Bob Loblaw is the nom de plume of a recently-retired Canadian...

Bob Loblaw is the nom de plume of a recently-retired Canadian physical geographer with an educational background in climatology (especially microclimatology) and permafrost. After an undergraduate degree with specialization in freezing soils, he worked for three years in industry and research related to arctic pipelines. He returned to graduate school, earned a PhD specializing in climatology, became an untenured assistant professor at a major Canadian university, and then perished in the publish or perish system.Turning to research and operational work in government, he has spent over 25 years working in a succession of national and international projects covering forest carbon dynamics, radiation monitoring, and instrumentation for automatic weather stations.He has participated actively in the comments at Skeptical Science for the past 10 years, and is now participating as an author.

Ad hominem, attack, what like you just did to "Bob Loblaw"?

Here's the whole demolition of Franks complete bunkum (not an ad hominem attack)
https://skepticalscience.com/frank_propagation_uncertainty.html

A Frank Discussion About the Propagation of MeasurementUncertainty

Posted on 7 August 2023 by Bob Loblaw, jg

Let’s face it. The claim ofuncertaintyis a common argument against taking action on any prediction of future harm. “How do you know,for sure?”. “That might not happen.” “It’s possible that it will be harmless”, etc. It takes on many forms, and it can be hard to argue against. Usually, it takes a lot more time, space, and effort to debunk the claims than it takes to make them in the first place.

It even has a technical term:FUD.

Acronym ofFear,uncertainty, and doubt, a marketing strategy involving the spread of worrisome information or rumors about a product.

During the times when the tobacco industry was discounting the risks of smoking and cancer, the phrase “doubt is our product” was purportedlypart of their strategy. And within theclimate changediscussions, certain individuals have literally made careers out of waving “theuncertaintymonster”. It has been used to argue that models are unreliable. It has been used to argue that measurements of global temperature,sea ice, etc. are unreliable. As long as you can spread enough doubt about the scientific results in the right places, you can delay action onclimateconcerns.

Figure 1: Is theUncertaintyMonster threatening the validity of your scientific conclusions? Not if you've done a properuncertaintyanalysis. Knowing the correct methods to deal with propagation ofuncertaintywill tame that monster! Illustration by jg.

At lot of this happens in the blogosphere, or in think tank reports, or lobbying efforts. Sometimes, it creeps into the scientific literature. Proper analysis ofuncertaintyis done as a part of any scientific endeavour, but sometimes people with a contrarian agenda manage to fool themselves with a poorly-thought-out or misapplied “uncertaintyanalysis” that can look “sciencey”, but is full of mistakes.

Any good scientist considers the reliability of the data they are using before drawing conclusions – especially when those conclusions appear to contradict the existing science. You do need to be wary ofconfirmation bias, though – the natural tendency to accept conclusions you like. Global temperaturetrends are analyzed by several international groups, and the data sets they produce are very similar. The scientists involved consideruncertainty, and are confident in their results. You can examine these data sets withSkeptical Science’sTrendCalculator.

So, when someone is concerned about these global temperature data sets, what is to be done? Physicist Richard Muller wasskeptical, so starting in 2010 he led a study to independently assess the available data. In the end, the Berkeley EarthSurface Temperature(BEST) record they produced confirmed that analyses by previous groups had largely things right. A peer-reviewed paper describing the BEST analysisis available here. At their web site, you can download the BEST results, including theiruncertaintyestimates. BEST took a serious look atuncertainty- in the paper linked above, the word “uncertainty” (or “uncertainties”) appears 73 times!

The following figure shows the BEST values downloaded a few months ago, covering from 1850 to late 2022. The uncertainties are noticeably larger in the 1800s, when instrumentation and spatial coverage are much more limited, but the overalltrends in global temperature are easily seen and far exceed the uncertainties. For recent years, the BESTuncertaintyvalues are typically less than 0.05°C for monthly or annual anomalies.Uncertaintydoes not look like a worrisome issue. Muller took a lot of flak for arguing that the BEST project was needed – but he and his team deserve a certain amount of credit for doing things well and admitting that previous groups had also done things well. He wasskeptical, he did an analysis, and he changed his mind based on the results. Science as science should be done.

Figure 2: The Berkeley EarthSurface Temperature(BEST) data, including uncertainties. This is typical of theuncertaintyestimates by various groups examining global temperaturetrends.

So, when a new paper comes along that claims that the entireclimatescience community has been doing it all wrong, and claims that theuncertaintyin global temperature records is so large that“the 20th century surface air-temperature anomaly... does not convey any knowledge of rate or magnitude of change in the thermal state of thetroposphere”, you can bet two things:

• The scientific community will be prettyskeptical.
• The contrarian community that wants to believe it will most likely accept it without critical review.

We’re here today to look at a recent example of such a paper: one that claims that the global temperature measurements that show rapid recent warming have so muchuncertaintyin them as to be completely useless. The paper is written by an individual named Patrick Frank, and appeared recently in a journal namedSensors. The title is “LiG Metrology, Correlated Error, and the Integrity of the Global Surface Air-Temperature Record”. (LiG is an acronym for “liquid in glass” – your basic old-style thermometer.)

Sensors2023, 23(13), 5976

https://doi.org/10.3390/s23135976

Patrick Frank has beaten theuncertaintydrum previously. In 2019 he published a couple of versions of a similar paper. (Note: I have not read either of the earlier papers.) Apparently, he had been trying to get something published for many years, and had been rejected by 13 different journals. I won't link to either of these earlier papers here,, but a few blog posts exist that point out the many serious errors in his analysis – often posted long before those earlier papers were published. If you start atthis post from And Then There’s Physics, titled “Propagation of Nonsense”, you can find a chain to several earlier posts that describe the numerous errors in Patrick Frank’s earlier work.

Today, we’re only going to look at his most recent paper, though. But before we begin that, let’s review a few basics about the propagation ofuncertainty– howuncertaintyin measurements needs to be examined to see how it affects calculations based on those measurements. It will be boring and tedious, since we’ll have more equations than pictures, but we need to do this to see the elementary errors that Patrick Frank makes. If all the following section looks familiar, just jump to the next section where we point out the problems in Patrick Frank’s paper.

Spoiler alert: Patrick Frank can’t do basic first-year statistics.

Some Elementary Statistics Background

Every scientist knows that every measurement has error in it. Error is the difference between the measurement that was made, and the true value of what we wanted to measure. So how do we know what the error is? Well, we can’t – because when we try to measure the true value, our measurement has errors! That does not mean that we cannot assess a range over which we think the true measurement lies, though, and there are standard ways of approaching this. So much of a “standard” that the ISO produces a guide:Guide to the expression ofuncertaintyin measurement. People familiar with it usually just refer to it as “the GUM”.

The GUM is a large document, though. For simple cases we often learn a lot of the basics in introductory science, physics, or statistics classes. Repeated measures can help us to see the spread associated with a measurement system. We are familiar with reporting measurements along with anuncertainty, such as 18.4°C, ±0.8°C. We probably also learn that random errors often fit a “normal curve”, and that the spread can be calculated using the standard deviation (usually indicated by the symbol σ). We also learn that “one sigma” covers about 68% of the spread, and “two sigmas” is about 95%. (When you see numbers such as 18.4°C, ±0.8°C, you do need to know if they are reporting one or two standard deviations.)

At a slightly more advanced level, we’ll start to learn about systematic errors, rather than random ones. And we usually want to know if the data actually are normally-distributed. (You can calculate a standard deviation on any data set, even one as small as two values!, but the 68% and 95% rules only work for normally-distributed data.) There are lots of other common distributions out there in the physical sciences - uniform Poisson, etc. - and you need to use the correct error analysis for each type.

Figure 3: the "normal distribution", and the probabilities that data will fall within one, two, or three standard deviations of the mean. Imagesource:Wikipedia.

But let’s first look at what we probably all recognize – the characteristics of random, normally-distributed variation. What common statistics do we have to describe such data?

• The mean, or average. Sum all the values, divide by the number of values (N), and we have a measure of the “central tendency” of the data.
  • Other common “central tendency” measures are the mode (the most common value) and the median (the value where half the observations are smaller, and half are bigger), but the mean is most common. In normally-distributed data, they are all the same, anyway.
• Thestandard deviation. Start by taking each measurement, subtracting the mean, to express it as a deviation from the mean.
  • We want to turn this into some sort of an “average”, though – but if we just sum up these deviations and divide by N, we’ll get zero because we already subtracted the mean value.
    • So, we square them before we sum them. That turns all the values into positive numbers.
    • Then we divide by N.
    • Then we take the square root.
• After that, we’ll probably learn about the standard error of the estimate of the mean (often referred to as SE).
  • If we only measure once, then our single value will fall in the range as described by the standard deviation. What if we measure twice, and average those two readings? or three times? or N times?
  • If the errors in all the measurements are independent (the definition of “random”) then the more measurements we take (of the same thing) the close the average will be to the true average. The reduction is proportional to 1/(sqrt(N).
    • SE = σ/√N

A key thing to remember is that measures such as standard deviation involve squaring something, summing, and then taking the square root. If we do not take the square root, then we have something calledthe variance. This is another perfectly acceptable and commonly-used measure of the spread around the mean value – but when combining and comparing the spread, you really need to make sure whether the formula you are using is applied to a standard deviation or a variance.

The pattern of “square things, sum them, take the square root” is very common in a variety of statistical measures. “Sum of squares” in regression should be familiar to us all.

Differences between two systems of measurement

Now, all that was dealing with the spread of a single repeated measurement of the same thing. What if we want to compare two different measurement systems? Are they giving the same result? Or do they differ? Can we do something similar to the standard deviation to indicate the spread of the differences?Yes, we can.

• We pair up the measurements from the two systems. System 1 at time 1 compared to system 2 at time 1. System 1 at time 2 compared to system 2 at time 2. etc.
• We take the differences between each pair, square them, add them, divide by N, and take the square root, just like we did for standard deviation.
• And we call it the Root Mean Square Error (RMSE)

Although this looks very much like the standard deviation calculation,there is one extremely important difference.For the standard deviation, we subtractedthe meanfrom each reading – and the mean is a single value, used for every measurement. In theRMSE calculation, we are calculating the difference between system 1 and system 2. What happens if those two systems do not result in the same mean value? That systematic difference in the mean value will be part of theRMSE.

• TheRMSE reflects both the mean difference between the two systems, and the spread around those two means. The differences between the paired measurements will have both a mean value, and a standard deviation about that mean.
• So, we can express theRMSE as the sum of two parts: the mean difference (called the Mean Bias Error,MBE), plus the standard deviation of those differences. We have to square them first, though (remember “variance”):
  • σ²=RMSE²- MBE²
• Although we still use the σ symbol here, note that the standard deviation of the differences between two measurement systems is subtly different from the standard deviation measured around the mean of a single measurement system.

Homework assignment: think about how these measures (RMSE, MBE) relate to the concepts of precision and accuracy.

Combininguncertaintyfrom different measurements

Lastly, we’ll talk about howuncertaintygets propagated when we start to do calculations on values. There are standard rules for a wide variety of common mathematical calculations. The main calculations we’ll look at are addition, subtraction, and multiplication/division.Wikipedia has a good pageon propagation ofuncertainty, so we’ll borrow from them. Half way down the page, they have a table of Example Formulae, and we’ll look at the first three rows. We’ll consider variance again – remember it is just the square of the standard deviation. A and B are the measurements, andaandbare multipliers (constants).

	Calculation	Combination of the variance
1	f =aA	σf2=a2σ2A
2	f=aA+bB	σf2=a2σ2A+b2σ2B+ 2abσAB
3	f=aA-bB	σf2=a2σ2A+b2σ2B- 2abσAB

If we leaveaandbas 1, this gets simpler. The first case tells us that if we multiply a measurement by something, we also need to multiply theuncertaintyby the same ratio. The second and third cases tell us that when we add or subtract, the sum or difference will contain errors from bothsources. (Note that the third case is just the second case with negativeb.) We may remember this sort of things from school, when we were taught this formula for determining the error when we added two numbers withuncertainty:

σ_f²= σ²_A+ σ²_B

But Wikipedia has an extra term: ±2abσ_AB, (or ±2σ_ABwhen we havea=b=1). What on earth is that?

• That term is the covariancebetween the errors in A and the errors in B.
  • What does that mean? It addresses the question of whether the errors in A are independent of the errors in B. If A and B have errors that tend to vary together, that affects how errors propagate to the final calculation.
  • The covariance is zero if the errors in A and B are independent – but if they are not... we need to account for that.
• Two key things to remember:
  • When we are adding two numbers, if the errors in B tend to go up when the errors in A go up (positive covariance), we make ouruncertaintyworse. If the errors in B go down when the errors in A go up (negative covariance), they counteract each other and ouruncertaintydecreases.
  • When subtracting two numbers, the opposite happens. Positive covariance makeuncertaintysmaller; negative covariance makesuncertaintyworse.
• Three things. Three key things to remember. When we are dealing withRMSE between two measurement systems, the possible presence of a mean bias error (MBE) is a strong warning that covariance may be present.RMSE should not be treated as if it is σ.

Let’s finish with a simple example – a person walking. We’ll start with a simple claim:

“The average length of an adult person’s stride is 1 m, with a standard deviation of 0.3 m.”

There are actually two ways we can interpret this.

1. Looking at all adults, the average stride is 1 m, but individuals vary, so different adults will have an average stride that is 1 ±0.3 m long (one sigmaconfidencelimit).
2. People do not walk with a constant stride, so although the average stride is 1 m, the individual steps one adult takes will vary in the range ±0.3 m (one sigma).

The claim is not actually expressed clearly, since we can interpret it more than one way. We may actually mean both at the same time! Does it matter? Yes. Let’s look at three different people:

1. Has an average stride length of 1 m, but it is irregular, so individual steps vary within the ±0.3 m standard deviation.
2. Has a shorter than average stride of 0.94m (within reason for a one-sigma variation of ±0.3 m), and is very steady. Individual steps are all within ±0.01 m.
3. Has a longer than average stride of 1.06m, and an irregular stride that varies by ±0.3 m.

Figure 4 gives us two random walks of the distance travelled over 200 steps by these three people. (Because of the randomness, a different random sequence will generate a slightly different graph.)

• Person B follows a nice straight line, due to the steady pace, but will usually not travel as far as person A or C. After 200 steps, they will always be at a total distance close to 188m.
• Persons A and C exhibit wobbly lines, because their step lengths vary. On average, person C will travel further than persons A and B, but because A and C vary in their individual stride lengths, this will not always be the case. The further they walk, though, the closer they will be to their average.
• Person A will usually fall in between B and C, but for short distances the irregular steps can cause this to vary.

Figure 4: Two versions of a random walk by the three people described in the text. Person A has a stride of 1.0±0.3 m. Person B has a stride of 0.94±0.01 m. Person C has a stride of 1.06±0.3 m.

What’s the point? Well, to properly understand what the graph tells us about the walking habits of these three people, we need to recognize that there are twosources of differences:

1. The three people have differentaveragestride lengths.
2. The three people have differentvariabilityin their individual stride lengths.

Just looking at how individual steps vary across the three individuals is not enough. The differences have an average component (e.g., Mean Bias Error), and a random component (e.g., standard deviation).Unless the statistical analysis is done correctly, you will mislead yourself about the differences in how these three people walk.

Here endeth the basic statistics lesson. This gives us enough tools to understand what Patrick Frank has done wrong. Horribly, horribly wrong.

The problems with Patrick Frank’s paper

Well, just a few of them. Enough of them to realize that the paper’s conclusions are worthless.

The first 26 pages of this long paper look at various error estimates from the literature. Frank spends a lot of time talking about the characteristics of glass (as a material) and LiG thermometers, and he spends a lot of time looking at studies that compare different radiation shields orventilationsystems, or siting factors. He spends a lot of time talking about systemic versus random errors, and how assumptions about randomness are wrong. (Nobody actually makes this assumption, but that does not stop Patrick Frank from making the accusation.) All in preparation for his own calculations ofuncertainty. All of these aspects of radiation shields,ventilationetc. are known byclimatescientists – and the fact that Frank found literature on the subject demonstrates that.

One key aspect – a question, more than anything else. Frank’s paper uses the symbol σ (normally “standard deviation”) throughout, but he keeps using the phraseRMSerror in the text. I did not try to track down the many papers he references, but there is a good possibility that Frank has confused standard deviation andRMSE. They look similar in calculations, but as pointed out above, they are not the same. If all the differences he is quoting from othersources areRMSE (which would be typical for comparing two measurement systems), then they all include the MBE in them (unless it happens to be zero). It is an error to treat them as if they are standard deviation. I suspect that Frank does not know the difference – but that is a side issue compared to the major elementary statistics errors in the paper.

It’s on page 27 that we begin to see clear evidence that he simply does not know what he is doing. In his equation 4, he combines theuncertaintyfor measurements of daily maximum and minimum temperature (T_maxand T_min) to get anuncertaintyfor the daily average:

Figure 5: Patrick Frank's equation 4.

At first glance, this all seems reasonable. The 1.96 multiplier would be to take a one-sigma standard deviation and extend it to the almost-two-sigma 95%confidencelimit (although calling it 2σ seems a bit sloppy).But wait. Checking that calculation, there is something wrong with equation 4. In order get his result of ±0.382°C, the equation in the middle tells me to do the following:

1. 0.366²+ 0.135²= 0.133956 + 0.018225 = 0.152181
2. 0.152181 ÷ 2 = 0.0760905
3. sqrt(0.076905) = 0.275845065
4. 1.96 * 0.275845065 = 0.541
   1. ...not the 0.382 value we see on the right...

What Frank actually seems to have done is:

1. 0.366²+ 0.135²= 0.133956 + 0.018225 = 0.152181.
2. sqrt(0.152181) = 0.3910
3. 0.39103832 ÷ 2 = 0.19505
4. 1.96 * 0.19505 = 0.382

See how steps B and C are reversed? Frank did the division by 2 outside the square root, not inside as the equation is written. Is the calculation correct, or is the equation correct? Let’s look back at the Wikipedia equation foruncertaintypropagation, when we are adding two terms (dropping the covariance term):

σf²= a²σ²_A+ b²σ²_B

To make Frank’s version – as the equation is written - easier to compare, let’s drop the 1.96 multiplier, do a little reformatting, and square both sides:

σ²= ½ (0.366²)+ ½(0.135²)

The formula for an average is (A+B)/2, or ½ A + ½ B. In Wikipedia’s format, the multipliersaandbare both ½. That means that when propagating the error, you need to use ½squared,= ¼.

• Patrick Frank has written the equation to use ½.So the equation is wrong.

• In his actual calculation, Frank has moved the division by twooutside the square root. This is the same as if he’d used 4 inside the square root, so he is getting the correct result of ±0.382°C.

So, sloppy writing, but are the rest of his calculations correct?No.

Look carefully at Frank's equation 5.

Figure 6: Patrick Frank's equation 5.

Equation 5 supposedly propagates a dailyuncertaintyinto a monthlyuncertainty, using an average month length of 30.417. It is very similar in format to his equation 4.

• Instead of adding the variance (=0.195²) for 30.417 times, he replaces the sum with a multiplication. This is perfectly reasonable.
• ...but then in the denominator he only has 30.417, not 30.417². The equation here is again written with the denominator inside the square root (as the 2 was in equation 4). But this time he has actually done the math the way his equation is (incorrectly) written.
• Hisuncertaintyestimate is too big. In his equation the two 30.417 terms cancel out, but it should be 30.417/30.417², so that cancelling leaves 30.417 only in the denominator. After the square root, that’s a factor of 5.515 times too big.

And equation 6 repeats the same error in propagating theuncertaintyof monthly means to annual ones. Once again, the denominator should be 12², not 12. Another factor of 3.464.

Figure 7: Patrick Frank's equation 6.

So, combining these two errors, his annualuncertaintyestimate is √30.417 * √12 = 19 times too big. Instead of 0.382°C, it should be 0.020°C – just two hundredths of a degree! That looks a lot like the BEST estimates in figure 2.

Notice how each of equations 4, 5, and 6 all end up with the same result of ±0.382°C? That’s because Frank has not included a factor of √N – the term in the equation that relates the standard deviation to the standard error of the estimate of the mean. Frank’s calculations make the astounding claim that averaging does not reduceuncertainty!

Equation 7 makes the same error when combining land and sea temperature uncertainties. The multiplication factors of 0.7 and 0.3 need to be squared inside the square root symbol.

Figure 8: Patrick Frank's equation 7.

Patrick Frank messed up writing his equation 4 (but did the calculation correctly), and then he carried the error in the written equation into equations 5, 6, and 7and did those calculations incorrectly.

Is it possible that Frank thinks that any non-random features in the measurement uncertainties exactly balance the √N reduction inuncertaintyfor averages? The correct propagation ofuncertaintyequation, as presented earlier from Wikipedia, has the covariance term, 2abσ_AB. Frank has not included that term.

Are there circumstances where it would combine exactly in such a manner that the √N term disappears? Frank has not made an argument for this. Moreover, when Frank discusses the calculation of anomalies on page 31, he says “theuncertaintyin air temperature must be combined in quadrature with theuncertaintyin a 30-year normal”. But anomalies involve subtracting one number from another, not adding the two together. Remember: when subtracting, you subtract the covariance term. It’s σ_f²=a²σ²_A+b²σ²_B-2abσ_AB. If it increasesuncertaintywhen adding, then the same covariance will decreaseuncertaintywhen subtracting. That is one of the reasons that anomalies are used to begin with!

We do know that daily temperatures at one location show serial autocorrelation (correlation from one day to the next). Monthly anomalies are also autocorrelated. But having the values themselves autocorrelated does not mean that errors are correlated. It needs to be shown, not assumed.

And what about the case when many, may stations are averaged into a regional or global mean? Has Frank done a similar error? Is it worth trying to replicate his results to see if he has? He can’t even get it right when doing a simple propagation from daily means to monthly means to annual means. Why would we expect him to get a more complex problem correct?

When Frank displays his graph of temperaturetrends lost in theuncertainty(his figure 19), he has completely blown theuncertaintyout of proportion. Here is his figure:

Figure 9: A copy of Figure 19 from Frank (2023). The uncertainties - much larger that those of BEST in figure 2, are grossly over-estimated.

Is that enough to realize that Patrick Frank has no idea what he is doing? I think so, but there is more. Remember the discussion about standard deviation,RMSE, and MBE? And random errors and independence of errors when dealing with two variables? In every single calculation for the propagation ofuncertainty, Frank has used the formula that assumes that the uncertainties in each variable are completely independent. In spite of pages of talk about non-randomness of the errors, of the need to consider systematic errors, he does not use equations that will handle that non-randomness.

Frank also repeatedly uses the factor 1.96 to convert the one-sigma 68%confidencelimit to a 95%confidencelimit. That 1.96 factor and 95%confidencelimit only apply to random, normally distributed data. And he’s provided lengthy arguments that the errors in temperature measurements are neither random nor normally-distributed. All the evidence points to thelikelihoodthat Frank is using formulae by rote (and incorrectly, to boot), without understanding what they mean or how they should be used. As a result, he is simply getting things wrong.

To add to the question of non-randomness, we have to ask if Frank has correctly removed the MBE from anyRMSE values he has obtained from the literature. We could track down everysourceFrank has used, to see what they really did, but is it worth it? With such elementary errors in the most basic statistics, is there likely to be anything really innovative in the rest of the paper? So much of the work in the literature regarding homogenization of temperature records and handling of errors is designed to identify and adjust for station changes that cause shifts in MBE – instrumentation, observing methodology, station moves, etc. The scientific literature knows how to do this. Patrick Frank does not.

I’m running out of space. One more thing. Frank seems to argue that there are many uncertainties in LiG thermometers that cause errors – with the result being that the reading on the scale is not the correct temperature. I don’t know about other countries, but the Meteorological Service of Canada has a standard operating procedure manual(MANOBS) that covers (among many things) how to read a thermometer. Each and every thermometer has a correction card (figure 6) showing the difference between what is read and what the correct value should be. And that correction is applied for every reading. Many of Frank’s arguments aboutuncertaintyfall by the wayside when you realize that they are likely included in this correction.

Figure 10: A liquid-in-glass temperature correction card, as used by the Meteorological Service of Canada. Image fromMANOBS.

Frank’s earlier papers? Nothing in this most recent paper, which I would assume contains his best efforts, suggests that it is worth wading through his earlier work.

Conclusion

You might ask, how did this paper get published? Well, the publisher isMDPI, which has a questionable track record. The journal -Sensors- is rather off-topic for aclimate-related subject. Frank’s paper was first received on May 20, 2023, revised June 17, 2023, accepted June 21, 2023, and published June 27, 2023. For a 46-page paper, that’s an awfully quick review process. Each time I read it, I find something more that I question, and what I’ve covered here is just the tip of the iceberg. I am reminded of a time many years ago when I read a book review of a particularly bad “science” book: the reviewer said “either this book did not receive adequate technical review, or the author chose to ignore it”. In the case of Frank’s paper, I would suggest that both are likely: inadequate review, combined with an author that will not accept valid criticism.

The paper by Patrick Frank is not worth the electrons used to store or transmit it. For Frank to be correct, not only would the entire discipline ofclimatescience need to be wrong, but the entire discipline of introductory statistics would need to be wrong. If you want to understanduncertaintyin global temperature records, read the proper scientific literature, not this paper by Patrick Frank.

AdditionalSkeptical Scienceposts that may be of interest include the following:

Of Averages and Anomalies(first of a multi-part series on measuringsurface temperaturechange).

Berkeley Earth temperature record confirms other data sets

Aresurface temperaturerecords reliable?