2005-04-15

We can’t predict the weather a week in advance. How can we do it 100 years in advance?

Tim Lambert has another nice post Global Warming Sceptic Bingo, with a pleasing number of the refutations from RC or here... its working, folks. I've been a bit busy building recently, but I notice that Tim doesn't have a refutation for We can’t predict the weather a week in advance. How can we do it 100 years in advance?. This may well be a really stupid argument, but lots of people make it, so its worth debunking:

To get you in the right frame of mind, consider an analogy: sea level at the beach. You can't predict the height of the next wave, or even when a wave will strike ten minutes from now. Yet the tide can be easily predicted years (centuries, probably millenia) ahead.

A better analogy is with throwing a (fair) die: you can't predict whether the next throw will be 1, 2, 3, 4, 5 or 6; yet you can be fairly sure that if you throw it 1000 times you'll get very bored. Sorry: If you throw it 1000 times, the average throw will be close to 3.5. And to pursue this a bit more, if you make the die a bit unfair (by, say, making the 6 twice as likely to come up) then you still can't predict what the next throw will be. But you can be sure that the long-term average will go up to... thinks... about 4 1/3.

Weather is, we are fairly sure, intrinsically unpredictable past a certain limit that isn't precisely known, but is about 1 month. In practice, current NWP (limited by computer size, model completeness and starting obs) can be useful out to about 2 weeks at a stretch. The weather is thus chaotic. As far as can be seen, climate isn't. Obviously, some features of climate can be predicted far further out: we know that winter will be warmer than summer, for a trivial example. But what about the trends in global mean temperature over 100 years? In this situation we have an imposed forcing (increasing GHG concentrations) on top of a chaotic system (weather) which appears to average to a non-chaotic system with intrinsic predicatability (climate).

If you trust the models, you can test this: if you start an atmosphere-only model with differences in the starting state differing only at the numerical-accuracy level (which is far below the obs error the NWP starts from) they diverge within a month. But if you then take the long-term mean of the runs, they are the same. If you start coupled models off with small differences and GHG forcing, they again differ on the weather, and the year-to-year variations in the global mean; but the long term trends match.

38 Comments:

Blogger Belette said...

Oh rats. G "I never post comments on blogs" Schmoot points out that my calc of the revised prob with 6 twice as likely is wrong: the true value is of course (1+2+3+4+5)/7+2*6/7=3 6/7. But the point remains...

6:55 pm  
Blogger Belette said...

And I've just realised that by interpreting "twice as likely" to mean, "twice as likely as it originally was", you can get another prob, viz (1+2+3+4+5)/5*2/3 + 6*1/3 = 4, I think (its 6*1/3 becuase the 6 now has a 1/3=2*1/6 chance of coming up; and (1+...+5) is *2/3 because thats the chance of one of them coming up (1-1/3), then /5 because each hasa 1/5 chance).

8:44 pm  
Anonymous Anonymous said...

I can't predict what the temperature in my lounge room will be tomorrow at 5pm, or Thursday, let alone next week. But I do know that if i turn a heater on in the lounge room now and leave it on, it will be warmer in my loungeroom tomorrow than it otherwise might have been.

My lounge room is analogous to the Earth, and the heater is analogous to CO2 trapping heat in the atmosphere.

9:45 am  
Anonymous John A said...

This comment has been removed by a blog administrator.

10:17 am  
Blogger Belette said...

Comments are expected to be polite. Overfamiliarity and calling my posts nonsense are an excellent way to get your comment deleted. If my full name is too long for you to type, "WMC" is quite OK.

4:10 pm  
Anonymous Anonymous said...

So leaving a post that doesn't agree with your point of view will result in deletion?

I wasn't impressed with your article because it doesn't actually explain why you can't forecast next week's weather, but know the climate in 100 years.

It seemed to me that you put in some information into a forecasting program and trust the result. The forecast is then tuned to take all your loadings, and then you get the result you require. That is not forecasting.

The reason you cannot forecast the weather, but you can forecast the climate in a 100 years is that in 100 years no one will remember or care about your climate forecast.

Climate forecasting only has one purpose, to gain credibility. It's accuracy is irrelevant because you don't need the funding in a 100 years, you need it now!

4:11 pm  
Blogger Belette said...

Why are septics so bad at reading comprehension? Like I said "Comments are expected to be polite. Overfamiliarity and calling my posts nonsense are an excellent way to get your comment deleted."

As to the substance of your comment: you say: "your article because it doesn't actually explain why you can't forecast next week's weather, but know the climate in 100 years.". Thats not quite what the post is about. What the post does is to demonstrate that *not* being able to forecast the weather a month ahead *does not* tell you anything about how good your climate forecasts are.

4:35 pm  
Anonymous Anders said...

Well, Belette, you start the article by saying "I notice that Tim doesn't have a refutation for We can’t predict the weather a week in advance. How can we do it 100 years in advance?"

and

"its worth debunking:"

Now, my reading comprehension may not be up to your standards, but to mee that seems to be saying you are going to refute something.

And you don't. And your first analogy really is not an anology to the case you are making. Firstly because the systems involved are totally different, secondly because you obviously do not have the necessary knowledge about ocean waves and their predictability.

You said you were going to refute a statement, so please at least give it a try.

12:14 pm  
Blogger Belette said...

Anders, you are right: your reading comprehension isn't very good. Have another go.

These are *analogies* not exact correspondences. Of course the systems are different.

Over at sci.env, JA (I think it was) has done a rather better job at demonstrating why the ocean analogy is imperfect.

But as the post says, the dice analogy is rather better. If you want to be honest at attacking your opponents arguments, you start with the strong ones first (Popper). So, have a go at the dice, and read sci.env for the ocean.

3:41 pm  
Anonymous Anders said...

Belette, I'll tell you why the dice is not an analogy. The reason you can't predict weather more than 14-20 days from now (where I live, even 7 days will be no better than a 50/50-shot) has to do with chaos. The system is turbulent, meaning chaotic, meaning unpredictable. Even with a full set of perfectly defined starting points, any simulation will be different from the rest within this short timeframe BECAUSE the system is chaotic. It does not matter how much computing power you throw in, you can't predict it more than those few days in advance.

Your dice, on the other hand, is not chaotic at all. Oh, yes, the results are totally random for each throw. But there is a system of order which can be described mathematically giving predictions of the sort you showed: in a thousand throws, the results will be that for any practical purpose ech number has come up 1/6th of the time (actually, it will probably take more than 1000 throws to prove this, but then we are down to mathematical fiddlings and I'm an engineer. 1000 is close enough).

The climate system does not have this type of inherent stability or systematic behaviour. So your dice are out, as is your attempt at an explanation.

The climate system is inherently chaotic and cannot be predicted, even for its mean state. This could be shown if the modellers would care to present all modelling results. However, as they choose to display only those results in conformity with the prevailing "consensus", you may get the impression that you can predict the mean state. But you can't.

7:14 am  
Blogger Belette said...

As far as can be told, you are wrong. The climate system *does* have a stable long-term behaviour. Winter is reliably colder than summer, and autumn and winter in between. There are long-term stable statistics.

As to what you mean by "conformity with the consensus", I really don't know.

4:09 pm  
Anonymous Anders said...

No, Belette, I am not wrong and you know it.

Please stick to what you started. If my explanation of your dice is wrong, tell me how.

7:06 am  
Anonymous Anders said...

Climate and weather are different, but still the same. Why? Because climate is the variation of weather over longer timescales. It is the same fundamental system, but by looking at it over longer intervals one may see how it differs from one period to another.

Meteorologists started to study climate only a hundred or so years ago. When they started they knew there had to be such a thing as climate. Some of them thought it only varied from place to place but some thought it also varied with time. So how do you go about studying longterm changes in weather? First you decide on a timeframe for climate. Everyone can appreciate that the variation takes a lot of time. At the same time it would be better if one could study more than one period during the lifetime of a scientist. So a 30-year interval was selected. It is long enough to capture variations, and short enough to allow for more than one perido to be studied in detail by a scientist. The problem is that as time goes by this interval will inevitably be seen by some as god-given rather than man-made. I.e. one would start to argue that climate really does shift in 30-year intervals because that is what the observations show. It is easy to see once you forget that the observations are made with the pre-requisite of the 30-year interval.

Enter Man-Made Global Warming as a thesis, and now you can start to count how many "predictions" use data for the "past 30 years"....

Oh, and one more comment on the dice. How many outcomes can the dice have? Six. So whatever you do with the dice, the outcome of any throw is either 1, 2, 3, 4, 5 or 6. It is pre-determined. Now, tell me, how many outcomes may the climate have? Stable/Unstable? Good/Bad? Or anything in between?

An analogy must at least have some resemblance to the other thing you are trying to explain.

7:44 am  
Anonymous Anonymous said...

A better analogy than dice:

The comment about dice being non-chaotic is a good one, so here's a better analogy for you. Consider the path of a snooker ball across a table. That snooker ball is composed of an unimaginable number of individual atoms, entangled in an intriniscally non-linear, chaotic and uncertain (in the Heisenberg sense) way.

Even neglecting the uncertainty principle no-one can, or ever will, be able to accurately predict the state of one of those atoms even a millisecond forward in time.

And yet, as I type this, Steve Davis and Ding Junhui are showing that not only can a single human mind accurately predict the path of this ensemble of chaotic dynamics, but can also predict the effect of the addition of a tiny amount of spin to that system.

Alternatively, consider Brownian motion and the diffusion of gases. Viewed under a microscope, we can see the intrinsically chaotic state of particles of different gases as the diffuse into one another. We simply can't predict the path of an individual molecule as it is buffeted about by other molecules.

And yet, we can predict, with uncanny accuracy, the rate at which those gases will diffuse and mix.

Gareth Owen

5:10 pm  
Blogger JS said...

An even better example of a chaotic system still open to numerical solution is the motion of the astroids in the solar system. It can be shown that the astroid belts display chaotic behavior, much like the weather. It is, however, entirely possible to make predictions as to the average astroid density (corresponding to the climate in our analogy).

- JS

4:30 pm  
Anonymous anders said...

The snooker argument is not very good either. Are you trying to say that we really can't predict the position of the ball at any time? That only goes for th electrons in the individual atoms of the ball, and is really of no interest to the snooker player. For him, the ball is solid matter and can be mastered. It is not chaotic, it is a very controlled environment, that snooker table. What is going on around it may be chaotic, but that is an entirely different story.

8:20 am  
Anonymous anders said...

For the asteroids, I can't see the analogy. The density of asteroids is...what?`Temperature? Wind speed? Rainfall?

What GCM's try to do is not only predict the density of asteroids in the next 100 years, but also tell you which path the major asteroids will take. If the system is chaotic, you simply cannot do that.

8:24 am  
Anonymous Paul Crowley said...

The one-sentence summary of this refutation is not the complex business with the dice, but the analogy with winter and summer. I don't know whether tomorrow will be hotter or colder than today, but I'm willing to make a large bet that it'll be warmer in August than it is now.

6:09 pm  
Anonymous Anders said...

I really don't get that bit...do you really mean that just because winter is colder than summer, the climate is stable? Are you telling me that the climate in the Arctic is stable now since winter is still colder than summer? Are you saying that it does not matter how much colder, just that it is colder?

If that is your argument then there is surely nothing to worry about as no climate model has ever predicted that winter will become warmer than summer. Thus, according to your logic, the climate remains stable today.

As the famous man said, it is not even wrong...

8:35 pm  
Blogger Belette said...

There are different meanings of "stable": the remains-constant meaning; and the smooth-response meaning. Clearly the arctic climate is not remains-constant. But as far as can be seen, it is smooth-response. The winter/summer point is that the climate is clearly not wildly unstable, in the sense of sensitive dependence on initial conditions, the way weather is.

8:58 pm  
Anonymous Anders said...

Aha...is that why there are so large annual and decadal fluctuations in sea ice, for instance? Because it is smooth? I'm just trying to understand what you mean by smooth vs. wildly unstable. Are you implying that weather is wildly unstable and unpredictable, and that for instance annual variations in sea ice are predictable and smooth?

9:24 pm  
Anonymous Anders said...

It is also quite interesting to note that you by introducing a stable climate in the sense of smooth-response actually do remove the threat of sudden climate changes. Following your logic, since winter is colder than summer then the climate system has a smooth-response type stability and we don't have to worry about sudden changes which are at the heart of climate alarmism. Thanks.

8:17 am  
Anonymous Anders said...

As there seems to be some lag in response time here I would like to add something else.

Climate is primarily described as the statistical interpretation of weather over time. In other words, it is a measure for how the "average" weather changes over longer timescales.

This means that the inherent uncertainty in weather predictions are fundamental also for climate. If what you are averaging is unpredictable at some timescale, then the average is also unpredictable, albeit at a possibly different timescale (intuitively the timescale wourl be longer).

Here in Europe we are shown attempts at regional short-term climate forecasts, i.e. what kind of weather is to be expected in the next 3 months. Such forecasts are, by meteorologists, given a 50/50 chance of being correct. They are not much better than a wild guess. In practice that is what we see as well.

So while the weather becomes unpredictable beyond a week, climate becomes unpredictable beyond a month or so.

8:27 am  
Anonymous Anonymous said...

Anders, I can't decide if you have a justifiable distrust of analogies, or just reject any comparison. Climate is individual weather observations/predictions integrated over time and area, taking longer-scale trends into account and allowing us to identify such trends. The observations or predictions may be inaccurate for a specific site or day, but are quite accurate overall. Go back to the law of large numbers. Economics can't tell me what my wage is, or even if I'm unemployed, but it can identify the state of the economy very well, and the effect of policy trends. This is not an anology, it's the exact same statistical propoerties operating. If you reject the weather/climate distinction, then you MUST reject other sciences that rely on aggregating individual data (such as economics, quantum physics).
Thanks, Stewart Longman

1:42 pm  
Anonymous Anonymous said...

The difficulty in judging the accuracy of a weather forecast is in choosing your parameters. For example if a forecast predicts the maximum temp tomorrow to be 16C but it is 16.5C are you going to fail it? If the forecast warns of showers in the afternoon but only a few spots occur- is that a fail? The British Met Office run accuracy checks all the time and have a range of acceptability for such data that seems emminently reasonable. In spite of popular opinion, their forecasts have improved over the years such that big corporations, farmers, the armed services etc pay for forecasts and are generally happy with them. Statistically the next day temperature forecasts are running at 80% accurate with 85% accuracy for rainfall.
If you think you can do better with a wet finger - think again.

Geoff Nelder

9:36 am  
Anonymous Anders said...

I don't know when these last two comments were made as I stopped monitoring this thread a long time ago.

Both comments miss the mark, though. No, I do not reject the climate/weather distinction. i have made it clear what that distinction is, and that the distinction does not take away the fundamental issues concerning long-term forecasts. Belette used his book of citations to make me look as if I went for the easy issues first, I nailed him on it and there was no reply. Telling.

If you do not understand the issues concerning turbulent and chaotic systems, then please do some reading. It is a very difficult subject but as a start I can recommend Roger Pielke Sr.'s website at http://climatesci.atmos.colostate.edu/ for a start. He has some posts on climate forecasting.

If you really believe that climate can be forecast as the overall development of wages in a given country, then I do have a bridge to sell.

9:42 am  
Anonymous Anders said...

Geoff Nelder, the wet finger approach works very well for some sites. Where I live it does not, but then the Norwegian Met Office, which cooperates closely with the British, have problems as well. In Oslo you will get a very high accuracy score by forecasting next days weather the same as todays.

But we are not discussing todays or next days weather. And if you look into such things as the British Met Office's 3-months forecast they state very specifically that they are 50-50 forecasts. This is because they are just now starting out trying to make such long-term forecasts and they have a lot to learn before they can assess whether it is indeed possible.

A 3-month forecast is starting to resemble a climate forecast. What makes you think they will be more accurate forcasting 1200 months when 3 months is 50-50?

9:49 am  
Blogger njh said...

It is common to believe that chaotic systems are completely unpredictable. This is however, rarely the case. Other people have given real world examples of chaotic systems (3 body problem, e.g.) with predictable long term behaviour. I have just run a simple experiment to see whether I can predict the average behaviour of one of the simplest parametric chaotic systems - the logistic map:

def trial(s, k):
x = s # starting point
for i in range(10): x = k*(1-x)*x
print x
for i in range(90): x = k*(1-x)*x
print x

This map takes x to k(1-x)x. We could think of k as perhaps the CO2 level in our system and x the daily temperature. Now it is true that it is impossible to predict the value in 100 iterations (chaos in mathematics means that the error in the result grows exponentially in time). To demonstrate this, try iterating with starting values of 0.3 and 0.300001

trial(0.3, 3.8)
> 0.933608886104 # 10 steps
> 0.7591191831 # 100 steps

trial(0.300001, 3.8)
> 0.933618765594
> 0.673912256944

You can see that in 10 steps things are very similar, but after 100 steps the values are completely unrelated (the previous values are 0.25 and 0.75ish resp!)

So this is a good example of chaos. Now, the claim is that given k, I can't predict the behaviour of an average (say the average of 100 values 10000 steps in the future). To show that this isn't true, I computed the average value of 100 values, 10000 steps in the future, starting from 100 points evenly spread from 0 to 1. I plotted all of these:

(can't use html, so you'll have to copy and paste)
http://njhurst.com/maths/chaos_average.png

You can see that despite the completely chaotic behaviour of the blue samples, the red average is very predictable. If I were a betting man I might wager 10:1 that the average of 100 values would be no more than 1% away from that red line.

So you see, just because the weather system is chaotic, it doesn't mean that it is unpredictable. For a start, we can bound the behaviour by looking at the energy going into and out of the system. Climate modelling is just successive refinement of this idea and is almost completely unrelated to how we model weather.

(I'll also note that claiming weather predictions are inaccurate based on TV figures is naïve - both weather and climate models actually produce a distribution, not a single value. We then need to ask whether these distributions are born out in practice; something you can't do from a single number. You might like to read about information theory to find out how one might test this.)

2:14 am  
Anonymous Anders said...

njh, I totally agree that using your television forecast is not very smart if you want to argue these issues. That's why I mentioned the statements from teh Norwegian and British Met offices. I do believe they take into account what you say. :-)

It is not correct to say that climate modelling is "almost completely unrelated to how we model weather", as weather modelling is part of climate modelling. It has to be, as that is the system you are modelling long term behaviour of.

Anyways. Yes it is true that chaotic systems can be forecast. To do that you would have to know something about their constraints, though. If they are chaotic within certain boundaries, then you could easily find their "mean state" and possibly put that to good use.

This is not the situation with the climate. As we still don't know how nature put us in ice ages (yes we have the overall picture, but not the details for a model) or get us out again, and what other effects there are from altered atmospheric chemistry we really do not know how the mean of the chaotic process might change in the future.

But with a simple system such as you have shown, it sure can be done. Show us with 1000 variables and 100 free adjustments. Please.

6:43 am  
Anonymous Anonymous said...

I'm sorry that you think you could possibly predict the inputs (into the climate) of the next hundred years. That, sir, is silliness. The analogy you're all failing to come up with is this. Will the crowd at the next movie I go see be quiet and courteous, or will it be loud and obnoxious. There is no way to tell as the inputs are incalculable, as are the inputs into climate. Unless, of course, you can predict volcanic eruptions, forest fires, termite reproduction rates, meteorite collisions, fossil fuel discovery and consumption, etc. If you can accurately predict ALL of these, then I say HELL YES, bring on the climate models. Otherwise, it is all speculation of the silliest variety.

Add to this silliness some data of the poorest quality, and you have a recipe for disaster unrivaled by any potential 'climate disaster' that has been dreamed up by the environmentalist movement.

I fear, the thing the environment needs protection from most is environmental protection.

--Stephen

7:02 pm  
Anonymous Anonymous said...

"Climate and weather are different, but still the same. Why? Because climate is the variation of weather over longer timescales."

What rubbish. Climate is not the "variation" of weather over longer timescales. It is the *average* of weather over longer timescales. Operating on this assumption that variance is the same as a mean has led Anders quite far astray here.

4:06 am  
Anonymous Anonymous said...

Anders, thanks for keeping the alarmists honest.

There are basically four groups of people with an interest in alarmist campaigns such as Global Warming.

Type 1: Economic/Political Interest. e.g. Russia. Whether they actually believe in Global Warming or not, their motivation is to politicize it for internal and international political purposes, and in their own economic interest. (They view success of the U.S. finiancially as competition to them, as if there is some maximum market size (which there is not)).

Type 2: Nothing better to do but be a greenie and to oppose establishmentarianism. They really have no concept of global markets, but just throw out claims like "George Bush didn't do enough to combat Global Warming this week". They really don't have the ability to thoughtfully analyze data on their own, but look at a photo of a mountain top in January and a photo of that same mountain in September and then call the melt 'Global Warming'.

Type 3: These are the third world nations who see the Western civilization as their oppressor, rather than their own government.

Type 4: These are the realists... the one who realize all the Global Warming is alarmist hype.

9:28 pm  
Blogger Eriza said...

I think we need to be more precise on this. The word "average", or the more technical term "expected value", has a specific meaning in probability theory, and it is in general can NOT be used to predict future outcome of an experiment. Referring to your die experiment, just because the average output of a fair die is 3.5, doesn't mean that the next outcome of a die-casting experiment will be somewhere between 3 and 4. In fact, you only have a chance of 67% that the experiment output is between 3 and 4, and 67% can not be considered as "certain enough". You need something like 90% or higher (99.9999% or something like that).

Back to the weather, just because we know the "average weather" (whatever that phrase means), doesn't imply that we can predict future weather condition.

11:32 am  
Anonymous Yves said...

"If they are chaotic within certain boundaries, then you could easily find their "mean state" and possibly put that to good use.

This is not the situation with the climate."

Go to the Sahara, then, or to Antarctica. I can say for sure that both will remain respectively hot and cold deserts for a while, regardless of the future GHG emissions, volcano eruptions and Madame Soleil. I can predict as "virtually certain" that on July 1, 2050, or 2200, at noon, the Sahara will be warmer than say 25°C. Can also predict that "very likely" there will be a catastrophic global warming caused by the Sun within 2 billion years. So what ? The interest of climate studies is to explore the boundaries between the stable and the chaotic behaviors, and the expected effect of different external events (GHG, volcanoes, Sun,...) on these boundaries, as well as of the recent history (internal variability). Chaos doesn't mean unpredictability, and broad generalisations like "we can't predict anything" are essentially of no interest.

Yves

2:30 am  
Anonymous Monty said...

There are eight weather models I've seen which predict 'global temperatures' for the years 2000 to 2100. The most optimistic says the increase by 2100 will be about 4 degrees F, the least 9 degrees F.

Between 1980 and 1995 there were more than 50'scientific' papers published predicting what air temperature would be if the carbon dioxide concentration doubled. One study predicted a change of 0.35 F, two predicted 2.5 degrees, and the other predictions ranged from 11.3to 15.7 degrees.

Why do these models vary from one another so much? I believe this is the answer: if meteorology were a science like physics, there would be only one model and it would predict accurately.

But it's not a science, and we should not believe the alarmists who seem to think it is.

10:28 pm  
Anonymous Anders said...

Anonymous said: "Climate is not the "variation" of weather over longer timescales. It is the *average* of weather over longer timescales. Operating on this assumption that variance is the same as a mean has led Anders quite far astray here."

*******
If you insist on a strict interpretation you might want to tell us how you came up with the idea that "variation" = "variance".

Or you could possibly try to think a little bit and then try to explain why the *average* of weather somehow does not vary over time or on different timescales.

Or maybe you should just concur that climate is the variation of weather over time, be it described as a mean, median, extremes or other meaningful measures. It is of little interest knowing how the mean changes unless you also describe the change in variance, don't you think?

11:29 am  
Anonymous Anonymous said...

shut the fuk up bich u mad dumb

11:33 pm  
Anonymous Anonymous said...

A dice is a chaotic system. The result (what you throw) is extremely sensitive to initial conditions (how you throw it).

So there!

1:07 pm  

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