Guest essay by Clyde Spencer
Introduction
The point of this article is that one should not ascribe more accuracy and precision to available global temperature data than is warranted, after examination of the limitations of the data set(s). One regularly sees news stories claiming that the recent year/month was the (first, or second, etc.) warmest in recorded history. This claim is reinforced with a stated temperature difference or anomaly that is some hundredths of a degree warmer than some reference, such as the previous year(s). I’d like to draw the reader’s attention to the following quote from Taylor (1982):
“The most important point about our two experts’ measurements is this: like most scientific measurements, they would both have been useless, if they had not included reliable statements of their uncertainties.”
Before going any further, it is important that the reader understand the difference between accuracy and precision. Accuracy is how close a measurement (or series of repeated measurements) is to the actual value, and precision is the resolution with which the measurement can be stated. Another way of looking at it is provided by the following graphic:
The illustration implies that repeatability, or decreased variance, is a part of precision. It is, but more importantly, it is the ability to record, with greater certainty, where a measurement is located on the continuum of a measurement scale. Low accuracy is commonly the result of systematic errors; however, very low precision, which can result from random errors or inappropriate instrumentation, can contribute to individual measurements having low accuracy.
Accuracy
For the sake of the following discussion, I’ll ignore issues with weather station siting problems potentially corrupting representative temperatures and introducing bias. However, see this link for a review of problems. Similarly, I’ll ignore the issue of sampling protocol, which has been a major criticism of historical ocean pH measurements, but is no less of a problem for temperature measurements. Fundamentally, temperatures are spatially-biased to over-represent industrialized, urban areas in the mid-latitudes, yet claims are made for the entire globe.
There are two major issues with regard to the trustworthiness of current and historical temperature data. One is the accuracy of recorded temperatures over the useable temperature range, as described in Table 4.1 at the following link:
http://www.nws.noaa.gov/directives/sym/pd01013002curr.pdf
Section 4.1.3 at the above link states:
“4.1.3 General Instruments. The WMO suggests ordinary thermometers be able to measure with high certainty in the range of -20°F to 115°F, with maximum error less than 0.4°F…”
In general, modern temperature-measuring devices are required to be able to provide a temperature accurate to about ±1.0° F (0.56° C) at its reference temperature, and not be in error by more than ±2.0° F (1.1° C) over their operational range. Table 4.2 requires that the resolution (precision) be 0.1° F (0.06° C) with an accuracy of 0.4° F (0.2° C).
The US has one of the best weather monitoring programs in the world. However, the accuracy and precision should be viewed in the context of how global averages and historical temperatures are calculated from records, particularly those with less accuracy and precision. It is extremely difficult to assess the accuracy of historical temperature records; the original instruments are rarely available to check for calibration.
Precision
The second issue is the precision with which temperatures are recorded, and the resulting number of significant figures retained when calculations are performed, such as when deriving averages and anomalies. This is the most important part of this critique.
If a temperature is recorded to the nearest tenth (0.1) of a degree, the convention is that it has been rounded or estimated. That is, a temperature reported as 98.6° F could have been as low as 98.55 or as high as 98.64° F.
The general rule of thumb for addition/subtraction is that no more significant figures to the right of the decimal point should be retained in the sum, than the number of significant figures in the least precise measurement. When multiplying/dividing numbers, the conservative rule of thumb is that, at most, no more than one additional significant figure should be retained in the product than that which the multiplicand with the least significant figures contains. Although, the rule usually followed is to retain only as many significant figures as that which the least precise multiplicand had. [For an expanded explanation of the rules of significant figures and mathematical operations with them, go to this Purdue site.]
Unlike a case with exact integers, a reduction in the number of significant figures in even one of the measurements in a series increases uncertainty in an average. Intuitively, one should anticipate that degrading the precision of one or more measurements in a set should degrade the precision of the result of mathematical operations. As an example, assume that one wants the arithmetic mean of the numbers 50., 40.0, and 30.0, where the trailing zeros are the last significant figure. The sum of the three numbers is 120., with three significant figures. Dividing by the integer 3 (exact) yields 40.0, with an uncertainty in the next position of ±0.05 implied.
Now, what if we take into account the implicit uncertainty of all the measurements? For example, consider that, in the previously examined set, all the measurements have an implied uncertainty. The sum of 50. ±0.5 + 40.0 ±0.05 + 30.0 ±0.05 becomes 120. ±0.6. While not highly probable, it is possible that all of the errors could have the same sign. That means, the average could be as small as 39.80 (119.4/3), or as large as 40.20 (120.6/3). That is, 40.00 ±0.20; this number should be rounded down to 40.0 ±0.2. Comparing these results, with what was obtained previously, it can be seen that there is an increase in the uncertainty. The potential difference between the bounds of the mean value may increase as more data are averaged.
It is generally well known, especially amongst surveyors, that the precision of multiple, averaged measurements varies inversely with the square-root of the number of readings that are taken. Averaging tends to remove the random error in rounding when measuring a fixed value. However, the caveats here are that the measurements have to be taken with the same instrument, on the same fixed parameter, such as an angle turned with a transit. Furthermore, Smirnoff (1961) cautions, ”… at a low order of precision no increase in accuracy will result from repeated measurements.” He expands on this with the remark, “…the prerequisite condition for improving the accuracy is that measurements must be of such an order of precision that there will be some variations in recorded values.” The implication here is that there is a limit to how much the precision can be increased. Thus, while the definition of the Standard Error of the Mean is the Standard Deviation of samples divided by the square-root of the number of samples, the process cannot be repeated indefinitely to obtain any precision desired!1
While multiple observers may eliminate systematic error resulting from observer bias, the other requirements are less forgiving. Different instruments will have different accuracies and may introduce greater imprecision in averaged values.
Similarly, measuring different angles tells one nothing about the accuracy or precision of a particular angle of interest. Thus, measuring multiple temperatures, over a series of hours or days, tells one nothing about the uncertainty in temperature, at a given location, at a particular time, and can do nothing to eliminate rounding errors. A physical object has intrinsic properties such as density or specific heat. However, temperatures are ephemeral and one cannot return and measure the temperature again at some later time. Fundamentally, one only has one chance to determine the precise temperature at a site, at a particular time.
The NOAA Automated Surface Observing System (ASOS) has an unconventional way of handling ambient temperature data. The User’s Guide says the following in section 3.1.2:
“Once each minute the ACU calculates the 5-minute average ambient temperature and dew point temperature from the 1-minute average observations… These 5-minute averages are rounded to the nearest degree Fahrenheit, converted to the nearest 0.1 degree Celsius, and reported once each minute as the 5-minute average ambient and dew point temperatures…”
This automated procedure is performed with temperature sensors specified to have an RMS error of 0.9° F (0.5° C), a maximum error of ±1.8° F (±1.0° C), and a resolution of 0.1° F (0.06° C) in the most likely temperature ranges encountered in the continental USA. [See Table 1 in the User’s Guide.] One (1. ±0.5) degree Fahrenheit is equivalent to 0.6 ±0.3 degrees Celsius. Reporting the rounded Celsius temperature, as specified above in the quote, implies a precision of 0.1° C when only 0.6 ±0.3° C is justified, thus implying a precision 3 to 9-times greater than what it is. In any event, even using modern temperature data that are commonly available, reporting temperature anomalies with two or more significant figures to the right of the decimal point is not warranted!
Consequences
Where these issues become particularly important is when temperature data from different sources, which use different instrumentation with varying accuracy and precision, are used to consolidate or aggregate all available global temperatures. Also, it becomes an issue in comparing historical data with modern data, and particularly in computing anomalies. A significant problem with historical data is that, typically, temperatures were only measured to the nearest degree (As with modern ASOS temperatures!). Hence, the historical data have low precision (and unknown accuracy), and the rule given above for subtraction comes into play when calculating what are called temperature anomalies. That is, data are averaged to determine a so-called temperature baseline, typically for a 30-year period. That baseline is subtracted from modern data to define an anomaly. A way around the subtraction issue is to calculate the best historical average available, and then define it as having as many significant figures as modern data. Then, there is no requirement to truncate or round modern data. One can then legitimately say what the modern anomalies are with respect to the defined baseline, although it will not be obvious if the difference is statistically significant. Unfortunately, one is just deluding themselves if they think that they can say anything about how modern temperature readings compare to historical temperatures when the variations are to the right of the decimal point!
Indicative of the problem is that data published by NASA show the same implied precision (±0.005° C) for the late-1800s as for modern anomaly data. The character of the data table, with entries of 1 to 3 digits with no decimal points, suggests that attention to significant figures received little consideration. Even more egregious is the representation of precision of ±0.0005° C for anomalies in a Wikipedia article wherein NASA is attributed as the source.
Ideally, one should have a continuous record of temperatures throughout a 24-hour period and integrate the area under the temperature/time graph to obtain a true, average daily temperature. However, one rarely has that kind of temperature record, especially for older data. Thus, we have to do the best we can with the data that we have, which is often a diurnal range. Taking a daily high and low temperature, and averaging them separately, gives one insight on how station temperatures change over time. Evidence indicates that the high and low temperatures are not changing in parallel over the last 100 years; until recently, the low temperatures were increasing faster than the highs. That means, even for long-term, well-maintained weather stations, we don’t have a true average of temperatures over time. At best, we have an average of the daily high and low temperatures. Averaging them creates an artifact that loses information.
When one computes an average for purposes of scientific analysis, conventionally, it is presented with a standard deviation, a measure of variability of the individual samples of the average. I have not seen any published standard deviations associated with annual global-temperature averages. However, utilizing Tchebysheff’s Theorem and the Empirical Rule (Mendenhall, 1975), we can come up with a conservative estimate of the standard deviation for global averages. That is, the range in global temperatures should be approximately four times the standard deviation (Range ≈ ±4s). For Summer desert temperatures reaching about 130° F and Winter Antarctic temperatures reaching -120° F, that gives Earth an annual range in temperature of at least 250° F; thus, an estimated standard deviation of about 31° F! Because deserts and the polar regions are so poorly monitored, it is likely that the range (and thus the standard deviation) is larger than my assumptions. One should intuitively suspect that since few of the global measurements are close to the average, the standard deviation for the average is high! Yet, global annual anomalies are commonly reported with significant figures to the right of the decimal point. Averaging the annual high temperatures separately from the annual lows would considerably reduce the estimated standard deviation, but it still would not justify the precision that is reported commonly. This estimated standard deviation is probably telling us more about the frequency distribution of temperatures than the precision with which the mean is known. It says that probably a little more than 2/3rds of the recorded surface temperatures are between -26. and +36.° F. Because the median of this range is 5.0° F, and the generally accepted mean global temperature is about 59° F, it suggests that there is a long tail on the distribution, biasing the estimate of the median to a lower temperature.
Summary
In summary, there are numerous data handling practices, which climatologists generally ignore, that seriously compromise the veracity of the claims of record average-temperatures, and are reflective of poor science. The statistical significance of temperature differences with 3 or even 2 significant figures to the right of the decimal point is highly questionable. One is not justified in using the approach of calculating the Standard Error of the Mean to improve precision, by removing random errors, because there is no fixed, single value that random errors cluster about. The global average is a hypothetical construct that doesn’t exist in Nature. Instead, temperatures are changing, creating variable, systematic-like errors. Real scientists are concerned about the magnitude and origin of the inevitable errors in their measurements.
References
Mendenhall, William, (1975), Introduction to probability and statistics, 4th ed.; Duxbury Press, North Scituate, MA, p. 41
Smirnoff, Michael V., (1961), Measurements for engineering and other surveys; Prentice Hall, Englewood Cliffs, NJ, p.181
Taylor, John R., (1982), An introduction to error analysis – the study of uncertainties in physical measurements; University Science Books, Mill Valley, CA, p.6
1Note: One cannot take a single measurement, add it to itself a hundred times, and then divide by 100 to claim an order of magnitude increase in precision. Similarly, if one has redundant measurements that don’t provide additional information regarding accuracy or dispersion, because of poor precision, then one isn’t justified in averaging them and claiming more precision. Imagine that one is tasked with measuring an object whose true length is 1.0001 meters, and all that one has is a meter stick. No amount of measuring and re-measuring with the meter stick is going to resolve that 1/10th of a millimeter.
Discover more from Watts Up With That?
Subscribe to get the latest posts sent to your email.
Clyde,
As you know, I have been blogging for years that one of the main blunders of climate workers has been their failure to report proper, formal, comprehensive estimates of error. Some authors have, but too many are in Pat Frank’s class, of which he says that he has never met a climate scientist who could explain the meaningful difference between accuracy and precision.
A formal error analysis that leads to proper error bounds is a boon in hard science. It allows the reader a snapshot of the significance of the planks in the hypothesis under test. As an example, if the first Hockey stock graphs had correct error bounds illustrated, they would likely not have passed peer review.
Please allow 2 comments, one from theory and one from practice to support your case.
Theoretical.
Reference –
https://en.wikipedia.org/wiki/Sampling_(statistics)
“sampling is concerned with the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population”
It involves several stages.
• Defining the population of concern
• Specifying a sampling frame, a set of items or events possible to measure
• Specifying a sampling method for selecting items or events from the frame
• Determining the sample size
• Implementing the sampling plan
• Sampling and data collecting
Most bloggers here have objected to the conventional path to a global temperature average because it fails to properly and completely comply with the stages above. If the population of concern is the surface temperature at each point on the globe, it fails because, for example, there is insufficient and uneven coverage of the globe. There are other blogger objections, such as temperature being an intensive property that cannot be averaged, and difficulties arising from constructing time series where there is daily movement from max to min on a rotating, precessing globe with many complications related to time of observation, let alone moisture complications..
Until the several stages above are completed in proper details, and shown to have been satisfied, one must regard as unreliable the current estimates of global mean surface temperature.
Practical.
As you note from an NOAA manual,
“Once each minute the ACU calculates the 5-minute average ambient temperature and dew point temperature from the 1-minute average observations… These 5-minute averages are rounded to the nearest degree Fahrenheit, converted to the nearest 0.1 degree Celsius, and reported once each minute as the 5-minute average ambient and dew point temperatures…”
NOAA receives data from various countries. From Australia’s BOM, readings are taken differently.
Firstly, we receive AWS data every minute. There are 3 temperature values:
1. Most recent one second measurement
2. Highest one second measurement (for the previous 60 secs)
3. Lowest one second measurement (for the previous 60 secs)
Relating this to the 30 minute observations page: For an observation taken at 0600, the values are for the one minute 0559-0600.
As Ken Stewart notes further,
https://kenskingdom.wordpress.com/2017/03/21/how-temperature-is-measured-in-australia-part-2/
“An AWS temperature probe collects temperature data every second; there are 60 datapoints per minute. The values given each half hour (and occasionally at times in between) for each station’s Latest Weather Observations are spot temperatures for the last second of the last minute of that half hour, and the Low Temp or High Temp values are the lowest and highest one second readings within each minute. There is NO quality assurance to flag rogue values. There is no averaging to find the mean over say one minute.”
One can examine if this Australian CLIMAT data is compatible with the in-house data of NOAA. It is not. There are biases. Currently, I believe that these are uncorrected, if indeed correction is possible.
………………………..
What is more, for many years the only relevant data collected each day were Tmax and Tmin from Liquid-in-Glass thermometers designed to record only those parameters. To obtain a mean, it was common to use (Tmax+Tmin)/2. However, many do not realise that in November 1994 (IIRC) the BOM changed from this mean, to report “average” daily temperatures as the mean of 4 temperatures taken 6 hours apart. The BOM has provided comparisons and the differences range to nearly 1 deg C over a long term comparison.
…………………………..
What is more more, the BOM reported years ago that metrication has an effect, one that is ignored –
http://www.waclimate.net/round/
This is a bias error of up to 0.1 deg C.
……………..
More, more, more.
I could go on to show the effects of rounding from deg F to deg C and back, but you can do this yourself.
……………………………….
The point is, when one examines the accuracy of the historic temperature record in detail, depending on its origins, one can find many inaccuracies, some well known, other unknown to many, that have 2 important aspects:
1. The magnitude of the accuracy error overall is if the order of 0.1 deg C
2. The error is a bias. The negative excursions do not wipe out the positives.
One can show that in the comparison of Australian data with NOAA global data, there are errors of this type that cumulatively probably exceed 0.2 deg C. Given that the official BOM figure for warming of Australia is 0.8 deg for the 20th century, this is a large error and one that cannot go away with more sampling, or with more “valid” adjustment.
…………………………….
The global surface temperature average of which you write, Clyde, does not stand close inspection.
As you noted, and I support.
When people like my old mate Steven Mosher write that the historic reconstruction of it is accurate, they are dealing with data that perhaps unknown to them contains errors of the type I have described above. So you can take such claims with a grain of salt.
Geoff.
I have a Tmax – Tmin mercury thermometer right outside of my front door. It is wonderful.
I tend to only shake the markers down when I need to know how cold it really got the night before.
I don’t care about how hot it got during the day. If it’s hot stay out of the sun!
Mad dogs and Englishmen…
There are Australian BOM records of an observer who read the wrong end of the peg for a time. Hope you followed the instruction manual yourself?
Cheers. Geoff
This kind of arcane, nitpicking discussion doesn’t do a thing to help the General Public understand that the Natural Climate Change Deniers have hoodwinked them into believing that the Earth is Warming when it is actually Cooling.
1) Is this discussion aimed at the general public?
2) Getting the general public to recognize the lunacy of trying to declare temperature records when the differences are being measured in hundredths or thousandths of a degree is part of getting them to recognize that global warming ain’t what it’s cracked up to be.
mickeldoo,
I’m sorry that you feel that the discussion is “nitpicking.” I was attempting to avoid the arcane mathematics that Windchasers so badly wanted, and make the case that the General Public should not blindly accept the claims made about the claimed warming. I might suggest that you prepare a guest editorial making the case for cooling and submit it to Anthony.
mickeldoo,
This is not nitpicking.
If you accumulate the various errors that are not yet but included in official analysis, you can plausibly account for a quarter of the officially estimated global warming over the last 100 years. Some analysts go even to half of the warming.
That is of fundamental importance for policy.
That is why some of us who care continue to invest precious time in attempts to clean up the records, despite the abuse from those less competent.
Geoff
(Short version of a longer essay that disappeared). Clyde, essentially we are in agreement. Here are 2 posts in succession to keep them shorter.
Part one. Formal matters.
From wiki, https://en.wikipedia.org/wiki/Sampling_(statistics)
“…concerned with the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population.” And
“The sampling process comprises several stages:
• Defining the population of concern
• Specifying a sampling frame, a set of items or events possible to measure
• Specifying a sampling method for selecting items or events from the frame
• Determining the sample size
• Implementing the sampling plan
• Sampling and data collecting”
The first stage, to define the population of concern, requires great care. In shorthand form here, in terms of Clyde’s essay, the population might be the temperature at ground level of all points near the surface of the globe. This then requires an immediate qualification, for there are infinitely many of these places. And so, the stages have to be worked through. Other bloggers here have already pointed out many of the complications in the way of a precise and accurate framework to compute a ‘global mean surface temperature”. Others have raised additional theoretic problems, such as temperature being an intrinsic property unable to be averaged; and trying to make a time series for a globe that is rotating and precessing while the temperature at a surface point ranges from Tmax to Tmin each day, raising a host of requirements to deal with just time of observation.
In summary, while a global mean surface temperature is an easy concept for a paper exercise, it is devilishly complicated. The best conclusion is that such an entity, a global mean temperature, is invalid and ought to receive a great deal more thought in its specification and measurement. Specifically, proper and accepted error estimates should be made at each stage of its construction. The visual use of error envelopes on a graphic can be a boon to readers. Used properly, it allows a rapid initial assessment of the significance of the hypothesis.
It is quite rare to read a climate paper whose treatment of accuracy, precision and error, including error propagation, is satisfactory and of the standard expected for hard science. This is one of the main reasons why some of us are sceptical of the climate field. There needs to be an enforcement of the proper treatment of errors in every paper, along the lines of that laid out for example by the Paris based Bureau of Weights and Measures, BIPM. The BIPM material requires detailed study. Here is a site where the measurement of one parameter, the standard metre, is covered.
https://www.google.com.au/webhp?sourceid=chrome-instant&rlz=1C1CHBF_en-GBAU734AU734&ion=1&espv=2&ie=UTF-8#q=international+bureau+of+weights+and+measures+meter
If the first of the hockey stick graphs had shown proper error estimates, they might have failed at the peer review stage. If they were applied now, one would find it hard to take it seriously.
Geoff.
Any paper, and I do mean any, that uses a temperature data series should start with the raw data and include the adjustments that have been made and why. This may mean using NASA, NOAA, or whoever’s algorithms, but they should be explicitly shown so that everyone can see and judge them. As you say, the treatment of accuracy, precision, and error should also be a requirement.
Jim ,
Have you seen any papers from the last 20 years retracted by their authors because they relied on temperature data that by now has been officially altered?
I have not.
Geoff
Jim:
You will not get all of the actual reasons why data is adjusted. NOAA’s program adjusts automatically.
That doesn’t mean that papers shouldn’t include that algorithm AND explain the errors it introduces AND detail the possible outcomes those errors cause.
(Short version of a longer essay that disappeared). Clyde, essentially we are in agreement. Here are 2 posts in succession to keep them shorter.
Part Two. Practical matters.
NOAA in USA collects temperature data from many sources for aggregation into a global composite. Australia sends its data in a CLIMAT file. There is a question of whether Australian data is immediately compatible with NOAA data. It is not. There are several examples why.
1. Reading electronic temperature devices. Clyde provides a quote from an NOAA brochure.
“Once each minute the ACU calculates the 5-minute average ambient temperature and dew point temperature from the 1-minute average observations… These 5-minute averages are rounded to the nearest degree Fahrenheit, converted to the nearest 0.1 degree Celsius, and reported once each minute as the 5-minute average ambient and dew point temperatures…”
Compare this with the Australian method, source, an email from a BOM officer (“we”) a few weeks ago, repeated on a Ken Stewart blog with some of his analysis of it.
“Firstly, we receive AWS data every minute. There are 3 temperature values:
1. Most recent one second measurement
2. Highest one second measurement (for the previous 60 secs)
3. Lowest one second measurement (for the previous 60 secs). Relating this to the 30 minute observations page: For an observation taken at 0600, the values are for the one minute 0559-0600.”
Some implications follow from Ken’s site, https://kenskingdom.wordpress.com/2017/03/21/how-temperature-is-measured-in-australia-part-2/
It is apparent that the NOAA method will not give the same answers as the Australian method. There is a bias and it is of a type where the positives and the negatives have no reason to cancel each other.
2. Converting automatic readings to a daily mean.
In Australia, the Liquid-in-Glass thermometer was largely replaced with the electronic temperature device about 1993. Before then, mean daily temperatures were calculated from the purpose built Max and Min thermometers by (Tmax + Tmin)/2. Since Nov 1994 the convention has changed. The mean is now that of 4 temperatures taken 6 hours apart each day. This introduces a bias in the Australian data, examples of which are given by Australia’s official BOM in a publication that shows the difference for a number of sites over several years each. There is a bias and again there is no good reason why the positives match the negatives. Indeed, where tested, they do not. The magnitude of the error is about 0.2 deg C tops.
3. Metrication.
4. Australia converted from deg F to deg C in September 1972. The BOM published here http://cawcr.gov.au/technical-reports/CTR_049.pdf that “The broad conclusion is that a breakpoint in the order of 0.1°C in Australian mean temperatures appears to exist in 1972, but that it cannot be determined with any certainty the extent to which this is attributable to metrication, as opposed to broader anomalies in the climate system in the years following the change. As a result no adjustment was carried out for this change.”
So here is another bias that makes it hard to incorporate Australian data seamlessly into a global average. It is a bias in one direction, so the positives and negatives do not cancel.
There are several of these bias components in the Australian data. It is not known to me if the NOAA procedures cope with this bias when blending a global average. (I doubt if they know all of them).
The conclusion has to be that the accumulated effect of such bias allows a rough estimate of up to about 0.25 deg C that is carried forward in the CLIMAT data. This has direct relevance to the topic of Clyde’s post. It means that it is often pointless to use a figure after the decimal for relevant temperatures. Those, like my old mate Steven Mosher who argue that exercises like comparing NOAA and BEST to each other and to satellite data like UAH and RSS are showing high precision and/or accuracy are not in full possession of the relevant data. In cases such as I have given here briefly, you can take their claims of goodness with a grain of salt.
Geoff.
Geoff,
Thank you for the additional information. I found it interesting. As I said in my introduction, “The point of this article is that one should not ascribe more accuracy and precision to available global temperature data than is warranted, after examination of the limitations of the data set(s).” It seems that most of the commenters understand that the temperature data set is a can of worms and that in attempting to use meteorological data for climatological purposes, a lot of problems have been overlooked. For example (ignoring the complaint that it is not even valid to average temperatures, which I need to spend some time thinking about) I think that the only way a better approximation to the average temperature could be obtained would be to determine the lapse rate at every weather station for the time a temperature is recorded, and then convert every ground temperature to a standard elevation, say 10,000 feet, and then average all the temperatures for the standard elevation. Although, air density and humidity will also have an impact on temperature, so I’m not sure it is really a tractable problem. Probably the only way that this could be done is with satellite observations.
Thanks, Clyde.
While my comments deal mainly with Australia’s flawed contribution to guesses about a global average temperature, you might imagine many other countries whose contributions contain even greater errors.
Thank you for your essay, a platform for more comments by bloggers.
Geoff
I believe this issue has been overthought, given its purpose. If we want a figure for the average temperature at the Earth’s surface for a given day/month/year, then use the raw temperature data as it is. If it’s 110 at Death Valley at noon UTC and 55 at Fisherman’s Wharf in SF, then those are the temperatures at the Earth’s surface at those times. Why should they be adjusted for elevation, humidity, etc. to achieve some “standard”?
This is from the GISTEMP FAQ:
Q. Why can’t we use just raw data?
A. Just averaging the raw data would give results that are highly dependent on the particular locations (latitude and elevation) and reporting periods of the actual weather stations; such results would mostly reflect those accidental circumstances rather than yield meaningful information about our climate.
This seems questionable to me. The raw temperature is “highly dependent on the particular location”? Well, of course it is. It’s colder at the poles and warmer at the Equator — and that is because of their “particular location.” The temperature at a given point and time is the temperature at that place and at that time. Whether or not that point is at -20′ or +5000′ ASL makes no difference — that is the temperature there at that time. What more can be asked?
I’m not sure what is meant by the “reporting period” of the weather stations, and the FAQ answer helpfully does not elaborate. If they mean the reporting schedule, what does it matter, since the entire record is being used? If station A records a temperature every five minutes and station B records a temperature four times a day, then that’s the data one has for the day. It can be averaged, and the resulting error can be calculated, and that’s your record for the day.
With all of the homogenization and adjustments made to the raw data, one would think they’re trying to arrive at the average temperature of some hypothetical geoid at sea level rather than the actual Earth’s surface. Is that the actual goal?
“Of the 17 hottest years ever recorded, 16 have now occurred since 2000.”
This irksome claim is just more of the lame alarmist narrative. From before 2000 to the present global temperatures have been on a PLATEAU. To say that 16 of 17 numbers on a plateau are the highest is near meaningless. And it completely ignores the situation before “recorded” history – eg. the Minoan, Roman and Medieval Warm periods.
http://4.bp.blogspot.com/-SExu0YHn_3M/UPyAypRopNI/AAAAAAAAKuI/ERH31pacPPI/s1600/Lappi_Greenland_ice_core_10000yrs.jpg
Clyde Spencer:
If you haven’t seen it then I think you will want to read this
http://www.publications.parliament.uk/pa/cm200910/cmselect/cmsctech/memo/climatedata/uc0102.htm
especially its Appendix B.
Richard
Richard,
Thank you for the link. It was interesting. While reading it, I had a thought: Because temperature will change with the specific heat of a parcel of air, which is a function of density and absolute humidity, (ala the universal gas law) can we expect weather station anomalies to change with elevation? That is, will anomalies tend to be different for stations at low elevations versus stations in mountains?
Clyde Spencer:
You ask me
Probably yes.
That is one of the many imperfections in the measurement equipment requiring a compensation model if a global temperature is considered as being a physical parameter with a unique value for each year.
Richard
Thank you Richard. Your letter to the investigation board is an excellent summation.
I also find it intriguing that the climate team blustered, denied, lied and obfuscated their responses to your facts. They effectively displayed their anti-social anti-science characteristics. Which implies they were already told that nothing would happen to the team.
Thanks for a great article on the vicissitudes of measurement. You are spot on in a subject where people lose their way frequently.
The discussion here was much more fruitful than I originally thought. For example, Windchasers had me flummoxed for a while, and at first I regarded his comments as diversions. They aren’t, and his comments actually opened my eyes to a couple of things. What he’s getting at is that if the quantity being measured is “the global average temperature,” then thousands of measurements averaged together would be more “accurate” (i.e. closer to the “global average temperature”) than would tens of measurements. He’s actually correct, but only if the spread of measurements across the globe were uniform spatially and temporally. Even then, it is a weak improvement until every square foot is averaged.
But his comment did bring me back to the question: what does a global average temperature even mean? (Yes, I know we are talking about “anomaly,” which makes the problem of significant digits much worse than averaging of measured temperatures.) For the life of me, I can’t see any value in the figure whatsoever until the entire globe is measured daily. And even then, it is only of use is determining (along with a complete humidity map) the energy of the atmosphere. The variations from weather station to weather station within the same locality are amazingly large. To think that the coverage we have today (30% of the earth’s surface) could be extrapolated with any meaning is probably not correct.
I welcome this kind of discussion, but without the snark – funny as a lot of it is.
The accuracy and precision approaches are rebutted above, repeatedly and quite effectively by many commenters.
The coverage we have today is grossly spotty. 30% of the Earth’s surface is not covered.
Yes, the USA has allegedly reasonable coverage, and Western Europe’s coverage is similar.
Alaska, Canada, Russia, Africa, South America, New Zealand’s coverage is sparse and even then concentrated around certain cities.
Australia’s coverage is somewhere in-between, but closer to sparse coverage since large areas are without cities or towns.
Antarctica’s coverage is lousy. The Arctic’s coverage is worse.
There used to be a cam shot of a temperature station in Antarctica that for a long period showed a temperature station bent over and covered in snow. When the team finally returned to right the station, the cam disappeared. Now we can’t see if the pole is bent and the station is covered.
Not to worry! NOAA has a program that spots anomalous readings and they’ll happily fill those anomalous datums with historical averages or preferably, with some other station’s temperature smudged up to 1200 km.
Michael,
Please see the comment I made to Windchasers earlier today as a followup to his first comment. He does not make a case for the Law of Large Numbers justifying increased precision.
Thousands of temperature measurements may be more representative of the average temperature, i.e. more accurate, but I still contest that they improve the precision. The accuracy improves for the same reason that the average of runs of die tosses improves, which is related to sampling. I maintain that the appropriate metric for uncertainty is the standard deviation and not the standard error of the mean. There are a number of caveats that have to be met. And, as more samples are taken in non-representative areas there is the potential for increasing the standard deviation. Also, no one has proposed how to handle differences in elevation. The reason Death Valley sees such high temperatures is because it is below sea level. So, it is difficult to make a blanket statement. What is needed is a thorough analysis of the propagation of error when combining many data sets.
One can’t calculate an anomaly until a multi-year average is calculated and it is critical how many significant figures are justified in that average because it bears on how the subtractions are handled.
To give the Devil his due, I think that the intent of calculating a global temperature average is to determine to what extent the biosphere is warming and try to anticipate the impact on living things. Yet, the focus should be on the daily highs, not the average. Also, the many caveats are being ignored in trying to press into service weather observations to answer climatological questions.
Clyde, you are absolutely correct when you say, ” I maintain that the appropriate metric for uncertainty is the standard deviation.” But that only applies to a given instrument measuring a specific item. Now, if we had a device that could measure the global temperature, then “standard deviation” would apply. The crux of the problem is that no such instrument exists. So, absent a global thermometer, we do the next best thing, and that is using regular thermometers to sample temperatures of the earth at various geographical locations. We then use all these measurements as an estimate of global temperatures. Now as a result of this procedure, we invoke all the math associated with the statistics of sampling. The “global temperature” now is subject to standard error, and not standard deviation. Because we are now using our sample to estimate the population mean, more observations are the rule. Now if you understand the concept of a closed thermodynamic system (which the earth is: http://www.bluffton.edu/homepages/facstaff/bergerd/nsc_111/thermo2.html ) then you’ll realize that the best measure of the temperature of the earth is with satellites observing outbound radiation from our planet. However, as with any methodology of estimating the population mean, even if you use satellites to measure this outbound radiation, you’ll realize that you are still constrained by the limitations of using a small sample to estimate the population mean. So, in the case of using microwave brightness as a proxy for surface temperatures, the “standard deviation” lies in the characterists of the bolometer in orbit, but the resultant measurement is subject to standard error in statistical sampling. The issue you have with the differences between standard deviation and standard error can be summarized as follows: I can measure the height of my son or daughter by making a mark on the door jam wood work. I may not know how many centimeters the mark is, but if I make the measurement every three months, it’s plainly obvious that my son/daughter is growing.
‘I maintain that the appropriate metric for uncertainty is the standard deviation”
Only if you are measuring the same thing,…for instance an object in a laboratory maintained at a specific temperature. Then measuring the temperature multiple times will allow you to calculate the mean, standard deviation etc for measuring at that temperature with that instrument.
When temperature is recorded with a thermometer in a stevenson screen it is a variable that is being measured. Temperature changes through the day, from hour to hour, from second to second. The temperature measured at this moment will not be the same as the temperature at that moment.
Normal/parametric statistical methods don’t apply
Michael darby,
You said, “Now, if we had a device that could measure the global temperature, then ‘standard deviation’ would apply.” Once again, I’m afraid that you are confused. If we had such an instrument, and took one reading to determine the temperature, there would be no standard deviation because the standard deviation is a measure of dispersion of samples around a mean. If we took several readings over time, we would get the changes and trend and a standard deviation would be unnecessary for the series of readings because the series gives us what we are looking for without the necessity of calculating an average at any point. (Unless you want to calculate the average of the series because you like to calculate averages.)
Yes, if determining the average global temperature was as easy as putting a mark on the woodwork, then determining trends and rates would be trivial. Unfortunately, it isn’t at all that simple and for that reason it is a poor analogy.
I’m signing off. Don’t bother to reply unless you insist on having the last word.
Clyde, you say: ” If we had such an instrument, and took one reading to determine the temperature, there would be no standard deviation” Do you have a smidgen of comprehension of measurement? Please clue me in on an existing thermometer that measures temperature perfectly without error bounds. All measurement instrumentation I’ve ever encountered will provide you with a +/- limitation. I suggest you refresh your understanding of how instrumentation error is determined before you reply to this.
Additionally, the analogy I’ve provided is perfect with regards to what is currently going on in climatology. We might not have the exact readings in degrees Kelvin/Celsius of Earth, but the marks on our thermometers are telling us that Earth is warming.
accuracy / precision hatten wir schon;
liegt mir stagelgrün an.
accuracy / precision hatten wir schon;
liegt mir stagelgrün an.
Clyde Spencer,
I am sure you are correct when you suggest that error variance is underassessed and underestimated in temperature series. However, I think that you yourself are overassessing the importance of measurement precision when temperature averages are taken over space or time. Measurement precision is totally swamped by the problem of accuracy of resolution. Your reference to Smirnoff – ”… at a low order of precision no increase in accuracy will result from repeated measurements” is relevant to repeat measurements targeted on estimation of a fixed parameter value, but is not highly relevant to a problem of computing an average index, where the precision of any one measurement is small relative to the total range of variation of the individual measures.
To illustrate the point, consider a hypothetical example where you set up 101 thermometers in a region and you aim to track daily movement in an average temperature index for the region. For each thermometer, you take a single daily temperature reading at the same time each day. You determine by calibration experiments that each individual thermometer reading has a standard deviation of 2 deg C relative to the true integrated average daily temperature in the immediate locale. Your daily temperature reading however is recorded only to the nearest degree C.
Each individual reading then carries two error terms, the first with sd of 2 deg C (a variance of 4) and the second – due to rounding error – with a sd of 0.2887 (a variance of 0.083). (These latter values associated with rounding error are exactly derived from a uniform distribution with a range of one deg C.)
The error variance in your final average of the 101 temperature readings is then given by the sum of the contributions of the accuracy error and the precision error, divided by the number of thermometers. This is equal to (4 + .083)/101 = 0.0404. This corresponds to a sd of 0.201. For comparison, if you had recorded your single thermometer readings to a precision of 3 decimal places, instead of to the nearest degree, the sd of the average temperature would be reduced to 0.199 – a tiny change.
Under these circumstances, you are justified in citing your average temperature index to at least one decimal place, despite the initial rounding error, but can make no claim to significant change in temperature between days until you see a difference of around 0.4 deg C. This, you note, is controlled by the accuracy problem, not the precision problem.
kribaez,
Would you agree that using the method of rounding to the nearest even number (3.5 to 4, 4.5 to 4, etc.) would eliminate the need for a rounding error calculation?
James,
If you are suggesting what I think you are, then you quadruple the variance associated with the rounding problem.
The rounding problem is identical to the binning problem when you are constructing a histogram. If you are using normal rules of rounding then the interval of each bin is identical. For example, if you are rounding to the nearest tenth of a unit, then the intervals are all equal to exactly one tenth. In the examples given here, where temperature is rounded to the nearest degree, the intervals are all exactly equal to one. For example, all of the values between 3.500001 and 4.4999999 will go into one bin, corresponding to the rounded value of 4.0. With your proposed scheme, the bin labelled “4.0” captures everything from 3.0 to 5.0 and has therefore twice the interval size, double the sd and four times the variance. This definitely makes the error from the rounding problem larger.
Did you perhaps mean rounding to the nearest whole number rather than to the nearest even number?
If so, then that is exactly what my example calculation above implies. As I have illustrated, the rounding problem does not go away, but the error it introduces into the overall averaging problem is very small – always providing that the range of variability of the input values is much larger than the precision of the measurement, as it is in my example and in realworld temperature measurements.
kribaez,
I must not have expressed myself very well. You said:
What I meant to say — and I saw this method suggested specifically to balance rounding errors — was that everything from 3.50000 to 4.50000 would round to 4. A value of 3.49999 is less than 3.5, and so would round to 3. A value of 4.50001 is greater than 4.5, and so would round to 5. It was only the exact x.500000 values that rounded to the nearest even number.
In the example, where would 3.50000 go? In the method I suggested, it would go into the 4 bin. In the example, where would 4.50000 go? In my method, it would also go into the 4 bin.
If one always rounds up, the error always is positive; if one always rounds down, the error is always negative. By rounding the x.50000 values to the nearest even number (I suppose one could use odd numbers just as well), the rounding error gets more evenly distributed, up and down.
You make an assumption here that may or may not be true. ” (These latter values associated with rounding error are exactly derived from a uniform distribution with a range of one deg C.)”. What if the manual readings are skewed? Say, people rounded high temps up and low readings down? This could easily have happened with land and ship readings.
Kribaez,
You come across as knowing more about the problem than I do. I don’t claim to be an expert, unlike some others here who hold themselves up as experts on the problem. I only know enough to get myself into trouble! What I set out to do is to call into question the practices in climatology in the hopes that someone like you might point the way to a more rigorous assessment of data handling and error propagation. It seems that there is a lot of hand waving in climatology and neither the Media nor the laymen they write for are in a position to question what they are told. Perhaps you could expand on your remarks above to provide Anthony with a piece to address my concerns.
Excellent article. It should be a sticky or a reference article for newcomers to this site.
I wonder whether it might be possible to use a spacecraft sufficiently far from earth, with a bolometer or other temperature sensor, which would read the “smeared” temperature of the planet. Not one focused on any particular spot of water or land or clouds, or the areas at night or during the day. I would image that it would have to have a polar position, probably one for each pole, and then average the two readings to get a “global” average. But then it would miss out on the tropics, so maybe the two satellites should be located right above the terminator on each side of the globe. The idea would be to measure the actual radiative temperature of the entire globe. I wonder whether anyone has done this for other planets in the solar system.
Just a wild thought.
Thank you for an excellent article Clyde Spencer!
Also a big Thank You to all the well informed commenters who helped improve the discussion tremendously!
Of course, not you binned!
Thank you, Brad Tittle, Neil Jordan and Writing Observer for teaching me about enthalpy! Now I have a bunch of links to further my education.
The accuracy of real time temperature data since 1850, and average temperature calculations, are both worthy of debate.
However, the real time data we have excludes 99.9999% of Earth’s climate history.
Even worse, the real time data we have is ONLY for one warming trend, probably still in progress, so new “records” are TO BE EXPECTED until that warming trend ends, and a cooling trend begins.
More important than the data quality, or extrapolating short-term temperature trends into infinity, are the following two questions:
:
(1) Is the current climate healthy for humans plants, animals and plants?
My answer is “yes”.
(2) Have climate changes in the past 150 years been unusual?
My answer is “no”
The answers to the two questions strongly suggest there is no current climate problem, and recent climate changes are not not unusual.
Therefore, people claiming a climate change catastrophe IS IN PROGRESS TODAY, are ignoring reality in an effort to scare people.
What the warmunists want is attention, money and power.
The false coming climate change catastrophe, allegedly in progress since 1975, is nothing more than a boogeyman used by leftists seeking political power … using the clever excuse they need more power to save the Earth.
It seems that leftists recognize that most voters are stupid, and gullible — so gullible they believe in a invisible climate crisis in spite of the fact that the climate is wonderful in 2017.
Anyone living in one place for several decades might have noticed slightly warmer nights … if they worked outdoors at night … and there is nothing else to notice!
Where’s the bad climate news?
Ice core studies tell us there were hundreds of mild climate cycles in the past one million years.
Each cycle consists of several hundred years of warming followed by several hundred years of cooling.
The length of each full cycle is estimated to average 1,000 to 2,000 years.
For real time measurements, and compilations of average temperature, we have data for only about 150 years — probably less than half of a full cycle, based on climate history.
Claiming that 2016 is the hottest year on record means very little because so few years of actuals are available.
If 2016 is really the hottest year since 1850, based on our very rough measurements, that just tells us the warming trend we believe started in 1850 is still in progress, and the cooling trend expected to follow has not yet started.
So what ?
Our planet is always in a warming trend or a cooling trend.
The measurements are very rough, so we can’t be sure the 1850 warming is still in progress — there has been a flat temperature trend between the temporary 1998 and 2015 El Nino temperature peaks — perhaps that flat trend was a transition between a multi-hundred-year warming and cooling trends?
Only time will tell.
Richard Greene on April 15, 2017 at 12:28 pm
…there has been a flat temperature trend between the temporary 1998 and 2015 El Nino temperature peaks.
RG, instead of useless complaining about the fact that you write on WUWT nearly the same stuff since longer time, I rather will give you a hint warmunistas certainly would prefer to hide: between 1850 and today, there were more flat temperature trends!
For example:
– between 1880 and 1910;
– between 1940 and 1975.
And these two were quite a bit harsher than that 1998 and 2015.
1880 to 1910 have too little data, especially from the Southern Hemisphere.
1940 to 1975 is considered a downtrend, not a flat trend.
You call my comments “useless complaining”, yet it is obvious you read my comment, and replied to it.
If you think my comments are “useless complaining”, and yet you read them, that would make you seem dumb.
First Hint:
When you see any comment by “Richard Greene”, which is my real name, stop reading and move on to the next comment.
I suspect English is not your first language, and hope you understand my hint.
If not, please reply here, and next time I will type my hint slower, so even you can understand !
Second Hint:
Do not go to my climate website for non-scientists, at
http://www.elOnionBloggle.Blogspot.com
I did not read every comment, I am aging too fast as it is, but the point seems to be missed that it is not even of much interest if 2016 was the warmest on record.
Everyone seems to agree that it has warmed, is warming and will likely continue to warm, for at least the short term, at some arguable rate. As long as we agree that some warming is happening then it would not be possible not to have record warm periods at multiple points until cooling ensues.
In other words, record warm years are totally normal and totally within the scope of the arguments of both warmists and luke warmists.
Since the degree of warming indicated by the record is insignificant and probably an outlier in the data, it has no validity as an argument for anyone. Media and alarmists are simply using it, as a factoid (of dubious value), in inappropriate ways.
I don’t know your age, but you display great wisdom that usually comes with age.
It does not matter if 2016 is slightly warmer or cooler than 1880.
Pick any two dates in the past 4.5 billion years and the average temperature will almost certainly be different (assuming we had accurate data to make a comparison).
The only part of your comment I’d like to correct, is one sentence:
“Everyone seems to agree that it has warmed, is warming and will likely continue to warm”
My comments:
I don’t agree that “it has warmed” — 1 degree C. of claimed warming since 1880, with a reasonable measurement margin of error of +/- 1 degree C., could mean the claimed warming is nothing more than measurement error — maybe not likely, but possible.
I don’t agree that it “is warming” — there has been a flat trend between the temporary 1998 and 2015 El Nino peaks and I have no idea if pre-1998 warming will continue after the “pause”, nor does anyone else know for sure.
I don’t agree it “will likely continue to warm” because no one can predict the future climate, therefore any “prediction” would be nothing more than a meaningless wild guess.
Clyde Spencer on April 13, 2017 at 6:17 pm
I maintain that the appropriate metric for uncertainty is the standard deviation and not the standard error of the mean.
Stays in contradiction with a number of sources you may download.
One of them is this:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1255808/
where you read
It is easy to understand even for the layman in statistics: the uncertainty decreases when the sample size increases. And the standard error is nothing else than the standard deviation divided by the square root of the sample size.
But there is no standard error for global temperature estimates because they are using area averaging, also called grid averaging. The temperature data is averaged separately for each grid cell, of which there are over a thousand. Each grid cell average has a standard error, but then these grid cell averages are averaged to get the global average. There is no known way to combine the various cell standard errors to get a global standard error. One can treat the grid cell averages as sampling data but that is completely misleading, because it ignores the errors in the cell averages.
David Wojick on April 18, 2017 at 9:23 am
I would like to thank you for your polite response which, as opposed to Greene’s aggressive and unscientific blah blah, is well worth a reply.
You write:
But there is no standard error for global temperature estimates because they are using area averaging, also called grid averaging.
1. That sounds indeed very nice! But do you really not know that
– satellite temperature readings are collected exactly the same way, namely in grids (e.g. for UAH, of 2.5° per cell, i.e. for the Globe 144 cells per latitude stripe x 72 latitudes – of which however the northernmost and southernmost three contain no valid data);
– UAH’s temperature record DOES NOT CONTAIN ANY even simple treatment of standard errors visible to anybody on Internet?
Please compare the temperature data published by e.g. Hadley
http://www.metoffice.gov.uk/hadobs/hadcrut4/data/current/time_series/HadCRUT.4.5.0.0.monthly_ns_avg.txt
described here
http://www.metoffice.gov.uk/hadobs/hadcrut4/data/current/series_format.html
with that of UAH
http://www.nsstc.uah.edu/data/msu/v6.0/tlt/uahncdc_lt_6.0.txt
While UAH publishes simple averages without any standard error information, the surface temperature record additionally contains 95% confidence intervals. Even Bob Tisdale did mention that at least for the HadCRUT4 data..
That is the reason why I load UAH data into Excel, what allows me to compute, for all nine zones and regions, a standard error using Excel’s linear estimate function; even if it ignores matters like autocorrelation, it gives excellent results.
2. David, I am a layman like you certainly are too. I lack knowledge about complex statistic methods, so your question of how to integrate single standard error estimates into a global one I can only answer with a hint on what I discovered using Google.
The very first link was interesting enough:
https://stats.stackexchange.com/questions/55999/is-it-possible-to-find-the-combined-standard-deviation?noredirect=1&lq=1
http://fs5.directupload.net/images/170419/4pr3dtl6.png
This is of course not the reference I would like to give you here (a complete article would be far better). But at least it represents a good approximation of how the math solution shall look like.
3. Everybody may process UAH’s grid data out of the files
http://www.nsstc.uah.edu/data/msu/v6.0beta/tlt/tltmonamg.1978_6.0beta5
through
http://www.nsstc.uah.edu/data/msu/v6.0/tlt/tltmonamg.2017_6.0
in order to obtain lots of additional info, e.g. the linear OLS trend per single grid cell, or of a latitude stripe, or of specific regions not provided in UAH’s file, e.g. NINO3+4 (5S:5W — -170W:-120W), etc etc.
It would be interesting to compute, following the description above, the combined standard deviation (or error) for arbitrary subsets of the 9,504 UAH cells.
But that’s a lot of work because GNU’s Scientific library probably does not contain the appropriate function like it offers for single estimates, so one has to do all the bloody job by hand.
I am not referring to combining sample sets, but rather to the standard error of an average that is made by averaging the averages of over a thousand temperature sample sets, one for each grid cell. If what you have pointed to does that then great, but I do not see how.
I am not exactly a layman. I know little about advanced statistical methods but a great deal about what are called the “foundations” of statistical sampling theory. My Ph.D. is in analytical philosophy and the foundations of mathematics are a part of that which I do work in. It has to do with looking at the postulates that underlie a body of math. In particular, statistical sampling theory is based on probability theory, which imposes some very strict requirements. It appears that grid cell averaging violates several of these, but that is a research question.
You are clueless Bindiddidion — the temperature data can’t be trusted because they are collected and compiled by people who can’t be trusted.
Statistics can not make faulty, biased, made up, and wild guessed temperature data more accurate — although most people can be fooled by false precision claims.
The warmunists claim CO2 controls the climate, which is false, and expect global warming because CO2 levels are rising, based only on laboratory experiments, unproven in real life.
Every month at least half the planet has no temperature data, so government bureaucrats use their own wild guesses.
At least half of the claimed warming since 1880 is from government bureaucrat “adjustments” to raw data, which often “disappears”.
Much of the temperature data are from instruments with +/- 1 degree C. accuracy, and yet government bureaucrats present global temperatures with two decimal places, and claim one year was hotter than another by +0.02 degrees C., which is grossly false precision.
Most of the warmunists claim to KNOW the future average temperature, which is false.
Some claim to have 95% confidence in their prediction of the future temperature, which is a nonsense number with no scientific meaning, and certainly false after three decades of very wrong global climate model predictions.
You are clueless Bindiddidion, because you don’t realize the coming global warming catastrophe is not science at all — it is a political tool used to scare people into accepting more and more powerful central governments.
Wild guess predictions of the future average temperature are not science.
Very rough estimates of the average temperature, compiled by people with a huge global warming bias, ARE DATA NOT WORTHY OF STATISTICAL ANALYSES.
The use of statistics on faulty data is a form of propaganda when used by the warmunists — the average temperature of Earth presented in hundredths of a degree C., for one example, impresses people a lot more than being rounded to the nearest one-half degree.
The use of statistics on faulty data is a form of stupidity when used by the warmunists — I have read articles at this website, for one example, examining monthly temperature anomalies in thousandths of a degree C. — three decimal places !
Statistics are nearly worthless when people collecting the raw data have an agenda, a near-religious belief in a coming global warming disaster, and a propensity to make repeated “adjustments” to the raw data that usually result in more ‘global warming’.
Statistics are nearly worthless when 99.9999% of historical climate data are not available for analyses, and no one has any idea what a “normal” average temperature is.
Statistical analyses of very rough temperature data, with not even close to global coverage, available only for a very tiny percentage of Earth’s history, and collected by bureaucrats hired only if they believe in CAGW, is mathematical mass-turbation.
I wrote:
“The use of statistics on faulty data is a form of stupidity when used by the WARMUNISTS — I have read articles at this website, for one example, examining monthly temperature anomalies in thousandths of a degree C. — three decimal places !”
My intended sentence was:
The use of statistics on faulty data is a form of stupidity when used by the SKEPTICS — I have read articles at this website, for one example, examining monthly temperature anomalies in thousandths of a degree C. — three decimal places !
Note that the only uncertainty that decreases with increased sample size is the pure (that is, probabilistic) error of sampling. There are may other forms of uncertainty, some of which can increase with sample size, such as systemic bias.
What we really need is a serious NOAA research program on all of the uncertainties in these temperature estimates. Here is my outline. Comments welcome.
A needed NOAA temperature research program
NOAA’s global and US temperature estimates have become highly controversial. The core issue is accuracy. These estimates are sensitive to a number of factors, but the magnitude of sensitivity for each factor is unknown. NOAA’s present practice of stating temperatures to a hundredth of a degree is clearly untenable, because it ignores these significant uncertainties.
Thus we need a focused research program to try to determine the accuracy range of NOAA temperature estimates. Here is a brief outline of the factors to be explored. The goal is to attempt to estimate the uncertainty each contributes to the temperature estimates.
Research question: How much uncertainty does each of the following factors contribute to specific global and regional temperature estimates?
1. The urban heat island effect (UHI).
2. Local heat contamination or cooling.
3. Other station factors, to be identified and explored.
4. Adjustments, to be identified and explored.
5. Homogenization.
6. The use of SST proxies.
7. The use of an availability sample rather than a random sample.
8. Interpolation or in-fill.
9. Area averaging.
10. Other factors, to be identified and explored.
To the extent that the uncertainty range contributed by each factor can be quantified, these ranges can then be combined and added into the statistical temperature model. How to do this is itself a research need.
The resulting temperature estimates will probably then be in the form of a likely range, or some such, not a specific value, as is now done. The nature of these estimates remains to be seen. Note that most of this research will also be applicable to other surface temperature estimation models.
David
Why waste more money?
Let NOAA provide ONLY useful information on weather today, and for the coming week.
The world has wasted far too much money compiling average temperature data, and then making policy decisions using that very rough data … in spite of no evidence the current climate is bad, or even much different than 150 years ago.
Because the research results would render these claims permanently useless, including in future Administrations. As Walt Warnick says, when you capture the enemy’s cannon, don’t throw it away, turn it on them.
Reply to Mr. Wojick comment on April 18, 2017 at 12:24 pm
Do you trust government bureaucrats to honestly compile temperature actuals?
Do you think that if we knew the average temperature in the PAST 150 years with 100% accuracy, those data could refute claims of a COMING climate catastrophe that’s off in the FUTURE ?
Bureaucrats can “cook the books” so global cooling can’t happen and every year is a few hundredths of a degree warmer than the prior year — wait a minute, it seems they are already doing that !
And please remember — runaway global warming is ALWAYS going to happen in the future — it’s been coming for 30 years, and must have gotten lost in New Jersey, because it has never arrived … and it will never arrive.
The perfect political boogeyman is one that is invisible, and always off in the future — that’s exactly what CAGW is.
My goal is to discredit the surface statistical models by exposing their many uncertainties and error sources. In addition to NOAA there is GISS, HadCRUT and BEST, maybe more. Only NOAA and GISS are federally funded so zeroing them will not stop the flow of alarmist numbers.
The statistical community has long said informally that a lot of the climate statistics are unreliable. I want them to say it formally via a research program. Turn the statistical cannon around and fire it on the alarmists.
David Wojick on April 18, 2017 at 9:13 am
1. NOAA’s global and US temperature estimates have become highly controversial.
Like GISTEMP’s, NOAA’s data is, as far as land surfaces are concerned, based on the GHCN V3 station network, whose three day temperature datasets (minimum, maximum, average) exist in two variants: unadjusted and adjusted.
To start, here is a comparison of GHCN unadjusted average data with GISTEMP’s land-only and land+ocean (I did never manage to obtain NOAA’s land-only data because it wouldn’t differ enough from GISTEMP’s):
http://fs5.directupload.net/images/170420/mmcuzmaf.jpg
You clearly can observe that GISTEMP’s data (the result of huge homogenisation and infilling) shows
– less deviations from the mean than does the raw, harsh GHCN record, thus less uncertainties;
– a lower linear trend than GHCN.
The linear trends ± 2 σ for the Globe, 1880-2016 in °C / decade:
– GHCN unadj: 0.214 ± 0.058
– GISTEMP land: 0.101 ± 0.001
– GISTEMP land+ocean: 0.071 ± 0.001
{ Please apologise for the exaggerated precision: when you build averages of averages all the time and shift lots of data from a 1951-1980 baseline to one at 1981-2010, you move into rounding errors when using only one digit after the decimal point. }
So if the GISTEMP people ever had the intention to cool the past in order to warm the present, as is so often pretended: why did they not keep their data exactly at the GHCN level?
2. The urban heat island effect (UHI)
It is known since longer time that if we draw
– a plot of GHCN containing only data from stations with population type ‘R’ (rural) and nightlight level ‘A’ (least)
and
– a plot of all the data
the latter’s trend for the Globe inevitably will be somewhat higher than that of the rural part:
http://fs5.directupload.net/images/170420/n4edxhti.jpg
The linear trends ± 2 σ for the Globe, 1880-2016 in °C / decade:
– GHCN unadj rural: 0.185 ± 0.079
– GHCN unadj all: 0.214 ± 0.058
Why should there be no UHI traces in temperature records? The Globe is what Mankind has made of it, huge towns and plants of 1 GW-el each producing 3.3 GW-th included. That is part of the warming process (yes yes yes: not ‘due to’ CO2).
3. Last not least: a similar comparison for the CONUS
http://fs5.directupload.net/images/170420/4melkfeb.jpg
CONUS is, in comparison with the Globe, an incredibly stable piece of land, and so show temperatures for it!
And that you see best when comparing there, during 1979-2016, GHCN surface data with UAH’s satellite record:
http://fs5.directupload.net/images/170420/gwqhedbf.jpg
I am calling for a research program and it sounds like you might apply for a grant. I take it that you do not disagree with any of my topics.
It has been a week or 2 since I took (or taught) a digital math class, but as I recall, we had some customers who required that after numerous geometrical manipulations (rotate, translate, intersect, zoom/resize…) we had to retain at least 8 decimal digits. Every multiply or divide potentially lost a bit.
The traditional way to minimize losses was a double-sized register for intermediate values. But there have long been software packages which kept designated numbers of bits.
Question: What effect does missing data (temperature readings not recordable due to broken thermometer…) on precision and/or accuracy? Can interpolation techniques avoid distortions in trends/series? And just for completeness (and because a warmist hysteric mathematician friend made a claim): Can accuracy and/or precision be “recovered” or “improved” by interpolating to fill in missing data? :B-)