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Observations, Reanalyses and the Elusive Absolute Global Mean Temperature

One of the most common questions that arises from analyses of the global surface temperature data sets is why they are almost always plotted as anomalies and not as absolute temperatures.

There are two very basic answers: First, looking at changes in data gets rid of biases at individual stations that don’t change in time (such as station location), and second, for surface temperatures at least, the correlation scale for anomalies is much larger (100’s km) than for absolute temperatures. The combination of these factors means it’s much easier to interpolate anomalies and estimate the global mean, than it would be if you were averaging absolute temperatures. This was explained many years ago (and again here).

Of course, the absolute temperature does matter in many situations (the freezing point of ice, emitted radiation, convection, health and ecosystem impacts, etc.) and so it’s worth calculating as well – even at the global scale. However, and this is important, because of the biases and the difficulty in interpolating, the estimates of the global mean absolute temperature are not as accurate as the year to year changes.

This means we need to very careful in combining these two analyses – and unfortunately, historically, we haven’t been and that is a continuing problem.

Reanalysis Analysis

Let me illustrate this with some results from the various reanalyses out there. For those of you unfamiliar with these projects, ”reanalyses” are effectively the weather forecasts you would have got over the years if we had modern computers and models available. Weather forecasts (the ”analyses”) have got much better over the years because computers are faster and models are more skillful. But if you want to track the real changes in weather, you don’t want to have to worry about the models changing. So reanalyses were designed to get around that by redoing all the forecasts over again. There is one major caveat with these products though, and that is that while the model isn’t changing over time, the input data is and there are large variations in the amount and quality of observations – particularly around 1979 when a lot of satellite observations came on line, but also later as the mix and quality of data has changed.

Now, the advantage of these reanalyses is that they incorporate a huge amount of observations, from ground stations, the ocean surface, remotely-sensed data from satellites etc. and so, in theory, you might expect them to be able to give the best estimates of what the climate actually is. Given that, here are the absolute global mean surface temperatures in five reanalysis products (ERAi, NCEP CFSR, NCEP1, JRA55 and MERRA2) since 1980 (data via WRIT at NOAA ESRL). (I’m using Kelvin here, but we’ll switch to ºC and ºF later on).

Surprisingly, there is a pretty substantial spread in absolute temperatures in any one year (about 0.6K on average), though obviously the fluctuations are relatively synchronous. The biggest outlier is NCEP1 which is also the oldest product, but even without that one, the spread is about 0.3K. The means over the most recent climatology period (1981-2010) range from 287.2 to 287.7K. This range can be compared to an estimate from Jones et al (1999) (derived solely from surface observations) of 287.1±0.5 K for the 1961-1990 period. A correction for the different baselines suggests that for 1981-2010, Jones would also get 287.4±0.5K (14.3±0.5ºC, 57.7±0.9ºF)- in reasonable agreement with the reanalyses. NOAA NCEI uses 13.9ºC for the period 1901-2000 which is equivalent to about 287.5K/14.3ºC/57.8ºF for the 1981-2010 period, so similar to Jones and the average of the reanalyses.

Plotting these temperatures as anomalies (by removing the mean over a common baseline period) (red lines) reduces the spread, but it is still significant, and much larger than the spread between the observational products (GISTEMP, HadCRUT4/Cowtan&Way, and Berkeley Earth (blue lines)):

Note that there is a product from ECMWF (green) that uses the ERAi reanalysis with adjustments for non-climatic effects that is in much better agreement with the station-based products. Compared to the original ERAi plot, the adjustments are important (about 0.1ºK over the period shown), and thus we can conclude that uncritically using the unadjusted metric from any of the other reanalyses is not wise.

In contrast, the uncertainty in the station-based anomaly products are around 0.05ºC for recent years, going up to about 0.1ºC for years earlier in the 20th century. Those uncertainties are based on issues of interpolation, homogenization (for non-climatic changes in location/measurements) etc. and have been evaluated multiple ways – including totally independent homogenization schemes, non-overlapping data subsets etc. The coherence across different products is therefore very high.

Error propagation

A quick aside. Many people may remember error propagation rules from chemistry or physics classes, but here they again. The basic point is that when adding two uncertain numbers, the errors add in quadrature i.e.

X\pm\delta x + Y\pm\delta y \approx (X+Y)\pm \sqrt{(\delta x)^2 + (\delta y)^2}

Most importantly, this means uncertainties can’t get smaller by adding other uncertain numbers to them (obvious right?). A second important rule is that we shouldn’t quote more precision than the uncertainties allow for. So giving 3 decimal places when the uncertainty is 0.5 is unwarranted, as is more than one significant figure in the uncertainty.

Combine harvesting

So what can we legitimately combine, and what can’t we?

Perhaps surprisingly, the spread in the seasonal cycle in the reanalyses is small once the annual mean has been removed. This is the basis for the combined seasonal anomaly plots that are now published on the GISTEMP website. The uncertainties when comparing one month to another are slightly larger than for the anomalies for a single month, but the shifts over time are still robust.

But think about what happens when we try and estimate the absolute global mean temperature for, say, 2016. The climatology for 1981-2010 is 287.4±0.5K, and the anomaly for 2016 is (from GISTEMP w.r.t. that baseline) 0.56±0.05ºC. So our estimate for the absolute value is (using the first rule shown above) is 287.96±0.502K, and then using the second, that reduces to 288.0±0.5K. The same approach for 2015 gives 287.8±0.5K, and for 2014 it is 287.7±0.5K. All of which appear to be the same within the uncertainty. Thus we lose the ability to judge which year was the warmest if we only look at the absolute numbers.

Now, you might think this is just nit-picking – why not just use a fixed value for the climatology, ignore the uncertainty in that, and give the absolute temperature for a year with the precision of the anomaly? Indeed, that has been done a lot. But remember that for a number that is uncertain, new analyses or better datasets might give a new ’best estimate’ (hopefully within the uncertainties of the previous number) and this has happened a lot for the global mean temperature.

Metaphor alert

Imagine you want to measure how your child is growing (actually anybody’s child will do as long as you ask permission first). A widespread and accurate methodology is to make marks on a doorpost and measure the increments on a yearly basis. I’m not however aware of anyone taking into account the approximate height above sea level of the floor when making that calculation.

Nothing disappears from the internet

Like the proverbial elephant, the internet never forgets. And so the world is awash with quotes of absolute global mean temperatures for single years which use different baselines giving wildly oscillating fluctuations as a function of time which are purely a function of the uncertainty of that baseline, not the actual trends. A recent WSJ piece regurgitated many of them, joining the litany of contrarian blog posts which (incorrectly) claim these changes to be of great significance.

One example is sufficient to demonstrate the problem. In 1997, the NOAA state of the climate summary stated that the global average temperature was 62.45ºF (16.92ºC). The page now has a caveat added about the issue of the baseline, but a casual comparison to the statement in 2016 stating that the record-breaking year had a mean temperature of 58.69ºF (14.83ºC) could be mightily confusing. In reality, 2016 was warmer than 1997 by about 0.5ºC!

Some journalists have made the case to me that people don’t understand anomalies, and so they are forced to include the absolute temperatures in their stories. I find that to be a less-than-persuasive argument for putting in unjustifiably accurate statements in the text. The consequences for the journalists may be a slightly easier time from their editor(?), but the consequences for broader scientific communication on the topic are negative and confusing. I doubt very much that this was the intention.


When communicating science, we need to hold ourselves to the same standards as when we publish technical papers. Presenting numbers that are unjustifiably precise is not good practice anywhere and over time will come back to haunt you. So, if you are ever tempted to give or ask for absolute values for global temperatures with the precision of the anomaly, just don’t do it!


  1. P.D. Jones, M. New, D.E. Parker, S. Martin, and I.G. Rigor, "Surface air temperature and its changes over the past 150 years", Reviews of Geophysics, vol. 37, pp. 173-199, 1999.

23 Responses to “Observations, Reanalyses and the Elusive Absolute Global Mean Temperature”

  1. 1
    Nick Stokes kirjoitti:

    ”. I find that to be a less-than-persuasive argument for putting in unjustifiably accurate statements in the text.”
    I find it a poor argument for NOAA putting the absolute average in their State of the Climate report. They explain elsewhere why you shouldn’t, and GISS explains it better and more emphatically. But still someone does it. Grrrrr.

    I see it as essentially a statistical issue. A station average is a sampled estimate of a population (places on earth) mean. Sampling requires great care if the population is inhomogeneous, to get proportions right. Absolute temperatures are very inhomogeneous (altitude, latitude etc), so great care would be required. But we don’t have much freedom to choose. What we can do is subtract climatology. That doesn’t improve freedom to optimise sampling, but it does greatly improve homogeneity, making it less critical.

    I did a sort of ANOVA analysis here to show how subtracting the climatology improved the standard error of the estimate by about a factor of 10. There is a follow-up here.

  2. 2
    Wim Röst kirjoitti:

    Missing: UAH and RSS temperatures

    [Response: Not relevant to global mean surface temperature. – gavin]

  3. 3
    John Ransley kirjoitti:

    Typo, first para under reananlyses:
    ”Since weather forecasts (the “analyses”) have got much better over the years because computers are faster and models are more skillful.”
    Delete ”since”?

    [Response: Yes. Thanks. – gavin]

  4. 4
    dallas kirjoitti:

    So based on the solar constant, current estimates of albedo and TOA energy imbalance, the absolute temperature of the Earth is about normal, but based on a subjective value of ”pre-industrial” Earth has a one degree fever. Plus or minus a half degree or so :)

    [Response: No. Warming since the late 19th C is around 1 ± 0.1ºC. – gavin]

  5. 5
    Eli Rabett kirjoitti:

    Gavin, You make an error common to most physical scientists. If you are talking about the variance of the distribution it remains constant no matter the number of observations . If you are interested in the variance of the mean, in other words how precisely you can believe you know the mean value, that improves as the square root of the number of measurements.

    [Response: This is only true if you are drawing from a random sample. Different reanalyses, like different climate models, are not random, and while ensemble averaging reduces errors, it does not converge to ’truth’ as the number of models is increased. But perhaps I am missing your point? – gavin]

  6. 6
    TTAndy kirjoitti:

    I second what Eli Rabett says. I would also like to say that your claim that ”the estimates of the global mean absolute temperature are not as accurate as the year to year changes” is at the very least counterintuitive.

    If we look at your error propagation section, we have to note that the error formula for the error of X-Y would be the same; even worse, since this is the formula for absolute, nor relative, errors, the relative error of X-Y can be far worse.

    I understand that the anomalies are really used to debias the data, but the way you explain it in this post doesn’t really lead us there. What’s worse, it’s not quite clear from your explanation why exactly ECMWF is a better way to do reanalysis of differences, and, even more, how it manages to combine anomalies specifically so that the aggregate is above (or below) each individual recombination input, as it seemingly contradicts the anomaly recombination approach as a superior one.

  7. 7
    Bob Loblaw kirjoitti:

    Gavin’s response to Eli’s comment sort of relates to my comment about the error propagation equation in the post. That equation is only correct when errors are random – i.e., the covariance between the errors in X and Y is zero. When covariance is not zero, an extra term applies.

    When adding two numbers, a positive covariance makes things worse, while a negative covariance makes things better. When taking a difference (i.e. subtracting), the opposite is true.

    Thus, when there is a systematic bias (not just random variation), creating a positive covariance between the error values, you can calculate differences much more accurately than the uncertainty in individual values. This is why anomalies work better for changes over time – a station’s systematic bias gets subtracted out (to the extent that it is constant).

    [Response: Yes, but in this case we are adding two variables whose uncertainty is independent. There is a stronger case to be made that this matters more when calculating the difference between individual years since the systematic issues in 2015 are basically the same as in 2016, thus the uncertainties there are almost certainly positively covaried, so the formula would overestimate the error in the difference. – gavin]

  8. 8
    Thomas kirjoitti:

    You’re the best gavin. I think it would be ’useful’ to put this out as another Ted talk by you to be easily shared via youtube etc (if time permits)

    re ”Some journalists have made the case to me that people don’t understand anomalies” I get your explanation but what the journos say is still true overall. Isn’t it?

    Part of the problem, imo/ime, is the fact that different baseline years for Anomalies are used throughout climate science, for temps but also other aspects, in different papers on the same topic, and thus show up in news reports in the media – for years. That seems to me to also create ”consequences for broader scientific communication on the topic [being] negative and confusing.” Yes?

    Terms like ”Pre-Industrial” as per the Paris +2C limit included are equally vague and/or confusing for the average wood duck aka Journo Pollie Denialist. :-)

    Even Warming since the late 19th C is around 1 ± 0.1ºC. is a tad non-specific and vague. Is that 1861-1890 mean? 1890 temp or 1881-1900, or 1880-1920?

    So is the term ”is around” equally vague, non-definitive and not specific. Hansen Sato would maybe put it as:

    ”Relative to average temperature for 1880-1920, which we take as an appropriate estimate of “pre-industrial” temperature, 2016 was +1.26°C (~2.3°F) warmer than in the base period.”

    The IPCC says it in other ways as well. It’s variations like this between ”scientists” that denier activists and marketing shills can regularly drive a truck of disinformation through which aggravates the confusion even more, imho.

    As Hansen also notes in that paper ref above … ”The United Nations Framework Convention[v] and Paris Agreement[vi] define goals relative to “preindustrial”, but do not define that period.

    Another example – ”In this graph the base period is switched from our traditional 1951-1980 to 1880-1920 for the reasons given in ”A Better Graph”, but of course we continue to also produce our graphs with the 1951-1980 base period, as shown below.”

    I have seen others using 18th century period as the ”real” Pre-Industrial baseline eg 1750. In saying this, I do understand that different periods and comparisons are being made for scientific reasons, as per the 1 mth, 3 mth, 12 mth and 5 yrs running means on the Hansen page – and that also requires different baselines depending on what is being evaluated.

    I get that, as do others with an eye for detail .. the avg wood duck does not and never will.

    To put it another way Gavin — ”Houston, we still have a problem.”

    Only the climate scientists, orgs bodies like the NASA IPCC AGU and Universities can fix this collectively themselves to minimise subsequent confusion in listeners and minimise distortions by denier quarters. ”How” is something for scientists to advocate for, not me. cheers

  9. 9
    Eli Rabett kirjoitti:

    Gavin, what you wrote was ”Most importantly, this means uncertainties can’t get smaller by adding other uncertain numbers to them (obvious right?).” and what Eli pointed out is that they certainly can if what you are interested in is the uncertainty in the mean. The issue if there is a random component (noise) in the data points. Whether it converges to a true value depends on whether there are systematic variations affecting the whole data set, but given a random component more measurements will converge to a more precise value.

    [Response: Yes of course. I wasn’t thinking of this in my statement, so you are correct – it isn’t generally true. But in this instance, I’m not averaging the same variable multiple times, just adding two different random variables – no division by N, and no decrease in variance as sqrt(N). Thanks though. – gavin]

  10. 10
    Thomas kirjoitti:

    While do not wish to derail the good scientific mathematical discussion here Gavin, I do have another related ’wish request” for the benefit of the avg person and journos understanding. I do get you and all the rest have better things to do with your time though. nevertheless something like the following may be ’useful’ overall and long term.

    RC or others equally qualified to summarise and then continually update this data to a ’consistently comparable standard’ including baseline info.

    – What’s the mean avg growth in global CO2 and CO2e last year and over the prior ~5 years
    – What’s the current global surface temperature anomaly in the last year and in prior ~5 years
    – project that mean avg growth in CO2/CO2e ppm increasing at the same rate for another decade, and then to 2050 and to 2075 (or some other set of years)
    – then using the best available latest GCM/s (pick and stick) for each year or quarter update and calculate the ”likely” global surface temperature anomaly into the out years
    – all things being equal and not assuming any ”fictional” scenarios in any RCPs or Paris accord of some massive shift in projected FF/Cement use until such times as they are a reality and actually operating and actually seen slowing CO2 ppm growth.

    – and if at some time in the future there is a major adjustment to GCMs modelling like plugging in a new science based assumption that x warming will actually/or has triggered negative feedbacks like ASI area/piomass loss, or methane hydrates emissions inott eh atmosphere versus the present GCMs that such changes in the GCMs be noted in these Summary Key data Updates.

    – and that every summary ever done is stored and accessible for comparison with later Updates in a way that the average lay person can ”see” the trend and direction of Temps and key GHG ppm inn the atmosphere

    – one could setup an initial data set that goes back to the year 2000 on the same page so people can see and grasp the changes in ”numbers” …. and that’s it. Is CO2/CO2e increasing or decreasing .. is Avg Mean Temp Anomalies increasing or decreasing – side by side, year by year – and what does that tells us about current BAU in 10 years from now, in 2050 and in 2075… everything else being equal?

    – I think these are numbers that most people could grasp much more easily the plethora of comparison graphs and numbers across different science websites, blogs and IPCC reports.

    – and let the science maths arguments about this ”summary” go one behind closed doors with a separate explanation sheet in detail for the more mathematical/science folks to know about.

    – K.I.S.S. Principle maybe helpful.

    sorry of this is a waste of your time and space here. thx T.

  11. 11
    DrivingBy kirjoitti:

    ”the correlation scale for anomalies is much larger (100’s km) than for absolute temperatures”

    Can someone explain what this means? I don’t have enough of whatever background is involved to know what is being correlated, and what type of (temp?) anomaly is being spoken of.

    [Response: The temperature in Montreal is generally much cooler than in New York, but it turns out that if Montreal has a cooler-than-normal month (a cold anomaly), then so did New York. Similarly, if the month was warmer than normal in NYC, it was likely to be warmer than normal in Montreal. The distance over which these connections are useful is about 1000km, as you can see from looking at a single month’s temperature anomaly pattern. This means that you can safely interpolate the anomalies between stations. This doesn’t work well for features that have a lot more small scale structure (like rainfall, or absolute temperatures, or cloudiness) though. – gavin]

  12. 12
    Pekka Kostamo kirjoitti:

    I believe it is most ineffective that the scientists and their institutions more or less randomly choose their reference periods.

    I asked one of the scientists producing these estimates why the Paris Agreement reference to ”pre-industrial” is not used. His response was that ”it is not the scientist’s role to take position on political matters”.

    ”Pre-industrial” is indeed a political choice, but also a choice that definitely already has been made. It has been aproved by all those 198 government representatives who signed the agreement. Some 135 countries have made it part of their national laws by ratifying the Paris Agreement, and therefore it is part of the base on which they design their climate policy and plans. Moreover, it is in general use in the media world wide.

    The responsible officials can handle the multiple baselines, one can hope. The general public and the politicians maybe not. Votes are counted, from time to time. A single baseline and a single number would probably be more effective.

    The frequently cited IMO/WMO recommended climate computation baseline (i.e. now 1981 – 2010) is basically reset to zero at 10 year intervals. It was designed in 1935 for quite different purposes. Global warming was not a major concern, then.

  13. 13
    Hank Roberts kirjoitti:

    > unjustifiably accurate

    That’s going to confuse the fifth-grade-level reader.

    Are there any clearer words for that sense?
    Perhaps ”unjustifiably exact” or ”unjustifiably precise”?

  14. 14
    Thomas kirjoitti:

    I have another wish — I wish that the Climate Scientists would create a more realistic Charctic and PIOMASS analysis that actually compared the Present with the 1880-1920 Median Baseline for a real ASIE Deviation/Anomaly (as they do for Global Temperature Anomalies)

  15. 15
    t marvell kirjoitti:

    ”One of the most common questions that arises from analyses of the global surface temperature data sets is why they are almost always plotted as anomalies and not as absolute temperatures”
    Well, why do they ask? Can the problems be better addressed?
    I suspect that the complaints are because the anomalies have little meaning when looking at data for any specific year or other time period. So what if the anomaly is the degree change from 1981-2010? When presenting data aimed at the public it is much better to give the change since the beginning of the industrial era, e.g. 1880-1900. I agree with comments 8 and 12.
    Also, I suspect that an important reason why anomalies are used is because it down-plays the difference between the various temperature series. That is, if one series consistently shows more temperature growth than a second series, the difference between the two is parceled between the pre- and post-mean parts of the series. Using 1880-1900 as a base point, the temperature series would depart more in 2017 then using 1981-2010 as the base.
    Using anomalies particularly bothers me because is forces one to think of temperature change as linear, whereas it appears to be exponential. That is, once cannot use logs with anomalies, or calculate percent changes.

  16. 16
    Clive Best kirjoitti:

    Suppose one were to measure the IR emission of Earth from say Neptune, to derive the Earth’s effective Black Body Temperature – Teff.

    1) Would Teff vary during one (earth) year ?
    2) Would Teff have changed at all since 1850 ?

    [Response: You don’t have to go to Neptune, you can just degrade the data from DSCOVR (there is a paper on this either out or in press). You’ll see a diurnal cycle (as a function of the continental configuration) and an annual cycle as a function of the imbalance in hemispheric seasonality. As for long term trends, that depends on the energy imbalance. At equilibrium at 2xCO2, Teff could be smaller or larger depending on the SW cloud feedbacks. Assuming that they are small for the time being, you would initially get a *decrease* in Teff as CO2 levels rose (blocking some IR), and then a gradual increase as the surface equilibriated. Given that we are still in the transient phase, I think you’d see a small decrease that would persist. This can be calculated from GCM output from historical runs though, so if I get time I’ll make a plot. – gavin]

  17. 17
    Mal Adapted kirjoitti:

    gavin, inline to #11:

    it turns out that if Montreal has a cooler-than-normal month (a cold anomaly), then so did New York. Similarly, if the month was warmer than normal in NYC, it was likely to be warmer than normal in Montreal. The distance over which these connections are useful is about 1000km

    This is ’autocorrelation’, amirite?

  18. 18
    Mal Adapted kirjoitti:

    Me, previously:

    This is ‘autocorrelation’, amirite?

    More specifically, is it ’spatial and temporal autocorrelation’?

  19. 19
    Eli Rabett kirjoitti:

    Although Eli has lost the paper and his memory, there were one or more publications which showed that the distance temperatures correlated varied with the season but were always quite a distance. Given modern computing power it might be interesting to include that in the analyses.

  20. 20
    P.Berberich kirjoitti:

    Why do you say absolute temperature when you mean temperature? Temperature and temperature anomaly make sense.

  21. 21
    P. Berberich kirjoitti:

    I think this is not a blog for physicists. The physical quantity is the temperature. You can measure it in K, °C, F or something else. Derived quantities are the relative temperature or the the temperature anomaly. When you make a physical model you have to compare the temperature with the model. In principle, you can also compare anomaly with anomaly. But this is not so accurate.

    [Response: Actually you are wrong. Modeling and predictions of anomalies are more accurate! – gavin]

  22. 22
    P. Berberich kirjoitti:

    Last week I looked for the monthly average temperatures of the Atlantic Ocean NH. Where can I find it?

  23. 23
    Mal Adapted kirjoitti:

    P. Berberich:

    I think this is not a blog for physicists.

    Physicists often say that 8^)! It’s actually a blog for earth scientists. Physics is a foundation of climate science, but climate science does not merely reduce to physics.

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