Temperature Anomalies and ‘Abnormalities’

Why do we use temperature anomalies instead of absolute temperatures even when studying small regions like the UK?

The last post showed that maximum annual ACORN-SAT  temperatures for Australia show little change since 1910, whereas maximum temperature anomalies did indeed show some warming. Here is a plot which summarises all of this.

Figure 1: Comparison of Maximum Temperature indexes for Australia

The top two signals are maximum temperature anomalies a) is based on the monthly highest temperature whereas b) is the monthly average daily maximum temperature. They are similar and show no change before 1990, and an increase thereafter. The bottom signal is the yearly maximum temperature for each station averaged over Australia and shows a fairly constant value of ~ 42C with little if any increase.

I wanted to look more closely into the universal  use of temperature anomalies in Climate Science rather than absolute temperatures.  Anomalies are always based on monthly averages relative to a set of ‘normal’ monthly values. This is intended to remove large seasonal changes, and to avoid strong time dependence caused by changes in spatial sampling. One month is the fundamental unit of time for anomalies. Daily values only contribute to the monthly average, after which they are discarded.  This means that there are some implicit assumptions involved in the use of anomalies.

  1. The basic time interval is fixed at one month. The anomaly for one station is the delta between the average value for the current month against its 30 year average for that particular month. The 30 year average  value is said to be the ‘normal’ expected value for that station and for that month.
  2. The  global monthly temperature anomaly is the area weighted average of all stations active for that month AND which have normals defined within the selected 30-year period.  The global annual temperature anomaly is simply the 12 month average of the monthly global anomaly values.
  3. Seasons are assumed not to vary long term as otherwise this would change the monthly normals, even if the annual average temperature for a station did not change.
  4. There is an underlying assumption that  global warming is the same over large regions of the planet and that all  stations within those regions warm in synchrony. Stations which have no readings during the 30 year interval are still often combined with nearby stations to form merged ‘hybrid’ stations, or else used to ‘homogenise’ nearby station trends. If the underlying assumption of region wide warming is not the true,  then homogenisation of near neighbours via pair-wise adjustments is simply wrong. Despite this, the end result of such homogenisation adjustments will always produce an apparent region wide warming, independent of whether there is any  underlying evidence for it.

Figure 2 shows a comparison between the temperature anomalies for all 1800 stations across Australia before homogenisation and that calculated from ACORN-SAT values after homogenisation.

Figure 2: Raw Max temperature anomalies(a)  compared to ACORN-SAT Max temperature anomalies (b). The difference between the two is plotted in (c)

Figure 2C shows that the homogenisation process itself has generated an extra ~0.6C increase in maximum temperatures across Australia.

Surprisingly enough it is not just observations of global warming that are always based on anomalies instead of absolute temperatures. Climate models too have difficulty in re-producing absolute temperatures correctly. One would imagine that models must balance energy between incoming solar and outgoing IR, and that this alone would constrain the global absolute average temperature. However all models disagree on exactly what that global temperature should be, and as a result they too rely on using anomalies to make useful predictions.

Figure 3. Model results on absolute temperatures from Ed Hawkins & Rowan Sutton

In the past Models have always had difficulty in achieving a net energy balance at the top of the atmosphere, and so  had to impose it arbitrarily. I suspect this current disagreement in absolute temperatures is related to this underlying problem.

Comparisons of model ‘projections’ to observed global warming are only valid under the implicit assumptions which underpin the use of temperature anomalies both by models and by measurements. In fact we might as well call this dual combination as a comparison of temperature ‘abnormalities’ !

Temperature Extremes

Finally I have calculated all the extreme temperatures ever recorded in Australia. These are the highest temperature in each year recorded at any ACORN-SAT station. The results are shown in Figure 4 and  are quite interesting.

Figure 4: Highest recorded temperatures in ACORN-SAT. Note the plateau after 2000.

The three extreme temperatures that exceeded 50C occurred  before 1985, and there is no evidence of any long term increase. However, there is a plateau after 2000 with all but 2 consequent years above 48C, but this is  also associated with much lower inter-annual variability. This does not look right to my eye, so I suspect this could be due to homogenisation adjustments.

A full list of all temperature extremes can be seen here. These are the hottest towns in Australia and probably best to avoid in the heart of summer !

This entry was posted in AGW, Australia, Climate Change, climate science and tagged . Bookmark the permalink.

21 Responses to Temperature Anomalies and ‘Abnormalities’

  1. Ron Graf says:

    Clive, you say: “If the underlying assumption of region wide warming is not the true, then homogenisation of near neighbours via pair-wise adjustments is simply wrong. Despite this, the end result of such homogenisation adjustments will always produce an apparent region wide warming, independent of whether there is any underlying evidence for it.”

    I now see what you meant by “pairwise homogenisation produces warming.” But I don’t understand how the stations that do not have a 30-year baseline, that are nonetheless being weighted due to their influence on the stations that do have the 30-year baseline, are systematically warmer. Why wouldn’t their influence be random?

    • Clive Best says:

      Those ‘stations’ that either start after 1990 or end before 1960 have no normals, but can still get combined to those that do in order to form one continuous station. The effect of this is then to adjust the longer time series. I am Italy at the moment so the only example I can find off hand is Dubbo.

      but there are others, including Sydney !

  2. Ron Graf says:

    It is striking how much difference there is in the trend of maximum temperatures depending on the station set or how it is processed. Hopefully, we can get to the bottom of why that is so.

  3. Lou Maytrees says:

    Just a comment from the peanut gallery. Your first group of 3 graphs show since 1910 – a) +1.4*C, b) +1.6*C and c) +1.3*C. So claiming Annual average maximum extremes is somehow different seems incorrect. And how you conclude that there is little change since 1910 is hard to fathom. Your graph shows at least a +1.3*C change.

    • Clive Best says:

      Sorry – Yes that is right . What I meant to say was that the average maximum temperature (C) showed little change. The curves are simply a 10 year FFT smooth on the data so if you read off these curves, then yes what you say appears to be true. However statistically there is no real change occurring before about 1985. Thereafter a) and b) show warming whereas c) doesn’t.

      Perhaps I shouldn’t have plotted those curves on top or maybe I am being a little too skeptical. I should really do a fit and then check the error on the parameters.

      • Lou Maytrees says:

        So according to those charts this means that since 1985 low temperature minimums are rising higher 3-4 times as fast as high temp maximums in Australia? That does not sound good to a layman.

  4. Nick Stokes says:

    point 4 is a muddle. Homogenisation is not related to anomaly formation. But it is also wrong. Homogenisation does not assume synchronous warming, or indeed anything about warming. There is a persistent belief that homogenisation forces stations to follow a sort of consensus trend, but this is not so. What it does is to try to identify discontinuities which might be a result of a non-climate event, such as a station move. Where there is a suspect, nearby stations are consulted to see if they also show a change, which would suggest the jump is real.

    If the jump is deemed to be artificial, it is corrected, primarily from within the series. The identified jump is undone. There might be a role for neighboring information in determining the correction, but it would be marginal.

    On anomalies, the primary reason why they are essential is to make the dataset more homogeneous (not related to the other homogenisation). Homogeneous means, as best possible, appearing to come from one distribution. You can get an average of an inhomogeneous set, but careful sampling is critical. As homogeneity increases, it is less critical. For temperature this is very important, because there is little scope to improve sampling.

    If you want to poll a population, there are several factors for inhomogeneity. On some issues, men and women have markedly different opinions. So it is very important to have the right proportions of both in a sample. This extends to subsets – if you want to make an inference about say rural/urban, you need to make sure it is not confounded with a sex bias.

    Subtracting some normal is a simple step toward removing one inhomogeneity – different means. You no longer have to worry so much about whether you have too many upland stations etc. And you don’t get spurious variations when a mountain location fails to report.

    Your point 3 about possible drift in normal has some validity. But it is much better to subtract a not quite right mean estimate than none at all.

    On the 30 year thing, I have long recommended the least squares approach that TempLS and BEST use, which fixes this issue.

    • Clive Best says:


      My wording was not very good. The traditional method of calculating normals (NOAA, CRU) needs stations which have coverage in the 30 year period. Therefore stations with smaller temporal range are excluded, and since BOM also use the same 1961-1990 normalisation period, they must do the same.

      You and Berkeley can include shorter time periods because you are using a least square fit that implicitly assumes that temperature is a continuous function of space and time. But is this not in itself some type of homogenisation?

      What I have observed though in ACORN-SAT is that if a station moves from say a post office to an airport then the corrections are not simple offsets, but instead actually change underlying trends. For example if you look above at the comment which shows Dubbo (now updated) you will see how homogenisation goes beyond that of simply aligning two overlapping time series by an offset. The earlier data pivots downwards about the join mark thereby producing a linear warming trend.

      Here is another example – Cairns.

      If you look carefully you can clearly see how trend adjustments extend from the join both into the future as well as the past.

      Can you justify that ?

      • Nick Stokes says:

        Here from here is a NOAA plot of their adjustments to Dubbo (adjusted-unadjusted)

        It’s unusual in that the adjustments are small and frequent, but they are discrete jumps. Now ACORN may do something different, but NOAA is the home of the pairwise algorithm.

        On the least squares model, there is no requirement for continuity of the global average. It is true that the method is designed to ensure that a trend, if present, will be found in the globally varying part rather than the averages. But it doesn’t assume that anything is continuous.

        • Clive Best says:

          The uncorrected GHCN data is after the component pieces have been spliced together. So for Dubbo that is the post office and the airport. In addition GHCN only contains monthly averages and no daily values.

          It is also strange that GHCN seems to have deleted two short sections of anomalies a) between 1914-1918 (1st world war !) and b) 1980-1984. I have seen this happen also in other GHCN stations. It looks like if a spike looks spurious and there is no nearby station which can correct it – they simply delete it.

      • Clive Best says:

        There is something I don’t understand. If you use the GISS station finder for Dubbo.


        Then you find nearby stations of Wellington, Gilgandra etc. which presumably are used in the adjustments of Dubbo and vice versa. However, none of these stations exist in the full set of BOM raw data for daily Maximum and Minimum. Where does GHCN get this data from ?

  5. Bryce Payne says:

    Ah, what a tangled web we weave…the untangling of which I will leave for those with time for more intense involvement except to say that summary necessarily reduces the amount of information available and, therefore, necessarily generates output that contains artifacts. It should be noted that one person’s artifact may be another person’s fact. Most summary methods are accurate and reliable to the extent the summary method used is appropriate to the data and objective at hand. There seems to be some lack of clarity among the various parties as to what, exactly, the appropriate data set is and the objective are.

    Clive, in that regard I do wonder about your last paragraph, which seems the clearest set of data you present (the only raw data?). If I am interpreting the data you present in the plot (and paragraph) correctly, then there is a single raw (absolute) data point for each year on the x-axis (one raw absolute maximum temperature at a single station on a single day in the given year, “the highest temperature in each year recorded at any ACORN-SAT station”) . If my interpretation is correct, then I have a question, a suggestion and a comment.

    Question: If the plotted data are raw, why would homogenization have any effect on this data, e.g., an effect on raw data at all or such that an absence of highest temperature >50deg C spikes after 2000 would appear?

    Suggestion: I would suggest re-plotting as a scatter plot instead of a line plot as there are no reasonable, direct relationships (“connections”) between any two adjacent points.

    Comment: To my eye, your plot seems both reasonable (including the post-2000 lack of “spikes”) and to indicate a warming trend in annual absolute highest temperature. To a degree (pardon the pun), this plot (if it is of the raw absolute highest temperature anywhere in Australia for each of the indicated years) speaks to the signal in raw data vs. summarized/homogenized/fitted data. The presumption should be that the highest absolute temperature occurring anywhere in Australia in a given year is within all reasonable practical limits independent of the same temperature in the year before, or after, or any other year. Further, there may, likely are, a limited number of stations where absolute highest temperatures occur, but, unless there is a time pattern among those stations, it does not alter the reasonable presumption of randomness. It, therefore, follows that if (by my quick count from the plot) 69 of the 90 (or 77% of) years prior to 2000 had absolute highest temperatures below 48deg C, but only 2 of 17 (12%) of years after 2000, a warming trend is indicated. I suspect that an appropriate fit/analysis of the 1910-2017 data set would say the same thing.

    As to the occurrence of no >50deg C spikes after 2000, my reaction is, “So?” It is not difficult (for me at least) to imagine that if there is a general area warming, particularly if it is limited to warmer night time lows as your other look at raw(er) data suggested, achievable absolute highest (daytime) temperatures might actually be lower than under less generally warmed conditions (stability/instability of localized, short-term near-ground thermal circulation patterns).

  6. Ron Graf says:

    Bryce, I understand you to be saying that Clive is taking the highest reading anywhere in Australia for each year. I don’t believe that is what he says. Here is the description for Figure 1.

    The top two signals are maximum temperature anomalies a) is based on the monthly highest temperature whereas b) is the monthly average daily maximum temperature. They are similar and show no change before 1990, and an increase thereafter. The bottom signal is the yearly maximum temperature for each station averaged over Australia and shows a fairly constant value of ~ 42C with little if any increase. [my bolds]

    In a prior post, “Australian extreme temperatures are falling,” I believe Clive is using the same plot for C as found in C in Figure 1 in the post above.

    Area averages of annual a) Maximum, b) Minimum temperatures and c) Extreme temperature ranges for all 1800 stations in Australia (far-flung islands excluded)

    This takeaway I find from Figure one is that extremes highs temperatures for the year are not increasing but daily Tmax is. But daily Tmax is not increasing as much as daily Tmin.

  7. A C Osborn says:

    The plateau at the end of the Maximum temp data is most likely caused by the use of Electronic Instruments rather than Alcohol or Mercury thermometers.

    • Clive Best says:

      Yes that may the solution !

      “Since 1 November 1996, the PRT temperatures from AWS were deemed the primary SAT measurement”

      PRT = platinum-resistance digital thermometers
      AWS = automated weather stations

    • Nick Stokes says:

      For my part, I think simple automation is the answer. The problem in searching the country for the highest temperature in each year is that you are very likely to pick up bad radings. The proposition that the hottest temperature ever in Australia was in Albany is pretty unbelievable. Albany faces the Southern Ocean in the far south of Western Australia. It’s where you would go to get away from the heat.

      • Clive Best says:

        Albany is definitely wrong. It appears just once in the list -1933 ! However, all the others look correct and appear multiple times in the list.


        Tar cola and Marble Bar look like places to avoid in January – wherever they may be!

      • paulski0 says:

        That day in Albany doesn’t seem to appear at all in GHCN-D, and there are no other days even above 40C. Perhaps removed in a basic QC check? Or the ACORN-SAT number is a transcription error?

        For the second warmest, Oodnadatta, the daily record from GHCN-D looks like ” rel=”nofollow”>this. You can see this warmest day in the blip at the start of 1960. Here’s the ” rel=”nofollow”>record for warmest January (the warmest month of the year here) days each year in Oodnadatta. 1960 is an unrepresentative blip and the trend is towards warmer January maxima.

        • Clive Best says:


          You’re right Albany is clearly a spurious measurement and should be discounted.

          Oondnadtta actually has two stations – the airport itself and the town which partially covers that 10y gap. The annual temperature anomalies do indeed show a linear rise since 1940 of ~ 1C.

          The problem with record maximum temperatures is the uncertainty with changes in instrumentation. The post 2000 readings are automated.

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