Thursday, June 11, 2009

Arctic Sea Ice Briefly Continued

I had a couple of recent posts, pointing out what appeared to be an inconsistency between the claim on a JPL page that the latest data showed arctic sea ice continuing to shrink and the publicly available data, which appears to show that a ten year decline reversed a bit over a year and a half ago. None of the commenters on the posts managed to explain away the discrepency, so I emailed someone at NASA. He was a pleasant and courteous correspondent, but seemed unable to distinguish between the question "do we have reason to expect arctic sea ice to continue to shrink" and the question "is what JPL said on this page about the evidence true?" Eventually he conceded that he was a media person, not a scientist, sent my question off to a scientist at the National Snow and Ice Data Center, and sent me the response.

That response again ignored the question of whether what JPL said was actually true, to focus on whether the conclusion they were arguing for was true. I emailed him, pointing out that what I was asking was not whether there was good reason to expect further shrinking but whether the JPL assertion about the current data was true or false.

I got back an evasive answer that came down to (not a quote) "the long term trend is down, so objecting that JPL says the current data shows that trend continuing when it doesn't is merely a technical semantic objection."

I concluded that he, unlike the gentleman at NASA, understood my question, and that his real answer was that it was all right to lie to people about the evidence as long as you were telling them what you thought was the truth about the conclusion. I sent him off a reference to the Orwell piece that discusses the dangers of suppressing the truth for fear that it would "play into the hands of" the opposition.

And I now know that nothing said by NASA/JPL ought to be trusted. Readers of this blog may want to check the JPL claim against the data for themselves before deciding whether or not they agree with that conclusion. I have provided the links above.


GregSJ said...

This reminds me of the argument about whether you are lying when you think you are telling the truth. In other words is a lie a false statement regardless of intent or is a lie a statement intended to be false.

This leads to the far more interesting question if you think you are telling someone a lie, but the statement happens to be true are you lying?

Steve said...

Life's too short and I shouldn't really be bothering, but you just don't get it. I'll have one more shot at illustrating the maths and then give up.

If you look at the noisy graph (your first one) and draw almost any trend line you like through the last short period, you can then go back over the rest of the graph and see that you can match that same short upswing unto a good quarter of the graph. That's what I mean by "noise".

Or, moving away from the contentious issue of Actual Scary Data, you could try this:

Take a formula, more or less any formula. Keep it simple, and lets use y=9x+30. Plot that, and you have a nice straight line of a given slope. Now, try a second graph, where you are plotting the same formula with a random factor added - say y=9x+19+(3d6) with 3d6 being what you get when you chuck three six sided dice (I'm hoping here that if you don't understand maths and stats, you may just understand D&D).

You will get a nicely noised up line that over the long term has the same trend as the first one, but over the various short term sections will appear to climb or nosedive several times faster for runs of seven or eight points at a time.

NOW do you get it?

Andy said...

THIS is the NASA I know - they bring a whole new meaning to the phrase "political science." I ran across this as a contractor all the time.

However this is not new. The medical community started it in the 1960's with the fraud based Framingham study publications (that show something other than the data taken - see for example the paper by Demer, Port et al. in the January 2001 issue of Lancet). Currently it is going on with vaccines, where EVERY SINGLE PAPER but one out of over 100 shows it is more likely than not vaccines cause autism, yet the medical community chants it isn't so and kangaroo courts go along with them.

Compared to the damage already done by medical shennanigans, simply destroying the economy under the pretense of preventing global warming is a very small price to pay.

I am sure it is ubiquitous, and brings to mind the vast number of academic opinions and experts who used to 'prove' blacks were inferior - an assertion very difficult to view credibly if one watches sports on TV!

The acceptability of simply lying to gain political power - as Hitler advocated and most politicians practice - is the inevitable consequence of public education. Students will be taught it is OK to lie if it is for the good cause of putting a bureaucracy in charge of something.

Matt Brubeck said...

I expect that Steve's argument is exactly what the NSIDC scientist was trying to tell you, and I agree.

Looking at the raw data ("Graph A" from your second post, which is not seasonally-adjusted), it's clear that the "actual" trend reverses twice a year. If you're going to demand that short-term reversals invalidate a trend, then you're equally wrong to say that the ice extent has been "rising for the past two years," since it's actually been shrinking for twelve months out of those two years.

Any meaningful discussion of long-term trends will need to separate signal from noise, and adjusting for cyclic trends is only one step in that process. By "trend" they clearly mean the long-term trend shown by the linear regression in the NSIDC report (the final graph in your second post), which is indeed still negative with the latest data included.

jimbino said...

I can't disagree with your argument, but it bothers me no end that you have not mastered use of the subjunctive mood in English.

"That response again ignored the question of whether what JPL said was [were!] actually true, to focus on whether the conclusion they were arguing for was [were!] true. I emailed him, pointing out that what I was asking was not whether there was [were!] good reason to expect further shrinking but whether the JPL assertion about the current data was [were!] true or false."

David Friedman said...

Several commenters seem to be confusing two rather different questions:

1. Does the recent data prove that the long term decline is ended?

The answer is that it does not--it is possible that the recent rise is merely random noise superimposed on a falling graph.

2. Is the recent data evidence for or against the claim that ice cover is continuing to shrink?

The answer is that it is evidence against. It isn't strong enough evidence against to prove that the shrinking trend is over. But it is evidence against, not for.

Isn't that obvious? If an increase isn't evidence against the continuation of a downward trend, what would be?

Finally, I put the following question to those defending the NASA/JPL page:

Suppose the page had instead said:

"While recent data shows some expansion of arctic sea ice area, we believe that this is only a temporary reversal and the long term shrinking trend will continue."

That is a more accurate description of the evidence than what was written. What do you think would have happened to the career of the NASA employee who wrote that page?

Russell Hanneken said...

jimbino, why is the subjunctive mood called for in the passage you quoted? (Sorry, I know this has nothing to do with David's original post, but I'm curious.)

Tim Lambert said...

Either 1. All those people are lying,
or 2. You don't know what a trend is.

I vote for 2.

A decreasing trend is not the same as monotonically decreasing.

GregSJ said...

In my opinion the question is not what is a trend but rather what does the latest data show.

The original quote states "The latest Arctic sea ice data from NASA and the National Snow and Ice Data Center show that the decade-long trend of shrinking sea ice cover is continuing."

It seems clear to me that the latest Arctic sea ice data does not support the trend continuing but rather shows a slight reversal (as the author has continually pointed out).

Thus much of this argument seems to be over semantics. Most commenters seem more concerned with the overall trend than the question concerning the specific point; whether the latest data supports the continuing trend (not whether it refutes it). Perhaps due to the sensitive nature of climate change, people seem to think pointing out the falsity of this statement is an attack on the claim that sea ice is declining. I have yet to see a place where the author has made such a claim. In fact his recent response seems to indicate that he believes the recent data may be no more than noise.

All and all I would like to believe that the recent data does show a reversal of the declining sea ice, because it would be a sign that humanity is reducing its impact on the globe. One would think that such potentially positive news would be greeted with optimism for the future rather than hidden. (Perhaps fear that the perils of global warming are not taken seriously is the real motivating factor. Thus bringing me back to my original comment about the rhetoric of when is a lie a lie.)

David Friedman said...

Tim writes:

"A decreasing trend is not the same as monotonically decreasing."

True. Hence one year of increase doesn't prove that the trend isn't decreasing.

But the JPL claim is not merely that recent increases aren't enough to prove that the trend isn't decreasing. It's that the recent evidence supports the trend--shows that the decrease is continuing.

Do you really believe that an increase is evidence of the continuation of a decreasing trend? If so, what wouldn't be?

Tim Lambert said...

An observation close to the trend line is evidence that the trend is continuing. One significantly above would be evidence that the trend has ended.

Patri Friedman said...

I am amazed that so many people agree that:

"The latest Arctic sea ice data from NASA and the National Snow and Ice Data Center show that the decade-long trend of shrinking sea ice cover is continuing"

Is true. Let me try to explain David's point another way (I'm talking to Steve, Matt B, and Tim L, here).

Consider yourselves as Bayesian reasoners. (If you don't know what that means, stop trying to argue with David about statistics!). You have some current belief about the global warming and the expected change in Arctic sea ice over the next decade. Say you think there is a 95% chance that it will shrink, at least at the rate indicated by the trend line from the *last* data set.

Now you see this new data set. You perform a Bayesian update. It seems quiet clear from the data that your update will *reduce* your estimate. Sure, there is noise, as Steve says. Sure, the observation is not so enormously far from the trendline as to make us massively update, as Tim seems to think is necessary for a new data point to be evidence against a model.

But all of that is irrelevant to the fact that the data is the wrong way from our trendline, and thus we must update our probability by decreasing it. We probably won't decrease it below 50% - this is just a few years of reversal, after all. So the old model is still fairly likely. We haven't invalidated the model. But we have provided evidence against it. Small evidence. Evidence that could be noise. But evidence nonetheless.

It doesn't seem right to me to interpret "show that it is continuing" as "provides slight evidence against it while leaving open the strong possibility that our previous beliefs were true". "Makes slightly less likely" may not mean "invalidates", but it doesn't mean "shows that it continues" either.

Matt B - throw a 1-year moving average on the original graph, and you get the same results, that the last 2 years have reversed the trend. So I don't see how it can be an issue of seasonal variation.

Anonymous said...

The graph goes up and down (noise) but with a general trend downwards - fact. The latest data we have available is of an upwards nature consistent with previous upward movements from within the definite downward trend. Is this a noisey-up or a trend-changing-up? It is impossible to tell since a trend-reversal-up would look exactly the same and it definitely isn't evidence that the downward trend is continuing which was the claim. Not sure which part Steve doesn't get.

Steve said...

Anonymous@2.15am: Is this a noisey-up or a trend-changing-up? It is impossible to tell since a trend-reversal-up would look exactly the same - which is exactly my point.

Tim Lambert said...

OK, if we are Bayesians then the relevant question is whether the new observation increases the probability that there is a trend of some particular magnitude. I think it should be intuitive that observations close the the trend line will increase that probability, irrespective of whether they are above or below the previous observation, but let's work a simple example.

Hypothesis A is that there is an increasing trend, such f(t) = t-1 with probability 1/4, f(t)=t with probability 1/2 and f(t)=t+1 with probability 1/4.

Hypothesis A' is that there is no trend and f(t) is 0,1,2,3,4,5,6 or 7, all equally likely (probability of each = 1/8)

We somehow know that these are the only two possibilities.

After making some observations we think that P(A) = 1/2 (and hence P(A') = 1/2).

Now we make another observation and find that f(5)=6. How do we update our beliefs?

Let B be f(5)=6.

P(B|A) = 1/4
P(B|A') = 1/8
P(B) = P(B|A)P(A) + P(B|A')P(A') = 3/16

Bayes theorem says:
P(A|B) = P(B|A)P(A)/P(B)
= (1/4*1/2)/(3/16) = 2/3

The probability of A being true has increased, so observing that f(5)=6 is evidence for the trend being true.

Now we make our next observation and find that f(6)=5. Oh no! It's less than the previous observation. How do we update our beliefs?

Let C be f(6)=5.

P(A) = 2/3 (because we updated it)
P(A') = 1/3
P(C|A) = 1/4
P(C|A') = 1/8
P(C) = P(C|A)P(A) + P(C|A')P(A') = 5/24

Bayes theorem says:
P(A|C) = P(C|A)P(A)/P(C)
= (1/4*2/3)/(5/24) = 4/5

The probability of A being true has increased again, so observing that f(6)=5 is evidence for the trend being true, despite the observation at t=6 being less than that at t=5.

Chris said...
This comment has been removed by the author.
Anonymous said...

Anonymous@2.15am: Is this a noisey-up or a trend-changing-up? It is impossible to tell since a trend-reversal-up would look exactly the same

Steve: which is exactly my point.

So if we agree we can't tell if the trend is continuing or not how can they claim it is continuing? *baffled face*

Paul Birch said...

A movement in a direction opposite to a purported trend disconfirms that trend. It reduces the correlation between the model and the evidence. It makes it more likely that the purported trend was never real or has now ended.

It must surely be obvious to anyone that JPL is not simply trying to make some subtle statistical point; they're deliberately spinning the evidence for political purposes.

Arthur B. said...

@Tim Lambert

If you are trying to decide between no trend at all and a downward trend, then indeed the new data is evidence for the continuing downward trend.

However, that requires you to exclude other hypothesis, why would you do so?

No one seriously argues that there is no trend in ice shrinkage, it's obviously a continuous process, not white noise.

You can posit a model where seasonally adjusted ice surface is mean reverting around a slowly moving average surface, a "trend"

In this case, the data is evidence that the trend is turning, not evidence against it.

Eric Rasmusen said...

"The latest Arctic sea ice data from NASA and the National Snow and Ice Data Center show that the decade-long trend of shrinking sea ice cover is continuing."

How about this, as good news for Republicans?

"The latest data show that the decade-long trend of increasing Republican residency in the White House is continuing."

Just disregard that noisy blip of the past four months.

Eric Rasmusen said...

This discussion reminds me of a trick I've seen used in global warming data: presenting a moving average instead of the actual data. Not only does this help you win your argument for a few years after the data starts refuting you, but it also conceals how noisy and unreliable the data really is.

Steve said...

Anonymous@5.42am: if we're only looking at that short interval in isolation, the short answer is that we can't - there's simply not enough data. However, if we look back over the historical range of data, then we see that such interludes have been part of a general downward trend, and this needs to be taken into account somehow (all other things being equal, things tend to stay the same or change at the same rate).

Now, if we could point to an event of some sort just at the beginning of the upward move that could be shown to have suddenly changed the situation, it'd be easier to see the uptick as the beginning of a new trend....

Tim Lambert said...

Eric, the definition of climate is average weather. Taking averages is not a commie plot, it's what we mean by climate.

Eric Rasmusen said...

True, there's an inevitable problem of deciding whether to use a spot observation (January 1 of each year) or an aggregate (the average temperature over a year). But that's different from using a moving average, which double-counts data.

A stats question: does using a moving average inevitably reduce variance? (it reduces the maximum observation, but it spreads the influence of that maximum over several years)

David Friedman said...

Let me see if I can put the argument in simple terms:

Case A: Two alternative hypotheses:

1: The downward trend is continuing.

2. The downward trend has ended--from now on we will have a roughly constant area of arctic sea ice (varying, of course, with the seasons in the usual way), with some random variation.

We have a new observation, showing the area the same as it was in this month last year. That result is consistent with either hypothesis, since we expect some random variation, but it is more likely with hypothesis 2 than with hypothesis 1. Hence observing that result raises our subjective probability for 2, lowers it for 1, which means that the result is evidence against 1, not evidence for 1.

This is the situation as I see it, with details varying according to what month you look at, or whether you look at anomalies for the past year and a half, or ... .

Case B: Two alternative hypotheses

1: As before.

2: Not only has the decline ended, so has the low sea ice area it produced. From now on, sea ice area will be its average value 1978-2000, with some random variation.

Observation as before. If the observation is closer to the previous trend than to the previous average--whether it in fact is isn't clear, depending on which version of the data you look at--then it is more probable under hypothesis 1 than hypothesis 2, raises your subjective probability for the former, lowers for the latter, and can reasonably be described as evidence for 1.

It seems to me that various people defending the JPL, including Tim, are implicitly considering Case B, not Case A. The problem with that is that an honest description of the result in that case would be "the latest data show that arctic sea ice is still lower than it was before the decline," not "the latest data show that arctic sea ice is still shrinking." The latter is a claim about case A, shrinking vs not shrinking rather than low vs not low.

And the JPL claim was explicitly about shrinking.

Frank Fractal said...

Define a series x(0), x(1), x(2), x(3), ... as follows:
x(0) = 0
x(i+1) = 0.99*x(i) + r(i)
where r(i) are Normally distributed and independent random numbers with zero mean and constant variance.
(This example is unrealistically simplified, but is meant to model a generic cumulative process. Ice accumulates from one year to the next, the amount added or removed in a given year being the random input.)

If you plot out a few hundred points of x(i), you are quite likely to see what appears to be a systematic trend, up or down. And yet you can easily calculate the mean of the distribution at every point, and find it is always zero. There is no trend.

This is because the x series is 'autocorrelated', a statistical property that makes a lot of the formulas of basic statistics invalid. Many methods assume the inputs are 'independent', and of course this is true for all the textbook exercises, so students come to assume it is always true. The real world is not so neat.

Someone asked whether the moving average inevitably reduced the variance. For independent errors, the variance remains constant. Variances of independent random variables add, so the average stays the same. But variance of a sum of correlated random variables is the sum of all variances and covariances, so the variance of the moving average of an autocorrelated series actually increases. When saying that the moving average reduces variance, this is because the standard interpretation is based on a low frequency signal with broad band noise spread evenly across all frequencies (that 'independence' assumption again), and you normally estimate the noise level by looking at just the high frequency variance. What is actually happening is that variance is being transferred from high frequencies to low ones by the moving average filter. This makes it look less noisy, but really it isn't.

In case some of you didn't follow all that, what it means is that there's no statistical evidence of a trend unless you make some unjustified assumptions.

Another statement the article makes is "Until recently, the majority of Arctic sea ice survived at least one summer and often several."

And yet, a quick glance at the data shows the range even back in 1979 to go from 5 to 15 million km^2. That is to say, 2/3rds melts every year. Perhaps they mean most winter ice has survived at least one summer?

I do sometimes wonder if such errors are a private act of rebellion on the part of some poor scientist being forced to 'write something about global warming'.

Eric Rasmusen said...

I've wondered whether any time series econometricians have looked at the temperature times series. Do climate scientists know about autocorrelation?

Suppose temperature at time t depends positively on temperatures at t-1, t-2, t-3, and t-4. Let there be temperatures of 0 for 10 years. Then have a random shock so the temperature rises 1 degree. Wouldn't that result in a positive trend for several years, as the lags worked their way through? Then, after that, the trend would go back to flat (though this process wouldn't revert back to the temperature of 0).

Mercy Vetsel said...

So we all agree that the "most recent data" shows expanding sea ice cover.

So we can just substitute...
"[The recent data showing expanding sea ice cover data] show that the decade-long trend of shrinking sea ice cover is continuing."

What I find must astonishing is that caught in a bald-faced lie, NASA JPL hasn't even been shamed into taking down the site let alone retracting it.

Also, it's astonishing that so many posters are trying to defend such an obvious untruth. Are these people really that easily deceived or are their just an inordinate number of Defenders of the Faith.


tut said...

"The latest data" in the way that JPL is using it is the whole graph, not just the tail end of it.

If they were referring to just a few years they would be incorrect, not in the direction they claim that it goes, but in claiming that it is evidence of anything at all in the context of climate.

Tim Lambert said...

David, your argument is wrong because your case A does not cover all the plausible hypotheses. If you think that "trend ended in 2008" is a possibility, then so is "trend ended in 2007" and "trend ended in 2006" and so on. If you consider all the alternatives to "trend continues", then an observation close to the trend line is less likely if the trend does not continue than if it does continue. An observation close to the trend line is evidence that the trend is continuing, just as the JPL press release said, and as everybody has tried to explain to you.

Tim Lambert said...

Yes, eric, climate scientists know about auto-correlation.

Frank Fractal said...


David's argument is correct. If you add additional possibilities into a hypothesis, its probability can only increase. P(A or B or C ...) is greater than or equal to P(A).

But you are correct in saying that not all the plausible hypotheses have been included, because the very idea of testing for a trend excludes all those models in which there are no trends, and the pattern is explained by other means. By assuming a model of 'linear trend plus noise', you can find the conditionally most likely hypothesis given that the model is true. But if the model isn't true, your output is junk.

And yes, certain climate scientists do know about autocorrelation, after it was pointed out to them by sceptics. But there isn't anything they can do about it because they don't know the true underlying model. And despite knowing that it's invalid, you still get climate scientists wittering on about the "underlying trend" continuing up, even though they ought to know that the existence of a trend is an assumption and the actual data is going down.

Eric Rasmusen said...

Frank, even if you don't know the underlying process, you can test for its properties-- whether there is autocorrelation, for example, versus whether there is a trend. I don't know much time series econometrics myself, so I don't know what test is appropriate.

Frank Fractal said...


Yes, you can identify some of the properties, but you're limited by having a finite time window. Sometimes the information you need is simply not in the data you have, as it only shows up at longer timescales, so you cannot distinguish between the true model and an infinite number of alternatives.

It's quite common to make the assumption that there is no such information. (What else can you do?) For example, the definition of climate as a 30-year average was based on having 30 years of data at the time the definition was made. But we don't know that 30 years is sufficient. Where does 'weather' stop?

There are better, more general models we can use. e.g. Cohn and Lins use ARFIMA, and report tests that take it into account. But we have no guarantee that the real climate fits ARFIMA either - the existence of apparent long-term periodicity, as in the 1500-year Bond/Dansgard/Oeschger events suggests not.

As Cohn and Lins said, it may be preferable to acknowledge that the concept of statistical significance is meaningless when discussing poorly understood systems.

Mercy Vetsel said...

Tut wrote:
"The latest data" in the way that JPL is using it is the whole graph, not just the tail end of it.
If they were referring to just a few years they would be incorrect

Okay, so let’s try substituting that meaning and see if it makes any sense:

PASADENA, Calif. -- The latest Arctic sea ice data from NASA and the National Snow and Ice Data Center show that the decade-long trend of shrinking sea ice cover is continuing.

Tut’s interpretation:
PASADENA, Calif. – The [last 10 years of] Arctic sea ice data from NASA… show that the decade-long trend of shrinking sea ice cover is continuing.

Hmm… That’s odd.

“The latest weather report shows that the week-long rainstorm is continuing.”

“Oh, the latest report calls for sunny weather today? No, no, no. I meant the latest average WEEKLY weather report.”

Just for fun, I sent an email to the bureau-bots at NASA calling them liars. I got back a response so mind-numbingly idiotic that I have to marvel at how efficiently institutionalized deception can corrode the capacity for intelligent thought.


Hammerhead said...

Beautifully lucid account of the notion 'climate' by Frank Fractal! I wish this view was expressed far more often in the mainstream news blather. It would seem that, for the present, 'climate' is as folksy a notion as 'season', actually maybe even more so, because we have a reasonably clear idea of the underlying causes of seasons.

Some commenter here posted the hope that if the sea ice is now reversing a trend (i.e., thickening) perhaps it shows that our responses to global warming are having the desired effect. Wow! Is it a belief that CO2 reductions would be causing this reversal? As far as I know, manmade CO2 levels are still RISING; the countries who signed Kyoto are all putting out even more CO2, not less. The fact that we have not had rising global temps for ten years and that the sea ice did not continue to shrink one year, even as CO2 climbs, seems a good reason to question the notion that CO2 was the cause of the higher temps observed in the 1990s.

Anonymous said...

Patri --
Bayesian is the rigorous way, if only we apply it with rigor.

You couldn't reasonably be "quite certain". Upon the Bayesian update, the change in the mean (for the trend you focus on) may or may not work your way. While the decreasing variance likely works against you.

It depends on how the forecasts are computed. The dumb way is to extrapolate ice data, valuing most recent data the highest. If so, you might win.

But real forecasts of ice cover include lots more data that past ice cover. They are part of the bigger climate picture, hence less sensitive to short-term ice trends. Extra ice added now might cause us to forecast more ice in 10 years, but by how much? If by the same amount as added now, the trend remains the same. If by a smaller amount, the trend only gets more negative.

Admittedly, you still have a point. Because the onus of proof is not on you, it is on JPL -- if indeed they claimed what you think they did.

Or if they didn't mean to claim that, JPL ought to clarify. And to abstain from misleading language in the future.


Anonymous said...

in fairness to JPL/NASA, would you post their response, if it isn't too long?

Eric Rasmusen said...

"There are better, more general models we can use. e.g. Cohn
and Lins use ARFIMA, and report tests that take it into account.

As Cohn and Lins said, it may be preferable to acknowledge that
the concept of statistical significance is meaningless when
discussing poorly understood systems."

That article looks worth reading. It does address the deeper
issues of how to test where it isn't clear which hypothesis is the
null and where data is limited.

The first step to take isn't all that profound, though. I hope it
isn't too boring if I lay out some basic possibilities. Compare
these hypotheses for temperature, where we'll call the starting
temperature 50 and u_{year} is a mean-zero random shock.

1. STRAW MAN. The temperature is

50 + 0*year + u_{year}

The expected value is always 50.

2. GLOBAL WARMING. The temperature is

50+ B*year+ u_{year}

The expected value is rising at rate B per year, regardless of what
happened in the previous year.

3. RANDOM WALK. The temperature is

Temperature_{year-1} + u_{year}

The expected value is the same as last year, so warming and
cooling shocks persist forever but there is no trend.

4. MEAN REVERSION. The temperature is

50 + C*(Temperature_{year-1} - 50) + u_{year} with C<1

The expected value is between 50 and the temperature last year,
so warming and cooling shocks persist but dampen out to near
zero effect in the long term.

5. GENERAL MODEL. The temperature is

50 + B*year + C*(Temperature_{year-1} - 50) + u_{year}

Model 1 has B=0, C=0.
Model 2 has B>0, C=0.
Model 3 has B=0, C=1.
Model 4 has B=0, C<1.

If the first random shock is a warm one, then models 2, 3, and
4 will all show a trend. JPL is wrong because if

Temperature_{year}< 50+ B*year+ u_{year}

that is evidence against GLOBAL WARMING and in favor of
Models 1, 3, and 4. (I think this remains true even if
temperatures are rising but below trend, i.e. Temperature_{year}
< 50+B*year.)

Some commentors were saying that a declining temperature still
supports GLOBAL WARMING over STRAW MAN. I think
it's true that any temperature over 50 supports GLOBAL
WARMING over STRAW MAN, though it will require the
estimate of B to be reduced. But a temperature decline is even
stronger evidence for MEAN REVERSION or RANDOM

This matters a lot, because if MEAN REVERSION is true,
policies to limit global warming are completely unnecessary, and if
RANDOM WALK is true, they are unnecessary at present
because temperatures are as likely to fall as to rise any more.

All this is just time series talk, and it's good to have structural
models to test. The global warming models of scientists *are*
structural models, and they match GLOBAL WARMING best
(though I think they have nonlinear trends). But since those
models don't explain the vast majority of either temperature or
climate changes (they explain zero about the changes before
1900, for example, and pretty near zero about year-to-year
changes since then), it's reasonable to try to figure out the
properties of the random shocks-- random shocks are really just
the "everything else" part of a model.

Mercy Vetsel said...


Me> [Essentially] You're a bunch of liars and NASA has degenerated into a bunch of clueless bureaucrats.

NASA> It sounds like you are interested in information about whether sea ice is still declining.

We provide an FAQ that answers this question.

Eric Rasmusen said...

Very funny!

That FAQ page seems to have a typo, and says that not only does 2008 have more sea ice than 2007-- as we've been talking about-- but apparently 2008 was an all-time record high! That makes it questionable even whether there is an overall trend, not just the meaning of the latest datapoint.

"In March 2008, Antarctica experienced a record maximum. For more information, read Is wintertime Antarctic sea ice increasing or decreasing?

Return to top
Is wintertime Antarctic sea ice increasing or decreasing?

Wintertime Antarctic sea ice is increasing at a small rate and with substantial natural year-to-year variability in the time series. While Antarctic sea ice reached a near-record-high annual minimum (SHOULD BE MAXIMUM, RIGHT?-ER) in March 2008, this does not indicate a significant long-term trend.

Frank Fractal said...


Yes, but you have to include a lot more possibilities as well. That the distribution of the shocks is not fixed, or Gaussian (rare outliers can have a significant effect with autoregression), that it also depends on the temperature further back than one year (e.g. due to ice thickness), that there is an oscillatory component to the driver (i.e. add a sinusoidal term, or several), that there is non-linear feedback that changes the relationship with the past as the amount changes (due to albedo and deep circulation changes), etc., etc., etc.

On Bayesian grounds, any observation will support your pet theory with respect to some hypotheses, and disconfirm it with respect to some others. The difficulty with the Bayesian approach here is usually setting priors on your belief in each hypothesis before having seen the evidence.

But you might find the following article interesting, also from JPL, explaining that it was actually because of another aspect of the weather, and not temperature at all (CO2-induced or otherwise).

Does that put a different light on the whole debate?

Frank Fractal said...

More detail here.

Anonymous said...

Tim --
You've demonstrated that the latest data MAY have made JPL more confident that the trend over, say, 2004 to 2014 will be negative.

Giving them the benefit of the doubt, let us believe that they
actually performed the Bayesian update, and saw the probability of a negative trend increase compared to their earlier estimate.

I can easily believe the above, if we talk about the decadal-scale trend -- 2004 to 2014. But for a shorter-scale trend, say 2008-2010, I am incredulous.

Granted, their words "decade-long trend" COULD limit their statement to decadal trends, such as 2004-2014. Unfortunately, it is too easy to read them as: throughout the last decade, the trend remained negative, and still is. This implies SHORT-TERM TREND -- so that it has a chance to change several times over during a decade.

You may agree that in the context (no ice graph shown with text), their wording is easily misleading.


Mercy Vetsel said...

"In March 2008, Antarctica experienced a record maximum."

We all know that global warming is causing ice to DECREASE in the Arctic.

What I found interesting from the FAQ was that global warming is also causing the ice cover to INCREASE in the Antarctic.

I guess I need to read the article again, because I seem to have forgotten the explanation -- something about winds, currents and flux capacitors.


Anonymous said...

David --
Tim has formal grounds to object to your framing of "case A". As I understand, you require the trend to be rigidly fixed except at one particular point where it may change. And you get to choose that point.

But, IMO, Tim is making too much of it. Case A is not very different from asking: does latest data make it more/less likely that the trend over (say) 2008-2018 will be negative? And same question should be asked for various other time spans.

It seems to me that most commenters here would accept this question, for one or another subset of time spans, as our judge.

Below, I define (for example) the 2008-2009 trend as one fully determined by the 2008-2009 data alone. This brings clarity. "Trend" needs a time-scale or a time span to be a meaningful term, and I make the time-span explicit and clear-cut.

For 2008-2009, you win.
For 2008-2010, you win.
For 2008-2012, you likely win.

On the other hand, for 1999-to-now, you lose.

For 2008-2018 it hinges on how we compute the probabilities. If we forecast by simplistic extrapolation of recent ice trends, you win.

But more sophisticated modelling involves other kinds of data and is less sensitive to short term ice trends. If that's the right way to compute the probabilities, 2008-2018 may be in JPL's favor. To know for certain, we need to see their calculations. (Or shall we give them the benefit of the doubt?)

The dispute largely comes down to semantics: does JPL's language implicitly exclude future? (as Matt B thinks.) Does it only allow decadal trends? What "shows" means: shows to the sophisticated JPL modelers, or shows to the simple man, easily impressed by short-term trends?

You may agree that some of the interpretations of the quote make it valid. "Lie" may be too strong a word; but you're right to expose their misleading language.

Granite26 said...


Thanks for the well reasoned argument. I (personally) don't agree with you, but no longer think that people on the other side are inately wrong.

VangelV said...

And I now know that nothing said by NASA/JPL ought to be trusted. Readers of this blog may want to check the JPL claim against the data for themselves before deciding whether or not they agree with that conclusion. I have provided the links above.

I agree David. You might be interested in the audit done by Anthony Watt. It shows that the surface stations that provide the NASA temperatures have some serious flaws.

Is the U.S. Surface Temperature Record Reliable?

And one last thing. It was reported that the record high temperatures reported at Honolulu airport cane from a malfunctioning temperature sensor at the ASOS station. Not only was the error by about 2 degrees it is placed right next to an asphalt access road, which biases the readings to the upside.

NOAA: FUBAR high temp/climate records from faulty sensor to remain in place at Honolulu

You Tube: ASOS in Honolulu 2 degrees high - climate records wrong

VangelV said...

Either 1. All those people are lying,
or 2. You don't know what a trend is.

I vote for 2.

I think that the evidence is for 1.

Here is Hansen and company pointing out that, "The U.S. has warmed during the past century, but the warming hardly exceeds year-to-year variability. Indeed, in the U.S. the warmest decade was the 1930s and the warmest year was 1934." Yet, shortly after the GISS data was 'adjusted' and claims of record highs could be made even as the GISS was reporting results that were diverging from UAH/RSS.

G-Man said...

"VangelV", give it a rest.

Parroting CA talking points isn't convincing.

Doc Merlin said...

About a year and a half ago we entered solar minimum. Climatologists like to say that this has no effect. Even If it doesn't, its an interesting coincidence.

Anonymous said...

Sorry I was wrong to say
"IMO, Tim is making too much of [his objections to case A]"
Case A is stacked against JPL so badly, Tim was 100% right to dismiss it.

Case A allows only 2 options for the trend: remain same, or become zero. The result is paradoxical: Every time the latest data point sits above the trend line, no matter how slightly, "Case A" sees that point as evidence, if weak evidence, that the negative trend has ended.
(Specifically, that it has ended at or near the right time: when the down-sloping trend line reached the level of the latest point.)

What if we allow the optimisation of the (constant) negative trend to better fit the new data? Still, the best fit will be achieved by switching to the zero trend at the right time.

Ironically, JPL must have suggested this framing themselves, with their cryptic "the trend is continuing". What's the alternative? "The trend has changed, no matter how slightly"? This alternative makes no sense: it is guaranteed to win. What else can we have as alternative? "The trend has flipped to zero" looks superficially reasonable. But, isn't.

Another irony, David didn't need subterfuge to win (or, nearly win). He only hurt his argument by putting forth "Case A".

Moral: don't trust anyone. Don't even trust anyone to make their own case.

VangelV said...

No one seriously argues that there is no trend in ice shrinkage, it's obviously a continuous process, not white noise.

Sorry but I do not see anything unusual about Arctic ice cover when compared to the historical records because we have had periods of low summer ice cover before and the Arctic anomaly is not really showing much warming.

And let us point out that global ice cover is above the mean for the satellite era because the Antarctic ice anomaly has been high enough above the mean to offset the NH decline.

Add to this the very inconvenient UAH anomaly of 0.04, which is lower than the average anomaly in 1980 and there is a problem claiming that we have had much warming outside of growing urban areas.

And let us not forget that the oceans are showing no heat accumulation since 2003, which is sufficient to falsify the entire AGW argument. Add to all this the May snows in Saudi Arabia and the UAE, killing frosts in Texas, Kansas and Oklahoma and the warming hype starts to become a hard sell to the average voter who is finally figuring out that the goal of bureaucrats is to provide an excuse for higher energy taxes and the justification of a massive transfer of wealth from consumers and fossil fuel producers to politically favoured companies and groups looking for subsidies.

There is nothing scientific about this argument because it is all about politics and deception.

VangelV said...

About a year and a half ago we entered solar minimum. Climatologists like to say that this has no effect. Even If it doesn't, its an interesting coincidence.

Just as it was a coincidence that the LIA was a period of low solar activity or that the twentieth century was a period of relatively high solar activity. Fortunately for some of us who are curious there is an experiment scheduled that should shed some light about the CRF hypothesis in the next year and will provide us with real data to examine.

VangelV said...

Parroting CA talking points isn't convincing.

CA? Did I provide any links to CA?

By the way, it was CA that discovered Mann's errors in MBH98/MBH99 and in the Steig/Mann latest fiasco, found Hansen's convenient Y2K error and a number of other errors. In fact, the readers at CA are so good at finding errors that NOAA, GISS and other organizations have stopped providing access to some of the data sets and algorithms. So much for credibility.

I found this little example of incompetence very interesting. Why is it that NASA, which gets billions of funding, can't keep track of stations that outsiders can locate by using Google and telephones?

And why does it use data from stations like Orland, Forest Grove, Tahoe, Marysville, Roseburg, Redding, Detroit Lakes, Lovelock, Melbourne, Tuscon, and many others that have the same type of defects and bias.

G-Man said...

You ought to change your handle to "CA_fanboy", "VangelV".

VangelV said...

You ought to change your handle to "CA_fanboy", "VangelV".

I certainly appreciate the ability of SM to find errors in peer reviewed papers and GISS data with such ease. But my argument in this case has little to do with CA but with the simple observation that the US surface record has serious issues that have not been addressed.