Mars melt and Global Warming

[lenny]

Everything I've seen about economics says that price with time graphs should use a logarithmic scale.

look in the wall street journal or the financial times: almost all graphs of stock value are linear in price and time; given the aims and time scales of the users of that information, price vs time is the more relevant quantity.

when studying financial time series, statisticians often move from price to returns and logarithms because the data then looks more like the available class of linear models.

your right of course that you have to be careful not to mislead people with the graphics, but in climate and weather we are more interested variations about some benchmark, often taken to be a long term average. there is nothing magic about that value of "zero" in the way that an economic value of zero is special. zero K is special, but we are far from that value, percentage changes relative to that value have little physical relevance, while temperatures like the freezing point of water do.

hmmm. there must be a better way to say this....

 

[varwoche]

Everything I've seen about economics says that price with time graphs should use a logarithmic scale.

There's nothing inherent in economic data that makes this true as a rule or even a majority case. It depends on the data set, the time span, and what the chart is trying to convey.

 

[CapelDodger]

Another question about these charts:

I know in the economics world when you want to show trends over time, you make your graphs with a logarithmic scale. That way, a 10% rise is always represented by the same distance on the graph, no matter how high or how low.

Logarithmic scales are used when looking for changes in rates of change rather than in absolute quantities - inflation rates, say, being graphed as prices on a log scale against time. A stable inflation rate is represented by a straight line. Rates of change in the rate of change can be inferred from the gradient of the graph.

Measurements of, for instance, temperature or CO2-load are absolute measurements and shown as such. A stable situation is again represented by a flat line. Rates of change can be inferred from the gradient of the graph.

So, why are all the GW graphs linear? The Celsius scale is linear, as is the ppmv of CO2 concentrations. So, in order to do these graphs properly, shouldn't they be using logarithmic scales? We are attempting to show change over time, after all.

If the doubling of CO2 from 280-560 was equivalent to doubling it from 560-1120 this might be the case. On a logarithmic scale the recent increase in atmospheric CO2 would be levelling off now, even though it's still increasing at 2ppm (an absolute amount, not a proportion of existing CO2-load) per annum. Which would be misleading, wouldn't it? It would tend to make people think the problem was waning when it's actually getting worse at the same rate. Each annual increase of 2ppm represents a smaller proportional increase in the cumulative total, but it's still 2ppm more CO2.

 

[CapelDodger]

Everything I've seen about economics says that price with time graphs should use a logarithmic scale.

It depends what you want to represent, and how you express the price. Historical grain-price series quite often calculate prices against a standard wage - often a mason's wage, funnily enough . (Is there a Freemason smilie? There surely ought to be.) Modern oil-price series are often priced against "constant dollars", dollars adjusted for inflation. You don't use logarithmic scales in such cases.

But one of the critiques of the linear scale in economics is that you're giving people the wrong impression. You might be showing people that your fund is growing, when in fact the rate of growth is decreasing. This would show very well on a ratio scale but a linear scale would make it look like the growth rate was continuing to rise.

And let's not kid ourselves that such tricks aren't used a lot. Not that they'd work on a savvy bunch like us .

In Al Gore's movie, he shows the hockey-stick and shows CO2 levels being way, way above what they were and growing at a much faster rate. He even gets up on a forklift to try and make the point. He did that, not because it's good science, but because he wanted to scare people with runaway CO2. Otherwise, he would have just shown the graph and not bothered with the forklift. Had the graph been done on a ratio scale, the rate at which CO2 levels are increasing would be shown more accurately, but they wouldn't scare people as much.

Al Gore made a movie. Science doesn't make good movies. It can make pretty soporific slide-shows for those who aren't passionate about the subject-matter. Al Gore is trying to raise awareness of the issue, so he makes extravagent gestures.

If you were told that the mercury-content of your tap-water went from 2 to 3 ppm in 2005 and from 3 to 4 in 2006, so the rate of increase has fallen from 50% to 33% therefore suggesting that the problem was being addressed, would you not be outraged? The cumulative amount is what's at issue in that case, and the same applies to CO2.

 

[CapelDodger]

can you just clarify if your claim is that any attempt at extrapolation is not science?

Going off on a tangent somewhat, but regarding models. I play pool a bit, the British pub-version, and there's a model in my brain dedicated to extrapolating from a particular shot. I consciously plan the break and the first shot in silent consultation with it, and having decided on the shot leave the details to the model. I don't try to apply geometry, the model tells me where and how to hit the cue-ball and I don't second-guess it. I concentrate on getting my stance and my bridge right - those are parameters the model is assuming.

I do pretty well, though I say so myself. I even have a trophy. Biggest Fish In Small Pond, 1987 .

Here we have a neural-network model, of course, which is very different from climate models. Climate models incorporate known physical laws, neural-networks just don't care. Climate models can be applied to Mars, but my pool-playing neural-network would be all over the place on a pentagonal table. Dart-playing neural networks don't learn how to hit a target, they learn how to hit a target from seven-foot-six. Stand closer and they can't adjust.

The accusations against climate modelling are essentially based on the idea that climate models are like neural-networks, that they assimilate data and build to something that gives a desired outcome. this is essentially wrong. It assumes that scientists (not just climate scientists) have a desired outcome - to demonstrate that the Western way of life is unsustainable - and manipulate the model to give that result. Whereas scientists actually have a different desired outcome - to be right. Or at the very least not egregiously wrong during the active part of their careers. The climate models they've produced have done a remarkably good prediction job over the last twenty years, while their detractors are mired in argument over minutiae dating from the early 90's. I guess the actual outcome has been too uncomfortable to engage with.

 

[shanek]

Logarithmic scales are used when looking for changes in rates of change rather than in absolute quantities

But isn't that exactly what the CO2 charts are meant to show?

If the doubling of CO2 from 280-560 was equivalent to doubling it from 560-1120 this might be the case. On a logarithmic scale the recent increase in atmospheric CO2 would be levelling off now, even though it's still increasing at 2ppm (an absolute amount, not a proportion of existing CO2-load) per annum. Which would be misleading, wouldn't it? It would tend to make people think the problem was waning when it's actually getting worse at the same rate.

"Getting worse at the same rate" should be represented by a sloped line on a logarithmic scale. The linear scale makes it look like it's getting worse at increasing rates.

 

[shanek]

Modern oil-price series are often priced against "constant dollars", dollars adjusted for inflation. You don't use logarithmic scales in such cases.

Uh, no, just expressing prices in real instead of nominal values does not mean you do not use a ratio scale.

Here's a good explanation of them:

http://www.harrybrowne.org/articles/RatioScales.htm

A ratio scale makes it possible to compare at a glance the magnitudes of changes that occur at different ranges. For example, if an investment rises from $1 to $2 during one time period, and later in the graph it rises from $3 to $6, a ratio scale will make it obvious that each rise was of the same magnitude. A linear scale would make it appear that the second rise was proportionally three times as great as the first rise.

On a linear scale, a vertical inch (or any other distance) represents the same number of units (such as dollars) wherever it appears on the graph. On a ratio scale, a vertical inch represents the same degree of growth wherever it appears on the graph.

Ratio scales are appropriate for investment prices, sales figures, income, or any other absolute amounts being plotted over a period of time. They should not be used to plot anything in which a relationship is already inherent in the amounts — such as percentages (like the inflation rate), ratios between two items (such as a gold-silver ratio or price-earnings ratio) — because the benefit provided by a ratio scale is already built into the figures being plotted.

Here's a realistic demonstration:

http://www.iea-macro-economics.org/efgp.html

Note that real dollars are still plotted on a ratio scale, whereas the growth rate is on a linear scale since it's already a percentage.

And let's not kid ourselves that such tricks aren't used a lot. Not that they'd work on a savvy bunch like us .

Generally not in front of economists who know better, though. And a company that published their financial data that way just might be getting a little visit from the SEC...

Al Gore made a movie. Science doesn't make good movies. It can make pretty soporific slide-shows for those who aren't passionate about the subject-matter. Al Gore is trying to raise awareness of the issue, so he makes extravagent gestures.

Don't get me wrong, the forklift thing was kind of funny. My problem is that he was talking about how fast the CO2 level was rising compared to earlier and yet he hadn't plotted his graph on a logarithmic scale.

The cumulative amount is what's at issue in that case, and the same applies to CO2.

Scientifically, yes, but politically (which is Al Gore's motivation, make no mistake) the issue is scaring people. And I contend that using a linear scale to plot out CO2 increase and then claim that it shows "runaway" levels is misleading at best, dishonest fear-mongering at worst.

 

[shanek]

Think of it this way: If you want to show that reducing emissions, while not reversing the trend, is making a difference, then you will want to plot that on a ratio scale, as the linear scale would (as in the fund example above) make it seem as if there's still "runaway" emissions. The ratio scale would show that our efforts are causing the rate of rising CO2 concentrations to decrease.

That is, if your motive is to educate people and not just scare them into passing your agenda.

 

[rockoon]

thanks for the questions.

can you just clarify if your claim is that any attempt at extrapolation is not science?

I did. Don't read anything more into what I said than I actualy said. I said what I meant. Clear now?

do you object to the study of future climate itself, or merely to the way it is being done now?

I said what I objected to, clearly and concisely. I object to CapelDodgers lies (more later), and I object to existing climate models being used to influence policy.

I say what I mean so please don't treat me like someone who doesn't.

 

[rockoon]

the type of graph depends on the point you are trying to make

You do not find fault with this?

I do.

 

[lenny]

If you want to show that reducing emissions, while not reversing the trend, is making a difference, then you will want to plot that on a ratio scale,.

i expect you'd want to plot what you wanted to show: the annual emmission per year on a linear scale, which would be going down.

as the linear scale would (as in the fund example above) make it seem as if there's still "runaway" emissions.

.
no, if the emissions were reduced, the slope of the curve on the linear scale would decrease.

the examples in your link refer to exponentional growth, where the slope keeps increasing (proportional to the current value of x): that really is a "runaway" scenario: why hide it? this is what happens with (initial) neutron counts inside nuclear bombs. the log scale makes such explosive growth easier to plot, but are often misleading.

The ratio scale would show that our efforts are causing the rate of rising CO2 concentrations to decrease.

regardless of the labels, plots only refelct the obs: they never tell us the causes.

 

[rockoon]

The accusations against climate modelling are essentially based on the idea that climate models are like neural-networks, that they assimilate data and build to something that gives a desired outcome. this is essentially wrong.

A lie.

The desired outcome of a climate model is to mimick existing samples of past climate. That is a desired outcome. Parameters are tweaked until that outcome manifests. The source of these tweaks is irrelevant. They are tweaks which have no other purpose than to manifest the desired outcome.

There is a big difference between tweaking a parameter and setting a constant based on its known measured value.

A parallel exists in astophysics where a "dark matter" parameter was tweaked. This parameter represents the unobserved. Much to the dismay of early models, "dark energy" was observed which throws off all that tweaking they were doing. All the prior large scale cosmological models became rubish overnight. The search for the omega constant became a completely meaningless enterprise.

New observations easily invalidate tweaked parameters.

to demonstrate that the Western way of life is unsustainable

Strawman, or a lie.

The climate models they've produced have done a remarkably good prediction job over the last twenty years

'cept for that pesky bit where they repeatedly fail to predict anything better than "warmer" - fairly easy target to hit

March 2006: 

And although current computer models fail to predict this warming trend, the scientists 
argue that the data is consistent with what would be expected as a result of increasing 
greenhouse gases. "Our next step," Turner says, "is to try to improve the models."

Improve the models without a new theory or new phenomenon? How would they manage that? Perhaps by tweaking? Sigh. I'd love to hear an explanation that doesnt involve tweaking.

 

[lenny]

the type of graph depends on the point you are trying to make

You do not find fault with this?

I do.

i admit i realised that this statement might have been something of a hook. thx for taking it.

if your aim is to communicate science, fairly and with all uncertainties as clearly stated as you can, you still have to make this choice. it is a basic dilemma of education.

you make a point and then explain it and its weaknesses. it would not be very informative for me to simply post years of temperature readings from heathrow airport (or longer records from the quad of an oxford college). or the price of tea in china. what you present and how you present it depends on the what you are trying to illustrate. how could it be otherwise?

there is no fault to be found in the fact that one is trying to make a point. i expect it is much more detrimental to understanding when we forget that this is what we are doing, as it makes it harder to find the flaws in our own position.

 

[lenny]

in your post 112

A lie.

you assign quotes to me that i never posted (as following the links you offer to my original posts prove).

please edit that post: i never said such things.

thx

 

[a_unique_person]

A lie.

The desired outcome of a climate model is to mimick existing samples of past climate. That is a desired outcome. Parameters are tweaked until that outcome manifests. The source of these tweaks is irrelevant. They are tweaks which have no other purpose than to manifest the desired outcome.

There is a big difference between tweaking a parameter and setting a constant based on its known measured value.

A parallel exists in astophysics where a "dark matter" parameter was tweaked. This parameter represents the unobserved. Much to the dismay of early models, "dark energy" was observed which throws off all that tweaking they were doing. All the prior large scale cosmological models became rubish overnight. The search for the omega constant became a completely meaningless enterprise.

New observations easily invalidate tweaked parameters.



Strawman, or a lie.



'cept for that pesky bit where they repeatedly fail to predict anything better than "warmer" - fairly easy target to hit

March 2006: 

And although current computer models fail to predict this warming trend, the scientists 
argue that the data is consistent with what would be expected as a result of increasing 
greenhouse gases. "Our next step," Turner says, "is to try to improve the models."

Improve the models without a new theory or new phenomenon? How would they manage that? Perhaps by tweaking? Sigh. I'd love to hear an explanation that doesnt involve tweaking.

I already linked to an explanation of one 'tweak', the amount of CO2 the oceans can absorb. That is unknown, clearly. But it can be measured, and from the measurement, and past climate behaviour, estimates made of what the future ability to absorb will be. One thing you can be sure of, the estimates can't be too far out, because the oceans will not suddenly cease to absorb CO2, or suddenly absorb much more CO2. The tweaks will need to be done, but the they will be pretty close to what will happen. If they are out, (and they will be out, by some extent), that won't mean that suddenly the earth will start cooling by some miracle.

 

[Schneibster]

you assign quotes to me that i never posted (as following the links you offer to my original posts prove).

Good lord, lenny, you actually read anything buffoon has to say? Watch out:

Negative information alert
This negative information can result in the loss of IQ points. This loss may become permanent under prolonged exposure. Immediate implementation of the mute button is strongly recommended to preserve your intellect.

 

[shanek]

i expect you'd want to plot what you wanted to show: the annual emmission per year on a linear scale, which would be going down.

Emissions per year should be plotted on a linear scale, yes, since the ratio is built-in to the numbers. But this graph was the overall concentration, which is (partly) the effect of the emissions reductions. That graph would answer the question, what effect is it really having? Which, I think, is important. And that graph should be plotted on a ratio scale.

no, if the emissions were reduced, the slope of the curve on the linear scale would decrease.

No, it wouldn't; it would continue to rise, and there would be no visual clue that the rate of the increase was lower than it was before.

 

[CapelDodger]

But isn't that exactly what the CO2 charts are meant to show?

CO2 charts show the CO2 content of the atmosphere, not the rate of chang. The rate of change can be inferred from the gradient of the graph.

"Getting worse at the same rate" should be represented by a sloped line on a logarithmic scale. The linear scale makes it look like it's getting worse at increasing rates.

If the rate of increase is stable - not getting worse or better - the gradient remains the same and the line straight. If the gradient increases (the line curves upwards) the rate of change is increasing, which should be of greater concern than the absolute cumulative total so far.

That's on a linear scale, which most people can understand. On your favoured logarithmic scale each year's 2ppm is a smaller proportional increase in the cumulative total, so the line would curve downwards - even though the absolute rate of increase remains stable. Which would be misleading.

When it comes to atmospheric CO2-load the rate of change is a secondary issue, the cumulative total is the primary issue. That's what causes the actual warming.

 

[CapelDodger]

Uh, no, just expressing prices in real instead of nominal values does not mean you do not use a ratio scale.

The ratio has already been accounted for in the calculation of real values. A logarithmic scale would not only be redundant but incorrect. Anyone faintly competent can read rates of change from a graph. In oil-price series people are generally looking for absolute comparisons, which are difficult to interpret from a logarithmic scale.

That rather makes the rest of the post redundant as well .

Price-series on assets that are owned on the basis of the rate of return they offer are naturally priced on a logarithmic scale where a stable rate of return is represented by a comforting straight line upwards.

 

[CapelDodger]

Think of it this way: If you want to show that reducing emissions, while not reversing the trend, is making a difference, then you will want to plot that on a ratio scale, as the linear scale would (as in the fund example above) make it seem as if there's still "runaway" emissions. The ratio scale would show that our efforts are causing the rate of rising CO2 concentrations to decrease.

The ratio scale would make it appear that efforts are having an effect even if the absolute rate of change remained entirely unaffected. It would even mask an increase in the absolute rate.

If the chart showing cumulative CO2 concentrations appears to you to demonstrate runaway emissions, what makes you think you're wrong?

That is, if your motive is to educate people and not just scare them into passing your agenda.

Your motive seems to be finding graphs that you find comforting. Unto the seventh differential; at some point you'll find a rate of increase that's on a downward trend.