That the world ocean is a continuous body of water with relatively free interchange between its parts is of fundamental importance to oceanography. Because it covers more than two-thirds of the earth’s surface, a map of the world ocean is essentially a world map. On ordinary world maps the interruptions forming the edges of the map are often placed in the oceans to show the continents to best advantage. If, on the other hand, oceanographic conditions as a whole are to be shown, it is desirable to have the map interrupted within the land masses and the world ocean shown as a unit.

Athelstan Spilhaus “Maps of the Whole World Ocean”
Geographical Review (1942) 32: 431-5.

A while ago, I posted an appreciative review of Helen Czerski’s Blue Machine—but I didn’t mention its (UK) cover image. So here, belatedly, is my dissertation on what’s going on with that cover, which features one of my favourite map projections.

The layout of the map is so unfamiliar, and the contrast of the cover image so low, that at first it’s possible to mistake it for something quite abstract—some swirling gold lines against a meaningless blotch of blue. But there are labels, and with their aid you can pick out Antarctica, Africa, Europe, Greenland, Australia … and the hideously contorted coastlines of the Americas and Asia.

This is a map designed to show the world ocean as single continuous entity, created by the geophysicist/oceanographer Athelstan Spilhaus. Spilhaus had been creating map projections of this sort since 1942, but this one comes from his Atlas of the World with Geophysical Boundaries (1991), and is probably the most well-known.

Of all the world maps you’ve seen, probably most follow the plan that Spilhaus calls two singular point interruption, using the north and south poles as the singular points. The spherical surface of the Earth is, figuratively, slit open along a meridian of longitude from one pole to the other, and then flattened according to some carefully worked-out mathematical transformation.

Often, the meridian of interruption is at 180°, so that the Greenwich meridian lies in the centre of the map, like this:

If you’re interested in displaying the Earth’s landmasses, then it’s pleasant happenstance that the 180° meridian passes through very little land, but it does slice right through the middle of one of my favourite islands, Wrangel, in the Russian Arctic:

From there, it crosses the Chukchi Peninsula in the Russian Far East and passes through three Fijian islands before arriving in Antarctica.

It’s impossible to find a meridian that completely avoids land north of Antarctica, but 168°45′W does a pretty good job. It passes through the Bering Strait just east of the Diomede Islands, shaves past just a couple of hundred metres west of Fairway Rock, then crosses the eastern end of St Lawrence Island in the Bering Sea, and the western end of Umnak Island in the Aleutians. Beyond that, it manages to cross the entire Pacific without touching land before arriving in the deep embayment of the Ross Sea in Antarctica. The resulting world map is centred on 11°15′E, the so-called “Florence meridian” (which passes through the Italian city of Florence), proposed by the German historian Arno Peters.

But if you’re interested in the nations of the Pacific, world maps based on the Florence meridian have the same problem as the Greenwich meridian—chopping that ocean in half and consigning it to the peripheries. Splitting the world along the 30°W meridian provides a reasonable solution, without dividing too much land:

and if you’re interested in the geographical relationships of the Americas, you can place them centre-frame by cutting along the 90°E meridian, albeit at the expense of splitting Asia in half:

Once the Earth’s surface has been sliced open in this way, there are many ways of “flattening” it into a global map. The projection I’ve used above was created in the 1970s, by Arthur H. Robinson for Rand McNally. It’s not very fashionable these days, but I like it.

Here’s another thing you can do once you’ve split the Earth’s surface along the 180° meridian. This one was developed in 1929 by Oscar S. Adams, in a mathematical paper for the U.S. Coast and Geodetic Survey. It can take various forms, but what’s shown below is usually called “Adams World in a Square II”:

At left, I’ve shown the line of the split along the 180° meridian; at right is what Adams did with it, opening out the point where the equator crosses the meridian (marked with a red dot) to form two corners of a square, with the poles at the other two corners. He had designed his map to be conformal, like the more familiar Mercator projection—that is, it preserves angles and shapes locally, at the expense of gross changes in scale as one approaches the edges of the map. The scale tends towards infinity at the corners of the Adams map, just as it does at the top and bottom of Mercator’s. It was primarily a neat mathematical exercise, and the Adams projection is not much seen in the wild.

Spilhaus adopted* the Adams II projection for his project of showing the world’s oceans as a single, continuous body of water. He did this by finding a 180° great-circle arc (analogous to a meridian of longitude, but not connecting the poles) that is confined almost entirely to land. It starts in China, at 30°N 115°E, and ends in Argentina, at 30°S 65°W. It crosses the “world ocean” at its narrowest point, the 85-kilometre-wide Bering Strait, which links the Pacific and Arctic Oceans. The line’s centre point is in Canada, just north of the border with the USA, at 49°34′N, 113°03′W.

Here’s how that works out:

But Spilhaus orientated his map like this:

The map edges are almost entirely land, becoming grossly distorted at the corners. But there are little isolated corners of ocean that have been chopped off, which I’ve marked in pale blue—the Sea of Okhotsk and the Yellow Sea along the top edge; the Gulf of Panama and a little rim of Pacific Ocean at left; the western Caribbean at the bottom.

But this is where things get clever, because Spilhaus’s map is tileable. After a 90° rotation, we can fit the bottom of the map to its left edge, and the top of the map to its right edge. Like this:

I’ve now shown how the cut-off bodies of water, in pale blue, have been reunited with their parent oceans. By slightly extending Spilhaus’s square map to include these areas, we can produce a map of the whole ocean as a single entity.

Given that our interest is in the ocean, we can trim off the hugely distorted continental corners of the map. At which point it makes sense to rotate things back to the orientation of the parent Adams projection, like this:

If you scroll up to the top of this post, you’ll see that the map used by Czerski’s UK publishers, Transworld, corresponds to the left side of the projection I’ve laid out above.

(All maps include Natural Earth data.)

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* Spilhaus never mentions Adams in his original text, but his projection is generally acknowledged to be an Adams variant.