By Nick Stokes,
There is much criticism here of the estimates of global surface temperature anomaly provided by the majors – GISS, NOAA and HADCRUT. I try to answer these specifically, but also point out that the source data is readily available, and it is not too difficult to do your own calculation. I point out that I do this monthly, and have done for about eight years. My latest, for October, is here (it got warmer).
Last time CharlesTM was kind enough to suggest that I submit a post, I described how Australian data made its way, visible at all stages, from the 30-minute readings (reported with about 5 min delay) to the collection point as a CLIMAT form, from where it goes unchanged into GHCN unadjusted (qcu). You can see the world’s CLIMAT forms here; countries vary as to how they report the intermediate steps, but almost all the data comes from AWS, and is reported at the time soon after recording. So GHCN unadjusted, which is one of the data sources I use, can be verified. The other, ERSST v5, is not so easy, but there is a lot of its provenance available.
My calculation is based on GHCN unadjusted. That isn’t because I think the adjustments are unjustified, but rather because I find adjustment makes little difference, and I think it is useful to show that.
I’ll describe the methods and results, but firstly I should address that much-argued question of why use anomalies.
Anomalies
Anomalies are made by subtracting some expected value from the individual station readings, prior to any spatial averaging. That is an essential point of order. The calculation of a global average is inevitably an exercise in sampling, as is virtually any continuum study in science. You can only measure at a finite number of places. Reliable sampling is very much related to homogeneity. You don’t have to worry about sampling accuracy in coin tosses; they are homogeneous. But if you want to sample voting intentions in a group with men, women, country and city folk etc, you have inhomogeneity and have to be careful that the sample reflects the distribution.
Global temperature is very inhomogeneous – arctic, tropic, mountains etc. To average it you would have to make sure of getting the right proportions of each, and you don’t actually have much control of the sampling process. But fortunately, anomalies are much more homogeneous. If it is warmer than usual, it tends to be warm high and low.
I’ll illustrate with a crude calculation. Suppose we want the average land temperature for April 1988, and we do it just by simple averaging of GHCN V3 stations – no area weighting. The crudity doesn’t matter for the example; the difference with anomaly would be similar in better methods.
I’ll do this calculation with 1000 different samples, both for temperature and anomaly. 4759 GHCN stations reported that month. To get the subsamples, I draw 4759 random numbers between 0 and 1 and choose the stations for which the number is >0.5. For anomalies, I subtract for each place the average for April between 1951 and 1980.
The result for temperature is an average sample mean of 12.53°C and a standard deviation of those 1000 means of 0.13°C. These numbers vary slightly with the random choices.
But if I do the same with the anomalies, I get a mean of 0.33°C (a warm month), and a sd of 0.019 °C. The sd for temperature was about seven times greater. I’ll illustrate this with a histogram, in which I have subtracted the means of both temperature and anomaly so they can be superimposed:
The big contributor to the uncertainty of the average temperature is the sampling error of the climatologies (normals), ie how often we chose a surplus of normally hot or cold places. It is large because these can vary by tens of degrees. But we know that, and don’t need it reinforced. The uncertainty in anomaly relates directly to what we want to know – was it a hotter of cooler month than usual, and how much?
You get this big reduction in uncertainty for any reasonable method of anomaly calculation. It matters little what base period you use, or even whether you use one at all. But there is a further issue of possible bias when stations report over different periods (see below).
Averaging
Once the anomalies are calculated, they have to be spatially averaged. This is a classic problem of numerical integration, usually solved by forming some approximating function and integrating that. Grid methods form a function that is constant on each cell, equal to the average of the stations in the cell. The integral is the sum of products of each cell area by that value. But then there is the problem of cells without data. Hadcrut, for example, just leaves them out, which sounds like a conservative thing to do. But it isn’t good. It has the effect of assigning to each empty cell the global average of cells with data, and some times that is clearly wrong, as when such a cell is surrounded with other cells in a different range. This was the basis of the improvement by Cowtan and Way, in which they used estimates derived from kriging. In fact any method that produced an estimate consistent with nearby values has to be better than using a global average.
There are other and better ways. In finite elements a standard way would be to create a mesh with nodes at the stations, and use shape functions (probably piecewise linear). That is my preferred method. Clive Best, who has written articles at WUWT is another enthusiast. Another method I use is a kind of Fourier analysis by fitting spherical harmonics. These, and my own variant of infilled grid, all give results in close agreement with each other; simple gridding is not as close, although overall the method often tracks NOAA and HADCRUT quite closely.
Unbiased anomaly formation.
I described the benefits of using anomalies in terms of reduction of sampling error, which just about any method will reflect. But there is care needed to avoid biasing the trend. Just using the average over the period of each station’s history is not good enough, as I showed here. I used the station reporting history of each GHCN station, but imagined that they each returned the same, regularly rising (1°C/century) temperature. Identical for each station, so just averaging the absolute temperature would be exactly right. But if you use anomalies, you get a lower trend, about 0.52°C/century. It is this kind of bias that causes the majors to use a fixed time base, like 1951-1980 (GISS). That does fix the problem, but then there is the problem of stations with not enough data in that period. There are ways around that, but it is pesky, and HADCRUT just excludes such stations, which is a loss.
I showed the proper remedy with that example. If you calculate the incorrect global average, and then subtract it (and add later) and try again, you get a result with a smaller error. That is because the basic cause of error is that the global trend is bleeding into the anomalies, and if you remove it, that effect is reduced. If you iterate that, then within six or so steps, the anomaly is back close to the exactly correct value. Now that is a roundabout way of solving that artificial problem, but it works for the real one too.
It is equivalent to least squares fitting, which was discussed eight years ago by Tamino, and followed up by Romanm. They proposed it just for single cells, but it seemed to me the way to go with the whole average, as I described here. It can be seen as fitting a statistical model
T(S,m,y) = G(y) + L(S,m) +ε(S,m,y)
where T is the temperature, S,m,y indicate dependence on station, month and year, so G is the global anomaly, L the station offsets, and ε the random remainder, corresponding to the residuals. Later I allowed G to vary monthly as well. This scheme was later used by BEST.
TempLS
So those are the ingredients of the program TempLS (details summarized here) which I have run almost every night since then, when GHCN Monthly comes out with an update. I typically post on about 10th of the month for the previous month’s results (October 2018 is here, it was warm). But I keep a running report here, starting about the 3rd, when the ERSST results come in. When GISS comes out, usually about the 17th, I post a comparison. I make a map using a spherical harmonics fit, with the same levels and colors as GISS. Here is the map for October:
The comparison with GISS for September is here. I also keep a more detailed updated Google Earth-style map of monthly anomalies here.
Clive Best is now doing a regular similar analysis, using CRUTEM3 and HADSST3 instead of my GHCN and ERSST V5. We get very similar results. The following plot shows TempLS along with other measures over the last four years, set to a common anomaly base of 1981-2010. You can see that the satellite measures tend to be outliers (UAH below, RSS above, but less so). The surface measures, including TempLS, are pretty close. You can check other measures and time intervals here.
The R code for TempLS is set out and described in detail in three posts ending here. There is an overview here. You can get links to past monthly reports from the index here; the lilac button TempLS Monthly will bring it up. The next button shows the GISS comparisons that follow.
Nick,
When you start with CLIMAT or ERSST, you cannot deduce much about accuracy, because there have already been mistakes made before then.
Whereas you claim that most stations from Australia use Automatic Weather Station data, AWS, there are errors in that also. Witness our year-old discovery that BOM were setting a cold minimum temperature and witness the debate – far from resolved – about why BOM use recording times for AWS temperatures that do not comply with international standards, like the use of a 1-second integration. But these errors might be small compared with what is perhaps the largest source of error in the methodology now used, namely the selection of which stations will go into the CLIMAT files. You are familiar with past assertions that historically, if you use stations from cold places, then drop them in favour of stations in hotter places, you will change the apparent warmth of the record, its trend and so on down the road to poor data. I have not seen a refutation of the claims that this dropping of stations has been answered. It is likely the cause of the difference between the oft-quoted early Hansen graph showing a big temperature dip roughly 1945-75, compared with the latest reconstructions from which the dip has been disappeared.
Even more fundamentally, in the case of the dog that did not bark, I have for a year now been repeatedly asking your BOM for a figures or figures that the BOM use to express total uncertainty in temperature data. I have asked, inter alia, if you say that a new temperature sets a new record, how much different from the former record-holder has it to be, to be statistically significantly different. The answer, after about 5 emails, has been … crickets.
(Of course I am not suggesting that you, Nick, are responsible for BOM conduct, but a neutral acientist should be aware of it and calling out problems from their beginnings.)
Can I suggest to you that an analysis of uncertainty about numbers, such as you are presenting here, has little meaning unless you include expression of the fundamental uncertainty in the numbers? When I write uncertainty, I mean primarily the old saws of accuracy and precision as taught to science students for the 50 years before 2000, at least to my poor understanding of what is lately taught about this fundamental concept. See the Nic Lewis comments about the Resplandy et al ocean heat paper. The error they made, overall, was to neglect formal error analysis (or to do it poorly). So I suggest that your contribution here might benefit from formality also.
Later, I have more to say about how and why standard deviations change in the ways you illustrate, plus how incorrect it is to assert that by using the anomaly method you are increasing the quality of the data you are tormenting. Later.
Cheers Geoff.
Nick,
There are dozens more comments I could make about your essay, but I shall be selective.
Here is one. You write ” For anomalies, I subtract for each place the average for April between 1951 and 1980.”
That procedure is only valid if the factors that cause variation in the 1951-80 period are the same as those for the rest of the series. To me, that is a hard test to pass. It would be wrong to assume that all was well.
Geoff.
Testing 1,2, 3
Dear Mod or Moderator,
I’ve tried my comment on the test page and it went up but I can’t seem to paste the same comment here. I’ve tried twice, shall I try again?
cheers,
Scott
Nick, first, thanks for your contribution. Most interesting.
Next, a question. You say:
My question relates to something that I rarely see addressed—the uncertainty of the anomalies. The problem, which you haven’t addressed in your comments, is that people generally do NOT carry the uncertainty through the procedure of calculating any given anomaly.
In that procedure, you calculate the mean value for each month, and subtract that month’s mean value from all of the records for that month.
However, what is NOT generally carried forward is the standard error of the mean value for the month. For example, you have not included this error in your calculations described above.
Comments?
w.
This is the heart of the problem of attempting to calculate global temperature.
Essentially two important differences are conflated and then glossed over.
Spatial sampling is a three dimensional problem, while anomalies may deal – nominally (per-say!) – with altitude issues, they don’t deal with directionality, or more accurately, the symmetry of the two dimensional temperature distribution.
It is assumed that because anomalies are used, the temporal correlation between any two points will have the same spatial scale in any direction. However, spatial anisotropy in the coherence of climate variations has been well documented and it is an established fact that the spatial scale of climate variables varies geographically and depends on the choice of directions. (Chen, D. et al.2016).
The point I am making here is completely uncontroversial and well know in the literature.
What Nick and all climate data apologists are glossing over is that despite the ubiquity of spatial averaging, its application – the way it is applied particularly – is inappropriate because it assumes spatial coherence. But climate data has long been know to be incoherent across changing topography. (Hendrick & Comer 1970).
In layman’s terms (Although I am a layman!) station records are aggregated over a grid box assuming that the fall-off or change in correlation between different stations is constant. So conventionally, you would imagine a point on the map for your station and a circle (or square) area around it overlapping other stations or the grid box border. However, in reality this “areal” area is actually much more likely to be elongated, forming an ellipse or rectangle stretched in one direction – commonly and topographical north/south in Australia.
But it is actually worse than this in reality because unless the landscape is completely flat, coherence will not be uniform. And that is an understatement because to calculate correlation decay correctly, spatial variability actually has to be mapped in and from the real world.
Unfortunately, directionality would be a very useful factor in the accurate determination of UHI effects, due to the dominant north/south sprawl of urban settlement. Coincidentally, all weather moves from west to east and associated fronts with their troughs and ridges typically align roughly north/south.
The other consequence of areal averaging is that it is a case of the classical ecological fallacy, in that conclusions about individual sites are incorrectly assumed to have the same properties as the average of a group of sites. Simpson’s paradox – confusion between the group average and total average – is one of the four most common statistical ecological fallacies. If you have the patience, it is well worth making your own tiny dataset on paper and working through this paradox as it is mind blowing to apprehend!
What I believe this all means is that the temperature record is dominated by smearing generally and a latitudinal smearing i.e east/west particularly. And this means for Australia and probably the US as well, that the UHI effect of north/south coastal urban sprawl is tainting the record.
Either way, if real changes in climate are actually happening locally, then this local affect will be smeared into a global trend – by the current practice – despite or in lieu of any real global effect.
So, yes I do think the globe has warmed since the LIA or at least the last glaciation but I don’t believe it is or can be detected in any of the global climate data products.
The focus on temperature as the single variable of interest has a fatal flaw, that being the poor quality of the instrumentation and particularly the siting. We know from Anthony’s crowd survey that the fraction of stations meeting all the criteria for accurate measurement of temperature is on the order of 2%, as I recall. Stations that meet most of the criteria bring us up to 11 or 12%. Most stations were not designed to measure temperature as a climate variable. They are in airports to help pilots and flight controllers.
The only system that was designed to measure temperature as a climate variable is the USCRN, with triplicate measurements using best equipment. But that is only about a dozen (?) years old and only in the US at 2% of the global surface area. So global land-based temperatures do not meet basic scientific criteria.
This leaves satellites, but RSS and UAH have made different choices about which satellite instruments they trust, and thus we have RSS 4.0 trends about 50% higher than UAH v6.
I conclude that temperature is not a useful variable. Energy would perhaps be better, but I don’t think we have a proper handle on the total energy leaving the earth. But suppose we can measure energy in and energy out with some accuracy. Then we might say that if energy in is greater than energy out we are warming. However, to get good mixing in the ocean might require 1000 years, so it would not necessarily be true that an imbalance in energy over periods of a year or a decade or even a century can give us a picture of the actual trend.
This leaves models based on physical mechanisms. But we know the model resolution is far below what is needed to deal with, say, thunderstorms. See Christopher Essex on that. Not to mention the overestimation problem that has become evident in recent years, even to the IPCC.
Maybe a few extra centuries of observations would give us a better picture of where we are going, or maybe we would just find that we are in a chaotic process and can’t really predict anything at all.
1. If the adjustments make little difference, why is there so much time, effort and money spent on them? The people doing so seem to think it makes a significant difference…
2. You claim the difference is small, but in a narrative where a few tenths of a degree over a century supposedly spells catastrophe, a little difference isn’t so little.
3. That the SD of the anomalies gives you a smaller number than the SD of the temps not relevant. What is relevant is which gives a better measure of what the change in the energy balance of the earth is. After all, is that not what we’re trying to understand? Is the rise in CO2 is causing a change in energy balance purported to be 3.7 w/m2 per doubling of CO2 plus feedbacks? If that is the goal, then both temps and anomalies are not fit for purpose because w/m2 varies with T^4, so an anomaly of 1 degree at -40 C has a completely different value than an anomaly of 1 degree at +40 C.
Two quotes from the essay:
…I find adjustment makes little difference…
And:
I used the station reporting history of each GHCN station, but imagined that they each returned the same, regularly rising (1°C/century) temperature. Identical for each station, so just averaging the absolute temperature would be exactly right. But if you use anomalies, you get a lower trend, about 0.52°C/century. It is this kind of bias that causes the majors to use a fixed time base, like 1951-1980 (GISS).
Over time the adjustments made to existing data (maybe that isn’t what the essay was talking about) do make a difference.
This graph
compares the change to the trend due to adjustments/corrections made to the data since 1997 and shows that the 1950-1997 trend depicted as it was in 1997 was 0.75°C/century and by 2018 that adjustments have increased that 1950-1997 trend to 1°C/century.
This graph
shows the distribution of positive and negative adjustments over the period 2002-2018. One can’t but notice that all adjustments (Annual average) to data since 1970 are positive. (Why is that?)
Links to data used in the above graphs:
1997
2002
Current
Anomalies are a good and valid method of comparing changes to “What it was then to what it is now.” However, changing the anomalies as reported decades ago doesn’t make a lot of sense. Every month GISS changes monthly entries on their Land Ocean Temperature Index including those that are over 100 years old. The results of that over time finally affect the overall trend as shown in the graphs linked above.
Nick Stokes, thank you for your essay.
davidmhoffer
It’s a fair question, but the fact is that it really does make very little difference to the overall trend. Anyone can check this for themselves, as Nick and others have been saying for years.
This really answers your first question. They have to be as meticulous as possible, given the possible policy implications and consequent scrutiny they are under. Ironically, the care taken to get it things as close to ‘right’ as possible has left the scientists open to allegations of malicious tampering.
Re 3: surely a change in temperature is a reflection of a change in energy balance in any system? This is true whether you’re measuring the temperature (which is just a measure of the rate at which the molecules jiggle) of water in a warming pot or the temperature of air in the atmosphere. If the temperature is rising or falling in any system over the long term, then it’s a fair sign that the energy balance of that is changing.
The need to give a value to anomaly comes about because you are UNABLE to offer an an accurate and precise measurements of that you are claiming to represent .
Its is a sign of weakness at a rather basic level in your data collection method and not a indication of ‘settled science ‘
The same for many proxies , where you can throw has much statics at it as you like , but the bottom line remains that they used because ‘they are better than nothing’ which is the alterative , not because the data is valid and of high quality .
Nick
You cannot get a correct weighting of stations unless ALL [terra] stations surveyed are balancing out together to zero latitude. Since most of your stations are all in the NH you get a totally incorrect result.
I did this balancing act with my data sets and find that the earth is in fact cooling, not warming.
{you can click on my name to read my final report]
Why do NOAA USCRN readings arrive so late. It’s now 15 November but they still only have readings up to September. They are lagging over 6 weeks behind. I thought these readings were automatically collected.
I have a problem with the period you use as reference for the anomaly 1951-1980.
It was during a period when the climate was cooling .
In the mid of the period some even asked how to avoid the coming ice age.
How looks a map with the anomaly compared to the period 1921-1950?
I think Nick’s careful and patient contribution is very worthwhile reading as are the many thoughtful responses. Stepping back, what I see is that there remain real worries about the vast exaggerations of immediate dooms with which we have now been threatened for nearly forty years and yet these have not only failed to materialise but we have seen positive benefits from the small and gradual temperature increases.
Worse, the hysterical claims have led to an outrageous misuse of world resources which should have been used to tackle much more pressing health and poverty issues. They are also been used to drive the most regressive tax policies against poor people worldwide along with disastrous and harmful energy policies.
Of course none of this in Nick’s fault, nor that of anyone who is prepared to genuinely debate on a reasoned basis the possibility that our industrial processes are potentially going to cause a big problem. But like several contributors I still see the causation link or mechanism that is driving CO2 alarmism as tenuous at best, especially as the latest estimates of CO2 sensitivity are getting lower and lower outside of the echo chamber that is the IPCC.
Hi Nick!
I think it is ok to assume that if there is UHI affects in the GHCN record those are introduced gradually and smaller before 1950 than 1980. A majority of the older station set is depending on infills for a common baseline period. If we infill with data from a period that is artificially warmer we will amplify this error. Since the baseline average is pushed higher our historical anomaly will show cooler than it actually was. UHI is one example average latitude is another that impacts in the same direction.
Wouldn’t setting a stations “anomaly base” at first overlapping years with neighbours in same or close by grid cells be less biased?
Like others, Nick, my response is so what? Nobody’s denying the earth is warming. It’s the cause that matters and there, I’m afraid, I’ve never seen any conclusive evidence that it’s Carbon-related. Anyone who does any form of statistical modelling will be very aware of the problems created by numerous variables, to say nothing of the complexities involved with climate.
So, my question is how do you go from this to the conclusion that trillions need to be spent to reduce carbon emissions? Big decisions require big proof and that, I’m afraid, doesn’t exist when it comes to what, exactly, is driving warming.
The real question is: do we even want a global temperature.? A more meaningful metric would be a temperature for each continent, and for each season, so we know what is happening to us, and to our regional environment.
R
I am always impressed by Mr. Stokes erudition and his willingness to post on WUWT.
Looking at his histogram (but without doing the necessary calculations) it appears that the blue and red distributions differ significantly. Perhaps he could state what distribution he assumes for each when calculating the means and standard deviations and whether he has analysed the distribution of the errors.
I am not happy with averaging or merging data. You throw away a lot of information and probably adulterate good data with bad data. I would like to see the temperature history from a number of well maintained stations scattered about the globe. Time of taking the readings is also very important. From these I could my own conclusions. has anybody published this work?
New research now shows that the creators of the CO2 greenhouse theory forgot quantum mechanics. Oops!
This new study brings in the quantum aspect, using Raman spectroscopy. What they discover is that both oxygen (O2) and nitrogen (N2) in certain quantum states also absorb and emit infrared. As one would expect from common sense. So “CO2 exceptionalism” is false: it is not the main IR interacting gas in the atmosphere. Its IR radiative role is in fact insignificant due to CO2’s low abundance of 0.04%.
http://notrickszone.com/2018/11/12/real-world-spectral-measurements-show-the-greenhouse-theory-is-wrong-all-gases-are-ghgs/
For CAGW this is game over.
Nick – Slightly off topic perhaps, but I’m curious if you can offer an answer.
A few years ago, when gathering some data to make a point, I found an hourly temperature chart for a single day in Denver. The afternoon temperatures dropped 30 F in a single hour. This prompted me to question what polling the temperature of moving air masses from fixed stations actually provides us. Rather than averaging the daily averages of temperature stations to produce a “Global Average temperature”, I want to know how much heat energy is in the atmosphere for a single point in time. This would mean that we’d average all temperature station readings for the exact same time. Some readings would be in day and some would be in night. If possible we could do this hourly such that there are 24 global averages over a single day since the Earth is rotating.
I understand we won’t be able to derive these values from historical records, so we would need to start these new set of records and wouldn’t be able to derive trends for quite some time. However, we’d be more accurately tracking global heat energy, right?
Thanks for the post, Nick. Very enlightening, and the links are great.
@Mosher
mind you
I think the way I did it, by looking at the derivatives of the speed of warming/cooling
you eliminate the need of adjusting for altitude and longitude.
54 stations, 27 each HS was apparently enough.
Click on my name to read my final report.
There is much criticism here of the estimates of global surface temperature anomaly provided by the majors – GISS, NOAA and HADCRUT. I try to answer these specifically, but also point out that the source data is readily available, and it is not too difficult to do your own calculation.
GIGO
Anomalies are made by subtracting some expected value…
GIGO
The End