By Christopher Monckton of Brenchley, David Legates, Willie Soon and Matt Briggs
Mr. Born has had another go at our paper Why models run hot, published in January 2015 (PDF here) in the Science Bulletin of the Chinese Academy of Sciences. Go to scibull.com, click on “most read articles”. and ours is the all-time no. 1 by a factor of ten. It’s a good read.
Let us begin by putting Mr. Born’s criticism into context. In essence, he is saying he would have liked our simple model to be more complex. Well, he is of course free to write his own model and get it into the reviewed literature. But our simple model, when calibrated against IPCC predictions, reproduced them faithfully when we adopted its parameter values, so, given that we made it quite explicit in the paper that we were adopting a rough-and-ready approach, we saw no reason to introduce pointless complications that would, without much increase in accuracy, have reduced the utility of our model, which is that it is accessible to anyone with a pocket calculator.
Keep it simple, stupid.
Mr. Born says the equilibrium feedback sum seems to be the only feedback sum our model uses. Well, of course it is: the impact of transient feedback values is represented in a simplified fashion by the transience fraction. That is what it is for. That is one of the many innovations in our paper, and one which is found by many to be a useful simplification.
Mr. Born draws a plot of “step responses” implied by our table of values for the transience fraction. The plot rather untidily reproduces the relevant portion of the graph from Roe (2009) from which we derived the values of the transience fraction, with one important exception. Roe’s y axis is temperature change. Mr. Born’s y axis is inadequately labeled “step response”, and it is not made explicit whether he is using a simple or normalized step response, or what the units (if any) are. He then argues with some of the points on his own graph. However, the inadequacy of the labeling and the confusing text make it difficult to understand what he means, so we cannot comment further.
In the absence of any information from the IPCC about the evolutionary profile of temperature response to different feedback regimes, we had simply used, and stated we had used, Roe’s evolutionary profile. We did not warrant it as unassailable, and we did say that people were free to take their own values, and we did additionally provide worked examples so that, at least for the next century or two, values sufficiently close to the IPCC’s values could be readily reproduced, and in our own centennial worked examples on all six RCP scenarios we used values close to those implicit in the IPCC’s transient-sensitivity predictions.
Next Mr. Born has a long and unnecessary excursus on whether the Planck parameter is a feedback or not. As our paper explains, echoing Roe, with whom our lead author had discussed this question, it is better understood as part of the reference frame for climate-sensitivity calculations.
In particular, Mr. Born would have liked a more complicated treatment of our transience fraction – i.e., the fraction of equilibrium climate sensitivity achieved in a given year after a stimulus has been applied to the climate. He would have preferred us to convolve entire time sequences instead of carrying out the simple multiplication that is at the heart of our model. However, the IPCC itself uses the simple multiplication method from time to time, and we provided worked examples to show that that method reproduced the IPCC’s climate sensitivity when its own parameters, specifically including feedback values, were input to our model. And we cited IPCC passages where the simple multiplication method was used. Indeed, it is often used in determining sensitivity from general-circulation models too: see e.g. Hansen (1984). Once again, Mr Born’s quarrel is not with us but with the IPCC and with the modelers. The point about a simple model is that it does things the simple way, for better or worse.
In logic, a model is a simplification and a simplification is an analogy, and every analogy breaks down at some point. Mr Born should feel free to make the model more complex if he wants: our paper is the manual for it, so he can simply read the manual and replace anything he does not like with something more complicated of his own. But his entire post would make scarce a jot or tittle of difference to equilibrium sensitivity, which was the principal focus of our paper.
Equilibrium sensitivity is the warming that might be expected to occur by the time the climate had settled back to a steady state in response to a direct forcing followed by the complete action of all temperature feedbacks consequent on that forcing. Now, it is a matter of definition that at equilibrium the transience fraction must in all cases be unity. So the vast majority of our paper that treats of equilibrium sensitivity is entirely unaffected by any doubts about the values one might choose to adopt for the transience fraction at various points before equilibrium is reached.
The remainder is not much affected either, for our centennial transience fractions are very close to those of the IPCC. If Mr. Born does not like them, yet again his quarrel is with the IPCC and not with us.
Mr. Born’s post, therefore, deals with a secondary aspect of our paper, and one in which just about any defect caused by what he may consider to have been an inappropriate choice of transience fractions by us (or by Roe before us) would in all realistic circumstances be dwarfed and swamped by uncertainties as to the values of both forcings and feedbacks. The recent news that the models and the IPCC have been artificially boosting climate sensitivity by adopting very large but unphysical negative aerosol forcings – something I have long suspected – is a case in point.
In the climate, a temperature feedback is an additional forcing, denominated in Watts per square meter per Kelvin of direct temperature change caused by the original forcing. The classic temperature feedback is the water-vapor feedback. As the atmosphere warms, by the Clausius-Clapeyron relation it can carry near-exponentially more water vapor, a greenhouse gas.
So the IPCC assumes that merely because the atmosphere can carry near-exponentially more water vapor it must do so. That is a convenient assumption, because it allows the IPCC immediately to double the direct warming expected from adding CO2 to the atmosphere. However, it is by no means clear that the water vapor in the atmosphere is increasing. For instance, the ISCCP satellite data show no change at all in recent decades except in the climatically crucial mid-troposphere, where the column water vapor appears to have declined somewhat – precisely the opposite of what the IPCC would like us to believe ought to happen.
Another example: Spencer and Braswell (2010, 2011) found cloud feedbacks negative, not – as the IPCC thinks – quite strongly positive. Both they and Lindzen & Choi (2009, 2011) found the feedback-sum net-negative. Considerations like these simply drown out any supposed defects in the choice of the transience fraction.
The point here is one that we made in the paper: the values of individual feedbacks, and even their signs, cannot be either directly measured by any empirical method or inferred to a sufficient precision for climate-sensitivity calculations by any theoretical method. They are guesswork. They cannot be empirically distinguished from one another or even from the forcings that generated them.
And the curve along which the influence of feedbacks on temperature is expected to evolve is likewise guesswork – and guesswork so problematic that the IPCC does not even attempt to plot it, except in graphs the size of a postage stamp in AR4, p. 803, Table 10.26. The IPCC would have us to believe that half of the warming caused by a forcing amplified by feedbacks should have occurred in the first century after the forcing, with the rest of the warming coming through only after hundreds (or, in the high-sensitivity case) thousands of years. They may – or may not – be right. But our values for the transience fraction are broadly in line with this consideration, after appropriate allowance has been made for the fact that time to equilibrium increases with the feedback sum.
We took, and said we took, a rough-and-ready approach, using a profile of feedback evolution over time taken from Roe (2009). And, notwithstanding a snidish comment from Mr Born that scientific papers ought to be rigorous, implying that ours was not, we had made it quite plain that Roe was using a pulse, not a growth of forcing over time. Rigor, in any paper concerning a model, requires up-front disclosure of what was done. We did that.
So having nailed down the upper bound of the transience fraction, which is by definition unity, let us look at the lower bound, which – if feedbacks are net-positive – is simply the ratio of the Planck sensitivity parameter 0.31 Kelvin per Watt per square meter and the equilibrium sensitivity parameter, which is in turn simply the equilibrium climate sensitivity in Kelvin divided by the original direct forcing in Watts per square meter.
All the user of our model has to do is set the transience fraction at 1 for equilibrium, run the model with all other parameters chosen by him to determine equilibrium sensitivity and hence the equilibrium sensitivity parameter, divide the Planck parameter by the equilibrium sensitivity parameter and, bingo, the instantaneous or initial value of the transience fraction in response to a direct forcing may be determined.
We actually provide handy equations in the paper for understanding these relationships. You will not find anything like so clear in the IPCC’s documents.
But what about the years in between instantaneity and equilibrium? Now, the IPCC has been criticized by its expert reviewers for not providing an explicit evolutionary path for climate sensitivity. However, one can deduce from the IPCC’s values for transient sensitivity that after 100 years about half of the equilibrium sensitivity will have occurred. We provided worked examples in our paper to demonstrate this. Indeed, that consideration alone is enough to show that the transience fractions in table 4 of our paper, about which Mr Born also seems to complain, are in the right ballpark.
Mr. Born, however, expects us to have done what the IPCC has not done. As so often, his quarrel is not with us but with the IPCC. For he has repeatedly complained that we had not explained how we had determined our values for the transience fraction. Nor does the IPCC.
Well, at least Mr. Born now knows what the instantaneous, 100-year and equilibrium values of the transience fraction are, for any given situation. And all of this was explained in our paper.
But what of the values in between? Mr Born opens his article by saying our lead author had “turned down” his “request” to explain how we determined the values of the transience fraction. He had said much the same in a very late-in-the-day and not very courteously expressed comment on our lead author’s response to his earlier article:
“Many of us were interested in precisely how Monckton et al. inferred the Table 2 values from the Gerard Roe paper. The explanation should have been easy to give. Yet the authors, or at least Lord Monckton, insisted on withholding that information.”
To allege that authors of a scientific paper have deliberately withheld requested information is to make a very serious allegation of professional misconduct. That is the allegation that Mr Born has now made twice, and in the bluntest terms.
So let us be clear as to the facts. Mr. Born at no time contacted any of us to ask for the information he now says we are “withholding” and “refusing to provide”. He must withdraw that allegation, and be very careful in future not to repeat it.
Now, Mr Born may argue that he had, at the foot of a previous comment thread, asked for the information he said we were “withholding” and now says we are “refusing to provide”. He will see, not far below his comment on that thread, the words “Comments are closed.” So we were not able to reply to him. We have no idea why comments were closed: but they were closed. It is not unreasonable, we think, to expect Mr Born to be a great deal more rigorous in verifying his facts before making unpleasant allegations that we have withheld or refused to supply information for which not one of us had received a request from him. Nor can he maintain that he had no email address for us: our lead author’s email address is published in our paper.
Notwithstanding Mr. Born’s discourtesy, we now provide the information requested.
Not all temperature feedbacks operate instantaneously. Instead, feedbacks act over varying timescales from decades to millennia. Some, such as water vapor or sea ice, are short-acting, and are thought to bring about approximately half of the equilibrium warming in response to a given forcing over a century. Thus, though approximately half of the equilibrium temperature response to be expected from a given forcing will typically manifest itself within 100 years of the forcing, the equilibrium temperature response may not be attained for several millennia (see e.g. Roe, 2009; Solomon et al., 2009).
In our model, the delay in the action of feedbacks and hence in surface temperature response to a given forcing is accounted for by the transience fraction. For instance, it has been suggested in recent years that the long and unpredicted hiatus in global warming may be caused by uptake of heat in the benthic strata of the global ocean. The construction of an appropriate response curve via variations over time in the value of the transience fraction allows delays of this kind in the emergence of global warming to be modelled at the user’s will.
In Roe (2009), a simple climate model was used, comprising an advective-diffusive ocean and an atmosphere with a Planck sensitivity 1.2 , the product of the direct radiative forcing 5.35 ln 2 = 3.708 Watts per square meter in response to a CO2 doubling and the zero-feedback climate sensitivity parameter 0.3125 Kelvin per Watt per square meter. The climate thus defined was forced with a 4 Watts per square meter pulse at the outset, and the evolutionary curve of climate sensitivity was determined and plotted.
In our paper, Table 2 gives approximate values of the transience fraction corresponding to equilibrium feedback sums f ≤0 and f = 0.5, 1.3, 2.1 and 2.9. Where the equilibrium feedback sum is less than or equal to about 0.3, the transience fraction may be safely taken as unity: at sufficiently small f there is little difference between instantaneous and equilibrium response. For f on 2.1 [1.3, 2.9], the value of the transience fraction is simply the fraction of equilibrium sensitivity attained in a given year after the initial forcing, as shown in Roe’s graph, reproduced at fig. 4 of our paper.
It is not possible to provide a similar table for values of f at equilibrium given in IPCC AR4 or AR5, since IPCC provides no evolutionary curve similar to that in Roe’s graph.
There. All is now explained, and in quite some detail. Mr Born may be tempted to ask why I did not explain all this before. The answer, of course, is that we did. All five of the preceding paragraphs are taken straight from our paper. He has been asking us to explain what is already explained, fully, in our paper. He has alleged, time and again, that we did not explain how our values for the transience fraction were arrived at. But it will be seen that we had taken considerable trouble over that, so that everyone could understand the basis for our own approximate values of the transience fraction, and could choose their own values if they preferred.
Mr. Born then takes us to task for basing our values of the transience fraction on Roe’s model, on the ground that that model was forced by a pulse rather than by small annual increments. Over the short term (i.e. the next couple of hundred years), our values of the transience fraction are manifestly consistent with those of the IPCC – see the worked examples in our paper. Yet again, therefore, Mr Born is arguing with us when he should be arguing with the IPCC. We are using its methods. It uses pulse analysis as well as step-by-step forcings in its modelling. Each method has its merits and demerits. If our model has what Mr Born considers to be defects at the margins, welcome to modeling.
If you want perfection, wait and do a hindcast. Even then, disentangling the natural from the anthropogenic contributions will be no easy task.
Mr. Born says we were not right to assume that for negative feedbacks the transience fraction could be safely taken as unity. Do the math. For a feedback sum on [-1.6, +0.32] Watts per square meter per Kelvin, equilibrium climate sensitivity falls on the remarkably narrow (and remarkably harmless) interval [0.8, 1.3] K.
Look at the curve of equilibrium sensitivity against loop gain in our paper. See for yourself. It at once becomes apparent that little error can arise from assuming the transience fraction is unity in such circumstances. But Mr. Born is free to adopt his own more precise values if he wants. They will make scarcely any difference to climate sensitivity – and, of course, all sensitivities in response to a net-negative feedback sum will be a third of the IPCC’s sensitivities, or even less. Respice finem.
Mr. Born says users of our model should adopt our transience values with caution. Well, of course they should. We made it quite clear once in the text and twice in Table 2, that the values for the transience fraction were stated to be “approximate”. Given the unknowns, of course they were approximate. How useful to be able to end on a note of agreement.
An anonymous contributor, one “Phil.” [a professor at Cornell -Anthony], has twice alleged in comments that the appendix to our paper, which was cut at the last minute by the editors on grounds of space, and which among other things provided a more explicit but still simple mathematical discussion of feedback-induced non-linearities, had never existed.
Now, our lead author had invited “Phil.” to email him if he wanted a copy of the appendix. Instead, “Phil.” merely repeated the allegation that our lead author had lied in saying there was an appendix. We can now confirm that neither “Phil.” nor anyone contacted any of us to ask for a copy of the appendix before he repeated his allegation. We can also confirm that the appendix has not been hastily cobbled together ex post facto but was indeed submitted with our paper and approved by our three diligent reviewers.
The serious and unfounded allegations both of Mr. Born and of “Phil.” are the sort of thing that those of us who have dared to question the party line they cherish must endure daily. Just ask our distinguished co-author Willie Soon, who has been hounded unmercifully throughout the media in the months following publication of our paper for having allegedly failed to disclose the identity of one of his funders, when the contract between his observatory and the funders, negotiated by them and not by him, obliged him not to mention the funder’s identity. He was blameless, but that has not prevented the usual suspects from mounting an expensive, organized, and persisting campaign of vilification against him.
Neither he nor any of us will be discouraged by the continuous nastiness to which we are subjected. So vile has been the treatment of sceptical researchers by the climate extremists that third parties looking in on this debate can see that on the skeptical side there is at least an attempt at rational discussion, while from the true-believers there is little but hate speech and false allegation piled upon false allegation.
That is no small part of the reason why the climate extremists are losing the argument. They are not conducting one.
Further development of the model
The model may readily be further developed to increase its sophistication, though such developments are beyond the scope of the present paper. For instance, an additional factor might be included in Eq. (1) to represent any desired contribution from anthropogenic forcings.
The model might also be made one-dimensional, by representing the latitude. One-dimensional energy-balance models (see  for an overview), originally developed by [50-51] and extended by [52-53], have been widely used to introduce students to climate modeling and to examine some peculiarities of the climate system. Some of the more interesting issues that appear when latitude is taken into account are polar amplification of sensitivity to a forcing, the snowball/snow-free bi-stability  and the small ice-cap instabilities  that arise from the positive ice-albedo feedback.
A one-dimensional model starts with (1) and, at each latitude φ, expresses the albedo α of the Earth and its clouds, its effective temperature TE, and the distribution of solar irradiance S as functions of x = sin φ. The one-dimensional model also implicitly assumes that the northern and southern hemispheres are reflections of one another with no net heat flux across the equator. To resolve the latitudinal dimension, the model may be grid-based, as in [52-53], or based on Legendre polynomials (as in ).
The model, however formulated, requires a further equation to describe the meridional or poleward transfer of heat. This energy-flux divergence D is proportional to –2T. Using Fick’s Law of Diffusion in (A1.1), it is expressed by
where the diffusion coefficient, , representing the poleward transfer of energy via oceanic and atmospheric advection, is a tunable parameter that yields a realistic equator-to-pole temperature gradient and can be simplified to render it independent of latitude, with a customary value ~0.65 W m–2 K–1. In  a diffusion coefficient is suggested that is dependent on x2 (consistent with the diffusion coefficient in ) so that tropically-averaged motions are better described,
where is the second Legendre polynomial and , are tunable parameters [see also 57]. Use of the second Legendre polynomial is fortunate in that should decrease toward the pole, as it does in (A1.2). Given the complicated motions of the atmosphere and ocean that transport the energy poleward, such diffusive approximations are conceptually appealing but may not be entirely physically-based . Formulation of diffusion using (8) introduces a term that varies as a function of the equator-to-pole temperature distribution which, necessarily, will alter the temperature response ΔTt to anthropogenic radiative forcings, thereby changing the response in Eq. (1). Specifically, addition of latitudinal diffusion will affect not only the transience fraction, rt, since the impact of diffusive heat transport and its response to ΔT will change the response time to anthropogenic forcing, but also the equilibrium climate-sensitivity parameter, λ∞.
The model may also be developed to represent non-linear temperature feedbacks. Where feedbacks are non-linear (see  for the derivation), Eq. (4) becomes Eq. (A1.3):
In the general case, therefore, the linear-feedback system-gain relation Gt = (1 – gt) –1 becomes Eq. (A1.4):
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