Spherical Triangulation gives identical results to Cowtan & Way

The Cowtan and Way temperature anomaly based on HadCRUT4.6 for 2017 has been released and it is 0.74C. This is uncannily similar to that calculated by Spherical Triangulation which is 0.73C. In fact both methods give essentially the same results for all  recent years. In my opinion though Spherical Triangulation is by far the cleanest method of deriving global coverage from available data. It avoids any assumptions whatsoever  because it is based purely on geometry.

Comparison of Cowtan & Way with hadCRUT4.6 and Spherical Triangulation.

Here are the actual values from both methods for comparison.

C&W S-Tri
1990 0.30 0.31
1991 0.29 0.30
1992 0.09 0.10
1993 0.14 0.14
1994 0.20 0.21
1995 0.33 0.34
1996 0.23 0.24
1997 0.38 0.39
1998 0.53 0.54
1999 0.29 0.29
2000 0.30 0.30
2001 0.45 0.46
2002 0.52 0.53
2003 0.52 0.52
2004 0.44 0.44
2005 0.58 0.60
2006 0.54 0.54
2007 0.56 0.58
2008 0.43 0.43
2009 0.55 0.56
2010 0.63 0.63
2011 0.49 0.50
2012 0.52 0.51
2013 0.55 0.57
2014 0.62 0.62
2015 0.76 0.75
2016 0.87 0.87
2017 0.74 0.73

The annual data can be downloaded :


and global monthly data



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20 Responses to Spherical Triangulation gives identical results to Cowtan & Way

  1. Ron Graf says:

    I would think the Kevin Cowtan and Robert Way might owe you a Cherry Coke. At the same time clearly your spherical triangulation seems for systematic and auditable and thus a preferred method from a scientific standpoint.

    Perhaps you could use this tool to evaluate Island stations to their proximate SST triangles to see if there is systematic bias in their trends, and if the trends correlate to degree of marine influence or show evidence of non-climate effects. This investigation would be a corollary to the recent Cowtan, Hausfather paper.

    • Clive Best says:

      Hi Ron,

      Yes I forgot that I promised to look at Islands and coastlines. I shall try to look into it!

      • Ron Graf says:

        Clive, thank you in advance for taking on my project for which I do not have the needed skills to adequately conduct myself.

        My targeted hypothesis is that the degree of marine character of island and coastal stations should be able to be diagnosed and classified based on the several variables that trend based upon the marine versus inland climate character. Since there are several independent variables making up the character the grade of each can be used to plot against the others to determine the precision of each and of the ensemble as a whole. If trend in temperature anomaly stands out of the pack that would indicate its bias from non-climate effects.


        1) Diurnal temperature range for it’s latitude.

        2) Seasonal temperature range for latitude.

        3) Diurnal temperature response – temperature’s mean peak and trough hour for it’s given day of the year at its latitude.

        4) Seasonal temperature response – temperature’s mean peak and trough day of the year for giving latitude.

        5) Transient climate response — The annual temperature anomaly trend for a given latitude. Since the ocean has higher heat capacity than land it should be the slowest to respond to a radiative imbalance caused by enhanced greenhouse effect.

        If number 5 does not follow the same plot trends as the others then it indicates non-climate effects since SST measurements cannot be affected by micro-climate inducements.

        Clive, obviously I appreciate anything you do so feel free to chop this any way you see most practical. Do you differ with any of my assertions here? Would you add any variable you think are easier to diagnose?

        As we’ve discussed prior, radiative effects from EGHE should also affect diurnal temperature range and response as well as seasonal temperature range and response. Although these should have weaker signals than annual temp anomaly since there is zero positive feedbacks, (though less confounded by climate variability,) if they are detectable and track each other that would establish a baseline for EGHE, which would be the first independent proof of the EGHE hypothesis.

  2. Nick Stokes says:

    Here is my similar plot, from here. TempLSmesh uses a similar triangular mesh, but with GHCN and ERSST data. I’ve shown GISS too, which uses much the same data as I do.

    They are all pretty similar, though the different data for C and W seems to have a small effect.

  3. Olof R says:

    Nice work. So there is very little difference between simple straight interpolation and the more complex method with kriging, ice masks etc.
    I think the kriging has an infill limit of around 2000 km whereas the triangulation infill is unlimited. Hence, there could be larger differences between the two methods in the early decades where data is more sparsely distributed, and C&W can’t fill the gaps completely.

    Also, if I could run your code, I would definitely try to triangulate Crutem4 data only, and make a global estimate of SAT based on met stations only, similar to Gistemp dTs. Gistemp dTs is not perfect, since it only infills data 1200 km and leave gaps in the middle of the oceans. Still, I don’t think Gistemp dTs exaggerates the global SAT trend very much, probably not more than 0.01 C/decade. For instance, Gistemp dTs has the trend 0.218 C/ decade in 1970-2017 and the rcp8.5 multimodel mean is 0.211.
    If one thinks that there is a geographical bias in a Crutem “dTs” product, it would be possible to test this by subsample model or reanalysis data to the Crutem coverage, and run it with the same code.

  4. Olof R says:

    Thanks Clive,
    Really interesting. I took the liberty to paste Gistemp dTs and CMIP5 rcp8.5 multimodel mean into your chart for comparison:

    The triangulated “Crutem dTs” looks better than Gistemp dTs. It follows the model mean very well from now back to the 1930ies. The older data disagrees, with larger warming trend in both Crutem and Gistemp compared to the model mean. Maybe the data is less representative for global conditions back then, too little maritime data compared to continental data, or too urban with significant UHI..?

    I don’t think that there is very much coverage bias in the Crutem dTs vs the global model average. Subsampling of model data to the crutem coverage, and triangulation with the same code (apples to apples) would give the answer..

    I have experimented with Crutem data and the simple Ratpac averaging method (populate 18 regions evenly with data (the regions are 30 degrees high and 120 degrees wide) and calculate an area weighted global average). Here’s a comparison for the period 1957-2017, when there is data from Antarctica;

    There is very little difference between the complete global model data, and the subsampled “CMIP 100”. Also, the 2017 temperature for the “Crutem 100” index is 0.92 C, very near that of your triangulated Crutem (0.93 C).

    • Clive Best says:

      It is interesting that the models follow the land data, but presumably the CMIP5 model mean is for land-ocean rather than land alone. However there is the additional point that the models predict surface air temperatures rather than SST. There was a paper on this by Ed Hawkins and co.

      I had an email from Kevin Cowtan who said it doesn’t probably matter what you do so long as you extrapolate data over the poles.

      You can download all my spherical data here:


      • Olof R says:

        Thanks for the data Clive, really appreciated..

        A little trend check

        “The global coverage era” 1957-2017:
        Crutem triang 0.1769 C/decade, CMIP5rcp8.5 mean 0.1764 C/decade

        “The modern warming era” 1970-2017:
        Crutem triang 0.2112 C/decade, CMIP5rcp8.5 mean 0.2132 C/decade

        The model data is global 2m SAT. The ocean 2m SAT is kind of elusive, only existing in models and reanalyses. The global observational datasets are usually blended SST and land SAT (plus land SAT extrapolated over sea ice) It’s complicated to make blended model data for apples-to-apples comparison, because one needs variable ice masks for every single model run.
        Crutem triang offers a simple method to estimate the global SAT. I am convinced you could publish it if you included subsampled model equivalents for comparison and validation of coverage bias.

        The Cowtan, Hausfather, et al team has produced a lot of articles with apples to apples model/obs comparisons, reconciling stuff, etc.
        Their latest paper, where they homogenised SST using co-located maritime met stations, has also connections to Crutem triang.
        I think they used the larger Berkeley earth data base to maximise the number of island and coastal met station.

        A new challenge could be to triangulate the Berkeley earth land dataset to global extent. They have 1×1 degree netcdf:s, but masked to land only. It should imo exist a global sat field in their production, until the moment they land mask it, but they have obviously never been interested in making a BEST “dTs” global SAT product

  5. Hans Erren says:

    One thing to keep in mind is that hatcrut is mixing water surface temperature and air temperature. Anybody who has been to the beach knows that these can differ dramatically. What do you know about air temperatures above ice?

  6. Ron Graf says:

    I noticed in Olof’s plot of land vs SST that the warming reversal of the 1940-1980 was led by land cooling. How does this fit with the theory of AMO, (the Atlantic,) being the driving force?


    • Clive Best says:


      Yes there is a hint of that. Land temperatures should follow ocean temperatures with no effective time lag, but the reverse should not happen!

    • Well, the AMO shape/variability is everywhere. Take any temperature index (global, sh, nh, land…), detrend it (just like the AMO is) and you get that AMO shape. So, it seems that the driving force is global and not the north Atlantic sst. Land leading cooling and warming fits well.

  7. NASA JPL correlated the multidecadal temperature variations to LOD variations. Marcus has kept working the problem as an independent investigator

    “Does an Intrinsic Source Generate a Shared Low-Frequency Signature in Earth’s Climate and Rotation Rate?”

    This is one of the remaining puzzles

      • The usual explanation for the cyclic dip in temperature that occurred after 1940 and lasted until 1960-1970 was an increase in aerosol pollution, which was gradually eliminated over time (think London smog). Yet, it’s hard to believe that this would cause a change in the Earth’s rotation rate. Any other explanation involving the ocean seems more plausible. But that’s not consistent with aerosol cooling, which may be why NASA JPL’s correlation finding doesn’t get much attention.

    • Ron Graf says:

      The tidal forces from the moon seem to be the strongest astronomical variable but the cycle, 18 years, is too short. Nicola Scafetta has several papers on matching the timing of the Great Conjunction (Saturn and Jupiter) and multi-decadal climate trend. Although the conjunction is a 20-year cycle, it’s only every third conjunction that points in the same direction in the cosmos relative to Earth, making it a 60-year cycle. Scafetta also hypothesizes that the 11-year (22-year for same polarity) is also Jupiter-Saturn synchronized. The question is how such a weak gravitational of magnetism effect could dominate. The answer: in the absence of other external influences the strongest noise sets the tempo.

      • Ron Graf says:

        Clearly the moon is a stronger gravitational influence but it’s not magnetically active.

        Back to the question about how land could lead ocean in cooling, which would mean a negative radiative imbalance, the multidecadal variation is showing a radiative signal, not an ocean driven one. How could magnetism affect forcing?

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