Where people live
July 2009 (index)
(Click any image to see a larger version.)
I'd never seen a map showing population density across the whole world, so I thought I'd make one.
Data
It's easy to get hold of the data. GRUMP provides data on how many people live at every grid square on the globe. The data comes at varying levels of detail; using squares of a quarter of a degree seems reasonable and allows a 1440x720 pixel image.
Projection
Which map projection to use? There's no perfect way to project a sphere onto a flat piece of paper. Consqeuently there are lots of map projections each of which do something well (preserving angles, areas, etc) but have some flaws.
The name "equirectangular with equator as standard parallel" sounds complex, but just means that we're plotting longitude horizontally, latitude vertically, on a simple linear scale (four pixels per degree in this case). This means that pixels towards the top and bottom of the image represent a larger image than pixels towards the equator. For now we'll live with this, as not many people live near the poles.
Linear scale
The next question is how to show the data. The first attempt is monochrome with colours corresponding linearly to the population in each square. The point with the most people (12,561,190 people) is black; points with no people are white; a point half-way between (6,280,595 people) would be the grey that's 50% black, and so on.
This gives us our first image:
Linear scale (click for large version)
At first sight it seems blank, but if you look closely you'll see some dots towards the top-right around India and China. In one sense this is quite a meaningful image: it tells us where the most heavily populated parts of the world are. But the linear scale only shows us the extremes. We have over a million data points but only thirteen of them have more than half the maximum.
Power scale
The second image is on a power scale. This time a point that's 50% black has a population of 12,561,1900.5=3,544.
Power scale (click for large version)
There's a lot more ink. Coastlines are all clear apart from the Arctic and Antarctic. We can see that India and China have large population density, but it's hard to make out some of the subtler differences. Even somewhere like the Falkland Islands with a tiny population shows up clearly. Also we can see some blockiness to the image because of artefacts of the way the data has been extimated in sparsely populated areas.
Mixed scale?
Our third attempt is to do something between the linear and power approaches.
This time we'll add a parameter k and say that a proportion of ink i
(so 100%=black, 0%=white) corresponds to a population of
p = (i-ik+k)M(ik+1-k) where M is the maximum population (12,561,190) for any point.
If k=0 then p = iM ; so it's the linear scale of the first image.
If k=1 then p = Mi ; so it's the power scale of the second image.
Intermediate values of k let us use intermediate scales. The third map uses k=0.35.
Mixed scale (k=35%) (click for large version)
This intermediate value improves on the previous two charts. It has enough of the linear scale that we can see clearly that India and China are major centres of population. But it also has enough of the power scale that we can see finer patterns such as concentration around the coasts, and particularly the Nile delta.
I like the final chart: it's the one that says the most and rewards close examination. But I would struggle to explain the scale to someone who wasn't comfortable with the formulae.
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