by Rud Istvan

UPDATE: Response from Christopher Monckton

The Monckton, Soon, Legates, and Briggs paper “Why models run hot, results from an irreducibly simple climate model” appeared in the January 2015 Science Bulletin of the Chinese Academy of Sciences (CAS). Hereinafter MSLB.

The paper discusses the divergence between climate models and observed temperatures, and develops the implications for climate sensitivity.

MSLB has created quite a kerfuffle. There was initial dismissal: it was claimed that Science Bulletin is an obscure journal with lax review standards, so the paper is no good. Bulletin turned out to be the Chinese equivalent of Science or Nature. Then came MSM efforts (NYT, Boston Globe, WaPo, even BarackObama.com) to discredit the authors. This has escalated into a more general attack on prominent skeptics like Christy, Pielke, and our gracious hostess [link]. These attacks are growing ugly, for example from BarackObama.com on 2/23/2015: “Bad things are coming for these boys and girls. (Name list) Keep your eye on the media. Several stories.”

Dr. Trenberth of NCAR provided NYTimes reporter Gillis a MSLB rebuttal, posted at Matt Brigg’s blog [link]. Gillis did not report Brigg’s reply. Trenberth dismissed the simple model simply because it is simple—and said the ‘pause’ is insignificant natural variation. Yes, but the now 18+ year pause/hiatus is in very serious disagreement with CMIP5 climate model simulations using criteria set out by climate modelers themselves in 2011 [link] . Trenberth’s comments to the NYTimes are indefensibly misleading in my opinion, and provide a vivid object lesson about consensus climate ‘science’ and its reporting.

There was a saying among WWII Army Air Force bomber pilots: “If you are taking heavy flak, you are over the target”. What is it about this target?

CMIP5 climate model simulations continue to diverge from observed temperatures because of the ‘pause’. This suggests the GCMs are oversensitive to increases in CO2 – CO2 continues to increase ‘business as usual’ per RCP8.5, while temperature hasn’t. MSLB discusses this divergence shown by their Figure 2, and then offers a non-GCM way to understand why this is happening and what it means for climate sensitivity.

MSLB proceeds in three steps: (1) derives the ‘irreducibly simple’ climate sensitivity equation, (2) estimates the 5 required parameters from mainly IPCC sources, and then (3) uses both to debunk IPCC sensitivity estimates. The first two steps are useful and instructive. The last step is unfortunately partly wrong. This post covers that last step first.

What’s wrong with MSLB

Background . There is no reasonable doubt that radiative physics says ‘greenhouse gases’ (GHGs) warm the atmosphere. (If SkyDragons need a layman’s explanation, read essay Sensitive Uncertainty in ebook Blowing Smoke.) ‘Grey earth’ modifications of the canonical Stefan-Boltzmann black body radiation equation (1.0C) produce either 1.1C or 1.2C per CO2 doubling. MIT Prof. emeritus Lindzen uses 1.2C. The climate sensitivity question is whether that physics is attenuated or amplified by Earth’s feedbacks, most importantly water vapor (a potent GHG) and clouds. Earth must have some feedback of some sign, operating on the simple physics of 1.2C in some way to produce some final equilibrium temperature response to doubled atmospheric CO2.

Both IPCC AR4 (CMIP3) and AR5 (CMIP5) GCMs estimate the resulting equilibrium climate sensitivity (ECS) at +3.2C on average. There is substantial GCM model-to-model variance, for example in AR4 WG1 Table 8.2. This gives a ‘simple average’ multiplier of (3.2/1.2) ~ +2.67. AR4 gave a point (mode) estimate of +3.0C (~ +2.5). AR5 only gave a likely range from +1.5C to +4.5C, and explicitly did not give a midpoint value, owing to the discrepancy between climate model and observationally derived values. GCMs derive feedback by doubling (or quadrupling) CO2, then simulating into the future at least 150 years. Most of us do not have the supercomputer resources to do so. Hence the utility of simpler sensitivity models for the rest of us. MSLB said, “The simple climate model outlined here is not intended as a substitute for the general-circulation models. … rather, it is intended to illuminate them. …The simple model provides a benchmark against which to measure the soundness of the more complex models’ predictions.”

Bode Model. The Bode feedback model is adopted from electronic circuit design, as MSLB points out. It is very simple. The multiplier over ‘grey’ SB 1.2C is just 1/(1-f), where f is the sum total of positive and negative feedbacks. As Lindzen explained to British Parliament (www.rlindzen@MIT.edu ) [my IPCC added in the red curve]

The Bode curve translates an IPCC estimate of ECS ~3 – 3.2C to a Bode feedback f of ~0.6 – 0.65 for f0 (no feedback, f=0) of 1.2C. It is the simplest possible feedback model, even simpler than the ‘irreducibly simple’ MSLB equation. We shall return to IPCC’s roughly f ~ 0.65, because it contains additional lessons about what is probably wrong with the IPCC GCMs.

Erroneous MSLB Assertion

JC note: I am having trouble formatting subscript/superscripts. To anyone that wants to follow the equations carefully, see this pdf file equations with the formatted equations and sub/superscripts

MSLB used a complicated method involving additional math not directly related to the irreducibly simple equation to calculate the equivalent of Bode f. Confusing, although apparently rigorous. The resulting Bode f equivalent is the closed loop gain gt = λ0 * ft where λ0 is the zero feedback radiative forcing (see below) and ft is the sum of all feedback radiative forcings like water vapor, lapse rate, clouds… MSLB estimates the IPCC ft from Figure 3 (which reproduces AR5 WG1 9.43): “The feedback sum ft (right-hand column) falls on 1.5 [1.0, 2.2] W(m2 K) for AR5, compared with 1.9 [1.5, 2.4] W/(m2 K) for AR4.” MSLB Table 1 provides calculated gt (IPCC Bode f) ranging from 0.31 to 0.75 for AR4 and AR5.

The IPCC Bode f could have been derived more simply. An ECS of 3.2C over Plank 1.2C yields a simple Bode multiplier of 2.67 ≈ 2.7 for (1/1-f). The IPCC feedback f is therefore ~0.63 since 1/(1-0.63) = 1/0.37 = 2.7. That is all MSLB had to do to be irreducibly simple in this part of the paper.

MSLB Figure 5 asserts that the more complexly derived values would result in unstable climates (the figure’s x axis should have been labeled g∞ per the accompanying text, a confusing chart/text discrepancy). MSLB therefore argues the GCM models are not trustworthy, because they result in unstable response regimes. It is evident by inspection that any Bode f under or around the inflection (below ~0.75) is stable. IPCC f ≈ 0.65 does not lead to an unstable climate. This conclusion is merely an unsupported “Process engineer’s design limit ≤+0.1” assertion.

As is clear from either Lindzen’s f plot or MSLB’s expanded equivalent gt plot, all of MSLB’s calculated IPCC feedback f values are well behaved.

None of the paper’s long ‘step 3’ ‘closed loop gain’ / Bode f discussion relates directly to the ‘irreducibly simple equation’ itself, or to its evaluation. It muddles the rest of the paper and obscures the equation’s utility, in my opinion.

What’s Right with MSLB

The mathematical derivation of the ‘irreducibly simple’ equation is impeccable. The ‘simple’ result (rearranged here for expository convenience) is:

ECS = (λ0/qt) ĸ ln(Ct/C0) rt /(1-λ0ft)

For those with math allergies, here is a translation into sort of English: ECS (equilibrium or ‘effective’ climate sensitivity) = λ0 (the traditional radiative forcing greenhouse effect with zero feedback. A radiative forcing equivalent to f0=1.2C in the Bode model, with the same result.

qt is the proportion of total GHG that is CO2. This just scales from the CO2 portion to the whole of anthropogenic GHGs.

ĸ is the CO2 GHG forcing constant.

ln (CO2 at t something/CO2 at t=0). This is just the expected rise in CO2. For sensitivity, the traditional test is doubled CO2, so this term is just ln(2) = 0.69.

rt (‘transience fraction’), the proportion of the eventual total climate response at time t. This lag arises mainly from ocean thermal inertia.

(1-λ0 * ft), which is where all the bodies are buried. Since ft is none other than the simple (now familiar) Bode f over some feedback time t.

Lets rephrase this ‘irreducibly simple’ equation yet again, in even simpler more common sensical English using no mathy stuff at all: Climate sensitivity equals the radiative forcing from all anthropogenic greenhouse gases including CO2, times the (known since Guy Callender in 1938) logarithmically declining impact of increasing CO2, times the transient lag to climate equilibrium, times some feedback f changing this direct CO2 effect.

We are left with the same old Bode feedback f, wrapped in some interesting additional parameters. The vicious consensus attack on MSLB cannot be motivated by such an innocuous uncontroversial equation/statement. It has to have been motivated by the conclusions derived from it. Lets look deeper.

MSLB derives values for the equation’s five ‘tunable’ parameters using mostly IPCC AR4 and AR5, and some mathematical cross checking on λ0.

λ0 ~0.31, the IPCC AR4/AR5 value.

qt ~0.83, the IPCC AR5 value (slightly dependent on RCP scenario).

ĸ ~5.35, the IPCC TAR/AR4/AR5 value.

rt is potentially more complicated. MSLB Table 2 and discussion develop a plausible range of values for various assumed ft. A reasonable range is perhaps 0.55 to 0.85. There is a simpler way to derive this ‘transience fraction’ (climate response lag) since rt is tantamount to the ratio of TCR to ECS. The AR4 models (WG1 8.6.2.3) have rt from 0.56-0.76. The newish Lewis and Curry estimate http://www.judithcurry.com/2014/09/24/lewis-and-curry-climate-sensitivity-uncertainty/ gives (TCR 1.3/ ECS 1.7) ~0.76, used here. Professor Lindzen points out that the higher a climate model’s sensitivity, the slower its total response. Higher sensitivity IPCC models should have a smaller rt … and they do [link].

That leaves ft forcings. But, it is easier to substitute f. Anyone can plug any f they think suitable into either the MSLB equation (for λ0 * ft) or into the simpler Bode equation 1.2C*[1/(1-f)]. Or, just use Lindzen’s graph. We found earlier that IPCC AR5 implicitly has an f about 0.65. This can be decomposed along MSLB lines. Water vapor feedback (including lapse rate) is about 65-80% of the total ft (AR5 WG1 figure 9.43 or MSLB Figure 3), so Bode fw ~0.45 to 0.5. The rest is about Bode fc ~0.15 to 0.20, which is mainly clouds since the other stuff is smallish and mostly offsetting. Rules of thumb thinking. Simple models do not need precision to provide instructive lessons.

Water vapor feedback fw

Climate models produce a tropical troposphere hotspot that does not exist in reality. See Prof. John Christy’s presentation to APS [link] . That is because modeled upper troposphere specific humidity is too high. The probable reason is the physical inability of coarse-resolution GCMs to simulate tropical convection cells (thunderstorms). They must be parameterized instead. Essays Models all the way Down and Humidity is still Wet (in Blowing Smoke) provide details. CMIP3/5 climate models also underestimate the precipitation that removes atmospheric water vapor– by about half (citations in the essays). Given these model/observation differences, perhaps the water vapor feedback is on the order of about half the climate models, notionally something like fw ~0.25.

Cloud feedback fc

Dessler’s 2010 clear/cloudy sky satellite paper actually suggests zero cloud feedback, contrary to what he claimed and what is on the NASA website. Essay Cloudy Clouds (in Blowing Smoke) provides much more detail. To a first order very rough observational approximation, cloud fc ~0. AR5 WG1 7.2 says it is uncertain, but certainly positive. (Phrased that crisply, the IPCC non sequitur is obvious). This provides a lesson on the consensus belief in models over observations, a belief deeply unsettled by the undeniable pause/divergence.

Combined, these observations suggest an ft on the order of (0.25), a little less than half the implicit IPCC f. Plug some ft like that into the irreducibly simple MSLB equation using the foregoing parameters, and out pops an ECS of about ~1.75. Or, just spot your preferred f on the x axis, and read ECS off the y axis of the Bode plot above. Use your own ‘red lines’. An f of about 0.25 provides an ECS remarkably similar to the Lewis and Curry result, which was derived using completely different and much more sophisticated methods.

Bottom line

The simple non-GCM models Trenberth dismisses have great utility. Observations now suggest Earth’s ECS is a bit more than half of what the IPCC has proclaimed as settled ‘GCM science’. Simple models like those discussed here can deconstruct f to suggest how and why. That unsettles the IPCC science. MSLB’s simple model has vociferously unsettled the ‘consensus’. Lower ECS silences the urgent, loud alarm to mitigate at COP21 in Paris—unless the consensus’ increasingly nasty public attacks succeed in silencing all the skeptics who point out simple stuff.

Bio notes: Rud Istvan has published three books

Rud has also authored frequent guest posts at Climate Etc. [link]

JC note: I appreciate Rud starting a technical dialogue on this controversial paper. As with all guest posts, keep your comments civil and relevant. Treat this as a technical thread; keep your comments/questions related to the Monckton et al paper; general comments about the controversy surrounding the paper should be made on the Conflict of Interest post.

***UPDATE: I have received a response from Christopher Monckton. Since it is longer than the original post, I am providing it as a pdf file that you can download [monckton]