egrey1)
Editor
July 25, 2015 3:46 pm

Hi Willis. I think you are correct when you say that I am “ASSUMING that the climate does not respond or react to a change in forcing in any but the most mechanical of manners” and that I am “not describing the real world”, but all I am doing is working on what is in the models. Please see the Footnote in the article – “It is important to recognise that the formulae used here represent the internal workings of the climate models.”.

Willis Eschenbach(@weschenbach)
Editor
July 25, 2015 10:04 pm

Thanks, Mike. I just wanted to emphasize that there are two worlds, Model World and Real World, and you are describing what goes on in Model World.
w.

Berényi Péter
July 25, 2015 11:24 am

It is important to recognise that the formulae used here represent the internal workings of the climate models.

Okay. Tell me something Jonas. According to the internal workings of the climate models which part of the climate system is supposed warm at a higher rate?
1. surface
2. troposphere

Mike Jonas(@egrey1)
Editor
July 25, 2015 3:56 pm

From memory, IPCC Report AR4 figure 9.1 (c) and (f) has the answer you seek (troposphere). But that’s at a level of detail that I don’t need here because in the end it all boils down into the ECS. And it doesn’t matter that the real troposphere didn’t actually do that, because in this article I am concerning myself here only with what is in the models.

Berényi Péter
July 26, 2015 1:26 pm

The image you are referring to is this:
It is in IPCC AR4
Climate Change 2007: Working Group I: The Physical Science Basis
9.2.2 Spatial and Temporal Patterns of the Response to Different Forcings and their Uncertainties
9.2.2.1 Spatial and Temporal Patterns of Response
If nothing else, it is quite clear from the presentation, that in the tropics much faster warming is expected in the upper troposphere, than at the surface, provided the temperature increase is caused by well-mixed greenhouse gases (c). Otherwise the pattern is different. That’s why the so called “tropical hot spot” is sometimes called a “fingerprint”.
Unfortunately the link to Supplementary Material, Appendix 9.C is broken, so no additional information is readily available.
According to the caption the pattern shown in the picture is “simulated by the PCM model”. Now, I do not have the slightest idea what the PCM model is. Neither have I information on how widespread this phenomenon is among computational climate models.
I ask you, because you seem to know this stuff. Also, a picture is not enough, the effect needs to be quantified.
And, ofcourse, it does matter if the real troposphere didn’t actually do that. That’s how science works. You compare theory to observations and if they do not match, with no explanation whatsoever, the theory is wrong. At which point people stop listening.
The “tropics” is usually defined as a stripe between 20N &. 20S. It’s not a narrow band, it is actually more than one third of the surface area of the globe.
We have actual data for this area for 36 years and a half, from January 1979 to June 2015.
surface: NOAA
From satellite observations I used TLT (Temperature Lower Troposphere) and TMT (Temperature Mid Troposphere) data. Both measure the average temperature of a quite thick layer of the troposphere.
http://images.remss.com/figures/measurements/upper-air-temperature/wt_func_plot_for_web_2012.all_channels2.png
But TLT has a lower average elevation (~3.5 km) than TMT (~7 km).
Now, let’s see observations for the tropical band:

       surface     TLT          TMT
land   198     199    99    123    83
ocean   85      73   101     37    84
both   111     102   101     57    84


The values are warming rates in mK/decade for the last 36.5 years.
Uncertainties are quite large, but one thing is clear. The pattern emerging from observations is absolutely inconsistent with theoretical predictions.
In general, the higher up one goes, the lower the rate of warming is, in stark contrast with theory.
There may be several explanations.
1. Theory is correct, however, warming is not caused by well mixed GHGs, but something else.
2. Theory is dead wrong and all computational models based on it belong to the trash can.
In either case, your analysis is irrelevant. No meaningful ECS can be derived from false premises ever.

Mike M.
July 25, 2015 11:30 am

Mike Jonas,
You wrote: “even if we were to immediately stop adding CO2 to the atmosphere, the planet would warm another ~0.6°C until it reached this new equilibrium state (confirmed by Hansen 2005). This is referred to as the ‘warming in the pipeline’.”
But that is not true. The oceans are a big heat sink, but they are also a big CO2 sink. So if we stop emitting CO2, the amount of CO2 in the atmosphere will start to drop, roughly cancelling out the effect of deep ocean T slowly rising. There is negligible warming in the pipeline.
If we were to reduce CO2 emissions to the level required to maintain a constant elevated atmospheric CO2, we would get the warming you describe. But, IMO, that additional warming should be properly attributed to the additional CO2 emitted.

Mike Jonas(@egrey1)
Editor
July 25, 2015 4:06 pm

Regrettably, there is a formatting problem in the article as posted. The original used a different font for stuff that I quoted vs my own stuff. This bit was quoted from SkS. After “A method for calculating the temperature contribution by CO2 is given by SkS in [6] :“, everything was a quote from SkS down to and including the word “pipeline”.
So they were SkS’s words, not mine.
[Italicized the section as indicated above. .mod]

Mike Jonas(@egrey1)
Editor
July 25, 2015 5:16 pm

mod – thanks. Please can you check Parts 2-4 as they post, because there are some long quotes in those too. TIA.
[Edits will occur only on your direction. .mod]

Walt D.
July 25, 2015 4:24 pm

. So if we stop emitting CO2, the amount of CO2 in the atmosphere will start to drop.This can not be assumed. If China doubling its CO2 production has produced no effect on the rate of increase in total CO2, then we can not assume that cutting CO2 will have any affect at all.

fonzarelli
July 25, 2015 5:34 pm

Walt, you are so right… Carbon growth has been in lock step with temperature since the inception of the mauna loa data set. [note the omission of corresponding cooling in the early 90s due to pinatubo (at 15 degrees north latitude) as this is southern hemispheric data…]
The rate of human emissions has no impact on carbon growth whatsoever. China can build as many factories as it wants, it will have no impact on carbon growth. Conversely humanity can cut back on carbon and it will have no impact on carbon growth either. AND it remains to be seen what carbon growth would be were there no human emissions at all…

Bart
July 26, 2015 10:41 am

Well, there might be some level of production that would begin to significantly affect atmospheric levels. But, we are a long way from that.

gymnosperm(@gymnosperm)
July 25, 2015 8:40 pm

“The oceans are a big heat sink, but they are also a big CO2 sink.”
Not in a warming regime. The oceans are currently a nominal one GtC sink. If the El NONO pans out the future could be flat or even positive.

Bart
July 26, 2015 10:44 am

There is no evidence which establishes that the oceans are a net sink, unless one invokes the wretchedly bad “mass balance” argument, which is based on completely circular logic.

gymnosperm(@gymnosperm)
July 26, 2015 12:51 pm

There is also no evidence that the oceans are sinking any “heat” from the atmosphere.
There is a problem however with the Carbon isotopic balance of the atmosphere. U. Steigenthaler and K.O. Munnich,http://globalecology.stanford.edu/SCOPE/SCOPE_16/SCOPE_16.html, measured air-sea and sea-air fractionation at +2 and -10 respectively net to atmosphere PDB.
The fundamental problem with an isotope integrated Carbon cycle is that the atmosphere wants to go negative ridiculously (orders of magnitude) too fast. You have to do stuff like dump so much Carbon into vegetation that vines would be crawling through windows to balance it.
I exaggerate, and it can be done assuming that plants fractionate both in and out, but it is a very delicate balance and the one Gt net sink at +2 to the atmosphere is very helpful. If the ocean were a net source at -10, isotopically balancing the atmosphere becomes impossible very quickly.

Pamela Gray(@pamelasuemakin)
July 25, 2015 11:42 am

Assumptions not supported also include the idea that oceans are so uncomplicated they are unable to hold heat for later distribution and that what goes in always comes back out in equal measure almost immediately in terms of a century of data. Both camps now question that assumption, that indeed the oceans have the capacity to absorb and release heat in short as well as longterm timescales such that the oceans and their teleconnections with atmospheric processes create the very noisy random walk data set of temperatures. This emerging acceptance of reality then requires the use of error bars before any current temperature can be compared to a long term climate average before knickers are twisted and panties bunched.

July 25, 2015 12:13 pm

True, the basic physics of heat dissipation, heat capacity, and the 2nd LoT explain why the ‘missing heat’ can’t pop out & say “Boo!”
http://hockeyschtick.blogspot.com/search?q=pop+out+boo

markl
July 25, 2015 11:48 am

The title of this article should be changed to “The Mathematics of One Climate Model”. How the modelers (for lack of a better term) can consistently support their models when none have come close to reality is beyond me. Are the forces behind them so strong and persuasive that they are willing to overlook facts that are readily available? It’s like a cult.

July 25, 2015 12:43 pm

It is a cult – GAIA is our mother and we must protect her from the evil plague of human infestation.

roaldjlarsen(@roaldjlarsen)
July 25, 2015 12:38 pm

What a funny world they live in. I wonder if they ever get to go out ..
Meanwhile, in the real world, it’s getting colder as the rest of us have to deal with the reality of a new ice age in one form or another.

Lance Wallace
July 25, 2015 12:38 pm

This is a very curious article, quoting Wikipedia, the SS kids, and IPCC 2007 for the basic model. The author states:
“Studies have given a possible range of values of 2-4.5°C warming for a doubling of CO2 (IPCC 2007).”
But more recent studies, dating from Otto et al and Nic Lewis, suggest the best estimate is more like 1.6, completely outside the reported range.
Perhaps the author will be discussing this in future parts, but right now he seems to exist sometime in the previous decade.

Mike Jonas(@egrey1)
Editor
July 25, 2015 4:35 pm

Because I am here trying to establish what’s inside the models, the aim is to use material that reflects what’s in the models, hence Otto et al and Nic Lewis aren’t relevant at this point. It’s not that they are wrong, it’s that they aren’t in the models and don’t reflect what’s in the models. In the rest of this series, I do get out to have a look at the real world!

richardscourtney
July 25, 2015 12:45 pm

Mike Jonas:
Thankyou for the first in your series of intended articles. I write to point out that you have already falsified the assumptions in the models with resulting falsification of the models’ projections.
You say

Plugging in our possible climate sensitivity values, this gives us an expected surface temperature change of about 1–2.2°C of global warming, with a most likely value of 1.4°C. However, this tells us the equilibrium temperature. In reality it takes a long time to heat up the oceans due to their thermal inertia. For this reason there is currently a planetary energy imbalance, and the surface has only warmed about 0.8°C. In other words, even if we were to immediately stop adding CO2 to the atmosphere, the planet would warm another ~0.6°C until it reached this new equilibrium state (confirmed by Hansen 2005). This is referred to as the ‘warming in the pipeline’.

Yes, but the ‘warming in the pipeline’ aka ‘committed warming’ has failed to materialise.
IPCC AR4 (2007) Chapter 10.7 can be read at
http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch10s10-7.html
and says

The multi-model average warming for all radiative forcing agents held constant at year 2000 (reported earlier for several of the models by Meehl et al., 2005c), is about 0.6°C for the period 2090 to 2099 relative to the 1980 to 1999 reference period. This is roughly the magnitude of warming simulated in the 20th century. Applying the same uncertainty assessment as for the SRES scenarios in Fig. 10.29 (–40 to +60%), the likely uncertainty range is 0.3°C to 0.9°C. Hansen et al. (2005a) calculate the current energy imbalance of the Earth to be 0.85 W m^-2, implying that the unrealised global warming is about 0.6°C without any further increase in radiative forcing. The committed warming trend values show a rate of warming averaged over the first two decades of the 21st century of about 0.1°C per decade, due mainly to the slow response of the oceans. About twice as much warming (0.2°C per decade) would be expected if emissions are within the range of the SRES scenarios.

In other words, it was expected that global temperature would rise at an average rate of “0.2°C per decade” over the first two decades of this century with half of this rise being due to atmospheric GHG emissions which were already in the system.
This assertion of “committed warming” should have had large uncertainty because the Report was published in 2007 and there was then no indication of any global temperature rise over the previous 7 years. There has still not been any rise and we are now way past the half-way mark of the “first two decades of the 21st century”.
So, if this “committed warming” is to occur such as to provide a rise of 0.2°C per decade by 2020 then global temperature would need to rise over the next 5 years by about 0.4°C. And this assumes the “average” rise over the two decades is the difference between the temperatures at 2000 and 2020. If the average rise of each of the two decades is assumed to be the “average” (i.e. linear trend) over those two decades then global temperature now needs to rise before 2020 by more than it rose over the entire twentieth century (it only rose ~0.8°C over the entire twentieth century).
Simply, the “committed warming” has disappeared (perhaps it has eloped with Trenberth’s ‘missing heat’?).
This disappearance of the “committed warming” is – of itself – sufficient to falsify the AGW hypothesis as it is emulated by climate models. If we reach 2020 without any detection of the “committed warming” then it will be 100% certain that all projections of global warming are complete bunkum.
Richard

gymnosperm(@gymnosperm)
July 25, 2015 8:57 pm

Yes, and the mechanism of the lag is not only the thermal inertia of the water but the inefficiency of air/water thermal transfer. There are only a few places on earth, if any, where the atmosphere is warmer than the water.

milwaukeebob
July 25, 2015 12:51 pm

Is this a Saturday spoof? It’s not April 1 – is it? The reason I ask is because IF the “math” represented is internal to the climate models, then the title is wrong. Yes, it’s a given the writer of a post gets to pick the title and one can assume the title will be as “reader inducing” as possible, but this one should read, “The CO2 Math Assumptions as used in Computer Climate Models” or at worst “CO2 Math Assumptions used in Computer Climate Models” or better “Is the CO2 Math used in Climate Computer Models Good Enough?” My point is – HOW, in this REAL world, at this point can we take this post seriously when “the whole series of articles is based on the premise that the climate computer models are correct”???

Mike Jonas(@egrey1)
Editor
July 25, 2015 4:43 pm

It’s a technique used by mathematicians – hence the title – you test an assertion (in this case the role of CO2 in the climate models) by assuming it is correct and see where it takes you. There is more to come…..

Bill Illis
July 25, 2015 12:53 pm

A very simple formula is:
Temp C Increase = 4.328*ln(CO2ppm) – 24.39
This is derived from the global warming theory and the 5.35 ln formulae. You can plunk any CO2 number into that formula and it will provide the the expected temperature increase at 3.0C per doubling (not including any lags). If you want it with the lags, well, the climate prophesy community changes the formula every time they run another set of climate model projections.
Temp C increase = 4.328*ln(560 ppm) – 24.39 = 3.0C
Temp C increase = 4.328*ln(400 ppm today) – 24.39 = 1.54C (now we see why so much adjusting needs to go on).

July 25, 2015 1:07 pm

The pea under the thimble is the huge assumed cooling of aerosols, the perfect fiddle factor.

Richard Petschauer
July 25, 2015 1:04 pm

At least four serious problems.
1. Assuming the climate models are correct, which data proves they are not.
2 Unverified climate sensitivity (temp rise for 2x CO2). Much too high because uses of climate models values.
3. Assuming CO2 growth matches emission growth. Its about half as much because oceans and trees absorb about one half.
4. Since CO2 forcing is a ramp function (log of exponential CO increase), not a step function, ocean heat storage causes a delay in time not a constant reduction in temperature. So temp changes per decade approach the same value as without heat storage and we are close to that time now since the ramp of CO2 forcing started may years ago. Ocean heat storage can’t explain the pause anymore.

Richard Petschauer
July 27, 2015 8:36 pm

Correction: For a ramp function of forcing, does give a constant reduction in temperature in degrees C, which becomes a decreasing percent reduction with time.

bsl
July 25, 2015 1:19 pm

It was claimed in the article that natural variability is not important based on a 2004 article by Meehl. This article draws its conclusions based on 2004 era climate models with assumptions that may not be considered valid today. It is a stretch to consider natural variability to be unimportant based on this article.

Pamela Gray(@pamelasuemakin)
July 25, 2015 3:26 pm

Spot on. 4 marks.

Crispin in Waterloo
July 25, 2015 1:49 pm

“2. Mathematical error in the calculation of the Planck response parameter λ, due to a false assumption of fixed emissivity, an error which continues to be promulgated by the IPCC (explained in section 3 of this Kimoto paper)”
This is a fairly easy matter to settle and doesn’t need us to calculate anything because it is a physical property. I think the issue will come down to the emission of different wavelengths with temperature, not something as simple as one narrow range. Whether such an effect can be observed over the tiny range expected in the coming century is suspect.
The important point in the Kimoto paper relates to the fixed assumptions of things that are not really fixed. That is fatal to the ‘standard’ calculations.
Willis’ point that the real atmosphere has strong negative feedbacks will not be dismissed easily. The effect of a drop in the tropospheric lapse rate from 6.5K/km to 6.3 K/km greatly changes the climate sensitivity but not the effect of thunderstorms or when they form.
The article seems to be written in a way that sets up the SkS version of reality to fail spectacularly.

July 25, 2015 1:58 pm

“This is a fairly easy matter to settle and doesn’t need us to calculate anything because it is a physical property. I think the issue will come down to the emission of different wavelengths with temperature, not something as simple as one narrow range. Whether such an effect can be observed over the tiny range expected in the coming century is suspect.”
I explained above why the emitting temperature of CO2 ~15 line-emission is “fixed” by physical chem/quantum theory to an emitting temp of ~193K. Climate scientists/modelers ever since Manabe et al have falsely assumed CO2 can radiate at emitting temperatures >193K and their papers show CO2 falsely emitting at temps up to 330K. This is physically impossible.
http://wattsupwiththat.com/2015/07/25/the-mathematics-of-carbon-dioxide-part-1/#comment-1993244
“The important point in the Kimoto paper relates to the fixed assumptions of things that are not really fixed. That is fatal to the ‘standard’ calculations. Willis’ point that the real atmosphere has strong negative feedbacks will not be dismissed easily. The effect of a drop in the tropospheric lapse rate from 6.5K/km to 6.3 K/km greatly changes the climate sensitivity but not the effect of thunderstorms or when they form. The article seems to be written in a way that sets up the SkS version of reality to fail spectacularly.”
Agreed.

Phil.
July 26, 2015 9:26 am

hockeyschtick July 25, 2015 at 1:58 pm
“This is a fairly easy matter to settle and doesn’t need us to calculate anything because it is a physical property. I think the issue will come down to the emission of different wavelengths with temperature, not something as simple as one narrow range. Whether such an effect can be observed over the tiny range expected in the coming century is suspect.”
I explained above why the emitting temperature of CO2 ~15 line-emission is “fixed” by physical chem/quantum theory to an emitting temp of ~193K. Climate scientists/modelers ever since Manabe et al have falselycorrectly assumed CO2 can radiate at emitting temperatures >193K and their papers show CO2 falselycorrectly emitting at temps up to 330K.

See explanation above.

July 26, 2015 1:29 pm

Phil. falsely claims “Manabe et al have correctly assumed CO2 can radiate at emitting temperatures >193K and their papers show CO2 correctly emitting at temps up to 330K.”
Phil. Phil Phil, the ~15um centered CO2 photons cannot increase their frequency/decrease their wavelength/increase their quantum energy beyond the “equivalent” TRUE blackbody emitting at 15um and 193K!

co2islife
July 25, 2015 2:11 pm

Here are some mathematics I’d like you to review. This is the chart used by the warmists to make the case that CO2 is the major GHG resulting in global warming.
http://www.john-daly.com/kunde74.gif
The problem is that the black body curves don’t match what comes out of a calculator.
http://www.hashemifamily.com/Kevan/Climate/BBR.gif
A true black body curve for temperature 288°K would have a peak at 10µ, not 15µ. What is the difference in atmospheric absorption between the curve that peaks at 10µ, and 15µ Does the skewing and kurtosis materially alter the amount of atmospheric absorption attributed to CO2 and H2O?

July 25, 2015 3:05 pm

Climate science has confused cause with effect. The cause of the 33C GHE from the ERL to surface, as well as the even larger negative 35C anti-greenhouse effect from the 255K ERL to tropopause at 220K is the gravito-thermal Maxwell/Clausius/Carnot greenhouse effect. Radiation from GHGs is the effect, not the cause of the gravito-thermal GHE. If you look at your first chart above, the “hole in the middle” is from GHGs H2O & CO2 ~13-17 microns (mostly H2O BTW) which “corresponds” to a blackbody temp ~215K. Although CO2 & H2O have a fixed emissivity less than true blackbodies, nonetheless, a blackbody at a peak emitting temp of 215K cannot warm any bodies at > 215K.
http://hockeyschtick.blogspot.com/2014/12/why-atmospheric-temperature-is-linear.html

Michael Hammer
July 25, 2015 3:39 pm

Hockeyschtick I am getting very tired of hearing this erroneous comment. Its based on a misconception. The object in question (planet Earth) is constantly receiving energy from an outside source the sun. Its temperature is determined (at least in part) by the rate at which it can lose energy. If that energy loss is impeded then Earth will be warmer than it would otherwise be. In this case, without GHG the Earth would be radiating to outer space (sink temperature 4K) whereas with GHG it is radiating to the GHG layer temperature 215K. In the latter case the energy loss is reduced (not reversed which you claim rightly is not possible) so the Earth ends up warmer. The surface is still losing energy just not quite as much.
A simple experiment, you go outside on a cold still night and rapidly start to feel cold. So you go back into the house which is at an average temperature of say 19C and almost immediately you start to feel warmer. Your body temperature is 37C and the room is only 19C so according to your comment the room cannot possibly be warming you yet you feel warmer. The reason is simple, you do not feel warmer because your metabolic rate abruptly increased, you feel warmer because you are losing less heat to the environment.
Another example, you feel cold in bed so you get up and put on a blanket, now you feel much warmer. But the blanket is a completely passive device, no internal energy source so it certainly cannot pass net energy to you – where would the energy come from? If we measure the temperature of the blanket its less than 37C so its colder than you are yet still we would say it warms you. Ahh but maybe you claim this is simply due to reducing convection. OK try a modification. Use a sheet of clear mylar and see how much it warms you, then use a sheet of mylar coated with a reflective layer of aluminium (sold as space blankets). The reflective coated mylar keeps you much warmer yet both the coated and uncoated sheets have the same effect on convection.

July 25, 2015 3:59 pm

Well, I’m getting very tired of hearing erroneous comments based on the misconception that GHGs limit convection, which they do not, and which is the misconception that the greenhouse effect is has anything to do with a real greenhouse, blankets, insulation in the attic, etc. ALL of which work by limiting convection, NOT “radiative forcing.” In actuality, GHGs INCREASE convection by preferentially transferring kinetic energy/HEAT to non-IR active gases 99.9% of the atmosphere, which INCREASES the rate of negative-feedback, cooling convection. In addition, the wet adiabatic lapse rate is 1/2 the dry, proving from observations that water vapor is a negative-feedback cooling agent.
You obviously have no clue about basic physical chemistry/quantum theory which places an absolute upper maximum upon the emitting temperatures of GHGs line-emissions. For CO2 ~15um emission the maximum possible emitting temp is 193K, IF CO2 was a true blackbody, which it is not (it emits less than a true BB at 193K).
You also have no clue that a body radiating at 193K cannot warm/transfer heat energy/increase the frequency of any body at a higher frequency/temperature/energy exceeding 193K.

Mike Jonas(@egrey1)
Editor
July 25, 2015 4:49 pm

Suppose that I am some infra-red leaving Earth as a result of it having been warmed by the sun. To my horror I discover that I am heading straight for the sun, and hence that my energy will be added to the sun’s, thus warming it (not by much, I admit) in contravention of the laws of science as interpreted by you. I’ve only got a few minutes to work out how to miss the sun. Please, how do I do it?

July 25, 2015 5:03 pm

Radiation is BI-directional between bodies, but can only be thermalized by bodies at a lower frequency/temperature/energy than the source’s emitting temperature. This is very basic quantum theory, and explains why HEAT ENERGY cannot be transferred from a cold to warmer body. The only thing a photon “knows” is its frequency/wavelength/energy content E=hv. A low-E/temperature photon cannot raise any electrons to higher orbitals in a higher E/T/frequency/warmer body, ie radiation is received by warmer bodies but cannot be thermalized/increase HEAT content/increase electron orbital heights of warmer bodies, given both quantum theory and the 2nd LoT.

July 25, 2015 5:19 pm

Thank you hockeyschtick! I’m also getting tired of this pseudo science.
Increased absorbtion means increased emission. Cold things can’t make warm things warmer. The mean temperature of the atmosphere is 255K. Temperature gradients are nicely and simply explained without the need for a Greenhouse Effect.

Michael Hammer
July 25, 2015 9:05 pm

Hmmm Hockeyschtick; not sure why you put such weight on basic chemistry or quantum theory, the field for science covering this is spectroscopy and since I have spent the last 40 years doing research for a major international spectroscopy company I feel I have some right to at least claim some basic knowledge of spectroscopy.
You mention a lot about raising electrons to higher orbitals. I think you might be confusing atomic emission with molecular emission. Atomic emission is about electrons moving between orbitals but it occurs at significantly shorter wavelengths (typically in the visible or UV). The thermal IR is about molecular emission which is about energy absorbed in vibrational states of molecules.
You also stated at least twice that a GHG is a less than perfect black body emitter. In fact, a GHG column is probably the closest one can come to a black body emitter and that is extremely close. For example, the atmospheric column of CO2 is equivalent today to about 3000 absorbance. That means its emissivity (1 = black body, less than 1 is a worse emitter than a black body) will be 1-10^-3000. Thats 0. followed by 3000 9’s. Don’t know about you but to me that’s a fair approximation to 1 unless you habitually work to more than 3000 significant digits.
You claim the maximum possible emitting temperature of CO2 is 193K. Where on earth do you get that figure from. The emission temperature is simply the temperature of the gas and it emits according to Planks law for that temperature times its emissivity. If the gas layer is optically thin then it will have a low emissivity but if it is thick (say >2-3 abs) then its emissivity to all intents and purposes is 1.
Your point about convection is not something I commented on. You may or may not be right on this score but I don’t see the relevance to this particular discussion.
With regard to the core point of “can a cool body raise the temperature of a warmer body”. To try a different explanation. The amount of heat a body loses depends on the difference between its temperature and its environment. Without GHG the environment temperature is 4K, with GHG the environment is more like 220K (at 15 microns). The second case has a lower temperature difference and thus loses less energy.

July 25, 2015 9:55 pm

“You claim the maximum possible emitting temperature of CO2 is 193K. Where on earth do you get that figure from.”
From Wein’s Displacement Law, which is derived from Planck’s Law. CO2 15um line absorption/emission is “equivalent” to a blackbody peak emission temperature of 193K. Since CO2 is a mere line-emitter at that fixed wavelength which obviously does not change regardless of concentration, does not have a Planck curve, and is not a true blackbody, the emissivity is less than a true blackbody at 193K, and the emissivity goes down with temperature. The reason why emissivity of GHGs goes down with temperature is the fixed emitting temperatures of their spectral lines. I already showed observations of this further up the thread, so won’t repeat that again.
CO2 photons at 15um/193K emitting temperature cannot transfer HEAT ENERGY to any body > 193K with a higher frequency/shorter wavelength/higher temperature/higher energy E=hv. Do you understand the difference between heat and radiation? Radiation from a lower frequency/temperature/energy body cannot be thermalized by a higher frequency/temperature/energy body. This is very basic quantum theory/physical chemistry/radiative theory.
With CO2 + H2O combined in our atmosphere (and which substantially overlap), the emitting temperature is ~215K as seen from space. Radiation from a 215K body cannot be thermalized/warm any body > 215K, including all geopotential altitudes of the troposphere, tropopause, and stratosphere which are all > 215K on global average.

Michael Hammer
July 26, 2015 2:33 am

Sorry hockeyschtick, but you are misinterpreting the meaning of Weins law. It simply specifies the wavelength at which the emission per unit wavelength of a black body peaks. Thus at 193K a black body (at all wavelengths) emits more energy per micron at 15 microns than at any other wavelength. With rising temperature the emission at all wavelengths increases but the emission at shorter wavelengths rises faster than at longer wavelengths so the peak of the emission curve (ie: the peak of Planks law plot) shifts to shorter wavelengths. You can see that if you look at the plots posted by CO2islife at 2:11 pm. Going from 210K to 290K the emission intensity at 15 microns increases monotonically with increasing temperature however while the peak of the emission curve is at about 13 microns at 210K it moves to around 10 microns as 290K. All Weins law states is the wavelength at which Planks law peaks. To re-iterate, the peak of the emission curve moves to shorter wavelengths with increasing temperature but the actual emission intensity at all wavelengths increases with increasing temperature.
By the way, in case you think I am a proponent of AGW or CAGW, I should point out I am very strongly skeptical and you can probably find several posts on the web which makes that abundantly clear – try Jennifer Marohasy’s website. I do however stand first and foremost for correct science wherever it leads.

Phil.
July 26, 2015 9:33 am

hockeyschtick July 25, 2015 at 5:03 pm
Radiation is BI-directional between bodies, but can only be thermalized by bodies at a lower frequency/temperature/energy than the source’s emitting temperature. This is very basic quantum theory, and explains why HEAT ENERGY cannot be transferred from a cold to warmer body. The only thing a photon “knows” is its frequency/wavelength/energy content E=hv. A low-E/temperature photon cannot raise any electrons to higher orbitals in a higher E/T/frequency/warmer body, ie radiation is received by warmer bodies but cannot be thermalized/increase HEAT content/increase electron orbital heights of warmer bodies, given both quantum theory and the 2nd LoT.

Yet another fundamental error by you. A photon of wavelength corresponding to the energy gap between two energy levels can be absorbed regardless of the temperature of the body from which it was emitted, as you point out it only ‘knows’ its frequency/wavelength/energy content. A 15micron photon emitted by the sun will reabsorbed by a CO2 molecule in just the same way as one emitted by the ice on the Antarctic plateau at 200K.

July 26, 2015 11:49 am

Phil. says “Yet another fundamental error by you. A photon of wavelength corresponding to the energy gap between two energy levels can be absorbed regardless of the temperature of the body from which it was emitted, as you point out it only ‘knows’ its frequency/wavelength/energy content.
Yet another misquote of what I’m saying to make your straw man argument. I’ve already stated a million times that transfer of radiation/waves/photons is BI-directional between hot and cold, but HEAT transfer is one-way only hot to cold. The reason is that all of the microstates in a warmer body are already saturated with the lower-energy microstates coming from a low-energy photon/wave, and therefore absorption of the lower-energy photon/wave cannot be thermalized.
Here’s why:
“A 15micron photon emitted by the sun will reabsorbed by a CO2 molecule in just the same way as one emitted by the ice on the Antarctic plateau at 200K.”
Of course, another straw man argument, the peak emission/absorption in LWIR of CO2 is at 193K. Therefore, CO2 will indeed absorb & emit radiation from 5800K Sun and from 200K ice in Antarctica. However, CO2 will not thermalize any peak 29um radiation from a 100K blackbody, i.e. heat energy cannot be transferred from cold to hot.
So, Phil., in an atmosphere at 300K, with any concentration of CO2 you prefer, what would the peak wavelength and emitting temperature of said CO2 be?

SkepticGoneWild
July 26, 2015 4:52 pm

Mike Jonas says:
“To my horror I discover that I am heading straight for the sun, and hence that my energy will be added to the sun’s, thus warming it”
OMG. Please tell me you are joking. The thing is, you forgot to complete your story. To your utter continuing horror, once you have warmed the sun, you are sent hurtling back to earth on a return mission, warming the earth even more, with the cycle repeating itself endlessly.
Alas, the First and Second Laws of Thermodynamics prevent this type of nonsense.

July 27, 2015 10:01 am

SkepticsGoneWild says: “Mike Jonas says:“To my horror I discover that I am heading straight for the sun, and hence that my energy will be added to the sun’s, thus warming it”
OMG. Please tell me you are joking. The thing is, you forgot to complete your story. To your utter continuing horror, once you have warmed the sun, you are sent hurtling back to earth on a return mission, warming the earth even more, with the cycle repeating itself endlessly.
Alas, the First and Second Laws of Thermodynamics prevent this type of nonsense.”
LOL exactly. And Mike Jonas, when your 193K CO2 photon reaches the 5800K Sun it does not warm by any infinitesimal amount the surface of the Sun. All of those much, much, much lower-energy microstates are already completely saturated in the Sun, therefore the 193K photon cannot be thermalized not increase the temperature of the Sun.

Michael Hammer
July 25, 2015 3:22 pm

Be careful CO2islife – your lower plot is for power density versus wavelength. The upper curve is for power density versus wave number. You cannot simply rescale the X axis to convert from one to the other. The two plots are fundamentally different (yes I know its confusing but its very real). The reason is that the vertical axis for one is watts/sqM/micron whereas the other is watts/sqM/wave number. 10 um equals 1000 wave numbers so a change of 1 wave number = 0.01 microns. 15 microns = 666 wave numbers so a change of 1 wave number = 0.022 microns. For the power density versus wave number plot, as one goes to lower wave numbers the equivalent interval in microns over which the power density is measured increases and that completely changes the shape of the plot.
If you check Planks formula expressed in wave number and wavelengths you will see the 2 formulae are completely different.

co2islife
July 25, 2015 4:36 pm

“Be careful CO2islife – your lower plot is for power density versus wavelength. The upper curve is for power density versus wave number. ”
Thanks for clarifying that:
Here are the two different black body graphs. This uses Wavenumber
http://www.spectralcalc.com/blackbody_calculator/plots/guest2081879440.png
This uses Wavelength:
http://www.spectralcalc.com/blackbody_calculator/plots/guest180013070.png

July 25, 2015 4:51 pm

CO2islife:
Additional background on why 193K CO2 photons cannot warm/transfer HEAT to 288K Earth:

Phil.
July 27, 2015 3:21 am

hockeyschtick July 26, 2015 at 11:49 am
So, Phil., in an atmosphere at 300K, with any concentration of CO2 you prefer, what would the peak wavelength and emitting temperature of said CO2 be?

The peak wavelength would be the Q-branch at ~667.5 cm-1 (14.98 micron) and the emitting temperature would be 300K.

July 27, 2015 10:16 am

Phil. July 27, 2015 at 3:21 am says, ”
hockeyschtick July 26, 2015 at 11:49 am
So, Phil., in an atmosphere at 300K, with any concentration of CO2 you prefer, what would the peak wavelength and emitting temperature of said CO2 be?
The peak wavelength would be the Q-branch at ~667.5 cm-1 (14.98 micron) and the emitting temperature would be 300K.”
Phil, the peak wavelength is indeed fixed at ~15um, and the “equivalent” peak radiative emitting temperature of a true blackbody perfect emitter with 15um peak emission is ~193K, not higher.
You only have to look to the OLR spectra for proof:
The fixed CO2 LWIR line emission is peaked at ~15um where the the OLR spectra shows the emitting temperature of a “corresponding” Planck curve is ~215-220K. This is despite the kinetic energy of the surrounding atmosphere being far higher than 220K. 220K is the minimum temperature of the tropopause. Radiation from a lower frequency/temperature/energy body cannot be thermalized by a higher frequency/energy/temperature body since all of the low-E microstates are already saturated.

Richard Petschauer
July 27, 2015 7:20 pm

Hockeyschtick,
Question: I have an infrared thermometer. If I open my kitchen freezer door, hold the device a few feet away so it is in the warm room and point it at the freezer, I get a temperature reading below freezing. How is this information being transferred?
It seems like something is transferring energy to the device, although less than if I point it at a wall in the room. This must be radiation, not conduction, convection or latent heat transfer..

July 27, 2015 8:18 pm

” It seems like something is transferring energy to the device, ”
Energy is transferring from the thermometer to the freezer.

July 28, 2015 11:56 am

Richard says, “Hockeyschtick,
Question: I have an infrared thermometer. If I open my kitchen freezer door, hold the device a few feet away so it is in the warm room and point it at the freezer, I get a temperature reading below freezing. How is this information being transferred?”
By the rate of IR loss from the thermometer to the freezer. IR thermometers use a thermister and the SB law (and falsely assume everything is a true blackbody absorber/emitter). They have a correction algorithm for IR heat loss from the thermister to an object so they can read objects at temps lower than the object.
The most accurate way to measure IR is to cool the detectors to a lower temp than the object being measured & thus no correction algorithm needed. This is what some of the professional, expensive pyrgeometers do.

Phil.
July 25, 2015 3:41 pm

You can’t compare the shape of the curve plotted as a function of wavelength with the one plotted as a function of wavenumber.

Richard Petschauer
July 27, 2015 9:00 pm

To Micro6500
From:
https://en.wikipedia.org/wiki/Infrared_thermometer
(My caps)
“An infrared thermometer is a thermometer which infers temperature from a portion of the thermal radiation sometimes called blackbody radiation emitted by the OBJECT BEING MEASURED.
The design essentially consists of a lens to focus the infrared THERMAL RADIATION on to a detector, which converts the radiant power to an electrical signal that can be displayed in units of temperature after being compensated for ambient temperature. This permits temperature measurement from a distance without contact with the object to be measured”:
Note: The atmosphere which consists of various greenhouse gases, does not act like a blackbody so the temperature will be less since the radiation will be less thsan a blackbody at the actual temperature at the effective altitude of the emission. For thick clouds it works good and can be used to estimate their approximate height by comparing with the surface temperature and using 6.5 C / km lapse rate.

July 28, 2015 4:24 am

” Note: The atmosphere which consists of various greenhouse gases, does not act like a blackbody so the temperature will be less since the radiation will be less thsan a blackbody at the actual temperature at the effective altitude of the emission. ”
But the 8u to 14u portion does look like a BB, it is true you do need to add the other forcing to it, but that is the measured temp for that band, because the thermometer doesn’t care what object it’s measuring, just how much IR there is.
It was about 5F this morning, iirc Co2’s forcing in total is about 22W/m^2, you can turn the 5F to watts/m^2 then add them together and turn it back to a temp, but it’s still very cold.

July 28, 2015 5:10 am

Actually it was -5F this morning, not 5F.
This is Concrete, Grass, Asphalt, Concrete, sky, concrete from ~7:00 pm yesterday, 9:00pm, 11:00pm, 6:30am right before the Sun came over the neighbors trees, and then ~8:00am
Once the Sun was on the grass, it’s temp was almost the same as the concrete (8:00am).

July 28, 2015 5:29 am

Here’s a more useful image
You can see air temps compared to surface temps. What you see is that air temps drop quickly, but surface temps lag considerably, in fact they never caught up to air temps before the Sun came up.
It’s also important to note that the length of the night from now till the end of December keeps getting longer, so there’s more time to cool the surface.

July 28, 2015 5:50 am

Measuring the Temperature of the Sky and Clouds – Page 2
Significance: Water vapor in the sky is responsible for the natural greenhouse effect that keeps the Earth warm enough for life to exist. Clouds formed from water vapor play a major role in controlling the temperature of the Earth. The activities in this project demonstrate that the open sky, while very cool, is much warmer than space and that cumulus clouds are much warmer than the sky.

July 26, 2015 9:53 am

“Sorry hockeyschtick, but you are misinterpreting the meaning of Weins law. It simply specifies the wavelength at which the emission per unit wavelength of a black body peaks.”
That is for TRUE blackbodies, but GHGs are not blackbodies, they are molecular-line-emitters without a Planck BB curve, although climate science incorrectly assumes that they are true blackbodies and have emissivity = 1 regardless of T, and which does not decrease with temperature as observations clearly show.
Energy of TRUE BB of temperature T (in kelvins) is calculated using this equation: E=kT where k is Boltzmann’s constant. Energy of a light with frequency f is calculated using this equation: E=hf where h is Planck’s constant. So spectral radiance of emitted light with frequency f from BB with temperature T is calculated using β(T)=((2hf^3)/(c^2))*(1/(e^(hf/kT)−1)) via Planck’s law.
Please provide a published reference stating CO2 can have an emitting temperature of 330K (like Manabe shows in his model) and thus have peak emission at 8.8 micron wavelength IR. Impossible.
Furthermore, as shown on page 1061 of Kimoto’s published paper, the assumption that Cess (and state-of-the-art models) make that εeff of the atmosphere is a constant is incorrect:
According to the annual global mean energy budget [Kiehl et al., 1997], OLR can be expressed as follows.
OLR = Fs,r + Fs,e + Fs,t + Fsun − Fb (14)
Fs,e: surface evaporation 78W/m2
Fs,t: surface thermal conduction 24W/m2
Fsun: short waves absorbed by the atmosphere 67W/m2
OLR: outgoing long wave radiation 235W/m2
From Eq. (9) and (14), the following equations are obtained.
εeffσTs**4 = εeffFs,r = Fs,r + Fs,e + Fs,t + Fsun − Fb (15)
εeff = 1 + (Fs,e + Fs,t)/Fs,r + (Fsun − Fb)/Fs,r (16)
Therefore, εeff is not a constant but a complicated function of Ts and the internal variables Ij, which can not furnish the differentiation of Eq. (9) to obtain Eq. (10):
λo = −∂OLR/∂Ts = −4εeffσTs**3 = −4OLR/Ts (10)
i.e. the Planck feedback parameter, and basis of climate sensitivity calculations running way too hot.

Merrick
July 27, 2015 5:54 pm

co2islife – I hate to jump in here and risk getting flamed – but you are wrong here. I mean, you’re right, the BB curve peaks near 10um at 288K, but it’s not clear to me how that wavelength scale got there in that top plot. Perhaps it was originally there and the authors just screwed up – because that’s the only thing wrong with the plot. The rest, especially the data referenced to the wavenumber scale, is right. But the wavenumber scale and the wavelength scale lines are not parallel, so I think someone added the wavelength scale later – like perhaps a “helpful” editor who thought he understood this and was helping the reader. That is simply wrong, and that where the error comes from.
The (wavenumber) curves are correct. An easy mistake to make is believing that the peak of the BB curve plotted by wavelength for some temperature will be the same when plotted by frequency (or as above in frequency-equivalent units like wavenumber). By which I mean that, for instance…
BB temp = 5795.537K
peak wavelength = 500 nm
through c -> 500nm = 599.585 x 10^14 Hz (i.e., frequency = c / wavelength)
By Wien’s displacement law:
peak frequency = 340.72 x 10^14 Hz
check it out yourself:
peak wavelength = b/T (b ~ 2900 micrometer K)
peak frequency = a T (a ~ 5.879 x 10^10 Hz/K)
So, the peak frequency by Wien’s Displacement Law is actually different from what one would expect by just looking at the peak wavelength by almost a factor of 2 near 6000K.
It annoyed me when I first realized this. But the units on the y axis have to change for the curve to be mathematically correct – and since the y axis units change the curve changes as well.

Ralph Kramden
July 25, 2015 2:52 pm

Obviously, all feedbacks to CO2 warming (changes which occur because the CO2 warmed) must be included in Tc
In my opinion this is the crux of the entire global warming debate. What are the feedbacks and how strong are they? I say the science is far from settled.

Richard Petschauer
July 27, 2015 7:32 pm

Right on Ralph!
And these feedbacks apply to any temperature change, including cooling, from any source, including natural ones.
And feedback should be referred to surface temperature changes, not to changes in radiative forcing at the top of the atmosphere as is the common practice promoted by the IPCC. This shortcoming explains why they do not handle the large effect of increased evaporation with sea surface temperature that cools the surface and increases radiation to space when the latent heat warms the cloud tops.

Curious George(@moudryj)
July 25, 2015 2:53 pm

“The net effect of CO2 on IR is therefore given by :
Rcy = 5.35 * ln(Cy/C0) – j * ((T0+Tcy-1)^4 – T0^4)”
It looks very scientific, but there is a lot of basic physics missing. Are all these “T”s day temperatures, night tempearures, summer temperatures, or winter temperatures? Has the author seen formulas taking into account the Earth’s rotation, inclination, and orbit eccentricity?
That’s where a true science would start, not at a simplified model of an unknown quality.

July 25, 2015 3:26 pm

It will be interesting to see where this goes. Another ‘simple model’ that generally reproduces GCM results using mainstream warmunist inputs and relationships. Presumably will be pressure tested.
There is already one ‘finding’ in part 1 that prompts an observation. Figure 6 deduces that Tn is roughly net zero. That is, no net natural variation. The computational period is roughly 1850-2010, 160 years, or roughly two 70-80 year full ‘cycles’ of some amplitude ‘sine wave’ natural variation. The early DMI arctic ice records, plus the DMI recent Arctic ice and Greenland ice mass balance data, hint at such a cycle. Moreover, having recently bottomed, with ice now on the upswing. With about that periodicy.
Plainly, on longer time intervals there is natural variation (MWP, LIA). Still Net Tn zero around the overall cooling trend from Holocene optimum? Dunno if paleoproxies have enough resolution to attempt the analysis.
Plainly, on shorter 30-40 year intervals natural variation does matter even if the full cycle Tn is roughly net zero. Even AR4 said so in discussing ~1920-1945, then ~1945-1970. BUT, the CMIP5 GCMs were parameterized to hindcast well from 2006 back to about YE1975, and under the ‘ Meehl assumption’ of little natural variation. Ergo, CMIP5 should run hot compared to the Tn downcycle portion–that is to somewhen in the 2030s. And GCMs have been doing just that since about 2000. These musings at least seem to fit loosely together.

July 25, 2015 3:35 pm

I’m working on my Ph.D. in mathemanics.

son of mulder
July 25, 2015 3:36 pm

T = Tc + Tn is wrong T = Tc + Tn +Tcn where Tcn is the temperature increase or decrease due to the interaction between c & n.

Mike Jonas(@egrey1)
Editor
July 25, 2015 4:53 pm

Your concept of Tcn is basically the CO2 feedbacks. I have been careful to build them all into Tc. So my Tc is your (Tc + Tcn).

son of mulder
July 26, 2015 12:28 am

Mike, consider a simple world with no atmosphere and where only albedo and CO2 can change. Add some CO2 and you get a Tc value. Instead of adding CO2 let the albedo change so less light is reflected and you get a Tn but let both happen and the new temperature difference is not Tc+Tn and there is no feedback ie CO2 doesn’t affect albedo and albedo doesn’t affect CO2. There is an entanglement because of the T^4 law of Boltzmann. Are you sure it is valid to simply adjust the Tn to a different value and then continue to use it for further calculations?

Mike Jonas(@egrey1)
Editor
July 26, 2015 12:52 am

Very good point, and hopefully I have avoided any pitfall here. Tc gets used in further calculations, but Tn does not.

Bill Hirt
July 25, 2015 3:38 pm

All this still leaves the question as to what caused the medieval warming period

Mike Jonas(@egrey1)
Editor
July 25, 2015 4:54 pm

Part 2.

Randy
July 25, 2015 3:53 pm

While we are talking co2 maths, can someone explain why human emissions have sped up in recent decades but the official rise in co2 stays consistent? Seems obvious some mechanism isn’t even hinted at yet let alone explained. Unless of course it is something other then humans driving up co2 levels.

fonzarelli
July 25, 2015 4:53 pm

Randy, glad to hear you ask that question. It is temperature and NOT human emissions that drive carbon growth. Carbon growth and temperature have been in lock step since the inception of the mauna loa data set (this is southern hemisphere land data which does not pick up the early 90s cooling due to pinatubo which is located at 15 degrees north latitude):
This still does not answer the crucial question of whether or not the rise is natural or anthropogenic. If it’s natural then perhaps henry’s law; if anthropogenic then temperature is causing an inefficiency in the carbon sinks as temps rise…

fonzarelli
July 25, 2015 4:56 pm

Test one, two…

Richard Petschauer
July 27, 2015 7:47 pm

Climate models still use a CO2 annual growrth rate of about 1%, which is supposed to approximate emmissions growth. However CO2 content has only been growing about half as much. So their forecasts of future warming are too pessimistic (not counting that their climates sensitivity is also too high). So apparently the oceans and forests are absorbing about one half of the emissions. The oceans would be absorbing a little more if they has not warmed a little. The forests should be absorbing more with time because of the increasing CO2 causing faster tree growth.

Steve Case
July 25, 2015 3:58 pm

“…the whole series of articles is based on the premise that the climate computer models are correct, using the mid-range ECS of 3.2.”
You know, if Equilibrium Climate Sensitivity [ECS] means a doubling of CO2 produces 3.2° of warming and that the logarithmic doubling starts at around 10 – 20 parts per million, then CO2 is around 45% of the green house effect if the green house effect is 33°.

Michael Hammer
July 26, 2015 2:44 am

Hi Steve; at 400 ppm the total CO2 column represents about 3000 abs. The line centre saturates by about 2 abs (99% absorption) which is more or less where the logarithmic relationship starts so we are somewhere between 10 and 11 doublings into saturation. If the total CO2 column absorbs about 30 watts/sqM it would seem that that each doubling would contribute around 3 watts/sqM. Now the sensitivity of earth in watts/sqM/C is normally quoted at around 3.7 watts/sqM/C so that would suggest the direct impact of doubling CO2 is somewhere around 0.8C -1C. The rest is feedbacks but that raises an interesting question – in almost all naturally stable systems (and climate is certainly a naturally stable system) feedbacks are negative. Indeed negative feedback is more or less a mandatory prerequisite for stability so the claim of not just positive feedback but massive positive feedback is truly extraordinary. The only evidence for it that I have seen is the prediction of a hotspot in the upper tropical troposphere – you know, the one that 1000’s of balloon flights can’t find any trace of!

Alan McIntire
July 25, 2015 4:08 pm

λ = dT/dF = dT/(5.35 * ln[2])= [2 to 4.5°C]/3.7 = 0.54 to 1.2°C/(W/m2)
We currently get an avearge of a little less than 240 watts/square meter from the sun.
Plugging in that 1.2 C(W/m2) gives 240*1.2 = 288 K, the current average temperature at earth’s surface.
Since radiation is proportional to the 4th power of the temperature, it’s SILLY to assume that last 3.7 watts will have anywhere NEAR the effect of the AVERAGE for 240 watts.
At this site, Nir Shaviv calculate a sensitivity of about 0.21 C (W/m2)
http://www.sciencebits.com/OnClimateSensitivity
And I suspect that even THAT is on the high side. I think what Nir Shaviv is actually calculating is
the effective temperature change if the sun increased its radiation in all wavelengths proportionally,
so earth would get an average of about 243.7 watts rather than the 240 average we currently get.
Using multilayer greenhouse models like
https://en.wikipedia.org/wiki/Idealized_greenhouse_model
or
http://www.geo.utexas.edu/courses/387h/Lectures/chap2.pdf
in actuality we’d be adding a fractional 3.7 watt layer to our current atmosphere, increasing surface
wattage from an average of 390 watts to 393.7 watts, giving an increase of 0.7 C and a sensitivity of
aboout 0.189 C(W;m2). Of course, our surface currently gets around 490 watts, but 100 watts of that
results in evaporation and convection, and doesn’t go into sensible heat. If a similar fraction of the 3.7 Watt increase ALSO goes into evaporation and convection, that reduces the sensitivity to about
0.189*(390/490)= 0.15 C(W/m2), what I consider to b a much more plausible figure than even Nir Shaviv gives.

co2islife
July 25, 2015 4:54 pm

OK, thanks for clarifying the wavenumber vs wavelength issue. Here is another question, using wavelength or wavenumber. Here is a chart of CO2’s absorption of IR under different concentrations. What % of the entire radiation from the earth does this increase represent? If we increase CO2 by a factor of 4, is that a material change in absorption given that H2O also absorbs those wave lengths.
http://members.casema.nl/errenwijlens/co2/co205124.gif
http://i787.photobucket.com/albums/yy154/RichardDH/AGW/emitt.jpg
http://earthobservatory.nasa.gov/Features/Iris/Images/greenhouse_gas_absorb_rt.gif
Is this chart correct? Is CO2 relatively transparent at 15 microns/666 wavenumber?
http://www.ar15.com/media/mediaFiles/1334/37782.GIF

TonyL
July 25, 2015 6:50 pm

Is this chart correct? Is CO2 relatively transparent at 15 microns/666 wavenumber?

In a word. YES. The 666 line seems to be overstated as it is. It really is a quite weak line. Very often, in IR spectroscopy, things are arranged such that strong lines are way saturated, so that the weak lines will show up and their wavenumber can be determined. When the system is adjusted so the strong lines are on scale properly, the weak lines are not even a bump on the baseline. Unless you already know, you would not even suspect they are there. This practice of generating distorted spectra is OK for most things, but is a disaster for quantitative work. As a result, there has been much confusion about the true relative intensities of IR lines.
BTW: The 15 micron line is 665 wavenumbers. It was informally changed to 666, from biblical reference, The Number Of The Beast. That made CO2 “The Molecule Of The Beast”. It seemed all too fitting when CAGW came along (much later). Some of us have been snickering ever since.

July 25, 2015 8:32 pm

6 protons
6 neutrons
6 electrons
This cannot be a coincidence !!!

July 25, 2015 8:34 pm

…. carbon that is, of course.

co2islife
July 25, 2015 10:33 pm

This practice of generating distorted spectra is OK for most things, but is a disaster for quantitative work. As a result, there has been much confusion about the true relative intensities of IR lines.

Is the absorption band then at 15 microns CO2 or H2O or Both?
http://earthobservatory.nasa.gov/Features/Iris/Images/greenhouse_gas_absorb_rt.gif

TonyL
July 25, 2015 11:50 pm

@ phil:
Everything in science happens for a reason, creepy how this works.
@co2islife:
Yes, the absorption band will be the sum of both contributors.
In spite of what is implied by the graphic, I suspect the water vapor dominates by far. Water, is after all, a very good absorber in the IR and there is a lot more of it. Water vapor is given as 2% – 5% of the atmosphere (CRC Handbook) which is 20,000ppm – 50,000ppm, compared to CO2 at 400ppm.
Just to underline the point, experimentally water is a huge pain in the IR lab. When collecting spectra, the samples have to be dry, dry, dry. Any solvents used have to be dry, dry, dry. And that can be a real challenge, depending on the solvent. Water absorbs strongly across the entire spectrum. Any water contamination will cause a big absorption band which will blot out any spectral features you are trying to see. In addition, the instruments have to be kept in low humidity climate controlled lab rooms. The whole water issue can be a huge PITA in IR land.
Nobody ever said “Watch out for CO2 contamination”.

TonyL
July 26, 2015 12:39 am

@Phil

6 protons
6 neutrons
6 electrons

The Atom Of The Beast

Phil.
July 26, 2015 9:47 am

Is the absorption band then at 15 microns CO2 or H2O or Both?
Both, but as you will see from the spectrum below, CO2 dominates.
http://i302.photobucket.com/albums/nn107/Sprintstar400/H2OCO2.gif

Phil.
July 26, 2015 9:48 am

The top spectrum is H2O the bottom one CO2.

Merrick
July 27, 2015 6:26 pm

??? 15 micron is EXACTLY 666.66666… wavenumbers. But the peak (the Q branch) is actually at about 670 wavenumbers, so not exactly 15 micron.

rgbatduke
July 30, 2015 5:00 am

In spite of what is implied by the graphic, I suspect the water vapor dominates by far.

Why not just look at top of the atmosphere spectrograms and stop “suspecting”? Water vapor often does “dominate”, but not for the most part in the bite taken out by CO2. The bite taken out by CO_2 is a) absolutely real and in pretty much all spectrographs no matter which part of the Earth you look at from the TOA; b) up against water vapor on one side, but the water vapor part goes up and down with the humidity. And water vapor has effects elsewhere in the spectrograph, not just on the long wavelength side of the LWIR curve. So do clouds.
The fact that water vapor dominates, especially in the tropics and over the ocean, does not mean CO_2 has no effect in either place. CO_2’s relative effect is greatest over the poles and desert (where it is usually/often dry) but its effect is zero nowhere.

Michael Hammer
July 26, 2015 2:59 am

Hi CO2islife; I posted a comment at 2:44 16th July which partly answers your question (just above) but to answer this issue in more detail, how much difference does raising CO2 conc make. Once the line center saturates further absorption occurs though increasing width of the absorption line and that is a logarithmic relationship (the line profile is close to gaussian and squaring a gaussian (ie: doubling concentration) yields a new gaussian with a larger sigma). As to whether the plot of CO2 absorption you showed is correct – yes it looks like it. CO2 has three very large absorption peaks at 2.7 microns 4.3 microns and 14.7 microns (3700 wavenumbers, 2300 wavenumbers and 665 wavenumbers approximately) All 3 can be seen on the plot. The 4.3 micron peak is the strongest but the other 2 are also very large. (This plot is probably for very low concentration CO2 over a short path length so the notches don’t go all the way to zero). However the Earth is not warm enough to emit significant energy at 2.7 or 4.3 microns so there is no significant energy at those wavelengths for the CO2 to absorb. The 14.7 micron peak is the important one and it is VERY strong relative to the amount of CO2 in the atmosphere. Even an atmospheric concentration of around 0.3 ppm would be enough to absorb all the energy radiated by earth’s surface at 14.7 microns. Your point about water vapour is very relevant. On the short wavelength side CO2 runs up against the atmospheric window so its impact is significant but at the long wavelength side it buts up against water vapour absorption. That means on the long wavelength side it is just absorbing energy that would anyway be absorbed by water vapour (well most of it, CO2 absorption seems to be somewhat stronger than the water vapour absorption). That would mean the apparent impact is close to halved.

Dudley Horscroft(@dudleyhorscroft)
July 27, 2015 9:12 pm

Michael Hammer, you say: “Even an atmospheric concentration of around 0.3 ppm would be enough to absorb all the energy radiated by earth’s surface at 14.7 microns.” and “Once the line center saturates further absorption occurs though increasing width of the absorption line and that is a logarithmic relationship”. So at 14.8 microns a lot more than 0.3 ppm will be required to absorb all the emitted energy at that wavelength, and even more CO2 at 14.9 microns, etc.
As 14.7 microns is a point, presumably this is shorthand for “14.65 to 14.75”?
Are these statements correct? Just to clarify my thoughts – and perhaps help those others here who are not atmospheric physicists or spectrologists.
And Mike Jonas, in the article you quote SkS as saying:
“Plugging in our possible climate sensitivity values, this gives us an expected surface temperature change of about 1–2.2°C of global warming, with a most likely value of 1.4°C. However, this tells us the equilibrium temperature. In reality it takes a long time to heat up the oceans due to their thermal inertia. For this reason there is currently a planetary energy imbalance, and the surface has only warmed about 0.8°C. In other words, even if we were to immediately stop adding CO2 to the atmosphere, the planet would warm another ~0.6°C until it reached this new equilibrium state (confirmed by Hansen 2005). This is referred to as the ‘warming in the pipeline’.”
The warming should be, say, 1.4C but it is only 0.8C. SkS attributes this to the inertia of the oceans which will eventually catch up and raise the warming by 0.6C to 1.4C, to make the earth correspond to the models. To do this the oceans would have to be warmer than they are, and they would cool, releasing energy to the atmosphere and the earth, to raise the observed temperature. This is totally in contradiction to: “In reality it takes a long time to heat up the oceans due to their thermal inertia.” which implies, at least to me, that the oceans have not materially warmed up yet. This also implies to me, that “if we were to immediately stop adding CO2 to the atmosphere” the result would be a COOLING by, perhaps 0.6C. Has no one picked this up before – surely I am not the first to have noticed this contradiction in the SkS argument – though I fancied that RichardsCourtney was about to do so in his post of “July 25, 2015 at 12:45 pm”. Without actually stating this was a contradiction, he correctly stated that this discrepancy had destroyed any resemblance of the Model World to the Real World

July 26, 2015 1:19 pm

Is the absorption band then at 15 microns CO2 or H2O or Both?
Phil.: “Both, but as you will see from the spectrum below, CO2 dominates.”
What are the respective concentrations you are using for these comparisons?
At current concentrations, H2O mostly overlaps CO2 ~15um band absorption/emission:
http://1.bp.blogspot.com/_nOY5jaKJXHM/TJe36s1JB0I/AAAAAAAABTE/kgD4VUKlyu0/s400/Fullscreen+capture+9202010+123527+PM.jpg

Phil.
July 26, 2015 7:30 pm

A spectrum at such low resolution doesn’t allow for a correct interpretation, as shown at high resolution there are many more lines in the CO2 spectrum and the few H2O lines fall in-between the CO2 lines.

July 27, 2015 10:19 am

Phil, as I asked above, what are the respective concentrations of water vapor and CO2 in your comparisons?

co2islife
July 25, 2015 4:59 pm

A few more questions.
1) If CO2 absorbs 100% of IR at 15 Microns, why does the earth transmit 50% at 15microns.
2) why does the CO2 band widen when CO2 remains 400 PPM?
3) Why does a CO2 window develop over the Antarctic, where CO2 no longer absorbs even though it is 400 PPM?
http://members.casema.nl/errenwijlens/co2/spectra.gif

bw
July 25, 2015 7:23 pm

CO2 does not accumulate in the atmosphere. It flows like a river.
Outside a physics text, the best single source of IR science relating to GHE is at
http://www.barrettbellamyclimate.com/index.htm
Note especially the MODTRAN sections.
http://www.john-daly.com/artifact.htm
Generally, CO2 adds nothing at all to the waterworld of Earth, the GHE is entirely water.
Adding CO2 is overwhelmingly beneficial to surface biology, plants and crop growth, especially in dry areas.

July 25, 2015 8:25 pm

What a great site – thanks (the barrettbellamy link).

gymnosperm(@gymnosperm)
July 25, 2015 9:43 pm

1. Water is not saturated.
3.Please explain this CO2 window over the Antarctic.

Phil.
July 25, 2015 9:52 pm

1) If CO2 absorbs 100% of IR at 15 Microns, why does the earth transmit 50% at 15microns.
All of the 15 micron IR from the Earth’s surface is absorbed (~190 units as shown on curve a), at an altitude corresponding to a temperature of about 220K the atmosphere has become sufficiently thin that emissions from the CO2 there is able to escape to space (~50 units).
2) why does the CO2 band widen when CO2 remains 400 PPM?
I’m not sure what you’re referring to here.
3) Why does a CO2 window develop over the Antarctic, where CO2 no longer absorbs even though it is 400 PPM?
There is a temperature inversion over antarctica, so the air at altitude is actually warmer than the surface, hence the bump above the surface emission is due to CO2 emissions from the warmer atmosphere. Note the ‘spike’ on the top of the ‘bump’ corresponding to the Q-branch of the CO2 spectrum.

co2islife
July 25, 2015 10:12 pm

“All of the 15 micron IR from the Earth’s surface is absorbed (~190 units as shown on curve a), at an altitude corresponding to a temperature of about 220K the atmosphere has become sufficiently thin that emissions from the CO2 there is able to escape to space (~50 units).”

That is exactly what I thought. How then does CO2 warm the lower atmosphere? How does warming the stratosphere result in warming the lower troposphere? Also, my understanding is that there is no stratospheric hotspot.
Also, the ocean are warming. How does CO2 warm the oceans?

Michael 2
July 25, 2015 10:24 pm

co2islife asks “1) If CO2 absorbs 100% of IR at 15 Microns, why does the earth transmit 50% at 15microns.”
The postulate and the question are imprecisely stated. CO2 absorbs and then re-emits infrared; the energy does not remain absorbed. A carbon-dioxide laser depends on this phenomenon for its operation. Thus it is better for understanding that CO2 retards or delays radiative energy transport; how long it takes for energy to go a particular distance. Furthermore, CO2 that has absorbed a photon might deliver that energy in a physical collision imparting the head mechanically rather than re-radiating a photon. The opposite mechanism also exists; it might pick up thermal energy mechanically and emit a photon which is more likely the mechanism at the top of atmosphere.
It is also the case that CO2 can only absorb a photon that impinges upon it; hence the mean path length of a photon depends a great deal on the absolute density of CO2 molecules. I use 10 meters as the mean path length, your mileage may vary. What that means is that 10 meters above the surface of the earth, half of the radiative energy that could be captured by CO2 has already been captured. Of that, 1/2 will re-radiate back down, the other half re-radiate back up. Of the 1/2 radiated down, which is 1/2 of the surface radiation, 1/2 will actually succeed in reaching the surface. That’s 1/8th. So it is that carbon dioxide is a “blanket” that reduces the net radiation because some of it (but not very much) is coming back atcha.
The other GHG’s operate in similar manner.
I do not understand your other two questions.

co2islife
July 25, 2015 11:00 pm

It is also the case that CO2 can only absorb a photon that impinges upon it; hence the mean path length of a photon depends a great deal on the absolute density of CO2 molecules. I use 10 meters as the mean path length, your mileage may vary.

This chart shows 3K mean path length (In think). I think it shows that the first 3K water vapor dominates, and its impact falls with altitude, which make sense given that it most likely condenses out or freezes. If I’m reading the chart correctly, it looks like you have to get at least 6K in the atmosphere before H2O falls enough for CO2 to have a material impact. Is my reading of this chart correct? If I am, how can CO2 be blamed for the lower atmosphere warming?
http://www.hashemifamily.com/Kevan/Climate/Earth_Atmosphere.gif

Phil.
July 26, 2015 9:52 am

Low in the atmosphere vibrational energy of an excited CO2 molecule is predominantly transmitted to the surrounding atmosphere by collisions not emissions.

Michael Hammer
July 26, 2015 3:10 am

Hi again CO2is life. Your questions are both very relevant and very insightful. For a GHG its absorptivity and emissivity at the same wavelength must be identical (can be proven that if that were not the case a cold body could warm a wamer body). That means while CO2 absorbs at 14.7 microns it also emits at 14.7 microns according to its temperature (as defined by Planks law). Thus CO2 throughout the atmosphere is simultaneously absorbing and emitting energy at 14.7 microns. Only the last 2 abs (the very top of the GHG column) can emit to space, the rest of the emission from CO2 throughout the atmosphere is re-absorbed by the gas above or below. For CO2 the top of the gas column seems to be at the tropopause or more accurately the lower stratosphere. Thus what CO2 does is to absorb 14.7 micron surface emission (288K) and replace it with emission from a black body (at 14.7 micron) at the temperature of the tropopause (220K).
As CO2 concentration increases this occurs over a slightly larger range of wavelengths. As to why there is no notch in the antarctic (your CO2 window) its because the temperature of the lower stratosphere (or tropopause) is actually warmer than the surface. CO2 still absorbs all surface emission and replaces it with tropopasue emission but now the tropopause temperature is warmer so the emission at 14.7 microns is increased not decreased. IE: CO2 at the poles cools the earth it does not warm it but the effect is minor compared to the warming it creates elsewhere. A very good observation on your part.

July 25, 2015 5:04 pm

Good mathematics based on worthless assumptions. Great sci fi writers make the absurd appear logical too. It’s only when you put the book down that you have to face reality and accept that restaurant mathematics can’t power spaceships and giant turtles aren’t swimming through space with worlds on their backs.
Just a quick look at the trajectory of the graphs should be enough to slap people awake to this fraud. Extend the graph to 1% CO2 concentration! Does this still appear to model reality to you???
You have a room with a radiator in it turned on. Place a giant block of ice in the middle of the room. Does the air inbetween the radiator and the ice get hotter? Does the radiator itself get hotter? Why not? The ice absorbs radiation and emits it in all directions. Why doesn’t the “back radiation” from the ice make the room warmer than it would have been without it?
Wake up to the greenhouse scam people!

Anthony Watts(@wattsupwiththat)
July 25, 2015 5:23 pm

There’s no scam here, only your misinterpretation.

Michael 2
July 25, 2015 10:44 pm

Unfortunately, you are comparing the thermal emissions of a block of ice to the thermal emissions of everything else in the room. This is a classic case of ignoring the elephant.
Everything in the room is already re-radiating back to the radiator; the ice will re-radiate considerably less. Hence, ignoring convection, the block of ice will reduce the temperature of the radiator; but I don’t ignore convection and it will still reduce the temperature of the radiator.
You can demonstrate this using an infrared remote-sensing thermometer. Everything radiates according to its temperature and emissivity.
Your face is sensitive to infrared heat. You can feel the heat of a stove as you walk by it; not because the air is warmer but you feel the effect of your skin absorbing infrared. Same with a freezer. Long before the cold air reaches your face, you feel the coldness — but it isn’t actually “cold” it is just the sudden absence of the usual ambiance of infrared we are constantly bathed in night and day.
If you were to compare the block of ice to deep space, then yes, having an adjacent block of ice would return just a little bit of infrared to the radiator, allowing it to be warmer for the same amount of heat energy into that system. Deep space will not reflect or re-emit any of the energy. Therefore, ice will allow the radiator to be warmer but only compared to deep space or anything colder than ice.

Michael Hammer
July 26, 2015 3:19 am

Wickedwenchfan you are not thinking. If the ice were not there the radiator would be radiating to the wall of the room at a temperature of say 19C. Placing the block of ice in the way reduces that temperature to 0C hence the back radiation with the ice is lower than without the ice so the presence of the ice lowers temperatures.

rgbatduke
July 26, 2015 6:34 am

Wickedwenchfan you are not thinking.

You could have just stopped there. If he actually built a simple model (even mentally) of a heated room that cools only to the outside by radiation to a 3 K surrounding black wall and maintains a temperature (in equilibrium with that wall) of 288 K, and then imagined putting a shell of ice around it in between the 3K wall and the wall of the house at 200 K, he might have a clue as to why interpolating cold stuff between warmed stuff in dynamic equilibrium and a still colder reservoir causes the warmed stuff to accumulate energy from its heater (the only actual source of energy) until it is at a higher temperature in order to remain in dynamic equilibrium with its suddenly warmer (but still far colder than it itself) surroundings.
But I’ve explained this to him many times (several over the last two weeks). All that happens is that he stops posting. It’s like a drive by shooting — he throws a line of pure nonsense out there and then refuses to even look at or address the trivial counterexample that refutes it.
One doesn’t even really need to understand the differential equations and physics to understand this example. All one needs is a smidgen of common sense.
If one is going to object to the standard model of the GHE that’s fine, but at least find a sound basis for what you criticize. Trying to assert that a cold trace gas can have no effect on the surface temperature just because you want to believe that and misquoting physics you don’t understand to try to prop up your belief is as mind-numbing as young earth creationists who insist that radiometric dating isn’t reliable because carbon dating has sometimes proven to be wrong (usually because somebody contaminated the data, but never mind why it is sometimes wrong, that’s enough to prove that radiometric dating in general can be off by billions of years to drop the life of the Universe to 6000 give or take a thousand, never mind all the other evidence or the fact that there are some 40 radiometric series used to date rocks and that in their overlap range they agree within expected error, which is way, way less than 14 billion years. Or even 1 billion years.
In this case there is absolutely zero doubt of the following statements:
* The simple single layer, purely radiative model for a greenhouse effect (which may or may not be terribly representative of the much more complex processes whereby the atmosphere warms due to the presence of greenhouse gases) does indeed prove that an interpolated absorber layer will cause a net warming of a surface heated with SW and cooled with LW.
* This process not only does not violate the first law of thermodynamcs (energy conservation), it is the embodiment of energy conservation in an open system. It is the first law of thermodynamics, with modulation of the resistance to energy transfer in the different channels.
* This process not only does not violate the second law of thermodynamics, one can actually and trivially compute the entropy changes of each step and prove that it is not violated. Net energy always flows from hotter places to colder places, it just does so at rates that are functions of things like the LWIR absoptivity in the single layer shell. That’s all that is required to observe warming, and the second law says nothing whatsoever about dynamics and rates of energy transfer, it only insists that systems be found in the most probable of possible states, not the least probable, given the conditions.
But there is literally no end to the misunderstanding and misquoting of these laws or simple applications of basic radiative physics to “prove” that something that has been directly measured and observed a few zillion times can’t happen, because if it did somebody might be justified in being worried about some of the possible effects of increasing CO_2 concentration in our atmosphere and they don’t want to believe that on what amount to religious grounds. Nothing will make them change their minds — not examples, not models, not spectrographs (that apparently they can’t understand anyway), not direct observation.
So why bother to try?
rgb

mkelly
July 26, 2015 6:59 am

RGB says: ” …why interpolating cold stuff between warmed stuff in dynamic equilibrium and a still colder reservoir causes the warmed stuff to accumulate energy from its heater (the only actual source of energy) until it is at a higher temperature in order to remain in dynamic equilibrium with its suddenly warmer (but still far colder than it itself) surroundings.”
——-
Agree. Insulation works. The sun is our heater not CO2 molecules.

July 26, 2015 11:31 am

Questions for Dr. Brown, if I may:
1. The line-emission bands of CO2 in the LWIR is centered at ~15um, regardless of concentration, correct? (& even if the bands are slightly widened by increase concentration, the center of the bands remains ~15um, correct?)
2. If CO2 was a true blackbody (even though it is a mere-line emitter), what is the peak/maximum emitting temperature of a blackbody with peak emission at ~15um?
3. Can radiation from a true blackbody with peak emission at 15um be thermalized and transfer heat energy to a true blackbody with a peak emission at 5um?

rgbatduke
July 30, 2015 6:34 am

1. The line-emission bands of CO2 in the LWIR is centered at ~15um, regardless of concentration, correct? (& even if the bands are slightly widened by increase concentration, the center of the bands remains ~15um, correct?)

Sure. The lines are determined by the quantum mechanics of the CO_2 molecule in isolation. Their width beyond their “natural linedwidth” is determined by how they interact with their environment, primarily a phase interruption process associated with collisions with other molecules called “pressure broadening”. The band is pressure broadened into a band as opposed to a bunch of comparatively sharp lines all through the troposphere, but in the stratosphere the lines resolve again. Some of the pictures you have been posting without understanding them show that — a band in one context but a bunch of finely resolved lines in another. Water does this more often than CO2.

2. If CO2 was a true blackbody (even though it is a mere-line emitter), what is the peak/maximum emitting temperature of a blackbody with peak emission at ~15um?

Why is the peak/maximum relevant? HS is making this same mistake. You can cut steel with a CO_2 laser containing CO_2 that is nowhere near the temperature of the melting/vaporizing steel. CO_2 radiates (in the 15 um band) when it is at 300 K. CO_2 radiates when it is at 250 K. CO_2 radiates at 200 K. It radiates at 400 K. The specific curve shapes that overlap the band will shift around, but it isn’t like it is forced to radiate at a temperature that one associates with its “peak” by some absurd alchemy involving $\hbar \omega = k T$. Again, learn to read the spectrographs you like to post. They actually do a peachy job of showing you what, in fact, CO_2 is doing as far as radiating energy away at the top of the atmosphere — radiating from a blackbody curve at 220K or 240 K or whatever, within the CO_2 absorptive window.

3. Can radiation from a true blackbody with peak emission at 15um be thermalized and transfer heat energy to a true blackbody with a peak emission at 5um?

Again, who cares? This is not a description of what is happening. Your question doesn’t even make sense. A “true blackbody” has a temperature, and a curve shape characteristic of that temperature. The wavelength of its peak emission is a function of the temperature so why even bring wavelength into it? If you apply Stefan-Boltzmann to two unit emiissivity metal plates facing one another across a vacuum, one warmer than the other, there is radiation going both ways between them and because the total radiated energy away from either plate goes as the fourth power of the temperature, of course more energy goes from the warmer plate to the colder than from the colder to the warmer.
But this has nothing to do with the composition of the plates as long as they have unit emissivity. That’s why the idea of a black body is powerful — it transcends the material composition, making it a universal concept of at least approximate utility even when the material has quantum structure.
In the context of atmospheric radiation, however, CO2 can without any doubt be heated up to a temperature where the peak of the pure blackbody spectrum is much shorter than 15 um. And if you do, it will brighten. If you heat up CO_2 to 500 C, do you think that it is somehow going to radiate as if it is at 190 C or whatever? HS seems to think so. No. All that happens is that it radiates from the BB curve associated with the temperature in the window of its pressure broadened spectrum. It is the need for this window that keeps N2 and O2 from radiating. They simply have no meaningful bands to radiate that overlap the BB spectrum associated with normal atmospheric temperatures, so they remain transparent to LWIR. From Kirchoff’s law, they can neither absorb nor emit at the wavelengths likely to be excited at the temperatures of the atmosphere, and consequently act only as a reservoir for the thermal energy they receive from shortwave solar radiation (where they do have some band overlap) and from thermal transfer from greenhouse gases in both directions.
So let me be perfectly clear. At the surface of the Earth, CO_2 is happily absorbing LWIR photons in its band and emitting LWIR photons in its band. Photons have no temperature. Let me repeat that — a photon has no temperature. Energy is not the same thing as temperature. A photon is perfectly happy to be absorbed by any molecule it happens upon that is in its ground state and resonant with the photon. It is perfectly happy to be emitted by any molecule that happens to be in an excited state to return to its ground state. These things are not modulated, per molecule, by “temperature”. Temperature simply describes the distribution and availability of energy in a system with many many ways of distributing the energy among its degrees of freedom.
I don’t know what good answering your questions is going to do, of course — they are framed as if they are some sort of challenge, but in the unlikely event that you are interested in learning, I’ve answered them, and have tried to redirect you into further learning before you make senseless pronouncements about what “can” and “cannot” happen. There is way, way too much of this on this list already.
rgb

July 30, 2015 11:49 am

rgb says, “Some of the pictures you have been posting without understanding them show that — a band in one context but a bunch of finely resolved lines in another.”
Of course i know this, and have written papers on spectroscopy, and posted such distinctions countless times on my blog, so it would really be appreciated if you would discontinue making false straw man statements about what I think or have not said, and then attacking me with those false straw men.
rgb once again makes a false analogy between ordinary Kirchhoff emission/absorption by CO2 at ~15um in our atmosphere [not amplified, stimulated, & coherent emission as in a light AMPLIFIED STIMULATED EMISSION of radiation LASER] . I’ve already explained several times on this thread why this is a completely irrelevant, false analogy and linked to the UC Davis Analytical Chem site which clearly explains why ““Unlike absorption, stimulated emission adds to the intensity of the incident light” in a CO2 laser:
http://chemwiki.ucdavis.edu/Analytical_Chemistry/Instrumental_Analysis/Lasers
The reason why a CO2 laser can melt steel is:
1. Stimulated emission increases intensity far beyond Kirchhoff absorption, which in our atmosphere = emission
2. The CO2 laser much shorter and much higher energy wavelengths of laser transitions in a CO2 laser are 9.6 & 10.6um as I showed in a diagram on this tread twice, irrelevant to the LWIR Earth bands centered around ~15um.
3. Stimulated emission from a laser makes use of a populations inversion of metastable states which many more electrons in the excited state than the ground state, which allows a very high intensity of coherent photons to be emitted.
4. Coherent waves from a laser are of much higher intensity since there is no destructive interference at the target
5. Not only is the beam very intense and coherent, it is also very thin, with little divergence, and very highly concentrated upon a small spot.
6. etc etc clearly demonstrating none of the above have any relevance whatsoever.
And nobody has been able to answer my question on how huge storms at the top of the Uranus atmosphere observed at 2800F are hot enough to melt steel. Presumably your answer is greenhouse gases, correct?
rgb says, “CO_2 radiates (in the 15 um band) when it is at 300 K. CO_2 radiates when it is at 250 K. CO_2 radiates at 200 K. It radiates at 400 K. The specific curve shapes that overlap the band will shift around, but it isn’t like it is forced to radiate at a temperature that one associates with its “peak” by some absurd alchemy involving \hbar \omega = k T. Again, learn to read the spectrographs you like to post. They actually do a peachy job of showing you what, in fact, CO_2 is doing as far as radiating energy away at the top of the atmosphere — radiating from a blackbody curve at 220K or 240 K or whatever, within the CO_2 absorptive window.”
Again you are making a false straw man argument of the opposite of what I’ve said, including here (to Phil):
The fact is no matter what the kinetic energy /temperature of CO2 is (assuming it is > 193K), the wavelength of the emission in the LWIR from CO2 will always be centered at ~15um, whether or not the kinetic energy/temperature of CO2 is 193K, 255K, 288K, 300K, 330K, 5000K etc.
The Planck’s/Wein’s laws equate BB frequency (v) and Temperature (T)
But even though CO2 is a mere molecular-line-emitter, not a true blackbody & much less than a true blackbody which has a Planck curve, bizarrely, Phil. somehow imagines CO2 is a magic super-blackbody with emissivity > 1, and which does not decline with temperature as observations have clearly shown.
In addition, in the OLR spectra I posted above you can see that at the ~15um CO2+H2O “hole”, the corresponding blackbody curve is that of a ~215-220K true BB, NOT a 280K, 288K, 300K, 330K blackbody, absolutely proving that I am correct and you Phil are absolutely incorrect.
rgb says “a photon has no temperature”
As I’ve said many times on this thread alone, the only thing a photon “knows” is its frequency/wavelength and Energy = hv. In turn, the peak temperature/energy of a true BB is determined by Planck’s Law for a particular frequency/wavelength/energy of a photon:
To assume CO2 can emit 15um photons than have higher energy than 15um photons from a true blackbody, and that those 15um photons can be thermalized by a blackbody at > 193K, breaks multiple laws of physics including 1st & 2nd LoT, Kirchhoff’s, Planck’s, Wein’s laws, Einstein’s photoelectric equation, photoelectric threshold wavelength, etc. [CO2 laser amplified stimulated coherent radiation absolutely does not occur naturally in the atmosphere and thus analogies to LASERs are false for the reasons above).

BFL
July 25, 2015 5:38 pm

Then there is this:
http://www.phy.duke.edu/~rgb/Toft-CO2-PDO.jpg
“It is simply not factually correct to state that there is some sort of disagreement between the simple predictions of the Greenhouse model and observation over the last 165 years, unless and until you successfully impugn the data itself, e.g. HadCRUT4 in this figure. There are reasons to impugn the data, mind you, but taking the data at face value the fit to the log of the CO_2 concentration is impressive even without adding a single 67 year period sinusoidal with an amplitude of around 0.1 C.”
And:
“if you like, I get a TCS of around 1.8 C plus or minus maybe a whole degree. If the pause continues for another decade, it might pull the best fit down to 1.4 C per doubling, for example, and still produce a pretty good fit but with larger “natural” excursions due to physics and phenomena the model obviously does not include.
What it is not is evidence against the assertion that CO_2 increases warm the mean planetary temperature. Nor does it in any way justify the assertion that a 20 year pause means that the greenhouse effect itself is incorrect or nonexistent. It is silly to make these assertions — that just because temperature hasn’t gone up for 20 years, the GHE itself doesn’t exist and is “wrong”. What the GHE isn’t is alone. It isn’t the only thing going on. It may not even be the most important thing going on.”
http://wattsupwiththat.com/2015/05/12/22-very-inconvenient-climate-truths/#comment-1932077
http://wattsupwiththat.com/2015/05/12/22-very-inconvenient-climate-truths/#comment-1933114

Bart
July 26, 2015 11:18 am

That plot annoys me no end. With 5 parameters, you can make the elephant wiggle his trunk.
It is no more compelling than the top plot here, where the apparent agreement falls apart completely if you extend the plot out farther.
http://i1136.photobucket.com/albums/n488/Bartemis/extrapolation_zpsse2orlyc.jpg

Cliff Hilton
July 25, 2015 5:56 pm

How much more CO2 could possibly be released into the atmosphere given available technology to use it and the limited amount available? What will the atmospheric CO2 ppm be as a result?

bw
July 25, 2015 7:29 pm

Nobody really knows. The best value from my understanding is that atmospheric CO2 concentration will peak at 560 ppm plus or minus 10 ppm around the year 2100

Peter
July 25, 2015 7:52 pm

I recently recounted all claimed supplies of coal, oil and natural gas and I got number around 1000ppm. But this only adds current 400ppm with 600ppm of all carbon reserves. So real number would be much smaller, I quite agree with bw’s 560ppm.

July 25, 2015 8:10 pm

…. and the way logarithms work, this would give rise to another half-doubling of the effect of CO2 above the 280 ppm pre-industrial level. We are now at 400 ppm, the first half-doubling (of effect), and the empirically observed effects of this, using rigorous scientific principles are between zero and immeasurable for any global climate parameter.
I don’t, however, expect that there is any warmist out there who can multiply “zero to immeasurable” by two without some psychiatric problem manifesting itself.

joelobryan(@joelobryan)
July 25, 2015 9:15 pm

Observed atmospheric CO2 ppm is a function of the kinetics of all CO2 sinks operating simultaneously with the releasing kinetics of all sources. Even in the most simplified equation setups, future predictions of pCO2 is a second order diff eq.
The implication of this is that “if emissions ceased tomorrow” ( a downstep change in total source kinetics), sink kinetics are higher and would lag due to biosphere greening of the higher CO2, longer growing seasons, and higher latitude biological growth (tree line advancement).

donald penman
July 25, 2015 10:10 pm

There is a flaw in the argument that the oceans take a long time to heat up and it is if surface temperatures are not rising we would not expect the ocean temperature to rise either. Is there a different Sun heating the oceans?

co2islife
July 25, 2015 10:24 pm

Another question. Then anthropogenic CO2 has been growing exponentially.
http://www.skepticalscience.com/images/co2_emissions.gif
Atmospheric CO2 however seem to have an unaltered linear growth rate.
http://www.optocleaner.com/CO2-NOAA.jpg
How can the claimed main source of CO2 be growing exponentially and not alter the slope of the atmospheric CO2?
The oceans have been warming. How much of the atmospheric CO2 is due to the warming oceans due to Henry;’s Law?

donald penman
July 25, 2015 10:38 pm

The big el ninos that we have had recently would be as a result of the surface temperatures rising and warming the ocean and not the el ninos warming the surface temperatures possibly.

July 25, 2015 10:42 pm

this is a classic example of getting “balled up in one’s Underwear.” It begins with the simplifying assumption that all forcing comes from Greenhouse Gas CO2 that cannot change state at the Earth’s surface or in the atmosphere. “Dry Ice” results when CO2 changes state, and that occurs at MINUS 109 DEFREES and one atmosphere of pressure. This temperature/pressure combination does not occur naturally. The vast amount of energy absorbed or released when CO2 changes state to “Dry Ice” is used for convenient and effective refrigeration. Now, consider that CO2 remains a gas over the entire temperature range where Water has TWO naturally occurring state changes in the atmosphere – water to water vapor and water to Ice. Both of these state changes occur in normal atmospheric temperature and pressure ranges, and are acknowledged by meteorologists to be dominant forces in the Earth’s weather. Water Ice has temperature inertia, requiring vast quantum amounts of energy, to melt it. Liquid Water is the result of melting, and water itself can absorb vast amounts of energy as liquid water until it vaporizes, Water that vaporizes absorbs another vast quantum of energy when it changes state to water vapor. Water vapor releases that vast quantum energy when it condenses, liquid water releases its vast quantum energy when it freezes. Both of these state changes occur in naturally occurring temperature and pressure ranges constantly worldwide, CO2 only has its gaseous absorption and radiation capacity, and at its 0,4% concentration in the atmosphere, it cannot possibly drive water through its states, or even appreciably heat or cool the vastly larger concentration of water, water vapor and water ice in the dynamic weather atmosphere of earth, where humidity reaches 100%. So, taking state changes and liquid water and ice and even Water vapor out of the thermal energy exchange formulas is taking the vastly dominant components out. If you do that, then modeling atmospheric temperatures using just CO2 in its constant state is simple but so insignificant as to be meaningless. Weather modeling is based on understanding energy transfers, and it focuses on water, clouds, evaporation and freezing water ice. Yet, this Anthropogenic CO2 driven model takes no account of it and claims that the 10% of CO2 released by humans can control it all. The basic assumption that water in all its states. Changing states, dealing in astronomical numbers of energy can be left out of ANY Earth Climate model is absurd.
P u t I t. I n. T h e. M o d e l.

co2islife
July 25, 2015 10:42 pm

Another question, here is a chart of the earth’s radiance under clear and cloudy skys. Can clouds really lower the outgoing radiation by 88°K from 288°K to 200°K? Given that CO2 is basically constant, how can CO2 be blamed for the change when H2O has such an overwhelming impact?
http://www.mathstat.dal.ca/~folkins/Cloud-LWspectrum.jpg

Michael 2
July 25, 2015 10:50 pm

co2islife “Can clouds really lower the outgoing radiation by 88°K from 288°K to 200°K?”
Point your remote-sensing infrared thermometer at the night sky. Where I live the temperature is below the bottom limit of -60 F. Point it at the underside of a cloud and even at night in the winter it measures about +20 F. The difference is enormous and the energy radiated down is obviously not going up.
“Given that CO2 is basically constant, how can CO2 be blamed for the change when H2O has such an overwhelming impact?”
The idea is expressed by the word “feedback”. A little extra heat evaporates a lot of extra water since the Earth is about 3/4 covered by water. Of course, many feedbacks exist, some amplifying the change and some working in opposition. Water is an enormously powerful transporter of heat from the equator to the poles; putting more of it into the atmosphere presumably permits more heat transport to the poles, causing them to warm faster than the tropics, which appears to approximately be the actual case. It would seem that an optimum probably exists.

July 25, 2015 11:55 pm

Exactly. There is another chart that helps understand. It is in the first post at paullitely.com. Water is so much dominant, with a broad absorption spectrum. CO2 has a very narrow absorption spectrum

Phil.
July 26, 2015 10:01 am

From your graph the upper curve is surface emission at about 280K with inter alia absorption by CO2 and O3 absorbing and higher in the atmosphere emitting (T ~220K & ~250K). The lower curve shows cloud tops emitting at ~200K with CO2 and O3 emissions from higher in the atmosphere (but warmer, ~220K).

Mickey Reno
July 25, 2015 11:27 pm

Who first decided that H2O takes a back seat to CO2 in the radiative forcing arena? I’ve heard the argument that says because individual water vapor molecules, on average, don’t live as long in the atmosphere, that this makes water vapor IR absorption a feedback. To me, that’s not at all persuasive. It’s like saying that if the atmosphere contained zero CO2, it could not therefore, contain any water vapor. And that’s clearly wrong and stupid. So how about we bifurcate the two contributions, and weight the bigger one (water vapor) appropriately, and give it the respect it deserves, mathematically speaking?

co2islife
July 26, 2015 5:46 am

I’ve heard the argument that says because individual water vapor molecules, on average, don’t live as long in the atmosphere, that this makes water vapor IR absorption a feedback. To me, that’s not at all persuasive.

Do the physics change the longer a molecule has been in the atmosphere? Can a photon differentiate between a CO2 molecule that has been in the atmosphere 1 day vs 5 years? Can a photon differentiate between a CO2 molecule created by man vs nature? Since when does “residency life” trump concentration? Also, no one seem to know what the “residency life” of CO2 is. I’ve seen estimates of 50 to 200 years in IPCC reports, and the best estimates I’ve seen put it about 5 years. Looking at the O2 chart CO2 varies on an annual basis by about 2%, so at most a CO2 molecule could be expected to reside in the atmosphere 50 years.
Unless there is a reason CO2 made with C14 is removed at a higher rate than C12, it looks like the expected residency life is at most about 40 years, and no where near 50. Almost 100% of the atomic bomb created C14 created around 1963 is gone. 50% was gone in 7 years.
http://scienceblog.at/pics/2013/20131004/abb2.gif

Phil.
July 26, 2015 10:10 am

Unless there is a reason CO2 made with C14 is removed at a higher rate than C12,
There is, C14 concentration in the atmosphere was doubled whereas that in the ocean was not, in the exchange process between atmosphere and ocean more C14 will enter the atmosphere than in the reverse. Also CO2 is transferred down into the deep ocean and is balanced by that due to upwelling from the deep ocean which is ~1,000 years old, any C14 coming back up will have undergone significant radioactive decay.

Ian Macdonald
July 26, 2015 12:18 am

The effect of CO2 backscatter can be quantified OK, but I have issues with the means of deriving the climate sensitivity to the backscattered energy, which would seem to depend on assuming that the predicted sensitivity values are as defined. This would seem to be very like those equations we’ve all encountered which are reducible to 1=1.

Frank
July 26, 2015 2:04 am

Mike wrote: Rcy = 5.35 * ln(Cy/C0) – j * ((T0+Tcy-1)^4 – T0^4)
It seems to me that you should replace j with e*o, an “emissivity” times the S-B constant. Your value of j gives an emissivity of 0.204. When the earth is treated as a graybody with a surface temperature of 288 degK, emissivity is usually around 0.6. (In a comment above, I discussed why emissivity isn’t a very appropriate concept for an atmosphere. Ignoring that for the moment…)
When equilibrium has been reached and Rcy = 0 (increased outward flux from the warmer surface compensates for the forcing from CO2:
Tcy = 5.35*ln(2)/(4*e*o*T^3) = ECS
If e = 0.615, ECS is 1.11 (near the usual value for the no-feedbacks climate sensitivity). If e = 0.204, ECS is 3.3 degC – roughly the assumption that went into your calculation.
So far, you haven’t taken into account feedbacks – the change in OLR is not simply -5.35*ln(2) after a doubling of CO2.

July 26, 2015 4:10 am

” So now to calculate the change in temperature, we just need to know the climate sensitivity. Studies have given a possible range of values of 2-4.5°C warming for a doubling of CO2 (IPCC 2007). ”
I find this hard to accept based on IR measurements of sky and the Earth’s surface
This a clear sky day, about noon
This is concrete, grass, asphalt and sky.
Now the sky temp is through the atm window, but you can add Co2 forcing to this value.
Midnight clear day
Same concrete, grass, asphalt and sky.
So at least in the window this the temp the ground sees.
I finally got up before sunrise, now it was in the 90’s yesterday, and cloudy most of the night
Same concrete, grass, asphalt and sky, only this time your seeing cloud bottoms with maybe a small opening to clear sky, if it was clear, yet almost 70F warmer that is from water vapor, matching the tropical air yesterday vs the Canadian air for the other charts. You see this change in this temperature chart from my weather station
First observation, if you add what I think is the full Co2 forcing to low humidity sky, that’s about 180W / M2, water vapor adds a significant amount of forcing (I don’t have off the top of my head what another 40F to 70F forcing is), but clouds add significantly to even that. The forcing from Co2 alone has to be related to the LWIR emitted from the ground, and the surface and the temperature of that surface matters, alot, much more than the change in co2.

co2islife
July 26, 2015 5:27 am

1) They have a mis-specified model where an insignificant variable (CO2) is made significant, and the independent variable (temperature) is made the dependent variable.
2) They are clearly modeling a non-linear variable (temperature) with a linear variable (Over the time period studied)(CO2). That is why CO2 continued higher, the models continued higher, and the observations flat lined.
3) They have an underspecified model that is missing the most significant variables, ie solar, H2O, albedo, etc etc.
4) There is an extreme level of group think in the climate community, resulting in them all forming relatively similar and relatively wrong models. These charts represent a wild goose chase, a CO2 Witch Hunt, where the conclusion, CO2, was reached before the model was created, so they all made the same mistake. They focused on CO2. That represents a bias, not science.
5) Simply running a simple regression on CO2 and Temperature will expose the flaw in their theory. Running a “Stepwise” regression analysis will discover the true drivers of the climate, and I’m 100% certain CO2 won’t be one of the most significant variables in any model developed by an unbiased computer.
6) Given that a computer can prove the CO2 theory pure nonsense as I’ve described above, I would work to keep this “science” out of the courts if I were a warmist.
7) They cherry picked an unusual and unrepresentative short time period when CO2 and Temperature did correlate relatively well to establish the relationships. They modeled a coincidence, not a causative correlation. Had they used the entire 600,000 year history of CO2 and Temperature data their models would have failed before they started. Not only did they model a coincidence, they created a model similar to lung-cancer causes smoking. They reversed the Y and Xs.

rgbatduke
July 26, 2015 6:51 am

For once I agree with a part of one of your posts. Of course it is with Roy’s observation and graphic, not your other (still absurd, sorry) arguments. It isn’t a matter of consensus — it is a simple matter of fact that nearly all of the GCMs have predicted that the climate faster than it turned out to warm, some of the by almost one whole degree C. I also don’t disagree with the assertion that trying to fit only the last 165, or 200, or 300 years of temperature data to CO_2 is a particularly good test of the unprovable assertion that “natural variation over this interval does not matter”. There is actually no reason whatsoever to believe that this is true, and historically — outside of the infamous hockey stick itself — excellent reasons to think it false.
Sadly, we have no good way to know the temperatures we are fitting back into the remote past by means of proxies. I do not mean to say that we don’t have temperature estimates — only that they are almost never presented with error bars for a good reason. If they were, it would be too obvious that the error bars are close to 1 C (and tend to be smeared out over time as well, not really known month by month or year by year) and hence nearly all of the temperatures reported are so uncertain as to be nearly useless for the purpose of fitting or proving a model or verifying that natural variation is or is not important on century time scales.
Roy’s figure alone is a good and sufficient reason to rethink the climate models, and a very good reason not to use them to set very expensive global policy on the basis of their prediction of “catastrophe”. It does not mean that CO2 is universally beneficial, totally harmless in any concentration, cannot cause warming (because that is almost certainly not true and you won’t find a single competent physicist including Roy Spencer and Dick Lindzen — or myself, to the extent that maybe I’m competent — make any such assertion).
You might try learning from this instead of posting the very figures that prove to anyone who understands them that what you claim is incorrect.
rgb

July 26, 2015 5:54 am

Mike Jonas is to be congratulated in starting a stimulating discussion on certain aspects of current models.
I expect that subsequent posts will expose the logical nonsense ‘in the extreme’ which models are/have become.
Thankyou .

co2islife
July 26, 2015 5:58 am

Who first decided that H2O takes a back seat to CO2 in the radiative forcing arena?

All evidence points otherwise. Nights over deserts show extreme variances from the daytime high temperatures. Areas with humid atmospheres show a very narrow range of diurnal temperature change. Antarctica shows extreme temperature variation from the wet coastal region to the dry inland region, and the temperature decay follows the loss of humidity. Bottom line, all climates have CO2 at 400ppm so CO2 can’t be the cause of the differences between humid and dry climates.
It looks like H2O can reduce the earth’s radiance by 288-200=88°K. CO2 is a constant, and doesn’t change. Only H2O can shift the IR spectrum, and vary the amount of heat trapped. CO2 can’t.

GOES-8 Imager radiances in water vapor and infrared channels 3, 4 and 5 were used for assessing outgoing longwave radiation (OLR) at the top of the atmosphere.

http://www.scielo.br/img/revistas/rbg/v21n1/a05fig03.gif

mkelly
July 26, 2015 5:59 am

T = Tc + Tn. (Formula #1)
———–
To be clear temperature is not additive nor are the equivalents.

co2islife
July 26, 2015 6:02 am
rgbatduke
July 26, 2015 7:19 am

I look forward to reading the series, as well as the “vigorous” debate that will no doubt accompany it.
My only comment so far is this. It is far easier to understand the GHE if one completely avoids looking at the Earth-Atmosphere-Ocean interface — the actual surface — and try to tally up things like back radiation, mostly because back radiation is mixed with conduction and convection and latent heat transfers and lateral heat transfers to the point where everything is both dubious and arguable. We cannot solve the coupled Navier-Stokes equations in our heads, nor can we solve them at adequate resolution from reasonably well known initial conditions with our best computers — manifestly, as co2islife’s reproduction of Roy Spencer’s figure above conclusively (IMO) demonstrates.
It is a lot easier to understand the GHE from spectrographs and from contemplation of the Earth as a system that is warmed at some rate by the sun through an atmosphere that is largely transparent to or reflective of direct sunlight (not terribly absorptive of, in other words). To remain at an approximate dynamical equilibrium temperature it has to radiate all of this power away so that ins equal outs, via radiation alone.
Some of the outgoing radiation comes directly from the surface and can be closely and reasonably associated with the blackbody curve for the temperature of the radiating surface. Some of that outgoing radiation is absorbed by the atmosphere, which is basically completely opaque at ground level to in-band LWIR in the absorption bands of greenhouse gas molecules. Note well — I do not reference back radiation, forward radiation, latent heat, what happens at the ocean’s surface to IR, whether or not convection is important — none of this matters. The surface does indeed lose energy to the near-surface atmosphere and pick energy up from the near-surface atmosphere in many, often complex ways, but the only thing that matters is that outgoing LWIR is almost instantly absorbed by the atmosphere in certain bands.
Way up at the top of the troposphere (at a variable, not terribly sharp height) the atmosphere becomes tenuous enough for radiation in the greenhouse gas bands to escape. Greenhouse gas molecules in thermal equilibrium with the general atmosphere at that height and above have around a 50% or better chance of radiating energy away from one of their in-band levels and having the photon make it out to “infinity”. Top of atmosphere spectrographs show that this energy is radiated away roughly consistently with a blackbody radiation curve in the absorption band of the relevant species at the temperature associated with that height.
Because of the (approximately adiabatic) lapse rate, the atmosphere at the height where transparency is achieved is usually much colder than the surface underneath.
The total radiation from any patch of the surface is thus (in very crude terms):
P = A * S + B * G
where A is the fraction of unblocked radiation, S is the power from the surface, B is the fraction of blocked radiation (at the surface) and G is the power coming from the greenhouse gases.
P must on average equal the incoming power from the sun for the earth to be in dynamic equilibrium. If it is smaller, the Earth accumulates energy from the difference and warms until S increases enough to rebalance the rates. If it is larger, the Earth loses energy from the difference and cools until the reduced S once again balances things.
Greenhouse gas concentrations and details in the quantum mechanics that dictate absorption make A, B and G all three somewhat variable on greenhouse gas concentration. The simplest way to understand the variation is that if one increases (say) CO_2 concentration, then the height where the atmosphere becomes sufficiently transparent for radiation in the CO_2 band to escape increases, as it depends on the mean free path of the in-band photons and whether or not they are likely to encounter another absorber molecule on the way out of the atmosphere. Increased height means colder from the lapse rate, which means that G goes down a hair. S has to go up a hair to compensate.
Note that this effect quite literally has nothing to do with what goes on near the surface. Surface energy can be transferred to the atmosphere by radiation, conduction, convection, latent heat, and by tiny pink unicorns that carry hot water bottles on their backs, as long as those unicorns don’t fly out of the atmosphere with the heat but allow it to escape via radiation. Increased concentration may or may not increase back radiation and this may or may not be interpreted as the “cause” of additional surface warming but it is a terrible way to tally it up because of the confounding stuff.
At the TOA it is simple. Detailed balance must be maintained, and to the extent that it is not the Earth warms or cools.
Note well that the Earth warms and cools much more than the CO_2-linked portion of this effect on a 1 to 5 year basis. IMO this means that it is never very far from true dynamical equilbrium, and I am deeply skeptical of any large amount of “uncommitted warming”. One gets a rather excellent fit to the data with a CO_2 driven warming model with no lag — temperature directly fit by a log of the concentration, with a warming per doubling of concentration of around 1.8 C. That doesn’t prove that there is no lag, but one does at the vary least have to show that a lagged, integrated model (that is of course much more complex) both fits the data and satisfies the fluctuation dissipation theorem when analyzing the laplace decomposition of the short time temperature fluctuations. I very much doubt that they are going to leave much room for a 100 year residual of any significant size.
rgb

July 26, 2015 11:18 am

“The simplest way to understand the variation is that if one increases (say) CO_2 concentration, then the height where the atmosphere becomes sufficiently transparent for radiation in the CO_2 band to escape increases, as it depends on the mean free path of the in-band photons and whether or not they are likely to encounter another absorber molecule on the way out of the atmosphere. Increased height means colder from the lapse rate, which means that G goes down a hair. S has to go up a hair to compensate.”
The geopotential height of the ERL is set by “triangulating” atmospheric center of mass, the fixed 255K equilibrium temperature with the Sun, and the tropospheric lapse rate, a function of gravity and Cp only. The ERL height is not affected by concentration of CO2 (other than a negligible effect of a tiny increase of Cp, which is *invesely* related to dT).

Michael Hammer
July 27, 2015 1:47 am

Again I have to disagree with you hockeyschtick. The top of the CO2 column, the level where radiation to space can occur, is in the lower stratosphere. The stratosphere exhibits temperature inversion ie: it gets hotter as you go up. By the time one gets to near the top of the stratosphere the temperature is back to about 280K so if the emission altitude rose it would reduce the warming effect. Alas of course things are not quite so simple.
However there is a MUCH (and I do mean MUCH) simpler way to prove CAGW false. The whole thesis of CAGW is that rising CO2 acts as a blanket reducing Earth’s energy loss to space so that with constant energy input there is an imbalance causing Earth to warm. Energy loss to space is measured as outgoing long wave radiation or OLR and this has indeed been measured since the late 1970’s. Thus for CAGW to be correct CAGW should have been falling during this time but unfortunately it has been rising. Opps!!!! Of course one could argue that OLR would rise as Earth’s temperature rises but then the rise in OLR would be the rise due to Earth’s warming minus the fall due to increasing CO2 ie: the rise would be very significantly less than predicted by warming alone. Ahh but unfortunately the rise in OLR is GREATER than would be predicted by the temperature rise alone. That means Earth is finding it easier to lose energy to space not more difficult and as far as I am concerned that falsifies CAGW beyond redemption.

July 27, 2015 10:31 am

Michael Hammer says, “However there is a MUCH (and I do mean MUCH) simpler way to prove CAGW false. The whole thesis of CAGW is that rising CO2 acts as a blanket reducing Earth’s energy loss to space so that with constant energy input there is an imbalance causing Earth to warm. Energy loss to space is measured as outgoing long wave radiation or OLR and this has indeed been measured since the late 1970’s. Thus for CAGW to be correct CAGW should have been falling during this time but unfortunately it has been rising. Opps!!!!”
Agreed, Dr. Nor van Andel’s posts on by blog have been pointing that out for years
http://3.bp.blogspot.com/_nOY5jaKJXHM/TI-1aWFUoFI/AAAAAAAABRs/tf6HawUmjC0/s400/Fullscreen+capture+9142010+104234+AM.jpg
http://hockeyschtick.blogspot.com/2014/10/analysis-shows-missing-heat-has-gone-to.html
“Again I have to disagree with you hockeyschtick. The top of the CO2 column, the level where radiation to space can occur, is in the lower stratosphere. The stratosphere exhibits temperature inversion ie: it gets hotter as you go up.”
No, radiation emission/absorption from CO2 occurs at all levels of the atmosphere from 0-80km+
For P < 0.1 atm, CO2 preferentially transfers energy via collision with the remaining 99.9% of the troposphere, which increases convective cooling. Nonetheless, CO2 does also absorb and emit ~15um/193K LWIR photons from 0-80+km, cooling the stratosphere, mesosphere, thermosphere.
What the warmists themselves cannot agree upon is how to explain why those 193K CO2 photos allegedly warm the much warmer troposphere, while simultaneously cooling just as warm or warmer stratosphere. No coherent answer to this exists, since it is unphysical.
The ERL is not in the stratosphere, it is in the mid-troposphere exactly at the center of mass of the atmosphere ~5.5km geopotential height.

Steven Mosher(@stevemosher)
July 27, 2015 2:06 pm

“The ERL height is not affected by concentration of CO2”
wrong.