Great circles

23 May 2007 0 920 VIEWS

Waves and swells in the open sea travel in a straight line in the direction of the wind that created them. A straight line drawn on a sphere linking any two points is known as a great circle. Ancient seafarers knew them and were able to follow great circles while navigating by the stars. The equator is one example of a great circle and all the lines of longitude (or meridians) which link the North and South Poles are also great circles. The equator is the only East-West latitude line (or parallels) that can be called a great circle.

Map Projections

While the idea of waves and swells moving in a straight line on a curved surface sounds pretty straightforward, it gets complicated when looking at plots and swell forecast charts which are projected onto a flat page. The diagram above shows how the Earth would appear from space, this type of map is known as an Orthographic projection and was known to Egyptians and Greeks more than 2000 years ago. The labelled great circle passing through the southwest of Western Australia shows one possible route that a swell may take on its way to land. Remember it’s simply a straight line drawn on a globe. Now let’s look at it with a different projection.

The chart above is known as a Mercator Projection (from Gerhardus Mercator in 1569) and is the most commonly used map projection for nautical purposes. This is because a route drawn between two locations on the map (a rhumb line) can be followed with a single compass bearing. One of the disadvantages of this type of projection is that the scale is distorted such that the size of land masses is exaggerated towards the poles. The yellow line is the same great circle line from the global plot.

Swell direction

Winds blowing along a great circle will generate waves and swell that will move away along the great circle path. Looking at the diagram above, it is theoretically possible for northwest winds off the east coast of North America to generate a south west swell in Western Australia. The effect of opposing winds and waves along the vast distance make it unlikely that much energy would be left and usually there would be something generated closer by which would cover up a small signal from so far away. A more visible example occurs during the southern hemisphere winter when the calm summer seas of California wake up with long range south swells which can travel well south of Australia along a great circle path from storms in the Indian Ocean.

So, while a local swell will arrive with a direction close to that of the wind which generated it, a distant swell may not. In the example for Western Australia, it could be the northwest winds of a storm west of South Africa’s Cape of Good Hope that creates a south west swell over here.

Open the swell windows

Here are some generalized plots showing areas and relevant wind directions for swells following great circle paths (yellow lines). Local coastline geometry will have the final say when waves feel the bottom and refract into bays and around points.

South Western Australia

As mentioned above there is a long range swell window extending all the way to the North Atlantic for South Western Australia. In addition, pretty much the whole Indian Ocean can provide swells for this coast.


Victoria

Heading east to Victoria and we see that it’s similar to Western Australia but with a tightening of the Atlantic swell window to a narrower region of the South Atlantic west of Africa and the more active southern part of the Indian Ocean.

New South Wales

Around to New South Wales and we’ve lost the Atlantic and Indian influence but the Southern Ocean is still there and the Pacific Ocean comes into the game. New South Wales has a variety of closer swell sources so the graceful curves of the great circle become less relevant. There is a narrow window for swells from the east which could be generated as far away as the coast of Central America but it’s blocked by the Cook Islands in the South Pacific. A narrow southeast path extends out to Chile on South America’s west coast, perhaps a strong northeast wind could push a brave swell west against Southern Ocean swells and gales all the way to Australia. While it would be great to see a northeast swell head down from distant Alaska and the Pacific Northwest coast, it’s unlikely that much will squeeze through the maze of islands in the southwest Pacific so the north to northeast swell window is quite restricted. Tropical cyclone swells and intense Tasman & east coast lows make up for this.

Southeast Queensland

Southeast Queensland is similar to New South Wales with a slightly wider window to the east and east-south-east before New Zealand blocks a large section of the South Pacific. The south and southeast swell window below New Zealand’s South Island extending to Antarctica is narrowed but lengthened slightly more than New South Wales. Once again we are mostly concerned with close sources of swell so the curvature of the great circle swell track on a Mercator map projection is not so evident.

Summary

When searching for a long range groundswell or planning a trip to some exotic surf location where all you might have is an idea of winds from the good old synoptic chart, remember the lovely curves of the great circle. It just might pay to check what’s happening in the next ocean over as well as the one nearby.

By Darell Strauss (Oceanographer)

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