Sunday, November 17, 2013

Cowtan and Way trends

A new paper by Kevin Cowtan and Robert Way in QJRoyMetSoc is getting a lot of discussion. See Real Climate here, SkS here and here, Lucia here and here, Cliamte Etc here.

The authors say:
"A new paper published in The Quarterly Journal of the Royal Meteorological Society fills in the gaps in the UK Met Office HadCRUT4 surface temperature data set, and finds that the global surface warming since 1997 has happened more than twice as fast as the HadCRUT4 estimate."

Some eyebrows have been raised at the size of the trend change from improving a relatively small area. I was surprised, too. So I did some calculations to see.

Update: The R code for calc and plotting is here. The data is provided by the authors here.

The need for the change

Met station coverage of the Earth is uneven. When grid averages are taken, and then combined for a hemisphere or global average, quite a lot of cells have no data. What to do?

The default is to leave them out of the average. But that is not a neutral decision. In arithmetical effect, they have been replaced by the average value of the cells with observations. And this may be a poor approximation. It should be improved with whatever information is available.

The particular issue with Hadcrut is data at the poles. In computing trends, missing cells are given the global average trend, but the poles are warming much faster. This is a big bias.

Cowtan and Way used UAH satellite data to get that improvement. I won't go into detail here about how they did it, but I'll just look at the dataset results. They looked in particulat at a period from 1997-2012 (16 years) which is commonly discussed as a pause. They showed trends including their hybrid method, which uses UAH-based infill:
DatasetHADCRUT 4     UAH            C&W hybrid
Treend C/dec0.046     0.0940.119
Actually, I don't think they cited the UAH trend, but I calculated it from the data they used.

So the new trend isn't that much greater than UAH. But to see just how modifying polar trends made the difference, I'll show the latitude averages for the 5° ranges.

Latitude averages

In computing these for the HAD 4 data, I replaced data-free cells with the global average for that month. So they aren't a good guide (for HAD 4) to actual trends, but, as described above, they do correspond to what effectively goes into the global average, so you can see the effect of changes. Here's the plot:

(An earlier version of this plot had the sign of latitude wrong)

As you'll see, the Antarctic and Arctic trends for the hybrid are large, but not so very much larger than UAH. I am still a little surprised that this is so, but it's not unbelievable.


Here are the numerical results as plotted:
LatitudeHAD 4UAHC&W hybrid


  1. It's Cowtan, not Cowton. I also got some input and quotes from the authors in my piece on the paper:

    1. Sorry about the title, now fixed. I think I did get it right elsewhere.

  2. Hi Nick,
    If you don't mind me asking - what data are you using for this computation regarding the CW2013 data - the data available on the website? Second - it would probably be useful to place the HadCRUT4 trends on the graph as well without including the null cells (that you've set to the global average) for comparison.

    1. Robert,
      I'm using the files on your website (in the zip file). The hybrid was had4_hybrid.dat.gz.

      I didn't compute the raw HAD4 trends because there was so little information. I wanted to contrast the "effective" trends, with global averages substituted for missing. The global HAD4 trend is the area-weighted average of the black curve shown.

    2. Update. I've posted data - see link above. I've got the latitudes with wrong sign in the plot - will fix.

    3. Thanks - the latitude plot did look strange that's why I asked about where you got the data. Makes much more sense now that it has been fixed.

  3. Nick, the highest trends should be in dec, jan and feb associated with sudden stratospheric warming events. A seasonal trend comparison would be interesting.

  4. Nick try comparing the zonal trends with the model mean zonal trends. If Cowtan is right then the global trends might match but I suspect the polar amplification is going to look horrible.

    This is like one of those plate spinning tricks. You manage to get one up and running smoothly only to discover that putting all your effort into that one has left the rest of them teetering.

    1. Sorry I should have added when I did a few of the latitudinal bands for CMIP3 I get the Cowtan method with Arctic trend 3X higher than the model mean (I only did 80N-75N so far)

  5. Yes, but I think that would only mean that the model means underestimate amplification. UAH shows quite a lot..

    1. It more likely means that the models cannot replicate natural variability.

  6. Hi Nick

    That's useful - one of the things we need is better ways to describe where the differences in the trends are coming from. However I think there are a few subtleties I can clear up.

    Firstly, the UAH trends are irrelevant to our results. We only use the spatial part of the UAH data - any temporal component, including trend, is thrown away.

    Secondly, since the UAH data is fairly smooth, the hybrid and kriging reconstructions are very similar over most of the planet. The only significant differences are in Antarctica (the Arctic is too small), primarily in the SH winter. From memory there are two major deviations, a cool one in 1998 and one more recent warm one. I've only looked briefly at the maps, but the biggest differences seem to come from Marie Bryd land, which due to the absence of Byrd station in HadCRUT4 is probably the most isolate land location. (The more important question is whether Marie Byrd land accounts for most of the difference - I haven't evaluated this yet).

    In the light of this, the trend at the SP is nothing to do with UAH, and I expect it is very close to the trend from the SP station alone. Robert's suggested analysis would have revealed this.

    We've got some interesting results from the Bromwich Byrd recon, and these have also uncovered some interesting features in the UAH data. The other interesting test this suggests is to patch in the Byrd reconstruction to HadCRUT4 and redo both reconstructions, and see how much of the difference between the kriging and hybrid results disappears.


    1. Thanks, Kevin,
      I included UAH mainly to show that the polar amplification in the hybrid result, though large, was not excessive compared to UAH.

      I'll look forward to seeing what happens with the Byrd results.

  7. > (An earlier version of this plot had the sign of latitude wrong)

    Whew. I was going to say, it didn't look plausible / every one was focussing at the wrong pole.

    As well as that, there's the "visual impression" problem that the x-axis is plain latitude, which misleads the eye. A version with cos(lat) scaling so you can see how much area is affected might be useful.

    1. I'm reading up about barplot(). I'll do vertical bars of cos() scaled width.