Emulating CRUTem Graphics

Because of the puzzles in trying to replicate the NOAA graphic from archived data, I’ve also tried to replicate the HadCRU plots from archived data. Hu McCulloch has criticized the highly inappropriate use of Mercator projections by climate scientists and, as an exercise, I figured out a fairly simple method of plotting these results in Mollweide projection (which seems like a pretty reasonable method, also shown below).

First here is October CRUTEM, followed by my emulation from the data archived at http://hadobs.metoffice.com/crutem3/data/CRUTEM3.nc as of today. I spent a while trying to match the color coding and am close enough for practical purposes. The archived data appears to contain some stations not in the webpage graphic e.g. in Canada.


Here’s a Mollweide projection of the CRUTem3 data. I’ll post up a utility for doing this from gridded data, as Hu is 100% right that Mercator projections should not be used. They are a bit easier to do, but it didn’t take me that much time to figure out how to do color coded Mollweide plots and you’d think that CRU, Hadley Center and NOAA should be able to do as well.

31 Comments

  1. Jeremy
    Posted Nov 20, 2008 at 6:17 PM | Permalink | Reply

    Ah, I remember high school when the poly-sci teacher was the one telling me that only a globe lacks distortions.

    Don’t be looking at me to make a flash applet with a 3D globe mapping of this kind of data…

  2. bill-tb
    Posted Nov 20, 2008 at 6:32 PM | Permalink | Reply

    While you are at it, can you define what is meant by ‘global temperature’, and how you measure temperature of a continuously changing body. My handy science manual says that is not possible, but maybe there are new discoveries not yet in the manuals.

    Does you plot take into account temperature variation with altitude? — ^_^

  3. Jeff K
    Posted Nov 20, 2008 at 6:55 PM | Permalink | Reply

    As a note – those are not Mercator projections but Lat/Lon equidistant cylindrical projections. The North/South distances are the same from the equator to the poles (Lat/Lon lines make squares). However, in Mercator projections, the North/South distances increases and streches (Lat/Lon lines make larger N/S rectangles closer to the poles).

    Outstanding site!!

    Jeff Krob
    NOAA/NESDIS

  4. Posted Nov 20, 2008 at 7:27 PM | Permalink | Reply

    Thanks, Steve, for presenting this data with the equal-area Mollweide projection. As discussed on the CA thread Equal Area Projections earlier this year, the CRU/GISS equirectangular projection exaggerates any anomalies in the already sparse Arctic and Antarctic data.

    However, as noted already by Jeff Krob in #3, the projection in your first and second maps is not Mercator, but rather equirectangular, aka Plate Carée. The CRU/GISS equirectangular projection exaggerates areas far from the equator in proportion to the secant of latitude. The Mercator projection preserves shapes by introducing an additional N/S distortion in the same proportion, with the result that it distorts areas by the square of the secant of latitude!

    The 1805 Mollweide projection subtly eliminates the area distortion, while mapping the poles onto single points, and projecting the central hemisphere into a circle. (See the lower image in comment 134 on the thread indicated above.) However, this forces lines of longitude to converge on a single point, and hence may make it hard to locate points near the poles.

    The 1772 Lambert Equal-Area projection preserves N/S direction, yet maintains equal-area, by instead compressing N/S distances in proportion to the cosine of latitude as the poles are approached. (See the middle image in comment 107 on that thread.) As noted earlier on CA by John Bell, the appealing 2:1 aspect ratio of the equal rectangular projection can easily be preserved by an offsetting uniform vertical dilation, as noted in #101 of that thread. This corresponds to a reference latitude of 40.08 degrees N. Would it be possible to plot this data in that projection?

    In any event, how the data is presented visually is secondary to getting it straight in the first place! Perhaps Jeff can help us figure out the NOAA/NCDC data. I see they are still sticking by their 11/17 position that this Oct. was the warmest on record.

  5. hengav
    Posted Nov 20, 2008 at 8:21 PM | Permalink | Reply

    Jeremy

    I dare you to… you should talk to someone at Google Earth to add it as a layer.

  6. Vernon
    Posted Nov 20, 2008 at 9:25 PM | Permalink | Reply

    This may be a simple way of looking at it but to get the “global temperature” would it not be better to take all the readings at the same time, and by that I mean the same GMT time or zulu time? We are talking about a sphere so how does trying turn a 3D object, where some stations are at Tmax and some at Tmin and most are in between, into at 2D representation where every station is at Tmax?

    • Keith W.
      Posted Nov 20, 2008 at 9:58 PM | Permalink | Reply

      Re: Vernon (#6), I would be happier if it did each station at Tave. Tmax would look to hot. It’s already bad enough that they do the monthly maps based upon anomaly, not actual temperature. If they did it on temperature, the Russian Hot Spots would be pits of dark blue compared to the other areas of the world.

  7. dh
    Posted Nov 20, 2008 at 10:05 PM | Permalink | Reply

    I have spent some time plotting temperature data using various projections.

    We settled on the Robertson Projection as the best compromise. All the various projections [hundreds] are in Matlab “map tool box”.

  8. Posted Nov 20, 2008 at 10:26 PM | Permalink | Reply

    dh #8 writes,

    We settled on the Robertson Projection as the best compromise.

    I think you mean the Robinson projection. See comment #71 on the “Equal Area Projections” thread.

    Unfortunately, this area-distorting projection is popular with IPCC. The Eckert IV projection (see Coyote’s comment #12 on that thread, as well as Steve’s #10) has a similar shape, but does not distort area, and so is to be preferred for plotting climate data.

  9. Nicholas
    Posted Nov 21, 2008 at 1:42 AM | Permalink | Reply

    This is semi-off-topic, but, Memo to climate scientists: PLEASE adopt software version-like numbering and storage of climate data.

    i.e. never delete or change a version of the data, and always specify the version used. If data is found to be wrong, or in need of correction, create a new copy with a higher version number and refer to this in your article/page/link/etc.

    This way history is preserved, and it’s possible for people (other scientists, “auditors”, whatever) to find and use the exact version you used, as well as see what has changed over time and when.

    It isn’t that hard, and it would be a boon to science.

  10. Ross Berteig
    Posted Nov 21, 2008 at 2:57 AM | Permalink | Reply

    I have to strongly back a move to equal area map projections… the overuse of simplistic projections that coincidentally exaggerate the expected large variations at the poles is just inexcusable. Especially when done by folk like NOAA and NASA who should at least know people who know better ;-)

    I like your Mollweide projection map, but it would be helpful if the lat/lon lines and other reference marks were lighter and not colored anything like one of the scale colors. Gray would work well for this example.

    Incidentally, I would hazard a guess that the scale color scheme is based on (or at least inspired by) the work of Cindy Brewer, found at http://www.colorbrewer.org/. She put a lot of thought and research into designing sets of colors to use for coloring maps for various purposes. Anyone engaged in presenting categorized data on a map should know about her work…

  11. Ross Berteig
    Posted Nov 21, 2008 at 3:04 AM | Permalink | Reply

    Another pet peeve of mine is the use of 5×5 gridcells which are increasingly distorted in shape as one approaches the poles. It can’t be all that hard to find an equal-area tessellation of a sphere with as many cells as needed. The computer graphics literature should be a rich source even if the mapping community doesn’t already have stock answers.

    • Geoff Sherrington
      Posted Nov 21, 2008 at 5:14 AM | Permalink | Reply

      Re: Ross Berteig (#13),

      Supported. Climate people can learn from ore deposit modellers and exploration people who have a long history of convenient and precise cartography, as well as knowledge of certain distortions that can arise from inappropriate choice.

  12. Jeff K
    Posted Nov 21, 2008 at 5:23 AM | Permalink | Reply

    I would guess that the Lat/Lon projections are used the most throughout NOAA (and others probably) is because that is the grid shape used by the global forecast models in both the daily operational NWS & longer-term Climate Data Centers. That is what they are comfortable with so that is how they publish it.

    Since I work in the GOES (Geostationary Operational Environmental Satellite) data processing area, our (raw) data is a space-view orthographic projection & we don’t really see the polar areas (or other E/W hemispheres). However, writing software on the side for meterological model data viewing (WINGRIDDS), I’m familiar with the Lat/Lon projections & I’m comfortable with viewing the data, understanding the viewing anomalies.

    I guess, if you want to project global data with the most geographic accuracy, IMO, you need three displays; Lat/Lon, North Polar Stereographic and South Polar Stereographic. The middle latitudes will average out ;-)

    When you want to look at the whole globe at the same time, you have to sacrifice something.

    Cheers!!

    Jeff Krob
    NOAA/NESDIS

  13. Aaron Wells
    Posted Nov 21, 2008 at 9:15 AM | Permalink | Reply

    When you want to look at the whole globe at the same time, you have to sacrifice something.

    Why?? Why can’t an animated GIF be used that uses a revolving sphere? Its not that complicated.

  14. Jeff K
    Posted Nov 21, 2008 at 10:55 AM | Permalink | Reply

    If you want to use a revolving sphere centered on the Equator, the areas around the poles will not be as clear as it would be looking down on the poles from above. If you tilt the perspective north or south to see a particular pole at a better vantage point, you loose the view of the opposite pole.

    If you want zero data distortion, yes, the space-view orthogontal is the best…but the data resolution is lost the closer you get to the edge of the view and since the Earth rotates on it’s poles, the view centered on the Equator never really shows the polar data in it’s fullest because, as stated before, the data resolution is lost as it ‘goes over the hill’ tward the poles.

    knowhatimean?

    Jeff Krob
    NOAA/NESDIS

  15. Willi Mc
    Posted Nov 21, 2008 at 11:27 AM | Permalink | Reply

    Would it be possible to have a revolving globe as viewed from the Sun, for a full year? If not, perhaps as it would appear once a month.

  16. Jeff K
    Posted Nov 21, 2008 at 1:12 PM | Permalink | Reply

    You can juggle the earth however you want…my previous point stands. If you want to look at the whole globe at the same time, you have to sacrifice something – data or geography *has* to be distorted. You can’t place a three-dimensional ball on a two-dimensional screen and see the whole surface perfectly.

    Remember – the key word here is ‘distortion’.

    • Dave Dardinger
      Posted Nov 21, 2008 at 9:50 PM | Permalink | Reply

      Re: Jeff K (#19),

      If you want to look at the whole globe at the same time, you have to sacrifice something – data or geography *has* to be distorted.

      Why not simply have two globes side by side and make the second the part that’s hidden by the first? Then everything is present at all times and while the material around the edges would be distorted, you can move whatever point you want to the center.

  17. Sam Urbinto
    Posted Nov 21, 2008 at 1:28 PM | Permalink | Reply

    5×5 degree grids at the poles are triangles with bases of around 10 and sides of 555 and those at the equator are almost squares of 555 x 555

    Which was the one where the areas were equalized per grid to something other than between 221 to 1667 sq km sizes?

    Re: bill-tb (#2),

    Wll. There’s not a global temperature. There’s samples of random locations turned into a global mean temperature anomaly by month. And a model ensemble outputs, such as one with a mean of 14 C.

    http://data.giss.nasa.gov/gistemp/tabledata/GLB.Ts+dSST.txt
    http://data.giss.nasa.gov/gistemp/abs_temp.html

  18. Hank
    Posted Nov 21, 2008 at 5:11 PM | Permalink | Reply

    Given all the empty cells, how much meaning do these maps have? What use are they? I hope nobody expects they can estimate missing values.

  19. Posted Nov 21, 2008 at 7:29 PM | Permalink | Reply

    Jeff Krob of NOAA/NESDIS (#15) writes,

    I guess, if you want to project global data with the most geographic accuracy, IMO, you need three displays; Lat/Lon, North Polar Stereographic and South Polar Stereographic.

    Rectangular and Polar projections are fine, but why cling, like Hansen of NASA/GISS, to the equirectangular lat/lon projection of Marinus or Tyre, or to the Stereographic polar projection of Hyparchus of Nicaea? Why not break out of the Hellenistic era and into the 2nd millenium, by using the far more advanced equal area cylindrical or azimuthal polar projections of Lambert of Alsace??

    See comment 107 of the CA equal area projection thread for the Lambert Cylindrical equal area projection (adjusted to a 2:1 aspect ratio in the middle image), and comment 43 of the same thread for the Lambert Az equal area projection (albeit from an interesting whole earth equatoral rather than hemispheric polar viewpoint).

    – Hu of Ohio State

    • Dave Andrews
      Posted Nov 22, 2008 at 1:25 PM | Permalink | Reply

      Re: Hu McCulloch (#22),

      Why not break out of the Hellenistic era and into the 2nd millenium, by using the far more advanced equal area cylindrical or azimuthal polar projections of Lambert of Alsace??

      I can think of two reasons,

      a) they’ve always used these projections and don’t understand the problem (although given Jeff K’s comments this seems unlikely)

      b) it suits them just fine to have the distortions, ie big red Siberia, big white Greenland icecap etc because it puts across a ‘message’ to the unaware

      c) I guess Steve will snip this because of b

  20. Posted Nov 21, 2008 at 9:14 PM | Permalink | Reply

    A bit OT – here’s a comparison of the satellite-derived LT anomaly versus the surface-derived anomaly in recent years. The satellite is the average of UAH and RSS while the surface is the average of GISS, NCDC and CRUT3:

    There appears to be a shift circa March of 2008. Or, maybe not – perhaps it is random movement. A global map comparing the satellite vs surface difference for March thru October 2008 versus the same period in 2007 would be interesting.

    • Kenneth Fritsch
      Posted Nov 22, 2008 at 1:16 PM | Permalink | Reply

      Re: David Smith (#23),

      David, I did an analysis of the anomaly differences between the UAH/RSS satellite and GISS surface (land and ocean) data sets for the period 1998-2007 on another thread here at CA (along with more extensive analysis in the 1979-2007 period). I did it on an annual basis and thus did not include 2008. What I am not certain from viewing your graph is whether you are subtracting the average of the surface records from the satellite ones.

      I think these more recent time descrepancies are important, since, while UAH and RSS differ over the long term trends from 19979-2007, in recent times (1998-2007) the re-nornmalized trends for UAH and RSS correlate very closely. If indeed the satellite MSU measurements are independent of the surface ones, as I have tentatively concluded, then I think these recent differences with the surface records deserve some detailed analyses.

  21. Mike Bryant
    Posted Nov 22, 2008 at 5:21 PM | Permalink | Reply

    I think someone already mentioned it, but why not a “skin”, or whatever they call it, for Google Earth? Then you can turn it as you wish.

  22. Posted Jan 21, 2009 at 2:11 PM | Permalink | Reply

    I don’t see the meaning of these maps either. Can someone explain? Maybe we should all get together for a CRUTem meetup eh!?

  23. Chad
    Posted Jul 29, 2009 at 9:39 PM | Permalink | Reply

    Hey Steve,
    I see this thread is very old and I hope you see this comment. I’m currently learning R and have been struggling trying to figure out how to plot gridded data on a map projection. The graphic you produced is exactly what I need to know how to do. Can you post the code for it please?

    • stephen richards
      Posted Jul 30, 2009 at 4:16 AM | Permalink | Reply

      Re: Chad (#29),

      have a look at the side bar. Steve has posted code and data and a learning/training page.

  24. Posted Jul 30, 2009 at 8:06 AM | Permalink | Reply

    Steve –
    Thanks for adding the equal-area Mollweide to the original post!

    There are also “interrupted” forms of the Mollweide that slit the N and S halves of the map along selected latitudes to reduce distortion of the continents.

    The top two equirectangular projections are Mercator-like in that they enlarge areas in high latitudes, but are not true Mercator, in that they only stretch distances horizontally and not vertically as well.

    The Lambert Cylindrical Equal Area projection I had suggested in #22 above compresses distances vertically in order to make up for the horizontal stretching, while preserving NS and EW directions. A 2:1 aspect ratio, as suggested on CA by John Bell, then gives the same average detail as the equirectangular, while eliminating shape distortions at 40.08° N and S. See comment 107 of the earlier post.

    But the Mollweide or interrupted Mollweide are equally good from an equal-area point of view. They distort NS directions, but nicely invoke the sphericality of the earth.

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