Many climate studies use an equirectangular projection, in which lines of latitude and longitude are equally spaced, to graphically summarize data. An example is the following figure from Hansen et al 1988, discussed here recently under the topic Hansen and Hot Summers:
John Goetz uses the same projection in his recent thread here, Historical Station Distribution
While this projection is handy for plotting locations, it unfortunately distorts areas by a factor of the secant of longitude. The result is that areas near the poles are greatly enlarged, albeit not by as big a factor as in the Mercator projection. The result is that a temperature anomaly near one of the poles, as in the lower panel of Hansen’s graph, will appear to be disproportionately important for average global temperature. Likewise in Goetz’s graphs, stations will appear to be far more sparse than they really are as we move away from the tropics.
In order to prevent this area distortion while retaining a rectangular map, the vertical axis must be compressed by a factor of the cosine of latitude in order to offset the secant effect. This is done in the 1772 Lambert Cylindrical Equal Area projection. The following image is linked from Carlos Furuti’s webpage on map projections:
Unfortunately, the Lambert projection greatly distorts shapes near the poles, and makes features difficult to locate. A much better option for presenting climate data without area distortion is the 1805 Mollweide projection
I posted these graphs earlier as comments (#62, 73) on the Historical Station Distribution thread, but as they were somewhat offtopic there and of interest in their own right, I am reposting them here.
In a comment on that thread (#66), Steve McIntyre has already remarked,
#62. Equi-area projections are used in many contexts. In terms of graphic presentations, you’re 100% right and anything other than equi-areal should be banned from scientific journals.
In practical terms at my level, the only issue is the availability of routines in R (and for someone else Matlab). Doug Nychka of NCAR maintains the R-package fields. He’s very responsive to inquiries. I’ll check the manual and otherwise check with him.
http://cran.r-project.org/doc/packages/mapproj.pdf has a package with equi-area maps.
Somebody should be able to locate parameters that yield a “good” map for representing areas in climate contexts.
Mr. Pete, #76, remarked, “If you modify latitude by sin(lat in radians) you get the simplest equal-area projection. No need to use fancier things for basic display.”
This is what is known as the Sinusoidal projection
I like the Mollweide much better, as it gives far less shape distortion, and uses the available space better: Both are the width of the equator and the height of the prime meridian.
However, Mollweide uses fraction = .79 of this box, while the Sinusoidal only uses = .64 of this box. Thus, Mollweide gives about 23% more informational area within the same size figure.
The formula for Mollweide is a little complicated, and involves solving a transcendental equation numerically (see above Wikipedia article for formula or Furuti’s site for derivation). However, if Mollweide could solve this with an 1805-vintage analog computer (pencil, paper, compass, straightedge and French curve), a modern digital computer should have no problem with it either.