Emulation, ±4 W/m² Long Wave Cloud Forcing Error, and Meaning

Guest post by Pat Frank

My September 7 post describing the recent paper published in Frontiers in Earth Science on GCM physical error analysis attracted a lot of attention, consisting of both support and criticism.

Among other things, the paper showed that the air temperature projections of advanced GCMs are just linear extrapolations of fractional greenhouse gas (GHG) forcing.

Emulation

The paper presented a GCM emulation equation expressing this linear relationship, along with extensive demonstrations of its unvarying success.

In the paper, GCMs are treated as a black box. GHG forcing goes in, air temperature projections come out. These observables are the points at issue. What happens inside the black box is irrelevant.

In the emulation equation of the paper, GHG forcing goes in and successfully emulated GCM air temperature projections come out. Just as they do in GCMs. In every case, GCM and emulation, air temperature is a linear extrapolation of GHG forcing.

Nick Stokes’ recent post proposed that, “Given a solution f(t) of a GCM, you can actually emulate it perfectly with a huge variety of DEs [differential equations].” This, he supposed, is a criticism of the linear emulation equation in the paper.

However, in every single one of those DEs, GHG forcing would have to go in, and a linear extrapolation of fractional GHG forcing would have to come out. If the DE did not behave linearly the air temperature emulation would be unsuccessful.

It would not matter what differential loop-de-loops occurred in Nick’s DEs between the inputs and the outputs. The DE outputs must necessarily be a linear extrapolation of the inputs. Were they not, the emulations would fail.

That necessary linearity means that Nick Stokes’ entire huge variety of DEs would merely be a set of unnecessarily complex examples validating the linear emulation equation in my paper.

Nick’s DEs would just be linear emulators with extraneous differential gargoyles; inessential decorations stuck on for artistic, or in his case polemical, reasons.

Nick Stokes’ DEs are just more complicated ways of demonstrating the same insight as is in the paper: that GCM air temperature projections are merely linear extrapolations of fractional GHG forcing.

His DEs add nothing to our understanding. Nor would they disprove the power of the original linear emulation equation.

The emulator equation takes the same physical variables as GCMs, engages them in the same physically relevant way, and produces the same expectation values. Its behavior duplicates all the important observable qualities of any given GCM.

The emulation equation displays the same sensitivity to forcing inputs as the GCMS. It therefore displays the same sensitivity to the physical uncertainty associated with those very same forcings.

Emulator and GCM identity of sensitivity to inputs means that the emulator will necessarily reveal the reliability of GCM outputs, when using the emulator to propagate input uncertainty.

In short, the successful emulator can be used to predict how the GCM behaves; something directly indicated by the identity of sensitivity to inputs. They are both, emulator and GCM, linear extrapolation machines.

Again, the emulation equation outputs display the same sensitivity to forcing inputs as the GCMs. It therefore has the same sensitivity as the GCMs to the uncertainty associated with those very same forcings.

Propagation of Non-normal Systematic Error

I posted a long extract from relevant literature on the meaning and method of error propagation, here. Most of the papers are from engineering journals.

This is not unexpected given the extremely critical attention engineers must pay to accuracy. Their work products have to perform effectively under the constraints of safety and economic survival.

However, special notice is given to the paper of Vasquez and Whiting, who examine error analysis for complex non-linear models.

An extended quote is worthwhile:

… systematic errors are associated with calibration bias in [methods] and equipment… Experimentalists have paid significant attention to the effect of random errors on uncertainty propagation in chemical and physical property estimation. However, even though the concept of systematic error is clear, there is a surprising paucity of methodologies to deal with the propagation analysis of systematic errors. The effect of the latter can be more significant than usually expected.

“Usually, it is assumed that the scientist has reduced the systematic error to a minimum, but there are always irreducible residual systematic errors. On the other hand, there is a psychological perception that reporting estimates of systematic errors decreases the quality and credibility of the experimental measurements, which explains why bias error estimates are hardly ever found in literature data sources.”

“Of particular interest are the effects of possible calibration errors in experimental measurements. The results are analyzed through the use of cumulative probability distributions (cdf) for the output variables of the model.

“As noted by Vasquez and Whiting (1998) in the analysis of thermodynamic data, the systematic errors detected are not constant and tend to be a function of the magnitude of the variables measured.

When several sources of systematic errors are identified, [uncertainty due to systematic error] beta is suggested to be calculated as a mean of bias limits or additive correction factors as follows:

“beta = sqrt[sum over(theta_S_i)^2],

“where “i” defines the sources of bias errors and theta_S is the bias range within the error source i. (my bold)”

That is, in non-linear models the uncertainty due to systematic error is propagated as the root-sum-square.

This is the correct calculation of total uncertainty in a final result, and is the approach taken in my paper.

The meaning of ±4 W/m² Long Wave Cloud Forcing Error

This illustration might clarify the meaning of ±4 W/m^2 of uncertainty in annual average LWCF.

The question to be addressed is what accuracy is necessary in simulated cloud fraction to resolve the annual impact of CO2 forcing?

We know from Lauer and Hamilton, 2013 that the annual average ±12.1% error in CMIP5 simulated cloud fraction (CF) produces an annual average ±4 W/m^2 error in long wave cloud forcing (LWCF).

We also know that the annual average increase in CO₂ forcing is about 0.035 W/m^2.

Assuming a linear relationship between cloud fraction error and LWCF error, the GCM annual ±12.1% CF error is proportionately responsible for ±4 W/m^2 annual average LWCF error.

Then one can estimate the level of GCM resolution necessary to reveal the annual average cloud fraction response to CO₂ forcing as,

(0.035 W/m^2/±4 W/m^2)*±12.1% cloud fraction = 0.11%

That is, a GCM must be able to resolve a 0.11% change in cloud fraction to be able to detect the cloud response to the annual average 0.035 W/m^2 increase in CO₂ forcing.

A climate model must accurately simulate cloud response to 0.11% in CF to resolve the annual impact of CO₂ emissions on the climate.

The cloud feedback to a 0.035 W/m^2 annual CO2 forcing needs to be known, and needs to be able to be simulated to a resolution of 0.11% in CF in order to know how clouds respond to annual CO2 forcing.

Here’s an alternative approach. We know the total tropospheric cloud feedback effect of the global 67% in cloud cover is about -25 W/m^2.

The annual tropospheric CO₂ forcing is, again, about 0.035 W/m^2. The CF equivalent that produces this feedback energy flux is again linearly estimated as,

(0.035 W/m^2/|25 W/m^2|)*67% = 0.094%.

That is, the second result is that cloud fraction must be simulated to a resolution of 0.094%, to reveal the feedback response of clouds to the CO₂ annual 0.035 W/m^2 forcing.

Assuming the linear estimates are reasonable, both methods indicate that about 0.1% in CF model resolution is needed to accurately simulate the annual cloud feedback response of the climate to an annual 0.035 W/m^2 of CO₂ forcing.

This is why the uncertainty in projected air temperature is so great. The needed resolution is 100 times better than the available resolution.

To achieve the needed level of resolution, the model must accurately simulate cloud type, cloud distribution and cloud height, as well as precipitation and tropical thunderstorms, all to 0.1% accuracy. This requirement is an impossibility.

The CMIP5 GCM annual average 12.1% error in simulated CF is the resolution lower limit. This lower limit is 121 times larger than the 0.1% resolution limit needed to model the cloud feedback due to the annual 0.035 W/m^2 of CO₂ forcing.

This analysis illustrates the meaning of the ±4 W/m^2 LWCF error in the tropospheric feedback effect of cloud cover.

The calibration uncertainty in LWCF reflects the inability of climate models to simulate CF, and in so doing indicates the overall level of ignorance concerning cloud response and feedback.

The CF ignorance means that tropospheric thermal energy flux is never known to better than ±4 W/m^2, whether forcing from CO₂ emissions is present or not.

When forcing from CO₂ emissions is present, its effects cannot be detected in a simulation that cannot model cloud feedback response to better than ±4 W/m^2.

GCMs cannot simulate cloud response to 0.1% accuracy. They cannot simulate cloud response to 1% accuracy. Or to 10% accuracy.

Does cloud cover increase with CO₂ forcing? Does it decrease? Do cloud types change? Do they remain the same?

What happens to tropical thunderstorms? Do they become more intense, less intense, or what? Does precipitation increase, or decrease?

None of this can be simulated. None of it can presently be known. The effect of CO₂ emissions on the climate is invisible to current GCMs.

The answer to any and all these questions is very far below the resolution limits of every single advanced GCM in the world today.

The answers are not even empirically available because satellite observations are not better than about ±10% in CF.

Meaning

Present advanced GCMs cannot simulate how clouds will respond to CO₂ forcing. Given the tiny perturbation annual CO₂ forcing represents, it seems unlikely that GCMs will be able to simulate a cloud response in the lifetime of most people alive today.

The GCM CF error stems from deficient physical theory. It is therefore not possible for any GCM to resolve or simulate the effect of CO₂ emissions, if any, on air temperature.

Theory-error enters into every step of a simulation. Theory-error means that an equilibrated base-state climate is an erroneous representation of the correct climate energy-state.

Subsequent climate states in a step-wise simulation are further distorted by application of a deficient theory.

Simulations start out wrong, and get worse.

As a GCM steps through a climate simulation in an air temperature projection, knowledge of the global CF consequent to the increase in CO₂ diminishes to zero pretty much in the first simulation step.

GCMs cannot simulate the global cloud response to CO₂ forcing, and thus cloud feedback, at all for any step.

This remains true in every step of a simulation. And the step-wise uncertainty means that the air temperature projection uncertainty compounds, as Vasquez and Whiting note.

In a futures projection, neither the sign nor the magnitude of the true error can be known, because there are no observables. For this reason, an uncertainty is calculated instead, using model calibration error.

Total ignorance concerning the simulated air temperature is a necessary consequence of a cloud response ±120-fold below the GCM resolution limit needed to simulate the cloud response to annual CO₂ forcing.

On an annual average basis, the uncertainty in CF feedback into LWCF is ±114 times larger than the perturbation to be resolved.

The CF response is so poorly known that even the first simulation step enters terra incognita.

The uncertainty in projected air temperature increases so dramatically because the model is step-by-step walking away from an initial knowledge of air temperature at projection time t = 0, further and further into deep ignorance.

The GCM step-by-step journey into deeper ignorance provides the physical rationale for the step-by-step root-sum-square propagation of LWCF error.

The propagation of the GCM LWCF calibration error statistic and the large resultant uncertainty in projected air temperature is a direct manifestation of this total ignorance.

Current GCM air temperature projections have no physical meaning.

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mothcatcher
September 19, 2019 6:36 am

Dr Frank

Many thanks for your fine exposition. This, and the more intelligent ripostes to your work, have been an education.

“…The CMIP5 GCM annual average 12.1% error in simulated CF is the resolution lower limit. This lower limit is 121 times larger than the 0.1% resolution limit needed to model the cloud feedback due to the annual 0.035 W/m^2 of CO₂ forcing…”

That’s the average. Are there any GCMs that get much closer in tracking CF? Forgive me if you have covered this already.

Pat Frank
Reply to  mothcatcher
September 19, 2019 10:25 am

First, let me take this opportunity to once again thank Anthony Watts and Charles the Moderator.

We’d (I’d) be pretty much lost without you. You’ve changed the history of humankind for the better.

mothcatcher, different GCMs are parameterized differently, when they’re tuned to reproduce target observables such as the 20th century temperature trend.

None of them are much more accurate than another. Those that end up better at tracking this are worse at tracking that. It’s all pretty much a matter of near happenstance.

Jim Gorman
Reply to  Pat Frank
September 19, 2019 11:44 am

Thank you Dr. Frank for bringing this to the world’s attention. Both error and uncertainty analysis are traditional engineering concepts. As an EE who has done design work of electronic equipment, I have a very good expectation of what uncertainty means.

You can sit down and design a 3 stage RF amplifier with an adequate noise figure and bandwidth on paper. You can evaluate available components and how tolerance statistics affect the end result. But, when you get down to the end, you must decide, will this design work when subjected to manufacturing. This is where uncertainty reigns. Are component specs for sure? Will permeability of ferrite cores be what you expected and have the bandwidth required. Will there be good trace isolation? Will the ground plane be adequate? Will unwanted spurious coupling be encountered? Will interstage coupling be correct? And on and on. These are all uncertainties that are not encountered in (nor generally allowed for in) the design equations.

Do these uncertainties ring any bells with the folks dealing with GCM’s? Are all their inputs and equations and knowledge more than adequate to address the uncertainties in the parameters and measurements they are using? I personally doubt it. The world wide variables in the atmosphere that are not part of the equations and models must be massive. The possibility of wide, wide uncertainty in the outputs must be expected and accounted for if the models are to be believed.

Clyde Spencer
Reply to  Pat Frank
September 19, 2019 12:03 pm

Pat,
“It’s all pretty much a matter of near happenstance.” Trade offs! However, it calls into serious question the claim that the models are based on physics when they don’t have a general solution for all the output parameters and have to customize the models for the parameters they are most interested in.

David L. Hagen
Reply to  Pat Frank
September 19, 2019 3:42 pm

Pat Frank Thanks. Here is a link to the pdf (via Scholar.google.com) of:
Vasquez VR, Whiting WB. Accounting for both random errors and systematic errors in uncertainty propagation analysis of computer models involving experimental measurements with Monte Carlo methods. Risk Analysis: An International Journal. 2005 Dec;25(6):1669-81.

Pat Frank
Reply to  David L. Hagen
September 19, 2019 9:25 pm

It’s a very worthwhile paper, isn’t David.

When I was working on the study, I wrote to Prof. Whiting to ask for a reprint of a paper in the journal Fluid Phase Equilibria, which I couldn’t access.

After I asked for the reprint (which he sent), I observed to him that, “If you don’t mind my observation, after scanning some of your papers, which I’ve just found, you are in an excellent position to very critically assess the way climate modelers assess model error.

Climate modelers never propagate error through their climate models, and never publish simulations with valid physical uncertainty limits. From my conversations with one or two of them, model error propagation seems to be a completely foreign idea.

Here’s what he wrote back, “Yes, it is surprisingly unusual for modelers to include uncertainty analyses. In my work, I’ve tried to treat a computer model as an experimentalist treats a piece of laboratory equipment. A result should never be reported without giving reasonable error estimates.

It seems modelers elsewhere are also remiss.

Tim Gorman
Reply to  Pat Frank
September 20, 2019 3:47 am

“From my conversations with one or two of them, model error propagation seems to be a completely foreign idea.”

It’s how they are trained. They are more computer scientists than physical scientists. The almighty computer program will spit out a calculation that is the TRUTH – no uncertainty allowed.

Most of them have never heard of significant digits or if they have it didn’t mean anything to them. Most of them have never set up a problem on an analog computer where inputs can’t be set to to an arbitrary precision and therefore the output is never the same twice.

Clyde Spencer
Reply to  Pat Frank
September 20, 2019 9:56 am

“0.1When reporting the result of a measurement of a physical quantity, it is obligatory that some quantitative indication of the quality of the result be given so that those who use it can assess its reliability. Without such an indication, measurement results cannot be compared, either among themselves or with reference values given in a specification or standard. It is therefore necessary that there be a readily implemented, easily understood, and generally accepted procedure for characterizing the quality of a result of a measurement, that is, for evaluating and expressing its uncertainty.”

https://www.isobudgets.com/pdf/uncertainty-guides/bipm-jcgm-100-2008-e-gum-evaluation-of-measurement-data-guide-to-the-expression-of-uncertainty-in-measurement.pdf

Reply to  Pat Frank
September 23, 2019 1:12 pm

“They are more computer scientists than physical scientists.”

By looking over code of ‘state of the art’ climate computer models, I can be almost sure they aren’t either.

Not computer scientists, not physicists. They are simply climastrologers.

Gator
Reply to  Adrian Roman
September 23, 2019 2:07 pm

I call them grantologists.

Andre
Reply to  mothcatcher
September 19, 2019 12:14 pm

Quote: “Many thanks for your fine exposition. This, and the more intelligent ripostes to your work, have been an education.”

This article made it for me. Clear as crystal. Reminds me of some years back I understood the fabrication of hockey sticks.

RobR
September 19, 2019 6:39 am

Pat, thanks for the plain language explanation of your paper.

Question: Given current and past temperature stability during ever-increasing CO2 fractions, should we not expect the probability of cloud formation to follow a normal distribution curve.

That is to say: Scientists are duty-bound to enumerate the maximum uncertainty in the entire universe of possibilities. Nonetheless, an outcome near the mean of the reference fraction, seems far more probable, than one at either extreme.

Beeze
Reply to  RobR
September 19, 2019 8:50 am

There’s no reason to expect a normal curve. This is the same conceptual shortcut that leads people to incorrectly apply stochastic error corrections to systematic error. In general, the distinction is precisely that systemic effects are highly unlikely to be normally distributed.

RobR
Reply to  Beeze
September 19, 2019 3:02 pm

Breeze,
I’m postulating that a dramatic change is less likely to occur than one closer to a current reference.

If I understand you correctly, you’re arguing for an equal probability for the gamut of potential outcomes. This position defies logic, as prevailing conditions indicate a muted response at best.

Probability forecasting is based on analysis of past outcomes.

Tim Gorman
Reply to  RobR
September 19, 2019 4:56 pm

Robr: ” This position defies logic, as prevailing conditions indicate a muted response at best.”

The natural variability of the just the annual global temperature average would argue against a normal probability distribution for the outcomes in our ecosphere, let alone on a regional basis. It is highly likely that there is a continuum of near-equal possibilities with extended tails in both directions. On an oscilloscope it would look like a rounded off square wave pulse with exponential rise times and fall times.

RobR
Reply to  Tim Gorman
September 19, 2019 6:01 pm

Tim G.,
I beg to differ as global temperature (in the face of rapidly increased CO2) have been remarkably flat; albiet with some warming.

Arguing for an even probability distribution, in the face of said stability, requires certitude in an exponential CF response to rising CO2

Tim Gorman
Reply to  Tim Gorman
September 19, 2019 7:01 pm

RobR,

go here: http://images.remss.com/msu/msu_time_series.html

You will see significant annual variation in the average global temperature. If you expand the time series, say by 500-700 years the variation is even more pronounced.

“Arguing for an even probability distribution, in the face of said stability, requires certitude in an exponential CF response to rising CO2”

Huh? How do you figure an even probability distribution requires an exponential response of any kind driven by anything? A Gaussian distribution has an exponential term. Not all probability distributions do. See the Cauchy distribution.

Beeze
Reply to  RobR
September 20, 2019 9:12 am

RobR,

The normal distribution is a very specific distribution, it is not just the general idea that dramatic change is less likely to occur than one closer to current reference.

Specifically, the central limit theorem (which justifies the assumption of normality) applies to “any set of variates with any distribution having a finite mean and variance tends to the normal distribution.” (http://mathworld.wolfram.com/NormalDistribution.html). The problem is that this describes a set of variables, not a phenomenon under investigation.

So while the set of variables that fully describe climate will obey the theorem, and any set of explanatory variables which we may choose to invoke to explain that phenomenon will also explain it. Since our collection of explanatory variables is almost certainly incomplete for a complex problem, the two distributions won’t line up. This will skew your observation, because it then isn’t governed by a fix set of variables that obey theorem.

That’s why Zipfian (long tailed) distribution are the norm. That means that, even though you might pin down the main drivers, the smaller ones can always have a larger effect on the outcome, since the harmonic series doesn’t converge, and the more terms you have, the quicker this can happen.

Six sigma may work in the engineering world, but not in the world of observing complex phenomena.

Pat Frank
Reply to  RobR
September 19, 2019 10:28 am

Rob, I can’t speak at all to how the climate self-adjusts to perturbations, or what clouds might do.

The climate does seem to be pretty stable — at least presently. How that is achieved is the big question.

Stevek
Reply to  RobR
September 19, 2019 11:21 am

Possibly if we believe cloud formation is caused by many independent random variables. This is central limit theorem.

Beeze
Reply to  Stevek
September 19, 2019 12:39 pm

There lies the rub: There’s no reason to believe “cloud formation is caused by many independent random variables”.

jorgekafkazar
Reply to  Beeze
September 19, 2019 3:18 pm

Surface irregularities creating local air turbulence. Humidity-driven vertical convection. Liquid water droplet (fog) density-driven vertical convection. Solar-heat internal cloud vertical convection. Water condensation via local temperatures. Solar vaporization of cloud droplets. Local air pressure variations. Wind driven evaporation of fog. Microclimate interactions. Rain. Wind-driven particulates. Ionization from electrical charges. Warmed surface convection currents. Mixing of air currents. Asymmetry throughout. Then add nighttime radiation to a non-uniform 4K night sky.

John Andrews
Reply to  RobR
September 19, 2019 7:50 pm

RobR
“Question: Given current and past temperature stability during ever-increasing CO2 fractions, should we not expect the probability of cloud formation to follow a normal distribution curve.”

No. We would probably find that the distribution is log normal if we looked at it. Many years ago I studied airborne radioactivity emission distributions and found that almost always the distributions were log normal.

rbabcock
September 19, 2019 6:41 am

There is so much chaos, uncertainty and feedbacks in the Earth’s climate it really doesn’t matter what the climate modelers do or don’t do, they will never get it right.. or even close.. ever.

Nicholas McGinley
Reply to  rbabcock
September 19, 2019 7:31 am

Touché!

tom0mason
Reply to  rbabcock
September 19, 2019 7:42 am

Yes rbabcock,
In Nick Stokes’ recent post I alluded to that when I asked —
“Nick,
Your diagram of Lorenz attractor shows only 2 loci of quasi-stability, how many does our climate have? And what evisdence do you have to show this.”
[corrected the dumb speling mastaeke]
To which the answer was —
Nick Stokes
September 16, 2019 at 11:04 pm

“Well, that gets into tipping points and all that. And the answer is, nobody knows. Points of stability are not a big feature of the scenario runs performed to date.”

So we don’t know how many stable loci there are, nor do we know the probable way the climate moves between them. Not so much truly known about our climate then, especially the why, when, and how the climate changes direction. So just how can you possibly model long term climate with so much ignorance of the basic mechanisms?

jorgekafkazar
Reply to  tom0mason
September 19, 2019 3:51 pm

“So just how can you possibly model long term climate with so much ignorance of the basic mechanisms?”

Easy: “🎶Razzle-dazzle ’em!🎶”

Barbara
Reply to  tom0mason
September 20, 2019 6:06 pm

I have been wondering this for years.

Nick said, “Points of stability are not a big feature…to date.”

They are everything in a complex non-linear system. We simply cannot assess what is “not normal” if we do not know what is normal, and understand the bounds of “normal” – i.e., for each loci there will be a large number (essentially an infinite number) of bounded states available, all perfectly “normal,” and at some point, the system will flip to another attractor.

We know of two loci over the last 800,000 years: quasi-regular glacial and interglacials (e.g., see NOAA representation here:comment image).

We really can’t model “climate” unless we can model that.

Latitude
Reply to  rbabcock
September 19, 2019 8:36 am

never…..when you do this to the input data

…you get this as the result

Frenchie77
September 19, 2019 6:42 am

But the GCMs are so beautiful we must keep using them even if they disagree with reality. We can’t have spent all this money on nothing.

Honestly, the GCMs have failed to accurately predict anything for the past 30 years. Have we found the main root cause or is this 1 of a 100 causes in the chain any on of which causes them to fail?

Eric Barnes
Reply to  Frenchie77
September 19, 2019 7:00 am

“We can’t have spent all this money on nothing.”

You are correct. It was spent to justify arbitrary taxation by the UN, politicians and bureaucrats across the globe. Everyone responsible for this scam should be forced to find real work, especially the politicians.

Clyde Spencer
Reply to  Eric Barnes
September 19, 2019 12:05 pm

Eric Barnes
” Everyone responsible for this scam should be forced to find real work, …”
Like breaking rocks on a chain gang!

Nicholas McGinley
Reply to  Frenchie77
September 19, 2019 3:22 pm

“But the GCMs are so beautiful we must keep using them even if they disagree with reality. We can’t have spent all this money on nothing.”
That may be the funniest comment I have heard this month!
Bravo!
Unfortunately, like much comedy, it is also incredibly sad when you really think about it for a while.

Andrew Burnette
September 19, 2019 6:44 am

Dr Frank,

I think you have taken a wise path by directly addressing the concern raised by Dr. Spencer (i.e., that with each model iteration, inputs change in response to model outputs and those changes are not adequately modeled), Well done.

Dr. Deanster
Reply to  Andrew Burnette
September 19, 2019 8:08 am

I agree. While Franks explanation is rather wordy for us lay folk, I noted to Nick Stokes, the difference between a CFD equation used in the normal sense, and the application of CFD in weather and GCMs, is that industrial CFDs use known parameters to calculate the unknown. GCMs use a bunch of unknowns to calculate a desired outcome.. It is a matter of days before the error in the CFD/GCM used in weather “blows up” as Nick put it … and that is because the parameters become more and more unknown over time. It stands to reason, if the equation blows up in a few days, it doesn’t stand a chance at calculating 100 years.

As such, all of the “gargoyles” of a GCM are nothing more than decoration. The reality is, the GCM ends up being a linear calculation based on the creators input of an Estimated Climate Sensitivity to CO2. Frank just made a linear equation using the same premise. For that matter, the other part of Franks paper dealing with a GCM calculating CF as a function of CO2 forcing is a false assumption. We have no empiric proof that CO2 forcing has doodley squat impact on CF. … thus its imaginary number for LWCF is just fiction. But … it doesn’t matter, it is the ECS that counts.

Good Job Dr. Frank

Reply to  Dr. Deanster
September 19, 2019 9:19 am

“that industrial CFDs use known parameters to calculate the unknown”
I don’t think you know anything about industrial CFD. Parameters are never known with any certainty. Take for example the modelling of an ICE, which is very big business. You need a model of combustion kinetics. Do you think that is known with certainty? You don’t, of course, even know the properties of the fuel that is being used in any instance. They also have a problem of modelling IR, which is important. The smokiness of the gas is a factor.

Which raises the other point in CFD simulations; even if you could get perfect knowledge in analysing a notional experiment, it varies as soon as you try to apply it. What is the turbulence of the oncoming flow for an aircraft wing? What is the temperature, even? Etc.

“It is a matter of days before the error in the CFD/GCM used in weather “blows up” as Nick put it”
No, it isn’t, and I didn’t. That is actually the point of GCM’s. They go beyond the time when weather can be predicted, but they don’t blow up. They keep calculating perfectly reasonable weather. It isn’t a reliable forecast any more, but it has the same statistical characteristics, which is what determines climate.

Gator
Reply to  Nick Stokes
September 19, 2019 9:52 am

LOL!!!

Stokes thinks our climate is as simple as an ICE! Priceless!

Nick, sometimes it is best to say nothing, rather than prove yourself to be a zealot and a fool. Please learn this lesson, and grow up.

See Nick. See shark. See Nick jump shark. Jump Nick, jump! LOL

Michael Jankowski
Reply to  Nick Stokes
September 19, 2019 10:03 am

“…You don’t, of course, even know the properties of the fuel that is being used in any instance…”

Of course you do. You think GM or BMW or whoever doesn’t know if it will be fed by E85, kerosene, Pepsi, or unicorn farts?

“…That is actually the point of GCM’s. They go beyond the time when weather can be predicted, but they don’t blow up. They keep calculating perfectly reasonable weather…”

Climate models don’t do weather.

Bob boder
Reply to  Michael Jankowski
September 19, 2019 10:14 am

could set up a bounded random weather generator that would do the same thing, doesn’t mean that it has any practical application

Reply to  Michael Jankowski
September 19, 2019 10:30 am

“GM or BMW or whoever doesn’t know”
They don’t know exactly what owners are going to put in the tank in terms of fuel type, octane number etc. But there are a lot of properties that matter. Fuel viscosity varies and is temperature dependent. It’s pretty hard to even get an accurate figure to put into a model, let alone know what it will be in the wild. Volatility is very dependent on temperature – what should it be? Etc.

fah
Reply to  Michael Jankowski
September 19, 2019 1:52 pm

Due to the needs of engineering, a great deal of experimental work goes in to determining relevant physical constants of the materials. Density and viscosity of various possible fuels as a function of temperature is no different. Several examples are

https://www.researchgate.net/publication/273739764_Temperature_dependence_density_and_kinematic_viscosity_of_petrol_bioethanol_and_their_blends

and
https://pubs.acs.org/doi/abs/10.1021/ef2007936

A big difference between inputs to engineering models and climate models is that such fundamental, needed, inputs are obtainable from controlled laboratory experiments, with well characterized uncertainties. When such values are used in engineering models, error propagation can proceed with confidence.

slow to follow
Reply to  Michael Jankowski
September 19, 2019 2:03 pm

A starter on fuel standards and definitions here:

https://www.epa.gov/gasoline-standards

Plenty more info just a google away.

Reply to  Michael Jankowski
September 19, 2019 3:05 pm

“A big difference between inputs to engineering models and climate models is that such fundamental, needed, inputs are obtainable from controlled laboratory experiments, with well characterized uncertainties”

Ha! From the abstract of your first link:
” The coefficients of determination R2 have achieved high values 0.99 for temperature dependence density and from 0.89 to 0.97 for temperature dependence kinematic viscosity. The created mathematical models could be used to the predict flow behaviour of petrol, bioethanol and their blends.”

0.89 to 0.97 may be characterised, but it isn’t great. But more to the point, note the last. They use models to fill in between the sparse measurements.

Michael Jankowski
Reply to  Michael Jankowski
September 19, 2019 4:16 pm

“…They don’t know exactly what owners are going to put in the tank in terms of fuel type, octane number etc…”

Amazing. You’re doubling-down on possibly the dumbest comment I have ever read on this site (and that includes griff thinking 3 x 7 = 20).

Gasoline refiners and automakers have had a good handle on this for a few decades. Things are pretty-well standardized and even regulated. Running a CFD on a few different octane ratings is nothing. And then a prototype can be tested using actual fuel (which is readily available). Manufacturer’s will even recommend a certain octane level (or higher) for some vehicles.

You really think engineers just throw their hands up in the air and start designing an ICE considering every sort of fuel possibility and then hope they get lucky? They design based on a fuel from the start.

Reply to  Michael Jankowski
September 19, 2019 4:34 pm

“Running a CFD on a few different octane ratings is nothing. “
Yes, that’s how you deal with uncertainty – ensemble.

“You really think engineers just throw their hands up in the air and start designing an ICE”
I’m sure that they design with fuel expectations. But they have to accommodate uncertainty.

tsk tsk
Reply to  Michael Jankowski
September 19, 2019 4:45 pm

0.89 to 0.97 may be characterised, but it isn’t great.

Written in all seriousness.

Then again this is the same individual who thinks the atmosphere is a heat pump and not a heat engine. *shrug*

Michael Jankowski
Reply to  Michael Jankowski
September 19, 2019 7:57 pm

“…Yes, that’s how you deal with uncertainty – ensemble…”

These are discrete analyses performed on specific and standardized formulas with known physical and chemical characteristics. The ICE design is either compatible and works with a given formulation or it doesn’t.

Unlike most climate scientists, engineers work with real-world problems. Results need to be accurate, precise, and provable. Ensembles? Pfffft. Save those for the unicorn farts.

Streetcred
Reply to  Michael Jankowski
September 19, 2019 11:37 pm

” They don’t know exactly what owners are going to put in the tank in terms of fuel type, octane number etc. ”

Balderdash, my BMW manual tells me what the optimum fuel is for use in my high performance engine … why would an owner even contemplate using inferior fuel ?

Maybe your old banger still uses chip oil, eh Nick ?

tom0mason
Reply to  Nick Stokes
September 19, 2019 10:22 am

While you’re here Nick would it be fair to say what Kevin Trenberth said in journal Nature (“Predictions of Climate”) about climate models in 2007 still stands —

None of the models used by the IPCC are initialized to the observed state and none of the climate states in the models correspond even remotely to the current observed climate. In particular, the state of the oceans, sea ice and soil moisture has no relationship to the obsered state at any recent time in any of the IPCC models. There is neither an El Nino sequence nor any Pacific Decadal Oscillation that replicates the recent past; yet these are critical modes of variability that affect Pacific rim countries and beyond. The Atlantic Multidecadal Oscillation, that may depend on the thermohaline circulation and thus oceanic currents in the Atlantic, is not set up to match today’s state, but it is a critical component of the Atlantic hurricanes and it undoubtedly affects forest for the next decade from Brazil to Europe. Moreover, the starting climate state in serveral of the models may depart significantly from the real climate owing to model errors. I postulate that regional climate change is impossible to deal with properly unless the models are initialized.
¯

¯
Therefore the problem of overcoming this shortcoming, and facing up to initializing climate models means not only obtaining sufficiently reliable observations of all aspects of the climate system, but also overcoming model biases. So this is a major challenge.

Are the model initialize with realistic values before they are run?

Reply to  tom0mason
September 19, 2019 10:35 am

“would it be fair to say”
Yes, and I’ve been saying it over and over. Models are not initialised to current weather state, and cannot usefully be (well, people are trying decadal predictions, which are something different). In fact, they usually have a many decades spin-up period, which is the antithesis of initialisation to get weather right. It relates to this issue of chaos. The models disconnect from their initial conditions; what you need to know is how climate comes into balance with the long term forcings.

Clyde Spencer
Reply to  Nick Stokes
September 19, 2019 10:59 am

Dear Dr. Nick Stokes (In deference to your acolytes who complained I wasn’t being sufficiently reverential.)

You said, “They keep calculating perfectly reasonable weather. It isn’t a reliable forecast any more, …” I didn’t think that there was so much difference between Aussie English and American English that your you would consider unreliable to be reasonable.

Reply to  Clyde Spencer
September 19, 2019 2:39 pm

Weather could be reasonable before we had reliable forecasts.

Streecred
Reply to  Clyde Spencer
September 19, 2019 11:40 pm

BoM finds it difficult to provide reliable weather forecasts for 24 hours ahead. How “reasonable” is that ?

Dr. Deanster
Reply to  Nick Stokes
September 19, 2019 12:59 pm

Ummm … Nick … I may not be as well versed about CFDs as you, but I’m pretty proficient when in comes to ICE. There is this thing called an ECM, and it hooks to the MAP, the O2 sensor, and a few others …. and as such, the ECM adjust the behavior based on known incoming data. That is how you get multi fuel ICE, … the ECM makes the adjustments to fuel mix and timing to insure that the engine is running within preset parameters that were determined using … drum role … KNOWN PARAMETERS. I would guess that a CFD was used to model the burn with those known parameters in the design phase, such that they can pre-program the ECM to make its adjustments … but again … you are talking about a live data system, with feedback and adjustment. The adjustments are made using KNOWN data and KNOWN standards.

But what I was talking about, is in fluid dynamics, you know the viscosity of the liquid, you know the diameter of the pipe, you know the pressure, you know the flow rate … you KNOW a lot of things … then your CFD shows how the liquid moves within the system. A GCM can take the current data, pressure systems, temperatures, etc, and calculate how a weather system is likely to move, however, the certainty of those models, as any Meteorologists will tell you becomes less certain with each passing day …. and when you get out to next week, it’s pretty much just a guess. A GCM run for next year is doing nothing but using averages over time. Problem with those averages, is they have confidence intervals, there are standard deviations for each parameter. The CF for Texas in July will be for example 30% plus or minus 12%., thus solar insolation at the surface will be X w/m2, plus or minus Y w/m2, Pressure will be … , etc etc etc. The problem with GCMs in Climate is they do not express their results as plus or minus the uncertainty. They give you a single number, then they run the same model 100 times. THIS IS A FLAWED way of doing things. In order to get a true confidence interval for these calculation, you have to run the model with all possible scenarios, which will be a probability in the 10s of thousands per grid point using the uncertainty ranges for each parameter, and that for each time interval, …. which would be a guaranteed “blow up” of the CFD. Further, the error Frank points to will begin to be incorporated into the individual parameter standard deviations, … ie., a systematic error in the system. Kabooom.

That is why its just easier to make a complicated program that in the end, cancels out all the parameters and uses the ECS …… same as a linear equation using the ECS.

Just sayin.

Reply to  Dr. Deanster
September 19, 2019 3:49 pm

“you know the viscosity of the liquid”
I wish. You never do very well, especially its temperature dependence, let alone variation with impurities.
“you know the pressure, you know the flow rate”
Actually, mostly the CFD has to work that out. You may know the atmospheric pressure, and there may be a few manometers around, but you won’t have a proper pressure field by observation.

fah
Reply to  Nick Stokes
September 19, 2019 4:27 pm

One needs to be clear about what one means by “model.” When it is used in the engineering sense of fitting a proposed equation to experimental data, such as the data for physical constants, “model” literally means that, a specific determinate, equation with specific parameter choices. (In the climate science regime, a more proper word would be “simulation.”) In engineering, the equation may be theoretically motivated or may simply be an explicit function that captures certain kinds of behavior such as a polynomial. That equation is then “fit” to the data and the variation of the measured values from the predicted values is minimized by that simple fit. Various conditions usually are also tested to see if the deviations from the fit correspond well or ill to what would be expected of “random” errors, such as a normal distribution. Such tests can typically show if there is some non-random systematic error either due to the apparatus or a mis-match of the equation to the behavior.
The Rsquared value provides the relative measure of the percentage of the dependent variable variance that the equation explains (from that particular experiment) over the range for which it was measured, under the conditions (i.e. underlying experimental uncertainties) of the experiment. In other words it is a measure of how well the function seems to follow the behavior of the data. A value of 0.9 in general is considered quite good in the sense that that particular equation is useful. Further, the values that come from the fit, including the uncertainty estimates, can be used directly in an error propagation of a calculation that uses the value. A more meaningful quantity for predictive purposes is the standard error of the regression, which gives the percent error to be expected from using that equation, with those parameters, to predict an outcome of another experiment. By that measure, engineering “models” typically are not considered useful unless the standard errors are less than a few percent, as is the case for the particular works cited. Experimental procedures are generally improved over time which generally reduce the uncertainties and provide more accurate (lower uncertainties).

By contrast, one should compare the inputs to climate simulations. Of particular interest would be what is the magnitude of the standard errors associated with them, whether estimates of them are point values, or functional relations, and whether the variations from the estimate used are normally distributed or otherwise.

TimTheToolMan
Reply to  Nick Stokes
September 20, 2019 6:56 pm

Nick writes

They go beyond the time when weather can be predicted, but they don’t blow up.

They do unless their parameters are very carefully chosen. But choosing those parameters isn’t about emulating weather, its about cancelling errors.

And then

It isn’t a reliable forecast any more, but it has the same statistical characteristics, which is what determines climate.

The only characteristics that might be considered “reliable” are those near to today. There is no reason to believe future characteristics will be reliable and in fact the model projections have already shown them not to be reliable.

fah
Reply to  Dr. Deanster
September 19, 2019 4:35 pm

Slight correction to the previous comment: where it said the standard error measures how well the function predicts the outcome of a future measurement, it should have included the words “in an absolute sense” meaning that it gives the expected percent error in the predicted future value. In that sense it can be used directly in a propagation of error calculation. Rsquared does not serve that purpose since it only measures the closeness to which the functional form conforms to the functional form of the data.

Pat Frank
Reply to  Andrew Burnette
September 19, 2019 9:28 pm

Thanks, Andrew. Your point is in the paper, too.

Carlo, Monte
September 19, 2019 6:52 am

Excellent summary that shows how the differential equation argumentation is just a big red herring.

Lance Wallace
September 19, 2019 6:55 am

“even the first simulation step enters terra incognita.”

Dr. Frank–

Your propagation of error graphs are hugely entertaining to me, showing the enormous uncertainty that develops with every step of a simulation. This is shocking to the defenders of the consensus and they bring up the artillery to focus on that wonderful expanding balloon of uncertainty.

But now with your new article on the error in the very first step, why bother propagating the error beyond the first step? Let the defenders defend against this simpler statement.

Clyde Spencer
Reply to  Lance Wallace
September 19, 2019 1:40 pm

Lance Wallace

There have been complaints that the +/- 4 W uncertainty should only be applied once.

Arbitrarily select a year (Tsub0) of unknown or assumed zero uncertainty for the temperature to apply the uncertainty of cloud fraction. The resultant predicted temperature of year Tsub1, now has a known minimum uncertainty. Now, since we selected the initial year arbitrarily, what is to prevent us from repeating the selection, this time using year Tsub1? Doing so, we are required to account for the uncertainty of the cloud forcing just as we did the first time, only this time we know what the minimum uncertainty of the temperature is before doing the calculation! We can continue to do this ad infinitum. That is, as long as there is an iterative chain of calculations, the known uncertainties of variables and constants must be taken into account every time the calculations are performed. It is only systematic offsets or biases that need only be adjusted once.

A bias adjustment of known magnitude will affect the nominal value of the calculation, but not the uncertainty. However, the uncertainty, which has a range of possible values, will not affect the nominal value, but WILL affect the uncertainty.

Reply to  Clyde Spencer
September 19, 2019 3:53 pm

Clyde,
“Now, since we selected the initial year arbitrarily, what is to prevent us from repeating the selection, this time using year Tsub1?”
And for year, read month. Or iteration step in the program (about 30 min). What is special about a year?

In fact, the 4 Wm⁻² was mainly spatial variation, not over time.

Clyde Spencer
Reply to  Nick Stokes
September 19, 2019 5:24 pm

Stokes,
The point being that the calculations cannot be performed in real time, nor at the spatial resolution at which the measured parameters vary. Therefore, coarse resolutions of both time and area have to be adopted for practical reasons.

Other than the fact that 1 year nearly averages out the land seasonality, it could be a finer step. However, using finer temporal steps not only increases processing time, but increases the complexity of the calculation by having to use appropriate variable values for the time steps decided on. But, as is often the case with you, you have tossed a red herring into the room. Using finer temporal resolutions does not get around the requirement of accounting for the uncertainty at every time-step.

Richard M
September 19, 2019 6:56 am

The problem with CF is just the tip of the iceberg. Also consider high altitude water vapor. As theorized by Dr. William Gray, it must also change due to any surface warming and/or changes in evaporation rates. Once again the models cannot track these changes at the needed accuracy to produce a valid result.

Just how many more of these factors exist? Each one adds exponentially to the already impossible task facing models.

Phoenix44
September 19, 2019 6:58 am

It is entirely obvious that GCMs disguise a (relatively) simple relationship between CO2 and temperature with wholly unnecessary (and necessarily inaccurate) complexity. A couple of lines on an Excel sheet will do just as well in terms of forecasting temperature – delta CO2, sensitivity of temperature to changes in CO2, one multiplied by the other. All you need to know to forecast temperature with any skill is the sensitivity. GCMs can then be run to show the effects on the climate of the increase in temperature.

But a simple model does not work, because a single sensitivity figure will not both hindcast and forecast accurately, even of a long term trend that allows for a significant amount of natural variation. So we get these huge GCMs which do not improve the situation but allow modelers to hide the problem, which is that any sensitivity to CO2 is swamped by natural variation at every level we can model the physical properties of the climate.

The fundamental problem remains, that sensitivity to CO2 is still unclear, and estimates vary widely. Yet that sensitivity is absolutely the key thing we need to know if we are to understand and forecast the impact of increased CO2 on the climate. If we actually knew sensitivity, and GCMs were a reasonable approximation of our climate, there would be no debate amongst climate scientists and no reasonable basis for scepticism.

Thomas Homer
Reply to  Phoenix44
September 19, 2019 8:11 am

Phoenix44: “The fundamental problem remains, that sensitivity to CO2 is still unclear”

Precisely! We can’t even determine how to derive CO2 sensitivity on Mars where it makes up 95% of the atmosphere. We don’t even know what to measure so that we can begin to derive the answer.

“If we actually knew [CO2] sensitivity, and GCMs were a reasonable approximation of our climate”

Then we could prove out the GCM by inputting Mars’ parameters and verifying the resulting output.

It truly is glaring how pitiful the “science” is that has been dedicated to deriving CO2 sensitivity.

Antero Ollila
Reply to  Phoenix44
September 19, 2019 11:13 am

Simple and complex GCMs give the same values for climate sensitivities and also for the warming values of different RCP’s. There is no conflict. Or can you show an example that they give different results?

Pat Frank
Reply to  Antero Ollila
September 21, 2019 2:29 pm

Yes. It’s all offsetting errors, Antero. Also known as false precision.

Kiehl JT. Twentieth century climate model response and climate sensitivity. Geophys Res Lett. 2007;34(22):L22710.

http://dx.doi.org/10.1029/2007GL031383

Abstract: Climate forcing and climate sensitivity are two key factors in understanding Earth’s climate. There is considerable interest in decreasing our uncertainty in climate sensitivity. This study explores the role of these two factors in climate simulations of the 20th century. It is found that the total anthropogenic forcing for a wide range of climate models differs by a factor of two and that the total forcing is inversely correlated to climate sensitivity. Much of the uncertainty in total anthropogenic forcing derives from a threefold range of uncertainty in the aerosol forcing used in the simulations.

p.2 “Note that the range in total anthropogenic forcing is slightly over a factor of 2, which is the same order as the uncertainty in climate sensitivity. These results explain to a large degree why models with such diverse climate sensitivities can all simulate the global anomaly in surface temperature. The magnitude of applied anthropogenic total forcing compensates for the model sensitivity.

ChrisB
September 19, 2019 7:01 am

An impressive and insightful treatise of errors and error propagation in the context of GCM. Thank you for explaining in plain language.

Nicholas McGinley
September 19, 2019 7:29 am

Just a few sentences in to this article, and I think I just had my “Aha!” moment I have been waiting and hoping for.
A black box.
That crystalizes it very clearly.

Dr Deanster
Reply to  Nicholas McGinley
September 19, 2019 2:42 pm

I think it would be more appropriately called …. [The Wiggly Box]. This is what a GCM represents.

dT=dCO2*[wiggly box]*ECS

Where dCO2 * ECS establishes the trend … and [wiggly box] adds the wiggles in the prediction line to make it look like a valid computation.

Andre
Reply to  Dr Deanster
September 20, 2019 12:02 am

“dT=dCO2*[wiggly box]*ECS”

Even better.

S. Geiger
September 19, 2019 7:31 am

Dr. Frank: “beta = sqrt[sum over(theta_S_i)^2],
“where “i” defines the sources of bias errors and theta_S is the bias range within the error source i. (my bold)”

Is it an issue that you are only evaluating a single bias error source; whereas, for the reasons previously discussed, we know the net energy budget to be essentially accurate. Errors in the LWCF are demonstrably being offset by errors in other energy flux components at each time step such that the balance is maintained (?)

Tommy
Reply to  S. Geiger
September 19, 2019 8:25 am

How can introducing another “error” increase your understanding of the real world.

It doesn’t.

Does it allow your model to better emulate a linear forcing model? Yes. Does it model the physical world? No.

Pat Frank
Reply to  S. Geiger
September 19, 2019 10:38 am

S. Geiger, please call me Pat.

I’m evaluating an uncertainty based upon the lower limit of resolution of GCMs. Off-setting errors do not improve resolution. They just hide the uncertainty in a result.

Off-setting errors do not improve the physical description. They do not ensure accurate prediction of unknown states.

In a proper uncertainty analysis, offsetting errors are combined into a total uncertainty as their root-sum-square.

AndyHce
Reply to  S. Geiger
September 19, 2019 6:07 pm

An energy budget in balance in a theoretical computation of decidedly many unknowns means what? Since the historical record indicates rather large changes in cycles of 60 to 70 years, 100 years, 1000 years, 2500 years, 24000 years, 40,000 years, etc. what is the logic that says any particular range of years should find a balance in input vs output? Perhaps pre-tuning for any particular short period intrinsically introduces a large bias because that balance is not there is reality.

DocSiders
Reply to  AndyHce
September 20, 2019 1:07 am

Assuming a balance exists integrated over a time span of anything shorter than a few centuries is crazy to assume. The obvious existence of far longer period (than centuries) oscillations guarantees periodic imbalances of inputs and outflows on grand scales.

September 19, 2019 7:33 am

Quote:
“I posted a long extract from relevant literature on the meaning and method of error propagation, here. Most of the papers are from engineering journals.”

I have worked 40 years in product development using measurements and simulations to improve rock drilling equipment and heavy trucks and buses.

We have a saying:
“When a measurement is presented no one but the performer thinks it is reliable, but when a simulation is presented everyone except from the performer thinks it is the truth.”

Thank you for publishing results that I hope will call out the modellers to give evidence of the uncertainties in their work!

Jim Allison
September 19, 2019 7:38 am

If I understand this correctly:

I find a stick on the ground that’s about a foot long in length. It’s somewhere between 10 and 14 inches long. I decide to measure the length of my living to the nearest 1/16th of an inch using that stick.

My living room is exactly 20 “stick lengths” long. I can repeat the measurement experiment 10 times and get 20 sticks long. My wife can repeat the measurement experiment and get 20 sticks long. A stranger off the street gets the same result. But despite dozens of repeated experiments, I can’t be sure, at a 1/16 of an inch accuracy, how long my living room really is because of the uncertainty in the length of that stick.

I need a properly calibrated stick, a ruler or a tape measure, before I can claim to know how long my living room is at that level of accuracy. If your device used to measure something is garbage, the results are going to be incredibly uncertain.

Matthew R Marler
Reply to  Jim Allison
September 19, 2019 2:12 pm

Jim Allison, good use of the measuring stick analogy.

Reply to  Jim Allison
September 19, 2019 2:37 pm

“I need a properly calibrated stick, a ruler or a tape measure, before I can claim to know how long my living room is at that level of accuracy.”
No, all you need is to find out the length of the stick in metres. Then you can take all your data, scale it, and you have good results. That is of course what people do when they adjust for thermal expansion of their measures, for example.

The point relevant here is that the error didn’t compound. It was out by a constant factor, even with multiple measures.

Matthew R Marler
Reply to  Nick Stokes
September 19, 2019 4:41 pm

Nick Stokes: No, all you need is to find out the length of the stick in metres.

That’s true. All you ever have to do to remove uncertainty is learn the truth. For a meter stick, however, the measurement of its length will have still an unknown error. Uncertainty will be smaller than in Jim Allison’s description of the problem, maybe only +/- 0.1mm; that uncertainty compounds. He can now measure the room with perhaps only 1/16″ error.

For Pat Frank’s GCM, of which the unknown meter stick is an analogy , what is needed is a much more accurate estimate of the cloud feedback, which may not be available for a long time. It’s as though there is no way to measure the meter stick.

Jim Allison
Reply to  Nick Stokes
September 19, 2019 7:09 pm

In this analogy, there was no error – everyone measured exactly 20 lengths. The measurement experiment delivered consistent results – it was a very precise experiment.

The uncertainty did compound though. Each stick length added to the overall uncertainty of the length of the room. Something that is exactly as long as the stick would be 10-14 inches long. If something is two “lengths’ long, it would be 20-28 inches long. Twenty “lengths” means that the room is anywhere between 200-280 inches long. See how the more you measure with an uncertain instrument, the more the uncertainty increases? This is accuracy, a different beast than precision.

I agree with you that if we could remove the uncertainty of the stick, and cloud formation, than we could find out exactly how long my room is and have better climate models. But billions of dollars later, we’re still scratching our heads at how much carpet I need to buy, and what climate will do in the future.

Tim Gorman
Reply to  Nick Stokes
September 19, 2019 7:30 pm

“The point relevant here is that the error didn’t compound. It was out by a constant factor, even with multiple measures.”

Huh? Did you stop to think for even a second before posting this? If the stick is off by an inch then the first measurement will be off by an inch. The second measurement will be off by that first inch plus another inch! And so on. The final measurement will be off by 1inch multiplied by the number of measurements made! The error certainly compounds!

It is the same with uncertainty. If the uncertainty of the first measurement is +/- 1 inch then the uncertainty of the second measurement will be the first uncertainty doubled. If the uncertainty of the first measurement is +/- 1 inch, i.e. from 11inches to 13inches, then the second measurment will have an uncertainty of 11inches +/- 1inch, i.e. 10inches to 12 inches coupled with 13inches +/- 1inch or 12 inches to 14inches. So the total uncertainty will range from 10 inches to 14 inches, or double the uncertainty of the first measurement. Sooner or later the uncertainty will overwhelm the measurement tool itself!

Reply to  Tim Gorman
September 20, 2019 12:23 am

Its simply a matter of units. If the stick is in fact marked with some antique marking like feet and inches, you’d still have a consistent measure, with no compounding. And when you looked up, in some dusty tome, the units conversion factor, you could do a complete conversion. Or if your carper supplier happened to remember these units, maybe he could still meet your order.

Tim Gorman
Reply to  Nick Stokes
September 20, 2019 4:57 am

“Its simply a matter of units. If the stick is in fact marked with some antique marking like feet and inches, you’d still have a consistent measure, with no compounding.”

You *still* don’t get it about uncertainty, do you? It’s *not* just a matter of units. You are specifying the total length in *inches*, not in some unique unit. The uncertainty of the length of the measuring stick in inches is the issue. Remember, there are no markings on the stick, it is assumed to be 12 inches long no matter how long it actually is, that is the origin of the uncertainty interval! And that uncertainty interval does add with each iteration of using the stick!

I don’t believe that you can be this obtuse on purpose. Are you having fun trolling everyone?

Kenneth Denison
Reply to  Nick Stokes
September 20, 2019 6:29 am

Tim +1

Jim Gorman
Reply to  Nick Stokes
September 20, 2019 7:18 am

Nick Stokes –> “you’d still have a consistent measure, with no compounding”. You are still dealing with error, not uncertainty.

Measurement errors occur when you are measuring the same thing with the same device multiple times. You can develop a probability distribution and calculate a value of how accurate the mean is and then assume this is the “true value”. This doesn’t include calibration error or how close the “true value” as measured is to the defined value.

You’ll note that these measurement errors do not compound, they provide a probability distribution. However, the calibration uncertainty is a systemic error that never disappears.

The mean also carries the calibration uncertainty since there is no way to eliminate it. In fact, it is possible that the uncertainty CAN compound. It can compound in either direction or it is possible that the uncertainties DO offset. The point is that you have no way to know or determine the uncertainty in the final value. The main thing is measuring the same thing, multiple times with the same device.

Now, for compounding, do the following, go outside and get a stick from a tree. Break it off to what you think is 12 inches. Visually assess the length and write down what you think may be the uncertainty value as compared to the NIST standard for 12 inches. Then go make 10 consecutive measurements to obtain a length of 120 inches. How would you convey the errors in that? You could assume the measurement errors offset because you may overlap the line you drew for the previous measurement one time while you missed the line the next time so that the errors offset. It would be up to you do the sequence multiple times and assess the differences and define a +/- error component to the measurement error.

Now, how about calibration error. Every time you take a sequential measurement the calibration error will add to the previous measurement. Why? When you check your stick against the NIST standard lets assume that it comes out 13 inches (+/- an uncertainty by the way). Your end result will be 1 inch times 10 measurements = 10 inches off. The 1 inch adds each time you make a sequential measurement! This is what uncertainty does.

Clyde Spencer
Reply to  Nick Stokes
September 20, 2019 11:04 am

Jim Gorman
Not only is there an inherent potential error in the assumed length of the measuring stick, which is additive or systematic, but the error in placing the stick on the ground is a random error that varies every time it is done, and is propagated as a probability distribution.

Brigitte
Reply to  Tim Gorman
September 20, 2019 1:54 am

Actually, in the sense of climate models, this isn’t relevant.

Take a metal rod, we measure it with a ruler we believe to be 100cm but we’re uncertain so it’s really 90cm +/- 10cm. The rod measures 10 ruler lengths so it’s length is 1000cm +/-100cm. That’s quite a bit of uncertainty!

Now, we paint the stick black and leave it in the sun (the black paint being analogous to adding co2). We remeasure and find it 10cm longer. Since this is less than the +/- 100cm original length of the rod it’s claimed that the uncertainty overwhelms the result.

But no, we can definitively say it’s longer and, if the expansion is roughly proportional, the uncertainty of the expansion is +/- 1cm.

The GCM’s don’t stand on their own. They are also calibrated (which from what Pat quotes below suggests the uncertainty doesn’t propagate) and we only want to know the difference when varying a parameter (in this case co2). So putting the uncertainty of an uncalibrated model around the difference from 2 runs of a calibrated model doesn’t seem to be relevant. Perhaps that’s why he has the +/-15C around the 3C anomoly but can’t explain exactly what it means?

Kenneth Denison
Reply to  Brigitte
September 20, 2019 6:39 am

Brigitte, it is know there is a +/- 12.1% error in annual cloud fraction in the GCMs. Put another way, the models include a cloud fraction that could be 12.1% higher or lower than reality. The GCMs apply a cloud fraction at every iterative step, i.e. annually. So the resulting temperature after the first iteration is affected by this +/- 12.1% in CF with maps to a +/- 4 w m-2 in forcing. Then in year 2 the GCM applies a cloud fraction which again has the +/- 12.1% error which further affects the temperature output in year 2. And again in year 3, etc. In this way, that one imperfection in understanding of cloud fraction propagates into huge uncertainty in the output temperature.

Pat Frank
Reply to  Brigitte
September 21, 2019 2:24 pm

Exactly right, Kenneth, thanks. 🙂

Antero Ollila
September 19, 2019 7:44 am

Quote from the story: “We know the total tropospheric cloud feedback effect of the global 67% in cloud cover is about -25 W/m^2.” That is not cloud feedback, it is cloud forcing. They are two different concepts. Cloud forcing is the sum of two opposite effects of clouds on the radiation budget on the surface. Clouds reduce the incoming solar insolation in the energy budget (my research studies) from 287.2 W/m^2 in the clear sky to 240 W/m^2 in all-sky. At the same time, the GH effect increases from 128.1 W/m^2 to 155.6 W/m^2, and thus the change is +27.2 W/m^2. The net effect of clouds in all-sky conditions is cooling by -19.8 W/m^2. A quite big variety of cloud forcing numbers can be found in the scientific literature from -17.0 to -28.0 W/m^2.

Cloud feedback is a measure in which way cloud forcing varies when the climatic conditions change along the time and mainly in which way it varies according to varying global temperatures.

IPCC has written this way in AR4, 2007 (Ch. 8, p. 633): “Using feedback parameters from Figure 8.14, it can be estimated that in the presence of water vapour, lapse rate and surface albedo feedbacks, but in the absence of cloud feedbacks, current GCMs would predict a climate sensitivity (±1 standard deviation) of roughly 1.9°C ± 0.15°C (ignoring spread from radiative forcing differences).” My comment: this is TCS, which is a better measure of warming in the century-scale than ECS.

In AR5 the TCS value is still in the range from 1.8°C to 1.9°C. It means that according to IPCC cloud forcing has been the same since AR4 and there is no cloud feedback applied. It means that the IPCC does not know in which way cloud forcing would change as the temperature changes.

I think that Pat Frank is driving himself into deeper problems.

Pat Frank
Reply to  Antero Ollila
September 19, 2019 11:18 am

Antero, your post contradicts itself.

You wrote, “Quote from the story: “We know the total tropospheric cloud feedback effect of the global 67% in cloud cover is about -25 W/m^2.” That is not cloud feedback, it is cloud forcing.

Followed by, “Cloud feedback is a measure in which way cloud forcing varies when the climatic conditions change along the time and mainly in which way it varies according to varying global temperatures.

So, net cloud forcing is not a feedback, except that it’s a result of cloud feedback. Very clear, that.

I discussed net cloud forcing is the over all effect of cloud feedback; pretty much the way it’s discussed in the literature (<a href="https://doi.org/10.1175/1520-0442(1992)0052.0.CO;2“>Hartmann, et al., 1992, for example). Your explanation pretty much agrees with it, while your claim expresses disagreement.

It seems to me you’re manufacturing a false objection.

John M Brunette, Jr.
September 19, 2019 7:45 am

This has to be a media blitz about this. These alarmists are pouring it on thick right right now. The claim that the turning point has arrived is true in one regard. They should be shown as the frauds they are, and that is they who have run out of time with their shams.

This absolutely must become major news.

Frank from NoVA
September 19, 2019 7:55 am

Dr. Frank,

This is very helpful. Bottom line, I take this to mean that even if one conceded that GCM tuning eliminated errors over the interval where we supposedly have accurate GAST data, the limited resolving power of the models means that projections of temperature impacts solely related to incremental CO2 forcing are essentially meaningless. Thank you.

Pat Frank
Reply to  Frank from NoVA
September 19, 2019 9:51 pm

You’ve pretty much got it, Frank. Tuning the model just gets the known observables right. It doesn’t get the underlying physical description right.

That means there’s a large uncertainty even in the tuned simulation of the known observables, because getting them right tells us little or nothing about the physical processes that produced them.

It doesn’t solve the underlying problem of physical ignorance.

And then, when the simulation is projected into the future, there’s no telling how far away from correct the predictions are.

Ron Long
September 19, 2019 7:55 am

Pat F., I like your style! Accumulated errors are the bain of scientists in whatever sector they reside. Yes, I have had occasions where I predicted a great gold ore intercept and when the drill core was coming out, was forced to say “what the hell is this?”. What a complex topic the climate is in general, and then try to add anthropogenic forcing and feedback and it’s impossible.

Pat Frank
Reply to  Ron Long
September 19, 2019 9:53 pm

The uncertainty monster bites again! 🙂

Consequences for you, Ron, but not for climate modelers.

Javier
September 19, 2019 7:56 am

air temperature projections of advanced GCMs are just linear extrapolations of fractional greenhouse gas (GHG) forcing.

This is obvious to anybody that has given thought to how GCMs have been programmed. GHGs are the only “known” factor affecting climate that can be projected. GCMs take the different GHG concentration pathways (RCPs) and project a temperature change. Although very complex, GCMs produce a trivial result.

Current GCM air temperature projections have no physical meaning.

Yet they appear to be dominating the social and political discourse. In the Paris 2015 agreement most nations on Earth agreed to commit towards limiting global warming partly by reducing GHG emissions. The main evidence that GHGs are responsible for the warming are GCMs.

When most people believe [in] something, the fact that it is [not] real is small consolation to those that don’t believe. In this planet you can lose your head for refusing to believe [in] something that is not real. Literally.

Latitude
Reply to  Javier
September 19, 2019 9:14 am

…and the proof is

When you put this in….

..you get this out…

Editor
September 19, 2019 8:02 am

“We know from Lauer and Hamilton, 2013 that the annual average ±12.1% error in CMIP5 simulated cloud fraction (CF) produces an annual average ±4 W/m^2 error in long wave cloud forcing (LWCF).

We also know that the annual average increase in CO₂ forcing is about 0.035 W/m^2.

On an annual average basis, the uncertainty in CF feedback into LWCF is ±114 times larger than the perturbation to be resolved.

The CF response is so poorly known that even the first simulation step enters terra incognita.”

Exactly, the effect of man-made CO2 is so small, relative to the error in estimating low-level cloud cover, it can never be seen or estimated. I think everyone agrees with that. To me, Dr. Stokes and Dr. Spencer are clouding (pun fully intentional) the issue with abstruse, and mostly irrelevant arguments.

ren
September 19, 2019 8:18 am

How does cloudiness increase during the maximum height of galactic radiation during the minimum solar activity? How much ionization in the lower stratosphere and upper troposphere increases?
http://sol.spacenvironment.net/raps_ops/current_files/Cutoff.html
http://cosmicrays.oulu.fi/webform/monitor.gif

September 19, 2019 8:23 am

“We also know that the annual average increase in CO₂ forcing is about 0.035 W/m^2.”

The GCM operators have pulled this number from obscurity. This flux cannot be calculated from First Principles, so where did they get it? I assume it is based on the increase in CO2 since 1880, or some year, and the increase in Global Average Surface Temperature from 1880, or some year. These are hugely unscientific assumptions.

Antero Ollila
Reply to  Michael Moon
September 19, 2019 9:26 am

It is a good question, from which source Pat Frank has taken this CO2 forcing value 0.035 W/m^2. As we know very well, the IPCC hs used since TAR the CO2 forcing equation from Myhre et al. and it simply
RF = 5.35 * ln (CO2/280), where CO2 is the CO2 concentration in ppm.

This equation gives the climate sensitivity forcing of 3.7 W/m^2, which is one of the best-known figures among climate change scientists. Gavin Schmidt calls it “a canonic” figure meaning that its correctness is beyond any questions. The concentration of 400 ppm gives RF-values 1.91 W/m^2. According to the original IPCC science, the CO2 concentration has increased to this present number from the year 1750. It means a time span of 265 years till 2015 and an average annual increase of 0.0072 W/m^2. So, it is a very good question from which source comes this figure 0.035 W/m^2?

Antero Ollila
Reply to  Antero Ollila
September 19, 2019 9:32 am

I figured it out, maybe. If an annual CO2-increase is 2,6 ppm, then the annual RF-value for CO2 is 0.035 W/m^2. It cannot be called an average value but it is in the high end of the present CO2 annual growth variations. A long term annual CO2 growth rate has been something like 2.2 ppm.

Pat Frank
Reply to  Antero Ollila
September 19, 2019 11:23 am

It’s the average change in GHG forcing since 1979, Antero.

The source of that number is given in the abstract and on page 9 of the paper.

Reply to  Pat Frank
September 19, 2019 1:32 pm

But how was it calculated?

Reply to  Pat Frank
September 19, 2019 8:34 pm

So I read Page 9 of your paper. Language a bit thick, but it did mention temperature records, sounded like from 1900 or thereabouts, or was it 1750?

So, all the GCM’s ignore the concept of Natural Variation, ascribe all warming from some year to CO2 “Forcing?”

This is not science, this is Chicken Little, “The Sky is Falling!!!”

What if it starts to cool a bit? GCM’s pack it in and go home?

This is ludicrous, and I do not mean Tesla’s Ludicrous Speed…

Pat Frank
Reply to  Pat Frank
September 19, 2019 9:57 pm

Michael, it’s just the sum of all the annual increases in GHG forcing since 1979, divided by the number of years.

That gives the average annual increase in forcing since 1979.

Reply to  Pat Frank
September 20, 2019 1:38 pm

“Michael, it’s just the sum of all the annual increases in GHG forcing since 1979, divided by the number of years.

That gives the average annual increase in forcing since 1979.”

This tells us nothing. How is a GHG “forcing” measured? I suggest that it cannot be.

Reply to  Michael Moon
September 20, 2019 8:32 pm

It is fine to try to beat the GCM operators at their own game. Fun, a challenge, a debate.

Do none of you know anything about radiation?

“We also know the annual average increase in CO2 forcing is about O.O35 W/m2.”

We know no such thing! Bring this number back, show me that it is not, instead, 0.00 W/m2!

From where came this number? Not from First Principles. This is the crux of the matter, no one has established the physics of any CO2 forcing whatsoever, all from unscientific assumptions that All of the Warming from some year, 1750, 1880, 1979, was caused by CO2!!!

Freaking kidding me, billions and billions of dollars on fake science?

What are you people doing?????

Barbara
Reply to  Michael Moon
September 20, 2019 11:16 pm

I think there is first principle support for CO2 forcing (e.g.: http://climateknowledge.org/figures/Rood_Climate_Change_AOSS480_Documents/Ramanathan_Coakley_Radiative_Convection_RevGeophys_%201978.pdf).

I think there are huge problems with the modeling (but I’m not sure the physics behind the hypothesized CO2-forcing this is one of them):

The uncertainty issue (across a multitude of inputs, not just LWCF), the fact that temperature anomalies may be modeled by a relatively simple linear relation to GHG forcing (implicating a modeling bias that mutes the actual complex non-linear nature of the climate to ensure temperature goes up with CO2), the lack of fundamental understanding of the character of equilibrium states of the climate across glacial and inter-glacial periods, among a myriad of other issues, along with uncertainties associated with GHG-forcing estimates, but not the physics of GHG-forcing.

Reply to  Barbara
September 21, 2019 10:08 am

“The absorption coefficient (K) is independent of wavelength”??? It most certainly is not, and they do not derive it, just pull it from obscurity.

Please, someone, anyone, tell me where this number 0.035 W/m2 comes from. I suggest that there is no evidence showing that, instead, it is not O.000 W/m2.

Pat Frank
Reply to  Michael Moon
September 21, 2019 5:44 pm

Is it so hard to search the paper, Michael?

From the abstract: “This annual (+/-)4 Wm^2 simulation uncertainty is
(+/-)114 x larger than the annual average ~0.035 Wm^2 change in tropospheric
thermal energy flux produced by increasing GHG forcing since 1979.
.

Page 9: “the average annual ~0.035 Wm^-2 year^-1 increase in greenhouse gas forcing since 1979

The average since 1979. Is that really so hard?

I posted some more recent numbers here Michael.

It’s no mystery. It just takes checking the paper.

Reply to  Michael Moon
September 21, 2019 8:51 pm

Pat Frank,

Non-responsive. You are a physicist. Someone else must have written down this number and you have posted it here, not questioning its derivation.

Once again, I suggest that it could just as easily be O.OOO W/m2.

“The average since 1979. Is that really so hard?” Are you giving me a simple statement of fact? Facts according to whom, derived how?

This is the basis of your entire contention, but it comes from just an assumption that all the warming since 1979, or some other year, is due to CO2.

This is bizarre now, a simple question, prove to us that this number has been established from First Principles.

I want to shoot down the entire basis of CAGW from CO2. Seems like you do too. There is no obvious physical basis. Have you considered this, or are you just debating the GCM’s?

Wow…

Reply to  Michael Moon
September 21, 2019 9:05 pm

Alright, so I followed your link, from the EPA?

You are not a physicist at all. No physicist would just write down a number without being able to back it up, as I was taught in engineering school.

Back it up.

This is the entire basis of your paper, which, if true, could be a huge victory, help stop this gigantic fraud. If you cannot back it up, you got nothing, just debating statistics, another soft science.

Tim Gorman
Reply to  Michael Moon
September 21, 2019 9:38 pm

You understand that what the value actually is doesn’t really matter don’t you? Dr Frank took the value used in the climate models to develop his emulation and to show that the uncertainty overwhelms the ability of the models to predict anything. He wasn’t trying to validate the value, he was trying to calculate the uncertainty. When you are playing away from home then you use the home team’s ball so to speak.

Pat Frank
Reply to  Michael Moon
September 21, 2019 10:44 pm

It’s an empirical number, Michael. Do you understand what that means?

I didn’t “write it down.” It’s a per-year average of forcing increase, since 1979, taken from known values. Is that too hard for you to understand?

Other people here have had trouble understanding per-year averages. And now you, too. Maybe it’s contagious. I hope not.

Lance Flake
September 19, 2019 8:31 am

Using a mathematical model of a physical process is a valid endeavor when the model matches reality to the degree of accuracy required for practical uses. A model can be created with any combination of inductive and deductive reasoning, but any model can only be validated by comparing its predictions against careful observations of the physical world. A model’s inputs and outputs are data taken and compared to reality. A model’s mathematics follow processes that can be observed through physical experimentation.

A good example of such a model is used to explain the workings of a semiconductor transistor. Without such a proven-useful model all of our complex electronic devices would have been impossible to develop.

GCM’s fail the basic premises of modeling. There practically can never be a complete input data set due to their gridded nature. Their architecture includes processes that have not been observed in nature. Their outputs do not match observed reality. They have no practical use for explaining the climate or predicting how it will change. They are simply devices to give a sciency feel to political propaganda.

Explaining why they are failures is interesting to a point. But after decades of valiant attempts to explain their obvious shortcomings they still are in widespread use (and misuse). This fact only bolsters the argument that they are not for scientific uses but political tools.

bonbon
Reply to  Lance Flake
September 19, 2019 9:44 am

They are doing tremendous political damage – a class already skittish with any physics, will become anti-scientific. To a modern industrial civilization, that is Aztec poison.

KcTaz
Reply to  Lance Flake
September 19, 2019 12:35 pm

An Engineer‟s Critique of Global Warming „Science‟
Questioning the CAGW* theory
http://rps3.com/Files/AGW/EngrCritique.AGW-Science.v4.3.pdf

Using Computer Models
 to Predict Future Climate Changes
Engineers and Scientists know that you cannot merely extrapolate data that are scattered due to chaotic effects. So, scientists propose a theory, model it to predict and then turn the dials to match the model to the historic data. They then use the model to predict the future.
A big problem with the Scientist – he falls in love with the theory. If new data does not fit his prediction, he refuses to drop the theory, he just continues to tweak the dials. Instead, an Engineer looks for another theory, or refuses to predict – Hey, his decisions have consequences.
The lesson here is one that applies to risk management

Matthew Schilling
September 19, 2019 8:39 am

This article is a Tour de force. It is a single broadside that reduces the enemy’s pretty ship, bristling with guns and fluttering sails, to a gutted, burning, sinking hull. Hopefully we see people abandoning ship very soon.

Editor
Reply to  Matthew Schilling
September 19, 2019 8:47 am

Matthew, It shows how much money and time can be spent to replace something that can be done with a linear extrapolation or a ruler and graph paper. GCM’s are models built by a U.N. committee of scientists and they look exactly like that.

Reply to  Andy May
September 19, 2019 9:08 am

You cannot do this with a ruler and graph paper.

Editor
Reply to  Nick Stokes
September 19, 2019 9:51 am

Nick, We can all use computers to make pretty videos with R. The numbers used to frighten small children and lefty loonies are always the increase in average surface temperature and computing that only takes a ruler and graph paper, as Dr. Frank and others have shown. The rest is smoke and mirrors and billions of dollars down academic drains.

Latitude
Reply to  Nick Stokes
September 19, 2019 9:54 am

but you can do this….even when they are tuned/hindcast to the bumps and giggles
…they don’t reproduce them

comment image

Gatorq
Reply to  Nick Stokes
September 19, 2019 10:00 am

Sure you can! You establish the alleged (and disproven) linear relationship of CO2 and temperature with your ruler (or hand held calculator), and then you build a Rube Goldberg machine to entertain the dimwitted.

Voila!

Frank from NoVA
Reply to  Nick Stokes
September 19, 2019 10:01 am

Nick,

Fair enough, sir. Is there any particular reference year for this NOAA data set such that it could be compared to one of their POES visualizations? Thank you.

Reply to  Frank from NoVA
September 20, 2019 12:16 am

No. As stated, GCMs don’t do weather, at least not years in advanced. And that includes ENSO. They can do all the mechanics of ENSO, and they happen with about the right frequency. But they aren’t synchronised to Earth ENSO. We can’t predict ENSO on Earth, and there is no reason to expect that GCMs could.

Pat Frank
Reply to  Andy May
September 19, 2019 10:03 pm

What does this teach us about explosions, Nick?

Ocean models don’t converge.

Realistic vs. physically accurate: worlds apart.

September 19, 2019 8:47 am

There seems to be no consistency with units here. Previous versions of the paper have asserted the rather bizarre proposition that the LCWF rmse of 4 W/m2 given by Lauer really has the units ±4 Wm⁻² year⁻¹ model⁻¹, because it is being averaged over years and models. And that was an essential part of the theory; carrying the year⁻¹ meant that it could be compounded over years. If it was month⁻¹ it would be compounded over months, with a much different result. The treatment in the paper was very inconsistent, but the insistence on the unit was spelt out:

“On conversion of the above CMIP cloud root-mean-squared error (RMSE) as ±(cloud-cover unit) year⁻¹ model⁻¹ into a longwave cloud-forcing uncertainty statistic, the global LWCF calibration RMSE becomes ±Wm⁻² year⁻¹ model⁻¹ The CMIP5 models were reported to produce an annual average LWCF RMSE = ± 4 Wm⁻² year⁻¹ model⁻¹, relative to the observational cloud standard (Lauer and Hamilton, 2013).”
The unit is even claimed to come from the source, Lauer and Hamilton, which is not true; they said it was 4 Wm⁻².

But now it has all gone away again. ±4 W/m² everywhere, even in the heading.

Editor
Reply to  Nick Stokes
September 19, 2019 9:20 am

Nick, The post contains:

We know from Lauer and Hamilton, 2013 that the annual average ±12.1% error in CMIP5 simulated cloud fraction (CF) produces an annual average ±4 W/m^2 error in long wave cloud forcing (LWCF).

How is this unclear?

From Lauer and Hamilton, page 3833:

These give the standard deviation and linear correlation with satellite observations of the total spatial variability calculated from 20-yr annual means.

The errors are annual means over twenty-year datasets and expressed as percentages. I don’t see the problem.

Reply to  Andy May
September 19, 2019 9:51 am

“I don’t see the problem.”
Inconsistency with units is a very big problem in anything scientific. Just what are the units of this datum from Lauer and Hamilton? They seem to be whatever Pat wants them to be at any point in time. It isn’t just carelessness; he at times explains why they should be so, and then drops that. Mostly, despite what he says, he does just refer to ± 4 Wm⁻², as here.

It is important for the arithmetic, As he says in introducing Eq 6:
“The annual average CMIP5 LWCF calibration uncertainty, ± 4 Wm⁻² year⁻¹, has the appropriate dimension to condition a projected air temperature emulated in annual time-steps.”
The converse of that is that ± 4 Wm⁻² has the inappropriate dimension. But the key is year⁻¹. That permits, or is intended to permit, annual compounding. That is a big part of the arithmetic. I objected that If you compounded monthly you’d get a much bigger number. Pat said, no, then (paraphrasing) the ± 4 Wm⁻² year⁻¹ would be ± 4/12 Wm⁻² month⁻¹. You can only do that with the extra time umit (and even then because of adding in quadrature it doesn’t work).

Editor
Reply to  Nick Stokes
September 19, 2019 9:59 am

Lauer and Hamilton used annual averages, which makes sense. They tried seasonal averages (page 3839), but settled on annual. I agree units are important, I just don’t see any problem with what Frank did. Your argument is valid, just doesn’t apply here as far as I can see.

Reply to  Andy May
September 19, 2019 3:17 pm

It’s a very big problem. There is one datum point, and there seems to be no agreement on what its units are. And Pat claims he is the only one who knows about dimensional analysis. And that the units, whatever they are, are very important.

Pat Frank
Reply to  Andy May
September 19, 2019 10:14 pm

You overlooked the annual index “i” Nick.

No one else has done.

Andy May is right. Lauer and Hamilton used annual averages. They’re referenced throughout the paper. Where per year is not stated, it is directly implied.

You’re playing the same game here as you tried when claiming that rmse has only positive roots. You’re taking a convention and abusing its meaning.

Reply to  Andy May
September 20, 2019 12:14 am

“Where per year is not stated, it is directly implied.”
Why on earth, when you are beating the drum about how only physical scientists understand proper treatment of measurement, can’t you state units properly? No proper scientists “imply” units. They state them carefully and directly.

So what is implied, then. What are the actual units of this 4 Wm⁻²? If you put ±4 Wm⁻² year⁻¹ into eq 5.2, you get u as K/year, and goodness knows what that could mean.

tsk tsk
Reply to  Nick Stokes
September 19, 2019 4:54 pm

So much like the splicing of data from two completely different data sources? I seem to recall someone doing some sort of trick like that in a publication or two…

Barbara
Reply to  Nick Stokes
September 20, 2019 6:32 pm

This is a non-issue.

Average natural background radiation dose to humans in the U.S. is about 3.1 mSv/yr.

I can also say this: The annual average radiation dose to humans in the U.S. is 3.1 mSv.

Those statements are equivalent.

Pat Frank
Reply to  Nick Stokes
September 19, 2019 10:09 pm

I replied to that complaint under your DE post, Nick.

Look at eqns. 5.1 and 5.1. They are annual steps.

Subscript “i” is a yearly index.

Steve Richards
September 19, 2019 8:53 am

A well written piece Dr Frank.

It seems so difficult to argue against your logic, having codified what many engineers have thought and said over the years. But I suspect the usual candidates will have a go at you.

Be brave, the logic is nearly complete.

September 19, 2019 9:06 am

“That necessary linearity means that Nick Stokes’ entire huge variety of DEs would merely be a set of unnecessarily complex examples validating the linear emulation equation in my paper.”
What is the basis of “unnecessarily”? You are using your very simple model which produces near linear dependence of global average surface temperature, to replace a GCM, which is certainly very complex, and saying that the simple model can be taken to emulate the error propagation of the GCM, even though it has none of the physics of conservation of mass, momentum and energy which actually guides and limits the propagation of error.

As a scientific claim, you actually have the obligation to demonstrate that the error behaviour is the same, it you are going to analyse it in place of the GCM. Not just wave hands about how close emulation of a single variable is.

Forgotten as always in this is that GCMs are not just devices to predict global average surface temperature. They cover a huge number of variables, including atmospheric temperature at all levels. Matching just surface temperature over a period in no way establishes that the models are equivalent. This is obvious when Dr Spencer points out that this silly error growth claim would be limited by the requirements of TOA balance. Well, the Earth has such a balance, and so do the GCM’s, but there is nothing in Pat Frank’s toy model about it.

The point of my proof that you can match a prescribed solution to any kind of error behaviour just reinforces the point that you have in no way established the requirements for analysing the toy in place of the real.

Editor
Reply to  Nick Stokes
September 19, 2019 9:39 am

Nice try Nick. But, the point is that the toy does just as good a job estimating global mean surface temperature as the GCM’s. The fact the the GCM’s attempt (and fail) to produce a matrix of temperatures throughout the Troposphere is irrelevant, all anyone talks about is surface temperature, which is sad I agree. Besides, John Christy has shown that the models are inept at estimating the vertical temperature gradient.

Creating yet another red herring does not hide the problems with model validation, or lack thereof.

Reply to  Andy May
September 19, 2019 9:55 am

“But, the point is that the toy does just as good a job estimate global mean surface temperature as the GCM’s. “
So would a curve fit, as the toy effectively is. But it tells you nothing about error propagation in the GCM.

And you can’t isolate single variables – in the GCM they all interact. There are all sorts of effects in the GCM which would ensure that the temperature can’t just rise 18°C, as Pat’s toy model (with no physics) can. Dr Spencer’s TOA balance is just one.

Gator
Reply to  Nick Stokes
September 19, 2019 10:03 am

And you can’t isolate single variables – in the GCM they all interact.

Which is why all GCM’s are pure fantasy, and why they are not proof of anything, except bias.

Editor
Reply to  Nick Stokes
September 19, 2019 10:11 am

Nick,
I agree with you (and Spencer) to a point. Dr. Frank’s work does not invalidate the GCM’s, nor does it explain the propagated errors in the models. The climate data we have does that quite well.
What his work does show, is that what the models were designed to do, compute man’s influence on climate, cannot be accomplished with them, because they cannot resolve the low-level cloud cover accurately enough. The error due to changing cloud cover swamps what they are trying to measure and is unknown. This has been known for a long time. Spencer, Lindzen, and others have written about it before. I think that Frank’s work compliments the others and is very helpful.
I realize you (and perhaps Spencer as well) are trying to throw irrelevant stuff to mask his main conclusion, similar to others efforts to trivialize the work Spencer and Christy did with satellite temperature measurements or the work that Lindzen did on tropical cloud cover ECS estimates, but it won’t work. The underlying problem with the climate models is they are not accurate enough to estimate man’s contribution to climate change, and they may never be.

Tommy
Reply to  Nick Stokes
September 19, 2019 11:49 am

“And you can’t isolate single variables – in the GCM they all interact. There are all sorts of effects in the GCM which would ensure that the temperature can’t just rise 18°C, as Pat’s toy model (with no physics) can. Dr Spencer’s TOA balance is just one”

Are you saying that if you don’t understand how one variable works, you should add many many more variables that you also don’t understand and…Magic ?

It sounds to me like you’re admitting the GCMs have an a priori conclusion (reasonable looking predictions that show an impact of co2 forcing). Of course you can curve fit enough variables to grt what you want. Does it model the real world, though?

Matthew R Marler
Reply to  Nick Stokes
September 19, 2019 2:05 pm

Nick Stokes: And you can’t isolate single variables – in the GCM they all interact. There are all sorts of effects in the GCM which would ensure that the temperature can’t just rise 18°C, as Pat’s toy model (with no physics) can. Dr Spencer’s TOA balance is just one.

Actually, Pat Frank’s analysis shows that you can isolate a single variable. Your point about there being many variables whose uncertainties ought to be estimated concurrently implies that Pat Frank has achieved an approximate lower bound on the estimation uncertainty.

The sum and substance of your commentaries is just that: the actual model uncertainty resulting from uncertainties in the parameter values, is greater than his estimate.

Reply to  Matthew R Marler
September 19, 2019 8:24 pm

“Actually, Pat Frank’s analysis shows that you can isolate a single variable.”
Well, it shows that he did it. But not that it makes any sense. Dr Spencer’s point was, in a way, that there is a Le Chatelier principle at work. If something changes, something else varies to counter the change. The reason is the overall effect of the conservation principles at work. Roy cited TOA balance as one.

But Pat Frank’s toy does not have any other variables that could change, or any conservation principles that would require them to.

Tim Gorman
Reply to  Nick Stokes
September 19, 2019 8:53 pm

Nick,

“If something changes, something else varies to counter the change. The reason is the overall effect of the conservation principles at work. Roy cited TOA balance as one.

But Pat Frank’s toy does not have any other variables that could change, or any conservation principles that would require them to.”

Why would Pat Frank’s emulation *need* any other variables if his output matches the output of the models? This just sounds like jealousy rearing its ugly head.

Conservation principles do not cancel out uncertainty. Trying to say that it does is really nothing more than an excuse being used to justify a position.

Pat Frank
Reply to  Matthew R Marler
September 19, 2019 10:35 pm

Roy Spencer’s analysis confuses a calibration error statistic with an energy flux.

His argument has no critical impact, or import for that matter.

Your comment, Nick, shows you don’t understand that really obvious distinction, either.

Either that, or you’re just opportunistically exploiting Roy’s mistake for polemical advantage.

Matthew Schilling
Reply to  Matthew R Marler
September 20, 2019 7:55 am

A question for Pat Frank: Would it be incorrect to think of an uncertainty value as a type of metadata, attached to and describing the result? The result addresses the question posed, while the uncertainty value speaks to the (quality of the) result.

Clyde Spencer
Reply to  Matthew R Marler
September 20, 2019 11:11 am

Matthew Schilling
Since Pat hasn’t responded, I’ll presume to weigh in. I think that metadata is an apt description for uncertainty.

Pat Frank
Reply to  Andy May
September 19, 2019 10:24 pm

Nick, “There are all sorts of effects in the GCM which would ensure that the temperature can’t just rise 18°C, as Pat’s toy model (with no physics) can. (my bold)”

Here we go again. Now even Nick Stokes thinks that an uncertainty in temperature is a physical temperature.

That’s right up there with thinking a calibration statistic is an energy flux.

You qualify to be a climate modeler, Nick. Your level of incompetence has raised you up into that select group

nick
Reply to  Pat Frank
September 20, 2019 8:27 am

Pat, for what it’s worth, but I as a physicist am shocked by the sheer incompetence that seems to be present in the climate community. The method you are using is absolutely standard, every physics undergraduate is supposed to understand it – and usually does without any effort. The mistaken beliefs about error propagation that the climate guys show in all their comments are downright ridiculous. Kudos to you for your patience explaining again and again the difference between error and uncertainty. Really hard concepts to grasp for certain people.
(I’m usually much more modest when commenting, but when people trumpet BS with such a conviction, then I can’t hold myself back)

Barbara Hamrick
Reply to  nick
September 20, 2019 5:41 pm

+1

Pat Frank
Reply to  nick
September 28, 2019 7:35 pm

Thank-you so much for the breath of fresh air, nick.

It means a huge lot to me to get support in public from a bona fide physicist.

As you can imagine, climate modelers are up in arms.

Even climate scientists skeptical of AGW are going far afield. You may have seen Roy Spencer’s critique, equating an uncertainty statistic with an energy flux, here and here, as well as on his own site..

Others have equated an uncertainty in temperature with a physical temperature.

If you wouldn’t mind, it would be of huge help if you might support my analysis elsewhere to others as the occasion permits.

Thanks again for stepping out. 🙂

Frank from NoVA
Reply to  Nick Stokes
September 19, 2019 10:22 am

Nick,

Is TOA balance a constraint on the GCMs? Wouldn’t there be any number of non-unique solutions to the models if it wasn’t?

Reply to  Frank from NoVA
September 19, 2019 3:14 pm

Sorry, a few too many negatives there for me to process. But yes, it is an important constraint.

Frank from NoVA
Reply to  Nick Stokes
September 19, 2019 4:58 pm

Thank you Nick. It sounded like a constraint to me. For this reason, I was puzzled by Dr. Spencer’s initial objection to Dr. Frank’s paper on the basis that GCMs achieve TOA balance. PS – Given your modeling expertise with DEs, did you ever do any work in quantitative finance?

Reply to  Frank from NoVA
September 20, 2019 12:06 am

Frank,
Oddly yes. I wrote a program Fastflo, an FEM PDE solver, intended for Fluid mechanics. We adapted it for modelling options pricing, and it became the basis of a plug-in for GFI FENICS. You can read about it here.

Beta Blocker
Reply to  Nick Stokes
September 19, 2019 10:55 am

Soden and Held’s postulated water vapor feedback mechanism is central to the theory that additional warming at the earth’s surface caused by adding CO2 to the atmosphere can be amplified, over time, from the +1 to +1.5C direct effect of CO2 into as much as +6C of total warming. (Citing Steven Mosher’s opinion that +6C is credible as an upper bound for feedback driven amplified warming.)

However, it is impossible at the current state of science to directly observe this postulated mechanism operating in real time inside of the earth’s climate system. The mechanism’s presence must be inferred from other kinds of observations. One important source of the ‘observations’ used to characterize and quantify the Soden-Held feedback mechanism is the output generated from the IPCC’s climate models, a.k.a. the GCM’s.

See this comment from Nick Stokes above:

https://wattsupwiththat.com/2019/09/19/emulation-4-w-m-long-wave-cloud-forcing-error-and-meaning/#comment-2799230

In the above comment, Nick Stokes says, “The point of my proof that you can match a prescribed solution to any kind of error behaviour just reinforces the point that you have in no way established the requirements for analysing the toy in place of the real.”

In his comment, Nick Stokes labels Pat Frank’s GCM output emulation equation as ‘the toy’ and the GCM’s the equation emulates as ‘the real.’

Referring to Soden and Held’s use of output from the GCM’s as observational data which supports their theory, it is perfectly appropriate to extend Nick Stoke’s line of argument by labeling the GCM’s as ‘the toys’ and the earth’s climate system itself as ‘the real.’

With this as background, I make this request of Nick Stokes and Roy Spencer:

Please post a list of requirements for producing and analyzing the outputs of GCM’s being used as substitutes for observations made directly within the earth’s real climate system. In addition, please include a glossary of scientific and technical terms which defines and clarifies the exact meaning and application of those terms, as these are being employed in your list of requirements.

Thanks in advance.

HAS
Reply to  Beta Blocker
September 19, 2019 1:52 pm

Right at the beginning of this debate I reminded the protagonists, particularly Nick, to be rigorous about the various constructs they were discussing. As you say there is the real world, the current set of GCMs, the linear emulator of that set of models. Add to that is some future set(s) of potentially improved GCMs and their potential emulators.

The questions being discussed relate to the way each perform on temp projection in and out of sample, and conclusions can only be drawn within the limitations of that framework.

I’ve decided in the end that rigour is to be avoided in favour of the rhetoric that that lack of it allows.

Reply to  Beta Blocker
September 19, 2019 3:12 pm

“Please post a list of requirements for producing and analyzing the outputs of GCM’s being used as substitutes for observations made directly within the earth’s real climate system. “
They aren’t a substitute for observing future states. We just don’t know how to do that yet.

But in fact they are used to enhance observation of the present. This is the reanalysis of data from numerical weather forecasting, which is really just re-running the processes of the forecasts themselves. It does build on the knowledge of the earth that we acquire from observation. And it is using programs from the GCM family.

Beta Blocker
Reply to  Nick Stokes
September 19, 2019 8:19 pm

Within the context of your ongoing debate with Pat Frank, your response indicates you have no intention of addressing what is a perfectly reasonable request.

Clyde Spencer
Reply to  Nick Stokes
September 19, 2019 11:17 am

Stokes,
You said, “They cover a huge number of variables, including atmospheric temperature at all levels.” And they also cover precipitation. They are notorious for doing a poor job of predicting precipitation at the regional level, with different models getting opposite results. This is further evidence that the models are unfit for purpose. So, what if they include “atmospheric temperature at all levels?” They may be “reasonable’ in the sense that they are physically possible, but are they “reliable?”

Jim Gorman
Reply to  Nick Stokes
September 19, 2019 12:21 pm

Nick Stokes –> You’re missing the trees for the forest. If I drove 100 miles and used 10 gallons of gas I could calculate my average miles/gallon a couple of ways. I could assume a simple (KISS) linear model and simply divide 100 by 10. Or, I could go off and develop all kinds of equations that simulate aerodynamics, tire friction, ICE performance (as you mentioned), etc., and end up writing Global Mile per Gallon Model (GMGM). Which one do you think would give me the better answer with the least uncertainty?

Matthew R Marler
Reply to  Nick Stokes
September 19, 2019 5:04 pm

Nick Stokes: You are using your very simple model which produces near linear dependence of global average surface temperature,

Pat Frank does not have a simple model of global average surface temperatures, he has a simple model of GCM-forecast global average surface temperatures. He also does not have a model of any other GCM forecast, only global mean temperature. He does not claim to show that GCM forecasts are unreliable in all things, such as global annual rainfall, only that they are unreliable on their most cited forecasts, global mean temperature. If they are truly reliable for their other forecasts, that will be remarkable. He has provided a template for how the unreliability of other forecasts might be estimated: start by regressing rainfall forecasts against forcing inputs, and go from there; if it’s another monotonic function with a tight fit, we’re golden.

In the mean time, know that the GCM forecasts of mean global temp are unreliable.

Pat Frank
Reply to  Matthew R Marler
September 19, 2019 10:28 pm

A very salient comment, indeed, Matthew.

You’ve exactly got what I did. It’s a real puzzle to me how something that straight-forward is such a mystery to so many.

Thanks. 🙂

Kenneth Denison
Reply to  Matthew R Marler
September 20, 2019 6:41 am

+1

Matthew Schilling
Reply to  Matthew R Marler
September 20, 2019 8:35 am

+1

Pat Frank
Reply to  Nick Stokes
September 19, 2019 10:19 pm

Irrelevant, Nick. My analysis is about air temperature projections, and nothing else.

GCMs are just linear extrapolation machines. The uncertainty analysis follows directly from that.

The emulation equation shows the same sensitivity to GHG forcing as any GCM. Embarrassing, isn’t it.

All the rest of your caviling about the internal complexity of GCMs is just so much raising of the dust. Their output is simple. And that’s the rub.

Kenneth Denison
Reply to  Pat Frank
September 20, 2019 6:45 am

“The emulation equation shows the same sensitivity to GHG forcing as any GCM.”

This is a very important point and one that I would expect GCM modelers to want to dig into. This result certainly opens the possibility that the GCMs are all subject to significant modeler’s bias that should be analyzed and run to ground.

It is almost unbelievable that these complex models would yield a linear relationship between GHG forcing and temperature. Clearly the climate does not behave that way, indicating that the GCMs are not representing reality.

That so many cannot see this point is astounding to me.

Great job Dr. Frank

Clyde Spencer
Reply to  Kenneth Denison
September 20, 2019 11:16 am

Kenneth Denison
+1

I would not expect the output to be linear. I have programmed System Dynamics models with linear inputs, and the outputs were invariably non-linear.

Barbara
Reply to  Kenneth Denison
September 20, 2019 7:04 pm

+1 Kenneth

bonbon
September 19, 2019 9:11 am

When CERN ran the CLOUD test with their particle beam and aerosols, the actually modelled the formation of Cloud Condensation Nuclei and got it wrong! Svensmark pointed that out in early 2018.
Since the GCM’s cannot handle hurricanes, with the joker card they lack resolution, they have no hope of handling Forbush decreases and CME’s.
So the reason in this case is not resolution, just lack of physics.

It is very refreshing to see resolution, uncertainty, error all clearly expressed.

Just a side note – Boeing engineering was forced to change the engines because of CO2, and used (outsourced) software to compensate, which failed. Someone decided physics and engineering could be sidelined. I just wonder if that software was ever run through such an uncertainty and error analysis?

J Mac
September 19, 2019 9:13 am

Dr. Franks,
An excellent ‘plain english’ explanation of your published paper and a succinct rebuttal of Nick Stokes differential equations dissembling. You logically constrained Stokes to a black box ‘time out’.
Thank You!

mkelly
September 19, 2019 9:28 am

There is no sensitivity to CO2. If there was then the specific heat table would say you must include forcing equation doing air or CO2 and infrared is involved. But it doesn’t.

MDBill
September 19, 2019 9:32 am

Thank you, Dr. Frank. Your analyses are logical, and further our understanding of the credibility of “Models”, which have become the underpinnings of planned political movements. If we can only get the policy makers, the general public, and especially the youth to understand that the huge investments being contemplated are merely building castles in the sand. I’ve seen too many of these half-baked good intentions in my lifetime. (“The Great Society”, Vietnam, Iraq, etc.) Again, thank you for the breath of fresh air you are providing!

Pat Frank
Reply to  MDBill
September 19, 2019 10:31 pm

Happy it worked out, MDBill.

One really beneficial outcome is to remove the despair that is being pounded into young people.

There’s every reason to think the future will be better, not doom-laden. That word should get out.

slow to follow
Reply to  Pat Frank
September 20, 2019 1:32 am

+10000000

The destructive impact of poor science promoted as certain fact is something which poses a bigger threat than inevitable and manageable changes in our environment.

slow to follow
Reply to  Pat Frank
September 20, 2019 5:06 am

Not sure if this live feed is visible from outside the UK, but if so it shows the level of conviction with which views based on GCM output are held:

Millions of people are joining a global climate strike

https://www.bbc.co.uk/news/live/world-49753710

Roy
September 19, 2019 9:35 am

Simulations start out wrong and get worse.

Is that the best one line summary of climate models ever written?

September 19, 2019 9:48 am

And I Nick Stokes’ Tavern did frequent
But came out not one whit
Wiser, than where in I went…

Reply to  Leo Smith
September 19, 2019 9:56 am

That’s the problem with random walk.

Matthew R Marler
Reply to  Nick Stokes
September 19, 2019 2:10 pm

Nick Stokes: That’s the problem with random walk.

Pat Frank’s procedure is not a random walk.

Tim Gorman
Reply to  Matthew R Marler
September 19, 2019 7:15 pm

I think Nick still believes that uncertainty is the same as a random error and since random errors tend toward the central limit theory that uncertainty does the same. Uncertainty, however, is not random!

Matthew R Marler
Reply to  Nick Stokes
September 19, 2019 7:23 pm

Nick Stokes: That’s the problem with random walk.

You have not, as far as I have read, explained why you think Pat Frank’s procedure is a random walk. Perhaps because the uncertainty is represented as the standard deviation of a probability distribution you think the parameter has a different randomly sampled value each year. That would produce a random walk. That is not what he did.

Reply to  Matthew R Marler
September 19, 2019 8:13 pm

“explained why you think Pat Frank’s procedure is a random walk”
Well, here is what he says on p 10:
“The final change in projected air temperature is just a linear sum of the linear projections of intermediate temperature changes. Following from equation 4, the uncertainty “u” in a sum is just the root-sum-square of the uncertainties in the variables summed together, i.e., for c = a + b + d + … + z, then the uncertainty in c is ±u_c =√(u²_a+u²_b+…+u²_z) (Bevington and Robinson, 2003). The linearity that completely describes air temperature projections justifies the linear propagation of error. Thus, the uncertainty in a final projected air temperature is the root-sum-square of the uncertainties in the summed intermediate air temperatures.”

Or look at Eq 6. The final uncertainty is the sqrt sum of variances (which are all the same). The expected value of the sum. How is that not a random walk?

And note that despite the generality of Eq 3 and 4, he is assuming independence here, though doesn’t say so. No correlation matrix is used.

Pat Frank
Reply to  Nick Stokes
September 19, 2019 10:37 pm

It’s not a random walk because it’s not about error, Nick.

It’s about uncertainty.

Matthew R Marler
Reply to  Nick Stokes
September 20, 2019 1:04 am

Nick Stokes: And note that despite the generality of Eq 3 and 4, he is assuming independence here, though doesn’t say so. No correlation matrix is used.

That part was explained already: the correlation is used in computing the covariance.

Reply to  Nick Stokes
September 20, 2019 1:06 am

“Uncertainty, however, is not random!”
“It’s about uncertainty.”

Uncertainty has a variance (Eq 3). And its variance compounds by addition through n steps (eq 4). That is exactly how a random walk works. Just below Eq 4:

“Thus, the uncertainty in a final projected air temperature is the root-sum-square of the uncertainties in the summed intermediate air temperatures.”

That is exactly a random walk.

Tim Gorman
Reply to  Nick Stokes
September 20, 2019 5:06 am

Nick,

“Thus, the uncertainty in a final projected air temperature is the root-sum-square of the uncertainties in the summed intermediate air temperatures.”

That is exactly a random walk.”

No, it is not a random walk. The uncertainties are no random in nature, therefore their sum cannot be a random walk.

Reply to  Nick Stokes
September 20, 2019 2:38 am

“the correlation is used in computing the covariance.”
Where? Where did the data come from? What numbers were used?

As far as I can see, the arithmetic of Eqs 5 and 6 is fully spelt out, with a hazy fog of units. The numbers are given. None relates to correlation. No term for correlation or covariance appears.

Clyde Spencer
September 19, 2019 10:30 am

“In the paper, GCMs are treated as a black box.”
As they should be because programs of that size are not easily examined and understood by those who are not paid to do so, and can expend the necessary time to step through the Fortran code. There is an old saying that “All non-trivial computer programs have bugs.” Parallel processing programs of the size of GCMs, rife with numerically-approximated partial differential equations, certainly qualify as being “non-trivial.”

Reply to  Clyde Spencer
September 19, 2019 10:37 am

“As they should be because programs of that size are not easily examined and understood”
So you write a paper about how you don’t understand GCM’s, so you’ll analyse something else?

Clyde Spencer
September 19, 2019 10:32 am

Pat,
I like the imagery of your “extraneous differential gargoyles.”

Pat Frank
Reply to  Clyde Spencer
September 19, 2019 10:38 pm

I had William of Ockham in mind when I wrote that, Clyde. 🙂

Gary Pearse
September 19, 2019 10:43 am

Pat, your work and the responses in critical articles and thoughtful comments here has been the best example of science at work at WUWT in a long time. Today’s response from you has clarified a complex issue. Many thanks. You have also inspired an (old) idea and a way forward in development of a more robust theory in your comments below:

“Does cloud cover increase with CO₂ forcing? Does it decrease? Do cloud types change? Do they remain the same?

What happens to tropical thunderstorms? Do they become more intense, less intense, or what? Does precipitation increase, or decrease?”

I think the answer to these questions is calling out loud and clear. Our fixation on satellite and computer tech has blinded us to the importance of old fashioned detailed fieldwork for getting at I am a geologist who has sweated out mapping geology on foot, canoe, Landrover, helicopter etc. on geological survey and mining exploration work in Canada, Africa, US and Europe.

We know the delta CO2 well enough. We need to make millions of observations in the field along with help from our tech and record local (high resolution) changes in temperatures, pressures, humidity, wind speeds and direrctions, details on development and physiology of thunderstorms. A new generation of buoys that can see the sky and record all this would also be useful.

Doubting that such a task could be accomplished? Here is a Geological Map of Canada that is a compilation of millions of observations, records and interpretations (a modest number of pixels of this is my work, plus ~ 35, 000km^2 of Nigeria, etc.)

https://geoscan.nrcan.gc.ca/starweb/geoscan/servlet.starweb?path=geoscan/fulle.web&search1=R=208175

Scroll down a page, tap the thumbnail image and expand with your fingers.

Pat Frank
Reply to  Gary Pearse
September 19, 2019 10:47 pm

Your comment, Gary, that, “I think the answer to these questions is calling out loud and clear. Our fixation on satellite and computer tech has blinded us to the importance of old fashioned detailed fieldwork for getting at I am a geologist who has sweated out mapping geology on foot, canoe, Landrover, helicopter etc. on geological survey and mining exploration work in Canada, Africa, US and Europe.” …

expresses something I’ve also thought for a long time.

Climate modeling has abandoned the reductionist approach to science. They try to leap to a general theory, without having done all the gritty detail work of finding out how all the parts work.

Their enterprise is doomed to failure, exactly for that reason.

It won’t matter how well they parse their differential equations, how finely they grid their models, or how many and powerful are their parallel processors. They have skipped all the hard-scrabble work of finding out how the parts of the climate system operate and how they couple.

Each bit of that is the work of a lifetime and brings little glory. It certainly disallows grand schemes and pronouncements. Perhaps that explains their avoidance.

Kenneth Denison
Reply to  Pat Frank
September 20, 2019 6:48 am

+100

Jim Gorman
Reply to  Pat Frank
September 20, 2019 7:53 am

Oh God, you have hit the nail on the head for all of post-modern science. It’s all about me and how much fame and fortune I can gather. Doing gritty work, that’s for peons, not for educated scientists.

+100

Matthew Schilling
Reply to  Pat Frank
September 20, 2019 8:39 am

Mic drop!

David Longinotti
September 19, 2019 10:45 am

I attempt a first-order analogy of the earth’s temperature with the water-level of a hypothetical lake. This causes me to question both the GCMs and Dr. Frank’s method of estimating their error bounds:

Suppose it is observed that the water level of some lake varies up and down slightly from year to year, but over numerous years has a long-term trend of rising. We want to determine the cause. Assume there are both natural and human contributors to the water entering the lake. The natural “forcing” of the lake’s level consists of streams that carry rainwater to the lake, and the human forcing is from nearby houses that empty some of their waste-water into the lake. Some claim that it is the waste-water from the houses that is causing most of the long-term rise in the lake. This hypothesis is based on a model that is thought to accurately estimate the increasing amount of water contributed yearly by the houses, as more developments are built in the vicinity. However, the measurement of the other contributor, the water that flows naturally into the lake, is not very good; the uncertainty in that water flow is 100 times greater than the modeled amount of water from the houses. Presumably, in such a case, one could not conclude with any confidence that it is the human ‘forcing’ that is causing the bulk of the rise in the lake.

Similarly, given the uncertainty in the contribution of natural forcings like clouds on earth’s temperature, the GCMs give us little or no confidence that the source of the warming is mainly human CO2 forcing.

We could remove the effects of clouds in the GCMs if we knew that their influence on world temperature was constant from one year to the next, just as in the analogy we could remove the effects of natural sources of water on the level of the lake if we knew that the streams contribute the same amount each year. But, presumably, we don’t have good knowledge of the variability of cloud forcings from one year to the next, and I think this is the problem with Dr. Frank’s error calculation. To calculate the error in the GCM predictions, what is needed is the error in the variability of the cloud effects from one year to the next, not the error in their absolute measurement. Perhaps this is what Dr. Spencer was getting at in his critique of Dr. Frank’s method. To analogize once gain, if my height can only be measured to the nearest meter as I grow, there is an uncertainty of one meter in my actual, absolute height at the time of measurement. But this provides no reasonable basis for treating the error in my predicted height as cumulatively increasing by many meters as years go by.

Reply to  David Longinotti
September 19, 2019 1:03 pm

Good God, David L,

That analogy so clouds my understanding.

I have never understood the approach of creating a mind-boggling analogy to help clarify an already mind-boggling argument. It’s as if you substitute one complexity for another and ask us to dissect the flaws or attributes of an entirely separate thing, in addition to trying to understand what is already hard enough to understand.

GENERAL REQUEST: Stop with the convoluted analogies that only confuse the issue more.

Antero Ollila
September 19, 2019 11:08 am

I figured it out, maybe. If an annual CO2-increase is 2,6 ppm, then the annual RF-value for CO2 is 0.035 W/m^2. It cannot be called an average value but it is in the high end of the present CO2 annual growth variations. A long term annual CO2 growth rate has been something like 2.2 ppm.

Pat Frank
Reply to  Antero Ollila
September 21, 2019 2:20 pm

Why is it such a big mystery, Antero? I described the method as the average since 1979.

The forcings I used were 1979-2013, calculated using the equations of Myhre, 1998:

In 1979, excess CO2 forcing was 0.653 W/m^2; CO2 + N2O + CH4 forcing was 1.133 W/m^2.

In 2013 they were 1.60 and 2.44 W/m^2.

CO2 = (1.60-0.653)/34 = 0.028 W/m^2.

Major GHG = (2.44 – 1.13)/34 = 0.038 W/m^2

The numbers to 2015 at the EPA page, give 0.025 W/m^2 and 0.030 W/m^2 respectively.

Robert Stewart
September 19, 2019 11:15 am

It’s not coincidental that much of the most persuasive criticism of the climate scam has come from professionals who deal in engineering and economic analyses such as McIntyre and McKitrick. Or from scientists like Dr. Frank who seek to use experimental data to prove or disprove theoretical calculations. There’s nothing like reality, whether measured in dollars or in the failure of devices, to focus one’s mind. Consider the manufacture of any large structure, say an airplane or a ship Mass production methods require that the components of the final product be assembled in an efficient process. The tolerances of each part must be sufficiently tight that when a large number of them are put together, the resultant subassembly can still satisfy similarly tight tolerances, so that the final assembly stays within tolerance. Boeing’s attempt to farm out subassemblies of the 787 was only partially successful because manufacturing practices in some countries simply weren’t at the level needed. This traces back to WWII and aircraft production facilities like that at Willow Run where Ford produced B-24s at a rate of about one aircraft per hour. B-24s were assembled at Willow Run using about 20,000 manhours, whereas the previous methods used by Consolidated in San Diego took about 200,000 manhours. Much of those 200,000 hours were spent by craftsmen working to get all the disparate, relatively low-tolerance pieces to fit together. Construction of huge tankers and bulk carriers face the same problem as very large subassemblies are brought together. Failure to control the tolerances of the parts and pieces means that the final assembly cannot be completed without costly reworking the parts. So reality lends a hand in focusing the engineering effort. Ten percent uncertaintiess in the widths of pieces that were to be assembled into the engine room of a tanker would be highly visible and painfully obvious, even to a climate modeler.

Stevek
September 19, 2019 11:18 am

Dr Frank,

If we have some idea of the probability distribution of the cloud forcing uncertainty, can get a probability distribution for the temperature at the end of 100 years that model gives ? Can another formula instead of the square root of sum of errors squared be used if we know more about the e distribution at each step ?

Pat Frank
Reply to  Stevek
September 19, 2019 10:55 pm

Stevek, how does one know the error probability distribution of a simulation of a future state? There are no observables.

Stevek
Reply to  Pat Frank
September 20, 2019 1:56 pm

Thank you ! That makes sense to me now and clears up my thinking. The uncertainty itself at end of 100 years must have a distribution that can be calculated if we know the distribution of all variables that go into the initial state ? You are not saying all points within the ignorance are equally likely?

Pat Frank
Reply to  Stevek
September 21, 2019 1:45 pm

Stevek, I’m saying that no one knows where the point should be within the uncertainty envelope.

To be completely clear: suppose the uncertainty bound is (+/-)20 C. Suppose, also, that the physical bounds of the system requires that the solution be somewhere within (+/-)5 C.

Then the huge uncertainty means that the model cannot say where the correct value should be, within that (+/-)5 C.

The uncertainty is larger than the physical bounds. This means the prediction, whatever value it takes, has no physical meaning.

TEWS_Pilot
September 19, 2019 11:28 am

“I want you to unite behind the science. And then I want you to take real action.”

Swedish climate activist Greta Thunberg appeared before Congress to urge lawmakers to “listen to the scientists” and embrace global efforts to reduce carbon emissions. https://twitter.com/ABC/status/1174417222892232705

Dr. Frank, have you received your invitation to present actual Science to the Commi….huh?….no “contrary views allowed”….”only CONSENSUS ‘Science’ is acceptable?”…..oh, well, sorry to have bothered you.

Pat Frank
Reply to  TEWS_Pilot
September 19, 2019 10:56 pm

No invitations, TEWS. You’re right. 🙂

September 19, 2019 11:59 am

I quote from chapter 20: Basic equations of general circulation models from “Atmospheric Circulation Dynamics and General Circulation Models” by Masaki Satoh”

One of the most uncertain factors in the reliability of currently used general circulation models is the use of cumulus parameterization. Since the horizontal extent of cumulus convection is about 1 km, the effects of cumulus convection must be statistically treated in general circulation models with horizontal resolutions of about 100 km. However, it is very difficult to appropriately parameterize all the statistical effects of cumulus convection, though many kinds of cumulus parameterizations are being used in current models. As the horizontal resolution of numerical models approaches 1 km, individual clouds can be directly resolved in the models, so that it is expected that we will no longer need to use such cumulus parameterization based on statistical hypothesis. Thus, the likely horizontal resolution of next generation general circulation models is a few kilometers. We expect the use of models with 10-km resolution or less will come within the range of our computer facilities. With such finer resolution models, the assumption of hydrostatic balance is no longer acceptable. We must switch governing equation of the general circulation models from hydrostatic primitive equations to non-hydrostatic equations. As for vertical resolution, we do not have a suitable measure of its appropriateness.

And Dr. Frank makes the following comment:
>>
The CMIP5 GCM annual average 12.1% error in simulated CF is the resolution lower limit. This lower limit is 121 times larger than the 0.1% resolution limit needed to model the cloud feedback due to the annual 0.035 W/m^2 of CO₂ forcing.
<<

So let’s talk about the grid resolutions of CMIP5 GCMs. Here is a link to a list of resolutions: https://portal.enes.org/data/enes-model-data/cmip5/resolution.

The finest resolution is down to about 0.1875 degrees (which is probably questionable). Most of the resolutions are around 1 degree or more. A degree on a great circle is 60 nautical miles. That is more than 111 km. Even the 0.1875 degree resolution is more than 20 km. Obviously they are using parameterization to deal with cumulus convection. In other words, cumulus convection is one of the more important physics of the atmosphere, and they are making it up.

Jim

Clyde Spencer
September 19, 2019 11:59 am

Pat,

Stokes has previously stated, “… yes, DEs will generally have regions where they expand error, but also regions of contraction.” As I read this, it isn’t obvious or easily determined just where the expansions or contractions occur, or how to characterize them other than by running a large number of ensembles to estimate the gross impact.

I think that an important contribution you have made is the insight of being able to emulate the more complex formulations of GCMs with a linear model. You are then able to demonstrate in a straight forward way, and certainly more economically than running a large number of ensembles, the behavior of uncertainty in the emulation. It would seem reasonable to me that if the emulation does a good job of reproducing the output of GCMs, then it should also be properly emulating the uncertainty.

Pat Frank
Reply to  Clyde Spencer
September 19, 2019 11:01 pm

It seems reasonable to me, too, Clyde. It also seemed reasonable to my very qualified reviewers at Frontiers.

Mark Broderick
September 19, 2019 12:13 pm

How about getting these same “models” to explain deep “Ice Ages” while co2 was much higher than today ? If they can’t do that then they are worthless to predict the future….

Mark Broderick
September 19, 2019 12:28 pm

Stoke… “… yes, DEs will generally have regions where they expand error, but also regions of contraction.” ?
How could any intelligent person “assume that the positive and negative errors would cancel each other out ?

Tommy
Reply to  Mark Broderick
September 19, 2019 2:30 pm

Completely agree. It’s mind boggling to me, but as far as I can tell that was Dr. Spencer’s argument.

Reply to  Mark Broderick
September 19, 2019 2:31 pm

“cancel each other out”
Who said that? Firstly, it isn’t positive or negative, but expanding and contracting. But more importantly I’m saying that there is a whole story out there that you just can’t leave out of error propagation. It’s what DEs do.

In fact, I think the story is much more complicated and interesting than Pat Frank has. The majority of error components diminish because of diffusion (viscosity). Nothing of that in Pat’s model. But some grow. The end result is chaos, as is well recognised, and is true in all fluid flow. But it is a limited, manageable problem. We live in a world of chaos (molecules etc) and we manage quite well.

Tommy
Reply to  Nick Stokes
September 19, 2019 4:51 pm

Who said errors cancel? Dr Spencer wrote this:

“The reason is that the +/-4 W/m2 bias error in LWCF assumed by Dr. Frank is almost exactly cancelled by other biases in the climate models that make up the top-of-atmosphere global radiative balance”

Reply to  Tommy
September 19, 2019 5:14 pm

“Dr Spencer wrote this”
Well, it wasn’t me. But it is a different context. He is saying, not that the biases are assumed to balance at TOA, but that they are required to balance. This is an application of conservation of energy in the model, and would prevent the sort of accumulation of error that Pat is claiming. Not that it even arises; he seems to have abandoned the claim that the units of the RMSE involved are 4 Wm⁻² year⁻¹.

Clyde Spencer
Reply to  Nick Stokes
September 19, 2019 5:40 pm

Stokes
You really don’t understand! Only the nominal (calculated) values output at each time step can be tested for “TOA balance” or any test of reasonableness. Unless the calculations are performed in tandem with the maximum and minimum probable values, the “accumulation error” (as you call it) isn’t going to show up. That is, the way it is done, with a single value being output, the uncertainties have to be calculated separately.

Pat is NOT claiming that the nominal value drifts with time, but rather, that the uncertainty envelope around the calculated nominal value rises more rapidly than the predicted temperature increase.

Reply to  Nick Stokes
September 19, 2019 6:45 pm

Clyde,
“Unless the calculations are performed in tandem with the maximum and minimum probable values, the “accumulation error” (as you call it) isn’t going to show up. “
I commented earlier about the tribal gullibility of sceptics, which you seem to exhibit handsomely. I noted, for example, the falling in line behind the bizarre proposition that the 4 Wm⁻² added a year⁻¹ to the units because it was averaged over a year (if it was). Folks nodded sagely, of course it must be so. Now the year⁻¹ has faded away. So, I suppose, they nod, yes was it ever different? Certainly no-one seems interested in these curious unit changes.

And so it is here. Pat creates some weird notion of an uncertainty that goes on growing, and can’t be tested, because it would be wrong to expect to see errors in that range. “You really don’t understand!”, they say. ” the “accumulation error” (as you call it) isn’t going to show up”.

So what is this uncertainty that is never going to show up? How can we ever be affected by it? Doesn’t sound very scientific.

Tommy
Reply to  Nick Stokes
September 19, 2019 6:59 pm

I know you didn’t say it (though you referenced and supported Dr. Spencer’s overall take elsewhere). And, it seems like you don’t disagree with the statement and think it’s relevant to Dr. Frank’s error accumulation argument (correct?).

Honestly, it seems to me folks are talking past each other.

The issue isn’t that “errors” accumulate in the sense that the variance of expected model outcomes would increase. They’re engineered not to.

The “error” of interest, and the one that does accumulate, is our confidence (lack of) the model is accurately modeling the Real World.

Do you disagree that the value proposition of the models is that they are predictive and that they are predictive because they (purportedly) simulate reality?

Reply to  Nick Stokes
September 19, 2019 7:51 pm

Tommy,
“that they are predictive because they (purportedly) simulate reality”
They simulate the part of reality that they claim to simulate, namely climate. It is well acknowledged that they don’t predict weather, up to and including ENSO. That is another thing missing from Pat Frank’s analysis. He includes all uncertainty about weather in his inflated totals.

That comes back to my point about chaos. It means you can’t predict certain fine scale features of the solution. But in that, it is usually reflecting reality, where those are generally unknown, because they don’t affect anything we care about. For example, CFD won’t predict the timing of shedding of vortices from a wing. It does a reasonable job of getting the frequency right, which might be important for its interaction with structural vibrations. And it does a good job of calculating the average shed kinetic energy in the vortices, which shows up in the drag.

Those are the things that you might want to do an uncertainty analysis on. No use lumping in the uncertainty of things you never wanted to know about.

Tommy
Reply to  Nick Stokes
September 19, 2019 8:30 pm

Nick, I appreciate your thoughtful reply, but I’m confused by this statement:

“Those are the things that you might want to do an uncertainty analysis on. No use lumping in the uncertainty of things you never wanted to know about.”

Isn’t the parameter Dr. Frank is isolating an input to the model at each iteration? Isn’t an input necessarily something want to know about?

And, given that:

“That comes back to my point about chaos. It means you can’t predict certain fine scale features of the solution”

But, if you can’t predict the small things that are iterative inputs to your model, how can you hope to predict the larger things (climate) that depend on them?

It seems to me that in order to remove the accumulation of uncertainty, you either have to remove Dr. Frank’s parameter of focus as from the model (with justification) or improve the modeling accuracy of it. You can’t whitewash the fact you can’t model that small bit of the puzzle by claiming you get the bigger picture correct, when the bigger picture is a composite of the littler things.

Tim Gorman
Reply to  Tommy
September 19, 2019 9:09 pm

+1

Pat Frank
Reply to  Nick Stokes
September 19, 2019 11:12 pm

Nick, “This is an application of conservation of energy in the model, and would prevent the sort of accumulation of error that Pat is claiming.

I claim no accumulation of error, Nick. I claim growth of uncertainty. You’re continually making this mistake, which is fatal to your case.

This may help:

Kline SJ. The Purposes of Uncertainty Analysis. Journal of Fluids Engineering. 1985;107(2):153-60. https://doi.org/10.1115/1.3242449

The Concept of Uncertainty

Since no measurement is perfectly accurate, means for describing inaccuracies are needed. It is now generally agreed that the appropriate concept for expressing inaccuracies is an “uncertainty” and that the value should be provided by an “uncertainty analysis.”

An uncertainty is not the same as an error. An error in measurement is the difference between the true value and the recorded value; an error is a fixed number and cannot be a statistical variable. An uncertainty is a possible value that the error might take on in a given measurement. Since the uncertainty can take on various values over a range, it is inherently a statistical variable.

The term “calibration experiment” is used in this paper to denote an experiment which: (i) calibrates an instrument or a thermophysical property against established standards; (ii) measures the desired output directly as a measurand so that propagation of uncertainty is unnecessary.

The information transmitted from calibration experiments into a complete engineering experiment on engineering systems or a record experiment on engineering research needs to be in a form that can be used in appropriate propagation processes (my bold). … Uncertainty analysis is the sine qua non for record experiments and for systematic reduction of errors in experimental work.

Uncertainty analysis is … an additional powerful cross-check and procedure for ensuring that requisite accuracy is actually obtained with minimum cost and time.

Propagation of Uncertainties Into Results

In calibration experiments, one measures the desired result directly. No problem of propagation of uncertainty then arises; we have the desired results in hand once we complete measurements. In nearly all other experiments, it is necessary to compute the uncertainty in the results from the estimates of uncertainty in the measurands. This computation process is called “propagation of uncertainty.”

Let R be a result computed from n measurands x_1, … x_n„ and W denotes an uncertainty with the subscript indicating the variable. Then, in dimensional form, we obtain: (W_R = sqrt[sum over(error_i)^2]).”

https://doi.org/10.1115/1.3242449

Pat Frank
Reply to  Nick Stokes
September 19, 2019 11:15 pm

Nick, “Now the year⁻¹ has faded away.

Wrong again, Nick. It’s indexed away. I’ve answered your querulousity several times.

Reply to  Nick Stokes
September 19, 2019 11:53 pm

Tommy,
“Isn’t the parameter Dr. Frank is isolating an input to the model at each iteration? Isn’t an input necessarily something want to know about?”
Not, it isn’t. There is a parametrisation, to which Pat wants to attach this uncertainty. It isn’t a new uncertainty at each iteration; that would give a result that would make even Pat blanch. he says, with no real basis, every year. I don’t believe that it is even an uncertainty of the global average over time.

“But, if you can’t predict the small things that are iterative inputs to your model”
Because many have only transient effect. Think of a pond as an analogue solver of a CFD problem. Suppose you throw a stone in to create an error. What happens?

The stone starts up a lot of eddies. There is no net angular momentum, because that is conserved. The angular momentum quickly diffuses, and the eddies subside.
There is a net displacement of the pond. Its level rises by a micron or so. That is the permanent effect.
And there are ripples. These are the longest lasting transient effect. But they get damped when reflected from the shore, or if not, then by viscosity.
And that is it, typical of what happens to initial errors. The one thing that lasts is given by an invariant, conservation of mass, which comes out as volume, since density is constant.

Reply to  Nick Stokes
September 20, 2019 12:26 am

Pat
“Nick, “Now the year⁻¹ has faded away.”
Wrong again, Nick. It’s indexed away. “

You’ve excelled yourself in gibberish. Units are units, They mean something. You can’t “index them away”.

Pat Frank
Reply to  Nick Stokes
September 21, 2019 1:18 pm

Nick, “You can’t “index them away”.

Let me clarify it for you, Nick. Notice the yearly index “i” is not included in the right side of eqn. 5.2. That’s for a reason.

But let’s put it all back in for you, including the year^-1 on the (+/-)4 W/m^2.

Right side: (+/-)[0.42 * 33K *4W/m^2 year^-1/F_0]_year_1, where “i'” is now the year 1 index.

Cancelling through: (+/-)[0.42 * 33K *4W/m^2/F_0]_1.

That is, we now have the contribution of uncertainty to the first year projection temperature, indexed “1.”

For year two: (+/-)[0.42 * 33K *4W/m^2 year^-1/F_0]_year_2, and

(+/-)[0.42 * 33K *4W/m^2/F_0]_2; index “2.”

(+/-)[0.42 * 33K *4W/m^2 year/F_0]_n; index “n.”

= (+/-)u_i

And those are what go on into eqn. 6, with units K.

You may not get it, Nick, but every scientist and engineer here will do.

Pat Frank
Reply to  Nick Stokes
September 21, 2019 1:22 pm

Nick, “It isn’t a new uncertainty at each iteration;

Yes it is. It derives from deficient theory.

Reply to  Nick Stokes
September 21, 2019 6:06 pm

Pat,
“but every scientist and engineer here will do”
Every scientist and engineer understands the importance of being clear and consistent about units. Not just making it up as you go along.

This story on indexing is just nuttier. To bring it back to Eq 5.1 (5.2 is just algebraically separated), you have a term
F₀ + ΔFᵢ ±4Wm⁻²
and now you want to say that it should be
F₀ + ΔFᵢ ±4Wm⁻²year⁻¹*yearᵢ
“i” is an index for year. But year isn’t indexed. year₁ isn’t different to year₂; years are all the same (as time dimension). Just year.

So now you want to say that the units of 4Wm⁻² are actually 4Wm⁻²year⁻¹, but whenever you want to use it, you have to multiply by year. Well, totally weird, but can probably be made to work. But then what came of the statement just before Eq 6:
“The annual average CMIP5 LWCF calibration uncertainty, ±4Wm⁻²year⁻¹, has the appropriate dimension to condition a projected air temperature emulated in annual time-steps.”
What is the point of modifying Lauer’s dimension for the quantity, saying that that is the “appropriate dimension”, and then saying you have to convert back to Lauer’s dimension before using it?

Pat Frank
Reply to  Nick Stokes
September 21, 2019 10:54 pm

Nick, “… but can probably be made to work.

Good. You’ve finally conceded that you’ve been wrong all along. You didn’t pay attention to the indexing, did you, so intent were you on finding a way to kick up some dust.

What is the point of modifying Lauer’s dimension for the quantity, saying that that is the “appropriate dimension”,

Right. There you go again claiming that an annual average is not a per year value. Really great math, Nick. And you call me nutty. Quite a projection.

… and then saying you have to convert back to Lauer’s dimension before using it?

The rmse of Lauer and Hamilton’s is an annual average, making it per year, no matter how many times you deny it. Per year, Nick.

I changed nothing. I followed the units throughout.

You just missed it in your fog of denial. And now you’re, ‘Look! A squirrel!’ hoping that no one notices.

Clyde Spencer
Reply to  Nick Stokes
September 20, 2019 10:47 am

Stokes,

It has been a long time since someone has referred to me as “handsome.” So, thank you. 🙂

Now, pleasantries aside, on to your usual sophistry. The graph on the right side of the original illustration (panel b) has a red line that is not far from horizontal. That is the nominal prediction of temperatures, based on iterative calculations. It does not provide any information on the uncertainty of those nominal values. Overlaying that is a lime-green ‘paraboloid’ opening to the right. That is the envelope of uncertainty, and is calculated separately from the nominal values, again by an iterative process. The justification for the propagation of error in the forcing is stated clearly (Frank, 2019): “That is, a measure of the predictive reliability of the final state obtained by a sequentially calculated progression of precursor states is found by serially propagating known physical errors through the individual steps into the predicted final state.”

I know that you are bright and well-educated, so other than becoming senile, the only other explanation for your obtuseness that seems to make sense if that you don’t want to understand it, perhaps because of your personal “tribalness.”

You might find it worth your while to peruse this:
https://www.isobudgets.com/pdf/uncertainty-guides/bipm-jcgm-100-2008-e-gum-evaluation-of-measurement-data-guide-to-the-expression-of-uncertainty-in-measurement.pdf

bit chilly
Reply to  Mark Broderick
September 20, 2019 12:07 am

You don’t have to assume, that’s where the fudge factors come in. When the model run starts to deviate beyond what would be termed reasonable a fudge factor is applied to bring it back into line. Given the known unknowns and the unknown unknowns involved in the climate it is the ONLY way the models can run in the territory of reasonableness for so long.

If any of these models were ever to be evaluated line by line i would be willing to bet my house in a legally binding document the above is the case.

Gator
September 19, 2019 12:38 pm

Thanks so much for all your perseverance Pat, I have been sharing your work with anyone who would listen, since I ran across it this past July. Once the public understands that all of the hype surrounding the “climate crisis” is based upon models, and that those same models are simply fictions created by those that “believe”, virtually all of this nonsense will end. And that is why your very important work is being misrepresented by those who stand to lose everything.

Pat Frank
Reply to  Gator
September 19, 2019 11:18 pm

Thanks, Gator. And you’re right, literally the transfer trillions of dollars away from the middle class into the pockets of the rich, and many careers, are under threat from that paper.

Ethan Brand
September 19, 2019 12:55 pm

Pat is making another critical explaination here that is not being addressed by most of the posters:.
How GCMs actually produce their output is completely irrelevant (black box). Whether a table lookup or the most advanced AI available..NOT relevant to his analysis. This point is being completely missed by most, and hence most of the criticism is irrelevant. Relevant criticism needs to address this key concept. To defend the skill of GCM output, defenders need to specifically address the CF uncertainty relative to CO 2 effects.

September 19, 2019 1:07 pm

Here:

https://wattsupwiththat.com/2019/09/19/emulation-4-w-m-long-wave-cloud-forcing-error-and-meaning/#comment-2799242

… Nick S wrote (among other things):

That is actually the point of GCM’s. They go beyond the time when weather can be predicted, but they don’t blow up. They keep calculating perfectly reasonable weather. It isn’t a reliable forecast any more, but it has the same statistical characteristics, which is what determines climate.

His particular wording there caught my attention, because, at first glance, it seems nonsensical.

How can climate models that produce outcomes following reasonable weather calculations determine a reasonably REAL climate forecast? What reliable prediction of climate could be fashioned from reasonable-but-unreliable forecasts? — that makes no sense to me. The unreliability of the concomitant weather forecasts would seem to propagate into the unreliability of the climate forecasts that the models produce.

Apples might be rotten, but they still determine the pie? A rotten apple is still a reasonable apple? A pie of rotten apples is still a reasonable pie? An unreliable forecast is a reasonable forecast?

A sum of reasonable-but-unreliable weather calculations would seem to constitute a reasonable-but-unreliable climate forecast. I think that what we primarily seek in climate models is reliable, NOT merely “reasonable”. Reasonable alone can be a mere artifact of internal consistency. Reasonableness in climate models seems to be built in — that’s what models are — reasonable representations of something, based on the reasoning in their own structure.

What is UNreasonable about this is that the model does not represent reality — it represents a reasonable model of reality that is unreliable — unfit to dictate real-world decisions. Using an unreliable model to dictate real-world decisions is unreasonable. It is the USE of climate models, then, that is UNREASONABLE.

Models probably have great use for studying the complexity of climate. They might be great educational tools. But they do not seem to be great practical tools to guide the development of civilization. They are UNREASONABLE tools for helping to shape civilization.

Tommy
Reply to  Robert Kernodle
September 19, 2019 3:10 pm

Exactly!

They’re a model of something and that something has temperature outcomes that are plausible for our reality (in addition to being politically convenient), but as far as I can tell some very smart people aren’t making the connection that this says NOTHING about what is actually going to happen in the real world.

Nicholas McGinley
Reply to  Robert Kernodle
September 20, 2019 8:52 am

It sounds to me that he is saying the results they get are what they expected, so they do not think they could be wrong. In fact they do not believe they CAN be wrong.
After all, it was just like they expected it would be.

DABidwell
September 19, 2019 1:10 pm

If a model can emulate a model, and we believe the first model is correct, wouldn’t if follow the second model also be correct? And does it matter how it does it as long as the emulation is correct (limited to mean surface temperature)? After reading through all the comments to date, I’m still not convinced as to why one model (GCM or spreadsheet) is better than the other. Sure one is fancier, but I can get to the ball in either vehicle.

Paramenter
September 19, 2019 1:30 pm

Prof. Frank,

Decent ‘version for dummies’ – explains and clarifies many questions that sprouted from the original article. By the way, your article is doing fairly well: “This article has more views than 99% of all Frontiers articles”. Your paper is also in the top 5% of all research outputs scored by Altmetric. Well done!

With respect to your current post:

“When several sources of systematic errors are identified, [uncertainty due to systematic error] beta is suggested to be calculated as a mean of bias limits or additive correction factors as follows:

“beta = sqrt[sum over(theta_S_i)^2]

Does this operation apply to each iterative step in calculation (i.e. in the model) or we calculate beta and it is subsequently used as constant in each iteration? Advocatus diaboli may argue that this quotation from Vasquez and Whiting means we add and square uncertainties, they propagate to next iterations but remain constant and do not add up.

Pat Frank
Reply to  Paramenter
September 19, 2019 11:24 pm

Paramenter, I’m just scientific staff, thanks Not a professor.

If one takes the model of Vasquez and Whiting and runs it through a series of sequential step-wise calculations to determine how a system changes across time, would the uncertainty in the final result be the root-sum-square of the uncertainties in all the intermediate states?

Paramenter
Reply to  Pat Frank
September 20, 2019 2:19 pm

If one takes the model of Vasquez and Whiting and runs it through a series of sequential step-wise calculations to determine how a system changes across time, would the uncertainty in the final result be the root-sum-square of the uncertainties in all the intermediate states?

I would say so. Still, how simulations work for instance in the field of CFD where are used for advanced aerodynamic analysis? Results obtained are used in design of wings and other components so it simply works. Such simulations carry millions of steps each run. Small uncertainty must be associated with each step but because sheer number of steps, adding and squaring uncertainty associated with each steps causes that uncertainty quickly grows and renders results useless. But that does not happen.

Quotation from Journal of Fluid Engineering is decent:

An uncertainty is not the same as an error. An error in measurement is the difference between the true value and the recorded value; an error is a fixed number and cannot be a statistical variable. An uncertainty is a possible value that the error might take on in a given measurement. Since the uncertainty can take on various values over a range, it is inherently a statistical variable.

It clearly distinguishes error from uncertainty, concept people even well-versed into stats struggling with. I reckon we need another post just with clear definitions!

Tim Gorman
Reply to  Paramenter
September 20, 2019 3:27 pm

Paramenter,

“Small uncertainty must be associated with each step but because sheer number of steps, adding and squaring uncertainty associated with each steps causes that uncertainty quickly grows and renders results useless. But that does not happen.”

If the uncertainty is very small then lots of steps still won’t overwhelm the result. Just how many variables in an aircraft simulation have a significant uncertainty? And these simulations *do* blow up under some conditions where the uncertainty becomes large.

Paramenter
Reply to  Tim Gorman
September 21, 2019 3:55 am

Hey Tim,

If the uncertainty is very small then lots of steps still won’t overwhelm the result. Just how many variables in an aircraft simulation have a significant uncertainty?

True, many if not all, parameters are well defined due to extensive experimental research, e.g. wind tunnels. Still, if we have millions of cells (each with its own small uncertainty) and millions of steps I cannot imagine how such uncertainty does not propagate and accumulate. But – I’m not an expert in this area so it’s question rather than any solid claim.

And these simulations *do* blow up under some conditions where the uncertainty becomes large.

Indeed. What I heard some conditions are also very hard to simulate, e.g. higher angles of attack where simulations may render wildly different results.

Tim Gorman
Reply to  Paramenter
September 21, 2019 5:13 am

Paramenter,

“Still, if we have millions of cells (each with its own small uncertainty) and millions of steps I cannot imagine how such uncertainty does not propagate and accumulate.”

Uncertainty does accumulate. The difference is that it doesn’t overwhelm the results. However, the simulations don’t give perfect answers. It’s why test pilots earn big bucks pushing the envelope of aircraft to confirm operational characteristics. Simulations can only go so far.

Pat Frank
Reply to  Paramenter
September 21, 2019 1:29 pm

Paramenter, when people parameterize engineering models, they use the models only within the parameter calibration bounds.

Inside those calibration bounds, observables are accurately simulated.

Climate models projections proceed very far beyond their parameter calibration bounds. The predictive uncertainties are necessarily huge.

Matthew R Marler
September 19, 2019 1:43 pm

Pat Frank, thank you for another good essay.

John Dowser
September 19, 2019 1:53 pm

“What happens inside the black box is irrelevant.”

This doesn’t sound quite sound, principally. Or perhaps more like: what’s expected to come out the box is very relevant. Since the box is a simulation with it’s own sets of feedback loops and equilibria, made invisible because of the nature of the defined box, one cannot simply make statements about the kind of propagation. There’s no simulation possible (in theory even) which actually reflects the exact processing. What matters is if the emulation can be used to approach real data, if it behaves *close* enough, even while perpetually “wrong”.

In the end it’s about about Dr. Frank’s conclusions being wrong but more how they’re closer to irrelevant to the models in use. The suggested uncertainty range and its relevant is uncertain as well. What matters in the end is if the model turns out to be useful and use it until it doesn’t.

If someone wants to base climate policies on JUST that, well, that’s another question.

Reply to  John Dowser
September 19, 2019 3:21 pm

Aren’t climate models themselves a sort of “black box”, since they are abstractions from reality?

And, in the sense that the models cannot “know” what some of the real quantities are, isn’t this a sort of “it doesn’t matter what goes on in the black box” state of knowledge? Yet, we value the output as reasonable.

We value output from these black boxes (climate models), where we don’t know what is going on precisely, and yet we should question models of these black boxes (Pat’s emulation equation) that produce their (climate models’) outputs with the same inputs?

It seems like the same sound reasoning is being applied to the climate-model emulation as is being applied to the climate models being emulated.

Emulations of simulations. A black box mimicking a group of black boxes. Lions and tigers and bears, oh my! — it’s all part of Oz — We’rrrrrrrrrrrrrrrrrrrrrrrrr off to see the Wizard ….

David Riser
September 19, 2019 2:36 pm

Pat Frank,
Well done, but it highlights how many people struggle with the concept of error propagation and how many hoops they will jump through to avoid doing the proper math and producing error bars or some other means of showing what the uncertainty is within their calculations.
v/r,
Dave Riser

Pat Frank
Reply to  David Riser
September 19, 2019 11:27 pm

Sad if true, David.

I recall reading a paper some long time ago, where the author expressed amazement that a group of researchers were using a slightly exotic way to calculate uncertainties in their results, they said, because it gave smaller intervals.

So it goes.

Jean Parisot
September 19, 2019 3:12 pm

What happens when the GCMs are tuned to match the pristine temperature station data?

michael hart
September 19, 2019 3:33 pm

“… systematic errors are associated with calibration bias in [methods] and equipment… Experimentalists have paid significant attention to the effect of random errors on uncertainty propagation in chemical and physical property estimation… “-Vasquez and Whiting

And therein lies the rub. Whatever they may be, climate modelers are most certainly NOT experimentalists.

DMC
September 19, 2019 3:39 pm

Hi Pat Frank

This may be of interest to you a ASP colloquium discussing modelling tuning / parameterizations including clouds in the context of model uncertainty

Robert of Texas
September 19, 2019 3:49 pm

“This is why the uncertainty in projected air temperature is so great. The needed resolution is 100 times better than the available resolution.”

No, I do not agree… Even if resolution is 100 times better for clouds, it does not follow that they have captured all of the various processes and feed backs that contribute to the overall climate. One has to assume that the models have captured all of the important processes, and that no undiscovered process or feedback will shift a yearly output enough to start a cascade effect. Its called a complex chaotic system (more than one chaotic process is involved).

One CANNOT predict the behavior of a natural chaotic system within a narrow-margin over enough time. One might be able to say, statistically, there is a “n”% chance of an outcome, but that “n”% will grow to a meaningless margin after enough time. 100 years is simply beyond any models – we just do not understand the climate processes well enough – clouds is just one set of processes we don’t understand well.

For example, let’s say that there is natural heating (forget CO2 as the magic molecule) and it drives a change in wind patterns over North Africa which carry greater loads of dust over the Atlantic. This then drives changes to condensation, which drives changes in temperatures for a large region, which…etc. The models simply cannot capture all this complexity. If you change the climate for a large enough portion of the Earth (say 10% to 20%) through such an unpredicted change, then the odds that it will impact other regions climate are large.

Climate models depend on averaging the measurements we think are important over a period we have made measurements in…they cannot predict the unknown, unmeasured, completely surprising changes that will occur. It is pure arrogance to believe we can “see” the effects of trace amounts of CO2 on the climate system.

Discovering that a complex computer model filled with differential formulas acts in a linear manner doesn’t surprise me one bit. I ran into this kind of behavior again and again when working on mathematical algorithms back in the 1980’s. I keep finding that all my tweaks and added complexity were completely overwhelmed by the already existing established more simple equations. It is a matter of scale…if the complex formulas that make up 99% of the code produce only 1% of the output, and the other 1% of the simple code produces 99% of the output then you will get a nasty surprise when you finally analyze the result. That is what you just did for them.

bit chilly
Reply to  Robert of Texas
September 20, 2019 12:23 am

Your example of increased dust from North Africa entering the Atlantic is even more complex. One result of that can be an increase in plankton by orders of magnitude from year to year. This then results in a similar increase in recruitment of various fish species dependent upon timing of plankton blooms (primary production has ramped up big time in the north east atlantic this year as will be seen in plankton surveys) for survival post larval stage.

All that increase in oceanic biomass is retained energy,not to mention that water with high concentrations of plankton also has the potential to store more heat in a similar way that silt laden shallow water warms quicker and to a higher temperature than clear water. Yes in the big scheme of things the above may be small potatoes (though i think the plankton alone might be a very large potato ) but there are many natural variations and processes that are not even considered in climate models, never mind “parameterized” .

Tim Gorman
Reply to  bit chilly
September 20, 2019 4:12 am

“but there are many natural variations and processes that are not even considered in climate models, never mind “parameterized” .”

It’s what Freeman Dyson pointed out several years ago. The climate models are far from being holistic simulation of the Earth. We know the Earth has “greened” somewhere between 10% and 15% since 1980. That has to have some impact on the thermodynamics, from evapotranspiration if nothing else. It could be a prime example of why temperatures are moderating in global warming “holes” around the globe. Yet I’ve never read where the climate models consider that at all.

michael hart