By Joe Born
Introduction
A long line of this site’s posts dated March 19, 2018, March 27, 2018, March 30, 2018, April 6, 2018, April 24, 2018, July 30, 2018, August 15, 2018, June 3, 2019, June 5, 2019, June 8, 2019, July 22, 2019, February 1, 2021, May 9, 2021, July 8, 2021, December 2, 2021, April 3, 2022, April 6, 2022, July 2, 2022, and September 9, 2022, advanced the theory that the reason for high estimates of equilibrium climate sensitivity (“ECS”) is that modelers failed to take sunshine into account. (ECS is the equilibrium-temperature change that doubling the atmosphere’s carbon-dioxide content would eventually cause.)
Slogging through that compilation of changing values, ambiguities, and non sequiturs was a dispiriting exercise, but a reasonably clear distillation of the theory eventually did turn up, in what was triumphantly called “the end of the global warming scam in a single slide.” By focusing last year on that slide we demonstrated that this forgotten-sunshine theory amounts to no more than bad extrapolation and that the purported feedback law on which the theory rests actually doesn’t rule high ECS values out at all.
Perhaps as a result of that demonstration a new slide was substituted and emphasis was shifted to a new definition of the feedback law that high ECS values were claimed to violate. In this post we use that new slide as our focus.
What we will find as a result is that the rule imposed by the new slide’s calculations is not a valid feedback law and that the new definition either (1) imposes linear proportionality that feedback theory doesn’t require or (2) fails, by allowing the nonlinearity that feedback theory permits, to rule out high ECS values. In the process we will dispose of some of the ancillary claims that have been made in support of this theory.
Background
To the extent that there actually is such a thing as ECS, many observation-based papers such as those by Lindzen & Choi, Otto et al., and Lewis & Curry have found its value to be significantly lower than most prominent models’ estimates. “However,” Christopher Monckton said of such papers’ authors, “they can’t absolutely prove that they are right. We think that what we’ve done here is to absolutely prove that we are right.”
The key, he says, is feedback theory. The climate is a feedback system, so it must follow the laws that apply to feedback systems generally. And since in absolute terms the global-average surface temperature isn’t much greater than it would be without feedback, he says, feedback law prohibits high ECS values. But he’s never defined with clarity just what the feedback law is that would rule high ECS values out.
That’s not to say that he’s never attempted such a definition. The noun clause in the following passage’s first sentence, for example, is one he’s primarily used until recently:
[T]he main point . . . is that such feedbacks as may subsist in a dynamical system at any given moment must perforce respond to the entire reference signal then obtaining, and not merely to some arbitrarily-selected fraction thereof. Once that point – which is well established in control theory but has, as far as we can discover, hitherto entirely escaped the attention of climatology- is conceded, as it must be, then it follows that equilibrium sensitivity to doubled CO2 must be low.”
We’ll call that clause his “entire-signal law,” and perhaps it can be so interpreted as to be valid. But, contrary to what the foregoing passage’s second sentence contends, the entire-signal law doesn’t necessarily imply low ECS values. To see why he nonetheless imagines it does, let’s consider how he views feedback.
In the climate context temperature feedback refers to the effects of temperature determinants that in turn depend on temperature. Water vapor and clouds, for example, affect temperature, which in turn affects evaporation and thereby water vapor and clouds. Similarly, albedo—i.e., the fraction of solar radiation that the earth reflects rather than absorbs—affects temperature, which in turn affects ice and snow cover and thereby albedo. Feedback is typically distinguished from “direct” effects of, say, the sun and the atmospheric concentrations of non-condensing greenhouse gases like carbon dioxide, whose minor temperature dependence is usually ignored in such discussions.
Fig. 1 illustrates how Lord Monckton looks upon the equilibrium global-average surface temperature E: as the sum of (1) the value R (“reference signal”) it would have without feedback and (2) a feedback response F equal to the product of E and a feedback coefficient f. The without-feedback temperature R can be thought of as the sum of “direct input signals” S and C, where S is the value that R would have if there were no non-condensing greenhouse gases and C is the difference between that value and the value to which such greenhouse gases raise R. (If thus adding temperatures makes you feel queasy, please hold your physics objections in abeyance and for present purposes just focus on the math. Similar forbearance is requested of those who unlike Lord Monckton look upon feedback as only a small-signal quantity, i.e., as operating only on departures from some baseline condition.)
It is widely accepted that if there were no feedback the equilibrium-temperature increase caused by doubling carbon-dioxide concentration would be modest; Lord Monckton’s new slide calls it 1.05 K, which he refers to as the “reference climate sensitivity,” or “RCS.” So the change in F for a 1.05 K change in R has to be large if ECS estimates are greatly to exceed that modest RCS value. According to the forgotten-sunshine theory, however, feedback theory tells us that large feedback-response changes are inconsistent with the fact that (at least according to him) the pre-industrial value of the total equilibrium feedback response F was only 24 K.
That pre-industrial value of F is represented (but not to scale) by the ordinate of the red dot in Fig. 2. The upper green dot’s ordinate represents (again, not to scale) what doubling carbon-dioxide content would change F to if ECS were high: the result of adding to F’s pre-industrial value the difference between the RCS value and a high ECS value. By in effect projecting through those points to F = 0 as the green dashed line suggests, Lord Monckton concluded that instead of making the feedback “respond to the entire reference signal then obtaining” climate modelers had made the “grave error” of forgetting that signal’s sunshine constituent S.
He claims the scientific literature supports this conclusion. For example, he frequently cites a 2010 Science article by Lacis et al. entitled “Atmospheric CO2: Principal Control Knob Governing Earth’s Temperature.” That paper’s ECS estimate is high, and presumably from the thereby-implied high extrapolation slope Lord Monckton inferred that according to Lacis et al. the feedback response would reach zero at the 255 K value they gave as the “emission temperature.”
But that’s a bizarre interpretation of Lacis et al.’s following passage:
A direct consequence of this combination of feedback by the condensable and forcing by the noncondensable constituents of the atmospheric greenhouse is that the terrestrial greenhouse effect would collapse were it not for the presence of these noncondensing GHGs. If the global atmospheric temperatures were to fall to as low as [255 K], the Clausius-Clapeyron relation would imply that the sustainable amount of atmospheric water vapor would become less than 10% of the current atmospheric value. This would result in (radiative) forcing reduced by [about 30 watts per square meter], causing much of the remaining water vapor to precipitate, thus enhancing the snow/ice albedo to further diminish the absorbed solar radiation. Such a condition would inevitably lead to runaway glaciation, producing an ice ball Earth.
Lacis et al. say evaporation and albedo feedback would persist, that is, even if the complete loss of carbon dioxide and other “noncondensable constituents of the atmospheric greenhouse” were to reduce the surface temperature to a value as low as the 255 K emission temperature. So the reason why Lacis et al.’s estimate was too high isn’t that they had “forgotten that the Sun is shining.”
As Fig. 2’s hypothetical feedback curve suggests, modelers more likely did indeed take sunshine into account but believed that the feedback coefficient f would be lower at lower E values than it is now, i.e., that F is a nonlinear function of E and thus of R. (Actually, F and E probably are not single-valued functions of R, but for the sake of discussion we’ll assume they are.)
Lord Monckton nonetheless thinks modelers neglected sunshine, so to take it into account he extrapolates from the origin. He thereby arrives at the lower feedback quantity represented by Fig. 2’s blue dot.
Extrapolation
After Lord Monckton had for years used the above-quoted entire-signal language to define the purported feedback law on which he based such calculations, “An Electronic Analog to Climate Feedback” illustrated how high ECS values can result even if the feedback does respond to “the entire reference signal.” (The feedback element in that electronic analog responded to the entire voltage difference between a virtual ground and an output node whose voltage was proportional to the entire sum of the input and feedback currents.) Lord Monckton thereafter introduced a “strict proportion” formulation we’ll see in due course. He still says of climate modelers, though, that “[w]hat the poor saps had forgotten is that the Sun is shining,” and his new slide, to which we presently turn, purports to depict that error and his “correction.”
We will see that in the new slide, too, his correction amounts to linear extrapolation from the origin and thereby imposes linear proportionality. Since linear proportionality isn’t a valid feedback law, though, he denies that the slide’s “corrected” calculation amounts to extrapolation:
To head off the trolls who tend to maunder on to the ineffectual effect that that calculation is ‘inappropriate extrapolation’, there is no extrapolation at all: for there was a temperature equilibrium in 1850. It was, of course, the perpetrators of the error, not I, who had extrapolated, in that they had imagined that the ratio of equilibrium to directly-forced warming in 2100 would be about the same as it was in 1850.” </blockquote>
But that first sentence is a non sequitur; nothing about the existence of an 1850 temperature equilibrium is inconsistent with the proposition that the new slide depicts the simple linear extrapolation we learned in high-school analytic geometry.
Remember how we were asked in high school to estimate a third point C on an unknown curve from two known points A and B? We would be given C’s x coordinate, and to estimate the y-coordinate difference between Points B and C we would multiply the x-coordinate difference between B and C by an extrapolation slope m calculated as the ratio that A and B’s y-coordinate difference bears to their x-coordinate difference.
Fig. 3 illustrates that operation, with R’s and E’s substituted for our high-school x’s and y’s. The hypothetical unknown E(R) function starts at the origin because E and R are absolute temperatures and therefore positive-valued, and for illustration purposes we’ve made that function more convex than high-ECS proponents probably would. The green dot represents the extrapolated estimate of the hypothetically true value that the top red dot depicts.
Such simple linear extrapolation is exactly what the first two rows of Lord Monckton’s above-copied new slide illustrate. (We’ll eventually see that the slide’s third row is just a distraction.) The slide’s first row represents calculating the extrapolation slope m = ΔE/ΔR, while its second row represents calculating ECS by taking the product of that extrapolation slope and the 1.05 K RCS value.
The slide’s first, “FALSE” column represents the climatology error that Lord Monckton has allegedly discovered. Its second, “CORRECTED” column represents the calculation that his feedback law dictates. Both columns take as their Point B the (R, E) = (263 K, 287 K) state of pre-industrial equilibrium that Lord Monckton says prevailed in 1850. But the two columns’ calculations arrive at different ECS values (4.2 K and 1.1 K) because they base their extrapolation-slope calculations on different Points A.
The “FALSE” column’s Point A is the (R, E) = (255 K, 255 K) state that Lord Monckton says modelers believe would prevail in the absence of non-condensing greenhouse gases: the with- and without-feedback temperatures E and R are identical because according to Lord Monckton modelers think the feedback response F would be zero at the 255 K temperature that (we accept for the sake of argument) would result if the sun were the only source of “direct” warming. Accordingly, the slide’s “FALSE” column calculates its ECS value 4.2 K by taking the product of the RCS value 1.05 K and the extrapolation slope m = 4 (= 32 K ÷ 8 K) calculated as the ratio ΔE/ΔR of the temperature differences ΔE = 32 K (= 287 K – 255 K) and ΔR = 8 K (= 263 K – 255 K) between Points A and B. (Obviously, Fig. 3 exaggerates RCS’s magnitude with respect to ECS’s, and it greatly exaggerates ECS’s magnitude with respect to ΔE’s.)
As we observed above, Lacis et al.’s paper provides no support for Lord Monckton’s contention that they “forgot the sun is shining.” Moreover, their reasoning appears to be the reverse of what Lord Monckton’s “FALSE” column depicts. Instead of inferring ECS from, among other things, the conditions that would have prevailed without carbon dioxide, they apparently started with an ECS value already calculated by other means and used it to infer from the climate’s current state what the conditions would be like at 255 K and maybe below. But for the sake of discussion we’ll accept Lord Monckton’s version of their ECS calculation. And, as Lord Monckton said, that calculation does indeed amount to extrapolation.
Contrary to his denial, though, so does his own calculation. Specifically, his “CORRECTED” column’s calculation is exactly the same as the “FALSE” column’s except that to impose linear proportionality it replaces that column’s Point A, (R, E) = (255 K, 255 K), with the origin, (R, E) = (0 K, 0 K), which Fig. 5 accordingly labels A’. Represented in that plot by the vertical distance from Point B to the blue dot, the “CORRECTED” column’s ECS value 1.1 K is therefore the product of the RCS value 1.05 K and the extrapolation slope m = 1.095 that according to Lord Monckton’s arithmetic is the ratio ΔE/ΔR of the temperature differences ΔE = 287 K (= 287 K – 0 K) and ΔR = 263 K (= 263 K – 0 K) between Points A’ and B.
In short, his correction imposes a linear-proportionality requirement that true feedback theory does not.
The Nose of Wax
His numeric examples always impose such linear proportionality, and linear proportionality seems to be required by the “strict proportion” language he has recently emphasized. Here’s how he recently expressed the new formulation:
As any professor of control theory (the science of feedback) would tell Them, at any given moment in the evolution of a dynamical system moderated by feedback, especially where that system is at that moment in equilibrium, the total feedback response must be attributed in strict proportion to the relative magnitudes of the direct input signals to which the feedback processes extant in that system at that moment respond.
Given the pre-industrial equilibrium state that Lord Monckton assumes, this linear-proportionality interpretation would indeed (if it were a valid feedback law) rule out high ECS values.
But note the language: the feedback response must be “attributed.” Attribution can mean a merely mental act, an act that has no physical consequence. I can attribute the current temperature to the price of tea in China, but that attribution tells me nothing about what will happen to temperature when the price changes. So whether that language actually imposes linear proportionality—and thereby rules out high ECS values—is murky.
Such murkiness seems to be a feature, not a bug; it enables him to treat his feedback-law description as a nose of wax, twistable to any form. He benefits from the impression, given by the “strict proportion” language, that feedback theory rules out high ECS values. But when he’s faced with the fact that linear proportionality is not a valid feedback-theory law he rejects the “rebarbatively-repeated but actually false representation that I assume linearity in feedback response.”
Here’s his rationale for divorcing “strict proportion” from linear proportionality of F as a function of R:
[W]e are not dealing with an evolutionary curve across time, where the feedback processes might not necessarily respond linearly to changes in temperature as the climate evolves. We are dealing with a particular moment, and a moment of equilibrium in the crucial variable at that.
What does that mean? Can we so interpret it as to divorce his verbal formulation’s “in strict proportion” language from the linear proportionality that his numerical examples actually implement? Well, in the next paragraph we’ll try.
Under doubled-carbon-dioxide conditions, just as under the pre-industrial, year-1850 conditions, all portions ΔF of the feedback response F “must be attributed,” he seems to say, “in strict proportion” to corresponding portions ΔR of the without-feedback temperature R: the proportionality coefficient k ≡ f/(1 – f) in ΔF = kΔR must be the same for all ΔF and corresponding ΔR. But there’s no physical experiment that could test that attribution. This is because E’s value under pre-industrial conditions—at that “given moment”—can differ from its value at a different “moment,” such as when carbon-dioxide concentration has doubled. Since f and therefore k can vary in response to changes in the with-feedback temperature E, the common k that prevails for all feedback-response portions ΔF under doubled-carbon-dioxide conditions needn’t be the same as the common k that prevailed for all portions under pre-industrial conditions.
Clear as mud, right? Sorry about that; it’s challenging to make sense of his verbiage. If you did follow that proposed interpretation, though, you’ll recognize that it does indeed avoid implying “linearity in the feedback response”; linear proportionality would require that k be independent of E, whereas the foregoing-paragraph interpretation does not. But you’ll also see that by allowing k to depend on and therefore potentially increase with E it fails to prohibit the high-ECS “FALSE” calculation or dictate the low-ECS “CORRECTED” calculation. In other words, such an interpretation wouldn’t imply what Lord Monckton set out to prove.
So here’s the situation. If his “strict proportion” language does require the linear proportionality that his numerical examples always impose, then it rules out high ECS values but the proof fails because the purported feedback law it defines isn’t valid. If that language doesn’t require linear proportionality, on the other hand, then his proof still fails, because even if the resultant feedback law isn’t erroneous it doesn’t require ECS to be low.
The Third Row
Lord Monckton makes a further assertion: that “after correction of climatology’s error in forgetting that the Sun was shining, even a minuscule change in the feedback-driven system-gain factor would engender a very large change in final warming per unit of direct warming, compared with 1850.” It’s not at all clear how he thinks low ECS values follow from this assertion, but apparently the new slide’s third row is intended as an illustration.
The third row purports to illustrate the ECS effects of a 1% “system-gain factor” increase. In the first column it increases E(R)’s slope dE/dR by 1% on only the RCS = 1.05 K interval between Points B and C. Not surprisingly, it thereby increases ECS by 1%, from 4.20 K to 4.24 K. In the second column, too, the third row increases E(R)’s slope by 1%, but this time throughout the entire 264.05 K interval between Points A’ and C. Here, too, the ECS increase would be 1%, in this case from 1.15 K to 1.16 K.
However, Lord Monckton ignored the fact that thus extending the slope change over the entire domain would increase not only E’s doubled-carbon-dioxide, Point C value but also its pre-industrial, Point B value. So instead of correctly calculating the new ECS value by taking the E-value difference between the new Points B and C he calculated it erroneously by taking the E-value difference between the old Point B and the new Point C. That would have resulted in an apparent increase of about 260%, from 1.1 K to 4.0 K, but apparently because of an arithmetic error the slide says the increase is 340%.
In short, he obtained an orders-of-magnitude difference by performing two completely different calculations. How does that prove that feedback theory rules out high ECS values? It doesn’t. And such absences of logical connection between premise and conclusion afflict much of what he says about his theory.
Not Very Nonlinear
Now, some observers may have actually worked through the logic and/or noticed that in none of the dozen or more head posts in which Lord Monckton has argued for the alleged feedback law has he ever provided a mathematical proof of the purported feedback law, given details of the series of experiments claimed to have been performed at a national laboratory of physics, or identified a passage in any control-systems textbook that states such a law (although his theory seems to have been based initially on a misinterpretation of Hendrik Bode’s Network Analysis and Feedback Amplifier Design). However that may be, it’s clear that not everyone has been distracted from the central question.
“What if the system gain factor is not invariant with temperature?” is how Lord Monckton described the way in which that question was raised by University of Alabama meteorologist Roy Spencer. The gist of his answer seems to be that, yes, E(R) can be non-linear, but it can’t be so non-linear as to result in a high ECS value.
Now, let’s be clear. One might plausibly argue that other skeptics who believe ECS is low thereby also imply that E(R) can’t be very nonlinear. But such skeptics would be reasoning from a low ECS value to a near-linearity conclusion. Lord Monckton instead reasons in the other direction, i.e., to a low ECS value from the premise that E(R) can’t be very nonlinear. And that raises the following question: Why can’t E(R) be that nonlinear if we don’t assume a priori that ECS is low?
Lord Monckton’s reasoning isn’t exactly syllogistic on that question, either. But it has sometimes involved the claim that according to the Intergovernmental Panel on Climate Change (“IPCC”) the “feedback parameter” and the “climate-sensitivity parameter” are “nearly invariant.” And here Lord Monckton mixes apples with oranges.
Specifically, discussions of such parameters tend to concern small-signal quantities and be restricted to the narrow range of global-average surface temperatures that man has experienced or is likely to. And, as the “‘Near-Invariant’” section of “Remystifying Feedback” explained, nothing about whatever near-invariance the IPCC has claimed over such ranges rules out high ECS values; Lord Monckton seems to have confused small-signal quantities with large-signal quantities.
His argument against such observations involved concocting a figure of merit, which he called the “X factor,” so designed as to exhibit large increases in response to small temperature changes and thereby give the impression that high ECS values would imply implausibly large system changes. As can be seen at time stamp 21:45 et seq. in the video of his July 2019 speech to the Heartland Institute’s Thirteenth International Conference on Climate Change, the X factor was the basis of his response to Dr. Spencer’s above-mentioned question. But the “Apples to Oranges” section of “The Power of Obscure Language” refutes that response, showing that it’s similar to the type of meaningless comparison that the new slide’s third row exemplifies.
Recap
The central claim of the forgotten-sunshine theory is a purported mathematical proof, based on feedback theory, that ECS is low. But the actual calculations apply the erroneous law that a feedback system’s output must be linearly proportional to what it would have been without feedback. And, although he denies that this is the law he’s applying, his various verbal formulations don’t rule out high ECS values if they’re interpreted in any other way. So the central theory fails.
An ancillary argument is that climate modelers’ feedback calculations don’t take sunshine into account. As we saw, though, the paper he most relies on for that proposition specifically discusses evaporation and albedo feedback at the emission temperature. That hardly amounts to forgetting sunshine.
Another argument is that high ECS values are inconsistent with IPCC statements of near-invariance. But we’ve seen elsewhere that he reaches such a conclusion only by interpreting those statements as dealing with changes in large-signal quantities, over a global-average-surface-temperature range much wider than humans have encountered or are likely to. And no justification was provided for adopting such an extraordinary interpretation.
Finally, he attempted to bolster the latter argument by using calculations like those in the new slide’s third row to give the impression that high ECS values would necessitate implausibly abrupt changes in other climate parameters. But working through such calculations reveals that they compare apples to oranges and have no logical connection to the proposition that high ECS values are inconsistent with feedback theory.
Conclusion
This all becomes apparent to critical thinkers who work through the math and logic. But not all readers have the time and inclination for such an exercise. Those who don’t may want to consider the following.
If modelers really had made so fundamental an error as failing to take the sun into account, Lord Monckton’s theory would be a scientific kill shot. Wouldn’t heavyweights like Richard Lindzen, William Happer, John Christy, and Roy Spencer therefore have embraced it? Wouldn’t the CO2 Coalition’s Web site have featured Lord Monckton’s theory? Wouldn’t Dr. Spencer have championed it on his blog?
But they haven’t. In fact, Dr. Spencer has instead written a rebuttal. The theory that feedback law rules out high ECS values is like the theory that there’s no greenhouse effect: although its conclusion is attractive, the theory itself is clearly wrong.
