Are we starting to cool: the case for the last three months

[VillagePlank]

Whilst we would obviously need to see more evidence before coming to any sort of conclusions, it does look, up here at least, that the warming may have at least flatlined. September was another below average month but it was also the coolest since 1986 in Shetland. It occurs to me that I may see the evidence of a "cooldown" first given my extreme northerly location.

Yes,

But has been fairly well intimated by not least SF, and WiB, is that this 'lull' simply begs a question and does not in and of itself amount to significant statistical evidence of change. It opens up a possibility of a change in the direction of a trend in the same manner that it opens up the possibility of the calm before the great AGW storm. As always, I suspect reality is somewhere in between, which, in my pathetic mind, means average or slightly above is to be expected with periods of warmth and coolness interspersed to keep weather watching interesting.

[The Enforcer]

13.8 in the end, so not a bad effort. October has come in at 10.9 or 11.0, depending on who you believe. It appears that there have now been 4 consecutive months lower than the rolling 10 year mean. However, in the light of what has gone before, both in the recent and slightly longer term, I can't help thinking this trend is somewhat reminiscent of trying to keep the titanic afloat with a rubber dingy. Still, interesting to see if the pattern continues.

Just posted the above in the other thread. Perhaps it is more relevant to this discussion.

[summer blizzard]

What is interesting to me, is that the rate of warming in the current cycle (July 2007-October 2007) has also slowed, in that from August to September, the anomoly difference was +0.9C, but only +0.4C from September to October, this indicates to me that we are likely to see at least one below average month during the November-March period.

[Stratos Ferric]

Here's the various updates for the last couple of months.

This is an update of the previous slide, coparing the current cool run to two previous instances of marked cooling in the CET, to test whether this current phase is likely to sustain, or be transitory. Too soon on the basis of this to say anything definitive, but at present what we have is no more than a correction to bring us back into the recent warming trend. Before we could get excited about this we would need at least 2 or 3 months of sustained and marked coolness.

These slides give a different cut, plotting the rolling means for 3, 6, 18 and 60 months.

This test is rather more definitive: if November comes in above par then we will be moving into territory where I would fairly confidently say that this is just a blip. More worryingly for winter, we'd be entering the cold part of the year on a rise. Of course, as per the UKMO's witer forecast, there's plenty of upside in which we could have a mild winter, but still comfortably below last year's outturn. I'd be favouring that at present myself.

[jethro]

Curious stuff, very informative SF.

I'm a little puzzled though, given that it has taken quite some time to get as high as we have been up until this "cooler" period, wouldn't it be more indicative of cooling if a downward trend followed the upward one in incline? 2 or 3 months of sustained and marked cooless has ALWAYS been a rarity in this country, I think I'd be more convinced if we were to see a continued, gradual cooling. What would you quantify as "marked coolness"?

[Iceberg]

To put some background into this we are talking (I assume) about UK only warming/cooling against a still rising and high global temperature (upto Oct 2007). So we are concentrating on the rise of cooler conditions via synotpics rather than anything else.

Also by cooling we still mean slightly above average (i.e Sept and Oct are both above average using the same method as 90% of the met world! ). This 10 year rolling mean is a rather silly idea for climatic averages as it does not cover the relavent decadal cycles, let alone the longer term multi decadal cycles. You are also much more likely to have widely postive and negative months is such as short time series.

It's bit like tossing a coin 10 times getting 7 heads and 3 tails, then flipping again getting a tail and saying that it's significant that it's below the likely occurance.

[West is Best]

Since this thread came into being the title could be revised to 'the case for the last four months' I wonder if that will continue to be the case ...

It's bit like tossing a coin 10 times getting 7 heads and 3 tails, then flipping again getting a tail and saying that it's significant that it's below the likely occurance.

The coin toss ... each time you flick it, it's 50:50, regardless of what happened before. The coin doesn't have a memory!

[Iceberg]

I am talking about significant statistical varience, 10 times doesn't give you that. Hence the 30 years average is so much better.

[West is Best]

I am talking about significant statistical varience, 10 times doesn't give you that. Hence the 30 years average is so much better.

Yes I seem to have had that argument with SF myself, when he was all for using the 10 year mean. He doesn't seem to me to be using it as much of late, which I find interesting.

By the way, in statistics strictly speaking I think you want the word 'mean' rather than 'average' n'est ce pas ...

[Pennine Ten Foot Drifts]

The coin toss ... each time you flick it, it's 50:50, regardless of what happened before. The coin doesn't have a memory!

Ah yes, an interesting philosophical debate that one, try thinking of it another way:

Whilst each toss must be an even chance, it is accepted that over a series of flicks the incidence of heads and tails is going to balance out at somewhere in the region of 50:50, i.e. over 100 flicks it will end up somewhere between 50:50 and 40:60 at most, so if you get a run of say 5 heads in a row, then the body of statistical proof means that with every flick that goes past continuing to be heads it has to be more likely that the next flick will be tails, because the chances of 100 flicks all being heads is miniscule compared to the chance that the 100 flicks will be somewhere near to 50:50 heads and tails.

[Stratos Ferric]

Curious stuff, very informative SF.

I'm a little puzzled though, given that it has taken quite some time to get as high as we have been up until this "cooler" period, wouldn't it be more indicative of cooling if a downward trend followed the upward one in incline? 2 or 3 months of sustained and marked cooless has ALWAYS been a rarity in this country, I think I'd be more convinced if we were to see a continued, gradual cooling. What would you quantify as "marked coolness"?

To put the analysis into context Jethro you have to read back to the start, just in case you haven't. I have deliberately chosen the only other examples in the CET series where we had a marked upwards spike in temperature; this is not the ONLY test available, but it has face validity givent he recent upward spike. This is important because re your point of marked cool being a rarity, it is perfectly clear from the two comparative sequences used that, in order to recoil to cold as they did, they indeed had sustained and marked cool - the early plots I put up show the actual data and there were some exceptionally cold months, and a long series at that - otherwise the cumulative dip shown on the plots would not have occurred would it?

The slope of the curve actually matters not - what those who are inclined to believe that temperatures have peaked need to see is sustained cooling. AS mentioned to WiB already in another post - this year to date we have had 3 sub-par months: hardly anything to get excited about (we had three last year and their cumulative negative impact was larger than the three top date this year have achieved), and the last three have show progressive relative [to norm] warming. If neither Nov or Dec come in under par then we will have hd no more sub-par months this year than for the previous dozen or so.

As to cold series being unusual, I know you and I have our occasional disagreements, but my main complaint is when you play a bit fast and loose with the assertions re the data without actually checking. Let's use just -1C below par as cold (sustained over a year that would represent a very unusual year-on-year drop in CET in ANY year), and before WiB accuses me of picking numbers to suit my argument, if we go much lower than the one cool month this year drops out of the comparison - which rather defeats the object really and would do little other than make stronger the case for current blip as being slight and trivial; in the last thirty years or so there are several notable series:

Dec - May 1996: 4/6 cold months;

Jul - Nov 1993: 7 sub par months in a row, three at 1C or more below par;

May - Nov 1987: 7 sub par months in a row, 2 being cold;

Jan - Sep 1986: 7/9 sub par months, 4 of which we cold;

Jan - Mar 1985: 3 cold months in a row with a cumulative dip of 5.5C;

Dec - June 1979: 7 sub-par months in a row, three being cold;

Apr - Oct 1974: 7 sub-par months in a row, 2 cold.

It is not that extended cool runs are rare in the UK; it is that they have recently become rare. In fact, you have to go back to Jan 1997 to find the end of the last three month sub-par sequence (c.f. 30 year rolling mean) before the one that ended in September. The set above had a recurrence rate of about one per three years. A statistical simplifaction gives a chance of around 1/64 of any run of six months being consecutively sub-par at random; clearly climate has some inertia, hence in cool period such runs must be more likely, and in warm(ing) phases less likely. There is not doubt we are warming, so the current lack of sustained cool is no surprise. As to whether there is anything in the current numbers to suggest a sustained dip, the answer still has to be 'no'. The rolling CET is falling at present, but this is not because of the introduction of unusual cool, but simply the loss of last autumn's exceptional warmth.

Ah yes, an interesting philosophical debate that one, try thinking of it another way:

Whilst each toss must be an even chance, it is accepted that over a series of flicks the incidence of heads and tails is going to balance out at somewhere in the region of 50:50, i.e. over 100 flicks it will end up somewhere between 50:50 and 40:60 at most, so if you get a run of say 5 heads in a row, then the body of statistical proof means that with every flick that goes past continuing to be heads it has to be more likely that the next flick will be tails, because the chances of 100 flicks all being heads is miniscule compared to the chance that the 100 flicks will be somewhere near to 50:50 heads and tails.

It's an alluring philospohy, but in fact it doesn't stack up. WiB is quite right - each toss is independent.

What is true is that if you toss a coin fifty times, you would expect 25/25 to be the outcome. In practice there will be a range of outcomes, but if repeated often enough the pattern will start to produce a normal curve. It is this that is important. Say I turn up a 40/10 sequence; next time around I am not likely to return this sequence, or anything beyond it - but this is NOT because it has just happened, it is because this outcome, statistically, happens to be unlikely when set against all other possible outcomes.

Yes I seem to have had that argument with SF myself, when he was all for using the 10 year mean. He doesn't seem to me to be using it as much of late, which I find interesting.

By the way, in statistics strictly speaking I think you want the word 'mean' rather than 'average' n'est ce pas ...

The arithmetic mean is one type of average, though it's fair to say that in everyday use most people would take 'average' to be 'arithmetic mean'.

WiB, tiresome though it is I shall say again - I always state which average I am using and why. As we saw on Friday when you suggested I was cherry picking data to suit my argument you ended up looking rather silly when I appliesd your chose alternative. I have stated ad nausaeum: I use the short mean when testing warming - set against the thirty year mean every month looks warm nowadays. If I really wanted to 'jerry' a case then I would always use the long average. The fact that my analysis does not always suit your new found zeal for cold does not make the analysis flawed: there are a number of other possibilities, one of the more obvious of which I suspect it will never occur to you to consider. I think I make the point at the start of this analysis - which, let's not forget, was started largely at your behest, that as soon as there is anything in the data to suggest cooling I will say so.

So far as I'm aware there is no rule on N-W to stop you repeating any analysis I do using your own preferred length of comparative series. If you ask me nicely I'll even check your maths for you before you post it.

To put some background into this we are talking (I assume) about UK only warming/cooling against a still rising and high global temperature (upto Oct 2007). So we are concentrating on the rise of cooler conditions via synotpics rather than anything else.

...

Is the UK now hermetically sealed?

You'll be telling me we've been unlucky with winter synoptics for the past decade next. You don't spend a lot of tie in the model thread do you?

[Godot]

Not to get too far off-topic, but the chance of heads and tails would always be 50/50, independent of the previous results. For example - the chance of getting 5 heads in a row is exactly the same as getting 4 heads and 1 tail :

0.5 x 0.5 x 0.5 x 0.5 x 0.5 = 0.03125 (1 in 32)

Edited November 4, 2007 by Goatherd

[stormforce 10]

Not to get too far off-topic, but the chance of heads and tails would always be 50/50, independent of the previous results. For example - the chance of getting 5 heads in a row is exactly the same as getting 4 heads and 1 tail :

0.5 x 0.5 x 0.5 x 0.5 x 0.5 = 0.0625 (1 in 32)

i think that sum is wrong if u check again.

[Godot]

Whoops, sorry. I didn't press control-c hard enough..! That's 1 in 4.

Edited November 4, 2007 by Goatherd

[jethro]

"As to cold series being unusual, I know you and I have our occasional disagreements, but my main complaint is when you play a bit fast and loose with the assertions re the data without actually checking. Let's use just -1C below par as cold (sustained over a year that would represent a very unusual year-on-year drop in CET in ANY year), and before WiB accuses me of picking numbers to suit my argument, if we go much lower than the one cool month this year drops out of the comparison - which rather defeats the object really and would do little other than make stronger the case for current blip as being slight and trivial; in the last thirty years or so there are several notable series:"

Thanks Stratos, very illuminating.

I'm not playing fast and loose honest, model watching is not my forte, it may as well be in Urdu for as much sense as it makes. I understand our climate to be a Maritime one, therefore sustained extremes are unlikely; just wanted clarification as to what you would consider to be sustained cold or marked drop in temps so I know what to look for when following the CET threads. What would you consider to be a marked decrease in temps for say November or December? Also, if there isn't a marked, sustained drop in temps, what would be the upper limit of your view for cooler but not that much cooler, how many consecutive months would it take for this to happen for to to think perhaps we are on a downward trend?

[VillagePlank]

Not to get too far off-topic, but the chance of heads and tails would always be 50/50, independent of the previous results. For example - the chance of getting 5 heads in a row is exactly the same as getting 4 heads and 1 tail :0.5 x 0.5 x 0.5 x 0.5 x 0.5 = 0.03125 (1 in 32)

The number of heads, assuming p=probability of heads, and q=probability of tails, so that p+q=1 (the coin never lands on its side, for instance) is more correctly predicted using the binomial theorem and results in a binomial distribution :

EDIT: Of course, Chebyshev's Inequality show's that the larger the dataset (or probability distribution) the closer the values will tend towards the mean (or in this case 50% heads, and 50% tails) ... (this, I think, has come up before with the law of large numbers ...)

Edited November 5, 2007 by VillagePlank

[Stratos Ferric]

...I understand our climate to be a Maritime one, therefore sustained extremes are unlikely; just wanted clarification as to what you would consider to be sustained cold or marked drop in temps so I know what to look for when following the CET threads. What would you consider to be a marked decrease in temps for say November or December? Also, if there isn't a marked, sustained drop in temps, what would be the upper limit of your view for cooler but not that much cooler, how many consecutive months would it take for this to happen for to to think perhaps we are on a downward trend?

There's an element of 'how long is a piece of string?' in that question. I shall run some numbers in a moment but my starting point for marked extreme in any month would be 2.0C either way.

Interestingly, the standard deviation for monthly anomalies c.f. the thirty year mean for most months of the year in the Hadley series is around 1.1-1.2, though for the winter months this increases to 1.7-1.9 (the figures are about the same for the 10 year mean). In a normal distribution around 95% of results should fall within 2SDs of the mean, however, given the SDs already stated, this means the theoretical 1:20 event is around +/- 3.5C in winter, but only around +/- 2.2C in summer.

For marked cooling I would be looking for the current rolling cumulative anomaly to dip down as in the plots posted further back. That said, it's less about slope and more about extent of cooling.

Here's a cumulative frequency plot comparing the the last twenty years to 1950-69, a warming period vs a cooling one.

To get me convinced of sustained and decent cooling we're going to have to see a number of things:

1 - more than 3 cold months per year c.f. the 10 year rolling mean, with the margin set at -1.0C. (not happened since 1996);

2 - at least one month a year with an anomaly of -2.0C or more (again, 1996);

3 - an excess of cold months over mild ones;

4 - a drop in rolling mean CET persisting across at least two years.

With more time it would be possible to come up with a more robust rule, based on previous events, but this wet finger will suffice for now.

[West is Best]

There's an element of 'how long is a piece of string?' in that question. I shall run some numbers in a moment but my starting point for marked extreme in any month would be 2.0C either way.

I think this is weak statistically speaking. All you are thereby asking for are outliers, and outliers are never a good statitician's benchmark. Freak months are rarely indication of trends. And 'rare' is also an appropriate word to use.

Much better either to plot mean trends, or medians. If you want to go with deviations then it would be best NOT to choose the outliers, but from a staticician's point of view to pick, say, the band between 70% and 90%. I've not checked the figures on that, but a rough guide would be say the band between 1.0C and 1.9C either side of the mean.

It's an alluring philospohy, but in fact it doesn't stack up. WiB is quite right - each toss is independent.

I can hear the angels' trumpets sounding now, if not in heaven then at least in the next nearest place at NW HQ. We have agreed on something!

Edited November 5, 2007 by West is Best

[Stratos Ferric]

I think this is weak statistically speaking. All you are thereby asking for are outliers, and outliers are never a good statitician's benchmark. Freak months are rarely indication of trends. And 'rare' is also an appropriate word to use.

Much better either to plot mean trends, or medians. If you want to go with deviations then it would be best NOT to choose the outliers, but from a staticician's point of view to pick, say, the band between 70% and 90%. I've not checked the figures on that, but a rough guide would be say the band between 1.0C and 1.9C either side of the mean.

WiB: the question was what would I consider marked cooling. That was my response. 1/20 is hardly a freak. In the context of the explanation that follows then I'm happy with the definition. It may well mean that the cooling in July-Sept that you have been championing doesn't really qualify for anything, but that simply serves to show that thus far it's a minor correction, nothing more.

I can hear the angels' trumpets sounding now, if not in heaven then at least in the next nearest place at NW HQ. We have agreed on something!

I'm not sure 'we' have agreed. I have agreed with you, and we are in agreement. It's a subtle point but I'm sure you're up to seeing it! I'm not beyond agreeing with you WiB; the issue is more that you're generally incapable of presenting something that is simultaneously sensible and objective enough to merit agreement. Either reality will have to get a lot cooler, or you will have to drop your starting position which is to douse everything you write in cold invective, before we find much of current fact to agree upon.

Edited November 6, 2007 by Stratos Ferric

[jethro]

There's an element of 'how long is a piece of string?' in that question. I shall run some numbers in a moment but my starting point for marked extreme in any month would be 2.0C either way.

Interestingly, the standard deviation for monthly anomalies c.f. the thirty year mean for most months of the year in the Hadley series is around 1.1-1.2, though for the winter months this increases to 1.7-1.9 (the figures are about the same for the 10 year mean). In a normal distribution around 95% of results should fall within 2SDs of the mean, however, given the SDs already stated, this means the theoretical 1:20 event is around +/- 3.5C in winter, but only around +/- 2.2C in summer.

For marked cooling I would be looking for the current rolling cumulative anomaly to dip down as in the plots posted further back. That said, it's less about slope and more about extent of cooling.

Here's a cumulative frequency plot comparing the the last twenty years to 1950-69, a warming period vs a cooling one.

To get me convinced of sustained and decent cooling we're going to have to see a number of things:

1 - more than 3 cold months per year c.f. the 10 year rolling mean, with the margin set at -1.0C. (not happened since 1996);

2 - at least one month a year with an anomaly of -2.0C or more (again, 1996);

3 - an excess of cold months over mild ones;

4 - a drop in rolling mean CET persisting across at least two years.

With more time it would be possible to come up with a more robust rule, based on previous events, but this wet finger will suffice for now.

Thanks for that SF. However, I'm even more confused now, could be that it's late and my tired brain is messing this up but....this isn't the pattern of warming since 1996 is it? I would have thought a more gradual decline, kind of like a mirror image in reverse of the last ten years would have been more of an indication surely? I agree with WiB, this does appear to be more like looking for outliers surely? Certainly a high (or rather low) benchmark would need to be achieved in order for you to consider it to be worthy.

[West is Best]

I'm not sure 'we' have agreed. I have agreed with you, and we are in agreement. It's

The italics were for speech: the sound of NW council making a declaration to trumpeteers. I wasn't saying I agreed with their statement!

You don't like the 10 year mean very much anymore it seems?

[Stratos Ferric]

The italics were for speech: the sound of NW council making a declaration to trumpeteers. I wasn't saying I agreed with their statement!

You don't like the 10 year mean very much anymore it seems?

WiB, you're becoming very boring. Perhaps you'll explain why you're of this opinion.

...For marked cooling I would be looking for the current rolling cumulative anomaly to dip down as in the plots posted further back. That said, it's less about slope and more about extent of cooling.

Here's a cumulative frequency plot comparing the the last twenty years to 1950-69, a warming period vs a cooling one.

To get me convinced of sustained and decent cooling we're going to have to see a number of things:

1 - more than 3 cold months per year c.f. the 10 year rolling mean, with the margin set at -1.0C. (not happened since 1996);

2 - at least one month a year with an anomaly of -2.0C or more (again, 1996);

3 - an excess of cold months over mild ones;

4 - a drop in rolling mean CET persisting across at least two years.

With more time it would be possible to come up with a more robust rule, based on previous events, but this wet finger will suffice for now.

My last reference to either mean period that I use.

[Stratos Ferric]

Here's the latest update to the analysis of WiB's hypothesis that we're now entering a cooling phase. The data used is anomaly c.f. ten year rolling mean and the series chosen for comparison against the current ten years are the two previous cuycles in the CET when the ten year mean has risen significantly above the thirty year mean - thus providing the best comparison in terms of context. I've assumed November finishes at 7.0C. Anything immediately either side of this is not material to the overall picture, which remains - still no more than a correction at present, and still evidence of warming in the background.

[Stratos Ferric]

And the latest update...

Nothing much to report really, a third consecutive month of near average temperature is not really making a case for cooling - we're still in the trend corridor; we'll need to see some marked cold months, or a very long sequence of the current just below normal pattern, before anyone can justifiably suggest that GW is dead.

[summer blizzard]

It should be noted, that the negative anomolies of July, August and December combined, still did'nt cancel out the anomolous warmth of April.