Guest Essay by Kip Hansen
Those following the various versions of the “2014 was the warmest year on record” story may have missed what I consider to be the most important point.
The UK’s Met Office (officially the Meteorological Office until 2000) is the national weather service for the United Kingdom. Its Hadley Centre in conjunction with Climatic Research Unit (University of East Anglia) created and maintains one of the world’s major climatic databases, currently known as HADCRUT4 which is described by the Met Office as “Combined land [CRUTEM4] and marine [sea surface] temperature anomalies on a 5° by 5° grid-box basis”.
The first image here is their current graphic representing the HADCRUT4 with hemispheric and global values.
The Met Office, in their announcement of the new 2014 results, made this [rather remarkable] statement:
“The HadCRUT4 dataset (compiled by the Met Office and the University of East Anglia’s Climatic Research Unit) shows last year was 0.56C (±0.1C*) above the long-term (1961-1990) average.”
The asterisk (*) beside (+/-0.1°C) is shown at the bottom of the page as:
“*0.1° C is the 95% uncertainty range.”
So, taking just the 1996 -> 2014 portion of the HADCRUT4 anomalies, adding in the Uncertainty Range as “error bars”, we get:
The journal Nature has a policy that any graphic with “error bars” – with quotes because these types of bars can be many different things – must include an explanation as to exactly what those bars represent. Good idea!
Here is what the Met Office means when it says Uncertainty Range in regards HADCRUT4, from their FAQ:
“It is not possible to calculate the global average temperature anomaly with perfect accuracy because the underlying data contain measurement errors and because the measurements do not cover the whole globe. However, it is possible to quantify the accuracy with which we can measure the global temperature and that forms an important part of the creation of the HadCRUT4 data set. The accuracy with which we can measure the global average temperature of 2010 is around one tenth of a degree Celsius. The difference between the median estimates for 1998 and 2010 is around one hundredth of a degree, which is much less than the accuracy with which either value can be calculated. This means that we can’t know for certain – based on this information alone – which was warmer. However, the difference between 2010 and 1989 is around four tenths of a degree, so we can say with a good deal of confidence that 2010 was warmer than 1989, or indeed any year prior to 1996.” (emphasis mine)
This is a marvelously frank and straightforward statement. Let’s parse it a bit:
• “It is not possible to calculate the global average temperature anomaly with perfect accuracy …. “
Announcements of temperature anomalies given as very precise numbers must be viewed in light of this general statement.
• “…. because the underlying data contain measurement errors and because the measurements do not cover the whole globe.”
The reason for the first point is that the original data themselves, right down to the daily and hourly temperatures recorded in humongous data sets, contain actual measurement errors – part of this includes such issues as accuracy of equipment and units of measurement – and errors introduced by methods to attempt to account for “measurements do not cover the whole globe” – various methods of in-filling.
• “However, it is possible to quantify the accuracy with which we can measure the global temperature and that forms an important part of the creation of the HadCRUT4 data set. The accuracy with which we can measure the global average temperature of 2010 is around one tenth of a degree Celsius.”
Note well that the Met Office is not talking here of statistical confidence intervals but “the accuracy with which we can measure” – measurement accuracy and its obverse, measurement error. What is that measurement accuracy? “…around one tenth of a degree Celsius” or, in common notation +/- 0.1 °C. Note also that this is the Uncertainty Range given for the HADCRUT4 anomalies around 2010 – this uncertainty range does not apply, for instance, to anomalies in the 1890s or the 1960s.
• “The difference between the median estimates for 1998 and 2010 is around one hundredth of a degree, which is much less than the accuracy with which either value can be calculated. This means that we can’t know for certain – based on this information alone – which was warmer.”
We can’t know (for certain or otherwise) which is different from any of the other 21st century data points that are reported as within 100ths of a degree of one another. The values can only be calculated to an accuracy of +/- 0.1˚C
And finally,
• “However, the difference between 2010 and 1989 is around four tenths of a degree, so we can say with a good deal of confidence that 2010 was warmer than 1989, or indeed any year prior to 1996.”
It is nice to see them say “we can say with a good deal of confidence” instead of using a categorical “without a doubt”. If two data are 4/10ths of a degree different, they are confident of a difference and the sign, + or -.
Importantly, Met Office states clearly that the Uncertainty Range derives from the accuracy of measurement and thus represents the Original Measurement Error (OME). Their Uncertainty Range is not a statistical 95% Confidence Interval. While they may have had to rely on statistics to help calculate it, it is not itself a statistical animal. It is really and simply the Original Measurement Error (OME) — the combined measurement errors and lack of accuracies of all the parts and pieces, rounded off to a simple +/- 0.1˚C, which they feel is 95% reliable – but has a one in twenty chance of being larger or smaller. (I give links for the two supporting papers for HADCRUT4 uncertainty at the end of the essay.****)
UK Met Office is my “Hero of the Day” for announcing their result with its OME attached – 0.56C (±0.1˚C) – and publicly explaining what it means and where it came from.
[ PLEASE – I know that many, maybe even almost everyone reading here, think that the Met Office’s OME is too narrow. But the Met Office gets credit from me for the above – especially given that the effect is to validate The Pause publically and scientifically. They give their two papers**** supporting their OME number which readers should read out of collegial courtesy before weighing in with lots of objections to the number itself. ]
Notice carefully that the Met Office calculates the OME for the metric and then assigns that whole OME to the final Global Average. They do not divide the error range by the number of data points, they do not reduce it, they do not minimize it, they do not pretend that averaging eliminates it because it is “random”, they do not simply ignore it as if was not there at all. They just tack it on to the final mean value – Global_Mean( +/- 0.1°C ).
In my previous essay on Uncertainty Ranges… there was quite a bit of discussion of this very interesting, and apparently controversial, point:
Does deriving a mean* of a data set reduce the measurement error?
Short Answer: No, it does not.
I am sure some of you will not agree with this.
So, let’s start with a couple of kindergarten examples:
Example 1:
Here’s our data set: 1.7(+/-0.1)
Pretty small data set, but let’s work with it.
Here are the possible values: 1.8, 1.7, 1.6 (and all values in between)
We state the mean = 1.7 Obviously, with one datum, it itself is the mean.
What are the other values, the whole range represented by 1.7(+/-0.1)?:
1.8 and every other value to and including 1.6
What is the uncertainty range?: + or – 0.1 or in total, 0.2
How do we write this?: 1.7(+/-0.1)
Example 2:
Here is our new data set: 1.7(+/-0.1) and 1.8(+/-0.1)
Here are the possible values:
1.7 (and its +/-s) 1.8, 1.6
1.8 (and its +/-s) 1.9, 1.7
What’s the mean of the data points? 1.75
What are the other possible values for the mean?
If both data are raised to their highest value +0.1:
1.7 + 0.1 = 1.8
1.8 + 0.1 = 1.9
If both are lowered to their lowest -0.1:
1.7 – 0.1 = 1.6
1.8 – 0.1 = 1.7
What is the mean of the widest spread?
1.9 + 1.6 / 2 = 1.75
What is the mean of the lowest two data?
1.6 + 1.7 / 2 = 1.65
What is the mean of the highest two data:
1.8 + 1.9 / 2 = 1.85
The above give us the range of possible means: 1.65 to 1.85
0.1 above the mean and 0.1 below the mean, a range of 0.2
Of which the mean of the range is: 1.75
Thus, the mean is accurately expressed as 1.75(+/-0.1)
Notice: The Uncertainty Range, +/-0.1, remains after the mean has been determined. It has not been reduced at all, despite doubling the “n” (number of data). This is not a statistical trick, it is elementary arithmetic.
We could do this same example for data sets of three data, then four data, then five data, then five hundred data, and the result would be the same. I have actually done this for up to five data, using a matrix of data, all the pluses and minuses, all the means of the different combinations – and I assure you, it always comes out the same. The uncertainty range, the original measurement accuracy or error, does not reduce or disappear when finding of the mean of a set of data.
I invite you to do this experiment yourself. Try the simpler 3-data example using the data like 1.6, 1.7 and 1.8 ~~ all +/- 0.1s. Make a matrix of the nine +/- values: 1.6, 1.6 + 0.1, 1.6 – 0.1, etc. Figure all the means. You will find a range of means with the highest possible mean 1.8 and the lowest possible mean 1.6 and a median of 1.7, or, in other notation, 1.7(+/-0.1).
Really, do it yourself.
This has nothing to do with the precision of the mean. You can figure a mean to whatever precision you like from as many data points as you like. If your data share a common uncertainty range (original measurement error, a calculated ensemble uncertainty range such as found in HADCRUT4, or determined by whatever method) it will appear in your results exactly the same as the original – in this case, exactly +/- 0.1.
The reason for this is clearly demonstrated in our kindergarten example of 1, 2 and 3-data data sets – it is a result of the actual arithmetical process one must use in finding the mean of data each of which represent a range of values with a common range width*****. No amount of throwing statistical theory at this will change it – it is not a statistical idea, but rather an application of common grade-school arithmetic. The results are a range of possible means, the mean of which we use as “the mean” – it will be the same as the mean of the data points when not taking into account the fact that they are ranges. This range of means is commonly represented with the notation:
Mean_of_the_Data Points(+/- one half of the range)
– in one of our examples, the mean found by averaging the data points is 1.75, the mean of the range of possible means is 1.75, the range is 0.2, one-half of which is 0.1 — thus our mean is represented 1.75(+/-0.1).
If this notation X(+/-y) represents a value with its original measurement error (OME), maximum accuracy of measurement, or any of the other ways of saying that the (+/-y) bit results from the measurement of the metric then X(+/-y) is a range of values and must be treated as such.
Original Measurement Error of the data points in a data set, by whatever name**, is not reduced or diminished by finding the mean of the set – it must be attached to the resulting mean***.
# # # # #
* – To prevent quibbling, I use this definition of “Mean”: Mean (or arithmetic mean) is a type of average. It is computed by adding the values and dividing by the number of values. Average is a synonym for arithmetic mean – which is the value obtained by dividing the sum of a set of quantities by the number of quantities in the set. An example is (3 + 4 + 5) ÷ 3 = 4. The average or mean is 4. http://dictionary.reference.com/help/faq/language/d72.html
** – For example, HADCRUT4 uses the language “the accuracy with which we can measure” the data points.
*** – Also note that any use of the mean in further calculations must acknowledge and account for – both logically and mathematically – that the mean written as “1.7(+/-0.1)” is in reality a range and not a single data point.
**** – The two supporting papers for the Met Office measurement error calculation are:
Colin P. Morice, John J. Kennedy, Nick A. Rayner, and Phil D. Jones
and
J. J. Kennedy , N. A. Rayner, R. O. Smith, D. E. Parker, and M. Saunby
***** – There are more complicated methods for calculating the mean and the range when the ranges of the data (OME ranges) are different from datum to datum. This essay does not cover that case. Note that the HADCRUT4 papers do discuss this somewhat as the OMEs for Land and Sea temps are themselves different.
# # # # #
Author’s Comment Policies: I already know that “everybody” thinks the UK Met Office’s OME is [pick one or more]: way too small, ridiculous, delusional, an intentional fraud, just made up or the result of too many 1960s libations. Repeating that opinion (with endless reasons why) or any of its many incarnations will not further enlighten me nor the other readers here. I have clearly stated that it is the fact that they give it at all and admit to its consequences that I applaud. Also, this is not the place continue your One Man War for Truth in Climate Science (no matter which ‘side’ you are on) – please take that elsewhere.
Please try to keep comments to the main points of this essay –
Met Office’s remarkable admission of “accuracy with which we can measure the global average temperature” and that statement’s implications.
and/or
“Finding the Mean does not Reduce Original Measurement Error”.
I expect a lot of disagreement – this simple fact runs against the tide of “Everybody- Knows Folk Science” and I expect that if admitted to be true it would “invalidate my PhD”, “deny all of science”, or represent some other existential threat to some of our readers.
Basic truths are important – they keep us sane.
I warn commenters against the most common errors: substituting definitions from specialized fields (like “statistics”) for the simple arithmetical concepts used in the essay and/or quoting The Learned as if their words were proofs. I will not respond to comments that appear to be intentionally misunderstanding the essay.
# # # # #
While there have been several comments that mention it, none have been very explicit with why the supposed law of large numbers is not necessarily applicable to climate temperature measurement. The fundamental problem is that most folks do not see the temperature data from the perspective of an instrumentation technician or engineer.
No instrument calibration technician will claim that instrument errors may be assumed to be randomly distributed around some true value. All that will be claimed is that the instrument was adjusted and verified to read within its specified accuracy limits in his calibration lab setup. Fresh from the factory, similar instruments often show the similar error profiles. Many years ago when working as an instrumentation technician, the practice was to adjust an instrument to match the calibration reference to within about one half the specified accuracy tolerance to allow a little slack for instrument drift over time. Whether instruments had the similar or different error profiles was not a consideration.
OK. So the instrument errors from true may not be assumed to be random, what else is there to consider? Well the issue is that a thermometer is actually reading its sensor temperature, not the world around it. It is the job of the instrumentation engineer to find a way to accurately and consistently couple that sensor to the process to be observed. As an example, that is the purpose of the Stevenson Screen enclosure used for our historic temperature data collection.
Does a thermometer mounted in a Stevenson Screen accurately and precisely provide air temperature observations? Only relatively speaking. Each thermometer and each installation of Stevenson Screen will have its own variations from perfect. The best accuracy claimed for these installations was plus or minus one degree Fahrenheit of true air temperature. Remember, we are dealing with the real world and even that level of accuracy was likely seldom attained.
What about modern electronic temperature measuring devices? A platinum resistance temperature detector (RTD) can easily provide a sensor accuracy of +/- 0.01 degrees Celsius. Allowing for errors and drift in the electronics used to read the RTD’s resistance, long term accuracy levels of better than +/- 0.05 degrees Celsius are fairly easily achieved. Remember though that is the sensor accuracy, not field true accuracy. With high accuracy instruments, how that sensor is installed in the field is the primary limitation to its overall observational accuracy.
What should you conclude from this? An instrument’s accuracy should never be assumed to be better than its specified calibration accuracy. Instrument errors cannot be assumed to be random. Averaging multiple observations from the same instrument or from multiple instruments may allow some noise reduction but it will not improve the accuracy of those observations. As described above, the law of large numbers does not apply to instrument observations.
Good practical statement GaryW
Gary
Excellent comments. As someone who has never been involved in any of the instrumentation issues, my focus is more on the human element. I think back over the last hundred(s) of years and visualize the tens of thousands (?) of individuals with innumerable different types of thermometers and different methods and different work habits and the issue of what time was the temperature read, etc etc and shake my head at anyone thinking that over this very long time span we can make valid comparisons. In our small organization with very tight controls and procedures, we had errors every single day. The aggregation of those involved in compiling temperatures is really a longitudinal organization with no tight controls and the opportunity for errors on a daily base worldwide boggles my mind. If we could wave a magic wand and have the same individual record every single reading over the globe for the last several hundred years, there would still be an incalculable number of errors.
GaryW
You say
That strongly suggests you have not read Appendix B of this.
I think you will want to read that Appendix and probably the rest of the link, too.
Richard
Richard,
I do not see how anything in Appendix B invalidates what I wrote. It seems that what it says is that some folks think that instrument measurements cannot be reduced to a mean global temperature value because all instrument errors cannot be known so those folks think it is OK to make a best guess and make another guess about the 95% error range of their guess.
Overall, as I read that appendix, the point it made was similar to what I wrote. Maybe I incorrectly took your comment and recommendation as a criticism.
GaryW
I made no criticism. I said I thought you would want to read an account by 18 scientists from around the world which made your point more than a decade ago.
Richard
Reply to GaryW ==> Thanks for that interesting and insightful Instrumentation Engineer’s Viewpoint — I think that helps some to clarify the issue.
Thank you GaryW for injecting valued experience to this discussion.
While the purpose and intent of the Stevenson Screen was to reduce error, hindsight observations reveal it as a prima donna device, since relocation by almost any distance is very often quoted as a reason to homogenise. Paint or whitewash old or new, height above ground or growing grass or bitumen or bare soil and many other variables have been noted.
You are entirely correct to note the responsibility of the user to provide reproducible surrounings for a high accuracy (in the lab) deviceo
To the extent that the actual record shows laxity of this purpose, claims of +/- 0.1 deg are doomed to drown in wordsmithing while the real world marches on.
Thanks, Kip. Excellent essay.
The idea that we can measure global average temperarture to 0.1degC is a ridiculous assetion. One only has to look at a weather map of the UK to know that we cannot measure the average temperature of the UK to 0.1degC despite the fact that the UK has far better spatial coverage than the globe as a whole. Mountain and coastal areas have their own micro-climates and they are often under sampled. That makes a big difference in a country like the UK.
Today, the weather report suggested that there was going to be a divide of fog broadly over the Penines. Under the fog the temperature was forecasted to be 1 degC, where there was no fog it was forecasted to be 8 degC. So which thermometers are being used to compile CET; the ones showing 1 degC, or the ones showing 8 degC?
The same is so with the difference between urban and rural temps which is frequently stated to be 4 to 6 degC difference, but can, of course, be more than that.
On a global basis, with all the station drop outs since the 1960s/70s, it cannnot possibly be the case that the margin of error is only 0.1degC, especially given that the distribution of the stations that have dropped out does not to be randon and equally distributed. .
In fact, I would suggest that the minimum margin of error is double the difference between what GAT waould show on raw undadjusted data, and what GAT shows in the compilation homogenised/adjusted data set.
Of course, one would hope that the homogenisation/adjustment is an improvement, but that might not be the cae. The homegenisation/adjustment may even make the data worse. For example, one frequently sees examples where adjustments made to take account of UHI are counter-intuitive.
Every institution who compiles a data set should be forced to show what the unadjusted raw data set shows, in addition to their homogenised data set.
I believe Kip is wrong here since we’re talking about the 95% uncertainty range. The probability that multiple readings are all at there extreme value gets lower as the number of readings increase, therefore the 95% uncertainty range should get narrower with more readings assuming unbiased and independent error distribution. The kinder garden example quietly assumes we’re talking about the 100% uncertainty range, but we’re not.
You can actually try this out with a die. With one die the probability of getting the extreme values (1 or 6) is 1/6. With two dice the probability that the average is at the extreme values drops to 1/36. No matter how many dice are in play the 100% uncertainty range is still 3.5 +/- 2.5, yes, but the 95% uncertainty range narrows with more dice.
I agree with Pax on this. I was going to use the dice example but chose to use Kip’s examples in a post which appears further down. As the number of measurements increases the probability that the true value of the mean is near the extremes is vanishingly small.
Reply to pax ==> If we were talking about statistical uncertainty range (of any percentage). We are not talking about statistical uncertainty at all. We are talking about measurement accuracy/measurement error.
The simplest way to look at it is: Mr. Jones, co-op weather stations volunteer, goes out to his Stevenson- screened thermometer and looks at it. The thermometer is reading is between 71 and 72 but closer, he feels, from his viewing angle today, to 71. He records 71. Now, 71 is not the actual temperature of his station at that time. It is only what he records on the official records. The truer, more accurate statement, is that the temperature recorded (when the record is viewed at some time in the future) was 71(+/-0.5) because we know that he was required to round to the nearest whole degree– thus all we know is that (if the thermometer was correct, in spec, calibrated, etc etc) that the temperature for that station at that moment as between 70.5 and 71.5. We write that knowledge as 71(+/-0.5). The likelihood that the temperature was actually factually exactly 71 is vanishingly small. We only know it was somewhere in that range, but not where. There is no scientific or mathematical reason to believe that any point in the range is more likely than any other point.
I understand the uncertainty involved in one reading. But I thought that you were making the argument that averaging a number of measurements does not decrease the uncertainty, I say that it does. If we say that the true temperature were 71.6 and you had 100 people read the thermometer and then took the average, then you would get an answer that was closer to the true value of 71.6. The probability that you would get exactly 71 is vanishingly small since this would require all 100 people to “feel” that it read 71. Therefore averaging draws the result closer to the true value. This seems obvious to me.
Reply to Pax ==> You are talking a statistical ideal. In my example to you just above, I showed that the recorded value “71” represents a value range from 70.5 to 71.5. Looking at the record, we can know nothing closer to the “actual temperature” than that.
Read the original essay above, just the maths part. See that finding the mean of values that are ranges — these look like this 71(+/-0.1) — produces a mean that must be expressed as a range.
The unfortunate fact is that a range of measurement is notated exactly the same as statisticians notate things like Confidence Intervals — which are animals of a different stripe altogether.
Actually do the three-data data set experiment described in the essay and see if it doesn’t change your viewpoint.
In my lounge, I have an old (about 30 years) spirit thermometer. Over the past few years, I have suspected that it under-records temperature. I was not of that view say 12 to 15 years ago.
Today, I checked it against a modern electronic (thermocouple type) thermometer. The difference between the two was 1.5deg C; the spirit thermometer reading cooler.
Of course, it is likely that both thermometers are wrong. But it is likely that the spirit thermometer has been degrading over time, particularly over the last few years.
Equipment changes and degradation alone are likely to give an error of not less than 0.1degC (I would guess more like 0.25degC). Indeed, I recall reading a paper on Stevenson Screen degredation that suggested that wearing/degradation of the paint/wood could be in the order of 0.4 to 0.5degC, and Anthony has also done experimentation on the impact of modern day latex paints.
The impact of this type of degredation is not normally distributed.
The scientists are kidding themselves when they claim that their data sets have an error margin of only 0.1degC, and we know why that is the case; the easiset person to fool is oneself especially when you have ‘a Cause’ to promote and/or to fund your relevance and pay check.
Yes Richard, liquid in glass thermometers degrade over time. Glass ‘creeps’. That is just one of the reasons that past temperatures are retrospectively ‘corrected’ ( homogenised).
‘correction ‘ is not the problem , its how you ‘correct’ that matters or rather your motivation for your ‘corrections’
Mercury/alcohol in glass thermometers read higher over time as the glass shrinks reducing the diameter of the liquid column.
thus, temperature readings are the most accurate the further back in time one looks, and no adjustment should be made to the past. the present should be adjust downwards, to allow for increasing readings with age.
@ur momisugly ferdberble
Precisely 🙂
(1.9 + 1.6) / 2 = 1.75 is mathematically correct but scientifically incorrect. If the measurements are accurate to one tenth, and the measurements are presented with a precision of one tenth, then the average cannot be presented with a precision of one hundredth. Measurements do not “gain precision” through averaging.
Oh yes they do. The average is not itself a measurement. This was the subject of a discussion we had many years ago on Dave Wojic’s Climate Change Debate. Even when presented with a spreadsheet illustrating this fact, some still clung to their mistaken belief. So it goes…
Example:
2+10+3+4=19
19/4=4.75 (average of the four single digit precision measurements)
The argument that this should be rounded to 4.8, or 5 makes no sense since:
4*4.8=19.2 and 4*5=20, neither of which are equal to 19.
Reply to Sal and The Git ==> There are lots of opinions on the “averages reported at precisions more precise than the original measurement accuracy.” I sometimes call this the “Average Number of Children problem”. The Average Number of Children under 18 at home in an American family last year is given by Census.gov as 1.9 children. A figure precise to tenths of a child, yet there is not a single family in the US that has 1.9 children, so while the precision is high, the actual precise average is nonsensical and has an “accuracy” of zero. We simply do not measure children in decimal portions. One child or Zero children or Two children, yes. 1.9 children no.
1.5 pairs of shoes? 0.5 wives? 17.23498 yardsticks in stock?
Some things and measurement data are not suited to expression as averages more precise than the measurement units.
1.9 children/couple is a meaningful number because the number of children is an integer. One is written as 1 but it is really 1.000 . . . , so 1.9 is scientifically accurate, but writing 3/7 as .427571 is not if 3 is just 3 not 3.000 … etc. etc.
Reply to luysii ==> I’m having trouble understanding your point….give the explanation another try will you?
I know that 1.9 is “scientifically numerically accurate” but remains nonsensical in the realm of real American families and is accurate to a percentage of ZERO% — as not a single family out of the ~ 122.5 million families in the USA, has 1.9 children.
Precision and accuracy are dependent on field of endeavor and application.
In truth, averages are convenient fictions that allow our minds to grapple with large populations. Exemplary for me was the Spitalfields exhumation conducted some years ago when a crypt was to be demolished. The human remains were given to forensic specialists who were asked to estimate the age at death. Their estimates were a decade or more younger than the actual age at death. The forensic experts knew that the average age at death in that part of London in the 19thC was very low. That average was badly skewed by the very high infant mortality with most dying during the first five years of life. Past the hump, there were plenty living into their 80s and 90s. Average age at death was 29 in the 1840s, but that didn’t mean there were an extraordinary number popping their clogs in their 20s and 30s.
Then all the climate models are wrong because they deviate from the real temperature by more than 0.1 degrees Celsius.
“. The result in short is, that one might be able only but under best conditions to reach an uncertainty of ± 1 to 2 K respectively. ”
Is this were true of the Global Averages Michael, surely we not be able to discern the surface measured series following the perturbations in the independent satellite series so clearly and yet confined within a +/-0.5 K range, as can be seen illustrated here for example. http://jennifermarohasy.com//wp-content/uploads/2009/05/tom-quirk-global-temp-grp-blog.jpg
though perhaps that’s not what you were suggesting.
This was of course in reply to Michael’s comment below, rather than to the author’s.
Hi Kip,
I can only support your reasons to question. Especially their claim to be able to “measure” anomalies as well as absolute global mean temperature with an uncertainty of only ± 0.1 K ist out of any practical and theoretical reosoning.
I work sind many years on this topic. For details see my paper in E&E http://www.eike-klima-energie.eu/uploads/media/E___E_algorithm_error_07-Limburg.pdf. The result in short is, that one might be able only but under best conditions to reach an uncertainty of ± 1 to 2 K respectively. That would of course finish all discussions about the question which year was the “hottest”! And with it plenty of others. I would like to discuss this result with you further, please contact me by email at limburg@grafik-system.de
regards
Michael Limburg
Reply to Michael Limburg ==> Thank you for checking in from Europe. As of yet, I have no opinion whatever on the real size of the original measurement error that ought to be applied to something as vast as the GAST (HADCRUT4 Land and Sea or otherwise). However, I’ll send you an email so we can touch base.
Thank you for taking the time to read my essay here at WUWT.
This Telegraph article just made the DRUDGE report, which assures millions of extra readers.
It calls fiddling with the temperature record “the biggest science scandal ever”. It also has a survey, which shows that [currently] 92% of readers agree.
Maybe the tide is turning…
If the fiddling is as great as stated by some(which is doubtful but there are several legit issues) then it is steepening the slope of the temperature increase with time.
If the end of the data collection period was fixed permanently, then the fiddling(defined as decreasing temperatures from decades ago and increasing recent temperatures) could be maximized.
However, here is the problem. If the fiddling temperature slope has been increased, let’s say from 1950 to 2010, it means that new observational data, must be fiddled with even more to maintain that slope or it backfires……………if you use the unfiddled, most recent data and compare it to the fiddled, just prior data and increased slope.
With time, it becomes harder and harder, then impossible to maintain the temperature fiddling slope unless actual temperatures do actually increase.
If 2014 temperatures were fiddled with to barely nudge us into the “hottest year ever” category, then, without temperatures actually rising, the 2015, 2016, 2017 temperatures must be fiddled with even more to get even hotter.
Fiddling during the first decade of this century, just makes it harder to show the next decade is even “hotter”.
Regardless of how clever those who fiddle with temperature data are, it would be harder and harder to continue to do this to accomplish the task with time…………in fact, if there was fiddling, it eventually backfires and requires a bigger increase in actual temperatures just to catch up to the recent temperatures + the fiddled higher amount.
Not claiming that the temperature records are completely reliable and definitely not all the instruments or their locations, just that any benefits to increasing the slope of the temperature uptrend are completely maxed out here.
Future temperatures will only look cooler compared to recent ones if this was the case. I found it hard to believe that this could be maintained or increased in the future to the level needed without it being more and more obvious.
Not really, Mike. When they run the homogenization program, ALL prior temperatures are adjusted based on “current” inputs. Is anyone in the general public going to remember the temperature stated in 2014, 2013, 2012, 1970, 1945, 1935 …
Not likely. The media will publish what is put in front of them and create a new scary headline.
We already have lots of examples of this and there is no hue and cry from the public. It is now easy to just keep producing computerized output to fit the agenda.
At least until the weather turns ugly and wakes everyone up.
But for now, let it stay warm. Much better than cold.
Managed to squeeze in a comment amongst the 12,000 and counting. Grauniad would have deleted how many?
http://www.telegraph.co.uk/news/earth/environment/globalwarming/11395516/The-fiddling-with-temperature-data-is-the-biggest-science-scandal-ever.html#comment-1842934203
It is the treatment of errors in measurement and data sets in climate science that has always amazed me. Amazed in the sense that, for too long, the alarmist scientists have been allowed to quote values to more decimal places than the errors quoted. When I read Physics, the calculation of errors and their application to experimental results was hammered into us little proto-physicists. If you handed in lab work and quoted results to a higher accuracy than your errors you failed. Not only that, you were laughed at for making such a basic and easily avoided mistake.
Now, everybody who has studied science knows this but it is rife in climate science. These people don’t even blush when they do it but must know they are being, to put it politely, less than rigorous.
Why change a habit that has been so rewarding ?
This is an area where the value of your ‘research’ exist that in the quality of your data but in the ‘impact’ , especially in the press , the release of your paper has . Look at he behaviour of climate ‘sciences’ leading voices and you will see why this approach is not seen has a problem, but as a normal way to work.
I think you’re making too much of sloppy English, viz: “The accuracy with which we can measure the global average temperature of 2010 is around one tenth of a degree Celsius.”
The sloppiest word is “measure”. It should read “construct” since it’s nothing more than a statistical inference and has little to do with reality. After all, what is it supposed to convey? Is it related to energy retained by the entire atmosphere and/or oceans or is that merely what we’re supposed to perceive it to mean? If so it’s hopelessly inadequate. For starters it totally disregards latent heat in various places.
The word “accuracy” is therefore not just sloppy but wholly inappropriate. Perhaps the entire thing would be better written as:
“The statistical confidence with which we can construct a hypothetical global average surface temperature for 2010 is around one tenth of a degree Celsius but this tells us nothing about how much energy was gained or lost by the planet since 2009.”
Or you could just append “+/- several Hiroshima bombs, give or take” for effect.
Reply to AJB ==> Alas, it is not my language, but the language of the Met Office UK. However, it is an important point in this issue that I (the author of this essay) am talking about — and believe that Met Office UK is talking about, “the accuracy with which we can measure the global average temperature”. It matters not whether they give a quantity that we agree with, they are talking about accuracy of measurement and NOT NOT NOT “statistical confidence” — that is what is so great about the way they stated what their Uncertainty Range was….accuracy with which we can measure….
Yes Kip, I’m aware of that and take your point. My point is the Met Office’s language is “sloppy”, not yours. Words mean different things to different folk. What they’ve written is as much farce as tragedy; it’s all in the eyes of the beholder. How is the man on the Clapham omnibus (maybe on his way to a media job somewhere) likely to interpret that? The Met Office’s target audience is surely not science specifically but the public at large.
Reply to AJB ==> Even the man on the Clapham omnibus can understand their statement “The difference between the median estimates for 1998 and 2010 is around one hundredth of a degree, which is much less than the accuracy with which either value can be calculated. This means that we can’t know for certain – based on this information alone – which was warmer.”
When at last at Wimbledon, I missed riding the omnibus, but enjoyed the down-and-dirty fish and chips!
LOL! I hope you had a portion of mushy peas with that. Constructing a global average temperature is about as useful as estimating the average size of pea and projecting the radius of carton the mush will eventually be served in. We already know the mush will be green though 🙂
Kip Hansen said in opening his guest post at WUWT,
then concluding his guest post at WUWT Kip Hansen said that most important point was,
Kip Hansen,
A very stimulating post. Thanks.
Why would a reasonable person involved in the climate science discourse consider the UK Met Office a hero (of the day) when it does something that (arguably) explains clearly in a professional manner what their logic, context and process is?
Your guest post helps us to understand better how there is open distrust of climate focused science if what you said the UK Met Office did is considered heroic instead of just (arguably) being basic professional conduct.
John
Reply to John ==> Of course, you are right that it is extraordinary that something as simple as stating their results with a frank and transparent guess-timate of the accuracy of measurement should elicit kudos, congratulations and a declaration of heroism. However, in Climate Science, this is the case today.
I do not offer my congratulations to them as sarcasm or irony. Their statement is somewhat of a Game Changer for governmental climate organizations. In one little statement, they validated the skeptical viewpoint of The Pause…..they eliminate all senseless arguing about data that are a mere few hundredths of a degree different, even those a tenth of a degree different. Of course, these are degrees C…the numeric values are thus larger digits when speaking in degrees F (degrees C being larger than degrees F — 0.1°C is about 0.18°F).
Thanks for checking in.
[Rather, “.. in Climate Science, this is not the case today” ? .mod]
Kip Hansen,
I really really want to share your level of optimism . . . I am optimistic . . . . but less so than you seem to be . . . I hope I am wrong in being less optimistic.
John
Reply to .mod ==> It is the case today that it is extraordinary that something [ syntactically, we could have anything here, like: as simple as stating their results with a frank and transparent guess-timate of the accuracy of measurement ] should elicit kudos, congratulations and a declaration of heroism.
[And thus: no edit requested, no edit granted. 8<) .mod]
I wonder what the error bars on past ‘adjustments and homogenisation’ of temperature data would look like?
It’s known as the Met. Orifice for good reason.
Enough bitching against the Met Office.
Read what they published, particularly, at their site given below their 2010-2013 update.
http://www.trebrown.com/hrdzone.html
The door in front of the office was changed from “No Smoking permitted inside” to “No Statistician permitted inside”
Kip
I’m not entirely sure I agree with the general conclusion of your post. Looking at your examples you have example 1, i.e.
Yep – I agree with you here. The measured value is 1.7 but the true value could lie anywhere between 1.6 and 1.8 – with each value in the range having equal probability of being the true value.
Now we move on to Example 2
And this
Now from this we can conclude that 1.85 could be the true mean of the 2 values (1.7 & 1.8) but there is only one way this could happen and that is if BOTH measurements were low by the “maximum” measurement error. Similarly 1.65 could be the true mean only if BOTH measurements were high by the “maximum” measurement error.
In fact, the mean of the actual measured values (1.75) has more chance of being the true mean because there are more combinations of measurements which will produce that value e.g. +0.1 & -0.1, +0.09 & -0.09, +0.08 & -0.08 ……. Etc.
As the number of measurements increases, the probability that the true mean is at the extremes of the measurement error decreases.
Reply to Finn ==> You have caught me short-forming the explanation. Of course, my examples are just the extremes, because we are talking about a range. The means of any of the intrim points will be within the means of the extremes…I thought that would be so obvious to the science-oriented crowd here that I did not explicitly state it In the end, it is the two far ends of the range of the means that we are interested in because they will give us the Range of the Mean. I try to clearly state that the actual value of the mean is a RANGE more properly expressed as:
What is the mean of the widest spread?
1.9 + 1.6 / 2 = 1.75
What is the mean of the lowest two data?
1.6 + 1.7 / 2 = 1.65
What is the mean of the highest two data:
1.8 + 1.9 / 2 = 1.85
The above give us the range of possible means: 1.65 to 1.85
with a central value of 1.75
Thus written 1.75(+/-0.1)
We have no interest whatever in any probabilities of anything. I can state an exactly correct range — in the physical world, every point within the range is just as probable as any other point. Means are only probabilities in statistics.
Your solution would be correct only if we thought that the world magically declared that actual temperatures (for instance) must be normally distributed in respect to their distances from the arbitary markings on both F and C graduated thermometers.
In the real world however, our actual temperatures, that data for which we have only represented as ranges, do not behave that way. They could be anywhere equally, but there is no reason that they couldn’t all be crowding the .0999999s.
No, Kip, every point within the range of a MEAN is not “just as probable”. On a single measurement – yes – but not when the mean of several measurements is calculated.
The dice example given by PAX (above) is a good analogy. The outcomes of a single throw of a die are exactly the same (i.e. 1/6) so the mean value after one throw has equal probability of being 1, 2,, 3, 4, 5 or 6.
The MEAN value after 2 throws, however, does not have EQUAL probability. E.G
The probability that the mean is 6 (i.e. 2 sixes) is 1/6 x 1/6 = 1/36 whereas the probability that the mean is 3.5 is 6/36 or 1/6. In other words it’s 6 times more likely that the mean is 3.5 than it is that the mean is 6 (or 1).
Perhaps I should just add that the probability that the mean is at either end of the measurement error becomes so small that it is effectively ZERO if about 5 or 6 measurements are taken.
Even when we use discrete values, as in the case of dice, the probability that the true mean is 6 (or 1) is tiny. After 5 throws of a die the probability that the mean score is 6 (or 1) is about 0.012%.
Reply to John Finn ==> Give me an example with values that are themselves ranges. That is what I (and most others here) have been talking about.
The range of die throw values is properly represented as 3.5(+/-2.5), with the limiting case that only whole integers are allowed. Every throw of the die will fall within that range — the range is 100% correct. This mean as a true range needs no probability — it is exactly arithmetically correct for all cases always.
Your mean, while six times more likely than some other number, is only 1 in six.
The actual arithmetical mean, expressed as a range, is always correct — 100% of the time.
Of course, I have cheated, haven’t I? I include all the possible values in the range.
As for my range of means for actual measurements, using temperatures as our real world, since the range is created by a rounding rule, and the whole integers are entirely arbitrary, there is no reason for the numeric median of the range of means to be any more likely than any other value in the range, since the range is NOT CREATED by the math, but by the original measurement.
Reality vs. Statisticians:
Welcome to the
Plant Hardiness Zone Map of the British Isles.
The plant hardiness zone map of the British Isles is the most detailed ever to be created for this region, and is the product of many months work studying the average winter climate statistics for the periods 1961 to 2000 recorded by the Irish and UK Met Offices.
The USA first undertook climatic studies to provide a guide map for plant hardiness of the North American continent. These were undertaken by two independent groups: The Arnold Arboretum of Harvard University in Cambridge, Massachusetts, and the United States Department of Agriculture (USDA) in Washington, D.C. See the USDA map.
When we took it upon ourselves to create the Plant Hardiness Zone Map of the British Isles we replicated the same zones, based on the same equivalent temperature scale as the USA to form a basic standardisation. However, we have changed the colour coding for the 7 split zones occurring in the British Isles to colours which are more meaningful to the average user. See the map using the USDA colour scheme. And click to hide it. You may also switch the map’s colour zone information off and on to display a physical map of the British Isles including the warmer major towns and cities, which apear as white patches, and also the various cooler elevations, which apear as darker patches.
Both our map and the USDA maps are inadequate due to factors such as the frequency and duration of cold outbreaks. The main problem is the fact that the British Isles lies so far north of the equator, where both winter and winter nights are long. No other place on the planet, which shares similar winter temperatures is situated so far from the equator, and therefore our problems are quite unique. The noticeable differences are to be seen in our zones 10a & 9b. Whereas, plants from other country’s zones 10a & 9b can whithstand short, colder outbreaks than us and survive, in the British Isles they must endure a winter which is several months long with low light levels and wet weather. Consequently, there are very few plants, labelled as zone 9 or 10 that can be grown here.
It is important to understand that average minimum air temperatures (protected from wind & direct sun) are used in defining these zones. Ambient temperatures will be lowered by local frost pockets and by wind-chill. Although, plants do not suffer from the effects of wind-chill like we do, they can get dehydrated and suffer from windburn in cold easterly winds. Therefore, you must read these zones as the maximum potential temperature for an area once windbreaks have been put in place. For example – If you see from the map that you are in a potential zone 9a then you can over winter plants outdoors, which are suitable for zones 8b, 8a, 7b etc. You will only be able to over winter plants suitable for zone 9a once protection has been put in place and a favourable microclimate created.
Essential reading: Predicting Cold Hardiness in Palms Trebrown Blog.
2010-2013 Update
We had plans for an updated Plant Hardiness Zone Map of the British Isles, and many months work had already gone into this by 2011. The general trend had been a period of increased warming over the decade since we first published the map. However, the British Isles were then hit by two successively cold winters and a third not quite so cold but nevertheless colder than we had been used to. The results of these cold spells has been to bring the pattern of the map back similar to what it was. There are only slight pattern changes from the original map, and for this reason we have decided to save work and retain the original map without an update, as this is the best match for the British Isles without any temporary warming patterns which may be misleading.
I just want to make sure that the ……
Please read again instead of arguing about +or- 0.00001C
Essential reading: Predicting Cold Hardiness in Palms Trebrown Blog.
2010-2013 Update
We had plans for an updated Plant Hardiness Zone Map of the British Isles, and many months work had already gone into this by 2011. The general trend had been a period of increased warming over the decade since we first published the map. However, the British Isles were then hit by two successively cold winters and a third not quite so cold but nevertheless colder than we had been used to. The results of these cold spells has been to bring the pattern of the map back similar to what it was. There are only slight pattern changes from the original map, and for this reason we have decided to save work and retain the original map without an update, as this is the best match for the British Isles without any temporary warming patterns which may be misleading.
Reply to rd50 ==> Ah, nice point. I had to defend this type of viewpoint in my Baked Alaska essay. Many climate concepts are only important locally and are — how do you say? — ‘break points’ — like your Plant Hardiness Zone Maps. Fairbanks, Alaska has had average temperatures level or slightly falling for 30 years, but growing season increasing — as growing season depends on contiguous frost-free days.
Likewise, precipitation as a yearly average is often meaningless. Farmers need rain in the right amounts and at the right times in the right amounts….far more important than annual averages. This is different for California snow pack — they need high annual numbers, the more the better. And so on….
So?
Do you see the point?
You go ahead about statistical analysis: accuracy, precision, average, corrections and on and on, but then you come back to reality: growing season, frost-free days, rain in the right amounts…..far more important than annual “global” averages…. Yes, I like this, getting back to reality. I like the Met Office, contrary to what I most often read here. I most often read here that the Met Office is terrible (or something like this).
As a farmer, the Met Office is great information as given by them above. (Just as an aside, this info to farmers from the Met Office is available in USA, Canada, Australia, China, India and probably other countries I will admit I did not look for).
The statisticians and their “global average” is stupid. Not the statisticians are stupid, the global average is stupid. There is no meaning to “global average” and I don’t care if their “global averages” are +or- 0.1 or 0.0001.
This is not to denigrate your effort in the statistical information area, far from this, I assure you. Thank you.
Reply to rd50 ==> Well, good. I see we agree after all!
Thanks for your input. Yes, and some here in comments object to the idea that anyone would say anything nice about the Met Office, just on [ misguided ] principle.
Hopefully, their forthrightness will impact other governmental agencies that produce metrics or information about climate. Did you read my essay on MCID ? It touches on this aspect of climate science metrics.
Yes I did read all the posts from the first to the last before I posted above.
So, what is the answer from all you posters +or- statistical analysis.
You gave no answer. Just complaints.
Reply to rd50 ==> I am not sure whom you are addressing with this.
I thought I was agreeing with you. Who is disagreeing?
I have found it useful here (and elsewhere on the blogs) to indicate who and what I am replying to. Sometimes comment nesting is confusing or puts your comment out of thread order or in the wrong thread altogether.
Sorry Kip Hansen. Not very familiar with the system here. I did answer above.
I appreciate your questions/answers to statistical analysis and following discussion. No problem with such.
I simply wanted to point out that the Met Office often under criticism here is very realistic and does not rely on +or- 0.1 C to give advice to farmers. And you also agreed with such, local is important.
Reply to luysii ==> I’m having trouble understanding your point….give the explanation another try will you?
I know that 1.9 is “scientifically numerically accurate” but remains nonsensical in the realm of real American families and is accurate to a percentage of ZERO% — as not a single family out of the ~ 122.5 million families in the USA, has 1.9 children.
Precision and accuracy are dependent on field of endeavor and application.
Kip: Thanks for responding. When things are measured in integers (like hits in baseball or the number of children in a family) the precision is (nearly) infinite. A batter either gets a hit or he doesn’t. A good hitter never gets .323 hits in a given bat. It’s an average, just like 1.9 children. To a population geneticist or someone trying to figure out if Social Security will be solvent in 30 years, 1.9 children is a very useful and (presumably) accurate number.
What experimentalists are taught (or should be) is that any observation is inherently error prone, and that no more significant figures should ever be reported as an average of a series of measurements than the number of significant figures in an individual measurement.
That’s what so great about the work you cite. They give the accuracy of the measurement at .1 C, meaning that the increment of .02 C trumpeted by the NYT has no scientific meaning.
I don’t know how many observations went into the final number for global temperature in 2014. Let’s say 10^9. Can we say that the average global temperature was xxx.123456 C? Mathematically we could, experimentally we can’t.
I hope this helps
Reply to luysii ==> It seems we agree after all.
Thanks for checking in here, and contributing.
To Kip Hansen.
Yes I read your previous post MICD. OK with it. How to relate different issues/differences? Certainly worth thinking about.
To Kip Hansen
Come to think about it, the Met Office is giving to farmers the kind of advice you discussed in your MCID post!
I love the Met Office. Forget the statisticians +/-0.1C.
BoM here in the Land of Under is justly criticised for its climate fantasies, but invaluable for their excellent weather forecasts. Perhaps they should stick to what they are good at 🙂 Speaking as a farmer (Ret.).
Going all the way back to the top, the figure that is actually being quoted is not the temperature but the temperature anomaly. This is the difference between two temperatures and thus suffers from error propagation effects. The quoted error should therefore be sqrt(2) greater than the error in the temperature measurement. If we take the raw +/-0.1 value, the correct error in the anomaly is +/-0.14. If we take the larger figure 0f +/-0.16 as quoted by Lord Monckton, the correct error in the anomaly becomes +/-0.23. Indeed, if we then compare two anomalies, the error in their difference becomes +/-0.2 (or in Monckton,+/-0.32). How long does this make the pause (sorry, hiatus)?
Reply to JMcM ==> Ain’t maths wonderful ?!?
You are right — for the reason stated and about a thousand other reasons — the stated 0.1°C is probably far too low.
Some of this discussion is silly, as many believe that the very attempt to “measure” or “calculate” the “Global Average Surface Temperature over Land and Sea” is doomed before it gets off the ground.
But, nonetheless, I appreciate the Met Office’s step in the right direction of scientific honesty and transparency.
There cannot be more significant digits in an answer than there is in the least accurate measurement in the data. Therefore, 1.2cm + 1.58cm does not equal 2.78cm, it should be 2.8cm…only as many significant digits as in the least accurate data point. I really can’t trust anything from a ‘scientist’ who doesn’t know this. So, when HADCRUT says the temperature was 0.56 degrees plus/minus 0.1 degrees, I know they are [] pseudo-scientists.
Oops, ignore the last “not” please.
Not sure why you would want to round in this case, it depends upon what these values represent.
If I were to make 2 metal objects to fit into a slot, object A = 12mm object B = 15.8mm then the slot would need to be 27.8mm wide.
If I wanted a sane life in manufacturing, I would allow for manufacturing and measurement tolerances:
Say A and B are +/- 1.0mm so
1) 12.1 + 15.9 = 28.0mm
2) 12.0 + 15.8 = 27.8mm
3) 11.9 + 15.7 = 27.6mm
So the uncertainty of +/- .1mm has ‘propagated’ to the final tolerance of +/-.2mm
The nominal measurement is 27.8mm and loses meaning if rounded.
Also, the slot for A and B needs to be toleranced, as it is produced by a distinct manufacturing process:
It needs to be large enough to hold A + B at their widest (28.0mm) so the slot needs to be, as a minimum, 28.1mm wide.
Real tolerances need to be kept, added, and the result will truly represent your ‘worst case’.
If your ‘doing maths’ then follow mathematical rules and conventions, but when working with ‘readings’ or ‘measurements’ of ‘real things’ do not throw away data.