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.