Feedback on Feedbacks

Guest essay by Rud Istvan

In recent weeks, there have been a number of WUWT guest posts on climate sensitivity related matters. Sensitivity is determined by feedbacks to increased CO2. The delta T to doubled CO2 in the absence of feedbacks is 1.1-1.2C. Monckton calculated 1.166C in his new (and unfinished) ‘Feet of Clay’ series of posts; Lindzen used 1.2 for simplicity (below). The slight difference is of no matter for this mostly conceptual post.

There have been a number of ‘skeptical’ comments and even guest response posts (FUBAR) that have gotten a lot of things ‘not quite right’ on this very important general subject including:

1. Feedback cannot be positive since conservation of energy (COE) would be violated.

2. Feedback cannot be positive since the climate would go unstable.

3. Bode feedback model does not apply to climate at all.

4. Positive feedback cannot be >0.1 as the Bode ‘amplifier’ goes unstable.

These misconceptions are underpinned by mis-definition of the greenhouse effect (GHE), by mis-definition of feedbacks, and by mis-application of the Bode feedback amplifier conceptualization to climate. Bode can ‘translate’ easily between actual climate feedbacks and a simplified conceptual climate system model, when correctly applied within realistic value ranges as Lindzen did in several of his previous papers.

The purpose of this guest post is simply to clarify the general subject matter so that WUWT denizens do not mindlessly repeat apparently erroneous misconceptions. It use only words and logic. No math for the math challenged, and only robust general data for the data challenged. Uses only some simple arithmetic plus some simple Socratic logic. It will therefore be a bit philosophical in nature, as only the big picture is intended. It uses only simple intuitive explanations. Quibbles concerning any of the above are hopefully irrelevant.

And it endeavors to use only previous WUWT guest posts or comments as references (just two footnotes, both relating to one sub-assertion concerning a perhaps little known factoid about observational/model precipitation). Google is your friend if you wish to verify any guest post assertion using only peer reviewed literature, as some warmunists unwisely demand. The Google-Fu clue words are in the text. Truth obviously does not lie only in peer-reviewed literature. Especially not politicized climate ‘truth’. ‘Truth’ is based on verifiable, repeatable scientific method results. And ‘truth’ cannot ever be proven (Gödel’s theorems); only the lack of ‘truth’ via falsification (Popper, Kuhn). As Einstein said, “A single experiment can prove me wrong”. See ebook The Arts of Truth for many confirming ‘Popperian’ examples including in the penultimate climate chapter. And for supporting details with many footnotes, see some essays in ebook Blowing Smoke, foreword by Judith Curry.

GHE

The Earth (both land and sea) is warmed by sunlight energy, aka incoming shortwave radiation (ISR)—and very little else. (Borehole temperature reconstructions show how little heat is coming up from Earth’s core to the surface, another speculative misconception—but that is a digression). Earth is cooled by outgoing longwave radiation (aka infrared, OLR). At any atmospheric CO2 concentration, incoming and outgoing must eventually balance first at the notional effective radiating level (ERL) high in the troposphere somewhere, and then for sure at the definitely measurable (by satellite) top of atmosphere (TOA). Earth then reaches some reasonably stable radiative temperature balance but for its other (for whatever reasons) natural variations (ice ages, MWP, LIA).

For purposes of this mostly conceptual post, lets stipulate surface averages ~287K, or ~14C in 1880, with a 0.8C ‘anomaly’ increase toward ~15C since 1880 as CO2 went from ~280ppm to ~400ppm now. Those are the IPCC norms. See several previous Bob Tisdale guest posts for referenced fact details. The specifics do not matter too much for the conceptual big picture here.

The GHE is not an increase in heat, does not involve CO2 ‘creating’ heat, and does not violate COE. All wrong conceptualizations of AGW basics. Earth’s heat energy input is provided by solar ISR, at about a constant 240wm-2 (Monckton FoC #3 table 1, and Nick Stokes comments to Fubar). GHE is the result of certain gas molecules, most importantly water vapor and CO2, ‘absorbing’ and then ‘scattering’ by omnidirectional re-emission, OLR photons. That is, those atmospheric molecules hinder OLR radiative cooling from Earth’s surface to space. A surface warmed by ISR but not cooled by an equivalent amount of OLR will warm until the increase in resultant surface temperature produces enough additional OLR to restore the net balance. That is the simple essence of the GHE. The precise calculations involve the Stephan-Boltzman law, altitude lapse rates, and other complicated considerations—but those details are not material to this conceptual general post. The net rebalanced temperature equilibrium where net incoming again equals net outgoing radiation energy for a doubling of CO2 is called the equilibrium climate sensitivity (ECS). More practically (concerning observational energy balance model (EBM) calculations of it), the ‘effective climate sensitivity’. (The difference between ‘equilibrium’ and ‘effective’ involves variations over very long time frames to minor stuff like vegetative albedo changes over many centuries. You want the highest ECS, go long like Hansen’s 1000 years paper. We neglect those additional quibbles in this post as a mere sideshow distraction.)

Tyndall first experimentally determined that H2O and CO2 gasses have this OLR retarding property in 1858-9, as reported then to the Royal Society. Lest anyone think this basic physics is wrong (aka Sky Dragons), experimentally deserts are relatively dry so relatively low water vapor. That is why they cool sharply on cloudless nights. Anyone can run this climate experiment for themselves in any desert to verify this for themselves. (But take along a real good sleeping bag water vapor substitute to remain comfortable.) Low atmospheric water vapor does not hinder OLR radiative night cooling from the ISR heated daytime surface. CO2 is the same, except since reasonably well-mixed deserts won’t show the same desert night cooling effect.

The quantum reason both gas molecules have this ‘OLR obstructing’ property relates to their physical molecular shapes. But that is another digression into interesting physics details unnecessary for this conceptual post. Suffice it to say it is also how microwave ovens work (on H2O).

Feedbacks

Properly defined, a feedback is a change in some climate property given a change in some other climate property. Conceptually, it is a first derivative of the property; a change in one with respect to a change in another. This simple calculus idea (first articulated by Newton and Leibnitz, therein lies another wonderful history of science unnecessary digression) has been the source of much unfortunate skeptical WUWT blogosphere confusion nowish.

Consider just three basic properties: CO2 concentration in the atmosphere, water vapor concentration in the atmosphere (specific humidity, NOT relative humidity), and cloud concentration in the atmosphere.

1. CO2 being a GHG will warm ceterus paribus. Stipulated base from a nominal equilibrium at 280ppm in 1880 at +14C. Consensual result 2x= ~+1.2C. Not disputable since just basic SB physics.

2. H2O gas being a GHG will warm ceterus paribus. Since there is much more H2O gas (the global average is about 1.8-2% of the atmosphere) than the ‘trace’ 0.04% CO2, water vapor must be the predominant GHE warmer. In fact, absent the Earth’s specific humidity, the planet would have been about -18C rather than +14C in 1880. This fact could be described by warmunists as a thermal runaway Δ32C catastrophe—except without it and the resulting natural temperature equilibrium given the water vapor positive primary effect, the Earth would have been frozen solid for many epochs supporting no life at all. So the simple water vapor primary warming effect is NOT evidence for modern CAGW feedbacks. It is life’s primary salvation on our watery blue planet.

3. Clouds are a primary negative forcing of about -20wm-2.

Notice that in 1880 (pre AGW), these three primary factors were in ‘equilibrium’ according to warmunist AR4 SPM figure 4. Logically parse that seminal AGW attribution figure. There are two primary warming properties offset by one negative property, but no thermal runaway is evident according to IPCC. How could that be? Because these are all primary factors rather than ‘first derivative’ feedbacks. The primaries obviously equilibrate in a damped (non-runaway) fashion. That is logically simple. The Earth ~T we experience is where water vapor warming roughly balances ISR to OLR under present Earth circumstances at ~287K , since it is the main GHG. The overall system is negatively damped by two simple negative primary cloud mechanisms. If water vapor increases, so will clouds at altitude via the temperature (hence condensation) lapse rate. Such clouds at some altitude have two secondarily primary negative ΔT damping mechanisms. First, on average more cloud means more albedo, which means less ‘heating’ ISR reaching the surface because more is reflected back to space before warming the surface. Second, more cloud eventually means more precipitation, which by definition lowers atmospheric specific humidity (while also releasing the related heat of condensation higher in the atmosphere where it has an easier GHE time radiating away to cool Earth—there is simply less GHE ‘insulation’ to fight through since thin blankets ‘warm’ less than thick blankets). So clouds cool by reflecting ISR and by removing warming water vapor. That is the primary negative Earth damping. No thermal runaway is possible in such a damped system. Nor has any ever been observed. Else we would not be here to guest post and comment. QED.

Properly defined feedbacks are the first derivatives of these primary mechanisms. That is, how do these primary properties change as the underlying fundamentals change? Do they get stronger or weaker? We know that primary delta CO2 changes as a log function of concentration; each doubling has the same effect as the previous doubling. 280=>560ppm is the same as 560=>1120ppm. And we know that the primary effect of each doubling absent other feedbacks is a bit less than 1.2C. We don’t know the first derivative direct feedback (δCO2/ΔCO2) as that involves the planetary carbon cycle. Changes in natural carbon sources and sinks as CO2 changes. It appears unsaturated (unlike the Bern model), which implies a negative feedback (Coccolithophorids have increased 10x in the North Atlantic in the past 30 years). Lets treat this first direct CO2 derivative as unknown, therefore about zero for the sake of general logical argument even though it is probably negative based on planetary land greening and ocean NPP. (Please, the Salby lectures on carbon cycle stuff is just so wrong in several ways including baseline facts and atmospheric saturation that JC and I decided not to even do a joint post on it—Salby does not merit a credible rejoinder at all. A separate post here could be forthcoming if sufficient WUWT denizen skeptics insisted [to further clear the Salby air]. But this digresses yet further.)

The CMIP3 and CMIP5 climate models estimate ECS (not using Bode at all, just mathematical/parameterized climate long term simulations of emergent properties) at about 3.2, implying a Bode feedback f of about 0.65 if f=0 is ~1.2 per Lindzen (below). We also know that several different ways of computing observational ECS give about 1.65 per a comment to CoF #3: “Lewis and Curry 2014 used only IPCC AR5 ‘official’ values to estimate 1.64 (median) using the observational EBM approach. They also provided confidence interval ranges around the central value, and showed the value was not sensitive to choice of EBM time frames. See their table 1 at Climate Etc. Guy Callender estimated 1.67 way back in 1938 in his paper to the Royal Met. Soc. A simple regression of log CO2 ppm versus HadCrut T gives 1.71 with an r^2 of 0.9. Both approaches are discussed in essay Sensitive Uncertainty in ebook Blowing Smoke. Lewis 2013 used Bayesian objective priors to estimate 1.6.

So we finally reached the core of the true feedback conundrum. There is a ~2x difference between model ECS ~3.2 and observation ECS ~1.65. But note than in neither the GCM model case nor the observational case is there any ‘thermal runaway’ or climate instability ‘tipping point’ implied. There is in either case no C in CAGW (absent the ever feared but non-existant ‘tipping point’ hobgoblins). That imagined instability is another misapplication of climate ‘derivative’ feedbacks based on misunderstanding/misapplying Bode.

A familiar example helps explain why the operational electronic amplifier design example (Bode) is inapt, a mis-definition of ‘tipping point’ instability in the climate context and also in the Bode feedback amplification context. The amplifier design is not the sound system; it is one of four components: the amp, the mic, the loudspeakers, and the ‘room’ environment.

It is self evident from most denizen’s personal experience that auditorium microphone/amplifier/loudspeaker sound systems are usually well behaved despite the existence of substantial feedbacks (the mike obviously ‘hears’ the speaker plus the amplified loudspeaker version of the speaker (with speed of sound delay), and feeds both sounds back to the amplifier for further amplification—a positive feedback by definition). Auditorium sound systems do not misbehavenly screech until the system Bode f present in the venue gets too high (usually f~>0.8, and usually at a fairly high pitched ‘screetch’ frequency since those are more easily reflected from walls back to the mike—which is why Bose sound systems also use a separate single omnidirectional sub woofer). That certainly is not f=0.1 giving a measly ‘stable’ Bode amplification of ~1.1x as Monckton’s FoC series figure 1 ‘max stable’ asserts. Such a sound system would be worthless. No politician would ever be heard at the back of the auditorium—which might be a good thing politically, but unfortunately does NOT happen in the real world. The FoC figure as labeled implies all auditorium sound systems are essentially useless. Obviously that is not true. There are two practical ways to solve this well-known physical feedback problem in actual sound systems. Place the speakers further from the mike so the acoustic feedback energy is sufficiently attenuated by distance to lower system f below ~0.8, or reduce the system amplification to lower f below system ~0.8. The former, not the latter, is usually done so that the crowds can still hear the speaker despite about 6x audio amplification; just put the loudspeakers in the far side corners, or better yet in the room’s back far corners. If a transitory problem, the latter (turn the amp down a bit) is usually done immediately by the mike guy running the sound system.

Reconciling Feedbacks and Observational ECS

The essence of the warmunist ECS 3 difference to observational ECS ~1.65 (e.g. Monckton FoC#3) must lie in correctly defined ‘first derivative’ feedback differences. There are only two significant ones, as all the other minor feedbacks roughly cancel to zero per both AR4 and AR5. These two are water vapor and clouds. Lets consider them in reverse order for simplicity’s sake. Dessler (2010) purported to find (per NASA website) a positive cloud feedback. But his r^2 was only 0.02, meaning no statistical difference from zero feedback despite his and NASA’s subsequent claims. Eschenbach used CERES at WUWT very recently to show the likely value was slightly negative. Zero or slightly negative makes no difference for this general post. Zeroish is just fine conceptually. Both CMIP3 and CMIP5 have a significantly positive cloud feedback.

AR3 made the clear written assertion that water vapor feedback doubles the CO2 no feedback primary result (IPCC TAR WG1 7.2.1.1). So ~1.2C absent feedbacks amplifies to ~2.4C. That translates to a simple WVF Bode f=0.5 assuming 2x CO2 is ~1.2C. Now, AR4 asserted the central ECS was 3.0, so net Bode ~0.65. (Notice this post is simply translating from amplification to feedback using Bode logic, nothing more, per the following Lindzen Bode curve with f0=1.2:

clip_image002

So modeled AR4 clouds must implicitly have a strongly positive Bode feedback of f=(~0.65-0.5)=~0.15, since all other forcings in both AR4 and AR5 roughly cancel to zero. (This is a conceptually qualitative rather than precisely quantitative argument, with which there is perhaps much to quibble about on the data margins—but not concerning the core logic.)

Lets translate all that back to ‘reality’ using simple Bode concepts with observed climate feedbacks in a general physical reconciliation to observational ECS. Clouds, ~f=0 per Eschenbach analysis of CERES. We also know that CMIP3 and CMIP5 understate precipitation by about half, especially in the tropics.[1], [2] So climate models should overstate WVF since they don’t get the precipitation water vapor reduction right. And these faulty precipitation models do not incorporate either the Linden adaptive infrared iris hypothesis (BAMS 2001), nor the closely related Eschenbach tropical Tstorm regulatory hypothesis posted many times previously here (both relate to lowering the net water vapor feedback). So, if WVF is approximately half of the IPCC 0.5 f based just on mis-modeled precipitation, then the total ECS per Bode f ~ 0.25 is ECS about 1.65 per the above curve. That is exactly what Monckton has computed separately, and what several other unrelated observational studies have estimated independently as cited above. A nice conceptual closure.

Summary

Feedbacks are properly understood as ‘first derivatives’ of basic climate properties, not those properties themselves. Since the climate according to warmunists was in proximate ‘property equilibrium’ circa 1880 per their basic CAGW theory, we can infer that the system was reasonably stable then with ISR equaling OLR given WVF, damped by clouds in two logical ways, albedo and precipitation (negative primary system response, a damped system that cannot undergo ‘tipping point excursions’). There is a likely small net positive ‘first derivative’ net feedback on the order of Bode f~0.25, which results in a still stable climate system (absent natural variations) with an ECS of about 1.65. No CAGW, and only a little AGW.

And that little AGW is still not provable since the difference between the warming from ~1920-1945 is not distinguishable from the warming of 1975-2000. Even IPCC AR4 SPM figure 4 could not attribute the earlier warming cycle to AGW, only to natural variation. Natural variation surely has not ceased to exist afterwards, since the world cooled in the interim period 1945-1975 despite rising CO2, and since it has not warmed since 2000 except for a now rapidly cooling 2015 El Nino—despite the fact that about 35% of all additional atmospheric CO2 concentrations measured since 1958 (Keeling Curve) came during the same post ~1999 period that did not meaningfully warm according to 4 different balloon radiosonde and 3 different satellite datasets. The final inconvenient fact:

clip_image004


[1] Stephens, GeWex WCRP 20: 5-7 (2010)

[2] Dai, J. Clim. 19:4605-4630 (2006)

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richard verney
September 12, 2016 2:22 am

I am looking forward to the author’s comments upon the points raised in this commentary. There appears a number of points raised that require his comment in order to take the debate forward.

Thomas Homer
Reply to  richard verney
September 12, 2016 6:17 am

I look forward to the author recanting his assertion that CO2 forcing is logarithmic. He at least admitted that he cannot apply this forcing to very high concentrations of atmospheric CO2, and I can easily show how implausible this logarithmic forcing is for very low concentrations of atmospheric CO2. (With only a single molecule of CO2 for each square meter of Earth’s surface area there would be 2^49 molecules of CO2 and by his logarithmic claim, that concentration of CO2 would be trapping over 70 degrees of heat.)
No scientist would make such a broad assertion that clearly does not hold true across all values, without providing some measure of qualification. For this reason I discount all of his reasoning and leave the contemplation of his word salad to others.
Now if he is interested in moving this debate forward, the author can provide detailed qualifications of his assertion. Of course, knowing that there is no CO2 forcing means that his qualifications will not be scientifically derived.

Reply to  Thomas Homer
September 12, 2016 6:24 pm

TH, none is needed. Google Fu. The logarithmic nature of CO2 doubling has been well established for many decades. I do not waste time debating ignorami. Educate yourself rather than proving you have no clue about radiative physics. Then get back.
Your comment/belief allows Obama to call all of us ‘Flatearthers’. I really resent that, and your ignorance of basic physics. Learn. Stop making stupid loser arguments. Please.

Reply to  richard verney
September 12, 2016 12:39 pm

RV, won’t happen. Monckton things he is right on everything; we’ve had that go around before. Greg thinks he knows everything. And so on. The post allows others use Google Fu to learn what the world has to say on each specific point made. Or, they can read the literally hundreds of footnote references to the Lindzen reviewed climate chapter of The Arts of Truth, or to relevant essays in Blowing Smoke with a foreword from Judith Curry. Let denizens learn and then form their own judgements on how things work. Makes for better general discussion.

September 12, 2016 4:24 am

A point about Planck and feedback
Feedback depends on where you draw the boundaries of the system.
E.g,. an amplifier has input and output and internal feedback.,
Plug a guitar in one end and a 4×12 in the other, and if you then consider that resultant mess as a diofferent system, that has feedback via and acoustic and electromechanical pathway.
Add in the neighbours banging on the walls, and we have another system with a social feedback element, and I will act as part of it and turn the volume down.
In order for global warming to happen, first of all you need to understand what is meant by the term
Shifting the same amount of heat from up high in the stratosphere to ground level is human relevant climate change for the same total heat content.
The main claim of AGW protagonists is that ex of any lag terms, CO2 will reduce heat loss at a given (surface) temperature. Thus leading to rising temperatures. That this flies in the face of Planck is covered by the fact that in the end Planck is abandoned as the earth is not considered to be a black body.
WE are then simply into the realms of effective albedo, to determine surface level incoming radiation, and the effective radiation temperature of the earth as seen from deep space, to determine the loss.
The CO2 mythology then becomes a case of postulating that night time effective radiation is in fact COLDER at the radiation ‘surface’ in the upper atmosphere, so the lower regions can get hotter, and still keep the radiation balance. This to be done by IR absorption in the atmosphere by CO2 and or water vapour.
However as far as I am aware, this increased lapse rate has been shown not to exist.
Which begs the question of whether or not the actual climate variation is in fact being determined less by loss of night time cooling, than by greater daytime heating, which implies either a change in solar output (its te sun, stupid) , or albedo (head in the clouds), or both.
IN that context spreading solar irradiance meters all over the planet, disguised as away of generating electricity, may actually prove to be of some use after all.

dave
September 12, 2016 4:32 am

The greatest thing that Lord Monkton can now do is to explain his views, especially how IPCC miscalculated climate sensitivity in simple plain words. This will be the only way that politicians and the media will understand. Most highly educated scientists cannot follow his advanced mathematics. What a great service Lord Monkton can do if he do this.

Bill Illis
September 12, 2016 5:01 am

Feedbacks can indeed be positive and not result in a substantial warming or runaway warming.
The real limiting factor is the Stefan Boltzmann equation in that temperatures only rise at the fourth power of the energy (forcings and feedbacks).
Runaway does not happen until the forcing and feedbacks results in temperatures getting to 100C somewhere on Earth so that the water boils away and enters the atmosphere.

September 12, 2016 6:58 am

This morning was a good example of what’s going on. We had low dew points yesterday, ~55F@4PM Air temp was ~76F. From about 5PM temps (75F) dropped 20F by 1AM. 2.5F/hour, from 1am to 7 am it dropped about 3F total, air temps were near dew point, rel humidity was 95%.
The day before it dropped 10F over 9 hours with 100% rel humidity it did rain some near the beginning, but it didn’t change the cooling rate.
We had a clear night last night, So this morning, I took my ir thermometer out, kiddy pool with a inch of water, on a deck 10′ in the air was 43F, air temps by thermometer was ~51F, so between the cold sky (-37F) and evaporation a isolated pool of water was 8F below air temps, my grass was a wet 51F, and my tan brick patio was 60F.
Co2 is not slowing nightly cooling.
But it’d be easy to argue my brick, and concrete, and asphalt driveway store far more heat than what Co2 does, by at least one order of magnitude (2.7W/m^2 vs ~20W/m^2).
When you examine night time cooling compared to yesterday’s temps, there is no loss of cooling at night.

September 12, 2016 8:34 am

IPCC defines ECS as Forcing/Lambda, where lambda is the sum of all feedbacks. If the feedback would be near zero [K W-1 m2], which is quite possible considering all uncertainties of the models used to estimate them, then ECS should approach ± infinity. This is sooooo absurdly wrong that nobody wants to notice.
See details: http://bit.ly/2cR9s8S

Reply to  Michel
September 12, 2016 9:53 am

A simple question is due here. I can see that SB can convert temperature into W/m^2 but what’s in the Gs box that can convert w/m^2 into T? Could it be that T represents stored energy in some mass? If so, it means that Gs has an integrator and the transfer function has a real pole. Static analysis goes out the window.

September 12, 2016 8:35 am

My, but what a load of rubbish from Istvan this time. I suppose he should be applauded for trying, but his Harvard Economics degree is simply far too inadequate for the task.
As a chemical process engineer of more than 40 years experience, I observe that it is a very good thing my colleagues in engineering do not ever listen to Istvan.
This is so wrong it would require weeks or more to explain it properly.
Posts like this do NOT advance the AGW skeptical cause.

Reply to  Roger Sowell
September 12, 2016 11:23 am

Mr. Sowell,
it is clear that you think his guest post is bad,then you insult him over it.
Since you didn’t post any examples of his claimed errors, despite your 40 years of experience as an Engineer,you are coming across as full of empty babbling words. Maybe YOU are not up to the task to address it,as it is too hard for you?
Surely you can do better than that,Roger?

Reply to  Roger Sowell
September 12, 2016 1:46 pm

For Sunsettommy, I don’t have the weeks and weeks required to correct the Harvard Economist impersonating/posing as a scientist. His English is very bad, his definitions are wrong, but at least he has the engineers laughing.
But, just for starters, the climate system is not at steady state, and heat input from the sun is not a constant 240 W/m2. Surface solar heating varies from 1,000 W/m2 or a bit more at noon in the tropics, down to 100 W/m2 and less at the terminator line.
Those who use averages in radiant heat transfer calculations in non-steady state problems set themselves up for failure. There is a 4th power of the absolute temperature that cannot be trifled with.
Those who mis-apply definitions and principles of dynamic process control can never obtain correct results.
Like I said, I applaud the Harvard Economist for trying. It is quite amusing.

September 12, 2016 9:19 am

Regarding vapor being so present in the atmosphere that the global average is about 1.8-2% of the atmosphere: Figures that I have seen for precipitable water in the atmosphere range from 25 to 30 mm for a global average, and I consider 26 mm as most credible. Using 30 mm, this means 30 kg of water vapor over the average square meter of the earth’s surface. The atmosphere’s average mass is 5.148E18 kg, over 5.1072E14 m^2 of surface area, or 10,080 kg/m^2. 30 kg/m^2 is close to .3% of this by mass, and this is a high side figure. Wikipedia says the total atmosphere is .25% water vapor by mass.
I think an appropriate figure is percent by volume, since that is how CO2 is reported. .25% H2O by weight is about .4% vapor H2O by volume, and .3% H2O by weight is about .48% by volume, since a water molecule has about 62% of the average mass of an air molecule.

Dave Rutledge
September 12, 2016 9:45 am

Thanks for a great post. As an electrical engineer involved in designing and selling microwave amplifiers that use positive feedback to increase the gain by only 1db (feedback gain factor of 1.1), I am painfully aware of how hard it is to get stable linear feedback gain. I have listened to many climate talks by people who casually employ quasi-linearity and enormous feedback gain factors and that complete ignore stability issues. However, Willis Eschenbach’s posts emphasizing the critical importance of non-linear damping factors at the higher temperatures have helped me understand better both the limitations of my background and those of climate scientists in dealing with feedback. In any event it all points to climate sensitivities in the range of 1.6 rather 3.2. It looks like Guy Callendar got it right in the 30s.

Reply to  Dave Rutledge
September 12, 2016 12:40 pm

Thanks Dave. Coming from you at Caltech, that is a much appreciated complement.

September 12, 2016 12:14 pm

Hell Rud,
Re your above comment on Salby
My work predates Salby by several years and make fewer claims.
I have yet to hear a credible rebuttal of my conclusions.
If you want to comment, please email me via my website.
Here is a general reference, my 2008 icecap.us paper is referenced within. See points 1. 2 and 3 below wrt Salby.
Regards, Allan
EVIDENCE SUGGESTING TEMPERATURE DRIVES ATMOSPHERIC CO2 MORE THAN CO2 DRIVES TEMPERATURE
September 4, 2015
By Allan MacRae
https://wattsupwiththat.com/2015/06/13/presentation-of-evidence-suggesting-temperature-drives-atmospheric-co2-more-than-co2-drives-temperature/
Observations and Conclusions:
1. Temperature, among other factors, drives atmospheric CO2 much more than CO2 drives temperature. The rate of change dCO2/dt is closely correlated with temperature and thus atmospheric CO2 LAGS [Lower Tropospheric] temperature by ~9 months in the modern data record
2. CO2 also lags temperature by ~~800 years in the ice core record, on a longer time scale.
3. Atmospheric CO2 lags temperature at all measured time scales.
4. CO2 is the feedstock for carbon-based life on Earth, and Earth’s atmosphere and oceans are clearly CO2-deficient. CO2 abatement and sequestration schemes are nonsense.
5. Based on the evidence, Earth’s climate is insensitive to increased atmospheric CO2 – there is no global warming crisis.
6. Recent global warming was natural and irregularly cyclical – the next climate phase following the ~20 year pause will probably be global cooling, starting by ~2020 or sooner.
7. Adaptation is clearly the best approach to deal with the moderate global warming and cooling experienced in recent centuries.
8. Cool and cold weather kills many more people than warm or hot weather, even in warm climates. There are about 100,000 Excess Winter Deaths every year in the USA and about 10,000 in Canada.
9. Green energy schemes have needlessly driven up energy costs, reduced electrical grid reliability and contributed to increased winter mortality, which especially targets the elderly and the poor.
10. Cheap, abundant, reliable energy is the lifeblood of modern society. When politicians fool with energy systems, real people suffer and die. That is the tragic legacy of false global warming alarmism.

Reply to  Allan MacRae
September 12, 2016 6:34 pm

AM, I will take a look but need a couple of days. Blogging is not my full time job.
2, 8,9, 10 probably correct. At least 1, 3, 5 dubious. Have to look at your stats in light of autocorrelation problems.
IMO there are much easier ways to convincingly refute CAGW. No C except in models. Small a in aGW. Really simple incontrovertible stuff. Delta CO2 lags shorter than ice cores, sketchy. See essay Cause and Effect for a dissection of four different examples.

Reply to  ristvan
September 13, 2016 12:51 am

Hi Rud,
RE #1 – Autocorrelation/”spurious correlation” was refuted in 2008.
The best the alarmists have come up with on the 9-month lag of CO2 after temperature is an alleged “feedback effect”, with zero supporting evidence – warmist cult nonsense, imo. See Figures 1 to 4 in my 2008 icecap.us paper or this plot:
http://www.woodfortrees.org/plot/esrl-co2/from:1979/mean:12/derivative/plot/uah/from:1959/scale:0.22/offset:0.14
RE #I and 2 – different lags exist for different (approx.) cycle lengths. #3 is just a summary of #1 and 2.
RE #5 -” Insensitive” means ECS is less than 1C, and probably a lot less, because the only signal observable in the modern data record is as described in #1. Similar to your “small a in aGW”. I say ECS is so small it is materially irrelevant.
I am confident about #1, 3 and 5 and others – my only reservation in all 10 points is with #6 re imminent global cooling, and I hope to be wrong there – because of #8, 9 and 10.
Politicians may have brewed “the perfect storm”, damaging the electrical grid with costly and destructive green energy schemes to “fight global warming”, even as the climate cools.
Regards, Allan

Reply to  ristvan
September 13, 2016 6:13 am

Rud you said: “IMO there are much easier ways to convincingly refute CAGW.”
I agree, but that is not my sole objective. Climate science interests me, and I suggest that both sides (warmist vs skeptic) of the global warming debate probably have “put the cart before the horse”.
Unlike some others, I do not say that temperature is the primary driver of increasing CO2, although that could be correct. Land use changes, fossil fuel combustion, etc could also contribute – but I do say that this increase in atmospheric CO2 is not harmful and is beneficial to humanity and the environment.
I am still reasonably confident that that the future cannot cause the past. 🙂
See also Humlum et al, January 2013, written five years after my paper:
http://www.sciencedirect.com/science/article/pii/S0921818112001658
Highlights
– Changes in global atmospheric CO2 are lagging 11–12 months behind changes in global sea surface temperature.
– Changes in global atmospheric CO2 are lagging 9.5–10 months behind changes in global air surface temperature.
– Changes in global atmospheric CO2 are lagging about 9 months behind changes in global lower troposphere temperature.
– Changes in ocean temperatures explain a substantial part of the observed changes in atmospheric CO2 since January 1980.
– Changes in atmospheric CO2 are not tracking changes in human emissions.
Best, Allan

Reply to  ristvan
September 13, 2016 3:03 pm

WRT CO2/temperature causation, I agree with Allan MacRae based on real world observations. So far, I’ve found no credible data showing that ∆CO2 causes ∆T. It may, but when something is not capable of causing any observed changes following a particular input, then the Null Hypothesis has not been falsified even if CO2 causes some minuscule warming. In order to falsify the Null Hypothesis, it must be shown that rising CO2 causes a measurable change.
But all such observations show a one way cause-and-effect: ∆T causes ∆CO2. And while rising CO2 may cause a slight rise in global temperature, there are no corroborating, confirming observations.
Therefore, ∆CO2 can be disregarded; it is just too small to make a measurable difference.

Reply to  ristvan
September 14, 2016 9:38 am

Thank you db, good comments.

Reply to  ristvan
September 17, 2016 4:38 am

Hello Rud?
Rud – Come in please.
db – have you heard from Rud?

Reply to  ristvan
September 21, 2016 4:10 am

Hello Rud,
Are you working on a response as you stated? If so, kindly notify me when and where you post it.
You can contact me through my website.
Regards, Allan
Post Script:
I discovered the close relationship between dCO2/dt as a function of temperature T in late 2007 (and the resulting ~9 month lag of CO2 after T) and posted my paper in January 2008 on Joe d’Aleo’s site icecap.us. Some of my scientist friends warned me that I would be attacked, and they were right.
I recall the baseless attacks from both sides of the fractious “mainstream” global warming debate, both sides inextricably wedded to their hypothesis that CO2 primarily drives global temperature. They continue to argue about “how much warming will result from increasing CO2”, a little or a lot – aka “My ECS is bigger than yours!”. 🙂
The strong winds from all their frantic arm-waving have abated, replaced by a nervous calm, as few want to venture into the scary depths of this important question. Most just want to ignore it, play with their ECS’s and wave away Salby and Humlum or even slander them. I met Salby recently in Calgary and he seems like a decent guy, who bears all the bullying with dignity – maybe all of you should give him a break.

Michael Carter
September 12, 2016 12:58 pm

“damped by clouds in two logical ways, albedo and precipitation (negative primary system response, a damped system that cannot undergo ‘tipping point excursions’).”
True, but I would not overlook changes in fluid circulation: atmospheric and oceanic currents. In the longer term we also have biological feedbacks

Reply to  Michael Carter
September 12, 2016 5:11 pm

Yes. Agree. I nodded to those in the direct c/dc comments referencing greening and coccoliths. But dunno for sure. Have better knowledge of WVF and clouds.

Richard Petschauer
September 12, 2016 8:53 pm

Feedback should be based on changes in surface temperature caused by changes in surface temperature through some physical mechanism because we are interested in surface temperature. The common IPCC method refers all changes back to forcing at the the top of the atmosphere. Hence ignoring the large negative feedback from increased sea surface evaporation with temperature. This evaporation cooling reduces the net surface warming and also moves heat to the atmosphere when the added humidity condenses into clouds with the released heat increasing radiation to space from cloud tops. Evaporation at one place combined with condensation at another place is how home AC systems work. Nature has a similar air conditioning system powered by the climate.
By this definition, the Planck effect is not true feedback but a change in temperature due to a change in forcing such as a change in net solar energy at the surface or warming in the upper atmosphere which migrates to the surface.
Most feedback in amplifiers is negative so the final gain will vary less in percentage that the variation of the components used. And automatic gain control (AGC), a form of negative feedback, has been used for years in radios and TVs going back to vacuum tube technology to compensate for large variation in the incoming signal strength from the broadcasting stations.

Reply to  Richard Petschauer
September 12, 2016 10:48 pm

“Hence ignoring the large negative feedback from increased sea surface evaporation with temperature.”
It doesn’t ignore it – it treats it correctly. Evaporation does not cool the climate. Water evaporates, condenses and returns to the sea in the state at which it started. How could that change enthalpy. It transports heat, but the objective of the TOA definition is to capture the total upflux of heat. At lower altitudes that flux is split between IR, LH transport and convection.

1sky1
Reply to  Nick Stokes
September 13, 2016 2:07 pm

Evaporation does not cool the climate.

Evaporation is the principal mechanism of heat transfer from the Earth’s surface to the atmosphere, exceeding all other mechanisms combined. It’s effect is to sharply reduce the surface temperature from the values obtained via the Schwarzschild-Milne equation governing radiative transfer. To be sure, that is not a feedback mechanism in any rigorous sense of that word. But the persistent resort to misleading half truths by AGW disciples in pop-sci forums is dismaying.

Reply to  Nick Stokes
September 13, 2016 3:02 pm

“But the persistent resort to misleading half truths”
So do you think evaporation does cool the climate?
I was responding to an assertion that IPCC “Hence ignoring the large negative feedback from increased sea surface evaporation with temperature.”. Do you think they should have included negative feedback from increased sea surface evaporation?
I said that LH transports heat. But the relevant thing is that no net cooling is created in the atmosphere being modelled.

Richard Petschauer
Reply to  Nick Stokes
September 13, 2016 6:44 pm

Nick,
There must also be heat balance at the surface and that is the place that is more important to humans. Look at the well known Trenberth et all and similar energy balance papers . IR Radiation leaves the surface at 396 Wm-2 and increases 5.4 / C. Latent heat through evaporation is 80 Wm-2 and increases 5.4 / C (about 6% / C from basic physics). This is now being ignored regarding what happens at the surface. So to reach a balance at the surface the radiation increase drops (lower temp) because of the help from latent heat transfer. This is negative feedback referred to the surface temperature. This is somewhat offset by the warming clouds increasing the back radiation to the surface. Yes there is such a thing. It can becresad with an IR thermometer. Radiation heat transfer between a warm and cooler body is proportional to (Twarm^4 – Tcool^4). The enthalpy concept is OK at the surface.
The liquid freon in your air conditioner evaporates in your home and cools it and then condenses outside, releasing heat and returns to your home to its original state. Just like water returns. So what is your point?.

1sky1
Reply to  Nick Stokes
September 14, 2016 2:19 pm

As RP correctly points out above, it’s the heat energy budget at the surface, not at TOA, that is the main practical concern. After all, that’s what determines the terrestrial emissions that are variously absorbed, re-emitted, scattered and transmitted by the atmosphere. Since radiation is ultimately the only ticket for energy to space, the fact that enthalpy tends to be conserved on a planetary basis regardless of evaporation is a rather trivial observation. Nor is it strictly true, because some energy is dissipated via photosynthesis and another portion is persistently converted to mechanical energy that drives winds, waves and currents. That’s what the real-world surface climate is all about.

September 12, 2016 9:26 pm

Properly defined, a feedback is a change in some climate property given a change in some other climate property.
You don’t hold with the engineering definition that a “feedback” is a response that alters the input?
If an increase in surface temperature causes an increase in surface evaporation rate, that is not a “feedback”. If the increase in surface evaporation rate causes an increase in cloud cover which reduces incoming radiant energy from the sun, that is a feedback. This definitional issue has been raised many times.
Your definition does not distinguish “effects” from “feedbacks”.

September 12, 2016 9:46 pm

The GHE is not an increase in heat, does not involve CO2 ‘creating’ heat, and does not violate COE. All wrong conceptualizations of AGW basics. Earth’s heat energy input is provided by solar ISR, at about a constant 240wm-2 (Monckton FoC #3 table 1, and Nick Stokes comments to Fubar). GHE is the result of certain gas molecules, most importantly water vapor and CO2, ‘absorbing’ and then ‘scattering’ by omnidirectional re-emission, OLR photons. That is, those atmospheric molecules hinder OLR radiative cooling from Earth’s surface to space. A surface warmed by ISR but not cooled by an equivalent amount of OLR will warm until the increase in resultant surface temperature produces enough additional OLR to restore the net balance.
So, “not an increase in heat” transforms somehow to an “increase in resultant surface temperature”? Obviously you meant something other than what you wrote. On the whole, your essay has more noise than signal. There is an increase in retained heat, not created by CO2, and there is no violation of COE; you got two out of three in that sentence correct, but then you added distracting stuff like a claim of Fubar; and in the end contradicted your opening clause.
I suggest you rewrite this, perhaps with the help of the poor PhD fellow who translated the Chinese paper that was put up a couple days ago. That had fewer mistakes.

September 12, 2016 10:26 pm

“I suggest you rewrite this”
A minor change needed to satisfy your extravagant objection – the GHE is not an increase in heat production. Or export. All true. If you pile on blankets, you get warmer, but you don’t generate more heat.

September 13, 2016 12:17 pm

Can someone please explain how the radiation model explains the lapse rate

Reply to  Nippy
September 21, 2016 5:14 pm

You can google that. Why waste time with an ignorami?

Gabro
Reply to  ristvan
September 21, 2016 5:17 pm

The singular is ignoramus.

September 13, 2016 3:40 pm

Very good article, as were your prior article — wish you had time for more of them here.
You should mention your book each time.
I automatically liked after seeing the word “warmunists”.
But I did have brief comments on these two sentences:
(1) “Feedbacks are properly understood as ‘first derivatives’ of basic climate properties, not those properties themselves.”
MY COMMENT: Is it possible that so little is known about the exact causes of climate change, that a variable we currently are sure is a “basic climate property” … is actually a feedback?
(2) “Since the climate according to warmunists was in proximate ‘property equilibrium’ circa 1880 per their basic CAGW theory … “,
MY COMMENT: Everybody who is anybody knows Earth’s climate was perfect on June 6, 1750 at 2pm — any change from the CO2 content and average temperature at that hour, on that day *** … is a catastrophe … and the only solution is more government regulations and taxes on everything related to energy.
*** Average temperature and CO2 data are close to wild guesses for 1750, of course, but after proper “adjustments” by goobermint bureaucrats, the data morph into ultra-sccurate numbers presented to the public in hundredths of a degree C.
Climate blog for non-scientists:
Free
No ads.
No money for me
A public service
— Liberals should stay away, or risk high blood pressure!.
http://www.elOnionBloggle.Blogspot.com

Reply to  Richard Greene
September 15, 2016 3:22 pm

RG, a belated return. On your point one, Imthink we know enough romget a general outline that fits loosely together with due allowance for Curry’s uncertainty monster. On your point two, I did not say perfect. i said in rough equilibrium save the long slow march out of the LIA.
As for warmunism. I give all idea credit to Vaclav Klaus, former heead of the Czech Republic, in his book Blue Planet in Green Chains. See last paragraph of essay Climatastrosophistry in ebook Blowing Smoke.
And your link is now in my iPad bookmarks list for periodic review.
Regards.

KevinK
September 13, 2016 4:30 pm

Richard Verney wrote;
“If the photons are being delayed merely by microns or by seconds, heck even by minutes then all that may be happening is that the coolest period of the night is being put back by micro seconds, or seconds, or heck even by minutes and nothing more than that.”
Exactly, the delay in the flow of photons merely changes the response time of the gases in the atmosphere causing them to warm up ever slightly faster at Sunrise and every slightly slower at Sunset. It also probably shifts the peak daytime temperature just slightly sooner in the 24 hour cycle.
Given the dimensions of the atmosphere (5-10 miles), the speed of light (still considered quite speedy at 186,000 miles per SECOND), and accounting for multiple passes through the system this delay is most likely on the order of a few tens (perhaps a few hundreds) of milliseconds.
For reference purposes there are about 86 MILLION milliseconds in a day.
Ironically enough the climate science community has been looking at the entire wrong end of the time scale. If you want to see the effects of additional CO2 in the atmosphere is is necessary to make temperature measurements every few milliseconds, not every day.
If the concentration of “GHE” gases was large enough AND they had sufficient thermal capacity then the delay may approach the “frequency” of the arriving daylight, In that case the “Radiative Greenhouse Effect” would be able to affect the average temperature at the surface of the Earth. In other words; some photons would be “leftover” from yesterday to make it a little warmer today.
Cheers, KevinK

KevinK
September 13, 2016 4:40 pm

Bartemis wrote;
“Let me ask you, when you turn off the lights in your house do all the photons being reflected off the walls (back radiation) stick around and keep your house illuminated ?”
Yes. My house is aglow with IR radiation at all hours. The walls hinder both convection and radiation of heat energy away from my home, so that I do not freeze at night.”
With all due respect those IR Photons are coming from the walls/ceiling/furnishings inside your house. They are created because all those items have been heated by your furnace/heat pump/solar cell/windmiil.
They are not created by LWIR from the other furnishing inside you house.
A dam works by slowing the velocity of water flow. This can be seen with a small 1 inch high “dam”.
The “Radiative Greenhouse Effect” does not change the velocity of light.
There is a difference between a diminished velocity and a delay.
So we have discussed; solar blankets, resistors, steel greenhouses and now we have dams as the prospered analogy for the “Radiatve Greenhouse Effect”.
The correct analogy is well known and has been around for over a century. That is the optical integrating sphere (aka an Ulbricht Sphere). It exhibits what a climate scientist would call 100% radiative forcing and yet the light coming out of it is not any “brighter” than the light entering it….. Where is the “Positive Feedback” ?????
Cheers, KevinK

Reply to  KevinK
September 14, 2016 11:04 am

If by “solar blankets” you mean MLI blankets, they definitely do work by impeding radiative egress of heat. They do exactly what you are saying cannot be done. And, they absolutely, positively, do work as designed.

Reply to  Bartemis
September 14, 2016 11:12 am

If by “solar blankets” you mean MLI blankets, they definitely do work by impeding radiative egress of heat. They do exactly what you are saying cannot be done. And, they absolutely, positively, do work as designed.

There’s a chapter in the book on that, it’s under reflection.

KevinK
Reply to  Bartemis
September 14, 2016 2:40 pm

Yes, MLI blankets work as designed IN A VACUUM to keep objects in a vacuum more stable with respect to temperature. They can be used to keep heat “in” or to keep heat “out”. But they do not make a passive object maintain a higher temperature permanently.
The object being blanketed has to be a source of heat (something consuming electricity and producing heat like electronics for example). Or the human body.
Wrapping MLI around a passive object (a round ball of metal) and launching it into space will not cause it to reach a higher temperature.
MLI is also wrapped around sensitive space telescopes which also have electrical heaters attached to provide a source of heat. Using the MLI in combination with a source of heat helps maintain the stable temperatures needed to keep large space borne structures stable.
For reference purposes a “source of heat” consumes energy (oil, electricity, wood) and emits thermal energy without cooling off. A “reservoir of heat” emits thermal energy and loses that thermal energy. If those loses exceed thermal energy gains it cools off.
An electric heater is a “source of heat”, a rock (like the Earth) is merely a “reservoir” of heat. Very important distinction.
Cheers, KevinK.

Reply to  KevinK
September 14, 2016 2:51 pm

a rock (like the Earth) is merely a “reservoir” of heat

On average it cools slightly more at night than it warmed the day before (75 million daily samples) over a year, but it’s easy to measure warm asphalt after a night of cooling, a few days ago my driveway was still 10F warmer than air temps, and almost 20F more than my yard.

Reply to  Bartemis
September 14, 2016 4:38 pm

“Yes, MLI blankets work as designed IN A VACUUM to keep objects in a vacuum more stable with respect to temperature.”
Indeed, they do. And, the way they do that is by slowing the egress of heat energy via radiation.
When in Sunlight, the MLI reflects back a lot of the incoming radiation. But, for the radiation that gets through, it keeps the satellite warmer than it otherwise would be for the same input radiant energy without the MLI.
“They can be used to keep heat “in” or to keep heat “out”. But they do not make a passive object maintain a higher temperature permanently.”
They absolutely do, which they must, if the preceding is true (which, it is).
This is cut and dried. Old news. Applied technology each and every day since the dawn of the Space Age.

Reply to  Bartemis
September 14, 2016 4:41 pm

“Yes, MLI blankets work as designed IN A VACUUM to keep objects in a vacuum more stable with respect to temperature.”
It is precisely the fact that the Earth’s atmosphere is not a vacuum, and has other modes of heat transport than just radiation, that is the weak point in the AGW argument.* I suggest you redirect your energies in that direction.
*Well, it’s a weak point. The major weak point, though it is not widely recognized as such yet, is that humans have little impact on atmospheric CO2 levels in the first place.

KevinK
September 13, 2016 5:49 pm

Opps; “prospered” should have been “proffered”. That one is on me, I can’t blame the spell checker.
Cheers, KevinK

KevinK
September 13, 2016 6:04 pm

Oh, also, there is an effect known as “self absorption” present in an optical integrating sphere. This effect does indeed cause a light bulb to “warm” from “back radiation”. The light bulb does indeed “see” the back radiated light and it does indeed warm (as proffered (got it right that time) by the “GHE” hypothesis),
However, there is one very important consideration that applies; the light bulb is only able to stay at a “warmer” state due to the presence of an external power supply. A light bulb (incandescent filament) is merely an energy conversion device; it converts electrons to photons. It’s efficiency (aka efficacy) is dependent on it’s temperature. When it is warmed by the back radiation it becomes slightly more efficient (a few tenths of a percent). The important thing to note is that is it the presence of an electrical power supply (constant voltage, or more preferred constant current) that is able to sustain this higher temperature.
Without the amplifying (aka gain) effect provided by the power supply the light bulb would quickly cool back down. This is in fact an example of “feedback” in a radiative physics situation. It is important to note that this is only possible due to the “gain” provided by the power supply. Without this externally supplied gain there would be no “feedback”. In fact if you unplug the power supply a light bulb inside an optical integrating sphere will merely cool down to room temperature just slightly slower (probably imperceptible without expensive instrumentation) than a light bulb that is not inside an integrating sphere.
Cheers, KevinK

gallopingcamel
September 13, 2016 8:17 pm

ristvan.
You are fundamentally in error because you assume the [CO2] leads temperature according to an equation originally stated by Arrhenius in 1896. This theory is false so the “Sensitivity Constant” you imagine is meaningless.
Here are a couple of links that explain:
https://diggingintheclay.wordpress.com/2013/05/04/the-dog-that-did-not-bark/
https://diggingintheclay.wordpress.com/2013/03/07/arrhenius-revisited/

Reply to  gallopingcamel
September 21, 2016 5:19 pm

Gk, one of us is wrong. i stongly, based on a century of physics, suggest it is you. Not worth wasting further time on such basic ohysics ignorance. Your links merely show how bad the blogosphere can be. For a ‘vaccination’ ‘cure’ get my ebook The Arts of Truth. Cheap, and deals with your problem extensively.

basicstats
September 14, 2016 7:38 am

Properly defined, a feedback is a change in some climate property given a change in some other climate property. Conceptually, it is a first derivative of the property; a change in one with respect to a change in another
This Bode stuff makes my eyes glaze over, but as a definition of feedback this just does not seem right. Apart from anything else, Monckton says feedback is unitless and derivatives are likely not. The feedback is the multiplier (as in economics) when a derivative is written in geometric series form. I think??

Reply to  basicstats
September 14, 2016 8:10 am

First if the feedback gain is (1-gh)^1 GH must unitless, the units of g are the inverse of the units of h.
The derivitives are the values that set g and h. We posit changes to the climate to see how it changes the relationship between forcing and temperature.
Feedbacks are not in the gain equation, just the derivatives.

Reply to  Thompson David
September 14, 2016 8:15 am

1 is unitless.
Boltzmann is W/m^2 per K, what does the inverse of that mean?

KevinK
September 14, 2016 5:07 pm

Bartemis/Tony/Steve;
“It is precisely the fact that the Earth’s atmosphere is not a vacuum, and has other modes of heat transport than just radiation, that is the weak point in the AGW argument.* I suggest you redirect your energies in that direction.”
I will direct my energies as I see fit, thank you very much. I am bored with reading old newspaper articles, surely you must be as well by now.
The “Radiative Greenhouse Effect” is an optical illusion, a mirage, a chimera…
This was shown By R. W. Wood over a century ago (and replicated again and again recently).
He also disproved the existence of “N Rays”, good thing too or the government would want to restrict our use of “N ray” producing metals…..
Cheers, KevinK.

KevinK
September 14, 2016 5:19 pm

Bartemis;
“But, for the radiation that gets through, it keeps the satellite warmer than it otherwise would be for the same input radiant energy without the MLI.”
NO, without an internal source of heat (like the three astronauts in the Apollo capsule) the satellite WILL NOT BE warmer “than it otherwise would be” without the MLI.
Of course that assumes that there even was three astronauts in an Apollo capsule………….
Have you ever even been near a space vehicle ? I help design them for a living, I have been next to many of them on the factory floor before they get launched. I have participated in design reviews where the thermal modelling that predicts the onboard temperature when they reach orbit is “scrubbed”, have you ?
Oh and by the way everybody is thrilled if the predictions match within plus or minus 5 degrees….
Plus or minus 5 degrees is “State of the Art” in predicting temperatures resulting from received/emitted radiation. Conductive is better, convective is worse.
Cheers, KevinK