Critique of “Propagation of Error and the Reliability of International Air Temperature Predictions”

From Dr. Roy Spencer’s Weblog

September 11th, 2019 by Roy W. Spencer, Ph. D.

I’ve been requested for my opinion by a number of folks about this new revealed paper by Stanford researcher Dr. Patrick Frank.

I’ve spent a few days studying the paper, and programming his Eq. 1 (a easy “emulation mannequin” of local weather mannequin output ), and included his error propagation time period (Eq. 6) to verify I perceive his calculations.

Frank has supplied the quite a few peer reviewers’ feedback on-line, which I’ve purposely not learn in an effort to present an impartial assessment. However I principally agree along with his criticism of the peer assessment course of in his current WUWT publish the place he describes the paper in easy phrases. In my expertise, “local weather consensus” reviewers typically give probably the most inane and irrelevant objections to a paper in the event that they see that the paper’s conclusion in any manner would possibly diminish the Local weather Disaster™.

Some reviewers don’t even learn the paper, they simply have a look at the conclusions, see who the authors are, and decide based mostly upon their preconceptions.

Readers right here know I’m crucial of local weather fashions within the sense they’re getting used to supply biased outcomes for vitality coverage and monetary causes, and their basic uncertainties have been swept underneath the rug. What follows isn’t meant to defend present local weather mannequin projections of future international warming; it’s meant to point out that — so far as I can inform — Dr. Frank’s methodology can’t be used to reveal what he thinks he has demonstrated concerning the errors inherent in local weather mannequin projection of future international temperatures.

A Very Transient Abstract of What Causes a International-Common Temperature Change

Earlier than we go any additional, it’s essential to perceive one of the vital primary ideas underpinning temperature calculations: With few exceptions, the temperature change in something, together with the local weather system, is because of an imbalance between vitality acquire and vitality loss by the system. That is primary 1st Regulation of Thermodynamics stuff.

So, if vitality loss is lower than vitality acquire, warming will happen. Within the case of the local weather system, the warming in flip leads to a rise lack of infrared radiation to outer house. The warming stops as soon as the temperature has risen to the purpose that the elevated lack of infrared (IR) radiation to to outer house (quantified via the Stefan-Boltzmann [S-B] equation) as soon as once more achieves international vitality steadiness with absorbed photo voltaic vitality.

Whereas the particular mechanisms would possibly differ, these vitality acquire and loss ideas apply equally to the temperature of a pot of water warming on a range. Below a relentless low flame, the water temperature stabilizes as soon as the speed of vitality loss from the water and pot equals the speed of vitality acquire from the range.

The local weather stabilizing impact from the S-B equation (the so-called “Planck impact”) applies to Earth’s local weather system, Mars, Venus, and computerized local weather fashions’ simulations. Only for reference, the typical flows of vitality into and out of the Earth’s local weather system are estimated to be round 235-245 W/m2, however we don’t actually know for positive.

What Frank’s Paper Claims

Frank’s paper takes an instance recognized bias in a typical local weather mannequin’s longwave (infrared) cloud forcing (LWCF) and assumes that the everyday mannequin’s error (+/-Four W/m2) in LWCF will be utilized in his emulation mannequin equation, propagating the error ahead in time throughout his emulation mannequin’s integration. The end result is a big (as a lot as 20 deg. C or extra) of ensuing spurious mannequin warming (or cooling) in future international common floor air temperature (GASAT).

He claims (I’m paraphrasing) that that is proof that the fashions are basically nugatory for projecting future temperatures, so long as such giant mannequin errors exist. This sounds cheap to many individuals. However, as I’ll clarify under, the methodology of utilizing recognized local weather mannequin errors on this vogue isn’t legitimate.

First, although, just a few feedback. On the optimistic facet, the paper is well-written, with intensive examples, and is well-referenced. I want all “skeptics” papers submitted for publication had been as professionally ready.

He has supplied greater than sufficient proof that the output of the typical local weather mannequin for GASAT at any given time will be approximated as simply an empirical fixed instances a measure of the accrued radiative forcing at the moment (his Eq. 1). He calls this his “emulation mannequin”, and his result’s unsurprising, and even anticipated. Since international warming in response to growing CO2 is the results of an imposed vitality imbalance (radiative forcing), it is smart you could possibly approximate the quantity of warming a local weather mannequin produces as simply being proportional to the entire radiative forcing over time.

Frank then goes via many revealed examples of the recognized bias errors local weather fashions have, notably for clouds, when in comparison with satellite tv for pc measurements. The modelers are properly conscious of those biases, which will be optimistic or damaging relying upon the mannequin. The errors present that (for instance) we don’t perceive clouds and all the processes controlling their formation and dissipation from primary first bodily ideas, in any other case all fashions would get very almost the identical cloud quantities.

However there are two basic issues with Dr. Frank’s methodology.

Local weather Fashions Do NOT Have Substantial Errors of their TOA Internet Vitality Flux

If any local weather mannequin has as giant as a Four W/m2 bias in top-of-atmosphere (TOA) vitality flux, it will trigger substantial spurious warming or cooling. None of them do.


As a result of every of those fashions are already energy-balanced earlier than they’re run with growing greenhouse gases (GHGs), in order that they don’t have any inherent bias error to propogate.

For instance, the next determine reveals 100 yr runs of 10 CMIP5 local weather fashions of their pre-industrial management runs. These management runs are made by modelers to be sure that there are not any long-term biases within the TOA vitality steadiness that may trigger spurious warming or cooling.

Determine 1. Output of Dr. Frank’s emulation mannequin of world common floor air temperature change (his Eq. 1) with a +/- 2 W/m2 international radiative imbalance propagated ahead in time (utilizing his Eq. 6) (blue strains), versus the yearly temperature variations within the first 100 years of integration of the primary 10 fashions archived at .

If what Dr. Frank is claiming was true, the 10 local weather fashions runs in Fig. 1 would present giant temperature departures as within the emulation mannequin, with giant spurious warming or cooling. However they don’t. You possibly can barely see the yearly temperature deviations, which common about +/-Zero.11 deg. C throughout the ten fashions.

Why don’t the local weather fashions present such conduct?

The reason being that the +/-Four W/m2 bias error in LWCF assumed by Dr. Frank is sort of precisely cancelled by different biases within the local weather fashions that make up the top-of-atmosphere international radiative steadiness. It doesn’t matter how correlated or uncorrelated these varied errors are with one another: they nonetheless sum to zero, which is why the local weather mannequin developments in Fig 1 are solely +/- Zero.10 C/Century… not +/- 20 deg. C/Century. That’s an element of 200 distinction.

This (first) drawback with the paper’s methodology is, by itself, sufficient to conclude the paper’s methodology and ensuing conclusions will not be legitimate.

The Error Propagation Mannequin is Not Acceptable for Local weather Fashions

The brand new (and customarily unfamiliar) a part of his emulation mannequin is the inclusion of an “error propagation” time period (his Eq. 6). After introducing Eq. 6 he states,

“Equation 6 reveals that projection uncertainty should enhance in each simulation (time) step, as is anticipated from the impression of a scientific error within the deployed idea“.

Whereas this error propagation mannequin would possibly apply to some points, there is no such thing as a manner that it applies to a local weather mannequin integration over time. If a mannequin truly had a +Four W/m2 imbalance within the TOA vitality fluxes, that bias would stay comparatively fixed over time. It doesn’t by some means accumulate (because the blue curves point out in Fig. 1) because the sq. root of the summed squares of the error over time (his Eq. 6).

One other curious facet of Eq. 6 is that it’s going to produce wildly totally different outcomes relying upon the size of the assumed time step. Dr. Frank has chosen 1 yr because the time step (with a +/-Four W/m2 assumed vitality flux error), which is able to trigger a specific amount of error accumulation over 100 years. But when he had chosen a 1 month time step, there can be 12x as many error accumulations and a a lot bigger deduced mannequin error in projected temperature. This could not occur, as the ultimate error needs to be largely impartial of the mannequin time step chosen. Moreover, the assumed error with a 1 month time step can be even bigger than +/-Four W/m2, which might have magnified the ultimate error after a 100 yr integrations much more. This makes no bodily sense.

I’m positive Dr. Frank is far more professional within the error propagation mannequin than I’m. However I’m fairly positive that Eq. 6 doesn’t characterize how a particular bias in a local weather mannequin’s vitality flux element would change over time. It’s one factor to invoke an equation that may properly be correct and applicable for sure functions, however that equation is the results of a wide range of assumptions, and I’m fairly positive a number of of these assumptions will not be legitimate within the case of local weather mannequin integrations. I hope statistician reminiscent of Dr. Ross McKitrick will study this paper, too.

Concluding Feedback

There are different, minor, points I’ve with the paper. Right here I’ve outlined the 2 most obtrusive ones.

Once more, I’m not defending the present CMIP5 local weather mannequin projections of future international temperatures. I consider they produce about twice as a lot international warming of the atmosphere-ocean system as they need to. Moreover, I don’t consider that they will but simulate recognized low-frequency oscillations within the local weather system (pure local weather change).

However within the context of world warming idea, I consider the biggest mannequin errors are the results of a lack of awareness of the temperature dependent adjustments in clouds and precipitation effectivity (thus free-tropospheric vapor, thus water vapor “suggestions”) that really happen in response to a long-term forcing of the system from growing carbon dioxide. I don’t consider it’s as a result of the elemental local weather modeling framework isn’t relevant to the local weather change subject. The existence of a number of modeling facilities from all over the world, after which performing a number of experiments with every local weather mannequin whereas making totally different assumptions, continues to be the most effective technique to get a deal with on how a lot future local weather change there *may* be.

My most important grievance is that modelers are both misleading about, or unaware of, the uncertainties within the myriad assumptions — each express and implicit — which have gone into these fashions.

There are lots of ways in which local weather fashions will be faulted. I don’t consider that the present paper represents one in every of them.

I’d be glad to be proved mistaken.

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