Consensus Climatology in a Nutshell: Betrayal of Integrity

Guest essay by Pat Frank

Today’s offering is a morality tale about the clash of honesty with self-interest, of integrity with income, and of arrogance with ignorance.

I’m bringing out the events below for general perusal only because they’re a perfect miniature of the sewer that is consensus climatology.

And also because corrupt practice battens in the dark. With Anthony’s help, we’ll let in some light.

On November third Anthony posted about a new statistical method of evaluating climate models, published in “Geoscientific Model Development” (GMD), a journal then unfamiliar to me.

WUWT readers will remember my recent post about unsuccessful attempts to publish on error propagation and climate model reliability. So I thought, “A new journal to try!”

Copernicus Publications publishes Geoscientific Model Development under the European Geosciences Union.

The Journal advertises itself as, “an international scientific journal dedicated to the publication and public discussion of the description, development, and evaluation of numerical models of the Earth system and its components.

It welcomes papers that include, “new methods for assessment of models, including work on developing new metrics for assessing model performance and novel ways of comparing model results with observational data.

GMD is the perfect Journal for the new method of model evaluation by propagation of calibration error.

So I gave it a try, and submitted my manuscript, “Propagation of Error and the Reliability of Global Air Temperature Projections“; samizdat manuscript here (13.5 mb pdf). Copernicus assigned a “topical editor” by reference to manuscript keywords.

My submission didn’t last 24 hours. It was rapidly rejected and deleted from the journal site.

The topical editor was Dr. James Annan, a climate modeler. Here’s what he wrote in full:

Topical Editor Initial Decision: Reject (07 Nov 2017) by James Annan


“Comments to the Author:


“This manuscript is silly and I’d be embarrassed to waste the time of reputable scientists by sending it out for review. The trivial error of the author is the assumption that the ~4W/m^2 error in cloud forcing is compounded on an annual basis. Nowhere in the manuscript it is explained why the annual time scale is used as opposed to hourly, daily or centennially, which would make a huge difference to the results. The ~4W/m^2 error is in fact essentially time-invariant and thus if one is determined to pursue this approach, the correct time scale is actually infinite. Of course this is what underpins the use of anomalies for estimating change, versus using the absolute temperatures. I am confident that the author has already had this pointed out to them on numerous occasions (see refs below) and repeating this process in GMD will serve no useful purpose.”

Before I parse out the incompetent wonderfulness of Dr. Annan’s views, let’s take a very relevant excursion into GMD’s ethical guidelines about conflict of interest.

But if you’d like to anticipate the competence assessment, consult the 12 standard reviewer mistakes. Dr. Annan managed many ignorant gaffes in that one short paragraph.

But on to ethics: GMD’s ethical guidelines for editors include:

“An editor should give unbiased consideration to all manuscripts offered for publication…”

“Editors should avoid situations of real or perceived conflicts of interest in which the relationship could bias judgement of the manuscript.”

Copernicus Publications goes further and has a specific “Competing interests policy” for editors:

“A conflict of interest takes place when there is any interference with the objective decision making by an editor or objective peer review by the referee. Such secondary interests could be financial, personal, or in relation to any organization. If editors or referees encounter their own conflict of interest, they have to declare so and – if necessary – renounce their role in assessing the respective manuscript.”


In a lovely irony, my cover letter to chief editor Dr. Julia Hargreaves made this observation and request:

Unfortunately, it is necessary to draw to your attention the very clear professional conflict of interest for any potential reviewer reliant on climate models for research. The same caution applies to a reviewer whose research is invested in the consensus position concerning the climatological impact of CO2 emissions.


“Therefore, it is requested that the choice of reviewers be among scientists who do not suffer such conflicts.


“I do understand that this study presents a severe test of professional integrity. Nevertheless I have confidence in your commitment to the full rigor of science.

It turns out that Dr. Annan is co-principal of Blue Sky Research, Inc. Ltd., a for-profit company that offers climate modeling for hire, and that has at least one corporate contract.

Is it reasonable to surmise that Dr. Annan might have a financial conflict of interest with a critically negative appraisal of climate model reliability?

Is it another reasonable surmise that he may possibly have a strong negative, even reflexive, rejectionist response to a study that definitively finds climate models to have no predictive value?

In light of his very evident financial conflicts of interest, did editor Dr. Annan recuse himself knowing the actuality, not just the image, of a serious and impending impropriety? Nope.

It gets even better, though.

Dr. Julia Hargreaves is the GMD Chief Executive Editor. I cc’d her on the email correspondence with the Journal (see below). It is her responsibility to administer journal ethics.

Did she remove Dr. Annan? Nope.

I communicated Dr. Annan’s financial and professional conflicts of interest to Copernicus Publications (see the emails below). The Publisher is the ultimate administrator of Journal ethics.

Did the publisher step in to excuse Dr. Annan? Nope.

It also turns out that GMD Chief Executive Editor Dr. Julia Hargreaves is the other co-principal of Blue Sky Research, Inc. Ltd.

She shares the identical financial conflict of interest with Dr. Annan.

Julia Hargreaves and James Annan are also a co-live-in couple, perhaps even married.

One can’t help but wonder if there was a dinner-table conversation.

Is Julia capable of administering James’ obvious financial conflict of interest violation? Apparently no more than is James.

Is Julia capable of administering her own obvious financial conflict of interest? Does James have free rein at GMD, Julia’s Executive Editorship withal? Evidently, the answers are no and yes.

Should financially conflicted Julia and James have any editorial responsibilities at all, at a respectable Journal pretending critical appraisals of climate models?

Both Dr. Annan and Dr. Hargreaves also have a research focus on climate modeling. Any grant monies depend on the perceived efficacy of climate models.

They will have a separate professional conflict of interest with any critical study of climate models that comes to negative conclusions.

So much for conflict of interest.

Let’s proceed to Dr. Annan’s technical comments. This will be brief.

We can note his very unprofessional first sentence and bypass it in compassionate silence.

He wrote, “… ~4W/m^2 error in cloud forcing…” except it is ±4 W/m^2 not Dr. Annan’s positive sign +4 W/m^2. Apparently for Dr. Annan, ± = +.

And ±4 W/m^2 is a calibration error statistic, not an energetic forcing.

That one phrase alone engages mistakes 2, 4, and 6.

How does it happen that a PhD in mathematics does not understand rms (root-mean-square) and cannot distinguish a “±” from a “+”?

How comes a PhD mathematician unable to discern a physically real energy from a statistic?

Next, “the assumption that the [error] is compounded on an annual basis”

That “assumption” is instead a demonstration. Ten pages of the manuscript are dedicated to showing the error arises within the models, is a systematic calibration error, and necessarily propagates stepwise.

Dr. Annan here qualifies for the honor of mistakes 4 and 5.

Next, “Nowhere in the manuscript it is explained why the annual time scale is used as opposed to hourly, daily or centennially,…

Exactly “why” was fully explained in manuscript Section 2.4.1 (pp. 28-30), and the full derivation was provided in Supporting Information Section 6.2.

Dr. Annan merits a specialty award for extraordinarily careless reading.

On to, “The ~4W/m^2 error is in fact essentially time-invariant…

Like Mr. andthentheresphysics, Nick Stokes, and Dr. Patrick Brown, Dr. Annan apparently does not understand that a time average is a statistic conveying, ‘mean magnitude per time-unit.’ This concept is evidently not covered in the Ph.D.

And then, “the correct time scale is actually infinite.

Except it’s not infinite, (see above), but here Dr. Annan has made a self-serving interpretative choice. Dr. Annan actually wrote that his +4 W/m^2 is “time-invariant,” which is also consistent with an infinitely short time. The propagated uncertainty is then also infinite; good job, Dr. Annan.

Penultimately, “this is what underpins the use of anomalies for estimating change…

Dr. Annan again assumed ±4 W/m^2 statistic is a constant +4 W/m^2 physical offset error, reiterating mistakes 4, 6, 7, and 9.

And it’s always nice to finish up with an irony: “I am confident that the author has already had this pointed out to them on numerous occasions…

In this, finally, Dr. Annan is correct (except grammatically; referencing a singular noun with a plural pronoun).

I have yet to encounter a single climate modeler who understands:

  • that “±” is not “+,”
  • that an error statistic is not a physical energy,
  • that taking anomalies does not remove physical uncertainty,
  • that models can be calibrated at all,
  • or that systematic calibration error propagates through subsequent calculations.

Dr. Annan now joins that chorus.

The predominance of mathematicians among climate modelers, like Dr. Annan, explains why climate modeling is in such a shambles.

Dr. Annan’s publication list illustrates the problem. Not one paper concerns incorporating new physical theory into a model. Climate modeling is all about statistics.

It hardly bears mentioning that statistics is not physics. But that absolutely critical distinction is obviously lost on climate modelers, and even on consensus-supporting scientists.

None of these people are scientists. None of them know how to think scientifically.

They have made the whole modeling enterprise a warm little pool of Platonic idealism, untroubled by the cold relentless currents of science and its dreadfully impersonal tests of experiment, observation, and physical error.

In their hands, climate models have become more elaborate but not more accurate.

In fact, apart from Lindzen and Choi’s Iris theory, there doesn’t seem to have been any advance in the physical theory of climate since at least 1990.

Such is the baleful influence on science of unconstrained mathematical idealism.

The whole Journal response reeks of fake ethics and arrogant incompetence.

In my opinion, GMD ethics have proven to be window dressing on a house given over to corruption; a fraud.

Also in my opinion, this one episode is emblematic of all of consensus climate science.

Finally, the email traffic is reproduced below.

My responses to the Journal pointed out Dr. Annan’s conflict of interest and obvious errors. On those grounds, I asked that the manuscript be reinstated. I always cc’d GMD Chief Executive Editor Dr. Julia Hargreaves.

The Journal remained silent, no matter even the clear violations of its own ethical pronouncements; as did Dr. Hargreaves.

1. GMD’s notice of rejection:


Subject: gmd-2017-281 (author) – manuscript not accepted

Date: November 7, 2017 at 6:07 AM


Dear Patrick Frank,

We regret that your following submission was not accepted for publication in GMD:

Title: Propagation of Error and the Reliability of Global Air Temperature Projections

Author(s): Patrick Frank

MS No.: gmd-2017-281

MS Type: Methods for assessment of models

Iteration: Initial Submission

You can view the reasons for this decision via your MS Overview:

To log in, please use your Copernicus Office user ID xxxxx.

We thank you very much for your understanding and hope that you will consider GMD again for the publication of your future scientific papers.

In case any questions arise, please contact me.

Kind regards,

Natascha Töpfer

Copernicus Publications

Editorial Support

on behalf of the GMD Editorial Board


2. My first response:

From: Patrick Frank

Subject: Re: gmd-2017-281 (author) – manuscript not accepted

Date: November 7, 2017 at 7:46 PM



Dear Ms. Töpfer,

Dr. Annan has a vested economic interest in climate modeling. He does not qualify as editor under the ethical conflict of interest guidelines of the Journal.

Dr. Annan’s posted appraisal is factually, indeed fatally, incorrect.

Dr. Annan wrongly claimed the ±4 W/m^2 annual error is explained “nowhere in the manuscript.” It is explained on page 30, lines 571-584.

The full derivation is provided in Supporting Information Section 6.2.

There is no doubt that the ±4 W/m^2 is an annual calibration uncertainty.

One can only surmise that Dr. Annan did not read the manuscript before coming to his decision.

Dr. Annan also made the naïve error of supposing that the ±4 W/m^2 calibration uncertainty is a constant offset physical error.

Plus/minus cannot be constant positive (or negative). It cannot be subtracted away in an anomaly.

Dr. Annan’s rejection is not only scientifically unjustifiable. It is not even scientific.

I ask that Dr. Annan be excused on ethical grounds, and on the grounds of an obviously careless and truly incompetent initial appraisal.

I further respectfully ask that the manuscript be reinstated and re-assigned to an alternative editor who is capable of non-partisan stewardship.

Thank-you for your consideration,


Patrick Frank, Ph.D.

Palo Alto, CA 94301



3. Journal response #1: silence.


4. My second response:

From: Patrick Frank

Subject: Re: gmd-2017-281

Date: November 8, 2017 at 8:08 PM



Dear Ms. Töpfer,

One suspects the present situation is difficult for you. So, let me make things plain.

I am a Ph.D. physical methods experimental chemist with emphasis in X-ray spectroscopy. I work at Stanford University.

My email address there is, if you would like to verify my standing.

I have 30+ years of experience, international collaborators, and an extensive publication record.

My most recent paper is Patrick Frank, et al., (2017) “Spin-Polarization-Induced Pre-edge Transitions in the Sulfur KEdge XAS Spectra of Open-Shell Transition-Metal Sulfates: Spectroscopic Validation of σBond Electron Transfer” Inorganic Chemistry 56, 1080-1093; doi: 10.1021/acs.inorgchem.6b00991.

Physical error analysis is routine for me. Manuscript gmd-2017-281 strictly focuses on physical error analysis.

Dr. Annan is a mathematician. He has no training in the physical sciences. He has no training or experience in assessing systematic physical error and its impacts.

He is unlikely to ever have made a measurement, or worked with an instrument, or to have propagated systematic physical error through a calculation.

A survey of Dr. Annan’s publication titles shows no indication of physical error analysis.

His comments on gmd-2017-281 reveal no understanding of the physical uncertainty deriving from model calibration error.

He evidently does not realize that physical knowledge statements are conditioned by physical uncertainty.

Dr. Annan has no training in physical error analysis. He has no experience with physical error analysis. He has never engaged the systematic error that is the focus of gmd-2017-281.

Dr. Annan is not qualified to evaluate the manuscript. He is not competent to be the manuscript editor. He is not competent to be a reviewer.

Dr. Annan’s comments on gmd-2017-281 are no more than ignorant.

This is all in addition to Dr. Annan’s very serious conflict of financial and professional interest with the content of gmd-2017-281.

Journal ethics demand that he should have immediately recused himself. However, he did not do so.

I ask you to reinstate gmd-2017-281 and assign a competent and ethical editor capable of knowledgeable and impartial review.

Geoscientific Model Development can be a Journal devoted to science.

Or it can play at nonsense.

The choice is yours.

I will not bother you further, of course. Silence will be evidence of your choice for nonsense.

Best wishes,


Patrick Frank, Ph.D.

Palo Alto, CA 94301



5. Journal response #2: silence.


The journal has remained silent as of 11 November 2017.

They have chosen to play at nonsense. So chooses all of consensus climate so-called science.


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Why would people expect Dr. Annan to allow publication of a paper that will show fault with his work, when he is obviously a believer in the Phil Jones mantra of “why should I show you my data when all you want to do is find fault with it.”

Keep chasing them Pat Frank.

Mike Bromley the Kurd

Brilliant dismantling of pal review.

Another very sad tale of loss of scientific integerty in this field. Thanks for bringing it to our attention.


Sad, blatant, unashamed….

For shame!

Hot under the collar

“It also turns out that GMD Chief Executive Editor Dr. Julia Hargreaves is the other co-principal of Blue Sky Research, Inc. Ltd.
She shares the identical financial conflict of interest with Dr. Annan.
Julia Hargreaves and James Annan are also a co-live-in couple, perhaps even married.
One can’t help but wonder if there was a dinner-table conversation.”

I believe ‘caught red handed in the cookie jar’ would be more accurate than conflict of interest.

Without being knowledgeable within the issues raised in this article, I just remembered this quote from the IPCC AR5;WGI report:
“When initialized with states close to the observations, models ‘drift’ towards their imperfect climatology (an estimate of the mean climate), leading to biases in the simulations that depend on the forecast time. The time scale of the drift in the atmosphere and upper ocean is, in most cases, a few years. Biases can be largely removed using empirical techniques a posteriori. The bias correction or adjustment linearly corrects for model drift.”
(Ref: IPCC;AR5;WGI Chapter 11 11.2.3 Prediction Quality; Page 967)

I, wonder what that means, but anyhow it doesn´t sound good.

Quinn the Eskimo

That sounds kind of significant. In English, the statement that “Biases can be largely removed using empirical techniques a posteriori,” seems to mean that the claim of model-observation agreement is the product of “a posteriori” “adjustments” to “model drift,” which increases with “forecast time.”

“Empirical techniques” – pretty fancy name for fraud.

It means that their results come from their posterior.


It means that the models do not give credible results, so they frig them afterwards to give the impression that they do.

The corollary of this is that the remaining warming remaining is mere an arbitrarily chosen value which chosen to be small enough to be credible whilst still serving the alarmist agenda.


My thought is that the models can be accurate with adjustments ‘a posteriori’ that is after the forecasts/projections/predictions have been made and the time for the supposed event has passed, then the model can be adjusted (changed from wrong to right) using the actual results.
So it’s useless as a prediction tool.


My attempt at translation. Basically, it means that we will continue revising our projections to agree with the observations on a periodical basis. Therefore, we will make our numbers look valid and we will get more grant money.

This is not describing GCM’s as currently implemented. It is describing the still experimental process of decadal prediction. It has long been understood that chaotic processes cannot for long be determined by their initial conditions. So climate modelling focusses on the attractor, which is approached independently of starting point. Decadal prediction is trying to get away from this, and this para is just describing the basic difficulty in maintaining dependence on initial conditions.

Nick Stokes

Decadal prediction is trying to get away from this, and this para is just describing the basic difficulty in maintaining dependence on initial conditions.

If that is the case, then how can the CAGW academic-bureaucratic-industry claim that they were accurately able to “tune” EVERY climate models’ output between 1980 and 2017 for the only two irregular, short-term (8-10 month) intervals volcanic activity between 1970 and 1990?

I don’t know if that is true, but I see no connection.


You have illustrated one of the major failings of climate science, which is to conflate the chaos of the transition from one equilibrium state to another (weather) with the deterministic equilibrium state being transitioned to (climate). The reason this arises is because climate models attempt to model the chaos of interactions, rather than model what the states MUST be.

The General Circulation Models used for weather forecasting and climate modelling ostensibly model the physics, except that they have innumerable knobs and dials to fit them to subjectively interpreted historical data, moreover; when used for climate modeling, the temporal and spatial resolutions used are far larger then those used for weather forecasting. The hope is that the correct macroscopic behavior will emerge by simulating low resolution weather far into the future based on constraints dictated by the recent past. To paraphrase a lunch time discussion with some colleagues about String Theory, “Given enough degrees of freedom any behavior can be reproduced by any model”. What this means for climate models is that the more adjustments are required to fit a model to expectations, the less certain its predictions of the future will be, and curve fitting GCM’s to expectations requires a plethora of adjustments.


“So climate modelling focusses on the attractor, ”
ye, sure, that’s probly why searching the whole AR5 with IPCC own tool (, you’ll find +11,000 occurrence of the word “projection” and … 2 (TWO !!) occurrence of word “attractor” , both in a single paragraph worth quoting:

A climate model driven with external forcing alone is not expected to
replicate the observed evolution of internal variability, because of the
chaotic nature of the climate system, but it should be able to capture
the statistics of this variability (often referred to as ‘noise’). The relia-
bility of forecasts of short-term variability is also a useful test of the
representation of relevant processes in the models used for attribution,
but forecast skill is not necessary for attribution: attribution focuses on
changes in the underlying moments of the ‘weather attractor’, mean-
ing the expected weather and its variability, while prediction focuses
on the actual trajectory of the weather around this att

Which translate into “here we admit in weasel words that we bullshit you in the face, don’t say you had not be told”

Just after that they write
” the new guidance recognized that it may be possible, in
some instances, to attribute a change in a particular variable to some
external factor before that change could actually be detected in the
variable itself”
I say WOW! I mean, with such a guidance, I can attribute to WUWT exposure the change in Nick Stokes’ state of mind index into skeptic zone, before that change could actually be detected in the variable itself (no, Nick , you haven’t your word in this. This is MY index, proprietory technology)
And even with this post-modern science criterium, they didn’t succeed in attributing extrem event to climate change?

How come that a decadal model will drift towards imperfect climatology (whatever that is) while a centennial model will not drift towards imperfect climatology?


The true nature of the attractor is the end state as it constrains the chaos. Climate modellers hope that the attractor emerges which will never happen as the attractor keeps the chaos from running in an open loop, or unconstrained manner. This is why the models are so dependent on initial conditions. If the models are correct, they will eventually converge to the same state, independent of initial conditions. If the end state was as chaotic as claimed, every summer and every winter would be significantly different from each other. The fact that the seasonal climate is quite consistent from year to year across the globe is strong evidence that the climate is no where near as chaotic as is often presumed.

Running a model with varying initial conditions does not result in the emergence of the actual attractor by cancelling out the chaos as claimed, but converges to a false attractor quantified by the many assumptions, one of which is the assumption of a much larger effect from CO2 then is possible.

“How come that a decadal model will drift towards imperfect climatology “
In science, as in life, we never have perfect knowledge. We have imperfect knowledge of the initial state, and imperfect knowledge of the climatology. GCM’s, recognising this, wind back a long way to start, so the imperfections in initial state will fade, to concentrate on climatology. Decadal tries to span this period, by working harder to get a good initial state. They would like to get the evolution from this state, for decadal prediction, but part of that gets confounded with the trend to (imperfect) climatology (which GCMs allow to go to completion before they start).

The quote was from a setion about decadal predictions. I find your explanation plausible. There are issues with tuning of general climate models but I guess these dont drift away that fast.


It is not uncommon for models to run off the rails, either too thermageddon hot house or icehouse states. The tuning of multiple parameters is what creates a reliable attractor for the model output to run to. That of course means that, within limits – wide limits it turns out with enough parameters, the modeler can tweak to achieve whatever climate sensitivity their confirmation bias wants.

Those model outputs that don’t conform to the resulting GroupThink are excluded from the intercomparison projects. Funding dries up, publications get rejected. Conform or perish is the lesson the modelers have learned.


“attractor” = initial assumption. As in: “It has long been understood that chaotic processes cannot for long be determined by their initial conditions. So climate modelling focusses on the initial assumption, which is approached independently of starting point.”

In other words, climate models are self-fulfilling prophesies, derived from initial assumptions and unhampered by reality, which is nothing more than the canvas on which a climate crisis is painted! The only time it is even necessary to mention reality is when it deviates from the models, at which point mainstream climate scientists come forth to explain why reality is wrong!

I would have thought that this astounding perversion of science would be impossible, but every time I think human stupidity has peaked, people come along and prove me wrong!

Quinn the Eskimo

Despite Nick Stokes’ attempt to distinguish between decadal prediction and climate modeling, the text of this section of AR5 makes that impossible:

It is important to note that the systematic errors illustrated here are common to both decadal prediction systems and climate-change projections. The bias adjustment itself is another important source of uncertainty in climate predictions (e.g., Ho et al., 2012b). There may be nonlinear relationships between the mean state and the anomalies, that are neglected in linear bias adjustment techniques. There are also difficulties in estimating the drift in the presence of volcanic eruptions.


“It is describing the still experimental process of decadal prediction”

SAY WHAT. !!!!! Did you read what you typed, and keep a straight face ?????

So all these TRILLIONS of dollars have been spent based on an EXPERIMENTAL PROCESS that can’t even get decadal predictions correct.


Nick, you have just DESTROYED the whole AGW agenda in that one sentence. !!


““So climate modelling focusses on the attractor, ””

On the attractor of CLIMATE FUNDING !!

“co2isnotevil November 12, 2017 at 9:10 am

The General Circulation Models used for weather forecasting and climate modelling ostensibly model the physics, except that they have innumerable knobs and dials to fit them to subjectively interpreted historical data, moreover; when used for climate modeling, the temporal and spatial resolutions used are far larger then those used for weather forecasting. The hope is that the correct macroscopic behavior will emerge by simulating low resolution weather far into the future based on constraints dictated by the recent past. To paraphrase a lunch time discussion with some colleagues about String Theory, “Given enough degrees of freedom any behavior can be reproduced by any model”. What this means for climate models is that the more adjustments are required to fit a model to expectations, the less certain its predictions of the future will be, and curve fitting GCM’s to expectations requires a plethora of adjustments.”

Excellent comment CO2isnotevil.

Wonderful phrasing!
“Subjectively interpreted historical data”, phrasing that reminds me of “interpretive dancers” working in red light districts.

Robert of Ottawa

It means they pull the answer out of their posterior 🙂

How else can you have an a posteriori imulation.

Robert of Ottawa



Maybe they need some Imodium…


Reminds me of a previous Prime Minister who stated “No one is the suppository of all wisdom”.
But perhaps climate science is?

using empirical techniques a posteriori.
the model will drift due to lack of precision errors. this is typically “corrected” by smearing the error linearly across all the nodes. which is itself a source of error.

The ~4W/m^2 error is in fact essentially time-invariant
this does not render the model immune to the effects of the error. this is at the heart of why computers are unable to reliably predict the future.

I do not agree that this is time invariant. however it is not annual either, unless the model increments are annual. otherwise the error compounds similar to compound interest. 4% compounded daily is greater then 4% compounded annually.

as such, calculating error annually is a lower bound as. models will cycle faster.

Clyde Spencer

It seems to me that the error (uncertainty) is compounded with each calculation. The time interval is an artifact of the units of time assigned to the looping or iteration. That is, the interval between calculations is irrelevant. It is the total number of calculations that determines the magnitude of the final uncertainty.


The paper says it is per year. Compared to the annual cloud forcing, 4 is quite significant: “Global cloud forcing (CF) is net cooling, with an estimated global average annual magnitude of about -27.6 Wm-2 [76, 77].”

” That is, the interval between calculations is irrelevant.”
No. The time interval of prediction is fixed, say to 2100. The interval determines the number of steps. If it’s monthly instead of annual, that’s 12 times as many steps till 2100, or about 3.5 times the spread. And who’s to say whether month or year is right?

“The paper says it is per year. “
Pat Frank’s paper says that. His source, Lauer and Hamilton, do not.
comment image


Nick. The root mean square error is just a standard deviation. The quote is a bit albiguous, but if I had to guess i’d say the authors linearly regressed the observed values on the mean of the predicted values that come out of a bunch of models.

A common way to report an analysis like that is to report the correlation between the two variables. The correlation is pretty good. The authors also report the root of the average sum of squared deviations (observed minus predicted) – which is merely, as I already said above, a sample standard deviation.

If the model predictions and the observed values annual, then the +/- 4 is per year. This value applies at each predicted value. It is subject to the assumption of homoscedasticity.

+/- 4, like any sample standard deviation, does not change systematically with N. The standard error of thr mean, however, does change with N.

To propagate that +/- 4 error, one would divide the +/-4 by the root of N and then do some partial derivative calculus.

I would also like to point out that if the observed values are themselves averages, then even the +/- 4 per year underestimates the error.

Yo do text book error propagation, you have to start with instrument error.


Clyde. There are rules for applying error propagation formula. Every novel calculation from measured values requires error to be propagated. In some softer sciences, this is often not done at all. In harder sciences and of course engineering, the stakes are way too high to ignore them.

Nick should try to make time to study error propogation if he still cannot field a valid counter argument to Pat Frank’s concern.

“If the model predictions and the observed values annual, then the +/- 4 is per year.”
They aren’t. The model steps every 30 minutes or so. The observations are more frequent than annual. Pat expresses the algebra of combining the averages in these two equations from the Supplementary:
First the averaging within each year:
comment image

Then the averaging of the annuals over 20 years:
comment image

The first, 6-2 is normal averaging, and yields an average with the same units as the things averaged, cloud cover unit. But when he averages over years (6-4), the units of the average change. It’s now cloud cover units per year. I haven’t been able to get any rational explanation of the inconsistency. But it determines the timescale. If he had subsummed over decades instead of years, say, then the units would have been per decade, with a three times slower propagation of error.

What do you think the units of average should be?


Nick. As you said he takes an average of the model predictions within a given year, does this for each one of 20 years, then takes a grand 20 year mean. I need more context so I will have to go and read the bit myself. One reason he might have selected an annual unit is bevause the observed values are annual units. I would like to know how he aggregated the measured cloud cover values as well (if he did at all).

Whatever the case, to get the rmse, he seems to have done what i described before based on the other part you quoted. Using regression, he can posit that the +/- 4 is uniform over the regression line, applying the error at small time scales as well. But I’m not sure that assumption would hold. Perhaps the observed values are sloppier or biased (over or under estimates) some years than others. In the absence of any additional info, it seems safer to me to stick to the annual time scale where things might behave in better accordance with the statistical assumptions.

” it seems safer to me to stick to the annual time scale”
It’s not a matter of safety. The time scale determines the alleged rate of growth of the error. And it’s arbitrary. If it’s safe to gather in years, then it’s safe to gather in decades (if only by summing the years). But you get a different result.

I’ve focussed on this because I think it shows the nonsense of his approach. I actually agree with Annan and the other referees that the errors described just don’t accumulate in the way Pat says. But when folks like Eric think they know all about that, there isn’t much point in pressing that directly. Instead I point to the flaw that I think should be evident to anyone. There just isn’t a proper timescale associated with the alleged accumulation. So they are just plucked out of the air. In an earlier thread Pat was claiming that this physical scale could be justified by the convention of publishing projections annually.

And I did think the sheer nuttiness of claiming that averaging changed the units (sometimes) would strike a chord. But apparently not.

Pat Frank

The periodicity of the global cloud cycle is one year; following the seasonal cycle.

The same annual seasonal cycle forms the rationale for reporting the global temperature as annual averages. The seasonal cycle is finished in a year, and the average annual temperature is representative of the year.

When Jiang, et al, [1] reported their multi-year, multi-model assessment of CMIP5 simulated cloud error, they did so as annual average error, for that reason. The average CMIP5 simulation error in cloud cover was ±12.1%.

Nick would say Jiang, et al. were exhibiting “sheer nuttiness for calling their time scale annual because the per-month average error is numerically identical. So is the per-second average.

Likewise, Nick will have Lauer and Hamilton expressing “sheer nuttiness” for reporting their data throughout as “annual means,” because Nick insists they’re really just monthly means. Also daily means. Also per-second means.

But average annual cloud cover does not change much year-to-year. Jiang, et al., note this, “…no significant trends in clouds and water vapor are found in the model averaging periods. These multiyear means are regarded representative of “recent past climate,” for which our analyses are intended.

Sheer nuttiness, Nick?

A Nick Stokesian diagnosis of “sheer nuttiness” will also apply to Phil Jones, John Kennedy at UKMet, Gavin Schmidt, and Richard Mueller for nuttily representing their global mean temperature records as an annual average.

Their annual average temperature is numerically identical to each year’s monthly average temperature.

Also daily, hourly, and per-second average temperatures, too. Because averaging smooths out the entire duration of the average into a single value at every time-scale.

The way out of the numerical dilemma is to recognize that only the yearly average has useful physical meaning.

What is the meaning an average that supposedly represents an hourly temperature across 365 days when each day varies strongly in temperature across 24 hours, and the hours traverse across months that cycle through the seasons?

What is the physical utility or meaning of an hourly average temperature for a given year?

What is the physical sense of an average that says every month across the year, summer and winter, had an average monthly temperature of, e.g., 12 C?

The only average temperature that makes physical sense is the annual average, representing the full cycle of the seasons. Annual averages can be usefully compared. Each mean samples the entire seasonal cycle of the year.

Annual mean is the only physically rational mean.

The same reasoning applies to mean annual error in simulated long wave cloud forcing. The monthly errors combined into an annual error that samples and represents the entire year.

Cloudiness changes by the day and by the month across the seasons and across the years.

The annual average of simulated cloud error across the cycle of seasons is the only average that makes physical sense.

It is the only average that has any real physical utility for, or applicability to, a multi-year projection expressed in annual steps.

The mean annual simulation error averaged across 20 years smooths out any year-by-year variations.

It provides a useful, physically relevant, model calibration error metric that can be used to appraise the predictive value of an air temperature projection.

And the annual mean average has physical meaning, no matter the other numerical constructs. An annual average error is the only error that can be propagated into an annual time-step.

Nick says the numerically identical monthly error could as well be propagated. And so it could be done, given monthly simulation time steps.

What would be the result? Hugely ballooning uncertainty envelopes. And they would be statistically valid.

However, they’d not tell us anything physically worthwhile because only the full annual seasonal cycle is representative of the range of simulation error produced by climate models.

Nor would their message be novel. The propagation through annual time steps already shows us that climate models have no predictive value.

A monthly propagation would reveal the identical conclusion. Nothing is gained. But physical relevance is reduced.

This kind of physical reasoning is a necessity within the physical sciences and engineering.

Nick has never displayed any understanding of how to think as a scientist. He has displayed no understanding of instruments, or of instrumental resolution, or of systematic measurement error.

And, as noted here, Nick doesn’t know how to extract physical meaning from an average.

And in these threads he’s used a tabular convention to make an opportunistic play that square roots are only positive, not plus/minus.

[1] Jiang, J. H., et al. (2012), Evaluation of cloud and water vapor simulations in CMIP5 climate models using NASA “A-Train” satellite observations, J. Geophys. Res., 117(D14), D14105, doi: 10.1029/2011jd017237.

Pat Frank

Nick, “I actually agree with Annan and the other referees that the errors described just don’t accumulate in the way Pat says.

It’s not “the way Pat says.” It’s the way Bevington and Robinson says.

It’s the way NIST says (see “Propagation of error formula”).

It’s the way every valid authority recommends propagating error through a calculation.

Long wave cloud forcing error is systematic model error. The models inject it into every single step of a simulation.

Propagation of that error is the only valid means of determining reliability of the projection of future temperature.

“It’s the way NIST says (see “Propagation of error formula”).”
What NIST is talking about has no relation to what you are doing. They describe how to combine errors in a composite formula. It uses a derivative to linearise, and then expresses the variance of a weighted sum.

You are talking about the solution of a differential equation, with a driving term. After discretisation, this is a recurrence system in A, which could be linear
A_(i+1) = -S*A_i + f_i
where A is in a GCM a huge vector, S a non-negative definite matrix, and f a vector of driving terms, which in your case could be considered errors. The point is that this isn’t forming a simple sum of the errors f. At each stage, it modifies and effectively reduces the contribution of past f. If S is constant, the i’th terms is
f_i – S*f_(i-1) + + S*S*f_(i-2) + …
And that is what you have to get the variance of.

This is fundamental in de solution, because the condition for stability is that S, as applied, has no negative eigenvalues, and there is some fuss if there are zero eigenvalues. I spent a large part of my professional life dealing with these issues.

Pat Frank

You’re making a simple problem complicated, Nick. GCM air temperature projections are no more than linear extrapolations of forcing. All your vector math notwithstanding.

As linear output machines, linear propagation of error is entirely justified no matter what goes on inside.

In any case, Nick, the NIST site refers the reader to Ku (1960 Notes on the Use of Propagation of Error Formulas J. Res. NIST 70C(4) 263-273.

In that paper, Ku discusses systematic errors. He writes, “When there are a number of systematic errors to be propagated, one approach is to take |Δw| as the square root of the sum of squares of terms on the right-hand side of (2.12), instead of adding together the absolute values of all the terms. This procedure presupposes that some of the systematic errors may be positive and the others negative, and the two classes cancel each other to a certain extent. (my bold)”

Ku there recommends exactly the root-sum-square approach as I took, under exactly the conditions describing GCM LWCF calibration error.

Garofalo and Daniels (2014) Mass Point Leak Rate Technique with Uncertainty Analysis Res. Nondest. Eval. 25, 125-149 recommend propagating systematic (bias) errors through a calculation by means of root-sum-square (rss), which again is exactly my approach. See under 2.4.1 Bias and Precision.

The identical rss approach is recommended to propagate systematic error in Vasquez and Whiting Accounting for Both Random Errors and Systematic Errors in Uncertainty Propagation Analysis of Computer Models Involving Experimental Measurements with Monte Carlo Methods Risk Analysis 25(6), 1669-1681. See their equation 2.

Phillips, Eberhardt, and Parry (1997) Guidelines for Expressing the Uncertainty of Measurement Results Containing Uncorrected Bias J. Res. NIST 102, 577-585 throughout discuss propagating uncorrected systematic bias by various forms of rss.

There’s no way around it.

I misspoke a little there. The conditions I wrote on S relate to the differential equation
This will be unstable if S has negative eigenvalues. The condition for the corresponding recurrence relation is that the eigenvalues of S should have magnitude less than one.

We are with tou Pat Frank.
Corruption is rampant unfortunately.


You mean avec tou 😉


Avec tu?


Or, avec vous. I guess he just split the difference.

Avec toi sounds better.


Oh Pat, it’s just a bad paper. And you know there are plenty of journals out there that will publish something like this (just try one of the Chinese journals, they give zero cares about the American culture wars). So the fact that you keep posting these rejection posts implies that you’re really more after stoking some anti-science outrage rather than just getting the thing out there. Sad state of affairs.

Cheers from a fellow scientist,

M Courtney

That may be true. But the peer reviewer was unable to find a valid criticism.
And nor could his partner.
So you are probably wrong.


The peer reviewer was unable to find a valid criticism?

“The trivial error of the author is the assumption that the ~4W/m^2 error in cloud forcing is compounded on an annual basis. Nowhere in the manuscript it is explained why the annual time scale is used as opposed to hourly, daily or centennially, which would make a huge difference to the results. The ~4W/m^2 error is in fact essentially time-invariant and thus if one is determined to pursue this approach, the correct time scale is actually infinite. Of course this is what underpins the use of anomalies for estimating change, versus using the absolute temperatures. I am confident that the author has already had this pointed out to them on numerous occasions (see refs below) and repeating this process in GMD will serve no useful purpose.”


Just needs to find someone who actually understands error propagation.

So far, its been beyond the reviewers understanding.

And no Chris, that was not pointing out an error, that was pointing out that the reviewer didn’t understand.

underpins the use of anomalies for estimating change, versus using the absolute temperatures.
nope. anomalies reduce the variance of the the data. this reduces the. standard error making the result appear statistically more reliable than it actually is. while at. the same time making natural variability appear smaller than it is.


“The trivial error of the author is the assumption that the ~4W/m^2 error in cloud forcing is compounded on an annual basis.”
trivial error needs no explanation.

“Nowhere in the manuscript it is explained why the annual time scale is used as opposed to hourly, daily or centennially, which would make a huge difference to the results. ”
Indeed. however, obviously, the shorter the time scale, the bigger the resulting error, so taking a year gives a lower bound of the error

“The ~4W/m^2 error is in fact essentially time-invariant”
Nonsense, that contradict the previous sentence. An error is like a profit margin, it is time dependent. 4% profit (or loss!) per hour, day or century are hugely different. Which was precisely stated in the previous sentance, meaning the reviewer contradicts himself.

“and thus if one is determined to pursue this approach, the correct time scale is actually infinite. ”
Please someone explain what “An infinite time scale” is supposed to mean in a time-step modelling process…?
Infinite time beetween two step, that is, a single run, zero iteration in the process? That would be nonsense.
An error that compound to finish at ~4W/m^2 at the end of the simulation (so, something like ~0.004 W/m^2 per step is the simulation has 1000 step) ? Wouldn’t more sense, either.
So, what does this mean?

“Of course this is what underpins the use of anomalies for estimating change, versus using the absolute temperatures. ”
nonsense again. The use of anomaly has just nothing to do with errors. It is a basic linearization technique (… linear system, again…).


Chris, look up the definition of a valid argument. The premise of the editor’s cricism is false. To believe otherwise would be to believe that Pat Frank has no idea what he wrote. So, you think implying Pat Frank makes stuff up is a constructive way to debate or argue?

It is disturbing that the arguments of global warming advocates so often are at root pathetic ad hominem nonsense. Benben’s comment is right in that category too.

I Came I Saw I Left

benben, does exposing the corruption of scientific integrity bother you? If not, why call such efforts anti-science and even bother to comment? Without integrity science means nothing.

Old England

Bebben’s comment suggests to me that he cannot be a ‘scientist’ as he claims to be.

F. Leghorn

Old England on November 12, 2017 at 6:08 am
Bebben’s comment suggests to me that he cannot be a ‘scientist’ as he claims to be.

The standards for “climate scientist” are way different from what you “hard science” guys are used to. You probably don’t even know what the “unicorn hypothesis” is.


It only takes one comment like this to safely ignore anything this person has to say from now until forever.


I imagine somebody with the nickname “benben” in diapers, sporting a silly bonnet, a rattle in one uncontrollable hand and the look of a glazed doughnut.


Agreed menicholas. I’ll add though that confronting and exposing a bully is often the best way to go. Each and every time.

Then, of course, the meme would be that it was published in a Chinese journal, and they will publish anything. Nice try Ben – no cigar. Papers stand on their merits, not reviews by conflicted editors/reviewers.

Cheers from a fellow scientist,

Louis Hooffstetter


What are your credentials and experience as “a fellow scientist”?
I just want to make sure we all understand which orifice you are talking out of.

Pat Frank

benben, “Oh Pat, it’s just a bad paper.

Mount your criticism, benben, “fellow scientist..” Bet you can’t do it.

Your silence will fully tell your vacuous tale.


Pat, I think benben is still trying to master his rattle.

Louis Hooffstetter

As Pat suspected, benben proves himself to be a cowardly troll.


There’s only one word for this: CORRUPTION OF THE SCIENTIFIC METHOD.

When I think about how the Climate Model Intercomparison Project CMIP5, it occurs to me that the exam for models gives a clue about which models were selected by IPCC:
«RCP8.5 is a so-called ‘baseline’ scenario that does not include any specific climate mitigation target. The greenhouse gas emissions and concentrations in this scenario increase considerably over time, leading to a radiative forcing of 8.5 W/m2 at the end of the century. While many scenario assumptions and results of the RCP8.5 are already well documented, we review in this paper some of the main scenario characteristics with respect to the relative positioning compared to the broader scenario literature. In addition, we summarize main methodological improvements and extensions that were necessary to make the RCP8.5 ready for its main purpose, i.e., to serve as input to the Coupled Model Intercomparison Project Phase 5 (CMIP5) of the climate community. CMIP5 forms an important element in the development of the next generation of climate projections for the forthcoming IPCC Fifth Assessment Report (AR5).»

The CMIP5 was not exactly a blind test, the expected radiative forcing wase given in the task, like:
Given that the expected output is 8.5 W/m2 at the end of the century, for the inputs provided in this task that is called: “RCP 8.5”. What output, in form of radiative forcing at the end of the century, is provided from your model at the end of the century?

Jane Rush

What are James Anan’s qualifications then? His partner Julia lists hers prominently on their Blue Skies website but nothing for him that I can see. Given his mistakes, I am curious as to what they are.

Julia Hargreaves are:
Institute of Astronomy & Corpus Christi College, Cambridge University, UK, 1991-1995
PhD in Astronomy and Astrophysics, 1995. Mass-to-light ratio of dwarf galaxies.

The Queen’s College, Oxford University, UK, 1988-1991.
BA in Physics (Class 2:1), 1991.

Adam Gallon

Helps if you spell Annan correctly, then a quick Google. He has a D.Phil from Oxford, he’s a mathematician.

Clyde Spencer

Adam Gallon,

I see that they are both relatively ‘newly minted,’ and trying to get a reputation. They frequently co-publish, raising the question at to whether the two of them carry any more weight than any one of them publishing singly.

It seems that mathematicians are typically used to dealing with exact numbers. Thus, they are not focused on how uncertainties can affect their results. “Out of sight, out of mind.”


Thank-you Patrick you only re-enforce my understanding that the climate models are nothing more than a circle-jerk routine for wannabe statisticians and math students out to make a name for themselves. Science it is not!

As I have said before (

I feel that Their models are a tragedy of incompetence. They have all the predictive value of homogenized astrology readings. If the GISTemp model (see ) is a good example then it is just a chaotic morass of unphysical, unscientific, codified guesswork, inaccurate estimations, and data manipulations. You might as well read tea-leaves!
Anyone here who works on these nonsensical models should be ashamed. Ashamed for taking money under false pretenses.

Louis Hooffstetter

tom0mason nails it!


Exactly right…incredibly expensive, wildly elaborate, amazingly detailed wild ass guesses…all the way down.
Some of us have come to this conclusion over time…and some of us have known it right from the very start.

M Courtney

The journal has remained silent as of 11 November 2017.

In fairness, it is the weekend.
This may not be over…

Well done Pat, the corrupt ‘pals review’ system needs outing.

Keep at it & Illegitimi non carborundum

“None of these people are scientists. None of them know how to think scientifically.”
That’s seven journals, now. And must be about 30 reviewers. On would have to entertain the possibility that they are right and Pat Frank is wrong.

Of course anything is possible. Taking into consideration the damage rampant conflict of interests can inflict internally, it’s much worse where you stand. Pity you didn’t see it.


“Taking into consideration the damage rampant conflict of interests can inflict internally, it’s much worse where you stand. Pity you didn’t see it.”

It’s a pity you don’t see the possibility it’s just a bad paper. Oh, you say “anything is possible”, but that’s a throwaway concession.

Mark T

It is a pity that neither of you can offer a valid criticism, either. Yet still you both beat your drums.

” neither of you can offer a valid criticism”
I have offerred plenty. You might like to explain this one
“How does it happen that a PhD in mathematics does not understand rms (root-mean-square) and cannot distinguish a “±” from a “+”?”
Do you think rms is a “±”? Do you know what he is talking about here?


I am curious where you are going with that one Nick … RMS is just a form of average hence the mean in the value. You seem to be implying that +- is not possible and if that is what you are implying let me give you a warning by example

USA you have 120 VAC voltage, Australia has 230 VAC both are RMS numbers. The voltage range is still quoted with a plus and minus

120 V and allow a range of 114 V to 126 V (RMS) (−5% to +5%)


230 V as the nominal standard with a tolerance of +10%/−6%

If you are implying it can’t go negative you probably need to withdraw your statement.

M Courtney

A root mean square is not ±. They are two different things. And neither is a +.
But taking the rms will lose the sign of the original factor. Re-read the article and it does make sense.

You are giving the impression of wilfully missing the point.

Surely Nick, you don’t really think that a calculation error, which can be positive or negative, will propagate in the same way as an error that only goes one way?
More importantly for climate science, does your partner agree with you?


I must say M Courtney I read Nick’s answer the same way and couldn’t believe he thought the square root somehow magically got applied to the systemic error to make it only positive. So you obviously got what I did from Nick’s comment.

” Re-read the article and it does make sense.”
Please explain that “sense”. RMS is a magnitude. It is positive. You square the voltage to make it positive, and then take he positive square root of the mean.

And LdB, you may have 120±something. But you don’t have ±120.

And LdB, you may have 120±something. But you don’t have ±120.

Hmmmn. Last time I measured an alternating voltage, I did measure +120 volts, followed shortly therefater by -120 volts, followed shortly thereafter by +120 volts … Never did measure a sq root of -1 either, but I know it exists.


I agree with that Nick and if you had stated it that way it would have made sense. The whole “+” sign in your answer is very confusing as no-one would ever put it in front of an RMS value so you lead us to think you must be talking about the error.


Can I ask one other question Nick on your response above, the author describes

4W/m^2 error in cloud forcing

So is your contention that 4W/m^2 is the constant presumably with some smaller error tacked on the back?

“The whole “+” sign in your answer”
It’s not my answer. I was quoting Pat’s article. As to what the 4 W/m2 really means, you need to go to the source paper, which is Lauer and Hamilton, 2013.

Yes Chris and Mark. Some are willing to entertain the idea CO2 warms the outside air. Accepting that level of probability, anything is possible.


Poor Nick. you are showing just how out of your depth you are.

RMS does not have a sign. It is a magnitude that can be in either direction.

Stick to basic mathematics, Nick…. no need to actually UNDERSTAND.


Just like saying that a sin wave has an amplitude of +1 is nonsense.

It has an amplitude of 1 which can be +1 or -1.

Sorry if basic comprehension of reality is beyond you, Nick.


Nick Stokes: “Do you think rms is a “±”? Do you know what he is talking about here?”

Nice try Nick, but you and I both knew he was giving us a list of two separate issues.

Back to the substance …..


“Do you think rms is a “±”?”

Nick, do you think it is NOT a “±”


Is your comprehension that seriously lacking ???


RMS = Root Mean Square.

Nick when you take the square root of a number , it is ALWAYS “±”

Basic junior high school stuff !!

“but you and I both knew he was giving us a list of two separate issues.”
Really? What are they?

“when you take the square root of a number , it is ALWAYS “±””
No. 2 is a square root of 4. -2 is another. RMS is the positive square root.




RMS is a magnitude.

It does not have a + or –

Where did you NOT learn your maths???

You seem to have a very simplistic comprehension of what anything actually means.

ZERO sense of any actual physical understanding.


Only when a number is given a direction does it become + or –

RMS can be either


You put a trend line through some numbers, then calculate the RMS error.

Are you saying the RMS error is always +ve and thus all errors are on one side of the trend line?

You truly are a mathematical INEPT !!


In this context, RMS error (magnitude ⸫ no sign) exists in BOTH + and – direction.

Get over it, and try to get some basic physical comprehension of what you are talking about.

The classic RMS is standard deviation. It is always positive.

I would invite anyone to find any reputable publication that shows a negative or ± RMS. Anywhere.

Is is a coincidence that the only people confused about the sign of RMS (apart from Pat Frank) come from the land of AC/DC?


Nick Stokes in response to my ‘but you and I both knew he was giving us a list of two separate issues [RMS and ±]’:

“Really? What are they?”

Now back on the earlier WUWT thread you were donkey deep in a discussion with Pat Frank about RMS calibration error statistics, and how this was not an energetic forcing statistic. The point he repeats above.

He separately makes the point that “±” isn’t “+”.

Now I could follow that, and I wasn’t even party to the earlier conversation.

As I said, “Nice try Nick …”

Can you get back to the substance?

“He separately makes the point that “±” isn’t “+”.”
Separately? With respect to what, if not rmse?

As to substance, the key is not so much his addition of a ± to the 4 W/m2 found in L&H but the extra adornment of a /year in the units. This is on the basis that if you average something over 20 years, the average acquires a /year unit. I think that is nonsense, but a critical immediate point is, why /year. Why not /month or /decade. Any ideas?


He separately makes the points that

(1) there is a difference between applying a + to a RMSE and applying a +/-
(2) there is a difference between the way you should treat calibration errors and forcing statistics

The substance of the first comes down to how you are using the statistic, and the second is how you treat an annual error if you are propagating errors in a simulation. (The per year bit is trivial, the statistic is derived from annual means).

Nick’s purpose here seems to be drowning the fish mostly. Pat provided evidence for a conflict of interest case. As the result Copernicus Publications has similar minority interest value as The Watchtower.



“The classic RMS is standard deviation.”

Which is ALWAYS “±” about the mean. Thank you for CONFIRMING THAT POINT.

You seem to be bathing in your IGNORANCE between magnitude (which is signless) and applied direction.

I can only assume you skipped basic mathematics in high school.

“Which is ALWAYS “±” about the mean”
Ask the 6σ people how ± they feel.

“The per year bit is trivial”
It isn’t trivial. It is the crux of the case. The units given there determine how many steps per unit time are taken in the random walk, and hence how fast the errors grow, in Pat’s model. It determines the time scale in a propagation model that otherwise has none.


RMS and RMSE are +/- because they are merely sample standard deviations. Just like all standard deviations, they become meaningful once an assumption is adopted concerning the nature of the distribution of the underlying population.

If the population under study is distributed Normal, 68% of the population will fall within +/- 1 standard deviation of the mean. Given the article quote Nick provided, +/- 4 reflects an estimate of the population standard deviation of the predicted variable which in this case id the observed values. The RMSE applies to each value of the predictor variable which in this case is the mean predicted value from a bunch of different models.

In the propagation formulas i have seen, one would divide the +/-4 by the root of N. If the values are annual scores, then N would be the number of years. This resulting standard error would then plug into the formula for error propagation. The formula ends up depending on the equation or function you are using to generate nrw numbers with (i.e. Pat Frank’s neat linear model that closely approximates the climate model output).

“RMS and RMSE are +/- because they are merely sample standard deviations”,/i>

So how do you do a one-tailed test if σ is ±1?


“Ask the 6σ people how ± they feel.”

That is probably the WEAKEST, most moronic thing you have said all post.

Maths isn’t about “feelings” NIck.

Seem you are destined to stay in the -3σ group.

You keep digging your ignorance deeper and deeper.


“So how do you do a one-tailed test “

You really are showing your ignorance, Nick

You CHOOSE which of the + or – tails you wish to test.

But according to you, a two tail test cannot exist, because σ is only positive.

And you are telling everyone that -σ does not exist.

You are getting DUMBER and DUMBER, Nick.. heading rapidly for DUMBEST !!!

“Maths isn’t about “feelings” NIck.”
But 6σ is.

Pat’s point is very simple. The error produced by each model iteration step is a random walk. Pat has calculated the approximate magnitude of each step of that random walk, and used that calculation to try to determine how the random walk will cause projected results to wander away from reality over time. The result is the joke size range of possible projections Pat has produced.

Count to 10

I’ve been having trouble following the argument here, but if you are right, that clarifies things. The original model has an uncertain “forcing” that is fixed as a constant at the beginning of each run (or “realization”). The author’s criticism is that the forcing should be re-randomized within its uncertainty each year. The reviewer’s criticism of the author is that a year is an arbitrary time to perform that randomization.
The original model assumes the uncertainty in the forcing is our ignorance of the true value of a physical observable that does not change over time, while the author interprets that uncertainty as a year to year variation in the physical observable. This would actually be an entirely valid reason to reject the paper, since these two things are completely different. To publish the paper, the author would have to justify the year to year variation separately, because his whole argument depends on that interpretation.

Count to 10 on November 12, 2017 at 9:04 am
yes. the error. propagation is cycle dependent and thus becomes time dependent because each. cycle has non zero finite time.

as such the error would be like compound interest. 4% annual compounded daily for a model that cycles 1 time per. day.

or more likely 4% compounded daily and ignore the annual completely.

Count to 10 I checked with Pat, he is happy with my use of the phrase “random walk”, though he cautions not to assume the error averages to zero over time.

F. Leghorn

I don’t know about the other journals but this one stinks to high heaven. The arrogance and bias in Anan’s and Hargreaves words come through quite clearly.

Even great papers were rejected by peer review Great papers, in real sciences. The situation is incomprehensibly worse in cargo cult sciences, in post normal and post modern sciences.

Yeah, I know, pseudo scientists will think of their favorite pseudo science as being as scientific as, let’s say, physics and think of their 95% ‘certainty’ as equal with the five sigmas of, let’s say, particle physics. And of course they will think that statisticulation and a little bit of pretending to have rational thinking by using logical fallacies in their ‘inferences’, or simply the principle of explosion in their ‘scientific’ method is enough to pretend to be a science.

What would one expect when even in physics there are attacks against falsifiability nowadays?

This is why engineers make better scientists. In engineering, not only do you have to understand the science, you need to understand it well enough for whatever it is you are engineering to actually work.

I Came I Saw I Left

“That’s seven journals, now. And must be about 30 reviewers. On would have to entertain the possibility that they are right and Pat Frank is wrong.”

That’s certainly possible, but IMO to be considered even reasonably intelligent one also would have to entertain the possibility that there is systemic corruption in the industry. And that the benefactors of said corruption would take a negative view of their profiteering being threatened via of exposure.


Until someone points out the errors in the paper, I’ll go with Pat Frank is right.


“That’s seven journals, now. And must be about 30 reviewers. On would have to entertain the possibility that they are right and Pat Frank is wrong.”

I suppose he could just go to some snarky lowrent overseas journal and pay them to publish…..

Louis Hooffstetter

Nick: Dr. Richard Feynman on how science works:

“In general, we look for a new law by the following process: First, we guess it, no, don’t laugh, that’s really true. Then we compute the consequences of the guess, to see what?, if this is right, if this law we guess is right, to see what it would imply and then we compare the computation results to nature, or we say compare to experiment or experience, compare it directly with observations to see if it works. If it disagrees with experiment, it’s wrong.

In that simple statement is the key to science.

It doesn’t make any difference how beautiful your guess is, it doesn’t make any difference how smart you are, who made the guess, or what his name is If it disagrees with experiment, it’s wrong. That’s all there is to it.”

For more than three decades, the projections of climate models have been negated by reality. They have proven to be less accurate than a monkey randomly flinging his poop at a wall of climate projections. So Dr. Frank is absolutely correct in saying “None of these people are scientists. None of them know how to think scientifically.” Having an advanced degree does not make you a scientist. To be a scientist, you must follow the scientific method. Climate modelers obviously don’t.



“Having an advanced degree does not make you a scientist.”
Showing a Youtube of Feynman doesn’t either.


I have often wondered what would happen if these computer model projections were run with the alleged warming effect of CO2 removed. Let us assume that the warming effect of more CO2 in the atmosphere is non existent and run the models on that basis just to see what happens. Surely it would be easy and inexpensive to do it and If the projections produced were closer to reality that would be quite a significant discovery. My guess is that they have already tried it and are too terrified to let on. “You know all that money that you spent trying to reduce emissions because we said that it was a massive problem? Oh well, our bad, turns out it isn’t a problem after all, not even a little one.


..but the advanced degree helps in recognizing the significance

“I have often wondered what would happen if these computer model projections were run with the alleged warming effect of CO2 removed.”
That is usually the first thing they do. It’s called a control run. Attribution of CO2 effect is worked out as the difference with CO2 present and absent.


Showing a youtube video of Feynman doesn’t make one a scientist, but it at least shows that you acknowledge what science is. Doing something other than what Feynman describes in the video and proclaiming it is science, shows that you don’t know what science is, or you do know, and are lying.


“I have often wondered what would happen if these computer model projections were run with the alleged warming effect of CO2 removed.”

They do almost nothing. With the CO2 levels unchanging, the models are quasi-stationary. There are no significant changes in climate ever if CO2 does not change. That fact alone falsifies the models. CO2 levels have been relatively constant for the last 5 million years, while climate has been significantly more variable than CO2. All physical evidence (science) indicates that the minor changes in CO2 levels that have occurred over the last 5 million years have been driven by temperature, not the other way around.


^ what jclarke just said…..+1

old engineer

On stoneyground’s comment about running the model without CO2. Nick Stokes is right. The control run is most often the first thing that is done. For instance see Figure 1. of Hanson’s 1988 paper. It is very interesting by the way, as it shows cooling from about 2010 to 2040.

old engineer

of course that should J, Hansen’s 1988 paper..

As Roy Spencer puts it. “95% of the models agree. The measurements must be wrong.”

Clyde Spencer

Nick Stokes,

By your own admission, numbers count. You routinely get a drubbing for your comments and analysis on this blog. You should entertain the possibility that the commenters here are right and that you are wrong.

Another possibility is that the conflict of interest is so entrenched in the lucrative publishing business that they have a vested interest in keeping the gates closed to gad flies.

“Another possibility is that the conflict of interest is so entrenched “
Even Ronan Connolly?


Every religion has it’s “peer reviewed” holy book. Every religion has an overwhelming majority consensus that it’s holy book is correct and also that the religion itself is correct. But all the religions contradict each other. That’s why they are called religions and not science. Religions can neither be proven right or wrong.
Science is based on hard numbers, facts and predictions that have means to be proven wrong. Peer review is only a form of error correction, it doesn’t prove that a paper’s thesis is right or wrong, only that the proof given is consistent with the known laws of nature and is logically consistent. It’s not an appeal to authority. Just because an eminent scientist hasn’t found a mistake in a paper doesn’t make the paper correct. Computer programs are regularly peer reviewed, yet programs still crash and are hacked. A million tests can be run successfully only to have a failure by a single wrong bit in the input data.
Climate “science” does not have a mathematical basis, ignores the laws of thermodynamics and relies only on consensus and various versions of it’s holy book, the IPCC report.
No climate scientist can come up with a proof of how CO2 will affect temperature using known natural laws. No climate scientist can come up with an average global temperature using known natural laws. It’s not even possible for a climate “scientist” to demonstrate the effects of CO2 on temperature using experimental techniques without resorting to fraud.
Until climate “science” has a solid basis mathematical basis like physics, it will remain forever a religion, forever argued over and forever unprovable, but with lots of peer review and a very robust consensus. Praise be to the IPCC and death to the heretics.


I have entertained the idea Franks is wrong, and yet his reasoning seems far more sound than the repeated insistence by modellers that error has no time dimension and does not propagate. Like Pat says, this is not physics. The models might be mathematically interesting, even useful in some contexts, but they are not physics.

And as the old saying goes, what makes physics more interesting than other pursuits (like, say, abstract mathematics) is that physics actually describes the world around us.

It’s almost as though modellers have enormous incentives to ignore/misunderstand the problem…

Pat Frank

talldave2, see the email below I received from Dr. Didier Roche, who was assigned by the journal to re-evaluate Dr. Annan’s decision to deny review.

It is a study in ‘find some reason, any reason, to reject.’

“Today’s offering is a morality tale about the clash of honesty with self-interest, of integrity with income, and of arrogance with ignorance.”

I noted that one of the reviewers of the paper for Earth Space Sciences was none other than Dr Ronan Connolly. Pat Frank made the reviews available in the previous post; the link is to here. Dr Connolly made a point of identifying himself. Dr Connolly, an independent scientist, will be known to WUWT readers through his frequent contributions here, often co-authored with Andy May; the lastest was in August. He gave a relatively sympathetic review, citing Koutsoyiannis, and Willie Soon. He thought radical changes were needed, and was somewhat doubtful that they would be made, but he said the paper might be publishable if they were.

The response at that stage was firstly a blast for not remaining anonymous, and then the usual listing of reviewer errors, eg
“The reviewer’s recommended major revisions are misconceived and, if followed, would leave nothing publishable”
And so, of course no changes were made.

Dr Connolly was not impressed. He recommended rejection, noting among other things:
“Despite this, the author has decided to resubmit his rejected manuscript to ESS essentially unaltered, albeit with some small changes addressing a few minor technical points and typos identified by the reviewers. Instead of attempting to modify his manuscript in light of the major criticisms made by all five reviewers (including myself), the author has chosen to write lengthy responses to each of the reviews claiming that they: “[have] no critical merit” (“Review #1”); “[are]…misconstrued… mistaken…[and] confused” (“Review #3” and “Review #4”); “fundamentally misguided” and unable to “[survive] critical scrutiny” (“Review #5”); as well as involving “the mistake[s] of a naive college freshman” (“Review #6”).

Well, Dr Frank was not impressed either. He wrote in response:
“This review is no more than a disgraceful polemic. The editor would have done better to exclude it on the grounds of bringing ill repute to the Journal. “
A few of his summary points:
“Summary Response:
This review:
1. Is analytically vacuous throughout
2. Inadvertently validated the manuscript study (items 7.2.2, 7.3.2)
3. Was expressly dishonest (items 1.3.1, 1.3.2, 1.4, 1.5.1, 1.5.2, 2.1, 3.2.1, 5.2.1, 6.9,, 9.2.4, 12.8, and 12.9)”

etc (11 rather similar points in all)

Then a detailed list starting with
“Unnecessary and shallow introductory complaints are deleted. However, certain points of critical failure or dishonesty require attention.”

And the list enumerated many points of Dr Connolly’s alleged dishonesty.

Now Dr Connolly is indeed an independent scientist, who certainly has no financial interest in trying to suppress Dr Frank’s theories. Yet he is bundled in with the rest.

And FWIW, I agree with Dr Connolly.

Like I said, Pat’s point is simple. The systemic errors are effectively a random walk, in terms of our ability to predict them. Therefore the errors accumulate over time. Pat estimated the approximate magnitude of the random walk step at each iteration of the calculation, and used the model calculation itself to determine how far the projection could drift from the correct value, because of this random walk of errors. Pat’s calculation show that the drift occurs very rapidly – that the models are unphysical.

Errors in such a non linear system do not accumulate as steps in a random walk. They are amplified and explode exponentially.

Gerry Parker

And yet, the models do not correctly predict the future.

How do you know?

Mark T

Because they haven’t.

Mark T


M Courtney

But they will in the future. You need to have faith.
That is the error in this paper that prevents its publication.
It deals with physics. When climate science is a branch of theology.


We have no idea if the models correctly predict the future. To date, they have failed to do so. We haven’t seen the future, so we don’t know if the models are right or not. That being said, we also have no reason to heed the models. Random modeling would probably produce equally accurate results. Without predictability, the models do us no good.


How do you know?….

…by their own admission they have to leave out too many things that are not “understood”

I Came I Saw I Left

Actually, we have an excellent idea if the models correctly predict the future, The future is now – for their many prior predictions that have not happened up to now. That destroys any confidence in their ability to predict beyond this point.

Heh, not only is the future now, the future was also yesterday; given the track record.

One very glaring assumption, which has not been shown to be true at current conditions, is that the heating (increased internal kinetic energy) from shining a strong light on a bottled gas in a lab will carry over to the far less constrained open atmosphere.


“How do you know we’re wrong?” seems to be the basis of the entire multi-trillion-dollar global policy consulting racket.

Well, Pat just explained how. Welcome to physics.

Mike Maguire

“I have often wondered what would happen if these computer model projections were run with the alleged warming effect of CO2 removed.”
That is usually the first thing they do. It’s called a control run. Attribution of CO2 effect is worked out as the difference with CO2 present and absent.”

Actually Nick, you’ve identified the exact problem. Since we don’t have a smoking gun to show what else it could be……….it must all be from CO2. Since no other factors can be identified and represented in model equations(from natural processes, for instance, that we know with certainty have had a powerful influence in the past-Medieval Warm Period-Little Ice Age for instance) the only way to get warming is to use, not just CO2(if we just used CO2 and it’s logarithmic effect on temperatures as it increases-that would not do it) but to use additional positive feedback equations from the increase in H2O……..based on a speculative theory that exists because we don’t know or at least can’t model the true effect of anything natural.

We can’t even correctly model the projected positive feedback from increasing H2O which includes more low clouds. This blocks the more powerful SW radiation of the sun, especially when the sun angle is high in the sky(and has the most heating power). So a powerful negative feedback has tremendous uncertainty in the models.

Instead of knowing the real reason for all the warming, we find the right equations, using CO2, then add the right positive feedback equations to get the desired result.
Comparing that to control models that have variations that don’t yield as much warming does not tell you that your equations accurately represent the actual processes in your simulation.

If I have a known product in a simple math addition problem that comes to 100 but don’t know the actual numbers which were added to yield 100, I can make up whatever numbers I want to get to 100. They don’t have to represent the real ones.
Maybe a climate modeler has some clues on some of the real numbers/equations that can be justified(like the physics of greenhouse gas warming of CO2). When that gets them part of the way to the solution, climate modelers look for additional equations(like those that represent positive feedback from H2O) to amplify the warming. When the solution(s) eventually match up to the desired warming……….that is not verification of anything except creativity in using mathematical equations that result in X amount of warming.

How can one have a 95% certainty level for a specific range with modeled data projections when much of this is just a guessing game?

And increase the certainty level after the models prove to be too warm?
A big element of certainty that we know about climate models so far is this: They have been too warm but are not being reconciled in timely fashion. Instead, mainstream climate science defends the indefensible.
Change the equations(guesses) so that the global temperatures are actually tracking close to the global climate model ensemble mean much of the time, with close to equal time below and above it.

Right now, the only time the global temperature can get to the model mean is at the top of an El Nino spike. Ignoring this is blatant bias and using the model for something other than science.




Ronan Connelly, is he the one that proposed a new phase in the atmosphere? On the whole I think the other member of the Connelly clan, yes Billy is the one that talks most sense

terra non firma

Climate Modelers make one overwhelming error: They can not realize that complex systems can not be resolved with complicated tools. They ought to study complexity-theory.

Ed Zuiderwijk

‘None of these people are scientists’.

The word you are looking for is ‘quacks’.

I had a similar problem. Couldn’t publish as the editor wanted keep a grub happy. Nothing to do with climate science or money, just personal.
When I pointed out how silly the objections were, including that not only did I consider something I’d supposedly hadn’t, there was a section with a title that was very explicit. The editor gave it back to him to review. Rejected because of grammatical errors like writing has been instead of had been.

The errors are effectively a random walk. Over time the random walk of errors causes the model to drift away from reality. Pat demonstrated that the period during which the models could be considered reliable is impractically short – the accumulation of errors rapidly renders the projection useless.

What is so difficult to understand?

The is no fudge factor which can be applied to correct the error, because we can’t predict what the error will be. The best which can be done is to determine how quickly the error undermines the usefulness of the model projections – which in this case is almost immediately.


“…the accumulation of errors rapidly renders the projection useless.” Yes. This was the main criticism of the models back in the 80’s. It is still the main criticism of the models today, and is basically the essence of Dr. Franks paper. But climate science took a turn away from science back in the 80s, and created a self-fulfilling prophecy, pretending it was science.

Nick Stokes summed it up nicely above, when he said: “It has long been understood that chaotic processes cannot for long be determined by their initial conditions. So climate modelling focusses on the attractor, which is approached independently of starting point.”

So what is the ‘attractor’ and what does it mean to ‘focus’ on it? It is none other than the CAGW theory itself! It is the assumed climate sensitivity of atmospheric temperatures to increasing CO2! Focusing on the assumed climate sensitivity simply means determining the temperature increase from our assumed energy increase, with all else being quasi-equal. The climate sensitivity was tuned by selecting a period of warming and assuming that the warming was entirely man-made. No other period of time would lead to such a high climate sensitivity. In fact, a similar time period immediately preceding the one selected, would have given a climate sensitivity of zero, or even negative.

Natural climate variability in the models is limited to volcanoes and the tiny changes in total solar irradiance. The calculation could be done on the back of an envelop. The models will always reach that same answer no matter what, since that is what they focus on. Exactly how they reach it can vary depending on the tweaks and nuances in the individual models, but they are all focusing on the ‘attractor’, and will get to it sooner or later. They cannot do otherwise.

The models are programed to reach the initial assumption. When they do, they are used as proof that the initial assumption was correct. What would you call that? I certainly wouldn’t call it science.


If they had used the previous 30 years….they would have shown temps falling


I thought that chaotic climate systems could have more than one attractor. If GCMs only consider one attractor, doesn’t that cripple their ability to have free reign in modeling reality?


noaaprogramer – you are assuming that the goal of the models is to model reality. That is not the case. The goal of the models is to model a man-made global warming crisis. The IPCC was tasked to find the human impact on climate. The IPCC has virtually ignored natural climate variability, aside from the most rudimentary understanding of it. While we have tons of historical and geological evidence that natural climate variability is robust and very significant, there is no attempt to understand or quantify it in mainstream climate science. In fact, there has been a significant effort to deny that it even exists.

One cannot begin to model reality if you refuse to even look at it.

Count to 10

So, it looks like the proble is that the quoted “error” he is quoting reflects the measurement uncertainty in a quantity that does not vary over time (in the model), but he is propagating it as if it were the yearly variation of a well known quantity. His paper is basically a lot of mathematical extrapolation from the single assertion that the uncertainty of a constant is actually the yearly variation of a parameter.
The bulk of his paper should actually be about justifying this assertion, and no journal should accept the paper without that justification.

The paper contains a justification of why the error is unpredictable and systemic. I confirmed with Pat the error functions as a random walk in terms of model ability to make reliable predictions. Each iteration of the model the error introduces a random walk drift. This random walk drift then forms part of the input for the next iteration.

The fact that model hindcasting sort of works despite the error simply demonstrates the models have been fitted to past data. The measured magnitude of the error and its impact on projected values means future projections rapidly tend to nonsense.

Louis Hooffstetter

“The fact that model hindcasting sort of works despite the error simply demonstrates the models have been fitted to past data.”

Yes, and that’s called CHEATING! Yet I’m amazed at how proud these witch doctors are of their ability to cheat!

Google ‘Climate Model Hindcast’ and check out how many papers trumpet the fact that climate models can spit out the right number when the modellers know what the number is supposed to be.


Eriv, so the errors are random because the target is moving? So some years more global cloud cover than others? Correct?


I do not suppose ,That its possible for Mr Trump Could publish it?

John Bills

I sure think Nick Stokes is a quack.
The state of climatescience in 2017:

Bill Illis

Even the CERES satellite is missing about 4 W/m2 of energy flows somewhere.

They just adjust ALL the numbers until they get something like the assumed annual energy accumulation rate (well, they use Hansen 2005 estimate of 0.85 W/m2/year which is not even the real measured number which is about 0.6 W/m2/year).

In climate science, you just adjust everything until it gives you what you want. It doesn’t have to reflect reality or even a known measured number, just whatever you want it to be.


ranting article, that is too long because it tries to adress too many issue.
“interest conflict”? Well, peer-review is all about asking permission off people that already are deep entrenched in the field, have reason to think they know (like: being asked to teach) and obviously will find YOU are mistaken if you try and show them wrong. You are the pupil here. Ever tried to show your teacher wrong? Only works with the best of the best; for all practical purpose, never works.


That sounds like the very basis of the lie “the science is settled.”


Not exactly. the peer-review system allows incremental additions to knowledge, it works provided the basis is solid and the whole science building is known to be “work in progress”, so peers welcome any addition (no threat to them) .
Unfortunately CAGW doesn’t have solid basis, and “the science is settled.” meme implies no work is needed anymore, so …

Louis Hooffstetter

Peer-review is like Socialism in that it sounds like a great idea but turns out to be a complete disaster when it is actually implemented.


@ paqyfelyc: Even in areas that have a solid foundation like mathematics, politics are involved in who gets published, who gets appointments, etc. Take for example Kronecker’s rejection of Georg Cantor’s revolutionary ideas in set theory, diagonalization, hierarchies of infinities, etc. all of which became mainstream.


@ Louis Hooffstetter
i agree. It lacks a destroying process, a review system where you don’t get points (fame etc.) when you get citations, but when you destroys peer papers for being wrong
@ noaaprogrammer
i agree, in fact. peer-review is a filter, and as such often turn “false positive” (accept bullsit or unworthy trivial results ) and “false negative” (reject good stuff, often for petty reasons)


Dr. Frank,

Can I suggest that you submit the paper to a post-publication-review journal such as PeerJ? They take papers in the Environmental Sciences. They are a well-respected journal (at least in my field), with a respectable impact factor. The paper is published as a preprint, and then allows the review process to be conducted openly and publicly, as well as encouraging wider public comment both on the paper and the reviews.

If your problem is with the reviewers, then maybe let the reviewers be reviewed at the same time as you are?!

Just a thought…

(I declare I have no CoI in this message)

Gerald Machnee

**“None of these people are scientists. None of them know how to think scientifically.”
That’s seven journals, now. And must be about 30 reviewers. On would have to entertain the possibility that they are right and Pat Frank is wrong.**
The Hockey Team and pal review is large.


No matter whose scientific arguments are possibly correct, the one overriding factor here is an obvious conflict of interest from the top. To me, this known quantity alone makes any judgments inevitably biased and therefore invalid.


I was interested enough in the origin of the Journals and the EGU (European Geosciences Union) to look a bit further and found that a number of open access journals are published under their aegis . I spent some time (which should have better employed tidying up the garden) browsing through some of the articles , in “Climate of the Past” and “Nonlinear processes in Geophysics ” from which I found that the surface mass balance of ice in the Antarctic has apparently been increasing in recent years (well to 2010) and that hurricane statistics in the Gulf and surrounding ocean are best described as being “on the edge of chaos” . Don’t know what that means but pretty sure it is not the model that Al Gore and the BBC are putting out.
One that rather destroyed the image of climate scientists being motivated by less than honest or altruistic motives is one which describes the cyclical changes in a simple (the authors call it a “toy model”) ocean + vegetated land model. Something like sawtoothed ice ages result . However in their conclusions the authors are refreshingly and rather charmingly self effacing :

“-Our paper is only trying to make a case for the possibility
of vegetation playing a more important role than contemplated
heretofore and does not claim in the least to have
definitively proven that this is so. A similar argument about
local versus global effects has been made with respect to
the oceans’ thermohaline circulation. Recall that the Stommel
(1961) paper – much quoted recently in the context of
multiple equilibria and symmetry breaking in the meridional
overturning of the Atlantic or even global ocean – was originally
written to explain seasonal changes in the overturning
of “large semi-enclosed seas (e.g. Mediterranean and Red
Seas)”; see, for instance, Dijkstra and Ghil (2005).
There is no better way of concluding this broader assessment
of our toy model’s results than by citing Karl Popper:
“Science may be described as the art of systematic oversimplification”
(Popper, 1982). It might be well to remember this
statement, given an increasing tendency in the climate sciences
to rely more and more on GCMs, to the detriment of
simpler models in the hierarchy.”

” science as the art of systematic oversimplification ” – another Popper phrase to add to those people here like to quote.

R. Shearer

Is a $10 million lawsuit in order?


I’ll comment here rather than your recent post on your paper. The main contention in it is that the models are effectively mathematically equivalent to a linear sum of forcing that is then iterated. There may be a few noise terms in there but this is the point in general. From here it’s easy to show that the uncertainties will compound i.e. the increasing systematic error envelope.

So the question is: can this equivalence be shown from first principles? As in is it in the design itself rather than just being similar in form? Because as someone who has built models before, and dealt with modellers, there may be a pedantic point to say the models are not linear sums even though they produce behaviour like it.

It’s a nuance point but it’s also a niggling one that means they can easily dismiss what you say.


The design replicates linear sums quite deliberately. As I have said before , replace all variables with the timetables of London buses, leaving the forcing intact and you end up with the same answers ( and errors).
Its numerology, GIGO, call it what you want, its nothing to do with science.
And people like Nick are so proud/bemused by their ‘shiny complicated models’ that they don’t realise it. And those that do, stay dumb because their noses are in the trough.


I went and searched for “climate model mathematics” and came across :

MATHEMATICAL MODELS OF LIFE SUPPORT SYSTEMS – Vol. I – Mathematical Models for Prediction of Climate – Dymnikov V.P.

Equation (1) in this short article (that is taken from a book) is that most if not all climate models can be reduced to a canonical state:

∂φ/∂t + K(φ)φ = −Sφ + f


Here, φ is the vector function
characterizing the state of the system, φ ∈ Φ; Φ is the phase space of the system which is
regarded as a Hilbert space with the inner product(⋅,⋅); ƒ is the external impact which
can depend on the solution; S is positive definite operator describing the dissipation in the system:
(Sφ,φ)≥ μ(φ,φ), μ > 0.
Κ (φ ) is the skew-symmetric operator linearly depending on the solution: (Κ(φ)φ,φ)=0.

So integrating over multiple steps will integrate the uncertainties in f. So the thing that Pat gets wrong is that the time period should actually be the time period of integration, which may be a month.

A sensitivity analysis would should that the models are useless if f is not properly bounded.

The alternative is to theorise a value for f but that just means the models are hypothetical exercises and not fit for anything.

“So integrating over multiple steps will integrate the uncertainties in f.”
No, it doesn’t. That’s a misunderstanding of differential equations, which is somewhat relevant to where Pat goes wrong. Suppose K is zero and f is constant. The solution is f/S+C*exp(-S*t), where C is constant that gives different solutions (fixed by initial conditions). It doesn’t increase linearly with f, as would an integral. In fact, it is a control equation which pulls the solution to a particular trajectory. And if f is something that fluctuates about zero, that will certainly not produce a greater rate of increase.

“It doesn’t increase linearly with f”
sorry, linearly with time t.


If you iterate the equation then the dt is removed and you move from step to step. If f is an external factor at t = 0 with uncertainty then this will affect the change of state. At time = 1 step then the error in f will affect the next result and so on.

You appear to be conflating continuous solutions with numerical methods. You are solving the equation rather than using the equation iteratively. My question originally was about whether forcing was treated as a linear factor. As it turns out it is canonically. So it should apply to all climate models.

And this equation shows that if you use a real world value you need to be very careful if the uncertainties are large as well as trying to find a suitable time period before it blows up. As others have pointed out, that’s good for weather.

I saw the same thing modelling plasmas compared to erosion caused be plasmas.

“You are solving the equation rather than using the equation iteratively.”
An iterative numerical process isn’t worth much if it doesn’t solve the equation.

An iterative process is a numerical way to model dynamics. You can run it to achieve a solution or just to see what happens. It depends on what you want to achieve. A control algorithm can be written as a differential equation but it doesn’t have a solution, just a range and possible limiting functions. I wrote such a function for ion thruster control.

The point is that if you have uncertainties in the inputs to each step you quickly can diverge from what you expect unless you account for these. That’s a pretty standard check in numerical modelling, Nick. And it’s what Pat is talking about.

“The point is that if you have uncertainties in the inputs to each step you quickly can diverge from what you expect unless you account for these. That’s a pretty standard check in numerical modelling, Nick.”
It’s what I have spent a large part of my professional life dealing with. It is what is illustrated with your equation, with K=0. If S is positive, deviations from the solution are corrected. The solution is stable. If S is negative, the solution is unstable. Errors grow. If it is a system of equations, you need all the eigenvalues of S to be positive. Your text actually specifies that (S is positive definite). People really know about this stuff. They need to.


They don’t know K, or phi, or S. That’s the point. They use the equation to try and solve for this. What is known is f (with uncertainty). So they iterate with a forcing number. That’s the issue.


you example is just irrelevant. As you pointed out, it is an example of fully controlled, exponentially damped, equilibrium bound system, where the pertinent variable isn’t φ, but φ-f/S, and where time basically has exponentialy decreasing importance (so of course the error do not depend on time: nothing does!)
Is Climate this sort of system? No it isn’t…

No one discuss the fact that some systems are able to controlable, and any error will be damped to effectively zero. That the whole point of control theory!

The purpose of the paper was to check what behavior can be expected in the case of climate models. The author says that in this case, the error propagates to infinity, that is, the ratio (φ-φ’)/(f-f’) is NOT bound in any way
(where f’ is the real, unknown, forcing; f-f’ is the error; and φ’ is the real trajectory with the real forcing f’)
Which is just basically a definition of a chaotic system, BTW.
In essence, the reviewer states that climate model are not chaotic. Which is double wrong. They ARE (as evidenced by the spaghetti), and since the climate is chaotic, they have better be chaotic too.

“you example is just irrelevant”
For heaven’s sake, it isn’t my example.


Nick, you have been found out. You don’t really understand the application of those lovely complicated models you run. You ‘believe’, you don’t ‘know’. There is a world of difference.
Oh, and you continue to show basic misunderstanding of statistics. But you continue to lie in vain attempts to cover your shortcomings
‘ People really know about this stuff. They need to.’ Yes they do, otherwise ‘real things’ would break or fall down. You clearly don’t, but it doesn’t matter except for the support people like you give to those who bleed economies around the world financing useless ‘energy projects’. That ultimately will cost lives, millions of them. I hope you sleep well.


“I hope you sleep well.”

I doubt Nick has even the slightest bit of shame or conscience that he is supporting an agenda that, in its own words, is trying to bring down western society.

And he will LIE and squirm and deceive and misrepresent, against all rational maths and science, as long as he can to keep his support for that evil, irksome agenda going,

Pat Frank

Micky, I haven’t checked the models themselves. I’ve only emulated their behavior.

However, a repeated criticism of my reviewers has been that the emulation equation is incomplete physics because it does not include a term for ocean heat capacity.

One can infer from that comment, that the models do just incorporate a linear extrapolation of forcing, but that it’s modified by other thermal responses.

Also, in one of my responses, I noted that the IPCC itself states there is a linear relation between forcing and projected air temperature, which they express as ΔTs = λΔF, where λ is model climate sensitivity.

That’s in Pyle, J., et al. (2016), Chapter 1. Ozone and Climate: A Review of Interconnections, in Safeguarding the Ozone Layer and the Global Climate System: Issues Related to Hydrofluorocarbons and Perfluorocarbons” IPCC/TEAP Geneva.

The emulation equation isn’t about physics, of course, which makes irrelevant the criticism that it’s physically incomplete.

I’ve read your paper and based on what I had a look at (the canonical equation above) and your findings with the emulation, the basic idea is that irrespective of what the details of climate models are doing, their behaviour is numerically equivalent to a much more simple linear sum of forcing. So it doesn’t matter what fancy maths is happening or how differential equations are being solved or limited, the effect can easily be replicated by a much more simple equation.

In doing so it highlights the sensitivity of the models to forcing and it appears that if you take for example, the yearly forcing, and include uncertainties in that value, the expansion of the range of possible temperatures makes the models become not very useful.

So the key element is the effect of the numerical wizardry is to produce a much more simple relationship that can be emulated. And this linear relationship is also expressed by the IPCC.

The key is that if you can emulate with a simple relationship and that it shows very good agreement with a whole host of models of different types, then the resultant core of the models is linear i.e higher order terms are being minimised.

It is actually a very nuanced argument Pat. It’s like using a complicated polynomial expansion only to find out your higher terms are all zero over the range of values you use it on!

Just to add: because you use an emulation, effectively like a reverse engineering process, and you don’t necessarily need to know exactly what is going on in the models, I believe this is why you are getting the responses.

Playing Devil’s Advocate: First of all, it’s not a derivation or understanding from first principles. It also does not detail how the forcing values are used to calculate the internal states, run or solve differential relationships and so on. A modeller would look at all the whistles and bells and say, no the model is not run like that.

However, mathematically, what matters is the result and how it behaves within a range of data. It is the reverse argument to many here who look for higher terms in temperature data, only to be told that a linear fit applies.

Whatever higher terms and processes are going on the result can be fit to a linear sum, which then implies that the behaviour of the model produces a result with characteristics similar to a linear sum. One being sensitivity to uncertainties as you have shown.

I don’t know if this is way you describe the argument though Pat. It might be lost in translation a bit. I could be wrong.


micky, I interpret Pat Frank’s work similarly. I haven’t yet seen a single valid rebutal of the core findings 1) a very simple linear finction can emulate complex climate model output. Kind of embarassing if you’re demanding super computers tl run your complex models, and 2) uncertainty in the parameter values that come frome measurement is neither reported nor accounted for in the model output, and the correspondemce suggests that many climate modellers do not care for or understand error propagation, and do not possess a very good grasp of basic statistics.


I also now see where Pat got the yearly error from. RMS error of the year is quoted in the L&H model so I can see why Pat uses the yearly emulation. It’s the highlight the problem using L&H as a candidate example.

“RMS error of the year is quoted in the L&H model”
It isn’t. They just quote rmse error 4 W/m2. . Nothing said about “of the year”. This is crucial to Pat’s numbers.



Pardon a layman’s question, but based on micky’s explanation of your paper (which helped put it in context for me), it sounds as though there are two separate issues: 1) climate models are essentially just linear sums of forcing, and 2) error propagation in a model of linear sums should be calculated in such-and-such a way.

If this is accurate, shouldn’t there be two papers then: One arguing and demonstrating the first point, and another the second? This seems especially necessary since the second point is the one that you’re really interested in, and it appears that it’s dependent on the first.

Just a thought.


Apologies to Pat. I read section 2.4.1 and the yearly uncertainty is because even the 20 year value is a sum of yearly calculations. Thats why the uncertainty is per year. The basis is a yearly value.


There has got to be a free market solution to this problem:
1) The Journals are controlled by activists, not interested in the truth. A climate journal needs to be edited by unbiased and disinterested people in the Stats, engineering and Mathematics fields. Rejected Climate Articles should be submitted to statistics or mathematics journals for publication. The existing climate science would never pass the rigor needed for publication in a real science journal.
2) Reproducibility and the Application of the Scientific Method would be a requirement for publication in any new Climate Journal. The very fact that the new journal announces that requirements would put the other journals on the defensive.
3) The new Journal could start by simply doing that happens here on WUWT. Existing published articles could be critiqued, and the flaws in their science and statistics could be exposed and validated by people in the math and science fields.

The first thing communist totalitarians do it take over the media and educational system. They have to control the message and censor all opposition. That is their well-known MO. Real scientists need to break that truth embargo imposed my the slimate climatists. There has to be a market for the truth, an entrepreneur just has to tap it. Aren’t there any scientific journals interested in the truth anymore?


WUWT Site stats

There is enough firepower there to generate interest in a new Journal. WUWT could team up with the other Global Warming Blog and start publishing an Alt-Science Journal, a journal clearly intended to challenge the status quo. The Alt-Title might appeal to the rebellious Millennials. Bottom line, there are no real barriers to entry to the Science Journal Industry, and WUWT has a vehicle to bring everyone together.

1) Hit counters are meaningless
2) New Journal? Try this:

Mark T

These people don’t even demonstrate a solid understanding of statistics, let alone how statistics would connect to physical phenomena.

Larry Good, P.E. CSSBB

Errors of measurement seem to be far better understood by physical scientists and engineers than mathematicians which is ironic given the concept’s roots in statistics.

Tom Halla

The editor and “reviewer” have definite conflicts of interest that bias them towards the consensus.

Even Ronan Connolly?

Pat Frank

What did Ronan Connolly get right, Nick?

More weirdnesses
“How does it happen that a PhD in mathematics does not understand rms (root-mean-square) and cannot distinguish a “±” from a “+”?”
Just about anyone understands that rms is positive. Who talks about their voltage being ±110V?

James Annan says
“Nowhere in the manuscript it is explained why the annual time scale is used as opposed to hourly, daily or centennially, which would make a huge difference to the results.”
He’s right; I made that point at some length. A referee pointed out this weirdness – PF takes a 20 year average of something in W/m2 and says that the result has units W/m2/year. But why /year, just because the time period was described as 20 years? It’s also 240 months; why not W/m2/month? As James Annan says, it would make a huge difference to the result.

Taylor Ponlman

“Who talks about their voltage being +-110V?” Well, an electrical engineer for one. Put a diode on one side of that +- feed and measure the result. Now reverse the polarity of the diode – get the same result? Now add a capacitor of sufficient size across the circuit and repeat the procedure. Answers the same in all cases? I think not, particularly depending on the type of measuring instrument. So it depends on your perspective and your needs. The consumer relies on the fact that is 110V appliance works when plugged into a 110V AC outlet, but try plugging a transformer-based device into 110DC. Obviously, it matters, so please don’t attack an attempt at clarity with a trivialization of his point.

No, the voltage may be ±, but the RMS measures the magnitude. An engineer would multiply the RMS by a phase term (after converting to peak to peak). It is James Annan who is correctly using magnitude.


Nick now try your answer with an AC voltage on a DC offset the situation Taylor describes with a half wave ripple.
The full wave rectified sine and half wave rectified sign whilst they have an RMS value you often put a +- in front of to show the DC offset direction.

I think I got your meaning but be very careful trying to make that absolute.

Jim Gorman


You’re giving away some of your lack of knowledge. RMS is not the magnitude of an alternating waveform. It is merely the value (magnitude) of an equivalent DC voltage that gives the same power. You can not determine the RMS value of an alternating current, especially an asymmetric one by a simple multiplying of a phase term.

As before, this is dealing with a real world item. Simple math doesn’t always apply. By the way what is the RMS value of a sine wave of +- 110vac +- 5v?

RMS means root mean square. It’s as simple as that. There are no ± (or -) signs in LdB’s table. Yes, of course for non-sunusoids you can’t use a simple amplitude and phase characterisation. But RMS still means root mean square. Positive.


So you are saying in your field the RMS of a series of all negative numbers is positive, that would make analysis fun 🙂


I know what you mean but in many field we add the sign in for meaning. You can go thru the process of trying to split hairs the sign isn’t part of the RMS value but that is being vexatious 🙂

“So you are saying in your field the RMS of a series of all negative numbers is positive”
Of course it is.


I should say if you want to play vexatious then I am going to tell you that you can’t do square roots of negative numbers so any offset negative waveform can’t have an RMS 🙂

“you can’t do square roots of negative numbers”
Again, RMS is root mean square. Root. Mean. Square. Before you do anything else, the argument is squared. Everything is then positive. The mean is positive, so has a sqrt. RMS(-V)=RMS(V).


You see where this goes Nick all you can do is add a minus out the front to get all the numbers positive
-X + RMS
Then I am going to tell you that formula shows you specifically that you can’t do the RMS because you had to put a term in front of the RMS and you kicked and own goal.

As I said I would settle for your answer without vexatious extension 🙂


The basic problem is the negative has meaning no electrician or QM person is going to accept a positive RMS value on a negative basis offset because you lose meaning. You may never accept our answer but equally we can’t accept yours.


To give you an example if I had a -20VRMS and +20VRMS waveform I would correctly deduce there is 40Volts RMS between them. In your case I would have 20VRMS and 20VRMS and I would conclude there is 0Volts between them. Do you see the answer is completely miss leading. I i write your it long hand using your offset above I get the right answer -20VDC + 20VRMS and 20VDC + 20VRMS but it’s a lot more complicated, so you can think of it as shorthand.


Nick says..”RMS is a magnitude”

Yes, that means it can be in either direction



“RMS is root mean square.”

Nick, you mathematical IMBECILE.

Root = square root

ALWAYS a “±” answer.

A long time since you did junior high maths, isn’t it Nick.

Go back and RE-LEARN.


You guys do realize you’re wasting all this time and space on the purely semantic distinction between expressing RMS as a magnitude only, whose value must always be positive (and therefore implicitly understanding the +/- as part of the definition of RMS), or expressing RMS with the +/- signs?


Is it just me or does Nick Stokes not understand the difference between a Magnitude and a Vector? RMS is magnitude. He keeps making it a positive vector.

“You guys do realize you’re wasting all this time and space on the purely semantic distinction”
You could say that. My point is that RMS is well defined and is positive. You could make sense of an alternative usage, and getting the semantics messed up is not the worst thing in the world. My point is, well, I’ll repeat PF:
“How does it happen that a PhD in mathematics does not understand rms (root-mean-square) and cannot distinguish a “±” from a “+””
He’s using JA’s perfectly conventional and correct usage to try to discredit him as a scientist.

One thing RMS and magnitude of a vector do have in common is that they are both positive.


“One thing RMS and magnitude of a vector do have in common is that they are both positive.” Bzzzttt. You just failed a basic 1st year type engineering exam question. Vector has a direction, could be negative or positive. Magnitude has no direction, it is just a magnitude, not positive or negative.

“Vector has a direction, could be negative or positive.”
Well, it has multiple components. But I have not spoken of sign of a vector. Only its magnitude, which is positive (and scalar).

“He’s using JA’s perfectly conventional and correct usage to try to discredit him as a scientist.”
I should add that the issue to me isn’t the unfairness of that. It’s the ignorance. Undergrads, even school students, are supposed to know how to use RMS. You can possibly justify an alternative usage, with great care for consistency, but to slam Annan for orthodox use just shows ignorance of that undergrad teaching.


You still aren’t understanding it Nick.

“Well, it has multiple components. But I have not spoken of sign of a vector. Only its magnitude, which is positive (and scalar).”

As soon as you assign a positive or negative to it, you change it from a magnitude to a vector i.e. you give it a direction relative to some co-ordinate system. A magnitude is neither positive or negative (but is is scalar). Gravity has a magnitude of 9.81m/s^2, whether is is increasing your velocity or decreasing your velocity, depends on the direction you assign it (+ or -) with respect to the co-ordinate system you are working with. These is very basic concepts on magnitudes vs vectors. You keep conflating them together. Like I said earlier, you would fail basic 1st year engineering exams with your comments thus far.

“As soon as you assign a positive or negative to it, you change it from a magnitude to a vector”
Does that work for your bank account? But anyway, I’m the one that is resisting applying signs. A magnitude is positive in the sense that your height is positive. What else would it be? In any arithmetic, it is treated as a positive number.

Remember, the excoriation of James Annan was for not providing a sign.


“Does that work for your bank account?”

Most certainly does. Magnitude of the transaction is the $ amount of the transaction. Whether it adds to the account or subtracts from it makes it the vector (I personally like ones that add :)).


“A magnitude is positive in the sense that your height is positive.”

Yes, people’s heights are always positive. Good observation. The magnitude of the error of measurements of those heights if you take the RMS of the errors will also be to use your thinking, a positive number. eg, 1cm. The effect of that error will sometime be positive and sometimes be negative, hence +-1cm.

The magnitude is 4W/m^2, but the effect is +-4W/m^2, not +4W/m^2. Do you still not see your logic error?


Your wasting your time Nick is clearly engaging it semantics and that is all he is interested in to justify an answer. What Nick is not willing to discuss is what the intent of RMS is, which is and lets quote it

To allow RMS amplitudes to sum directly

Nick is ignoring the intent to be deliberately deceptive.

Nick has the same argument that you can’t have negative money, hence a number such as -$10 can’t be written in an account. You either put it in a different column or color it red would be Nick’s argument.

If Nick or Climate Science is going to engage in this level of semantics they need to publish a formal definition of terms because you can’t use any known standards that are in use by the general community.


Nick, I would also warn you that if you look at all the truely great science papers in physics and I applied your level of semantics I don’t know any of them that would actually have been published.

There are a number of line by line analysis of Einsteins 1905 paper around and most will pick up the couple of errors. Using your level of semantics it would have been thrown out or is at the very least completely wrong.

I am pretty sure you could reject any paper based on semantics if you really put your mind to it.

“Nick has the same argument that you can’t have negative money”,/i>
No. I just said that it would be odd to say from its sign status that it is a vector. I have experienced negative money.

“and lets quote it”
I don’t know what you are quoting there. But it is very rare than you can add RMS directly. More often it is in quadrature. You can add the squares.

“Climate Science is going to engage in this level of semantics “
No, the semantics are from Pat Frank. He blasted James Annan for what is simply standard usage (also used by his source). And surely that raises the question – what’s going on here? What kind of world are we in?


If you and climate science in general go to this level you are on a slippery slope.

I haven’t got the time but if someone wants to do it go to all the important papers in climate science and just look at the quantities and exact wording. Find how many mistakes there are and then suggest they reject the papers based on semantic errors because that is where we have come to.


I guess it would also be interesting to ask Nick about papers with the expression -Energy in a physics paper. Energy is after defined almost everywhere as a positive value. Can I have -Energy in a paper?


Wow. So much commemt space was abused by this RMS nonsense.

Jim Gorman

As above, don’t trivialize. RMS of what? A square, triangular, sine wave? How about an asymmetric waveform that could have a negative value? How about a +-110v +_5 v.


Sorry Jim missed you had answered that. Yes hopefully we have explained Nick to be careful taking that to far.

With RMS of anything, you square it, which has to be positive, take the mean, and then the positive square root. The answer is a magnitude and has to be positive.


No it doesn’t Nick just look at the waveforms above turn the 2nd and 3rd upside down. You need to be able to separate the two waveforms and one is positive the other is negative. You possibly can’t do that in your problem but it happens in many problems. We get the same thing in QM where we have RMS to some Ket basis.

Pat Frank

Nick, “With RMS of anything, you square it, which has to be positive, take the mean, and then the positive square root. The answer is a magnitude and has to be positive

Now you’re bringing in external physical meaning, Nick, which changes everything.

And which explanation (physical meaning) you’ve always resisted whenever it produced conclusions you didn’t like, such as in the physical meaning of a time-average.

When only one root of a square root has physical meaning, within the context of science or engineering, that root is chosen for that reason: i.e., by reason of an externally located physical meaning.

The rms calculation itself always, repeat always, produces the ±root.

The fact that only physically meaningful roots are chosen in science has no bearing on the general result that RMS is always plus/minus.

“The rms calculation itself always, repeat always, produces the ±root.”
Does your calculator say that? Your computer? It’s nothing about physical meaning. It is a standard definition. RMS is always the positive square root.

Again my challenge – if it as you insist, point to just one reputable publication that uses that convention. For the actual RMS numbers. Your L&H source certainly doesn’t.

Pat Frank

Here you go, Nick, Wiki itself:

In experimental sciences, the [plus/minus] sign commonly indicates the confidence interval or error in a measurement, often the standard deviation or standard error. The sign may also represent an inclusive range of values that a reading might have.

Standard deviation: rms conditioned by loss of one degree of freedom.

“Here you go, Nick”,/i>
Going round and round endlessly on this incredibly elementary stuff That link is actually to a page on the ± symbol. And it describes its use in defining a confidence interval. That says that the CI is a±b, where b is some rmse, sd or a multiple. That is the CI, but b, the RMSE, is a positive number. It makes no sense to speak of a±±4.

Still no progress with the challenge – to find an RMSE actually specified as, say, ±4, as you say Annan and L&H should have done.

“you know you are referring to a quantity which alternates between +110 and -110”
No. It alternates between about +155 and -155. The point is that RMS is a well-defined term, and is positive. It wouldn’t matter so much that Pat Frank has an eccentric view on it (it isn’t his worst) but one has to respond if he uses Annan’s prefectly conventional use to claim that he isn’t a scientist etc.

“your extremely selective quotation of a reviewers criticism without taking any account of the author’s response to that criticism”
I quoted both rounds, criticism and reply. But the main thing is the stream of accusations directed at Dr Connolly’s honesty (not to mention intellectual vacuity etc). Dr C is an independent scientist who often writes at WUWT. I think he’s a sceptic in good standing. So what is the basis for this? It can’t be supposed CoI.

“Your second point is just plain false.”
OK would you like to quote the parts of the author’s reply that would change the meaning from what I wrote?

Pat Frank

Nick, “The point is that RMS is a well-defined term, and is positive.

Wrong. RMS is always ±.

4^2 = 16
(-4)^2 = 16

sqrt(16) = ±4 and nothing else.

It’s that easy and you never fail to get it wrong, Nick.

Pat Frank

Nick’s numerical conundrum was resolved here, and again here, and by micro6500 here.

And that set doesn’t exhaust the retinue.

I can’t tell whether you really don’t get it, Nick, or whether you’re just sticking to an obscurantist narrative.

“If asked I would say that RMS is a magnitude just like he does. If he is right..”
then James Annan was right. It’s Pat who is making an issue of something elementary, that wouldn’t be significant anywhere else..

“it takes him nowhere”
It seems from these posts that it’s Pat’s paper that is going nowhere.


Pat is right to take issue since it is crucial to the topic that all parties understand and are perceived to understand by one another exactly what is being referred to by uncertainty and error. It is painstakingly obvious that many of the reviewers do not get it.

Jim Gorman

Just to elucidate a little. The RMS value of a waveform is the equivalent DC value that would generate the same heating value if dissipated in a resistance. The DC value can be positive or it can be negative with respect to ground. The same amount of heat is dissipated either way, i.e. +-RMS.

“RMS is always ±.”
Your link does not talk about RMS. It talks about what you must do if taking the square root of a quadratic equation. And then indeed the result must reflect the range of possible solutions of that equation. But that is not relevant here. RMS is a measure of the magnitude of variation. It was positive everywhere in Lauer and Hamilton. It was positive in the table of values that LdB showed. I repeat my challenge, if “RMS is always ±” then just show any reputable publication where an RMS is shown so. Now I expect, like LdB, you’ll come back with stuff like a±σ, where σ is some RMS or standard deviation. But while that does express the error range, the measure σ, RMS, is a positive number. The expression wouldn’t make sense otherwise.

Now as I said elsewhere, I’m not so bothered that this is yet another of your “Pat Frank only” notions. The issue is that you savagely condemned James Annan for his standard usage (exactly as used by L&H), which can only show that you just don’t understand it. And it is high school stuff..

Pat Frank

Nick, that link shows why taking a square root always produces a plus/minus.

It proves the generality of which rmse is a particular case.


Nick. You are just saying that a standard deviation, as in the parameter, is typically expressed without +/-. So I can pass a paramete value into a function that describes a distribution and that parameter is the standard deviation and it is typically not passed as negative.

The +/- comes into play when a point estimate is made.

In Pat’s 4 +/- case, point estimates are made and there is no reason to suggest that only one tail is required, so +/- is correct.

“so +/- is correct”
So do you mark your students wrong if they don’t provide it?


This is about precision in language as much as it is about precision in measurement. A lot of meta reviews and meta evaluation happening rather than the math, stats, and error analysis that should be happening. We’ve all established that context determines the convention here. Knowledge and awareness of the context (among other things) is cuing fitness to evaluate the submission and the appropriateness of the conduct of the editors and reviewers. So under some circumstances I’d say Pat Frank’s point on +/- was ruthlessly pedantic, but in this case i think he’s within bounds. Picking on his point was a waste of time.

Qualifier: I am not a mathematician nor a statistician. So take what I say with a grain of salt:

Find a Journal who specializes in the nuances of mathematics, statistics and physics, one that is dedicated to tearing apart models and looking for holes. You’ll reach a broader audience. The problem may stem from nihilism, the problem may stem from an abject rejection of any idea that threatens the money train. But your problem is trying to beat down a fortified castle wall with the equivalent of a soap bubble.

Find another castle who’s door is open…preferably a neighboring one that has tunnels running under the climate one–undermining from within. Once an error is discovered, it can not be ignored by those that understand the error.

Just a suggestion, but I’d start shopping that paper to other parties of interest.


Debating the physics and statistical content of the paper is actually a distraction in this posting as it is about integrity, as noted in the title of the post. It would seem that violating the reviewer’s own stated rules regarding maintenance of said integrity should be sufficient to make that point to all that bias is involved in the process and it lacks integrity.


Integrity only counts if we’re talking skeptics. Believers can’t have conflict of interest because they are “pure and saintly”. Funding bias is only on skeptics, as is bad motivations (oil company checks and so forth). Again, all believers are pure and saintly, untainted by personal gain. Everyone knows this. Trying to impune these people is just very bad behaviour. And it hurts their teeny, tiny little feelings, so cut it out.

Schrodinger's Cat

I don’t pretend to understand the details of the error propagation at the centre of this dispute, but on the one hand it is seen as incompetence and lack of integrity and on the other side it is said to be an obvious error.

What surprises me is that even on its second exposure on this site the technical dispute has still not been resolved though there are plenty of critical comments on both sides. But then, why am I surprised? It seems that climate matters defy agreement as a universal rule.

Yet as others have pointed out, regardless of the technical matter, GMD seems not to have followed its own guidelines and illustrates the level of integrity we associate with pal review.

Outstanding essay. Every media outlet that aspires to maintain the highest ethical standards should publicize the essay as a case study of unethical behavior or worse. Dr. Frank: In my opinion, you could skip the “in my opinion” phrases.


“every media outlet that aspires to maintain the highest ethical standards”

I believe there may be no such thing out there.


Every non-governmental media outlet strives to maintain profits so that it can pay salaries and other operating costs with a residual profit to the owners. Any that doesn’t, doesn’t remain around very long.
If they call themselves a non-profit, private media outlet, then they are merely using a convenient accounting method for the purpose of tax-avoidance by the owners.

Every government media outlet merely serves the political interests of the government in power. Any government media outlet that doesn’t do so, doesn’t remain around very long.

Pat Frank

I didn’t want to be sued for defamation, Tom B. Or to put Anthony into such peril.

Jim Gorman

So called climate scientists refuse to deal with the real world uncertainties and errors that happen in measuring real world things like temperature. They are all mathematicians that are terribly sure that their number crunching and statistical analyses are done correctly and they probably are. However, they are ignoring, mostly willfully, the most important part of the science, error and uncertainty.

Their mistake is that they are not dealing with pure numbers and they refuse to admit that any given number can be fuzzy out to the limits of uncertainty {recorded temperatures) thereby contaminating their well designed output of a simple number. They never dealt with that when learning about how to do math on regular finite numbers that were exact.

Every time they show a graph or state a number without including error and uncertainty they are misleading people into thinking they seeing exactly what will happen. Nothing could be further from the truth. Someday, people will ask them how they could ignore this. I hope they have a good answer.


“It turns out that Dr. Annan is co-principal of Blue Sky Research, Inc. Ltd., a for-profit company that offers climate modeling for hire”

The name of the modeling company is of course how a modeler’s model has to see the planet for it to have any physical validity. Which of course to say, that if Earth didn’t actually have a condensing 1%-3% precipitable GHG component, the models would do a much better job of estimating the forcing effects on climate of non-precipitable GHG changes.

A true blue sky planet with a small ocean:land ratio – the Earth is not. The Earth of course has a 7:3 ocean:land ratio. Those large oceans have decadal-scale internal non-linear cycles which the models cannot replicate. The planet has significant clouds, cloudy days, and rain which alters albedo over large areas in ways the models cannot caluculate. Water’s phase changes and large latent heats produce significant convective energy transport (at scales smaller than the calculable grid box) in ways which cannot be calculated by first principles. Thus the modelers parameterize those quite non-blue sky features.

So yes, a true blue sky planet is the climate modeler’s Platonic utopia. Damn those clouds and rain.

Even a water world will have a deterministic climate which is actually easier to calculate than our mix of land and water. The problem is that climate science sees the chaos of weather which blinds them to how predictable the LTE state must be consequential to some change.

It would be interesting to see a water world modelled using a pedantic GCM. Many of its knobs and dials will go away, leaving only the core assumptions to affect the results.


A decent modeler will exactly do that: simulate not just current Earth, but Earth in a lot of states: snowball, no land, land in a single mass, all land,…

Yes. One of the tests I do for any model of a causal system is to vary initial conditions and make sure it converges to the same answer each time. If it doesn’t, then there’s something wrong with the model.

Yogi Bear

‘Consensus Climatology in a Nuccitellishell’


As far as I can see, the problem with all of AGW is the suppositions are built into the models. It’s a giant circular argument. However, to prove or disprove the theory would require starting over with scientists who knew nothing of the theory and were asked to account for the current temperature rise based on the elements of climate we currently understand. This is probably impossible. Almost all theories I’ve seen either assume CO2 is the driver or one of the major drivers, assume one variable is dominent such as the sun, ocean currents, etc, and all have to guestimate many of the components of climate. Finding scientists that could take known factors and generate a model of today’s climate with no assumed conclusions may not be possible. Barring such an exercise, we will remain mired in the “my theory is right” battle forever or until such time as the earth gets very hot or very cold. Even then, the blame game will continue.


Yes! It is a giant circular argument. Still, the models could be scientifically useful if the modeling was done with the assumption that the result will be wrong, and then compared to what has really happened in an attempt to gain understanding. That would be in line with the scientific method. It would be a form a trial and error. But it would fail miserably as political motivation, which needs more definitive, alarming statements to persuade the masses.

The atmospheric scientific community was left with a choice: stick to science and settle for very little funding, or move away from science, giving the funders what they wanted, and vastly increase funding. Over time, they abandoned science for scientific funding. This is exactly what Eisenhower warned us about in 1961, when he said: ““Partly because of the huge costs involved, a government contract becomes virtually a substitute for intellectual curiosity. We must also be alert to the equal and opposite danger that public policy could itself become the captive of a scientific-technological elite.”

Both of these predictions have come to pass with an accuracy that climate models can only dream of. Government contracts have replaced intellectual curiosity as the main driver of the scientific community. And government policy is being driven by self-anointed, scientific elites, as the distinction between science and government fades, to the detriment of both.

The regrettable reality of the bias and ignorance issues highlighted by Dr. Frank’s essay is that the wall of censorship created by Geoscientific Model Development on a small scale and by apparatchiks in massive government bureaucracies on a very large scale, so far, has been impenetrable.

Consider the U.S. Global Change Research Program (USGCRP). USGCRP “was established by Presidential Initiative in 1989 and mandated by Congress in the Global Change Research Act (GCRA) of 1990 to “assist the Nation and the world to understand, assess, predict, and respond to human-induced and natural processes of global change.” Thirteen Federal entities participate in the USGCRP programs
(Department of Commerce, Department of Agriculture, Department of Defense, Department of Energy, Department of Health & Human Services, Department of the Interior, Department of State, Department of Transportation, Environmental Protection Agency, National Aeronautics & Space Administration, National Science Foundation, Smithsonian Institution, U.S. Agency for International Development).

In the 1990 mandate, human-induced climate change is a given. That implies to me that from at least 1990 to the present, billions of dollars have been spent to indoctrinate the world on the untested hypothesis of CO2-driven global warming and not a cent has been spent to challenge orthodox thinking. Unorthodox thinking is prohibited by the mandate. Every result from their studies is a “What if” result. Where are the “What if not” studies?

What chance do a few rational scientists have against this vast Establishment juggernaut of money and power? The resources are in place to accomplish good science. The mandate of the USGCRP must be redirected by Congress to emphasis finding the truth instead of managing a multi-billion-dollar program to promote a political doctrine. That would really be draining the swamp. I wish I could be optimistic that the efforts of Dr. Frank and a few others will lead to positive changes in thinking about climate change. Sadly, I fear that those who desire change are whistling in the wind.

Casual Reader

Looked up Annan & Hargreaves on Facebook (gasp). A married couple. She seems to be fond of cats and lists herself as self employed.

I Came I Saw I Left

Imagine… A married couple thwarting publication of a paper that threatens their livelihood. Simply inconceivable.

Casual Reader

I used to review potential contractors for construction projects. Companies that swept the floors on a project would claim to be project managers in their slick sheet brochures. You have to look at financial statements and tangential things, not just the company resumes. Is Blue Sky a slick sheet website trying to get on the AGW cash bandwagon? I doubt they carry enough weight to justify all this discussion.

The most recent product of the U.S. Global Change Research Program is a Congress mandated quadrennial report that is archetypal of how the Establishment perpetuates group think on climate change. The report is filled with hyperbolic language intended to invoke apprehension about present and future threats of an out of control warming planet. The report has been widely publicized in scientific journals and elsewhere, including WUWT ( Check it out again re Dr. Frank’s experience with Geoscientific Model Development.


There is no consensus on the AGW conjecture because scientists never registered and voted on the matter. Science is not a democracy. The laws of science are not some form of legislation. Scientific theories are not validated by a voting process. Much of the so called peer review is largely political in nature. Passing peer review does not make something correct or valid.

Clyde Spencer

This is an example of someone who is sloppy in his attention to detail in significant figures in measurements. He is demonstrating what is wrong with the alarmist position.


He wrote, “… ~4W/m^2 error in cloud forcing…” except it is ±4 W/m^2 not Dr. Annan’s positive sign +4 W/m^2. Apparently for Dr. Annan, ± = +.

where is “Dr. Annan’s positive sign” ? I don’t see one, this is a false charge made up to suit then rant.

Apparently for Pat Frank ~ = +

If that is where this vitriolic attack on Annan starts, I won’t bother my time with the rest.

I recall last time this “paper” came up it got fairly dismal reception here on WUWT, too.

Mark T

When there is no sign it is a plus, by definition. I can understand why you had to stop, you simply don’t understand basic mathematical symbolism and were incapable of understanding the rest. This is probably the weakest of his arguments (and even that was too much for you), all things considered.

Pat Frank

Unspecified sign is always positive by default, Greg.

Further, later in his paragraph, Dr. Annan wrote, “Of course this is what underpins the use of anomalies for estimating change…,” which treats the value as an offset error and is an unambiguous indicator that he meant positive-sign 4 W/m^2.

Nothing in my post constituted a “vitriolic attack.”