Today I'd like to take a break from my recent topics of discussion and look at an example of why people shold be skeptical of the messaging by global warming advocates. This post isn't about science. I'm not going to argue about any facts or theories. I'm not going to question or put forth facts or evidence.
None of those things matter today. Regardless of what one believes about global warming, everyone should be able to agree on a basic principle: Results should be presented in an accurate manner that does not create a misleading impression of what the results show. And based upon that principle, everyone should be able to agree this display is rubbish:
I'm not questioning the data used to make this display. The data doesn't matter today. What matters today is the data is being displayed in a misleading manner.
That chart shows global temperatures over the last 150 or so years in a spiral pattern. Because there are a couple things to unpack in it, it might help to examine a different graphic first. Consider the one found in this link (sorry, I couldn't figure out how to embed it):
That shows the evolution of ice in the Arctic and Antarctic areas. The two smaller spirals in it show each region's individual ice levels while the larger spiral shows the total ice level. Toward the end of the spiral, there's a dramatic decline. Or at least, it appears dramatic. Look at these two circles:
How much of a difference do you think there is in size between these two circles? It's double. More specifically, the circle on the left is 1.96 times the size of the circle on the right. That's because these represent pizzas.
If you have to decide between a 10 inch and 14 inch pizza, you might think four inches isn't that much. You'd be wrong. A 14 inch pizza is twice as large as a 10 inch pizza. That's because the area of a circle increases by the square of the radius. A circle with a radius of five inches (10 inch diameter) has an area of 3.14 * 5^2, or 78.5 square inches. A circle with a seven inch radius (14 inch diameter) is 3.14 * 7^2, or 154 square inches.
With this in mind, look at the two spiral charts above. Each month of the year has its data plotted at a certain angle. If the data were the same in each month of a year, you'd have a perfect circle. As the data values change, the radius for that particular point changes as the radius is determined by the data.
Now remember what we saw with the pizzas. Going from a seven inch radius to a five inch radius is a change of ~30%. That's not what the eye sees though. When we see a circle or spiral, our eyes don't focus on the radius of that circle. Our eyes focus on the area. As we saw with the pizzas, a change from a seven inch radius to a five inch radius reduces the area by ~50%.
Plotting any series with a trend in a spiral pattern like this will exaggerate the apparent rate of change. Consider this particularly bad example:
While some credit is deserved for the graph having radius markers on it, the reality is people looking at that animation will not focus on the radius markers. What they will see is the enormous change in area. They will see temperatures rising to 100 times the original levels when in reality the (projected future) temperatures only increases a twenieth of that. That means the visual impact is exaggerated by ~2000%.
That's not the only problem though. Remember how I said I wanted to look at the ice level charts first because they were simpler? Those animations were simpler because the amount of ice cannot drop below 0. Temperatures can. You can see that in the temperature spiral as some past temperatures are inside the 0C line.
Here's the thing, circles can't have a radius smaller than one. To create these temperature spirals with values below zero, the center of the circle cannot represent zero. It has to represent some other number. What number though? In these charts the number is -1, but why? Why use -1 instead of -2 or -0.5? There is no inherent reason one number is a better centerpoint for the circle than another.
This is important because it affects the area of the circle. Starting at -1 means 0C is 1, 1C is 2, 2C is 3 and so forth. This means the area goes 3.14, 12.56, 28.27, 50.27, 78.54, 113.10. If we set the centerpoint of the circle at -0.5 instead of -1, those values would change to 0.79, 7.07, 19.63, 38.48, 63.62, 95.03. Take note of how 113.10/3.14 is 36.02 while 95.03/0.79 is is 120.29. That shows how much the visual impact is exaggerated by plotting this data in a spiral is affected by the arbitrary choice of what temperature value to set the center of the circle at.
The numbers I've discussed come from basic geometry. Climate scientists understand these numbers every bit as well as I do. They also understand that humans typically focus on the area of a circle rather than the radius. Why then are charts like these heavily promoted and praised as wonderful tools informing people about global warming?
I don't care to guess what the answer to that question is. It doesn't matter. I don't think climate scientists are looking at these plots and cackling as they think about how good they are at deceiving people. I wouldn't care if they were. What I care about is rubbish charts like these are accepted by the scientific community that is claiming to inform the public about global warming.
Guess what guys? If you post misleading charts, people should distrust you. If you want to use this approach to displaying your data, that's fine. It's okay to plot data in a way people won't instinctively grasp. You just need to clearly explain to them how they should interpret your chart. Or you could do this:
The left chart shows how you'd plot data proportional to the radius. The right chart shows how you'd plot data proportional to the area. It would be easy for the people who have made these spiral charts to show their spirals on both of these. They could explain to people why the resulting animations look so different. That would let their audience see the spiral animations and actually understand what they meant.
I understand many people won't care about this. Doing as I suggest wouldn't be "sexy." It wouldn't create a compelling case. What would it would do is be fair and accurate. The spiral charts being created by climate scientists and promoted by global warming advocates are neither.