In The News

[Yorkshiresnows]

P.P., nobody does their rounding like that... rounded, 2 + 2 = 4. If your input data supports it, 2.2 + 2.4 ~= 5. Though I see the point you're trying to make, it's irrelevant to generalise like this. The point was (it was one of the Muir Russell findings) that MacIntyre and his ilk could easily get the data if they wished and perform their own analysis. And also that the data in question, (CRU temperature series) has been independently verified by several other temperature series, and the CRU series itself replicated. What big problems do you see in a temperature series that has been verified several times over? If it was the only one in existense, you would have a point, but it's not, so your point is rendered irrelevant.

The M&M's have no greater claim to be professional statisticians than Mann, or Tamino for that matter. But why don't you analyse the millennial-scale timeseries yourself? Simple averaging produces a bent 'hockey stick' (Medieval comparable to mid-late 20th Century), a Mann-type algorithm, where records have greater relevance if their correlation to 20th Century warming is greater, produces a straighter-shafted stick where the 20th Century is unprecedented. But the data is there for you to try! I suspect the truth lies between these two (unprecedented in some but not all is the message from other palaeo-records), but the significance is this:

1: nobody sensible debates the instrumental record seriously, ie the world is warming.

2: very few people debate that CO2 rise is contributing to that warming significantly.

3: a more bent stick = more climate sensitivity.

4: more climate sensitivity is a very bad thing. I hope Mann's closer to the truth because it implies a lower climate sensitivity and therefore warming closer to 2C than 5C in the coming century.

Is the Hockey Stick relevant to anthropogenic climate change? Yes, but only for determining climate sensitivity - romantic notions of what our Viing ancestors put up with, or our Roman ancestors for that matter, are not terribly relevant as the forcing factors active in their climates were different to the forcing factors operating now. The graph doesn't tell you anything much about the physics operating in the atmosphere, or the other forcing factors at work. That's why Mann himself thinks the graph is overplayed, but unfortunately I imagine the politicians liked a pretty, simple and striking graph they could comprehend...

sss

Starry Skies

2 + 3+ 4 is not settled.

Co2 is a greenhouse gas and will warm the climate, whether it is a major forcing factor is quite another matter as you well know. There are other theories that can explain the majority of the 20th century warming (PDO / SOLAR etc) that cannot be easily dismissed, particularly when the IPCC'S own projections are currently way off the actual mark and there is so much uncertainty over role of clouds in the much needed positive feedback effects.

If in the next 5-10 years we see a resumption of warming even with low solar activity and a -PDO / AMO, the perhaps your statements will hold greater weight ...... but right now the jury is still well out.

A more bent stick means that the world has seen large temperature swings in the past (that could be explained by natural cycles) ...... and opens the argument as to whether we are in one of them now. This basically implies that the climate is more often in a period of flux than not. A straight hockey stick (hopelessly flawed as produced my Mann) implies that the 20th century warming is unprecedented in around 2000 years and therefore man's greenhouse gas emissions are likely to blame and are overpowering any possible cyclical factors. That is .... the power of CO2 forcing is overwhelming any background signals there are.

Y.S

Edited July 15, 2010 by Yorkshiresnows

[pottyprof]

P.P., nobody does their rounding like that... rounded, 2 + 2 = 4. If your input data supports it, 2.2 + 2.4 ~= 5. Though I see the point you're trying to make, it's irrelevant to generalise like this.

No. You didn't see the point I was trying to make. The point was it is easy to create errors if you are rounding figures. Which it the correct figure? 4 or 5? Or perhaps 4.6 more accurate? I'm not generalising. There is an important point here. A tiny amount of inaccurate input can make a huge difference to the output and can be virtually impossible to spot. The more eyes that look at the data, the more confident anyone can be that the data is correct and so are the results. As I have already said, I am not saying the data is inaccurate, just that there is a valid point for letting interested parties check over the full data.

[sunny starry skies]

P.P., that's why we have independent replication of datasets. Verification of the numbers is of course important, and goes on all the time, but the results are far more robust when they are replicated separately.

YS: I didn't say they were 'settled', but quite what is wrong with 2,3 and 4? For (2) I think the figure is ~95-98% of publishing researchers in the field agree with that. (3) you ought to agree with, as it's required to produce a significant/distinguishable MWP from natural forcing! (4) high climate sensitivity is certainly a bad thing - given our forcing of climate with CO2, which you admit has some effect (*). The effect will be worse with high sensitivity compared to low sensitivity.

(*) This is about 0.8-1.2C per doubling of CO2, not including feedbacks, which are dominantly positive for fast feedbacks. This is not in doubt at all. The magnitude of the feedbacks (water vapour, albedo etc) that take us to between 2-5C warming is of course in some doubt.

http://www.pik-potsd...edillo_2008.pdf

http://www.atmos.was...90_ice-core.pdf

http://chriscolose.w...fect-revisited/

The relevance of the 'bent' or 'straight' hockey stick is slight though, and the only crucial thing it tells us is something about sensitivity. It's a simplistic, romantic notion to consider that our climate may be similar to the Vikings, the Romans or the Neolithic... or the dinosaurs (choose your favourite) and so we have nothing to worry about. The forcings are different now - we have set a different table on which the climate system operates. Consider riding a bike down a steep hill with a sharp corner at the bottom. Now consider riding down the same hill again, only this time halfway down you find your brakes are not working. Do you think as you reach the bottom of the hill "it's OK, I've done 35m.p.h. at this point before, nothing to worry about"?... The hockey stick tells us something about the steepness of the hill, CO2 is the grease on the brakes.

Seeing as this thread is supposed to be 'in the news' here's a draft paper from NASA GISS (Hansen et al, presumably will be 2010), found at Climate Progress:

http://data.giss.nas...0_draft0601.pdf

http://climateprogre...d-hottest-year/

Now CP is full of rather a lot of bluster and considered biased by some, but read the paper itself and there's a really good discussion of the progression of global temperature and how that progression has continued through the last decade and we are now at an all-time 12-month running mean record, despite low solar, negative PDO and though an El Nino, hardly a super-El Nino. Also some interesting comment about public perceptions and last winter's remarkable -ve AO weather.

Speaking of bias, Anthony Watts has sunk to a new utterly despiccable low, highlighting an aggressive comment on his blog that compares academics to cockroaches:

http://rabett.blogsp...s.html#comments - scroll down to 15/7/10 12:21 PM where it's highlighted. I hope the original is removed promptly.

This is particularly reprehensible because 'cockroaches' is how the Hutus described the Tutsis in radio broadcasts in 1994:

http://news.bbc.co.u...ica/3257748.stm

Watts and MacIntyre are both guilty of sending mobs after scientists they don't like (Watts on John Abraham, MacIntyre on CRU). It is disgusting and has no place in a debate on the science. To them, when the data, the physics and the enquiries don't support them, it is all they have left. I hope we can all agree that whatever our differences in opinion, and however deeply they run, there are certain lines that should not ever be crossed.

The only consolation in all that is that the fantasist Monckton is hanging himself by his own petard in trying to threaten John Abraham for daring to engage in a scientific discussion whereby Monckton's failure to grasp facts is exposed . See the above Rabett run post, and the one below from Skeptical Science:

http://www.skeptical...p=2&t=60&&n=277

He's been roundly rebuffed by lawyers for St Thomas University - you don't threaten legal action because you lost an academic debate Mr Monckton!

I'll end a rather long post on a lighter note:

.

sss

[Methuselah]

Isn't McIntyre a retired mineral engineer and McKitrick a economist? Neither of them are professional statisticians.

Yes, Dev. Which is why I seldom, if ever, take such people seriously. They are merely dabblers...McKitrick, for example, would be better-off improving economic models, IMO - rather than meddling in matters outside his area of expertise...

[Gray-Wolf]

http://lwf.ncdc.noaa.gov/sotc/index.php?report=global&year=2010&month=6

Over 2 months out of 'Nino and we're still posting global temp records. 4 Years(?) into solar min (quite a lag if this is your 'bag') so why have we got to this point? Has a low solar allowed cloudless skies over the Northern Atlantic leaving it as hot as a bath or is it just adding to the man made 'trend' in temps?

Only 2 years ago folk were parading a 'global cooldown' (even last winter some were cock-a-doodle-doing).

This certainly is 'in the news'

[jethro]

What I don't understand is if it's taken 30 odd years to get this warm, why would it only take a year or two to cool back down again?

Given that roughly 70% of the world's surface is covered by oceans which act as a giant storage heater, surely simple physics should dictate that it will as long, if not longer to cool down? It isn't going to happen in a blink of an eye. Touting a lack of dramatic cooling as proof that AGW is happening makes as much sense as touting last winter as evidence against.

[jethro]

Here's the latest from Joe B at Accuweather http://www.accuweather.com/world-bastardi-europe-blog.asp?partner=accuweather

The evidence for AGW has been under scrutiny by University of Pennsylvania Law School, I haven't read it yet but thought some here may find it interesting.

http://opinion.financialpost.com/2010/06/06/legal-verdict-manmade-global-warming-science-doesn%E2%80%99t-withstand-scrutiny/

http://www.probeinternational.org/UPennCross.pdf

[Gray-Wolf]

I'd agree J' ,what's more there's plenty more in the 'storage heater' that hasn't shown it's hand yet. What I think you 'miss' is the potential for this to trip a number of 'tipping points' from where the climate will not recover down to previous levels and ,if anything ,warm further. The latest paleo studies seem to suggest that this amount of GHG forcing (in the past) has meant radical changes to the planets climate 'tick-over' state.

As ever ,time will tell all but surely some of the signals of this change now occurring are becoming ever more obvious?

On the solar side the folk are saying we should now be reaping the 'low solar irradience' but this is being 'swamped' (as a 'signal' ) by the heating that has gone before.

The state of the central polar ice suggests that oceanic mixing is occurring there at present (all smashed ice so no 'damping' of the ocean swells) and the recent L.P. over the region suggests plenty of swells as opposed to the 'calm' of a H.P. which normally resides there.

As I've mentioned before (and still heard of no evidence to the contrary?) the loss of the unique zoning to the Arctic ocean means no return to ice volumes of the past (though, as we found last winter ,'extent' is another matter! even with a seasonal pack we'll still get ice cover over winter but the positive feedbacks over summer are the worry here).

For the 4th year studies of the out gassing of the permafrost are ongoing so by Aug we'll also find if this is accelerating or decreasing and what this means for our current projection of climate shift (things continue to be occurring well before the models predict?).

We are still awaiting the 'busy' 'cane season and if the 'Saharan dust' continues to limit development of storms on our side of the pond then the heat distribution we need will not occur leaving an even warmer Atlantic than we see today.

I'm sure if the global climate system was as simple as 'warming and 'cooling' you'd be right in your P.O.V. but the evidence of 'tipping points' over recent geological time would suggest a more 'Lovelokian' system with tipping points in the carbon cycle that lead to global temp shifts to a different 'point of balance'.

How long do we have to reach this point or has it already been breached and we now await rapid and dramatic change to our global climate?

The promise of a -ve PDO and another winter of AO similar to last years must surely show some impacts over time??? How long have we been PDO-ve now?

If these signals do not behave as we have measured before then we must engage in the possibility that something is now different and the systems are responding to that 'difference'?

Edited July 16, 2010 by Gray-Wolf

[VillagePlank]

What I don't understand is if it's taken 30 odd years to get this warm, why would it only take a year or two to cool back down again?

Given that roughly 70% of the world's surface is covered by oceans which act as a giant storage heater, surely simple physics should dictate that it will as long, if not longer to cool down? It isn't going to happen in a blink of an eye. Touting a lack of dramatic cooling as proof that AGW is happening makes as much sense as touting last winter as evidence against.

Yep - I've been trying to say something similar for quite a while now. Consider the following, derived from here

1. The atmosphere does not have much capability to store heat. The heat capacity of the global atmosphere corresponds to that of only a 3.2 m layer of the ocean.
   
2. The thermal inertia of a 90 m layer can add a delay of about 6 years to the temperature response to an instantaneous change (this time corresponds to an exponential time constant in which there is a 63% response toward a new equilibrium value following an abrupt change).
   
3. As a result, actual changes in climate tend to be gradual. With its mean depth of about 3800 m, the total ocean would add a delay of 230 years to the response if rapidly mixed.
   
4. However, mixing is not a rapid process for most of the ocean so that in reality the response depends on the rate of ventilation of water between the well-mixed upper layers of the ocean and the deeper, more isolated layers that are separated by the thermocline (the ocean layer exhibiting a strong vertical temperature gradient).
   
5. The rate of such mixing is not well established and varies greatly geographically. An overall estimate of the delay in surface temperature response caused by the oceans is 10–100 years.
   

As far as I aware this is scientific fact - of course, I am happy to concede if this is not the case and that NOAA have got it all wrong.

I must, therefore, entirely reject any implied hypothesis that a global cooldown is either imminent or expected. The science simply doesn't say that. It says that the oceans take a variable amount of time, dependent on the thermocline. Now, there is a simple model that demonstrates this ... it looks something like this:

dx/dy=-Ax+C

Hmmm. I'm sure I recognise that ...

:lol:

Edited July 16, 2010 by VillagePlank

[Gray-Wolf]

I think folk kid themselves that the recent 'upturn ' in temps can be matched by an equal 'downturn' when ,in effect, the upturn has been a long time in the making and it is only it's recent 'manifestation' in global temps that is focused on. The energy taken to warm oceans/melt ice kept temps stable for the majority of this new era until the point where some of that energy became 'spare' and so influenced global temps.

I'd be more inclined to look at the higher end of the time span need for us to regain the 'old' global temp regimes/workings than the lower and if GHG's are the mechanism for driving things then this just will not occur so long as we (and nature) increase their atmospheric concentrations.

If we do not pass the 400ppm for CO2 this year I'll be gladdened!

[Thundery wintry showers]

YS: I didn't say they were 'settled', but quite what is wrong with 2,3 and 4? For (2) I think the figure is ~95-98% of publishing researchers in the field agree with that. (3) you ought to agree with, as it's required to produce a significant/distinguishable MWP from natural forcing! (4) high climate sensitivity is certainly a bad thing - given our forcing of climate with CO2, which you admit has some effect (*). The effect will be worse with high sensitivity compared to low sensitivity.

If I'm reading this post about point (3), and by extension (4), correctly, it's making a large assumption here: that high sensitivity to certain natural forcings therefore means high sensitivity to anthropogenic forcings- again this doesn't automatically follow. The people who argue that AGW may be being overestimated tend to use a stance that sensitivity to natural forcings may be underestimated and sensitivity to anthropogenic forcings overestimated. I've found the evidence for this unconvincing so far, but it isn't yet beyond the realms of possibility either, and therefore, points 3 and 4 are not set in stone.

Regarding these "tipping points" I think it's highly unlikely that we will tip the climate irreversibly into warmth. Concentrations of greenhouse gases have been much higher in the past than they are now, and the same goes for global temperatures, yet we subsequently had ice ages. But what human activity could do is considerably extend the Holocene interglacial period or even end the Pleistocene glacial period altogether, pushing us into another warm era before another ice age sets in tens of millions of years later. In that sense it would be irreversible within our lifetimes, but not on geological timescales.

[Yorkshiresnows]

Yes, Dev. Which is why I seldom, if ever, take such people seriously. They are merely dabblers...McKitrick, for example, would be better-off improving economic models, IMO - rather than meddling in matters outside his area of expertise...

Hi Pete

Right, lets have enough of the complete clap trap.

Both the guys you critisise are respected mathematicians in their own right ...... it was the maths used in the original papers that interested them in the first place.

Also, neither worked with the other but joined in a common purpose after both realising what a complete load of godswollop the Hockey stick was. They arranged to meet after both coming to the same conclusions concerning the data manipulations.

Please read some of the references or maybe even take a look at the accepted peer reviewed published rebuttle made by McIntyre and Mckindick and then come to a considered conclusion. I am sure that once read you will find at least some of the arguments compelling.

I recently challenged 5 of my colleagues (one is a registered mathmatician) to read the 'Hockey-stick' illusion and referenced the papers 98/99 by Mann, the updated 2008 Mann (+ climate audit and real climate forums data) and asked their general opinions. Not one was happy with the Hockey-stick and all could not believe how the original paper could get peer reviewed and accepted without anybody looking at the maths or requesting the data to check on mathematical methods used.

That Mann then went on to chair and write the relevant chapter in the IPCC third assessment report (conflict of interest or what !!), where his papers took centre stage is also at the very least questionable.

Your quote concerning 'meddling in matters outside area of expertise' is just so very wrong.

Each expert pannel that was commisoned to look into this area critisised Mann's use of various statistical manipulations, particularly in the are of correlation statistics, the use of Bristlecone pines, short-centering of data, truncation of data series, back-filling of missing proxy data amongst others.

If it wasn't for these two 'meddlers' then the closed science policy of this area of climate science would still be operating and folks would be unaware of the serious flaws that operate in the area of tree-ring proxy data and the methods used to draw out meaningful data from complex multi-proxy data series.

Rant over

Y.S

Here's the latest from Joe B at Accuweather http://www.accuweath...ner=accuweather

The evidence for AGW has been under scrutiny by University of Pennsylvania Law School, I haven't read it yet but thought some here may find it interesting.

http://opinion.finan...stand-scrutiny/

http://www.probeinte.../UPennCross.pdf

Cheers Jethro,

Interesting read.

Y.S

[Gray-Wolf]

TWS, you always seem to use the word 'irreversibly' when looking at the carbon cycle facilitating a climate flip to a warmer setting. I do not think anyone would suggest this but ,as we see in the past, a long period of stable 'warm setting' for the climate is the concern.

As Richard Alley pointed out to us (in his E-Mail to me) we can expect at least another 2 precessional cycles before we look to Milankovich type forcings bringing about a flip back to the 'cold setting' and the decent into the next glacial epoch.

The worry appears to be that instead of 46 thousand years of a similar climate to today our greenhouse forcings may allow climate to settle into a 'warmer' epoch with an ice free pole and partial melting of both Greenland and Antarctica which would have severe consequences for the way we live today.:lol:

[Thundery wintry showers]

But what human activity could do is considerably extend the Holocene interglacial period or even end the Pleistocene glacial period altogether, pushing us into another warm era before another ice age sets in tens of millions of years later. In that sense it would be irreversible within our lifetimes, but not on geological timescales.

I think that may broadly match your last paragraph? There's definitely a risk of human activity messing up the timings of glacial events and warm epochs in the geological near term, and leaving us in another warm phase which could persist for longer than humans have existed for. I think humans would be able to adapt to that eventually but not without major casualties along the way, and thus yes, it is a serious concern.

Perhaps the issue is one of interpretation- some of your posts come across as implying that we can cause climate changes that can never be reversed, as opposed to being reversible only over geological timescales, but it is true that in the context of human lifetimes both would provide the same impacts.

Edited July 16, 2010 by Thundery wintry showers

[Methuselah]

My point, YS, is not that anybody who criticises AGW is a crank or, that the 'hockey stick' is the be-all-and-end-all of the debate - far from it! It's just that I'd sooner trust the opinions of someone well-versed in climatology and mathematics than even the world's greatest mathematician, on a subject about which he/she may no only very little...Just as I would if said mathematician was talking about the likely existence (or not) of space aliens...

IMO, being a great mathematician doesn't necessarily make one an expert in all other branches of science?

There's plenty of reason to be sceptical, however.

[Gray-Wolf]

Sorry TWS, my mistake (kitten currently driving me mad as it attacks every key stroke/mouse move).......

I owe you a beer down in the lounge (at least), we appear to share the same concerns just at differing intensities!!!

[VillagePlank]

I'd sooner trust the opinions of someone well-versed in climatology and mathematics ...

Since both are very broad fields, I suspect that you'd do well to find such a person. Personally, I would edge into the mathematics area over climatology on the basis that maths is the language of science, and climatology is a science which must, necessarily, be expressed in that language.

Edited July 16, 2010 by VillagePlank

[Gray-Wolf]

Since both are very broad fields, I suspect that you'd do well to find such a person. Personally, I would edge into the mathematics area over climatology on the basis that maths is the language of science, and climatology is a science which must, necessarily, be expressed in that language.

...unless we're using very broad brush strokes and then we can just natter about it?...........I'll get me coat......

[sunny starry skies]

My point, YS, is not that anybody who criticises AGW is a crank or, that the 'hockey stick' is the be-all-and-end-all of the debate - far from it! It's just that I'd sooner trust the opinions of someone well-versed in climatology and mathematics than even the world's greatest mathematician, on a subject about which he/she may no only very little...Just as I would if said mathematician was talking about the likely existence (or not) of space aliens...

IMO, being a great mathematician doesn't necessarily make one an expert in all other branches of science?

There's plenty of reason to be sceptical, however. :unsure:

Indeed, the best scientists are genuinely sceptical! I actually agree with both Pete and to a lesser extent VP here. You would ideally have someone well-versed in both techniques, but the reality is that you can't easily have a fully qualified person (ie research-grade) in both. So which is better, the mathematician/physicist who turns their hand to a branch of environmental/climate science, or the reverse? I've seen both at first hand, and surprisingly it is not as simple as you make out VP. It turns out that the concepts, and the ways of thinking required to do detailed science in glaciology or palaeoenvironmental science are very different from the concepts and methods required by mathematicians, physicists or computer programmers.

For example, I saw an otherwise excellent physicist doing a PhD utterly fail to grasp the concepts in their glaciological modelling project, much to the chagrin of the supervisor, who at least in part regretted going for the physicist rather than a numerically-capable Quaternary scientist/geographer/geologist. I think the issue is that while mathematics may be the language of glaciology or palaeo data analysis, I think the language of data analysis is easier to teach to the numerically-able Quaternary scientist than the more obscure language of palaeoenvironmental science is to the mathematician, who is bounded by different training, preconceptions and rule systems that don't always apply. There's also a preconception that somehow the maths is "harder" to learn, but I don't think that holds water at all. Of course that is not a universal observation and there will be excellent exceptions, but it is wrong to suggest that it is easy for a mathematician to get to grips with the complexities of spatial environmental/climatological problems, challenging data etc, especially if they have no specific training in the field.

sss

Edited July 16, 2010 by sunny starry skies

[Yorkshiresnows]

My point, YS, is not that anybody who criticises AGW is a crank or, that the 'hockey stick' is the be-all-and-end-all of the debate - far from it! It's just that I'd sooner trust the opinions of someone well-versed in climatology and mathematics than even the world's greatest mathematician, on a subject about which he/she may no only very little...Just as I would if said mathematician was talking about the likely existence (or not) of space aliens...

IMO, being a great mathematician doesn't necessarily make one an expert in all other branches of science?

There's plenty of reason to be sceptical, however. :lol:

Okay Pete,

Point taken

Y.S

[noggin]

Cor, blimey....here's something to get picking over, courtesy of NASA.

http://science.nasa.gov/science-news/science-at-nasa/2010/15jul_thermosphere/

There appears to be confirmation that solar activity affects the climate and, in some circumstances, it seems that C02 can act as a coolant.

As I am quite pooped, having just got in from work, it is currently beyond my mental capabilities to study the report properly, but there seems to be plenty of stuff to chew over!

Peace and love to all.

[VillagePlank]

It turns out that the concepts, and the ways of thinking required to do detailed science in glaciology or palaeoenvironmental science are very different from the concepts and methods required by mathematicians, physicists or computer programmers.

If I may digress, I would like to do what, at first glance, seems like a very difficult concept to grasp. Mathematics in n dimensions. Please try and stick with this ... there's an old adage that for each equation one might write down you halve the readership.

Everyone (I hope) is aware of Pythagoras' theorem. Actually, this is a consequence of the cosine laws, but that's another story. Pythagoras set out the following relationship:

This is something we all learnt at school, I hope; and therefore doesn't require explanation. If we want to find out what a is, we can rearrange the relationship as follows:

Essentially, since a is squared, we reduce a by it's square root, and since we've done it to one side of the equation, we must also do it to the otherside. Now, as it turns out, the notion that we are measuring the side of a right angled triangle in two dimensions, means that there must be two terms on the right-hand side. This is no coincidence, but I shan't go into a proof here. If we rewrite the equation, we can represent the dimensions in the equation itself. Here, we denote the dimensions by putting a subscript to the terms, and we rename the terms to d so we can see what's going on. Here's what it looks like:

So far, so good? We've taken Pythagoras and we've rearranged, and rewritten it so that is thoroughly representative of a triangle in two dimensions. We can see what we're looking at now.

There is another point about Pythagoras that I'm sure you will notice. The dimensions are added together and then the square root is found. Now there is a way in mathematics that represents summation. Here's what it looks like:

Here, we use the sigma symbol to denote that what comes after it must be added together. We put the starting number at the bottom, and we put the ending number at the top. We also use the subscript for d to denote the variable that we are cycling through. Here, I've finished at m (n=m)

Now, whether you like it or not, if you've followed the previous you now have a way of figuring out the side of a triangle in any number of dimensions. And it's understandable. You don't need to visualise it - I know of one person who can think clearly in five dimensions, and I know of no-one ever to exist who can think in more than five: me I have problems with four! There is no mystery to this. It is thinking clearly and moving through simple ideas and mapping them onto more complex ones.

This is provable too, and comes from first principles. One last thing - the square root sign always looks clumsy to me, and I prefer to use exponentials. Here it is rearranged to look elegant:

Since the square root is identical to the number raised to the power of 1/2.

Now, back to climatology. If we want to look at a stations temperature series through time we can represent this with a vector. A vector is a way of representing a number that has a value, magnitude, and a direction. GFS publishes wind 'numbers' as vector since we can represent wind as a value, it's speed, and it's direction, as a compass heading. We can do the same with temperature.

The temperature vector isn't as simple as the wind one, unfortunatly. We need to represent where the temperature is measured: longtitude and latitude, we need to measure the value of the temperature and we also need to measure when it was takend. We, therefore, end up with the following representation:

{longtitude,latitude,^oC,date}

which is a special kind of set called a tuple. Now, we are talking four terms, so we are talking four dimensions. If we also wanted to measure station height we can extend it to five dimensions by adding that idea to our tuple.

What's the point? Well, since we now have a field of vectors because we want to look at many stations in many places over many dates, we can use this, since we have represented that data in a fairly standard way, to exploit other mathematical principles such as vector calculus (in many dimensions), and our data succoumbs to standard analysis. For all the prevarication, hyperbole, and blogosphere nonsense, we know from first principles, that it is not beyond normal analysis.

So, is a mathematician able to apply skills to climatology? I think so. Can a climatologist apply his skills to mathematics - it really depends on his/her education. Mathematics is the language of science, and the use of it is utterly required.

After all, if you've followed this post (and one of my biggest weaknesses is getting what is in my head onto paper, or explaining it to someone else) would you have thought that, today, you, personally, could accurately write down a way of measuring vectors in n dimensional space from first principles in a way that is provable? That's what this post describes.

Isn't n-dimensional mathematics the exclusive preserve of super-intelligent people with PhD's?

I think not.

Edited July 17, 2010 by VillagePlank

[jethro]

Cor, blimey....here's something to get picking over, courtesy of NASA.

http://science.nasa....l_thermosphere/

There appears to be confirmation that solar activity affects the climate and, in some circumstances, it seems that C02 can act as a coolant.

As I am quite pooped, having just got in from work, it is currently beyond my mental capabilities to study the report properly, but there seems to be plenty of stuff to chew over!

Peace and love to all.

I won't pretend to understand all of that Noggin but there is one sentence which aroused my curiosity...

"The density anomalies," they wrote, "may signify that an as-yet-unidentified climatological tipping point involving energy balance and chemistry feedbacks has been reached."

That wouldn't perchance be one of those in-built mechanisms which have prevented the Earth boiling out of existence over the millennia? Or perhaps a new clue to the puzzle of how and why TSI doesn't explain the temperature anomalies on Earth?

[Thundery wintry showers]

If I may digress, I would like to do what, at first glance, seems like a very difficult concept to grasp. Mathematics in n dimensions. Please try and stick with this ... there's an old adage that for each equation one might write down you halve the readership.

Everyone (I hope) is aware of Pythagoras' theorem. Actually, this is a consequence of the cosine laws, but that's another story. Pythagoras set out the following relationship:

...

Pretty well explained there VP, I personally have no problem with that kind of mathematics, and it's good to see another "first principles" analysis. I have no problem with A-level maths or extensions of it, it's the abstract nature of some degree-level maths that often does my head in!

[VillagePlank]

Pretty well explained there VP, I personally have no problem with that kind of mathematics, and it's good to see another "first principles" analysis. I have no problem with A-level maths or extensions of it, it's the abstract nature of some degree-level maths that often does my head in!

Thanks TWS - never too sure about how to phrase this stuff. The point I am trying to make is that you don't need to be a member of the academic elite to understand this stuff. Hopefully, when people see n dimensional mathematics they will now see that it really is a simple construct (since using pythag we can build any n-dimensional construct: rather like computer graphics being divided into lots of triangles) - and that visualisation is not critical to understanding this stuff. I blame generation upon generations of very very poor mathematics teachers, myself.

I was fortunate to be born with insatiable curiosity, which has been very handy as I was a complete drop out as I child. I was lucky to get the very few GCSE's I did get. Luckily I saw sense in my 20's and started reading books.

If I may be so bold: look into set theory. Once you know that, and have an example of a few applications, everything else pretty much fits into place, and can always be taken back to the first principles therein. It's not often taught outside of software engineering or mathematics degrees, unfortunately - but we all do remember Venn diagrams from school? A simple as it sounds - that's the basis of all mathematics, and, therefore, all science.

Edited July 17, 2010 by VillagePlank