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:

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:

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

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