By Roger Caiazza,
In a special to the Washington Post Oliver Uberti opines that “Trust in meteorology has saved lives. The same is possible for climate science”. The former senior design editor for the National Geographic and co-author of three critically acclaimed books of maps and graphics does an excellent job tracing the history of weather forecasting and mapping. Unfortunately he leaps to the conclusion that because meteorological forecasting has worked well and we now “have access to ample climate data and data visualization that gives us the knowledge to take bold actions”.
Uberti writes:
“The long history of weather forecasting and weather mapping shows that having access to good data can help us make better choices in our own lives. Trust in meteorology has made our communities, commutes and commerce safer — and the same is possible for climate science.”
I recommend reading most of the article. He traces the history of weather observations and mapping from 1856 when the first director of the Smithsonian Institution, Joseph Henry, started posting the nation’s weather on a map at its headquarters. Eventually he managed to persuade telegraph companies to transmit weather reports each day and eventually he managed to have 500 observers reporting. However, the Civil War crippled the network. Increase A. Lapham, a self-taught naturalist and scientist proposed a storm-warning service that was established under the U.S. Army Signal Office in 1870. Even though the impetus was for a warning system, it was many years before the system actually made storm warning forecasts. Uberti explains that eventually the importance of storm forecasting was realized, warnings made meaningful safety contributions, and combining science with good communications and visuals “helped the public better understand the weather shaping their lives and this enabled them to take action”.
Then Uberti goes off the rails:
“The 10 hottest years on record have occurred since Katrina inundated New Orleans in 2005. And as sea surface temperatures have risen, so have the number of tropical cyclones, as well as their size, force and saturation. In fact, many of the world’s costliest storms in terms of property damage have occurred since Katrina.”
“Two hundred years ago, a 10-day forecast would have seemed preposterous. Now we can predict if we’ll need an umbrella tomorrow or a snowplow next week. Imagine if we planned careers, bought homes, built infrastructure and passed policy based on 50-year forecasts as routinely as we plan our weeks by five-day ones.”
“Unlike our predecessors of the 19th or even 20th centuries, we have access to ample climate data and data visualization that give us the knowledge to take bold actions. What we do with that knowledge is a matter of political will. It may be too late to stop the coming storm, but we still have time to board our windows.”
It is amazing to me that authors like Uberti don’t see the obvious difference between the trust the public has in weather forecasts and misgivings about climate forecasts. Weather forecasts have verified their skill over years of observations and can prove improvements over time. Andy May’s recent article documenting that the Old Farmer’s Almanac has a better forecast record, for 230 years, than the Intergovernmental Panel on Climate Change (IPCC) has for 30 years suggests that there is little reason the general public should trust climate forecasts. The post includes a couple of figures plotting IPPC climate model projections with observations that clearly disprove any notion of model skill.
Sorry, the suggestion that passing policy based on 50-year climate science forecasts is somehow supported by the success of weather forecast models is mis-guided at best.
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Roger Caiazza blogs on New York energy and environmental issues at Pragmatic Environmentalist of New York. This represents his opinion and not the opinion of any of his previous employers or any other company with which he has been associated.
Meteorological models are updated with new data every 2 hours or so. Were they not, they’d quickly depart from meaningful predictions of weather.
Climate models are not and can not be updated with future climate data. Ever, obviously. There is no ground for comparison of climate model output with the output of a meteorological model. The extrapolations are entirely different animals.
Oliver Uberti is completely misguided in proposing their equation.
Climate models have no predictive value.
Pat, using your methodology what is the probability that CMIP5 would produce a trend that is within ±0.01 C/decade of the observed trend over a 140 year period?
Given the fact that the first 100 years of that 140 year period is little better than made up, not much.
Just a little bit ago, you were making the absurd claim that the data for 100 years ago was only accurate to 0.25 to 0.35C. Now you are claiming the models match that data to within 0.01C.
Just how badly do you want to discredit yourself?
“Just a little bit ago, you were making the absurd claim that the data for 100 years ago was only accurate to 0.25 to 0.35C”
I never said it was only accurate to 0.25 to 0.35C. I actually said this. On an annual basis it is ±0.15 and +0.10 C for periods around 1880 and 1940 respectively. Berkeley Earth shows about ±0.2 and ±0.1 C for 1880 and 1950 for monthly anomalies. For annual anomalies it is about ±0.12 and ±0.08 C respectively. See Lenssen et al. 2016 and Rhode et al. 2013 for details. 100 years ago was 1920 where published uncertainties are about ±0.15 and ±0.09 C for monthly and annual anomalies respectively. So it’s actually better than the 0.25 to 0.35C range you gave above.
“Now you are claiming the models match that data to within 0.01C.”
I never said models match that data to within 0.01C. I actually said this. The BEST trend is +0.087 C/decade vs the CMIP5 trend of +0.079 C/decade over the period 1880 to 2020. The RMSE on a monthly and 13-month centered mean basis is 0.165 C and 0.116 C respectively.
“On an annual basis it is ±0.15 and +0.10 C for periods around 1880 and 1940 respectively.”
They all ignore systematic measurement error. (890 kb pdf)
Also here.
These people – UKMet/CRU, GISS, Berkeley Earth — all behave as though they have never made a measurement or struggled with an instrument.
Even the resolution of the historical LiG thermometers is no better than ±0.25 C.
Their work is hopelessly incompetent.
“They all ignore systematic measurement error.“
No they don’t. You can argue that they don’t handle systematic error adequately. But you can’t argue that they ignore the issue because they don’t.
“Even the resolution of the historical LiG thermometers is no better than ±0.25 C.”
Yeah, at best. Fortunately this kind of error is mostly random and where it isn’t anomaly analysis will cancel it out. And while we’re on the topic did you know that LiG based stations Tmax are 0.57 C lower and Tmin 0.35 C higher as compared to MMTS stations (Hubbard 2006)? That is an example of real systematic bias that is not ignored. Other biases that are not ignored are the TOB carryover and TOB drift bias (Vose 2003).
“These people – UKMet/CRU, GISS, Berkeley Earth — all behave as though they have never made a measurement or struggled with an instrument.”
“Their work is hopelessly incompetent.”
You’re hubris here is astonishing.
BTW…I tested your hypothesis that the lower limit on global mean temperature uncertainty is ±0.46 C. I did this by comparing GISTEMP, BEST, HadCRUTv5, and ERA with each other from 1979 to present. If your hypothesis were correct then we should see a disagreement between them at σ = 0.65 C. Instead the actual disagreement is σ = 0.053 C implying the uncertainty of each is σ = 0.037 C which is consistent with published uncertainty estimates provided by these datasets and significantly less than σ = 0.46 C.
Hockey pucks—without this assumption, your entire house of cards falls.
Projection.
Wrong in every particular, bdgwx. None of them deal with systematic measurement error. They pass it off.
Instrumental resolution is not error. It is not random. It is the limit of detection sensitivity. Resolution is clearly a foreign concept to you.
Finally, your discussion about the ±0.46 uncertainty just shows you don’t know the difference between physical error and calibration uncertainty.
You display no knowledge at all of any of it.
“None of them deal with systematic measurement error.”
Lenssen 2019, Rhode 2013, Quayle 1991, Hubbard 2006, Vose 2003, Menne 2009, etc.
“Instrumental resolution is not error.”
Yes it is. If the instrument is only capable of reporting to 1 decimal place then the error is rectangular at ±0.5. That is in addition to any accuracy and precision error that it may have as well.
“It is not random”
Yes it is. Well, unless you want to argue that the instrument prefers rounding in one direction or another which would be very unlikely.
“Finally, your discussion about the ±0.46 uncertainty just shows you don’t know the difference between physical error and calibration uncertainty.”
I do know the difference between physical error and calibration uncertainty. And I know that if two measurements of the same thing each have ±0.46 C (1σ) of uncertainty then the differences between those two measurements will distribute normally with σ = 0.65 C. And I know that the real differences between GISTEMP, BEST, HadCRUTv5, and ERA were actually σ = 0.053 C implying the uncertainty of each is σ = 0.037 C. This is despite the fact that each group uses a different technique consuming different subsets of available data.
This…
“If the instrument is only capable of reporting to 1 decimal place then the error is rectangular at ±0.5.”
…should have been…
“If the instrument is only capable of reporting with 0 decimal places then the error is rectangular at ±0.5.”
AGAIN—you conflate uncertainty with error.
Good catch. I should have used the word uncertainty in my post at 7:55am. Note that error is the difference between a specific measurement and the true value while uncertainty is the range in which the errors from repetitive measurements fall into. Because I was referring to the range in which the error could be I should have used the word uncertainty. Let’s try this one more time.
“If the instrument is only capable of reporting with 0 decimal places then the uncertainty is rectangular at ±0.5.”
“uncertainty is the range in which the errors from repetitive measurements fall into”
You just won’t learn the difference will you. Every time you make a repeated measurement of a single thing, uncertainty occurs. IT HAPPENS ON EACH MEASUREMENT. You can’t eliminate it because it is not random.
Uncertainty means you don’t know and can never know what the true measurement should be each and every time you make a measurement. It is always there and you simply can’t account for it with a statistical analysis. Think of it this way. Statistically, any value within the uncertainty interval is just as likely as any other value, but you can never ever determine what the probability of any individual point in that interval is since they all have a similar probability.
Wrong in every particular again, bdgwx.
Lessen, et al., 2019 describe systematic error as “due to nonclimatic sources. Thermometer exposure change bias … Urban biases … due the local warming effect [and] incomplete spatial and temporal coverage.“
Not word one about systematic measurement error due to irradiance and wind-speed effects. These have by far the largest impact on station calibration uncertainty.
Next, resolution is instrumental sensitivity. Any displacement below the resolution limit is physically meaningless. Resolution is not error. A resolution limit is not random error, and it has nothing to do with round-off.
You wrote, “I know that if two measurements of the same thing each have ±0.46 C (1σ) of uncertainty then the differences between those two measurements will distribute normally with σ = 0.65 C.“
You don’t know that because it’s wrong.
Each measurement may take an identical value or some disparate value. However each value will have a calibration uncertainty of ±0.46 C. Their sum or difference will have an uncertainty of ±0.65 C.
Systematic measurement errors due to uncontrolled environmental variables have no known distribution.
Your “σ = 0.053 C … σ = 0.037 C” are again to 3 significant figures past the decimal; again claiming milliKelvin accuracy.
It’s quite clear you don’t know the subject, bdgwx.
“Not word one about systematic measurement error due to irradiance and wind-speed effects. These have by far the largest impact on station calibration uncertainty.”
Great. Provide a link a publication discussing this, the magnitude of its effect, and how much systematic error it causes in a global mean temperature measurement, how much it biases the temperature trend. I would be more than happy to review it. And yes, I’ve already read the Hubbard 2003 and Hubbard 2006 publications. Note that the biases Hubbard discusses were addressed in datasets in a targeted manner early on and now more generally via pairwise homogenization by most datasets today.
“Next, resolution is instrumental sensitivity. Any displacement below the resolution limit is physically meaningless. Resolution is not error. A resolution limit is not random error, and it has nothing to do with round-off.”
Of course that is error. If a thermometer can only respond to a change in temperature of 0.5 C then it might read 15 C even though the true value was 15.4 C. That is an error of -0.4 C. And if you take repetitive measurements with it you’ll find that these errors distribute randomly in rectangular fashion.
“Systematic measurement errors due to uncontrolled environmental variables have no known distribution.”
Then what does your ±0.46 value embody exactly and why did you use 1σ to describe it?
“Your “σ = 0.053 C … σ = 0.037 C” are again to 3 significant figures past the decimal; again claiming milliKelvin accuracy.”
No. I’m not. I’m claiming the differences of measured monthly global mean temperature anomalies falls into a normal distribution with σ = 0.053 C (Excel reports 0.052779447215166) which implies that the individual uncertainty is σ = 0.037 C ( Excel reports 0.037320705033122). I took the liberty of reducing the IEEE 754 values to 3 sf as compromise between readability and not being accused of improperly rounding or truncating to make the values appear higher/lower than they actually are. None of this means that I’m claiming millikelvin accuracy. In fact, the data is saying that it cannot be as low as 0.001 because it is actually 0.037 which is consistent with the various uncertainty estimates provided by the community. I’ll repeat 0.037 K does NOT mean millikelvin uncertainty.
And ultimately why do GISTEMP, BEST, HadCRUTv5, and ERA5 differ by only σ = 0.053 C if the claimed uncertainty is σ = 0.46 C?
“Great. Provide a link a publication discussing this…”
Here, here, and here.
See also Negligence, Non-Science and Consensus Climatology.
“I would be more than happy to review it.” A useless enterprise, given the lack of understanding you display.
+++++++
“Note that the biases Hubbard discusses were addressed… etc.”
You’re just talking through your hat. Again.
Systematic measurement error due to uncontrolled environmental variables cannot be addressed except by inclusion as calibration uncertainty. Included to qualify every reported temperature.
+++++++
If a thermometer has a resolution of ±0.5 C, a temperature of 15.4 C cannot be read off the instrument. Temperatures less than the limit of resolution are invisible to the instrument. You show no understanding of the concept.
+++++++
“σ = 0.053 C” you’re claiming 3 significant figures again, equivalent to an accuracy of 0.001 C. And you neither see it nor, apparently, understand it.
+++++++
“if the claimed uncertainty is σ = 0.46 C?”
Uncertainty is not error. It does not describe the divergence of individual measurements, or of separate trends. It describes the reliability of the measurement.
You’ve not been correct on any point, bdgwx. Not one.
“Here, here, and here.”
The first two are your own publications which have not been received well by your peers and which I’ve shown cannot be correct. I cannot see that the third is even relevant.
“If a thermometer has a resolution of ±0.5 C, a temperature of 15.4 C cannot be read off the instrument.”
That’s my point. If the temperature displays 15 C then the error is – 0.4 C.
“σ = 0.053 C” you’re claiming 3 significant figures again, equivalent to an accuracy of 0.001 C.”
I don’t know how to make this anymore clear. σ = 0.053 C is the result from Excel’s STDEV.P function. It is the standard deviation of the differences between monthly global mean temperature measurements. It is NOT a claim of accuracy or uncertainty of 0.001 C. In fact, it is the opposite. It is saying the uncertainty cannot be as low as 0.001 C. And it doesn’t matter if I report the value as 0.05 or 0.053, 0.0528, or 0.052779447215166. All of those numbers are significantly greater than 0.001.
You’re an idiot who cannot be taught.
If you’re trying to “teach” me that 0.052779447215166 is equivalent to or even on par with 0.001 then I’m going to have to pass.
“I’ve shown cannot be correct.” Big talk. Where?
And I claim in utter confidence that you’re blowing smoke.
“If the temperature displays 15 C then the error is – 0.4 C.”
How would you know in practice? None of the historical LiG thermometers or MMTS sensors included a high-accuracy reference thermometer.
All one has in any case is a previously determined calibration uncertainty, which adds as the RMS in any average or anomaly.
“I don’t know how to make this anymore clear. σ = 0.053 C is the result from Excel’s STDEV.P function.”
An incredible display of utter ignorance. Any report of an uncertainaty to ±0.001 C is a claim of 0.001 C accuracy.
First year college, any physical science. Any high school AP science class.
You’ve been wrong in every instance, bdgwx. You and bigoilbob are such a pair.
“Where?”
I downloaded the monthly data for HadCRUTv5, GISTEMPv4, BEST, and ERA. I compared the monthly data from each dataset with the other datasets from 1979/01 to 2021/08 all 3072 combinations. The differences between the values fell into a normal distribution with σ = 0.052779447215166 C. This implies the uncertainty on each is σ = 0.037320705033122 C. That is significantly lower than the claimed uncertainty of σ = 0.46 C.
“How would you know in practice? None of the historical LiG thermometers or MMTS sensors included a high-accuracy reference thermometer.”
I’m not certain what the error is for each measurement. That’s why we call it uncertainty. Remember, my response is to your statement “Resolution is not error.” My point is not that we know what the error is for every measurement, but that we know that resolution limitations cause error.
“An incredible display of utter ignorance. Any report of an uncertainaty to ±0.001 C is a claim of 0.001 C accuracy.”
Nobody is reporting an uncertainty of ±0.001 C and certainly not me. In fact my analysis suggests the uncertainty is much higher at ±0.037 C. Then you, Carlo Monte, and Gorman criticized my choice of 3 sf for the display of the uncertainty totally missing the essence of the meaning of the value. So now I’m reporting the full IEEE 754 form as σ = 0.037320705033122 C allowing you guys do whatever rounding you want and hopefully avoiding the whole significant figures discussion. Just know that no reasonable significant digit or round rule will result in ±0.037320705033122 C being equivalent to or even on par with ±0.001 C.
“First year college, any physical science. Any high school AP science class.”
It’s more like middle school math. ±0.037320705033122 C is literally an order of magnitude greater than ±0.001 C.
“That is significantly lower than the claimed uncertainty of σ = 0.46 C.”
Uncertainty is not error. Nor is it the difference between alternatively processed sets of identical raw data. You’re making the same mistake over, and yet over again.
“The differences between the values fell into a normal distribution with σ = 0.052779447215166 C.” A display of utter ignorance concerning measurements.
“My point is not that we know what the error is for every measurement, but that we know that resolution limitations cause error.”
Your point is doubly wrong. First, resolution limits mean physical differences below the resolution limit are invisible. That’s not error.
Second, systematic measurement error from uncontrolled environmental variables is not random and unknown for each measurement. However, a calibration experiment can provide a standard uncertainty for each and every measurement. That uncertainty is estimated as ±0.46 C.
Every single LiG and MMTS surface temperature measurement has that uncertainty appended to it.
“Nobody is reporting an uncertainty of ±0.001 C and certainly not me.” You were. And in your post here you’re reporting an accuracy of one part in 10^15.
“It’s more like middle school math. ±0.037320705033122 C is literally an order of magnitude greater than ±0.001 C.”
Really, it’s too much, bgdwx. Your 16-digit number conveys knowledge out to 15 places past the decimal. That’s the issue. Not the magnitude of the number.
You’re arguing from ignorance and dismissing all the objections from people whose career involves working with measurement data.
Pat, I want you to ponder this question as well. Given an annual global mean temperature uncertainty of σ = 0.46 C what would the uncertainty of each grid cell in the HadCRUTv5 grid have to be?
The representative uncertainty in the temperature average within an arbitrary grid-cell depends on the number of meteorological stations within it.
Any given station average has an associated representative ±0.46 C uncertainty. The grid-cell average uncertainty is the rms of the included station uncertainties.
As the number of station averages going into a grid-cell average or global average becomes large, the representative rms uncertainty tends to ±0.46 C.
Note this quote from the paper (pdf): “The ideal resolutions of Figure 1 and Table 2 thus provide realistic lower-limits for the air temperature uncertainty in each annual anomaly of each of the surface climate stations used in a global air temperature average.”
The uncertainty per grid-cell should be obvious.
Some grid cells have zero meteorological stations, however.
HadCRUT uses a 5×5 lat/lon grid which means there are 2592 cells. The global mean temperature value is sum(Tn/N) where Tn is the value of one grid cell and N is the number of grid cells. In other words, it is the trivial average of the grid. So if the uncertainty of sum(Tn/N) is ±0.46 C then what is the uncertainty of Tn?
The representative uncertainty from systematic error in each and every measured temperature is ±0.46 C.
They combine in every average as their root-mean-square. When N is large the rms is sqrt[(N*(0.46)^2)/(N-1)] = ±0.46 C.
Try it yourself, with N = 2592.
That point is made in my 2010 paper, and has been made above. Must I repeat it again?
I did try it. I created 10000 grids each with 2592 cells. For each grid I assigned each cell a true value and a measured value. The measured value has error injected consistent with ±0.46 C of uncertainty. In the first experiment I assumed the uncertainty was normal, for the second I assumed it was rectangular, and for the third I assumed it was triangular. In each experiment the errors fell into a normal distribution with σ being 0.009, 0.005, and 0.004 respectively.
I repeated the experiment this time with a 500,000 cell grid like what ERA uses. The σ for each of the 3 experiments in that case was 0.0007, 0.0004, and 0.003 for normal, rectangular, and triangular distributions of ±0.46 C.
No they don’t. You are not measuring the same thing. The temp you measured is gone and in the past. When you look at a temp in 1-1-1910 and it says 75 +/- 0.5 and you look at a temp in 1-2-1910 and it says 75, how do you average those and say uncertainty is reduced? the first temp could have been 74.5 and the second 75.49 or any other combination. You have no way to know for sure and you can analyze that all you want but you’ll never find a way to insure that you know what either actual reading was except for 75 +/-0.5!
I did the experiment. I generated 2 values centered on 75 with error injected consistent with ±0.5 uncertainty and computed the mean 10000 times. For uncertainty that was normal, rectangular, or triangular the final error of the mean of the 2 values ended up being distributed normally with a standard deviation of 0.353915064758854, 0.202383818797022, and 0.145120246179076 respectively. It is interesting to note that for the case where the ±0.5 uncertainty is normally distributed the error of the mean is expected to be 0.5/sqrt(2) = 0.353553390593274 so theory and experiment agree nicely here and it proves that the uncertainty of the mean is lower than the uncertainty of the individual measurements in the scenario you crafted. I encourage everyone including you to replicate this experiment.
Your artificial “experiment” gave you exactly the answer you programmed it to give.
No it didn’t. I never entered 0.353553390593274 anywhere in my program. That value appeared organically from the ±0.5 normally distributed uncertainty of the two 75 values we are averaging. Don’t take my word for it though. Do the experiment yourself.
You generated an experiment to test whether multiple measurements of the same thing will generate a normal distribution around a true value. In other words your experiment was a failure – since the goal is what you get for uncertainty for temperature data which is *NOT* a random distribution around a true value.
He generated a random distribution around a “true value” – in other words what you would get from multiple measurements of the *same* thing. Temperature measurements are *not* measuring the same thing.
Jim’s scenario was 2 temperatures one being on 1-1-1910 and the other begin on 1-2-1910. Just because both happen to be 75 doesn’t mean they were same thing. Do you want me to redo the experiment with different values so there is doubt that they are different things and see if makes a difference?
“distributed normally with a standard deviation of 0.353915064758854“
In-farking-credible: 😀
It’s too bad your Excel output can’t be extended, bdgwx. After all, your limits of accuracy are infinitely expandible.
Your experiment shows that if you generate random error, you find random error. That’s definitive proof, alright.
Hopeless.
Personally I’m glad Excel only uses IEEE 754. Extended precision calculations would be brutal for me. I’m finding it annoying enough as it is typing in 15 digits each time.
What my experiment showed is that a normally distributed uncertainty of ±0.5 leads to a reduced uncertainty of the mean of two values that follows σ/sqrt(N) where N = 2. The experimental value was 0.353915064758854 which agrees reasonably well with the expected value of 0.353553390593274.
“What my experiment showed is that a normally distributed uncertainty of ±0.5 leads to a reduced uncertainty of the mean of two values that follows σ/sqrt(N) where N = 2″
But temperature is *NOT* a normally distributed value around a true value. Your two measurements should represent independent, random populations with a population size of one. There is no “true value” with such and therefore there is no normally distributed uncertainty.
Uncertainty of independent random measurements, by definition, has no probability distribution, normal or otherwise. An uncertainty interval is *NOT* a normal distribution. It is a distribution where one value has a probability of 1 and all the rest have a probability of zero. That is *NOT* a normal distribution. The problem is that you don’t know which value in the uncertainty interval has a probability of 1!
You are *still* confusing error with uncertainty!
Take these two height measurements: 5′ 2″ +/- 1″, and 7′ 1″ +/- 1″. Do they represent a normal distribution around a “true value”?
What *YOU* think you found was the standard error of the mean, not the uncertainty of the mean. The uncertainty of the mean is driven by the uncertainty of the measurements. For independent, random, uncorrelated measurements you cannot minimize the accuracy of the mean by dividing by √N. With two values, N = 2 is the population size, not the sample size. The mean is the mean (there is no standard error of the mean) and the standard deviation is the √variance between the two values.
“But temperature is *NOT* a normally distributed value around a true value.”
Pat says it is. In fact, Pat says that annual mean station temperature anomalies distribute normally around the true value at σ = 0.46.
“Pat says it is. In fact, Pat says that annual mean station temperature anomalies distribute normally around the true value at σ = 0.46.”
I have not, have never and would never write or say such a thing.
I’ll be charitable and figure you’re delusional, bdgwx.
So is it triangular, rectangular, or something else?
The error distribution varies with environmental variables (time) in any one instrument and between instruments. It is never known to be normal.
I linked you to my WUWT post on error distribution in field air temperature measurements.
The post summarizes my peer-reviewed published papers on the issue. Apparently you didn’t consult it. Do look this time.
Just stop, bdgwx. As a working physical methods experimental chemist of 30+ years standing, I’m telling you that you don’t know what you’re talking about.
Tim Gorman is a working engineer. He works with measurements and must get their reliability right for reasons of operation, safety and economy. He’s telling you your approach is wrong.
So give it up.
You never bothered with the interactive sampling demos did you?
How many times does the phrase “errors are not uncertainty” have to be repeated before you stop mixing up what the two concepts truly means.
I’m sure what you did was generate a perfect Gaussian distribution around a “true value”. That is what an error distribution where you make multiple measurements of the same thing will generate. I have no doubt that the true value has a very small Standard Deviation when you do your calculations.
However, you either didn’t read my earlier post or didn’t understand it. When you divide the population Standard Deviation by the sample size, you are calculating the Standard Deviation of the mean of the sample means, e.g., the SEM or as you call it the uncertainty of the mean. The SEM has no meaning when you have already calculated the mean and SD of the population.
As I said before the formula is:
SEM = SD / √N
Your very division of the Standard Deviation defines your data as a population distribution and not a Mean of Sample Means. Calculating an SEM is meaningless when you already have a population where you can compute the mean and SD.
The SEM is only useful when you can’t measure the entire population and must use sampling. The SEM then tells you how closely your samples mean is to the population mean. From that you can multiply the SEM by the √N to obtain the estimated population Standard Deviation. Since you already have the SD, your last calculation is worthless.
I’ll post this again. You should read it over and over until you understand it. It is an article that was worth posting by the U.S. government. Specifically the NIH/NCBI. It is not a worthless blog post by a nobody.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2959222/#
One last point. In the real world, every one of those 10,000 measurements you calculated would have an uncertainty involved with it. Each and every one of them. That means you would not know what the exact measurement was every time you made one of the 10,000 measurements. That widens your uncertainty interval considerably whether you realize it or not. The uncertainties don’t cancel and nothing you can do mathematically will reduce them. The value within the interval is unknowable.
“I did the experiment. I generated 2 values centered on 75 with error injected consistent with ±0.5 uncertainty and computed the mean 10000 times.”
Uncertainty is not error. Write that down until you internalize it.
If you “generated” an error value then you did *NOT* calculate uncertainty, you calculated calibration error. You can only find calibration errors like this by comparing the measuring device with a standard reference in an established environment bubble. This isn’t possible in the field when each measurement is taken.
In essence you generated a random distribution around a true value based on multiple measurements of the same thing. In other words, your experiment was a failure. Temperature measurements are *NOT* multiple measurements of the same thing.
How about this. Since you are unwilling to do the experiment how about you tell me how you want it done and I’ll do it for you. This exercise will at least tell us what you mean when you say “error” and “uncertainty”.
Why do you ignore this obvious fact?
I didn’t ignore it. I entered the temperature of 75 for 1-1-1910 and 75 for 1-2-1910 and model uncertainty consistent with ±0.5 independently for each day. The error of the mean distributed normally with σ = 0.353915064758854 which agrees reasonably well with the expected value of σ = 0.353553390593274.
“Of course that is error. If a thermometer can only respond to a change in temperature of 0.5 C then it might read 15 C even though the true value was 15.4 C. That is an error of -0.4 C. And if you take repetitive measurements with it you’ll find that these errors distribute randomly in rectangular fashion.”
You truly don’t have any experience with physical science, do you?
Are you challenging 1) that instrument resolution limitations leads to measurement error and 2) that if the true value is 15.4 and the measured value is 15 then the measurement is -0.4?
How did you determine the true value was 15.4?
Assume you know the true value is 15.4 C. Assume the instrument read 15 C. Under that scenario would you challenge the fact the error is -0.4 C?
Who cares? This is a total non sequitur to uncertainty.
It is good that you mentioned “the same thing”. Temperature measurements are NEVER OF THE SAME THING. Consequently, you HAVE NO ERROR OR UNCERTAINTY DISTRIBUTION to be used to analyze what a true value may be.
The same thing implies a common basis for analyzing an error distribution. Temps don’t have that. Uncertainty can’t be reduced by averaging two data points with the same uncertainty. I’ll say it again, uncertainty is what you don’t know and can never know. If your uncertainty is is 0.5 you must PROPAGATE it throughout. That doesn’t mean reduce it.
Completely and totally 1000% wrong, this is ONLY true if the distribution is normal, which in general is NOT KNOWN.
Pat wrote this in his paper. And don’t think the irony of Pat using 3 sf here went unnoticed.
±σ = sqrt(0.283^2 + 0.359^2) = ±0.46 C
You silly person, if you had actually understood what he wrote, you might have grasped that the paper was ONLY dealing with the uncertainty caused by the cloud fraction uncertainty growing at each model iteration step.
There are OTHER sources of uncertainty, duh.
“You silly person, if you had actually understood what he wrote, you might have grasped that the paper was ONLY dealing with the uncertainty caused by the cloud fraction uncertainty growing at each model iteration step.”
That’s not even remotely close. Pat clearly states that ±0.46 is calculated as ±σ = sqrt(0.283^2 + 0.359^2) = ±0.46 C where 0.283 is attributed to noise and 0.359 is attributed to resolution. This is for station temperature measurements. This has nothing to do with cloud fractions or even models.
bdgwx was referring to my paper (pdf) on uncertainty in the global average annual temperature record, CM, not the paper on climate models.
The published record is yet another piece of scientific crockness.
Ah ok, my bad, it wasn’t clear from his comments. I’ll have to re-read…
Earth to bdgwx: the reported uncertainty is two significant figures. Note the data in Hubbard and Lin.
Typically, one calculates with one more significant figure than the measurements allow. One then rounds the final value to the requisite level of accuracy.
Standard practice, bdgwx. You clearly didn’t know that, either.
“Standard practice, bdgwx”
Agreed. I have no issue with that.
So then retract your comment of October 21, 2021 8:32 am.
It is not random. It is not random. It is not random.
A single measurement doesn’t not have a distribution where random error can cancel. If the measurement error is 1 degree, it remains one degree. You can not take a different measurement at a different time or place and say you can cancel random measurement errors for each reading.
You can average two or one million readings and that error propagates into the average from each and every measurement. To say they cancel you must assume that the errors have a random distribution, but you can’t verify that at all. As much as you would like to claim that, you have no basis for knowing what the correct values of each measurement should be. It simply can’t be proven through statistics.
If you are trying to pawn off the “error of the mean” again, you are wasting everyone’s time. That has nothing to do with analyzing systematic error in each and every temperature data point.
Hi Jim – nice to see you and your cogent views enter here. 🙂
Thank you. I try to do my best.
Even if my memory of your lies wasn’t perfect, it still remains that your claim in the post immediately above directly contradicts your earlier comment.
Can you quote the statements you feel are contradictory? If I’ve made a mistake I want to correct it.
Let’s review here.
The difference between the HadCRUTv5, GISTEMPv4, BEST, and ERA datasets falls into a normal distribution with σ = 0.052779447215166 C implying the uncertainty on each is σ = 0.037320705033122 C.
I report these values as σ = 0.053 C and σ = 0.037 C respectively following the standard sf rules. Note that the source data had 3 sf so my result has 3 sf.
Pat Frank, Carlo Monte, and Gorman completely divert away from the essence of these values and make a big stink about 1) these values being basically equivalent to ±0.001 even though they’re not even close and 2) me using the standard sf rules.
Meanwhile Pat Frank takes the σ = 0.2 figure from the Folland 2001 publication and runs it through sqrt(N*σ^2/(N-1)) = 0.200 for a 30-yr mean then through sqrt(0.2^2 + 0.2^2) = 0.283 and then combines that with the σ = 0.25 figure from Hubbard 2002 run through sqrt(N*σ^2/(N-1)) = 0.254 for a 30-yr mean then through sqrt(0.254^2 + 0.254^2) = 0.359 for a grand total of sqrt(0.283^2 + 0.359^2) = 0.46 which uses 2 sf even though the calculation was based on data from Folland with only 1 sf. And yet somehow I’m the one doing the sf rules wrong because I used 3 sf because the source data was 3 sf. Don’t hear what I’m not saying. I’m not challenging Pat’s handling of sf here. I have no issue with it. What I am saying is that this sf discussion is a diversion and distraction away from the core essence these figures.
Furthermore, Pat’s own source Folland does not agree with the σ = 0.46 uncertainty.
We’re still left with these questions…
Why do HadCRUTv5, GISTEMPv4, BEST, and ERA differ by only σ = 0.052779447215166 C implying an uncertainty of σ = 0.037320705033122 C?
How can we reconcile Pat’s σ = 0.46 C claim with my result and results like Folland 2001, Lenssen 2019, Rhode 2013, etc which are consistent with mine?
And assuming σ = 0.46 C for a global mean temperature what would the σ have to be on a grid cell using the HadCRUT grid which has 2592 cells?
“The difference between the HadCRUTv5, GISTEMPv4, BEST, and ERA datasets falls into a normal distribution with σ = 0.052779447215166 C implying the uncertainty on each is σ = 0.037320705033122 C.
Uncertainties add whether you add or subtract populations. Variances add when you combine random populations.
As variance goes up so does the population standard deviation.
Once again, you appear to be conflating standard error of the mean with uncertainty of the population and thus its mean. They are *NOT* the same.
“me using the standard sf rules.”
You *still* don’t seem to get significant figure rules. If the temperatures are reported to the unit digit then how do you get 0.036 as a correct figure based on significant figure rules? The MEASUREMENTS and the uncertainty should have the same number of significant digits.
“And assuming σ = 0.46 C for a global mean temperature what would the σ have to be on a grid cell using the HadCRUT grid which has 2592 cells?”
There are so many problems with this that it is hard to address it completely. FIRST – standard error of the mean is *not* the accuracy of the mean. The uncertainty of the mean is the propagated uncertainty from all population components. Second, If each temperature measurement is considered to be an independent, random, uncorrelated measurement, i.e. 2952 separate values each with an uncertainty of δ = u, then you get the sum of u1 … u2952. You can either do a direct addition or a root-sum-square addition. Uncertainties are treated in somewhat the same manner as variances of combined independent, random variables — the variances all add. Since the standard deviation of the population is the sqrt of the variance the sd goes up as you add more independent, random populations and the variance goes up. You do *not* divide the resulting variance by the population size (i.e. V/N) to get the population variance. The population variance *is* the population variance by definition. The sd is √V , not √V/√N.
First…I didn’t even compute a mean in my analysis. All I did was log the difference between two values. Do you know why the differences formed into a normal distribution with only σ = 0.052779447215166 C?
Second…I’m just asking what the uncertainty is for a grid cell in HadCRUT’s grid which has 2592 cells? If you want to use RSS then do so. What answer do you present?
Did you even read the paper? Or did you just skim until you found an RSS calculation?
You must have missed the “lower limit” bits.
Oh I definitely saw that. I also saw that it is the lower limit for the annual anomalies; not monthly anomalies. Monthly anomaly uncertainty is higher than annual anomaly uncertainty so the implication is that Pat believes the lower limit on the monthly uncertainty is higher than ±0.46 C.
“I also saw that it is the lower limit for the annual anomalies;”
No, it is not. The quote tells you what that ±0.46 C, is, and you somehow were blind to it.
Here it is again: “The ±0.46 C lower limit of MMTS uncertainty is therefore applicable to every measurement…” Every measurement has an appended ±0.46 C uncertainty. Every. Single. Measurement.
“Monthly anomaly uncertainty is higher than annual anomaly uncertainty so the implication is that Pat believes the lower limit on the monthly uncertainty is higher than ±0.46 C.”
Wrong again. Why not actually read the paper, bdgwx?
If you have read it, and have come away with the view you parlay here, you’ve understood none of it.
You misunderstood the meaning of Folland’s assigned ±0.2C reading error, too. Significant figures don’t play into it at all.
And there’s the issue. You think the uncertainty of the mean is the same as the uncertainty of the individual elements in the population. That’s not right. You don’t need to take the word of statistics text, expert statisticians, and myself though. Prove this out for yourself with monte carlo simulations.
You need to decide, are the elements in a population or are they a sample.
I showed you in a comment above what the formula relating population SD to sample means, e.g. the SEM and gave you links to demonstrations of how they relate.
Read what you said. There is no uncertainty of the mean when you are dealing with a population. What you have are parameters like Mean, Standard Deviation, Skewness, and Kurtosis. The “uncertainty of the mean” is a bastardization of the Standard Error of the Sample Mean (SEM) that is derived from samples of the population. When you divide by the √N you are CALCULATING THE SEM.
When you have the entire population, and calculate the mean, there is no uncertainty of the mean. It is what it is and it should be resolved based upon using Significant Digit rules. The uncertainties of each and every measurement in the population does propagate through to the mean.
You can calculate an estimate of the population SD when you are dealing with sampling by MULTIPLYING by the √N. But N is the sample size, not the number of members of all the samples added together.
If you assume your all the individual members are really a sample and that there is only one sample you still find the SEM which is the standard deviation of the one sample you have. Then you multiply that by the √N where N is the number of individual members of your sample.
I’ll repeat shat I posted above from the NIH link: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2959222/#
Please post a reference that contradicts this. You are trying to do an Appeal to Authority without quoting any authority. I have posted authority after authority. You should take the hint that you should not do an Appeal to Authority without showing the Authority.
If you want to be the authority yourself, don’t post anonymously. Let us know what your bono fides are. I am not ashamed to show my real name, you shouldn’t be either. I am not ashamed of my engineering degree nor what I have learned in industry over 30+ years of working with innovative equipment.
“You think the uncertainty of the mean is the same as the uncertainty of the individual elements in the population. That’s not right.”
Uncertainty in the mean converges to the uncertainty in the individual measurements (your elements) when the measurement uncertainty is a representative estimate, and the number of measurements going into the mean is large.
I proved that in my 2010 paper. (pdf) See Case 3b, page 973.
No Monte Carlo simulation can test the outcomes of errors of unknown magnitude and distribution.
You plain do not get the difficulty of evaluating the physical error and reliability of real-world measurements.
Neither do consensus climatologists, by the way.
So when I report a result to 3 sf because my source data is 3 sf I’m wrong. But when you report a result to 2 sf even though one of your sources was 1 sf it’s okay because sf doesn’t come into play at all in your case?
You need to define what “sf” means first. If it is Significant Digits, exactly where do you get temps to 3 SigFigs prior to 1980 or so? Exactly what report are you talking about with 2 SigFigs vs 1 SigFig?
Folland’s ±0.2 C reading error is an assigned value. It is neither measured, nor estimated. It therefore has no significant figures. It’s accuracy is assigned as though infinite.
One can therefore further assign an infinite number of zeros past the decimal after the two. As many as you like.
Folland says the measurement error for LAT observations is “estimated”. He literally uses the world estimated.
How was the estimate calculated? Guess, percentage, etc. Show some math!
And I pointed out that, ‘This estimate was not based on a survey of sensors nor followed by a supporting citation.”
Folland’s ±0.2 C error estimate is a guess.
It almost would not have mattered what number they guessed. They assume all error is random, and then just 1/sqrt(N) it all away.
The whole field of consensus climatology is full of similarly self-serving assumptions.
Even the multiplying by 1/✓N is a joke! The data is either a sample OR it is a population. It can’t be both. Dividing the population Standard Deviation (SD) by ✓N will give the SEM which is worthless if you already have a population. If you declare it a sample, then you multiply the sample standard deviation (SEM) by the ✓N to get the estimated SD! Too bad they never declare what they are using.
Yeah, I noticed that the Folland 0.2 figures was an estimate without citation as well. That’s all the more reason to leave that figure as-is with 1 sf. And for the record I think individual station uncertainty is much higher than the Folland estimate even when using anomaly analysis.
And nobody is assuming ALL error is random. These datasets go to great lengths to identify and correct for systematic error like what is caused by station moves, instrument changes, time of observation changes, etc. via pairwise homogenization and other techniques. And they already know about calibration errors like what Hubbard and various others document. Furthermore, there are several reanalysis datasets which corroborate the traditional datasets. The maintainers of these datasets are not the idiots you make them out to be.
“That’s all the more reason to leave that figure as-is with 1 sf.“
Assigned values have no significant figures. Reasserting your prior mistake doesn’t make it correct.
“And for the record I think individual station uncertainty is much higher than the Folland estimate …”
Non-sequitur. Folland’s estimate is for read error, not station uncertainty.
“… not station error even when using anomaly analysis.”
Taking anomalies increases the uncertainty as the rms of the errors in the measurement and the e.s.d. of the normal.
“And nobody is assuming ALL error is random.“
Diversionary. We’re not talking about ALL error. We’re talking about systematic measurement error.
P. Brohan, et al., (2006) Uncertainty estimates in regional and global observed temperature changes: A new data set from 1850 doi:10.1029/2005JD006548
Under 2.3.1.1. Measurement Error “The random error in a single thermometer reading is about 0.2 C (1 s) [Folland et al., 2001];…”
They take the assigned read error, which is necessarily a constant, treat it incorrectly as random, and then average it away as 1/sqrt(N). That’s QED for my side.
“These datasets go to great lengths to identify and correct for systematic error…”
Heroic lengths, actually, but to make an underestimate. Look at Figure 2a in Folland, 2001 embedded below.
Those error-lines are 2-sigma! The largest uncertainties are SST biases and sensor exposure, and their maximum values are ±0.07 C in 1860. Absolutely ludicrously unrealistic underestimates.
No mention at all of LiG resolution of ±0.25 C, which alone dwarfs their comical estimate.
“And they already know about calibration errors like what Hubbard and various others document.”
Except Folland never mentions calibration error, or systematic measurement error.
Folland Figure 2 Legend: ”Uncertainties (2-sigma) due to: data-gaps and random errors estimated by RSOA (heavy solid); SST bias-corrections (heavy dashes); urbanisation (light dashes); changes in thermometer exposures on LAT (light solid).”
Calibration error is nowhere to be seen in the list of errors, neither in Folland 2001, nor in Brohan, 2006.
Evidently they have no knowledge of calibration errors; errors that are absolutely basic to data analysis in all branches of physical science.
“… reanalysis datasets which corroborate …“
Reanalysis uses climate models to extrapolate observations globally. They have no choice but to reproduce the observations on which they depend.
“The maintainers of these datasets are not the idiots you make them out to be.“
I never made them out to be idiots. I’ve made them out to be incompetents. Any knowledgeable reading of their methodology as quoted above will confirm that judgment.
Pat,
Here is a document from the mid-1800 that indicate how to graduate (in fine detail) a thermometer. It states that graduations were in 1°F increments. I don’t know how anyone could estimate centigrade random errors to +/- 0.2°, especially if they were recorded in integer values. The uncertainty would have to be, with integers, +/- 0.5° and 0.2° C is entirely within the uncertainty range. To get 0.2°, the graduations would have to be at 1/2 degree increments and the recordings to the nearest 0.5 degree.
I have not found any records of 1850 markings having that degree of graduation, even for centigrade. I have searched everywhere on the internet for antique fahrenheita and centigrade thermometers and have found none with 0.5° graduations. I suppose one could argue that the random error actually surrounds the ability to discern where on each side of 0.5° a mercury could lie but one still can’t tell where the actual mercury was and the uncertainty interval is what should rule.
https://www.jstor.org/stable/111186?seq=1#metadata_info_tab_contents
Thanks, Jim. I have the Walsh paper, though not as fine a copy as the JSTOR version.
I’ve looked into old LiG meteorological thermometers, too. The picture below is a good quality Dixey meteorological min-max thermometer dating from Victorian times, say mid to mid-late 19th century.
The fine divisions are a Fahrenheit scale and the wider (outside) divisions are the Réaumur scale (0 = freezing water, 80 = boiling water).
The Fahrenheit is graduated in 1 F divisions. They’re visually fine. There’s no way a station keeper could field read it to better than ±0.25 C.
I have a picture of a Taylor meteorological min-max from the mid 19th century graduated in 5 F increments. The field resolution on that instrument couldn’t be better than 1 F. There’s likely no idea how widespread the usage of 5 F division thermometers was.
I’ve another with 2 F divisions. No published estimate of their prevalence, either.
If you divide a Standard Deviation by √N you get the Standard Error of the Sample Mean which is an interval within which the mean should lie. It is also not meaningfull since you are dealing with a population, so you already know the Standard Deviation. The SEM is only used when you have a sample of the population and it is used to caclulate an estimate of the population Standard Deviation.
Since they have implicitly defined the data as a population, there is no need to deal with sampling calculations. As you say it is an artificial way to show a smaller value.
Showing yet another lack of understanding about uncertainty. You cannot correct data with uncertainty by using other data with uncertainty (e.e. pairwise homogenization). The uncertainty in such a case *grows* when you try to homogenize the data.
That is also part of the problem with trying to infill a grid using averages of surrounding grids. All those stations have uncertainty. When you create an average the final uncertainty *grows*, it is some kind of a sum of the individual uncertainties. Yet this uncertainty is never accounted for in the “in-filled” data.
If these are considered to be independent, random variables then their variance after combination is the sum of the individual variances. Uncertainty grows in the same manner.
When they move a station, install newer equipment, or change the collection time, etc then the old record should be ended and a new one started. I understand the push to have a continuous record but it is only fooling one’s self that you can “correct* past uncertain data or “adjust” new uncertain data to account for these changes.
“How can we reconcile Pat’s σ = 0.46 C claim with my result and results like Folland 2001, Lenssen 2019, Rhode 2013, etc which are consistent with mine?”
Simple. I take systematic irradiance and wind-speed measurement error into account.
Your faves do not.
Nor do you.
They’re wrong. So are you.
All of the worlds leading experts on the global mean temperature including expert statisticians are all wrong while you’re right?
Lots of scientists do make this error. Why do you think this was written in the first place, and secondly, put on an NIH website?
The SEM tells you nothing about the error or uncertainty of a population mean. It really only tells the interval within which the mean of the sample means lies. (Go through the demonstrations I posted above of how it works!) From the width of that interval one can surmise that the mean of the sample means (SEM) very precisely tells you what the population mean is. That is one reason for using Significant Digit rules even when calculating sample means.
Too many scientists erroneously assume they are dealing with a sample and that by dividing the sample’s Standard Deviation (e.g., the SEM) by the √N they are calculating an uncertainty. They are not. They are calculating the SEM of a mean of samples means taken from the samples. Think SEM of the SEM. That makes no sense!
Remember once you declare you have a sample, then the object is determine the mean and SD of the population. You do that by multiplying the SEM by the √N, not by dividing.
All the worlds leading experts on the global mean temperature including expert statisticians explicitly assume all measurement error is random. They uniformly ignore systematic measurement error due to irradiance and wind-speed effects.
Every worker who does the above is wrong.
If they all do it, and they do, they’re all wrong.
That’s not my word. That is the verdict of the methodologically correct practice that governs experimental scientists.
Sensor field calibration experiments have been published, bdgwx. Berkeley BEST, GISS, UKMet/UEA all studiously and willfully ignore them. Including Zeke Hausfather.
Were those known calibration errors taken into account, all those groups would be left with nothing to say. And there’s the inspiration for their negligence and silence.
milli-Kelvin?
HAHAHAHAHAHAHAHAHAHAHAH
Where are you seeing milli-Kelvin?
“The BEST trend is +0.087 C/decade vs the CMIP5 trend of +0.079 C/decade over the period 1880 to 2020. The RMSE on a monthly and 13-month centered mean basis is 0.165 C and 0.116 C respectively.”
You’re claiming three significant figures past the decimal, bdgwx. MilliKelvins.
Ah…it was from a different post. Note that the first two numbers are not in units of K. They are K/decade which is different from K. It is only the last two numbers that are in units of K and those are root mean squared error values which Excel actually reports to 15 sf because it uses IEEE 754. I did reduce this to 3 sf for readability.
And if you understood anything about uncertainty, you might understand how this distinction is irrelevant.
Right on, C,M. 🙂
Thanks, Pat! I have been around and around with these guys and their wild claims, but they just persist.
So in essence you do believe that Excel’s report of 15 sf is correct but you just reduced it so we peons could read it.
A very good explanation of what you think Significant Digits rules are for in physical measurements. For scientific purposes what rules did you use in choosing 3 digits over 2 or 4?
I remind you of this from the Washington Univ of St. Louis chemistry department:
Yes. I think Excel does IEEE 754 arithmetic correctly. If you feel as though I’m trying to hide something by reducing the number digits for readability I’ll be more than happy to report all digits in the future and let you do whatever rounding you see fit.
/shakes head/ — demonstrating AGAIN that you have no comprehension of what Jim is trying to convey.
This is so ignorant of physical science that you have confirmed what most folks guessed.
You haven’t bothered to look at any of the links I have posted have you? Floating point computations have NOTHING to do what-so-ever with SIGNIFICANT DIGIT RULES.
I just can not believe that you could have made a statement like this! There is absolutely no doubt in my mind that you are a mathematician who has never taken a lab course in chemistry, physics, or engineering. You would have failed them if you couldn’t quote Significant Digit Rules from memory and use them religiously when making measurements and manipulating them.
I’m not challenging any of the established significant digits rules. What I’m challenging is the claim that an RMSE of 0.165434942894202 K for monthly anomalies as computed by Excel is not in any way equivalent to saying we can predict the global mean temperature to within a millikelvin. You can can round that number to however many sf you want and it will always still be significantly greater than 0.001 K.
RMSE — a quantity that can ONLY be evaluated if TRUE VALUES are known!
Another duh.
If it doesn’t do significant figures correctly then it is not doing arithmetic correctly.
Pat didn’t do the significant figures correctly. He had source data with 1 sf and reported his result to 2 sf. Does that mean his arithmetic that yielded σ = 0.46 is incorrect?
“He had source data with 1 sf and reported his result to 2 sf.”
Folland’s ±0.2 C reading error is assigned, not measured. It is an exact figure, which means it does not fall under the rule of significant figures.
Folland says “We estimated the two standard error (2σ) measurement error to be 0.4 C in any single daily LAT observation”.
And just how was that “estimate” derived? A guess maybe? Show the math used to reach an estimate.
Folland’s estimate is an assigned value. They can have no idea what the read-error was of past station managers.
Folland’s guess is discussed in detail in my paper, bdgwx. Try reading it.
I did read it. That’s how knew what formulas you used to calculate σ = 0.46 (which I replicated somewhere in the comments section) and how knew one of your source inputs was given to 1 sf only. I also read the Folland publication which is how I knew the σ = 0.2 value he provided was an “estimate”. BTW…don’t think I didn’t notice Tim Gorman saying if you don’t use the sf correctly then you aren’t doing the arithmetic correctly and that you spoke highly of Tim Gorman earlier. Personally I don’t in anyway think that means your arithmetic is wrong here. I think you’re still wrong; but for other reasons.
“…how knew one of your source inputs was given to 1 sf only.”
Assigned values do not have significant figures. Let’s see, you’ve made that same mistake about four times, now.
“BTW…don’t think I didn’t notice Tim Gorman… etc.”
Tim Gorman has never claimed that an assigned estimate had significant figures. You own that mistake.
“I think you’re still wrong; but for other reasons.”
Reasons that have invariably been ignorance-laden.
It’s not an assigned value. It is an estimated value.
And my point wasn’t that Tim Gorman said that an “assigned estimate” had significant figures. My point was that he said if you didn’t do sf correctly then you didn’t do the arithmetic correctly which is an absurd assertion because even if I could convince you that your use of sf was wrong that wouldn’t automatically make your use of RSS wrong.
BTW…just so you understand my position here I want you know this whole sf conservation is a complete distraction. I don’t think your 0.46 is wrong because of the number of sf anyway. You could have published the value as 0.5 and I would still think it is wrong. Just like I think it is wrong to claim that ±0.037 is equivalent to ±0.001 which is what got this whole conservation started in the first place.
There was no published analysis. Not even a hint. It’s an assigned value.
I didn’t use RSS in the 2010 air temperature paper.
“You could have published the value as 0.5 and I would still think it is wrong.”
Think as you like. You’ve demonstrated nothing.
“Just like I think it is wrong to claim that ±0.037 is equivalent to ±0.001…”
Your ±0.037 C represents a claim of accuracy to ±0.001 C. They have an identical number of significant figures past the decimal.
That was your mistake, and that began this whole conversation.
Hip hip hooray. It is simply proof that Significant Digits no longer matter, only the amount of digits that a calculator or computer can spit out when calculating averages. If irrational numbers come up, heartbeats race because you can have an average with 100 decimal place or more! Doesn’t matter if you can only measure to the 10’s digit, by GUM we can divide by the √N and reduce the uncertainty to 4 decimal places.
PF said: There was no published analysis. Not even a hint.
I know!
PF said: It’s an assigned value.
It is an “estimate” (Folland’s word choice). It is a guess. It is not an exact value so it doesn’t get infinite significant figures like how you deal with an exact value. It is what it is with 1 significant figure.
PF said: “I didn’t use RSS in the 2010 air temperature paper.”
±σ = sqrt(0.283^2 + 0.359^2) = ±0.46
That is the root sum squared (RSS) method.
PF said: Your ±0.037 C represents a claim of accuracy to ±0.001 C.
That statement is just as absurd now as when you originally made it. I don’t think you even know what the ±0.037 C figure even means. Let me illustrate in no uncertain terms what is going on here. Your statement that ±0.037 C is a claim of ±0.001 C accuracy would be EXACTLY the same as if I had stated your ±0.46 C figure is a claim of ±0.01 C accuracy.
“It is what it is with 1 significant figure.”
Assigned values have no significant figures,
“±σ = sqrt(0.283^2 + 0.359^2) = ±0.46
That is the root sum squared (RSS) method.”
It is the root-mean-square method done with two values.
“Your statement that ±0.037 C is a claim of ±0.001 C accuracy would be EXACTLY the same as if I had stated your ±0.46 C figure is a claim of ±0.01 C accuracy.”
Correct. And so it is. You finally get it.
PF said: “Assigned values have no significant figures,”
It’s an “estimated” value provided with 1 sf. Folland made no claim whatsoever that the value was exact. That is all the more the reason to honor Folland’s figure as-is including the 1 sf.
PF said: “It is the root-mean-square method done with two values.”
RMS = sqrt(1/N * sum(Xn^2, 1, N))
RSS = sqrt(sum(Xn^2, 1, N))
PF said: “Correct. And so it is. You finally get it.”
Wow. So now your published value of ±0.46 C for the uncertainty on annual global mean temperature anomalies is equivalent to saying the uncertainty on the annual global mean temperature anomalies is ±0.01 C? Would I be correct in assuming that you believe that Berkeley Earth is claiming ±0.001 C on annual global mean temperature anomalies because they publish uncertainties to 3 sf here? And this begs the question…if you think the uncertainty on annual global mean temperature anomalies is ±0.01 C then why go through all of that effort to publish an uncertainty of ±0.46 C? And furthermore how could you possibly be claiming an uncertainty as low as ±0.01 C for the annual global mean temperatures when no else gets a value that low? Do you see how absurd this is?
“It’s an “estimated” value provided with 1 sf. Folland made no claim whatsoever that the value was exact.”
Assigned values take the assigned magnitude, bdgwx.
Folland can have written estimated. You can shilly-shally about as you like. The 2-sigma 0.4 C does not present significant figures and is an assigned number; assigned, which makes its value discrete.
In RMS, when using an empirical mean, one degree of freedom is lost. The denominator in the sqrt becomes N-1. When N = 2, as in the specific case of two entries, N-1 = 1, and RMS looks like RSS.
Page 972 just beneath equation 6 in my 2010 paper explicitly makes this point, and repeats in on page 974 paragraph 1.
Your confusion about this merely shows you’ve never worked with empirical data.
“Wow. So now your published value of ±0.46 C for the uncertainty on annual global mean temperature anomalies is equivalent to saying the uncertainty on the annual global mean temperature anomalies is ±0.01 C?”
No. It says that the calibration uncertainty is good to two sig-figs past the decimal. As are all the temperatures reported in H&L 2002.
“Would I be correct in assuming that you believe that Berkeley Earth is claiming ±0.001 C on annual global mean temperature anomalies because they publish uncertainties to 3 sf here? “
They’re claiming to know the global temperature to 0.001 C accuracy. Which is a reflection of their incompetence.
Your questions are quite a revelation, bdgwx. It’s suddenly clear that you’re fatally confused about the meanings of uncertainty, accuracy, and significant figures.
Writing 0.46 represents a statement that the last digit is physically relevant. That is, one knows the stated value to within 0.01 of its nominal magnitude.
You’ll recognize a statement that the limit of knowledge in a value is ±0.01 is not the same as stating that the value itself is ±0.01.
“And this begs the question…if you think the uncertainty on annual global mean temperature anomalies is ±0.01 C then why go through all of that effort to publish an uncertainty of ±0.46 C?”
Hopelessly wrong. And by now, if you’ve read the above, you’ll know why.
Let me put it this way: the ±0.01 C is the uncertainty in the ±0.46 C uncertainty.
If one wanted to be explicit about the uncertainty in the uncertainty, one could write it, (±0.46±0.01) C. Do you get it now?
“And furthermore how could you possibly be claiming an uncertainty as low as ±0.01 C for the annual global mean temperatures when no else gets a value that low? Do you see how absurd this is?”
Having read this far, do you see the nonsensicality of your (one hopes) prior view, now jettisoned?
You really need to study up on metrology, bdgwx. Your ignorance on the subject appears total.
WUWT had Mark Cooper’s post about the metrology of thermometers, here. You might want to review it.
His summary points will be familiar to you. In abstract, climatologists are methodologically incompetent.
Mark: My main points are that in climatology many important factors that are accounted for in other areas of science and engineering are completely ignored by many scientists:
My guess is that the hysteresis in 5 is ignored because most lab rats don’t understand what it is. My guess is that bdgwx doesn’t either.
Mr. Cooper was correct. It appears that most climate scientists do not understand the difference in using samples and in using the entire population. Nor do they understand that while measurements may be independently done, that doesn’t mean the values thus generated are independent. When you measure the same thing multiple times the readings all inform one of what the expected value of the next reading will be, at least to a level of uncertainty – thus the readings themselves are not independent. When you are measuring multiple things single times the readings do *NOT* inform one of what the expected value of the next measurement will be – it could be *anything*. The mean is simply not informative in this scenario. Both must be treated separately as far as statistical analysis is concerned.
What’s the difference? It’s not a measured value. It’s not a calculated value. It’s a guess, pure and simple.
You are showing your biases as a mathematician/computer programmer and not a physical scientist.
A physical scientist doing algebra while calculating knows that significant figures must be carried through the calculation. Otherwise the algebra doesn’t come out right. Algebra uses arithmetic. If the algebra doesn’t come out right then the arithmetic wasn’t done correctly either!
K/decade is a time function, it is a non-stationary function. Doing *anything* with a non-stationary function is dangerous and liable to to give spurious results.
The probability of reproducing the past trend is very high, bdgwx, because CMIP5 models and all the other climate models are tuned to reproduce that trend.
Models reproduce the same historical temperature trend even though their climate sensitivity varies over a factor of 2-3. Because they’re tuned (adjusted) to reproduce that trend.
Look at the attached figure: emulation equation 1 will reproduce the historical air temperature trend. Will it therefore predict future air temperatures?
What are the probabilities future trend predictions then?
???
Those probabilities are given in my paper. They’re physically meaningless.
bdgwx, I hope you know that this “paper” has been laughed out of the room, as soon as Pat finally found an easy mark to “peer review” it. It took him years.
Feel free to check out the functionally nonexistent “article impact”, for which we all thank the Imaginary Guy In The Sky. Statistics from Bizarro world, and he can’t even keep his units straight…..
Only you have laughed and a few others. I hope you someday have the knowledge and experience in making detailed scientific measurements that Doctor Pat Frank has.
You attack Dr. Frank using a logical fallacy of Appeal to Authority yet you fail since you appeal to no one in particular. You should do better!
“Only you have laughed and a few others.”
Agree. Most just politely ignore Pat Frank. Channels the pregnant Simpsons pauses, followed by a subject change when Homer emits an especially confusing spiel.
“You attack Dr. Frank using a logical fallacy of Appeal to Authority yet you fail since you appeal to no one in particular. You should do better!”
I came late. Dr. Franks silliness was both prebutted and instantly rebutted.
https://andthentheresphysics.wordpress.com/2019/09/08/propagation-of-nonsense/
https://www.drroyspencer.com/2019/09/critique-of-propagation-of-error-ahttps://moyhu.blogspot.com/2017/11/pat-frank-and-error-propagation-in-gcms.htmlnd-the-reliability-of-global-air-temperature-predictions/
https://moyhu.blogspot.com/2019/09/another-round-of-pat-franks-propagation.html
https://moyhu.blogspot.com/2017/11/pat-frank-and-error-propagation-in-gcms.html
Quoting Nitpick Nick, good job BOB. He is yet another climastrologer who knows nothing of the subject.
Nick Stokes refuted: https://wattsupwiththat.com/2019/09/19/emulation-4-w-m-long-wave-cloud-forcing-error-and-meaning/
Roy Spencer refuted: https://wattsupwiththat.com/2019/10/15/why-roy-spencers-criticism-is-wrong/
Mr. ATTP couldn’t even figure out where the error term came from, despite that the paper spends 3 pages explaining the exact origin. His essay is a study in confusion.
Once again, you cite the incompetent in support of the ignorant.
Three blogs and _Dr. Spencer’s non-math based critique. Those are really your basis for authority? Where is a reviewed paper that refutes his math with math that shows something different?
Here is one objection to Pat Frank’s thesis:
“As Gavin Schmidt pointed out when this idea first surfaced in 2008, it’s like assuming that if a clock is off by about a minute today, that tomorrow it will be off by two minutes, and in a year off by 365 minutes. In reality, the errors over a long time are completely unconnected with the offset today.”
Those critiquing Pat Frank’s theses can’t even make a cogent argument.
If your clock is losing 1 minute per day then in a year it will have lost 365 minutes! The uncertainty in the reading of the clock grows with each iteration of the reading (i.e. daily).
Dr. Frank’s critics are trying to conflate a calibration error with the uncertainty growth. THEY ARE NOT THE SAME THING. A mis-calibrated clock will have the same offset no matter how many iterations you have. Even a stopped 12 hour clock will be right twice per day! The ultimate calibration error!
This is *NOT* the same thing as a clock with the wrong gear ratio causing an increasing uncertainty in the true value with each iteration. And that is what the uncertainty Pat Frank addressed in his paper.
AND YOU DON’T KNOW ENOUGH ABOUT UNCERTAINTY TO BE ABLE TO TELL THE DIFFERENCE! Using an Appeal to Authority argument is false from the beginning, An Appeal to Authority where the Authority isn’t an actual Authority is doubly false!
If you think Dr. Frank is wrong then show us the math.
Thank-you, Tim. I was pretty stunned at Gavin’s ignorance, too. Your outspoken critique had me laughing. 🙂
Your analogy of a clock with wrong gear ratios is great. Given the inconstancy of environmental variables, it’s almost as though the clock would have arbitrarily non-spherical gears.
More mindless bluster from bob. Reduced to recycling failure and nonsense.
BOB to the rescue! Of course BOB’s understanding of uncertainty any better than bwx’s.
It looks like ±8 C (1σ) after 30 years? Given this what are the odds that models ran more than 30 years ago would be within 1C, 0.5C, 0.1C, and 0.05C of today’s temperature?
Wrong question, bdgwx.
The correct question is, ‘What is the physical reliability of an air temperature projection from a model run of 30 years ago?’
Answer: zero.
You probably don’t know that Hansen himself judged the trend of his scenario B (almost certainly the projection you have in mind) as “fortuitous.”
In his own words (pdf), “Curiously, the scenario [B] that we described as most realistic is so far turning out to be almost dead on the money. Such close agreement is fortuitous. For example, the model used in 1988 had a sensitivity of 4.2°C for doubled CO2, but our best estimate for true climate sensitivity is closer to 3°C for doubled CO2.“(my bold)
Guess what “fortuitous” means.
Look at Figure 8 in my paper, bdgwx. Emulation equation 1 produced the identical projection as Hansen’s A, B, and C (apart from noise), using his own forcings.
What are your odds for that correspondence?
Will you now worship eqn. 1 as you do Hansen’s 30-year-old model?
Fortuituous translated means “we tuned it perfectly”!
I think my question is pretty good and very relevant. At the very least we should be able to test your hypothesis by looking at several model predictions from 30 years ago.
The odds that your emulation equation would match reasonable well is very high because it is nothing more than a curve fit with no fundamental basis in physical reality. I would be very skeptical about its ability to equally match future temperature trajectories. Hansen’s model on the other hand does a fundamental basis in physical reality because it is global circulation model that is complying with conservation of energy, conservation of mass, conservation of momentum, thermodynamic laws, radiative transfer, etc. That doesn’t mean I would worship it either, but it has more validity than a curve fit.
You just keeping digging the hole you are in deeper and deeper — uncertainty is a measure of your knowledge about a measurement. It does not mean measured values will be within the range!
“It does not mean measured values will be within the range!”
That’s right. I never said otherwise. When expressed in 1σ form as Pat did it means there is 32% chance that it will fall outside that range. I’ll pose the question to you since you get it. Assuming ±8 C (1σ) after 30 years what is the probability that models ran more than 30 years ago would be within 1.0 C, 0.5 C, 0.1 C, and 0.05 C of today’s temperature?
Are you making up your own version of statistics now?
What probability distribution are you insisting is active?
I’m assuming it is normal because Pat said it was 1σ. If that’s not correct perhaps we can get Pat to clarify what distribution it actually is. Good ahead and do the PDF calculations assuming it is normal.
Go back and check your assumptions, you can stuff any manner of strange distributions into the formula and it gives you a sigma regardless.
Uncertainty does NOT imply any probability distribution.
“I’m assuming it is normal because Pat said it was 1σ.”
It’s an empirical SD. No distribution is implied.
“If that’s not correct perhaps we can get Pat to clarify what distribution it actually is.”
No one knows. Take a look at the empirical error distributions here, bdgwx. https://tinyurl.com/arm6w9a8
It’s a blog post at WUWT on calibration errors in temperature measurements. They’re not normally distributed. An empirical SD can be calculated, but it does not imply a normal distribution.
The physical universe is messy. So are measurements. We do the best we can. But very little comports itself to mathematical niceties. Assumptions of functional uniformity are almost invariably violated. Closed solutions are rarely possible.
I sincerely doubt bdgwx or nyolci either one bothered to read your analysis – especially that associated with your Fig. 12.
If the warming today is supposed to be 1.5C per decade that implies 0.15C per year. Yet the uncertainty of the temperature measurements today is about +/- 0.3C. In other words there is no way to discern a 0.15C/year value unless you totally ignore the uncertainty associated with the data. Which, as you note, seems to be the standard practice among climate scientists today. Shame on them! They are tarnishing the reputation of true physical scientists and engnieers along with their own!
You’re right, Tim. It will take generations of scientific integrity to win back the trust those folks have betrayed.
You didn’t try any of the links to demos on sampling did you. You do realize there are other statistical parameters to describe a distribution, right? Just because you can calculate an SD doesn’t mean you know anything about the distribution. Have you ever heard of kurtosis or skew?
You can’t even see the problem with what you are asking!
Use a blue crayon with a wide tip to draw your trend line with an uncertainty of +/- 8C. Can you even *see* a 1C, .5C, .1C or .05C temperature difference underneath that trend line?
If your graph paper covers a range of +/- 10C so the crayon line will fit on the paper, how do you see any temperature differences smaller than +/- 8C on the paper? The crayon line will cover up most of the paper!
“When expressed in 1σ form as Pat did it means there is 32% chance that it will fall outside that range.”
Not correct. The ±46 C is an empirical standard deviation. No distribution is implied or assumed.
Then how do you know it’s not normal?
What were the distributions of the Folland ±0.2 and Hubbard ±0.25 values used to calculate that ±0.46 value?
As noted above, Folland’s ±0.2 C is an assigned figure and is thus exact.
The graphic below is Figure 2 C from Hubbard & Lin 2002. Day + night field calibration measurement error. The distributions of the various systematic measurement errors are illustrated there.
Note that all the distributions radically violate the assumption of a normal distribution. All of that is referenced in my 2010 paper.
The usual courtesy has one reading and comprehending another’s work before criticizing it.
Those distributions are for absolute temperatures; not anomalies.
And just why would converting to anomalies reduce either measurement error or uncertainty? Show some math.
Here is an example:
Z = X +/- err –> Z1 = X – Anom +/- err
Why does subtracting a constant reduce measurement error? It’s too bad you might end up with an anomaly of 0.5 +/- 1 but that is life. Show us how the math works in your mind!
It’s because the anomaly baseline Tb is also subject to the same calibration bias.and distribution as shown in the Hubbard publication so dT = (Tx + B) – (Tb + B) = Tx – Tb.
Those distributions are of calibration error. You not only have not read the paper, you didn’t even read the abscissa.
That’s right Pat. They are distributions for calibration error. Now what do those distributions look like when temperatures are expressed as anomalies?
BTW…I read the whole paper and several of Hubbard’s other papers including publications which use Hubbard’s results. This is how know that your claim that climate scientists are ignoring his work is wrong.
Why do you think subtracting a constant value from a temperature should change the population distribution. Anomalies are a way to “hide” the variance in temperatures. Evidence – you can’t convert a Global Average Temperature back to the individual parts that make it up. If you can’t do that, then you have created a metric that has no meaning when it comes to any statistical parameter (standard deviation, kurtosis, skew, etc./) of the original population.
“That’s right Pat. They are distributions for calibration error.”
Good, we now agree on something.
“Now what do those distributions look like when temperatures are expressed as anomalies?”
The calibration errors are combined as rms with the e.s.d. of the station normal to yield the total uncertainty in the anomaly.
That is, the uncertainties become larger when taking an anomaly. The profiles of the distributions won’t change much. Non-normal, all.
“BTW…I read the whole paper and several of Hubbard’s other papers …”
One would never have guessed.
“… including publications which use Hubbard’s results.”
Cite them. Bet you can’t do it.
“This is how know that your claim that climate scientists are ignoring his work is wrong.”
I claim you know no such thing.
Hubbard and Lin 2001 has been cited 18 times (3 of which are my papers). See the list here: Not one of citations is an estimate of global air temperature.
Your climate scientists(sic) have utterly ignored systematic calibration errors.
A fine cloud of smoke you’ve blown.
“The profiles of the distributions won’t change much. Non-normal, all.”
They most certainly will. I tested this myself. I created right shifted distributions like what Hubbard shows and modeled a population of true values with measurements that were consistent with the distributions I created. When taking the average of the absolute measurements the mean was biased in the same way the original distribution was. But when I switched to using anomaly analysis the bias went away. In both cases the errors fell into a normal distribution. Why do you think that happened?
“Cite them. Bet you can’t do it.”
Menne cites Hubbard’s work. Menne is the one who developed NOAA’s pairwise homogenization algorithm to correct for biases in the record.
“Why do you think that happened?”
It happened because you started with a normal distribution.
The Hubbard and Lin calibration data are not shifted normal distributions. They are non-normal distributions.
Calibrations made at different times are very likely to give their own unique non-normal, distributions.
“Menne cites Hubbard’s work.” With no citation given. Let’s see if you know what you’re talking about.
+++++++++++
Menne & Williams (2009) Homogenization of Temperature Series via Pairwise Comparisons
doi: 10.1175/2008JCLI2263.1 cites Hubbard & Lin 2006.
Hubbard & Lin 2006 discusses only the impact of changing sensors. No mention of sensor calibration or systematic measurement errors.
Menne at al., (2009) The U.S. Historical Climatology Network Monthly Temperature Data, Version 2 doi: 10.1175/2008BAMS2613.1 again cites only Hubbard & Lin 2006.
Menne’s systematic effects include only “changes to the time of observation, station moves, instrument changes, and changes to conditions surrounding the instrument site.”
Not a word about sensor field calibration or systematic measurement error.
Menne, et al., (2010) On the reliability of the U.S. surface temperature record doi: 10.1029/2009JD013094 again cites only Hubbard & Lin 2006.
Not a word about sensor field calibration or systematic measurement error.
Menne, et al., (2012) An Overview of the Global Historical Climatology Network-Daily Database doi: 10.1175/jtech-d-11-00103.1 cites four papers in which Hubbard is a co-author (2004, 2005 & 2006), none of which describe sensor calibration.
Not a word about sensor field calibration or systematic measurement error.
Lenssen, et al., incl. Menne (2019) Improvements in the GISTEMP Uncertainty Model doi: 10.1029/2018JD029522 does not cite Hubbard, does not mention calibration, and treats all measurement errors as random values that average away.
Not a word about sensor field calibration or systematic measurement error.
Dunn, et al., incl. Menne (2020) Development of an Updated Global Land In Situ-Based Data Set of Temperature and Precipitation Extremes: HadEX3 doi: 10.1029/2019JD032263
No citation to Hubbard, not one word about sensor calibration or systematic measurement error.
+++++++++++
Evidently you don’t know what you’re talking about, bdgwx. And that’s the charitable view.
Systematic measurement error is completely neglected in the published surface air temperature record. The purported scientists also ignore the resolution limits of the instruments.
They behave as desk-jockeys who have never made a measurement or struggled with an instrument.
Their uncertainty bars are a bad joke. The whole field has descended into pseudoscience. The failed product of willful incompetents.
“It happened because you started with a normal distribution.”
No I didn’t. I started with the Hubbard distributions.
“The Hubbard and Lin calibration data are not shifted normal distributions.”
I didn’t say they were normal distributions What I said was that they were right shifted distributions.
“Calibrations made at different times are very likely to give their own unique non-normal, distributions.”
Yeah. I agree. I can model that too if you like.
“No citation to Hubbard, not one word about sensor calibration or systematic measurement error.”
There is a citation to Hubbard’s work…just not the one on the calibration error. This is likely because it was determined that it didn’t matter. My point is that Menne knows about Hubbard’s research and both likely had a lot of offline correspondence because that’s what experts in the field do. And the reason the calibration error doesn’t matter is because any shift or bias in the distribution will cancel out with anomaly analysis and any non-normal shape on the individual measurements will morph into a normal shape when many of them are averaged per the CTL. I did the experiment and confirmed this myself.
“The whole field has descended into pseudoscience. The failed product of willful incompetents.”
Wow.
“No I didn’t. I started with the Hubbard distributions.”
No, you didn’t start with the Hubbard distributions because all the calibration error distributions in Hubbard and Lin 2002 are non-normal. All of them. Every single one of them.
They cannot [fall] into a normal distribution when their mean is subtracted. None of them. Because their distribution is not merely a right-shifted Gaussian.
“Yeah. I agree. I can model that too if you like.”
Don’t bother. So far, you haven’t modeled anything correctly.
“There is a citation to Hubbard’s work…just not the one on the calibration error.”
Then it was irrelevant. Why’d you exemplify it, then?
“This is likely because it was determined that it didn’t matter.”
Once again, you invoke incredulous laughter.
“My point is that Menne knows about Hubbard’s research and both likely had a lot of offline correspondence because that’s what experts in the field do.”
Your point was more likely to observe in a nondescript way that Menne cited Hubbard and hope that I didn’t check and discover your opportunistic misappropriation of an irrelevant citation.
The rest of your handwave is speculative story-telling of events that almost certainly didn’t happen.
“And the reason the calibration error doesn’t matter is because any shift or bias in the distribution will cancel out with anomaly analysis …”
Systematic error does not cancel out with anomaly analysis. The uncertainty in the measurement adds to the e.s.d. of the normal to produce a larger uncertainty in the anomaly than was in the measurement.
A dead surety of result that workers in the field flee assiduously, and so do you.
“… and any non-normal shape on the individual measurements will morph into a normal shape when many of them are averaged per the CTL.”
The CLT does not imply what you aver. The CLT merely returns a Gaussian distribution about the true mean of a set of values, given a random selection from the set of values.
Subtraction of the mean does not change the shape of the distribution. It does not change or remove the non-normality of the error distribution. It does not remove the uncertainty in the mean.
The average of multiple systematic error distributions cannot be assumed to be Gaussian. Assuming so is transparently self-serving.
“I did the experiment and confirmed this myself.”
We’ve seen your experiments. They’ve been invariably wrong.
If you got that result using the CLT, then your experiment was mal-constructed, giving an incorrect outcome for reasons noted above.
bdgwx:
Frank:
This seems to be a sticking point with so many of the mathematicians, computer programmers, and climate scientist.
The term “true mean” is *NOT* the same as a “true value”. If the data making up the population is independent and random then there is no true value even though there may be a true mean.
This statement is instructive: “Two random variables X and Y are said to be independent if “knowledge of the value of X takes does not help us to predict the value Y takes”, and vice versa.” (Statistics 101-106 by David Pollard)
If you have a data set like single measurements of different things then your X values do *not* help predict the value of Y because there is no “true vale” associated with those measurements.
If you have a data set of multiple measurements of the same thing then your X values *do* help predict the value of Y because they represent a distribution around the true value.
While the measurements of the same measurand may be independent on their own, the actual measurement is not. Each of the measurements depends on the same thing, the thing being measured. There is a direct dependence of the measurements. This allows an approximation of a “true value” to be determined.
Measurements of *different* things are truly independent, The measurements themselves are independent and the measurands are independent as well. Thus there is no :”true value” that can be determined from the measurements. There is a “true mean” that can be determined but it is meaningless physically.
From “Central Limit Theorem and the Law of Large Numbers Class 6, 18.05 Jeremy Orloff and Jonathan Bloom”
“The mathematics of the LoLN says that the average of a lot of independent samples from a random variable will almost certainly approach the mean of the variable. The mathematics cannot tell us if the tool or experiment is producing data worth averaging”
PF said: “No, you didn’t start with the Hubbard distributions”
Yes. I did.
PF said: “because all the calibration error distributions in Hubbard and Lin 2002 are non-normal. All of them. Every single one of them.”
Yeah, I know.
PF said: “They cannot [fall] into a normal distribution when their mean is subtracted.”
I never said that. What I said is that the distribution of the average forms into a normal distribution. And when that average is in anomaly form the right shifted nature of the original Hubbard distributions disappears.
PF said: “Then it was irrelevant. Why’d you exemplify it, then?”
It is very relevant because it is an example of a systematic error that is not random and does not get suppressed with anomaly analysis. It must be dealt with via pairwise homogenization or similarly effective strategies.
PF said: “Systematic error does not cancel out with anomaly analysis.”
Patently False.
Some kinds of systematic error absolutely cancel out. This is very easy to see with the formula dT = (Ta+E) – (Tb+E) = Ta – Tb. The systematic error E is removed in the process of forming dT (the anomaly).
The hang up here is that this assumes E of Ta is the same as E of Tb. It turns out that this is not exactly the case. See Hubbard 2006 and Vose 2003 for examples of how the systematic error can change with time. Read Menne 2009 for one strategy on how to deal with this problem.
PF said: “Subtraction of the mean does not change the shape of the distribution.”
I never said it did. What I said is that when subtracting the mean the anomaly will have an uncertainty distribution with the left/right shift removed. And don’t confuse the process of forming an anomaly with taking the average of a bunch of anomalies. The anomaly will have the left/right shift removed but the shape of the distribution will remain. It is the process of averaging a bunch of anomalies in which the shape of the distribution becomes normal. Don’t take my word for it. Try it out for yourself.
PF said: “The average of multiple systematic error distributions cannot be assumed to be Gaussian. Assuming so is transparently self-serving.”
You could be right about that. That’s why earlier I offered to test it. My original experiment used only a single distribution from Hubbard’s work at a time.
PF said: “If you got that result using the CLT, then your experiment was mal-constructed, giving an incorrect outcome for reasons noted above.”
I didn’t get the result by using the CLT. I didn’t use the CLT anywhere in the experiment. I also didn’t start with a normal distribution or a distribution with a mean of 0. I started only with the Hubbard distribution which is neither centered nor normal. The result occurred organically by only forming anomalies and averaging those anomalies.
So what? You haven’t changed the distribution of the population in any way. All you have done is formed a distribution of various sample means into a distribution around a mean.
The anomaly form doesn’t change anything. The uncertainty *still* follows the anomalies. You haven’t changed those uncertainties at all. And it is those uncertainties that determine the uncertainty of the mean, not the distribution of the sample means.
Why is this so hard to understand? If *all* of the models are running hot compared to reality then you can calculate the mean of those model outputs and that mean is still going to be too hot. (those model outputs *are* anomalies, btw) You won’t have changed the uncertainty of the mean you calculated at all. That mean you calculate is *not* a “true value”, it still remains far from the observations. The difference between the mean you calculated and the observations has to be described by the uncertainty attached to that mean.
Pairwise homogenization doesn’t affect the uncertainty. You can’t correct uncertain values using other uncertain values. You can only eliminate uncertainty by using a calibrated reference measuring device for each measurement. Using uncertain values to correct other uncertain values only results in an *increased* uncertainty!
“Patently False.
Some kinds of systematic error absolutely cancel out. This is very easy to see with the formula dT = (Ta+E) – (Tb+E) = Ta – Tb. The systematic error E is removed in the process of forming dT (the anomaly).”
Nope.
You are assuming E is constant and affects Ta and Tb in the same manner. With independent, random variables determined by measuring different things using different measuring devices you have to way to determine the size of E for each measurement, it won’t be a constant. That’s why uncertainty is quoted as an interval.
Just an aside, using dT is misleading. You would be better off saying
(delta)
Uncertainty doesn’t have a distribution. The actual measurements my have a distribution but uncertainty is an interval. As we’ve discussed in the past, the true value has a probability of 1 and all the other values in the interval has a probability of 0. That is not a probability distribution. When you have independent, random measurements of different things there is *NO* true value. There is a mean but it is not a true value, just a true mean.
The anomaly is a value calculated from measurements which have uncertainties of their own. That means that anomaly value has an uncertainty. Whether you add or you subtract the baseline and current measure, the uncertainty of the baseline value and the current measurement have their uncertainties propagated into the anomaly. If the uncertainty of the baseline is +/ 2C and the current measurement has an uncertainty of +/- .6C then the sum of the uncertainties is +/- 2C+.(on the far side of 2).
No amount of “shifting” will change this.
You are *still* trying to minimize the uncertainty in some manner that doesn’t fit standard uncertainty methods and protocols.
Meaning, once again, you tried to come up with an artificial definition of uncertainty. You didn’t actually treat the anomaly uncertainties at all. You just ignored them – as almost all climate scientists do. The uncertainty of a value is *NOT* the standard error of the mean.
TM said: “So what? You haven’t changed the distribution of the population in any way.”
But we did change the distribution of the error of the average. That’s the point.
TM said: The anomaly form doesn’t change anything. The uncertainty *still* follows the anomalies.
The randomness of the uncertainty still follows the anomalies. But the shift or bias does not. That’s the point.
TM said: “Nope. You are assuming E is constant and affects Ta and Tb in the same manner.”
That’s right. And I even discussed and gave you examples of how E is not constant and how that systematic bias is handled.
TM said: “Just an aside, using dT is misleading. You would be better off saying δ (delta)”
Agreed. Though actually it’s probably better to use Δ. I put that character in my notepad file so it’s easy to pull up and use in posts in the future.
TM said: “Uncertainty doesn’t have a distribution.”
The Hubbard 2002 uncertainty does and that’s the primary focus of this discussion.
TM said: “As we’ve discussed in the past, the true value has a probability of 1 and all the other values in the interval has a probability of 0. That is not a probability distribution.”
The Hubbard 2002 distributions show the probability. No value has a probably of 1 or 0. They are all somewhere in between. You can also see where the probabilities peak and how that correlates to the average bias.
TM said: The anomaly is a value calculated from measurements which have uncertainties of their own. That means that anomaly value has an uncertainty.
Agreed. And I never said otherwise. What I said was that forming anomalies removes the shift in the distribution. It does not remove the random variation. In other words for MMTS the stddev will stay at 0.25, but the mean will shift from +0.21 toward 0.00.
TM said: “You are *still* trying to minimize the uncertainty in some manner that doesn’t fit standard uncertainty methods and protocols.”
I’m not the one minimizing uncertainty here. It is the averaging process of many observations that minimizes the uncertainty. It has nothing to do with I did or didn’t do.
TM said: “Meaning, once again, you tried to come up with an artificial definition of uncertainty.”
Nope. I used the uncertainty distributions that Hubbard 2002 provided. I did not create my own definition. I used Hubbard’s uncertainty distributions as-is.
So what? That just means you calculated the mean more precisely by narrowing the Standard Error of the Mean. It has nothing to do with the uncertainty of the mean that is propagated from the constituent parts of the data set.
You *still* haven’t grasped that concept. How precisely you calculate the mean has absolutely nothing to do with uncertainty!
Of course the bias will follow. It is part of the uncertainty! You don’t *KNOW* the absolute bias of each measurement of different things. Do *you* know the bias in the thermometer inside your house thermostat? Have you calibrated it against a reference thermometer? If you don’t know the bias and haven’t calibrated then any calibration error is unknown and becomes a part of the uncertainty associated with the measurement it gives!
If you don’t know the calibration bias then how do you shift the measurement it to eliminate it? Just pick an arbitrary number? That seems to be the process you typically follow.
You are STILL stuck on the scenario of measuring the same thing multiple times – and in this case using the same measuring device.
If E is not constant, which it won’t be with multiple measurement of different things using different measuring devices (i.e. temperature measurements) then you don’t know the systematic bias and there is no way to handle it other than by including it in the uncertainty calculation.
If it has a distribution then it is *NOT* uncertainty. It might be an *assumed* distribution of some kind but uncertainty simply doesn’t have a distribution. If you do not know the systematic bias then it has to be included in the overall uncertainty calculation and it loses any probability distribution you might think it has.
This sounds to me a lot like a lab rat or mathematician who “assumes” a lot about reality instead of going out and actually making observations. Just assume the measuring devices all have a Gaussian distribution of systemic bias and assume it just all averages away!
Only the true value has a probability of 1, by definition. If you must then consider that the true value has a probability of 1 of being within the uncertainty interval and that all values outside the interval has a probability of zero.
What Hubbard did was assume a probability distribution where values closer to the mean are more likely than a value further away, something between a Gaussian distribution and a trapezoidal distribution. Once again, that is what you would expect for MULTIPLE MEASUREMENTS OF THE SAME THING where your values are around a true value.
Why do you ALWAYS fall back onto the scenario of multiple measurements of the same thing and try to say it is the same scenario of single measurements of multiple things? This is the common mistake used by do many in science today. If these people ever worked in reality, where there was personal liability affecting their reputation and financial well-being, they would soon learn that data sets of multiple measurements of the same thing are far different than single measurements of multiple things.
“What I said was that forming anomalies removes the shift in the distribution.”
What shift? Systematic bias or calibration error? How can forming an anomaly remove those when each of the values used to form the anomaly has an uncertainty? If you don’t know what the systematic bias or calibration error is for each measuring device then it is impossible to allow for it. You can’t correct for it by using a single, assumed value – that value might be right for some measurements and totally wrong for others. You may as well just assume that all stated values are 100% accurate and proceed using that assumption. That’s what the climate scientists today do. And then they fool themselves even further by thinking that the SEM is the propagated uncertainty from the combination of the assumed 100% accurate data points.
All you have done is centered the distribution through a transformation. That doesn’t change the shape of the distribution at all. You’ve just moved the y-axis so that the mean is at 0. How does that get rid of anything? It doesn’t get rid of any systematic bias or calibration error!
Averaging doesn’t minimize uncertainty because you don’t average uncertainty. You propagate it. Uncertainties add, sometimes directly and some time using root-sum-square. You don’t divide that sum by anything to get something smaller. You are still laboring under the misconception that SEM is the uncertainty propagated to the mean from the members of the data set. IT ISN”T!
“Yes. I did” [start with Hubbard’s distribution]
No, you didn’t. As shown below. Utter incompetence, or … what’s the alternative?
“I never said that [they [fall] into a normal distribution when their mean is subtracted].”
Yes, you did. Right here: October 27, 2021 6:44 am.
“What I said is that the distribution of the average forms into a normal distribution.”
No, you didn’t. In your Oct. 27 6:44 am you wrote , “the errors fell into a normal distribution.“ after subtraction of the mean. The errors, bdgwx, not the average.
You’ve shifted your ground. Evidently, you’ve realized you were mistaken. Not a valid debate tactic — shifting one’s ground — is it.
“And when that average is in anomaly form the right shifted nature of the original Hubbard distributions disappears.”
The Hubbard distributions are already (T_m minus T_s) differences, where T_m = Temp measured and T_s = Temp standard.
There is no “anomaly form” of an error distribution. Subtracting the error mean removes the bias but does not change the distribution.
One never knows the magnitude or even the sign of systematic error in a field measurement. There is no known error mean to subtract. The local error bias value is unknown as is the local error distribution.
In practice, one can only assign the calibration uncertainty to the field measurement, and live with that.
“It is very relevant because it is an example of a systematic error that is not random and does not get suppressed with anomaly analysis. It must be dealt with via pairwise homogenization or similarly effective strategies.”
You proffered an irrelevant Hubbard 2006 citation in your October 27, 2021 9:46 am. Hubbard 2006 does not discuss systematic measurement error, which was the subject in hand.
You’ve apparently forgotten the subject of your own argument.
Menne’s Hubbard 2006 has no relevance to non-random systematic measurement error. You’re just making things up.
“Pairwise homogenization” doesn’t remove uncertainty in anyone else’s world than yours. On sane planets, it only converts measurement science into numerology.
“Patently False” [that systematic error does not cancel out with anomaly analysis]
Demonstrated true by every single one of the Hubbard and Lin 2002 non-normal measurement error distributions.
“Some kinds of systematic error absolutely cancel out. This is very easy to see with the formula dT = (Ta+E) – (Tb+E) = Ta – Tb. The systematic error E is removed in the process of forming dT (the anomaly).”
You’re assuming a known constant error offset. The same utterly mindless assumption that mesmerizes the mind of everyone purporting climatology.
“The hang up here is that this assumes E of Ta is the same as E of Tb. It turns out that this is not exactly the case.”
So you go on to refute your own claim.
In any case, your assumption is never known to be the case for field-measured air temperatures.
“See Hubbard 2006 and Vose 2003 for examples of how the systematic error can change with time. Read Menne 2009 for one strategy on how to deal with this problem.”
Vose, 2003 is about time of observation bias. Hubbard, 2006 is about instrumental changes. Neither is about systematic measurement error. Thus, both are irrelevant to the discussion.
It looks as though you’re just throwing stuff at the wall, and hoping something sticks.
The Hubbard 2006 conclusion should have chastened you.
“I never said it did.” (I.e., that subtraction of the mean changes the shape of the distribution.”
You wrote exactly that idea in your October 27, 6:44 am, as noted above.
“What I said is that when subtracting the mean the anomaly will have an uncertainty distribution with the left/right shift removed.”
That is your ground-shifting fall-back. And it’s wrong because it assumes that all the errors have a common constant bias.
Yours is never, ever a valid assumption in a set of field temperature measurements.
“And don’t confuse the process of forming an anomaly with taking the average of a bunch of anomalies. The anomaly will have the left/right shift removed but the shape of the distribution will remain.”
You’ve reiterated the point I’ve been making all along, and one you have consistently denied until you realized your mistake.
“It is the process of averaging a bunch of anomalies in which the shape of the distribution becomes normal. Don’t take my word for it. Try it out for yourself.”
Averaging anomalies does not change the shape of the error distribution of the measured temperatures; the subject of our discussion.
Nor does taking anomalies knowably remove systematic measurement error; particularly when neither the sign nor the magnitudes of the errors are available.
Indeed, taking differences may increase systematic error.
The unknown error distribution implicit about any field-measured temperature cannot be modeled because it is in fact unknown.
The variation in the error distributions from measurement to measurement is not known to follow a random distribution. The error distributions cannot be assumed to average to a normal distribution.
“You could be right about that. [I.e., that the average of multiple systematic error distributions cannot be assumed to be Gaussian. Assuming so is transparently self-serving.]
“That’s why earlier I offered to test it. My original experiment used only a single distribution from Hubbard’s work at a time.”
You can’t test it. You can’t model an unknown. It’s quite clear that the assumption of random iid values underlies all of your supposed tests.
“I didn’t get the result by using the CLT. I didn’t use the CLT anywhere in the experiment.”
Your October 27, 2021 9:46 am: “And the reason the calibration error doesn’t matter is because any shift or bias in the distribution will cancel out with anomaly analysis and any non-normal shape on the individual measurements will morph into a normal shape when many of them are averaged per the CTL. I did the experiment and confirmed this myself.”
Your forgetfulness has reached extraordinary proportions.
“I also didn’t start with a normal distribution or a distribution with a mean of 0. I started only with the Hubbard distribution which is neither centered nor normal. The result occurred organically by only forming anomalies and averaging those anomalies.”
Hubbard’s error distributions are differences — T_m minus T_s biases. They cannot be converted into anomalies. The original temperature measurements do not appear in H&L 2002. You could not have produced anomalies; you claim an impossibility.
Taking anomalies against a station normal does not remove systematic sensor measurement errors. Taking anomalies only increases the uncertainty of the original measurement.
Uncertainty in an anomaly is u_a = sqrt[(u_T)^2+(u_N)^2], where u_T is the uncertainty in the individual measured temperature and u_N is the uncertainty in the station normal.
The uncertainty in the station normal is the rms of all the systematic uncertainties in all the measured temperatures going into the station normal.
There’s no legitimate getting around it, bdgwx. Incompetent workers, or dishonest ones, may neglect it.
PF said: “No, you didn’t. In your Oct. 27 6:44 am you wrote , “the errors fell into a normal distribution.“ after subtraction of the mean. The errors, bdgwx, not the average.”
Yes I did. You truncated the quote and removed the context. Here is what I actually said.
When taking the average of the absolute measurements the mean was biased in the same way the original distribution was. But when I switched to using anomaly analysis the bias went away. In both cases the errors fell into a normal distribution.
PF said: “You’ve shifted your ground.”
I stand by what I said. When you process the average of a large set of observations using anomalies analysis there is no longer a shift in the distribution and the distribution itself goes normal. And to make this perfectly clear I’m talking about the distribution of the errors of the average.
PF said: “The Hubbard distributions are already (T_m minus T_s) differences, where T_m = Temp measured and T_s = Temp standard.”
Yeah, I know. I read the paper. T_m is the observations of the stations being tested and T_s is the Young 43347 observation and is considered the standard or “reference”.
PF said: There is no “anomaly form” of an error distribution.
Strawman. I never said there was. When I use the word “anomaly” I’m using it exactly how everyone else does. That is it ΔT = Tx – Tb where Tx is the observation in question and Tb is the baseline temperature computed as an average of a sufficiently large set of individual Tx observations at the same station. It has nothing to do with error itself. It is simply difference between a specific observation and the average of observations at the same station.
PF said: “One never knows the magnitude or even the sign of systematic error in a field measurement.”
But we do know how those errors are distributed. See Hubbard 2002 as example.
PF said: “In practice, one can only assign the calibration uncertainty to the field measurement, and live with that.”
That’s not what Hubbard 2002 says. In fact, the main purpose of that publication is to present a model for bias correcting station observations in real-time. Refer to figure 4 for the skill in Hubbard’s model in shifting those distribution back toward neutral for absolute temperatures (not anomalies). He’s saying you don’t have to live with the systematic error (accuracy), but you do have to live with the random error (precision). Note that I’m using ISO 5725 definitions for accuracy and precision here.
PF said: “Hubbard 2006 does not discuss systematic measurement error, which was the subject in hand.”
He most certainly does. What he says is “The station average temperature biases caused by instrument changes were +0.57 and -0.35 C for monthly maximum and minimum temperatures (Figure 1), which are slightly larger magnitudes than found in Quayle’s results.” This is an example of a systematic error that contaminates regional and global temperature records. He further warns that it is not appropriate to use these figures as adjustment offsets. Menne clearly got the message and switched from using constant offsets to using pairwise homogenization. I mention this because it challenges your belief that the maintainers of these datasets are incompetent and have no idea how what kind of biases are contaminating their records.
PF said: ““Pairwise homogenization” doesn’t remove uncertainty in anyone else’s world than yours.”
Strawman. I didn’t say it removed uncertainty. I said it removes systematic bias.
PF said: “Neither is about systematic measurement error. Thus, both are irrelevant to the discussion.”
Let’s be precise here. Neither says anything about systematic measurement error for specific observations. But they say a lot about the systematic measurement error for observations taking in aggregate like what you do when you form a timeseries of monthly means. That it makes it spot on relevant to our discussion.
PF said: ” referring to this statement “What I said is that when subtracting the mean the anomaly will have an uncertainty distribution with the left/right shift removed.” you say That is your ground-shifting fall-back. And it’s wrong because it assumes that all the errors have a common constant bias.”
First…I never said the distribution changes shape here. What I said is that the distribution shifts toward zero (the mean gets closer to zero).
Second…It does assume the errors remain constant. They won’t because station change instruments and that will change the distribution of the errors. That is a type of systematic error that Hubbard 2006 addresses. It is also important to note that the Hubbard 2002 model also assumes the distribution are constant and yet it has very good skill in removing the systematic error.
PF said: “You’ve reiterated the point I’ve been making all along, and one you have consistently denied until you realized your mistake.”
Strawman. I never denied this. I never thought otherwise. And I went to great lengths to explain exactly this to you. Remember, I’m the one that is actually doing the experiments here.
PF said: “Averaging anomalies does not change the shape of the error distribution of the measured temperatures; the subject of our discussion.”
But it does change the shape of the distribution of the errors of the average. That is what we are discussing. Specifically we are discussing the uncertainty on global mean temperatures. Those are calculated by taking the trivial average of all cells in a grid mesh.
PF said: “Nor does taking anomalies knowably remove systematic measurement error; particularly when neither the sign nor the magnitudes of the errors are available.”
Yes it does! Try it. ΔT = (Tx+Bx)-(Ty+By). Even when Bx = 0.9*By the bias ΔT is 0.1 * By which is significantly less than the bias of Tx which is 0.9 * By and Ty which is 1.0 * By. Don’t hear what I didn’t say. I didn’t say that anomaly analysis removes all bias. It doesn’t. It especially does not remove systematic biases like instrument changes, station moves, time-of-observation changes, etc. For those scientists use different techniques.
PF said: “Your forgetfulness has reached extraordinary proportions.”
This is fair criticism. When I said “the individual measurements will morph into a normal shape when many of them are averaged per the CTL.” what I should have said instead was “the individual measurements will morph into a normal shape when many of them are averaged consistent with the expectation of the CTL.” Make no mistake I did not in any way shape or form use the CTL itself in my experiment. I should be careful with my wording.
PF said: “Hubbard’s error distributions are differences — T_m minus T_s biases. They cannot be converted into anomalies.”
I didn’t convert them into anomalies. What I converted into anomalies were observations just like how HadCRUT, GISTEMP, BEST, etc. do it. If you know how these datasets work then you’ll understand what I did.
PF said: “Taking anomalies against a station normal does not remove systematic sensor measurement errors.”
Yes it does. Try it out for yourself.
PF said: “Taking anomalies only increases the uncertainty of the original measurement.”
I total agree. I never said otherwise. In fact, the uncertainty of the anomaly is the RSS of the uncertainty of the baseline and the uncertainty of the observation. I have never challenged that. What it does do is remove systematic error. This allows stations with different systematic error to be compared on a more equal footing.
PF said: “There’s no legitimate getting around it, bdgwx. Incompetent workers, or dishonest ones, may neglect it.”
I get it. You think everyone but you is incompetent. But for me I know I’m just an amateur blog commenter. If I knew about the Hubbard, Quayle, Peterson, etc. works and I thought to actually do the experiments to see just how error distributions behave when you form observations into anomalies and when you average them both in time and space you better believe the experts took it to a whole new level. They are far smarter than I will ever be. They probably haven’t thought of everything, but they’ve certainly considered more than you are trying insinuate and certainly more than they’ve published.
There are three kinds of transformation you can do on a data set, centering, standardization, and normalization.
Centering uses X-x to move the distribution along the horizontal axis. x is usually the mean.
Standarization uses (X-x)/σ where x is usually the mean
Normalization uses [X – min(X)]/[max(X) – min(X)]
None of these change the shape of the distribution, they are all linear transformations. There are transformations that can change a non-normal distribution into one that looks like a normal distribution (I am not very knowledgeable on these) but I know that you need to transform the data back befoe actually displaying it. The transformations typically gives the median value instead of the mean when the transformation is reversed.
In any case it doesn’t appear that you did anything other than recenter the distribution at zero. The variance and the standard deviaton would not change in this scenario. Thus no errors would be eliminated.
And, as Pat and I both have pointed out, to create an anomaly you *had* to use a baseline that has its own uncertainty interval after propagating all of the component uncertainties forward into the average. Thus the uncertainty associated with the anomaly will *grow*, not cancel.
Bottom line? I have no idea what you think you did. Subtracting a common value from the data points will only result in re-centering the data to a different point on the horizontal axis. It cannot and will not change the distribution in any way.
I have yet to figure out what you think “anomaly analysis” is. If it is a straight subtraction then all that happens is that the distribution gets re-centered, NOTHING else can or will happen.
If you are doing a non-linear transformation which can change the shape of the distribution then you need to tell us what that non-linear transformation actually is and justify your use of it!
Nor do I know what you mean by “distribution of the errors of the averages”. It sounds like you are, once again, trying to conflate Standard Error of the Mean (which applies when you have multiple SAMPLES) with calculation of the population mean. The means of the samples will usually result in a normal distribution. But you can’t do both SEM and population and come up with anything useful. You either have samples of a population or you have a population. You need to pick one and stick with it.
If you are doing SEM then your distribution only applies to the sample means and not to the population as a whole. If you are using the population then there is no distribution around the mean, the mean is the mean – and that population mean will have the uncertainty propagated from the constituent components of the population. Which, btw, the mean calculated from the samples will also inherit.
Once again you did not read a scientific paper for meaning or completeness. You are cherry-picking something you hope will stick to the wall when you throw it.
from Hubbard, 2002:
Hubbard in his 2006 article on instrument change states:
for specific stations at the transition of CRS to MMTS. However, it does indicate that a regional average [MMTS-CRS] constant adjustment used in the U.S. HCN is not applicable for the individual stations when local or subregional trend analysis is to be undertaken. For example, gridded temperature values or local area-averages of temperature might be unresolvedly contaminated by Quayle’s constant adjustments in the monthly U.S. HCN data set or any global or regional surface temperature data sets including Quayle’s MMTS adjustments. It is clear that future attempts to remove bias should tackle this adjustment station by station.” (bolding mine, tpg)
If your baseline temperature included any measurements contaminated by adjustments, Quayle’s or others, then use of the baseline to formulate anomalies is equally contaminated.
You are typical of most supposed climate “scientists” today who simply have no field experience in metrology at all. Not everything is reducible by statistical analysis and it doesn’t matter how much you wish that hammer could be used on everything.
In summary, all you have done is center the distribution to a different location on the x-axis. You didn’t actually reduce anything by doing so. Creating an anomaly data set only *increased* the uncertainty, it didn’t decrease it doesn’t represent bias in any form.
“But it does change the shape of the distribution of the errors of the average. That is what we are discussing. Specifically we are discussing the uncertainty on global mean temperatures. Those are calculated by taking the trivial average of all cells in a grid mesh.”
Meaning you totally ignore the uncertainty of those values making up the average of the grid mesh. You assume they are all 100% accurate and that the GAT, therefore, is 100% accurate.
The uncertainty of the global mean temperature is based on the uncertainty of the values making up the distribution, it is *NOT* based on how precisely you calculate the mean of those values.
I refer you back to the graphs of model outputs vs observations. All of the model outputs run hotter than the observations. If you precisely calculate the mean of all the models you will STILL NOT lessen the uncertainty of that mean – which is at least the difference between that mean and the actual observations. It’s a perfect example of why the standard error of the mean is *NOT* the same thing as the uncertainty propagated to the mean by its constituent components.
Why do you leave out the uncertainty in your equation?
Your ΔT has an uncertainty component.
ΔT + u_t = (Tx +/- u_x ) – (Tb +/- u_b)
Where ΔT = Tx – Tb and u_t = u_x + u_b
The uncertainty of ΔT *grows* and you simply cannot ignore that fact as so many climate *scientists* do!
u_b = √(u_1^2 + u_2^2 + … + u_n^2)
Why do you continue to ignore uncertainty propagation?
You left out the uncertainty in ΔT!
As Pat has pointed out you don’t know the biases. What *is* the value of Bx and By? You don’t know the sign of the biases so why do you subtract By from Bx? What if the sign of one of the biases is negative? Say Bx = -0.9By? Suddenly your bias has become 1.9Bx! You simply don’t know the sign or the value of the bias so how do you account for it? Where did the 0.9 come from?
Anomaly analysis doesn’t remove *any* bias. It can’t. You can’t determine bias from uncertain measurements. The bias is lost within the uncertainty interval and is forever unknowable.
The only way you can determine the bias is through referencing *each* measurement against a reference standard measuring the same thing at the same time as the recorded measurement. You simply don’t have that setup at each temperature measuring stations!
Why do you think Hubbard created his experimental setup including the reference station?
I fail to see the difference! Individual measurements WHEN SAMPLED will create a normal shape around the mean. That in no way changes the distribution of the measurements themselves!
You are *still* confusing SEM with uncertainty generated by the population!
And not one single one of those propagate any uncertainty from the individual measurements into their final value. Not one. They do the same thing you do. Assume all measurements are 100% accurate and then you can just ignore the uncertainty associated with the measurements. And you can then say the SEM is the uncertainty!
ROFL! You simply can’t admit that this methodology is totally against metrology methods and practices!
PF said: “Taking anomalies against a station normal does not remove systematic sensor measurement errors.”
Sorry, it simply cannot. As Hubbard also pointed out.
Baselines determined over time will include systematic bias due to calibration and sensor drift. These are unknowable and impossible to determine but they *will* impact the uncertainty of any baseline average done over a period of time. In addition, any bias estimates would have to include knowledge of the micro-environment at each station, eg. ground surface.
The uncertainty in the baseline will ADD to the uncertainty created from subtracting the baseline from an individual measurement. Uncertainties add, they don’t subtract, not even when you are subtracting two stated values.
It *can’t* remove systematic error from the anomaly. The systematic error is included in the uncertainty interval and is unknowable. How do you separate the systematic error from the other causes that contribute to the uncertainty? Doing an anomaly doesn’t somehow magically separate the systematic error from the other sources of uncertainty!
I’m sorry but Pat is correct. You still haven’t been able to separate out SEM from population uncertainty after having it explained to you over and over. You simply don’t seem to understand Hubbard, Quayle, etc. You don’t read their papers for completeness and understanding.
You are trolling through the internet, cherry picking whatever you think might support your assertion that SEM is population uncertainty. Your experiments are all nothing but SEM calculations, even when you have the entire population at hand. You *still* don’t even seem to understand that “n” is the sample size and not the population size. It’s not even the sum of all the elements from each sample.
SEM is *NOT* a measurement of bias in a population. It is the distribution of the sample means – and *only** of the sample means.
All the experts thought Galileo was wrong also. Way too much of climate science today totally ignores the precepts of metrology and uncertainty. Like Pat said, I don’t know if that is a result of ignorance, laziness, or dishonesty. And I don’t care. It is wrong whatever is behind it.
Scenario 1: multiple measurements of the same measurand.
Scenario 2: single measurements of different measurands.
These are totally different scenarios and must be treated differently for uncertainty. SEM tells you something useful in Scenario 1 but not in Scenario 2.
Far too many so-called climate scientists can’t even recognize what being truly independent and random means. They assume it applies to both scenarios.
If X1 gives you *any* predictive value to what X2 might be then the measurements are not truly independent. That is what happens when you do multiple measurements of the same thing. If X1 gives you *no* predictive value to expect for X2 then the measurements are truly independent.. That is what happens when you do single measurements of different things.
One leads you to a true value and true mean. The other only leads you to a true mean but can never lead you to a true value!
Why is that so hard for so-called climate scientists to understand?
“Yes I did [start with Hubbard’s distribution]. You truncated the quote and removed the context. Here is what I actually said.”
I paraphrased, bdgwx, providing the meaning absent the length.
You’re claiming that taking anomalies and removing the mean error bias causes the error distribution itself to become normal.
H&L 2002, Figure 2 provides the error distributions, complete with mean bias offset. Those distributions are T_m minus T_s, which make them functionally equivalent to T_m minus T_N anomalies (T_N is the station normal).
Subtracting the mean bias does nothing to the shape of the error distributions. You claim subtracting the bias should normalize the distributions (“fell into a normal distribution”). You’re wrong.
And as stated before, you could not have done your anomaly experiment with the H&L 2002 data because the raw temperature measurements are unavailable. Whatever it is you think you did, you didn’t do anything relevant. And whatever you think it means, is wrong.
“When you process the average of a large set of observations using anomalies analysis there is no longer a shift in the distribution …”
Taking anomalies against a station normal does not uncover an error distribution. Right from the start, you’re comparing cheese and chalk.
“And to make this perfectly clear I’m talking about the distribution of the errors of the average.”
Anomalies are not errors about an average. Anomalies are the differences of individual measurements about their average. Those differences are not errors. Cheese and chalk, bdgwx.
“Strawman. I never said there was. When I use the word “anomaly” I’m using it exactly how everyone else does.”
Anomalies are not errors. Anomaly distributions are not error distributions. It’s now clear that the difficulty is found in your confusion of anomaly with error.
“[Anomaly] has nothing to do with error itself.”
And yet above, you reiterate,
“When taking the average of the absolute measurements the mean was biased in the same way the original distribution was. But when I switched to using anomaly analysis the bias went away. In both cases the errors fell into a normal distribution.”(my bold)
in which you equate anomalies with error.
“But we do know how those errors are distributed. See Hubbard 2002 as example.”
H&L 2002 error distributions are representative only. They do not provide error distributions that impact measurements at other sites or taken at other times.
The error distributions of historical station temperature measurements are entirely unknown.
“Refer to figure 4 for the skill in Hubbard’s model in shifting those distribution back toward neutral for absolute temperatures (not anomalies).”
H&L 2002 demonstrates successful derivation of a real-time filter for measured air temperatures.
They measured real-time local solar irradiance and local wind-speed coincidentally with the temperature measurements.
These environmental variables parameterized an empirical equation that estimated the systematic bias in each measured air temperature induced by those environmental variables.
No historical meteorological station employed real time filters, nor could have done.
The H&L 2002 real time filter is irrelevant to the historical air temperatures that are the focus of my work. Once again, you have failed to grasp the meaning of H&L’s work. And of mine.
“He most certainly does. What he says is “The station average temperature biases caused by instrument changes were +0.57 and -0.35 C …”
Instrumental changes are not systematic measurement error due to uncontrolled environmental variables. You know that.
Your citation of Hubbard, 2006 is irrelevant to the subject at hand. You know that too.
And yet you continue to push the obviously irrelevant. One can only conclude that you are so loathe to admit your mistake that you’re willing to dissemble. Either that or you thoroughly do not know what you’re talking about.
“I mention this because it challenges your belief that the maintainers of these datasets are incompetent and have no idea how what kind of biases are contaminating their records.”
My judgment is on the willful neglect of systematic measurement error due to uncontrolled environmental variables. Your equivocal demurral does not touch that. Not a smidgen.
“Strawman. I didn’t say [pairwise homogenization] removed uncertainty. I said it removes systematic bias.”
It doesn’t remove systematic sensor measurement error.
Your pairwise talisman doesn’t remove systematic biases, either. It merely modifies them in ways unknown.
The absolute error in any given station is unknown. Adjusting one to coincide with another with an assumed error removal, is an exercise in wishful thinking.
“[Vose, 2003, & Hubbard, 2006] say a lot about the systematic measurement error for observations taking in aggregate like what you do when you form a timeseries of monthly means. That it makes it spot on relevant to our discussion.”
Cheese and chalk again, bdgwx. Time of observation bias and instrumental changes *obviously* have nothing whatever to do with systematic measurement errors. You’re being disingenuous. Or, more charitably, revealing a profound ignorance.
“First…I never said the distribution changes shape here. What I said is that the distribution shifts toward zero (the mean gets closer to zero).”
Your own words, in what is your very same post: “When taking the average of the absolute measurements the mean was biased in the same way the original distribution was. But when I switched to using anomaly analysis the bias went away. In both cases the errors fell into a normal distribution.”(my bold)
It appears you suffer from a conveniently opportunistic memory-loss.
“They won’t because station change instruments and that will change the distribution of the errors. That is a type of systematic error that Hubbard 2006 addresses.”
But instrumental changes are not what we’re discussing. We’re discussing instrumental systematic measurement errors. You insistently make the same careless mistake over and yet over again.
“It is also important to note that the Hubbard 2002 model also assumes the distribution are constant and yet it has very good skill in removing the systematic error.”
Hubbard 2002 does no such thing.
H&L 2002 uses experiment to test the hypothesis of constant impact of solar irradiance and wind-speed upon measured air temperature. The errors are found dependent on those variables. They are not constant.
The significance of H&L 2002 is clear to anyone familiar with experiment. You evidently are not.
“Strawman. I never denied this [the shape of the distribution will remain after subtracting its mean]. I never thought otherwise.”
Your words: on removing the bias, “the errors fell into a normal distribution.”
There’s that memory-loss thing again.
“And I went to great lengths to explain exactly this to you. Remember, I’m the one that is actually doing the experiments here.”
You’re not doing experiments. Granting credibility, you’re producing numerical models that recapitulate your assumptions.
“But [taking anomalies] does change the shape of the distribution of the errors of the average.“
No, it does not. Taking anomalies combines the uncertainty of the normal with the uncertainty distribution of the measurements. Neither of which is known for the historical air temperatures.
“Specifically we are discussing the uncertainty on global mean temperatures. Those are calculated by taking the trivial average of all cells in a grid mesh.”
And the average of each grid-cell is conditioned with the rms uncertainty that includes the systematic measurement error of all the measurements from all the stations in that grid-cell.
The GMT is itself conditioned with the rms uncertainty derived from all the grid-cell uncertainties. That’s QED my position.
Yes it does [taking anomalies removes systematic error]! Try it. ΔT = (Tx+Bx)-(Ty+By). …”
You’re assuming Bx = By = constant. Mindless.
“what I should have said instead was “the individual measurements will morph into a normal shape when many of them are averaged consistent with the expectation of the CTL.”
Thank-you. Nevertheless, we’re not talking about the shapes of measurement distributions. We’re talking about the distribution of systematic measurement errors. They’re not normal. They are not known to morph into normality.
“I didn’t convert them into anomalies. What I converted into anomalies were observations just like how HadCRUT, GISTEMP, BEST, etc. do it.”
But we’re talking about the H&L 2002 calibration error distributions. Not the global temperature data sets.
The systematic errors within the historical station measurement values are unknown. Hidden within. Nothing you do can reveal them.
“Yes [taking anomalies against a station normal does remove systematic sensor measurement errors]. Try it out for yourself.”
H&L 2002 Figure 2 proves you’re wrong. The multiple independent sensor measurement error distributions shown here prove you’re wrong.
Station normals are not conditioned with an error statement, in any case. They’re conditioned with a ± uncertainty.
Subtraction merely converts a ± into a ∓. There’s a triumphal whoop-de-doo for you.
Taking anomalies involves T_m±u_m – T_N±u_N = T_a±u_a, where ±u_m is sensor calibration error and ±u_a is the uncertainty in the anomaly.
±u_a = sqrt[(u_m)^2 + (u_N)^2].
To complete, ±u_N = sqrt{sum[(u_m_i)^2]/(n-1)}, where m_i is the ith of ’n’ station measurements.
There’s no way out, bdgwz.
“In fact, the uncertainty of the anomaly is the RSS of the uncertainty of the baseline and the uncertainty of the observation.”
The uncertainty in the anomaly is the RMS of the component uncertainties, taking into account the loss of one degree of freedom.
“What [taking anomalies] does do is remove systematic error.“
Wrong, for reasons shown above. Systematic sensor measurement error in any case varies with time and location. It is never constant.
“I get it. You think everyone but you is incompetent.”
No. Those particular people are demonstrated incompetent. Many well-educated scientists and engineers have agreed with my work. The 2010 paper passed very competent review.
See also the comments of Tim and Jim Gorman. They are both engineers, whose work absolutely demands strict adherence to uncertainty analysis. They know what they’re talking about. I suspect poster Carlo, Monte is likewise trained.
My uniform experience with climate scientists is that they are untrained in physical error analysis. It’s as a foreign language to them. Evidently, it is to you too.
“… but they’ve certainly considered more than you are trying insinuate”
Clearly, they have not done. Treatment of systematic sensor measurement error is entirely absent from their published work.
Pat, Thanks for the complement. I learned about measurements early in life. Our father was a renowned mechanic who specialized in Farmall and International Harvester equipment. I spent many an evening listening to him on the phone trying to diagnose problems with farmers so that he had the right materials and tools when he visited them to work on equipment in the field.
He taught us to use calipers, micrometers, dial gauges, etc. when working on engines. Farm tractors especially spend hours running at spec’d speeds and you didn’t want to scrimp on your analysis of bearing surfaces and clearances or you would spend your own money fixing warrantied work.
I’ll guarantee that some of the folks here have never made measurements where their livelihood depended on doing so correctly and informing customers or your own business as to the needed requirements along with budgetary costs.
That same detail work followed me through my career in both engineering and system management. As I progressed into management, there were folks who thought I was too intent on detailed measurement of data and that close enough was a better way to operate. That isn’t me.
I have been a ham radio operator since 1963 and have designed and built many pieces of high performance radio equipment and kept my fingers in building even through the SMD phase. Although I can no longer manually do some of this work, I maintain a test environment with HP, Tektronix, and Rigol equipment. I believe in Deming’s philosophy of DO IT RIGHT THE FIRST TIME.
Sounds like you got great training from an early age, Jim. That tree grows straight.
Kudos to your dad. You were lucky to have him and, clearly, he you.
First, a bunch is not a statistical term. Are you combining populations or sample means.
Averaging sample means is illogical since they are from different populations and they can not be considered to be IID, e.g., the random variables can not be considered to be identically distributed.
Averaging populations is allowed with a big caveat, variances add when combining populations. This destroys any assumption that:
See these links for an explanation.
https://www.emathzone.com/tutorials/basic-statistics/combined-variance.html
https://intellipaat.com/blog/tutorial/statistics-and-probability-tutorial/sampling-and-combination-of-variables/
https://www.khanacademy.org/math/ap-statistics/random-variables-ap/combining-random-variables/a/combining-random-variables-article
Conclusion: If you add populations distributions to obtain a combined average, then the variances add. The variance is an indication of uncertainty in what the mean actually represents. Inevitably the errors grow and do not cancel out.
First, what is a bunch of anomalies? You do not use precise scientific language and it is difficult to deal with your arguments.
Certainly averaging an independent “bunch of anomalies” will probably
tend to a normal distribution. However is it meaningful? There are assumptions that must be met to properly use this CTL attribute. The main one is known as IID, Independent and Identical Distribution. This is usually applied in sampling where samples are taken from the same population and the distributions of the samples are controlled to meet the Identical Distribution requirement.
I assume by bunch, you mean anomaly distributions from different stations. Do they all have the same distribution of temperatures? Are their variances the same? If not what you are in essence doing is averaging Clydesdale and Shetland horses together, think NH vs SH. Doesn’t exactly fit the CLT requirements does it?
Then when you find out there are different variances, you know there is an extra step you must take. You can certainly combine the values and calculate a combined mean but you must also add the variances together. See the following links.
https://www.emathzone.com/tutorials/basic-statistics/combined-variance.html
https://intellipaat.com/blog/tutorial/statistics-and-probability-tutorial/sampling-and-combination-of-variables/
https://www.khanacademy.org/math/ap-statistics/random-variables-ap/combining-random-variables/a/combining-random-variables-article
https://apcentral.collegeboard.org/courses/ap-statistics/classroom-resources/why-variances-add-and-why-it-matters
Lastly, creating anomalies by subtracting a mean does not change any statistical parameters. I’ll post two images, one on this message and one on another message. They show what the statistical parameters are for a group of temperatures. As you can see, simply subtracting a mean does not change the distribution in any meaningful way. Only the axis values change but not the parameters.
Here are the anomalies.
+1
Have you ever decided if these are dealing with a population (divide by √N) or a sample (multiply by the √N). As I have pointed out if dividing by √N that is a redundant calculation and is meaningless. If you have a sample then you should be multiplying by √N/
“At the very least we should be able to test your hypothesis by looking at several model predictions from 30 years ago.”
That’s not a test. Your proposal evidences your lack of understanding.
Your “model predictions” have no physical meaning. Their correspondence, or not, with the temperature trend since 1988 indicates nothing.
The emulation equation reproduces the air temperature projections of advanced climate models. All of them. That’s its reality.
How do you propose we test your hypothesis then?
I made no hypothesis, bdgwx. I just propagated a calibration uncertainty through an iterative calculation.
It’s methodology; totally standard practice in the physical sciences to evaluate predictive reliability.
Just the other day, an engineering physicist (Ph.D. UC Berkeley) discussed the paper with me. He’d read it twice, and was in complete agreement. He’s not the only one.
And how do you propose we test that propagation of calibration uncertainty through an iterative calculation to see if it adequately describes error with real data?
First experiment:
Go pick up a set of random boards, preferably from ditches around where you live or work.
Measure all the boards. Write down all the stated values plus their uncertainty. Calculate their mean. Cut a sheet of drywall or plywood to be that average height.
Now build a stud wall using those boards, attach your average plywood sheet to the stud wall, and measure the gaps you find where the plywood is either taller or shorter than the stud wall.
Those gaps will be the uncertainty surrounding the mean you calculated.
You can run this experiment as many times as you want with as different sets of random boards from ditches. You can average all the means of the sample sets together in order to minimize the standard error of the mean for all those sample sets.
IT WON’T MAKE THOSE GAPS ANY SMALLER WHEN YOU BUILD THE STUD WALLS AND ATTACH A SHEET OF PLYWOOD CUT TO THE “AVERAGE” MEASUREMENT.
Second experiment:
Take two of your randomly selected boards and lay them end-to-end. Measure the length of the combination. Does it equal twice the average you calculated in Exp. 1?
Experiment 3:
Lay five of the random boards end-to-end. Measure the length and record the stated value and its uncertainty. Does the combined length equal the sum of the stated values for the five boards? If it doesn’t then how far off is the sum of the stated values from the measured value?
The emulation equation successfully reproduces the air temperature projections of advanced climate models. Linear forcing goes into climate models, and linear temperature projections come out. QED.
The emulation equation successfully reproduces what climate models are observed to do. It can therefore be used to propagate climate model calibration error through the iteration.
Propagation of calibration uncertainty does not describe error. It describes an ignorance width.
Must this distinction be endlessly repeated for you?
“The odds that your emulation equation would match reasonable well is very high because it is nothing more than a curve fit with no fundamental basis in physical reality. I would be very skeptical about its ability to equally match future temperature trajectories.”
ROFL!!!
That is all the climate models are! The climate scientists all admit the models don’t do clouds right. They don’t do enthalpy right ether! They don’t do land/sea heat transport right either!
All they are are a bunch of equations that, after a few years, boil down to nothing more than y = mx + b! Primarily by guessing at some parameter values that may or may not have any relationship to physical reality.
Not a single model has predicted ANY of the pauses in warming. Not one! Not the 20 year pause and not the current 8 year pause. They just keep right on with their mx + b trend!
“Hansen’s model on the other hand does a fundamental basis in physical reality because it is global circulation model that is complying with conservation of energy, conservation of mass, conservation of momentum, thermodynamic laws, radiative transfer, etc”
Clouds? Heat transport? Latent heat? enthalpy?
Their models don’t even recognize that they are trending multi-mode data! So how can they make allowances for it?
When you see an mx + b trend being used as a forecast for future temps you can rest assured that it is trash.
What is the probability of T = mx + b properly predicting the future? What is the probability of someone picking the right m value?
Answer: The probability decreases hyperbolically the farther into the future past the last measurement point.
It’s always a projection
Let’s review where we are.
Pat’s figure 1 seems to indicate that the error in CMIP5 projections is σ = 15 C after 100 years and about σ = 8 C after 30 years.
I asked Pat what the probability is of CMIP5 having a warming trend within 0.01 C/decade over a 140 year period.
I state that the RMSE of CMIP5 vs BEST on monthly basis is 0.165434942894202 C which reported as 0.165 C. Carlo Monte and Pat then say that this is equivalent to millikelvin accuracy even though it is not even close to ±0.001 C. We get into yet another diversionary discussion regard sf even though I complied with the standard rules.
Meanwhile Pat says the probability of CMIP5 matching observations is very high despite his error analysis because it was tuned to match observations. That is a reasonable argument even if it doesn’t tell the whole story so I then ask what is the probability of a model which was ran 30 years ago matching observations to within 1C, 0.5C, 0.1C, and 0.05C of today’s temperature?
Pat then says that this is the wrong question and that the question should be “What is the physical reliability of an air temperature projection from a model run of 30 years ago?” which he answers as zero. I have no idea what objective criteria is being applied to adjudicate “physical reliability” and arriving at an answer of zero, but whatever.
So the questions now are…
What does the σ = 8 C after 30 years even mean?
Why do none of the models ran 30 years ago have anywhere near 8 C of error?
Where did you pull this number from?
How did you determine their errors?
It comes from Pat’s publication figure 6.
“I have no idea what objective criteria is being applied to adjudicate “physical reliability” and arriving at an answer of zero, but whatever.”
If the uncertainty is 8C then how do you tell any difference less than 8C? Since uncertainty of the population carries over to anomalies calculated from that population how do actually know what the anomalies are doing? If you draw a trend line that is 16C wide (±8C) anomalies could lie anywhere under that trend line. They could zig-zag, go up, go down, or even do a random walk. How would you know?
“Why do none of the models ran 30 years ago have anywhere near 8 C of error?”
Who says they don’t? They certainly missed all the pauses in temperature change since 1998. All you are going by is that the model graphs don’t show their actual uncertainty range! So what? Does that mean there isn’t any uncertainty range?
Have you built your stud wall yet?
“8 C of error?”
Uncertainty is not error. It says nothing about where the numbers come out. It only provides an indication of reliability.
So your ±8 C of uncertainty after 30 years does not in any way describe the difference between model predictions and actual observations?
There are no actual observations from 30 years in the future.
Uncertainty is an ignorance width, not an error divergence.
When the projection uncertainty is larger than any physically reasonable possibility, the message is that ignorance of the future state is total.
The uncertainty around Jim Hansen’s 1988 scenario A, B, and C (paper Figure 8), indicates the level of physical knowledge in the projections. High uncertainty tells us that actual physical knowledge of the climate state is zero, and the projections have no physical meaning.
What this means is that the parameter sets Jim Hansen used to produce his projections are not unique. A large number of alternative sets of model parameters can produce the same projections, because parameters are chosen to have off-setting errors.
No one knows the physically correct magnitudes of the model parameters. So, they’re chosen to reproduce past observations. Model tuning causes the errors to adventitiously cancel one another (which does not remove physical uncertainty) and then cross-your-fingers.
All the models also feature a hyper viscous atmosphere, by the way, so as to suppress enstrophy.
Climate simulations blow up if the atmosphere is allowed to develop without a high viscosity that suppresses smaller-scale energy flux.
Jerry Browning has a lot to say about this. https://doi.org/10.1016/j.dynatmoce.2020.101143
His work shows that current climate models are solving ill-posed equations. Hence the need for a physically nonsensical atmosphere.
“There are no actual observations from 30 years in the future.”
Of course there is. Models ran in the 1980’s exceeded their 30 year forecast and there is definitely observations available through this period.
“Uncertainty is an ignorance width, not an error divergence.”
Your definition of uncertainty may be different than everyone else then. For example, when Hausfather describes the uncertainty of the CMIP models he is speaking of the expectation of observations relative to the prediction. In other words we expect the annual observation of 95 out of 100 years to fall within the 95% CI envelope and 5 out of 100 to fall outside of that same envelope.. Similarly when I discuss uncertainty it is always in the context of the distribution of the difference between prediction and observation.
Me: “There are no actual observations from 30 years in the future.”
bdgwx: “Of course there is.” Crystal ball science, Observations are not available from the future.
For you now to call upon observations after time has passed as though they were relevant to past projections at the time when those projections were made — which is the meaning of your claim — is logical nonsense.
“Your definition of uncertainty may be different than everyone else then“
It is to laugh.
Tell you what: rather than explaining it all yet once again — an explanation you will reject anyway out of standpoint prejudice — suppose you get yourself a copy of Bevington and Robinson, “Data Reduction and Error Analysis for the Physical Sciences, 3rd Edition.” Turn to page 55 and read the section under “A Warning About Statistics.”
Then read pages 5-6 and 14 about uncertainty and the definitions of error and uncertainty.
Then realize that uncontrolled variables produce errors of varying but unknown magnitude in both temperature measurements and in climate model simulations. The latter because the climate is dynamic rather than static.
When real-time errors are unknown and variable, one’s only recourse is to determine a likely range of error magnitudes by way of calibration under conditions as close as possible to the experimental conditions. Field measurements against a high-accuracy standard for thermometers, hindcasts against known climate states for models.
Given the determined set of errors from calibration experiments, one calculates a calibration uncertainty. That calibration uncertainty must then be applied to every station air temperature measurement or every air temperature projection.
That is standard practice.
This is from your Hausfather link: “The uncertainty range reflects the statistical uncertainty of the observations and the 95% range of trends across all the models.“(my underline)
You have misunderstood Hausfather’s definition. His definition is standard in climate modeling: uncertainty is the spread of model projections about their own mean. Mere precision.
I discuss that mistake in my paper.
His statistical uncertainties of the observations themselves are ludicrously small for reasons I’ve already given. Ludicrous to any practicing experimental scientist or engineer, anyway. I don’t expect you to accept that either, but then your arguments are ludicrous as well.
Thanks for the book reference.
Ditto.
Pat, are you challenging the fact that observations are now available for 1990 to 2020 and which can be used to assess the difference between model prediction’s from 30 years ago against observations today?
No.
But as noted, and as Jim Hansen agreed, those prior projections were physically meaningless.
Their comportment, or not, with subsequent observations remains physically meaningless.
You’ve no way out, bdgwx.
And I’ve not misunderstood the 95% CI envelope of the CMIP models. It is indeed the range in which 95% of the ensemble members fall into. This range exists because variability in observed temperatures is expected and the different ensemble members are reflecting this expectation. That range is our expectation of the observation. We expected it stay within that range 95% of the time. In other words we expect the temperature to stay within the 95% CI band of the mean 95% of the time and fall outside the band 5% of the time.
“That range is our expectation of the observation.”
No, it is not. That range is the expected model spread.
The expected observation is an utter unknown.
Model outputs are mere physically meaningless speculation.
Yes it is. This is the same as with any model ensemble whether it be the GEFS, EPS, SREF, etc. for weather forecasting or CMIP5/6 for climate forecasting.
Man you have the disease bad. Even the IPCC declares these to be PROJECTIONS from assumed interactions and not forecasts. They have said forecasts are not reliable. Yet here you are saying that they are. I don’t know how you define certainty and uncertainty but you need to rethink what you think you know!
No they’re not. Climate models are parameterized epidemiological constructs. Their output merely reflects their input assumptions.
Climate model projected future temperatures are speculations. They are not predictions of future observables.
“And I’ve not misunderstood the 95% CI envelope of the CMIP models. It is indeed the range in which 95% of the ensemble members fall into.”
You’ve shifted your ground bdgwx.
In your post of October 23, 2021 4:56 pm , you wrote, “In other words we expect the annual observation of 95 out of 100 years to fall within the 95% CI envelope and 5 out of 100 to fall outside of that same envelope.”
Your initial position was that climate models predicted observations. Now you’ve changed your position to be that climate models can repeat their own projections.
In other words, you now agree with my position as stated in the October 23, 2021 6:48 pm comment. Climate model spreads are mere precision.
I stand by my statement. The 95% CI envelope for ensemble modeling is our expectation of the possible range for observations. This is true whether we are speaking of GEFS, EPS, SREF, etc. for weather forecasting or CMIP5/6 for climate forecasting.
Go ahead and stand by your mistake, bdgwx. You’re still wrong.
“It is indeed the range in which 95% of the ensemble members fall into. “
If *ALL* of the ensembles are wrong then what does the range of the ensembles mean?
It’s what uncertainty is meant to address. It’s the difference between standard error of the mean and the uncertainty associated with the mean that we’ve been trying to get you to understand, with absolutely no success.
You can calculate the mean of the ensembles as precisely as you want, i.e. minimize the standard error of the mean, but it doesn’t result in anything useful as far as telling you the accuracy of the mean with respect to reality.
One (SEM) is a statistical metric which depends on assuming the data being analyzed is 100% accurate and assuming the data distribution at least approaches Gaussian in order to be meaningful.
The other (uncertainty) tells you something about the accuracy of the data and the resulting mean. It doesn’t assume the stated values of the data is 100% accurate nor does it need to assume that the data distribution at least approaches Gaussian.
Almost none of the models approach observations, they are all biased high. Assuming their mean is 100% accurate in describing reality is a real WHOPPER of a delusion.
“This range exists because variability in observed temperatures is expected and the different ensemble members are reflecting this expectation. “
No, the variability is because of the assumptions used in programming the models, especially the *assumed* tuning parameters used in each model in order to account for factors which aren’t truly modeled, e.g. clouds.
Pick a different tuning value for clouds in Model 1 and Model 2 and you will get a variability in the two model outputs.
Since all of the models eventually turn into y = mx + b projections all the models are essentially doing is picking different values for “m” and using different starting points “b”. That is why they are projections and not forecasts.
“If *ALL* of the ensembles are wrong then what does the range of the ensembles mean?
“It’s what uncertainty is meant to address.”
The crux issue. Succinctly expressed! 🙂
“uncertainty it is always in the context of the distribution of the difference between prediction and observation.”
Uncertainty is not a prediction. It is an interval where you have no knowledge of what the actual measurement is.
You referenced Hausfather, yet gave no quote of what he asserted in relation to propagation of measurement uncertainty.
Why do you think the IPCC is recalibrating models and ECS? They are running hot, you surely don’t deny that too. That should tell you that the IPCC is UNCERTAIN about their projections. What more evidence do you need that the model outputs are in an interval where no one knows what the correct values are? They are doing this for output projections that aren’t even a year old!
The interval you are talking about is actually a relative accuracy figure.
|(Measured – Actual)| / Actual
That IS NOT UNCERTAINTY.
Have you looked at the ensemble range of models as they go out 100 years? How do you know that an 8C uncertainty range is unreasonable. Even the IPCC knows that forecasting a coupled, non-linear chaotic climate system is never going to happen. Why do you think that is? Why have they not quoted an uncertainty interval for the model projections compared to reality?
You still not understand the difference between error and uncertainty. After all the links and explanations you appear to not have the ability to learn. I going to stop calling you a mathematician and start calling you an arithmetician, that is, someone who can’t move beyond dealing with plain numbers as numbers on a number line.
You continue to treat the 8C as an error and it is not. If it was an error range, yes you could add it to a measured temperature and compare it to a temperature from a model. IT IS NOT AN ERROR. It is an uncertainty. That is a range where you can not reliably consider a temperature from a model to be accurate. Note the word reliable. It doesn’t mean that the prediction won’t come true. It means that at the time the projection is made that you can’t consider it as reliable. That is why the IPCC won’t include an uncertainty range in their projections. They would have to also entertain the question of whether their “scientific” projection means anything.
While the same is possible for climate science, it is not currently reasonable, given the state of divergence between the predictions and the collected data. I am not a climatologist and I don’t play one on TV, but I have been an engineer for over 30 years with the latter half of that being involved in verification and validation of materials, components and systems. When predictions are not supported by the collected data, that always means the predictions are incorrect. Whether the poor modeling is based on an incomplete understanding of the system, or whether the poor modeling is incorrect regarding the sensitivity of the system to different variables, the only reasonable conclusion is that the model has no reliable predictive value and should not be used to make design decisions.
Additionally, much of the modeling is based on accurate observations that were obtained over a very short time scale, geologically or globally, and which ignore many different inputs into the system that do not align with the man-caused climate change narrative. That isn’t science.
I don’t see how weather forecasting has improved in my life time, all I see is since the advent of Doppler radar is in improvement of warning the general public of happening now weather events.
They cannot with any accuracy predict where a hurricane or sever thunderstorm will hit five days before. They do know said event might be day to day but they knew that 50 years ago. They have no idea of it strength said events are going to be and when it hit and lately they over estimated hurricane strength and that because of Doppler radar.
At least now we know where a tornado will hit soon because of Doppler radar. Yet the seven day forecast is still as useless as it was seventy years ago. The long range forecast are worse, farmers now hire outside firms to give them a clue because the US weather service has built in “global warming” in their long forecast which has made said forecast useless.
Forget about flood forecast since they now rely on models and don’t do the field work(like knowing the snow depth and water content of real measurements) said flood forecast are worthless. At least that the case in the Red River Valley of the north.
Anything less than perfection is useless?
5 day forecasts today are about as accurate as 3 day forecasts were 50 years ago.
Ditto for forecasts of hurricane tracks and strength.
From the article: ““The 10 hottest years on record have occurred since Katrina inundated New Orleans in 2005.”
Not if you go by the UAH satellite chart. It shows NO years between 1998 and 2016 as being the hottest years.
Uberti is just regurgitating NOAA climate propaganda. Which shows his lack of grasp of the subject.
“We trust” Speak for yourself! I found all weather forecasting to be garbage for decades. We used to have actual meteorologists who actually forecasted weather. Now it’s a talking head telling us what the computer model spat out. And the NWS is most definitely NOT in the business of keeping any one safe or saving lives.
They have a legal disclaimer (like all forecasting sites) that says “In no event will NWS be liable to you or to any third party for any direct, indirect, incidental, consequential, special or exemplary damages or lost profit resulting from any use or misuse of this data.”
This means if your business that pours concrete plans a pour on a day forecasted to be sunny, yet, as is often the case, the forecast was 100% wrong and instead it rains, you then lose a lot of money being unexpectedly shut down by the downpour. Since the NWS’ incorrect forecast was directly responsible for your business’ plan to pour concrete, it thus falls on them to accept blame for being so wrong it cost you business thousands.
And that’s why they put a disclaimer, and why they logically cannot be said to be concerned with our well-being in any way. They have clearly stated that they do not accept ANY responsibility of ANY KIND for the consequences of their poor forecasts and incorrect data.
If they really cared about keeping us safe, saving lives, or not incurring economic harm, they would have near-perfect forecasts and no disclaimer. Instead they run a computer model, parrot what it spits out, and then claim they’re “keeping us safe” or “saving lives” or some other bullcrap PR line.
No, their poor, usually 100% wrong forecasts have killed untold scores. I’ve had my life risked due to wrong forecasts on numerous occasions, so I have learned to do my own forecasting based on the sat. images, radar images, and other data. You should all do the same.
Only a fool would “trust” a weather forecast in 2021.
I remember in high school science class back in 1964 when we would take the weather map from the newspaper every day, showing highs, lows, and frontal boundaries, and add it to a pin-up board. We could do a better job of predicting 24-48 hour weather than the weather man himself. It’s not a whloe lot different today.
Weather information is greatly improved since I was a child. There’s no comparison between then and now.
The forecasts are good for about five days and are fairly accurate.
The real big improvement I see is the way extreme weather is covered in real time, at least in my area of Tornado Alley. When storm fronts come in, the stormchasers go out on the prowl for tornadoes and the weather radar finds the tornadoes and notifies the chasers and the chasers keep us all informed as to where the tornadoes are located and what they are doing.
The severe weather forecasts are good enough that they can station the stormchasers in places ripe for tornado development, and they are pretty accurate at narrowing it down.
Major heat and cold waves are discretely solar forced and can be predicted at any range. They are a cause and not a product of climate change.
For example. Europe will see a major heatwave in 2045, of the same type as the heatwaves of 1934, 1949, 1976, 2003, and 2018. The weekly scale timing of the event is ordered by the relative positions of the inner planets.
https://www.linkedin.com/pulse/major-heat-cold-waves-driven-key-heliocentric-alignments-ulric-lyons/
Milutin Milankovitch had proposed the discrete solar forcing of heat and cold waves, he was denounced as insane. I regard the belief that major heat and cold waves are chaotic internal variability as insane.
It only took 10,000 to 100,000 forecasts compared to what actually happened to make meteorological forecasts this good. So, it will only take another 1-10million years to get that good at predicting the climate.