Global weather in a Pierce Quincuncial projection

I recently came across Peirce’s Quincuncial map projection, invented by the philosopher C. S. Peirce in 1879. Pierce projected each hemisphere of a spherical earth on to a square in such a way that lines of longitude and latitude cross at right angles. His projection is not used very much, perhaps because it is absent from standard mapping libraries such as Proj.4. Jason Davies’ elegant tessellated version (below) reproduces Peirce’s original.



The Peirce Quincunx (PQ) has nice features for the display of global weather and climate data. Firstly, as a conformal map, it does not distort the shapes of relatively localized objects such as the cyclones present in global weather patterns. The Mercator projection is also conformal, but is notorious for it’s large scale distortion. PQ scale distortion is generally smaller, becoming large only near the four equatorial singular points.

Secondly, PQ is pole-friendly. The poles are special points in the climate system because the jet streams circulate about them. It seems perverse to display climate information using map projections (such as geographic) which are singular at the poles. Other examples of pole-friendly projections include transverse Mercator and oblique cylindrical equal area.

The video shows 850mb PQ wind speed raster maps for October 2015 based on 6-hourly 0.25o resolution gdas data. 1 video second corresponds to two days of weather data.

There is a nice discussion of PQ implementation in R here. To create raster maps, both forward and inverse projections were required. These functions are available in tcl‘s mapproj library and can be called from R. More details later.



  1. Hi Joe,
    [I posted this previously on the wrong thread so you may have missed it]

    It is great to see you are still active. I posted a question on your thread on the Australian wind energy study asking if your journal paper on that excellent study is still progressing and if so what is the status, or if you have given up on it. It was an excellent study and it would be very valuable to have it published in the peer reviewed literature as you did for you EirGrid study. I hope you are still proceeding with it.

    Could you please let me know if it is in progress or if you have given up in it. I really hope you will publish it.

    Kind regards

  2. Hi !

    Thank you for this. I am looking for a way to plot my data in a PeirceQuincuncial projection with R.
    I tried to use the code you give here:, but without any success.

    Could you provide a code to plot for example the following points:

    A -19,05 169,916666666667
    B 42,4855555555556 -77,2936111111111
    C 12,5066666666667 2,52444444444444
    D -20,6177777777778 28,0727777777777778
    E -11,2947222222222 -69,8155555555555556

    That would be a great help !
    Thanks in advance,
    and best regards


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