## Great Evans above

Jo Nova carries a rather interesting piece today about some work done by her husband David Evans, who thinks he has uncovered a rather major flaw in the mathematics at the core of the basic model of the climate.

The climate models, it turns out, have 95% certainty but are based on partial derivatives of

dependentvariables with 0% certitude, and that’s a No No. Let me explain: effectively climate models model a hypothetical world where all things freeze in a constant state while one factor doubles. But in the real world, many variables are changing simultaneously and the rules are different.Partial differentials of dependent variables is a wildcard — it may produce an OK estimate sometimes, but other times it produces nonsense, and ominously, there is effectively no way to test. If the climate models predicted the climate, we’d know they got away with it. They didn’t, but we can’t say if they failed because of a partial derivative. It could have been something else. We just know it’s bad practice.

This sounds plausible to me. What do readers here think?

## Reader Comments (199)

Well that's what I was trying to say, but not in maths dialect but in the vernacular of the Oxfordshire housewife. Or maybe I'm fooling myself. I've always suspected the practice of presenting results in terms of averages when they are unsuitable. I've challenged modellers to try a square metre of surface and compare with observatiosn, on the basis that if they can't get that right they can't get a planet right either. I've asked for checkable intermediate results. I've asked why they don't chuck out the too-hot-for-school Canadian model.

I'm now waiting to see what RGB makes of the Evans claims. It's all over my head right now.

There's an interesting post at Fabius Maximus which is related to peeking into this:

What are the chances of that happening? Can anybody do this?

I asked once what the input to climate models was vs. what is pre-defined and got a lump of coal in my bag.

Andrew

It sounds like Mannian statistics is alive and well to me. With these people the end always justifies the means.

Here is some MIT courseware which discusses why partial derivatives cannot be used with dependent variables:

http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/2.-partial-derivatives/part-c-lagrange-multipliers-and-constrained-differentials/session-43-clearer-notation/MIT18_02SC_MNotes_n1_2.pdf

^^^

You mean:

The end always justifies the Greens.

@mikec at 2:00 PM

"What are the chances of that happening? Can anybody do this?"

Would we know if they haven't aleady ................. AND are embarrassed with the results?

The 95% certainty comes from the knowledge that they will always be onto a new version of the software before the old one is proved to be wrong. The new one is 95% likely to be right because it has up to date adjustments. The 5% discrepancy is because the programmers don't know what the 'real' data will be from one month to the next although it's safe to bet there will be warming.. one way or another.

Off topic but I think that it is important to get basic concepts correctly defined.

GHG’s slow the heat loss like any insulation does.That statement is incorrect. The earth is not a bed or a house. It is a sealed system in a perfect thermal insulator, space. The only way for the earth to lose or gain energy is by electromagnetic radiation or gravitation. Heat energy loss could only be slowed if the incoming EM energy is converted to potential energy, say by green plants. This does happen on a small scale. But if the heat energy loss is truly slowed, the earth will fry. The heat energy lost will always equal the heat energy gained minus the small amount that is converted into potential energy. By burning 88 million barrels of oil a day, I suspect that humans are now more than compensating for the kinetic to potential conversion of electromagnetic energy by green plants.

GHGs do not slow the loss of heat energy from the planet as the irradiative loss must always equal the irradiative gain or the temperature rises uncontrollably. What GHGs do is to increase the atmospheric lapse rate making it warmer on the surface.

I tried to read Evans' post and gave up when my brain started to hurt - not that I ever seriously thought I would understand it properly.

What I did understand is that if you try to make sense of "a coupled non-linear chaotic system, ... the long-term prediction of future states is not possible.”

I seem to remember the IPCC used to think so as well!

As usual in these situations: Wot Rhoda Sed.

Partial derivatives are respectable objects in general, and dependent variables in particular are generally what you want to take partial derivatives of. Highlighting this corner of calculus may be somewhat misleading.

As far as I can see, the substantial accusation here may be that interactions amongst variables are being ignored. That could be the primary problem, and the unsatisfactory partial derivatives are but a consequence of it.

Here are a couple of folksy examples quite often used in training engineers in industrial statistics, a discipline that includes the design of experiments intended to identify interactions between pairs of variables, or amongst 3 or more variables.

Example A. (1) Dependent variable: sweetness of a sip of tea from the top of teacup (2) Influencing variables: amount of sugar added so far, and amount of stirring so far. If no sugar is added, the effect of stirring is zero. The partial derivative d(sweetness)/d(stirring) = 0. But if sugar is added, that partial derivative is no longer zero since the stirring will have a positive effect. Thus it would be seriously misleading, from a tea-taste engineering perspective to test the effect of stirring on its own (we get the zero effect), and the effect of sugar on its own (we get a weak sweetening effect), because when both are present, they interact to provide a relatively dramatic sweetening.

Example B. (1) Dependent variable rate of increase of bunnies (2) Influencing variables: number of adult males present, number of adult females present. If we do a classic schoolbook experiment of holding everything constant, we might well test for the effect of females on their own (zero), and males on their own (zero). But then we'd be astounded at the population explosion when the two got together. Because there is an interaction effect between them.

These examples are silly enough, but help get points across. A great many engineering problems or puzzles have been solved by statistically-designed experiments able to detect interaction effects. If it is the case that the GCMs ignore important climate system interactions then they are indeed even more of a joke for climate prediction than their performance to date would lead us to believe.

I have no doubt that David Evans has got it right. When you consider the interactive nature of temperature, volume, pressure and humidity just to name a few variables important in our climate, you can see the problem. It makes no sense to pretend that they are independent.

I'm interested in why models with such huge implications were constructed with built-in flaws. There are hundreds of such models and they have been around for years. Take, for example, the Met Office, that jewel in the crown with its cutting edge expertise and hundreds of scientists. They must be very familiar with the models. How do they explain this?

I have no doubt that David Evans has got it right. When you consider the interactive nature of temperature and humidity you can see the problem. It makes no sense to pretend that they are independent.

I'm interested in why models with such huge implications were constructed with built-in flaws. There are hundreds of such models and they have been around for years. Take, for example, the Met Office, that jewel in the crown with its cutting edge expertise and hundreds of scientists. They must be very familiar with the models. How do they explain this?

Aye, the problem is coupled non-linear chaotic systems. When chaos theory arrived, I was then puzzled that science didn't wholeheartedly drop any attempt at extrapolating the past in the two big examples of stockmarkets and climate. Benoit Mandelbrot's brilliant book "The (mis)Behaviour of Markets" nails this.

It's as if the major leap in understanding which is chaos theory has now been reversed, or dismissed as an inconvenient truth.

My best guess is that the Slingos and Bettses of this world know full well that climate forecasting is as absurd as attempting to forecast the FTSE but that their salaries depend on giving it credence. Put another way, their integrity takes second place to their personal interests.

The alternative explanation - that they are ignorant of chaos maths - seems unlikely. To be charitable, even Einstein famously dismissed quantum mechanics, saying "God doesn't play dice with the universe". Well, Albert, well Julia, he does.

Re: John Shade and his rabbits.

There is also a point where adding one more male to the herd will not increase the output of baby rabbits. That "one more male" may be the second one.

Evans point about partial derivitives in the case of climate models is correct.

A specific example is Lindzens adaptive infrared iris. When a recent paper (Stevens, AMS June 15, link at post following, J. Climate 28: 4794-4819 2015) added it to a climate model, the sensitivity lowered halfway to observational 1.5-1.7 (Lewis and Curry, Lewis at Climate Etc withnthe new aerosol estimate posted 3/19/15). See Mauitsen and Stevens Nature Geoscience 8: 346-351 May 2015. See the companion posts by myself and Judith Curry on May 26 2015 at Climate Etc for a fuller discussion. Evans is elucidating basic maths background for which this is one of physical examples.

I am attending a lecture by Mike hulme in Dublin, anyone know how he deals with skeptic questions?

Jo Nova married? I'm too heartbroken to comment....

As a guy who finds maths concepts rather tough, I think Dr Evans explains it rather well. My biggest problem was having to keep referring back to remind myself what the symbols represented, short-term memory being increasingly precious as time passes. You can, in fact, get the gist of it without following the equations at all, as his descriptive is very good. As Rud points out, the partial derivatives layout is only another way of putting what we have all discussed before.

But I would like to see more critiques of it from outsiders better able to judge the math than I can.

The test of this will be, whether the climate establishment will engage with this, or just scornfully ignore it. One of the frustrations of a sceptic who is open to being convinced otherwise, is encountering the devout refusal of the warmist side to enter a real discussion.

It occurs to me that my previous rejections of the concept of climate sensitivity as generally understood ( for which I have occasionally been gently admonished for threadbombing) are supported by the Evans claim. Basically it's far to complex to say double this and that happens. To use a climate sensitivity figure for prediction is just too vain.

This does not affect the validity of using climate sensitivity to compare model outputs to each other or to reality, which is IMOHO* the only valid appication of the concept.

* in my Oxfordshire housewife's opinion, of course.

The climate models are wrong because they try to stitch together a global mean from local variables, without regard for the actual, globally defining condition of the atmosphere (not to mention the even more fundamental error, that their "physics", even locally, is simply wrong to begin with); the result is a Frankenstein's monster of "global climate" that does not, in fact, exist. My 2010 Venus/Earth comparison of temperatures, over the full range of Earth-tropospheric pressures, clearly showed the Standard Atmosphere model of the Earth's troposphere (known for over a century) represents the real "global mean", and its defining, temperature "lapse rate" structure is the sole, or overwhelmingly predominant, governor of the global mean surface temperature. Dr. Evans describes himself as a modelling expert, but like everyone else in the atmospheric sciences he is approaching the problem with the same ignorant "bottom-up" (from local to global) view as the consensus climate scientists, whose "basic theory" he accepts. That theory is wrong, as my Venus/Earth comparison clearly showed, as they used to say, "to those with eyes to see". And Redbone's comment above, about the supposed effect of GHGs ("greenhouse gases") on the lapse rate, is wrong: Due to the hydrostatic condition of the atmosphere (upon which the Standard Atmosphere--precisely confirmed by the Venus/Earth comparison, remember--is based) the lapse rate depends only upon the near-surface gravitational acceleration g and the effective specific heat of the air; "greenhouse gases" don't have any effect on that whatsoever (all the way from 0.04% CO2 on Earth to 96.5% CO2 on Venus).

Everyone has had nearly 5 years to learn this (actually, nearly 25 years, since the relevant Venus data was obtained, from which ANYONE could have, and should have, done the Venus/Earth comparison I did--so I maintain there has not been a competent climate scientist in that length of time). It is most telling that almost no one, on either side of the debate, has deigned to learn it.

I think Evans may be confused. In normal mathematical usage the partial derivative is purely formal and is computed using formally. If w = x^2+y^2+z^2, partial w/partial z = 2z. This is the textbook definition and is the meaning used in say all PDE books. If y is also a function of z, then the TOTAL derivative of w with respect to z, called dw/dz is 2z + dy/dz. There is nothing contradictory or computationally problematic about this per se. Where you get into trouble is if the PDE is ill-posed as many interesting ones are.

David Young - are x, y and z in your example independent?

If I understand David correctly, he is saying that while looking at the changes to two variable you effectively freeze all the others. You can add them all together as you suggest, but in climate change this is not how the real world works since the variable are interactive and do not conveniently freeze.

This thread shows one of the stupid problems in the climate debate in sharp relief. With all due respect (a lot of respect) to the mathematicians why are we discussing mathematical/statistical proof that climate models are wrong?

We already know they are wrong because the predictions are always wrong.

We seem to have a great need for them to admit it (which I doubt they will ever do) but we do not need that admission.

The problem is that the action which costs the world so much just keeps on rolling onwards (or backwards) and I think that is where we should do better.

PDEs ODEs are very mystical ways to explore solution spaces

I never found a good philosophical treatise on them

you would need a minimum of anaytical competence to discuss them, and unfortunately that skill is lost , just like hunting mammuths, driving horse coaches, doing trigonometry, or checking the fuel consumption of your VW Jetta

Dung – I agree with you. Unfortunately, a great many people assume (a) the science is correct and (b) climate changes over several decades so they ignore wrong model predictions as being a temporary blip.

We could wait until the next ice age to prove that the models are wrong. David Evans has studied the models in detail and hopes that when mistakes are exposed, some of the real scientists out there will stand up and agree that the models are indeed flawed.

DY may have already pointed this out, but I suspect Evans is indeed confused. I think he's confusing how you might determine various things (like feedback responses) from a particular climate model, and how the model itself is run. Climate models are evolved in time. Feedback reponses, climate sensitivity, etc. are emergent properties from a climate model run. However, if you want to actually estimate a specific feedback response then you might hold everything fixed - apart from that one factor - and see how the model responds to a change in temperature. That way you can determine that particular feedback response (which is indeed how something changes with temperature). That, however, does not mean that climate models are actually evolving one dependent quantity with respect to another dependent quantity.

I'm not convinced there is an intrinsic problem of this nature in CMIP5 and other 3D coupled global climate models. If there is, I imagine it would arise not from the nature of the models but in the formulation of the, often questionable, parameterised approximations used when they are unable to represent sub-grid scale or other climate processes in basic physical terms.

Evan's quotation “While the forcing–feedback paradigm has always been recognized as imperfect, such discrepancies have previously been attributed to variations in “efficacy” (Hansen et al. 1984), which did not clarify their nature.” doesn't have any implications or how well (or badly) GCMs predict warming under increasing greenhouse gas concentrations, merely on how the warming is accounted for.

David Young (5:21PM). How about this simple example of an equation containing interacting variables, using your notation:

w = x + y +xy

The first pd of w wrt x is 1+y. (if dy/dx = 0 for simplicity) If y is not a constant during some period of interest, then the partial derivative's value will also vary.

I'm guessing that the other David's concern about GCMs is that they may presume constant first (or higher) derivatives where there ought to be some consideration of them varying. His hunch is that the derivatives are computed ( or estimated or parameterised?) assuming that all else is unchanging. At least, I think that is the case. I hope I will quickly be corrected if I have misunderstood this.

What is truly amazing is that such a basic flaw has remained hidden for so long. Surely there must be other experts in this field of mathematics who will either confirm or refute Evans' revelations? Or are these experts going to keep out of the debate in order to keep their careers on track.

ATTP, sensitivity is emergent only the sense that is is not explicity part of the computation. But is is very much an explicit result of the computation. And those computatioms most definitlymuse numerical methods to solve partial differential equations. NCAR CAM3 has a piblicaly available complete manual. Go read NCAR/TN-464+STR like i have, if you question any of this.

A good physical example of faulty partial derivatives such as Evans has impecably described is a component of water vapor feedback, Lindzen' adaptive infrared iris (BAMS 2001). The adaptive part is exactly the partial derivative flaw. Everything else is not constant as one thing changes. When brute force added to a climate model, adaptive iris significantly reduces sensitivity toward what has been observationally estimated since 1880 (e.g. Lewis and Curry 2014). Read Mauritsen and Stevens, Nature Geoscience 4/20 2015, NGEO2414. Read my and Judith Curry's companion posts on this recent paper at Climate Etc. on 5/26/2015.

John--

It is OK if the partial derivative varies. What is not OK is if x and y are not independent. This is very well explained by the link provided in the Jo Nova column (which is the same link given above by RickA).

Since many of the partial derivatives (holding temperature constant) are for feedbacks such as aerosols, clouds, lapse rate, etc. that depend on temperature, the partial derivative loses meaning.

Isn't this article just saying that we can't model multiple feedbacks at once and be able to determine which estimates of the feedbacks are the reason it matches reality - or not.

We've known for years that the tuning doesn't work and cannot tell us why the tuning doesn't work.

I'm not saying "Nothing to see here, move along". But I am saying, "Let's not rubber-neck at this car-crash of science".

Nic Lewis, i agree with you. Essay Models all the way Down, and my recent guest post on models at WUWT cover this problem with real illustrations. At the heart of unavoidable parameterizarion lies the anthro/natural attribribution problem. The pause, and all that. But Evans post 4 does is show that the core comceptual model can neither be verified not validated because of dodgy basic math assumptions.

It will be interesting to see where he takes this. Hopefully in the end something like your observational sensitivities emerges, and not something silly.

While what Evans points to is not a problem if the governing equations are correct, if he means that real dependencies are ignored in the model formulation, then he is obviously correct as all modelers know. The computational grids are so course that most of the important action can't be resolved, so it must be modeled by sub grid models or things like turbulence and this is where it is well known and obvious that the models are wrong, the only question is if they are disastrously wrong. That's a subject of debate, with the apologists relying on non rigorous intuition that the climate attractor is very stable and therefore computable even with very large errors all over the place. This is really rather deep pseudoscience it seems to me.

Rud,

How is "an explicit result of the computation" any different from "emergent". The point is that we are not inputing the feedbacks into the models, they're emerging from the models/calculations. However, the more basic issue is that Evans is - I think - confusing how one may estimate the feedbacks (for example) with how the models are actually evolved.

My take on this is very close to Nic Lewis' as stated above. For the benefit of Ken Rice, who cannot control the dialogue here by deleting relevant responses, lets just take convection or turbulence as an example of how the feedback errors might be large. Old algebraic turbulence models computed the effect of unresolved turbulent scales just from the local flow properties, a sub grid model. Modern turbulence models compute the effect globally by solving auxiliary PDE's and are vastly more accurate because turbulent effects in any cell depend on its effect in every other cell. The error in older models was very real and often large, but due to computational limitations it was all that could be done on old computers. BTW, the error does NOT go away at steady state, even for very stable and steady flows as our climate intuitionists would have us believe it does for climate.

Does Richard Betts ever comment here any more? I would like to hear his views on the subject.

I do think the partial diff issue is a consequence rather than the problem, however as marketing ploy it's worked (as this thread attests).

In model formulation and fitting, particularly in multi-scale modeling of complex phenomena, it is very easy to leave out or lose what subsequently proves to be material factors (and feed backs are only one such). Relationships in the model may not work as they do in the real world (and assumptions derived in model world don't work in real life - remembering that partial diff world is just a model world). This can be for a whole host of reasons.

And yes, this can then have the particular consequence that an emergent property from the model like climate sensitivity can emerge wrong (sorry aTTP).

As ATTP points out Evans never really says what he is waving his hands about.

If he is talking about partial derivatives used in the calculation he has not shown which partial derivatives are taken wrt which dependent variables. For example, the Navier Stoke Eq which is the physical basis of GCMs includes partial derivatives wrt time and position, all of which are independent variables.

If he is talking about something else, it would be good if he explained what. In a GCM calculation climate sensitivity is a result of the calculation not an independent or a dependent variable.

Finally he would do well to read example 2 here about how one handles partial derivative wrt dependent variables in the ideal gas law

Evans is not Evan wrong. He is confused.

"There is also a point where adding one more male to the herd will not increase the output of baby rabbits. That "one more male" may be the second one." --Speed"You'd be shocked, if you knew the awful things that rabbits do. And often, too."

"Hopefully in the end something like your observational sensitivities emerges, and not something silly." --Rud Istvan"Something silly" could be reductio ad absurdum.

Speaking of the Gas Laws, this document from MIT uses the Gas Laws to explain that when the variables are not independent, the differential expression has no definite meaning. I believe that is the point being made by David Evans.

http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/2.-partial-derivatives/part-c-lagrange-multipliers-and-constrained-differentials/session-43-clearer-notation/MIT18_02SC_MNotes_n1_2.pdf

"In a GCM calculation climate sensitivity is a result of the calculation" Eli Rabett

But how do you know that it's the right answer?

I am sure David Evans is right. All IPCC Climate models run too hot in their projections (predictions) as that is exactly what they were designed to do, in order to increase Global Warming/Climate Alarm. Fortunately Nature is always ready with self-regulating Systems in place.

Don't forget David Evans is doing a whole series of posts on his work and the partial derivative error is just the first one. Also I think you have to read all his posts to make sense of how he is approaching the demolition of the climate models.

TinyCO2, what Evans has just elegantly demonstrated by his general formulation of the logical core is that no one can ever know that. It is mathematically impossible. Therefore neither model validation nor verificarion are possible. Even a 'right answer' could just be a fluke. That idea goes well beyond the simpler notions that the pause and observational sensitivity show show the CMIP5 models are wrong. The observational 'falsification' still leaves the conceptual door open to model 'improvements'. Evans is saying genuine improvement is inherently impossible to know, from first principles. That is a bigger, bolder, and maybe in the future more powerful statement about supposedly 'settled' science.

Once again agreeing with Dung; M Courtney too. We hardly need an analysis at this level when abuse of fundamental statistics is rife in climate science (and plenty of other places besides). The quality might lift if we replaced the scientists' computers with 4-function calculators -- data dredges would be less attractive and focus might move to meaningful analysis.

The flaw that Evans has highlighted reminds me of "Support Your Local Sheriff". The reluctant hero is handed the previous sheriff's badge, sporting a fair sized ding. He brightens saying "Hey, I guess this badge saved his life", only to be told "Maybe it would have if it hadn't been for all the other bullets".

97% of climate scientists have yet to be proved right, but won't admit they are wrong.

Members of the 97% are quick to find fault, with someone from the 3%, who has not agreed with them.

If 100% of 97% is never right, it would be wrong to ignore the remaining 3%, in the search for anything that might be right.

If all 100% of the 97%, each paid 3% of their earnings from the last 20 years, to the 3% for one year, it might get any doubt resolved quicker, and cheaper than any further funding to those who have never been right.

What could be simpler? Or cheaper? Or less destructive to mankind? The odds on a fraction of the 3% must be better than the odds on 100% of the 97%. But only in surreal climate science.

Robert Swann, "Support your local gunfighter"

Reminds me of a current plot about concealed cheating computer programming, designed to con the public and government agencies. The Green Blob want substantial financial punishments to pay for their expensive double standards.