Reflections on the Planets
Here is a chart from Wilkinson, illustrating the bubble plot method, where a third variable is encoded by the size of the marker. Unfortunately, planets are not a good data set for demonstrating bubble plots; we automatically assume these differently-sized circles are representations of the planets to scale. We’re also not very good at discriminating between the sizes of small circles: is Earth 0.4 or 0.5? Is Mercury 0.2 or 0.1?
The units are not very friendly, either. Albedo is just the percentage of electromagnetic radiation reflected by a planet, and AU are units equal to the Earth's distance from the sun. Why temperature was chosen as a third variable is unclear (and why use degrees Kelvin?). Sure, it varies linearly with distance from the sun on a log–log scale, but that’s no surprise. The only exception is Venus, whose temperature is a consequence of a carbon dioxide atmosphere, not albedo; if anything, its cloud layer lowers the temperature by reflecting sunlight. So the graph is not really telling a coherent story.
What could be improved? We can start by just plotting albedo against distance, using more intuitive units for both. Now some of the variation that was masked by the bubble plot begins to emerge:
This is a fairly basic chart, but it still isn’t telling a story. To flesh it out, I added relative sizes, changed the brightness of the planets to match albedo, and annotated some of the outliers. The graph has become a little too cluttered, because the pattern of data points is being swamped by supplementary information, but at least now there’s some sort of narrative going on. And it prompts questions, like why does the Earth have such a high albedo when it’s mostly ocean?
A little more research, and I realized Earth’s albedo is mostly determined by cloud cover. That was the key to understanding why Venus and the gas giants were so reflective, and dry balls of rock like Mercury and Mars weren’t. So I resimplified the chart to make that point, stripping off some of the irrelevant information.
Now the graph has a point to make, and you can just tell it’s happier.
References: The original chart is from Leland Wilkinson’s The Grammar of Graphics (Springer 1999). What piqued my interest was a fascinating discussion of what color the planets really are. Planetary albedo data are taken from part of NASA’s site, Wikipedia supplied the Earth albedo data, which merely lists “Edward Walker” as its reference (as does every other site on the internet, blithely copying Wikipedia of course.) The old Wikipedia page cites, gulp, “Walker, E., 1987: Pictures of Preschoolers Out in the Snow. Dishwasher Picture Publishing, Volume 26, 151–1103.” So you may want to take those figures with a grain of salt.
Comments
You've reduced the dimensionality of the data by removing temperature. I suspect the graph was intended to illustrate the dependence of surface temperature on distance from the sun and albedo in the absence of an atmosphere (no greenhouse effect). I think adding a second point for each planet to the original graph representing calculated surface temperature would then show the dependence of surface temperature on three variables: distance from the sun (amount of solar radiation), albedo (proportion of solar radiation absorbed), and atmospheric composition (surface radiation trapped).
For the Earth, at least, an albedo of 0.29--which corresponds to the "bond albedo" (which I didn't know about until today) the amount of light reflected vs. incident solar radiation--is the appropriate value:
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/albedo.html
Posted by: Rob Simmon | March 5, 2007 4:51 PM
Yes, I deliberately dropped temperature from the original graph. The narrative of Wilkinson's graph was "planets are exactly the temperature you would expect, except for Venus. Venus has a very high albedo; perhaps that's why." Of course, that's precisely wrong. If one wanted to explain planetary temperature with a graph, as you point out there are four variables to plot; perhaps one could do it with a 3D plot and color coding, but it might be simpler to just ignore albedo (since it really has no effect on temperature as Wilkinson's graph shows), have distance and temp as the axes, and use a second point, perhaps linked to the planet's marker with a dotted line, to show how much lower the temperature would be if there were no atmosphere.
Thanks for the suggestions!
Posted by: Mike | March 5, 2007 10:58 PM
An update: some sensible discussion on the Edward Tufte boards pointed out that distances of millions or billions of kilometers are meaningless to most people, and I'm inclined to agree (particularly on a log scale like I'm using). But AU is even more meaningless to anyone without some scientific training, and that's basically everyone. Remember, half of Americans, according to recent polls, have trouble remembering the Earth goes round the sun. How about "Earth orbits", or a numbered AU scale, but 1 tagged with "distance of Earth from sun"?
Posted by: Mike | August 16, 2007 10:28 AM
Sorry to open up an old topic, but I can tell you why they use Kelvin as opposed to other temperature scales. It is because the Celsius and Fahrenheit scales have arbitrary zeros, while the zero of Kelvin is the real minimum for temperature. The temperature vs. distance relation expected in the graph is only a power law when temperature is measured in Kelvin, not when measured with the other two scales (which will have negative temperatures, not so easy to plot logarithmically). Plotting the temperature in Celsius in this case would be like trying to plot mass vs. (radius - 5000 km) for spherical bodies on a log-log plot, which would not be linear like plotting mass vs. radius.
Posted by: CS | November 18, 2008 10:53 AM