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.

pq

 

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.

Ascension Island and the ITCZ

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“Considering that these islands are placed directly under the equator, the climate is far from being excessively hot; this seems chiefly caused by the singularly low temperature of the surrounding water, brought here by the great southern Polar current.. very little rain falls, and even then it is irregular.” – Darwin (Voyage of the Beagle) describing the climate of the Galapagos.

Ascension Island is located in the tropical South Atlantic (8^oS). A visitor expecting to find lush tropical vegetation is suprised, just as Darwin was surprised by the climate of the Galapagos.  Saint Helena, 1300km to the South-West (16^oS) is also dry. So too is the island of Santiago, Capo Verde 2700km to the North (15^oN). On a recent trip to these islands I  was left wondering where the tropical rainfall was.

Rendered by QuickLaTeX.com

Tropical rainfall is tied to the intertropical convergence zone (ITCZ) where trade winds from Northern and Southern hemispheres (NH & SH) converge. Convergence implies uplift and uplift of moist air produces convective rainfall. ITCZ tends to follow maximum sunshine seasonally about the equator, which explains the timing of the wet season at a given location. This begs the question, why are some tropical oceanic islands almost entirely dry while others at similar latitude are very wet?

I used historical atmospheric circulation data from ERA-interim reanalysis to try to shed light on this puzzle.  Mean monthly divergence of surface (10m) wind field was computed at 0.75^o resolution based on the years 1979-2015. The ITCZ corresponds to the band of strongly negative divergence (convergence) near the equator (in mathematical notation \bf{\nabla} \cdot \bf{U} < 0).

divergence

ITCZ moves with seasons as expected. However ERA data show that over much of the Atlantic and Pacific oceans, it is (a) narrow, and (b) shifted significantly towards the NH (by about 5^o). This is why the convergence manages to miss Capo Verde, Ascension and Saint Helena almost entirely which accounts for the surprisingly dry climate of these islands. On the other hand, ITCZ dips far enough South to bring heavy rain to Fernando de Noronha (3^oS off the coast of Brazil) during April.

The large NH bias of ITCZ[1] is a fundamental fact of the climate system. For example, it is a factor in the rarity of hurricanes in the SH. NH bias is believed to be related to the observation that SH is \approx1.25^oC cooler than NH, which is in turn related to imbalance of ocean heat transport between hemispheres.

[1] Why the ITCZ Is Mostly North of the Equator?