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# Scale on "Global Warming" graphs

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By softwareNerd from Software Nerd,cross-posted by MetaBlog

Since graphs are visual, we tend to measure them visually at first glance. At first glance, "steep" means visually steep. Consider these two graphs of company profits. Visually, one appears to show stagnating profits, while the other appears to show growth. Yet, the facts depicted are absolutely identical. The only difference is the y-axis scale. This is one of the oldest tricks in the book. Many company annual reports have stuff like this.

When Al Gore present his "global warming" graph, it looks something like this. the upward slope is visually steep. That's the message Gore wants his audience to take home. However. we aren't illiterate, so we take a second look. What's the scale? Is it appropriate? There appears to be an upward trend, but how do we judge if it is significant?

An expert may have an involved answer, but how do I -- a lay-person -- go from first glance to second-glance?

Here is how I approach the notion of an appropriate scale as a layperson: I try to relate the information to some concrete of the same type, which is familiar. If I have a familiar concrete of the same type, and overlay this information over that, I can better relate the visual to reality. So, here is the lay-person attempt:

1. This is a graph of temperature, so let me consider some familiar climate/weather temperature. Let me choose a city in the middle of the U.S. Let's say, I choose temperature variations in Topeka, Kansas.

1a. Google finds information on Topeka's averages for each month.

1b. I convert to Centigrade (because that's what the "global warming" graph uses)

1c. I express the mean of all months as "0 C", and express others as Centigrade above or below. (This does not change the scale, simply the naming of the Y-axis, to make it similar to Gore-style charts.)

2. That was a single "average" year. Next, I ask myself what Topeka's temperature would look like if it had the same "average-year" type of temperature year after year. So, instead of 12 months on the x-axis, I pack in about 30 years. Since I did this manually, it's not exactly even. Still, I would expect the actual year-after-year variations to be far more uneven. So, this is a pretty good depiction of what Topeka's temperatures would look like over 30 years is it is are basically unchanging.

Eyeing the tops and the bottoms, we can see what an almost zero-trend would look like.

3. Now, use the "zero-trend" as a background and overlay the "global warming" graph onto it, bringing the scale of that graph down to match the scale of this one. Here is what we get:

Are you scared now?

Compared to our flat background, the "global warming" graph does show an upward trend, but imagine Gore presenting this graph to his audience. Would it have the same impact?

It is the same data, after all.

I do concede that I'm presenting this as a lay-person. Maybe an expert will explain why this graph that looks insignificant from a lay-person's viewpoint is really significant. That's fine. However, to present this as if it is obviously a steep and significant slope is to play the charlatan.

Look at this correctly scaled graph and add in the fact that some experts question the data and say that it really isn't even as "steep" as depicted. Pardon me if I'm skeptical!

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Good show, SoftwareNerd. That had to take quite a bit of effort!

You're exactly right, you have to get a grip on what these numbers mean. You need to bring it within the range of your consciousness by relating the numbers to what you know. It takes effort, but it does allow you to grasp on a complex subject matter, otherwise everything is just floating. This is why I say you always need perspective, otherwise you won't understand what a set of numbers really mean to your life.

Another thing to look at is how those temperatures affect your life day to day. Living in that sort of climate, Kansas example, is quite normal for day to day activities from my experience. Just using your example as it is, not making any bigger point.

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Your analysis is synonymous to concluding that the universe is flat because around the black hole where I live, the spacetime curvature is so great that, when plotted next to the curvature of the universe as a whole, the latter looks completely flat. Your knowledge of the local is not enough to deduce the meaning of the whole. Does this make sense, or should I clarify further?

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Crichton's State Of Fear has some stuff along your lines.

Edited by HP11

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To clarify, nothing in my post should be construed to imply that there is no significant upward trend in global mean temperature. All the post says is: the graph alone does not tell us anything.

My objection is to folks like Gore who trot out visual slopes as if their audience cannot tell that one can make a visual slope just as steep as on wishes.

Edited by softwareNerd

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To clarify, nothing in my post should be construed to imply that there is no significant upward trend in global mean temperature. All the post says is: the graph alone does not tell us anything.
There is something you can also say: a graph can never tell you the significance of anything. There are a lot of senses of "significant" such as "should we worry", but one of the most basis is "are these meaningfully different?", or "are there two concepts here or one?". If the average annual temperature of a city is 52.9 in 2007 and 52.7 in 2006, is that a significant fact -- is 2006 "really different" from 2007, or are both an instance of the fact that the average annual temperature is, more broadly, 52.8 and the actual temperature varies somewhat?

The notion of being "significant" is tied to a context, and you have to justify the choice of context. If you narrowly focus on 40 years, you can compute a p-value that might show that there is a "significant" upward trend over the immediately preceding 20 years compared to the 20 years before that, but there's no justification for restricting the context to just 40 years. When the hypothesis is "Man has, though industrial actions, caused a significant rise in global temperature", the context has to be broad enough to rule out known alternatives.

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I remember hearing in environmental science class (which was in high school, so not the most authoritative) that global warming pundits have long acknowledge that the rise in temperatures is "only" projected to be tenths of a centigrade over the years--but it is still enough to melt miles of icecaps. I vaguely remembering their heuristic as follows: The thermometer represents an increase in the energy present in a unit of space around the termometer, so the increase of energy in that space corresponding to an increase from 0.0 to 0.1 goes rather unnoticed. However, when every such unit of space throughout our atmosphere contains that additional quantity of energy, this is a massive surge of total energy present in the atmosphere.

All the same, while I do believe there is good enough evidence to suspect that the earth is warming, I have seen no evidence that would make me begin to suspect that the warming is man-made--and I'd go so far as to say that I'm relatively sure carbon dioxide has nothing to do with the matter at all.

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I remember hearing in environmental science class (which was in high school, so not the most authoritative) that global warming pundits have long acknowledge that the rise in temperatures is "only" projected to be tenths of a centigrade over the years--but it is still enough to melt miles of icecaps. I vaguely remembering their heuristic as follows: The thermometer represents an increase in the energy present in a unit of space around the termometer, so the increase of energy in that space corresponding to an increase from 0.0 to 0.1 goes rather unnoticed. However, when every such unit of space throughout our atmosphere contains that additional quantity of energy, this is a massive surge of total energy present in the atmosphere.

Well, that is a bit of a slight of hand.

Yes it might be a large amount of energy represented by a small change in temperature given the whole mass involved, but relative to the total energy contained by the mass (which is also represented by it's temperature) it is still very small. Temperature is still the yardstick, regardless of their attempts to say it's not.

And the fact is the amount of energy only is relevant given the context. Ice still melts at 0C so increasing temps in the antarctic from -20 to -19.1 on average isn't gong to have the massive effect that everyone things. Only when you go to the margins, and show somewhere that is impacted, such as a melting glacier to people see it, and while environmentalists use this to scare everyone that this one thing on the margin will happen everywhere, it's just not the case.

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Off the top of my head, I think the right scale would be one that allows for Y axis to range from the maximum and minimums of average temperatures for the period beginning with the existance of mammals on earth. That would provide a relevant framing of the data for humans. Tufte's first book on visualizing data provides advice on the creation of such charts.

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Are you saying that the right way to determine the (y-axis) scale is by the significance of the data to something we wish to investigate?

If so I agree, and good point.

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Ifat,

Yes, that and one other point: graphing the right data...

When one looks at a graph, and sees something twice as high in Year X, as compared to year Y, the visual message is "twice as high". Even if one can see -- by the scale -- that they've not started the zero of the data point at the visual (x,y) zero (profit graph in my example). Such a graph is visually dishonest.

Another trick is to abandon the use of the absolute values and only plot the rate of change, or (as in Gore's graph) the variation (aka "anomaly"). In such graphs, the presenter hopes that the audience will confuse "temperature" with "variation in temperature". The graph shows a line shooting up. The hope is that the audience will say: "wow! temperatures have shot up", when -- in fact -- they have not.

That type of graph may be fine in the right context. What is that context? It is a context where the audience knows, or has been shown, that it is not absolute temperature that matters, but only the "anomaly" of the average.

If he wishes to graph the variation, then an honest approach would be to relate it to some other variation that the audience can relate to. Of course, my example of Topeka simply errs in the other direction. However, the point is that his is no more right that the Topeka one. Neither is right or meaningful unless the presented explains why. The onus is on Gore to show that his graph has significance. Instead, as presented, it is simply a line with little meaning.

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The best documentary I have ever seen on global warming is called The Great Global Warming Swindle produced by BBC. It showed how everything Al Gore talks about is a load of B.S. and how the CO2 levels in the atmosphere FOLLOW the rise in temperature by several hundred years, and does not PRECEED it, completely reversing the man-made global warming logic.

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