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Climate Hustle

## Climate time lag

#### Posted on 8 July 2009 by John Cook

The previous post on CO2/Temperature correlation sparked some interesting comments on climate time lag. Unfortunately, the discussion went pear shaped with some ideological anti-intellectualism and things got a little bitchy after that. Nevertheless, climate time lag is an important subject that deserves more attention. Several metaphors were invoked in an effort to explain the phenomenon including stove hot plates and warming baths. However, I find the best way to understand climate time lag is a direct look at the science.

Our climate receives its energy from the sun. The amount of energy the planet absorbs from the sun is calculated from this equation:

### Incoming Energy Flux= πR2S(1-A)

R is the radius of the earth, S (the solar constant) is the energy flux from the sun and A is the Earth's albedo - around 30% of sunlight is reflected back to space. The earth also radiates energy into space. The amount of energy emitted is a function of its temperature:

### Outgoing Energy Flux = 4πR2εσT4

σ is Boltzmann's constant, T is the absolute temperature in degrees Kelvin and ε is the average emissivity of the earth. Emissivity is a measure of how efficiently the earth radiates energy, between 0 and 1. A blackbody has an emissivity of 1. Greenhouse gases lower the earth's emissivity. When the climate is in equilibrium, energy in equals the energy out.

### S(1-A) = 4εσT4

What happens if the sun warms (solar constant S increases) then maintains a sustained peak? This is what occured in the early 20th century when solar levels rose then plateaued at a hotter state in the 1950's. The radiative forcing from the warming sun is not particularly large - between 0.17 W/m2 (Wang 2005) to 0.23 W/m2 (Krivova 2007) since the Maunder Minimum. Nevertheless, let's assume for the sake of argument that there is some amplifying effect (perhaps the cosmic ray effect on clouds) so that the warming sun has a substantial effect on global temperature.

When the sun warms, initially more solar energy is coming in than is radiating back out. The earth accumulates heat and it's temperature rises. As the earth warms, the amount of energy radiating back out to space increases. Eventually, the energy out matches the incoming solar energy and the planet is in equilibrium again. The time lag is how long it takes climate to return to equilibrium.

How long does the climate take to return to equilibrium? The lag is a function of climate sensitivity. The more sensitive climate is, the longer the lag. Hansen 2005 estimates the climate lag time is between 25 to 50 years.

How would climate have responded to the solar levels maxing out in the 50's? For the next few decades after the 50's, the radiative imbalance would've gradually decreased until the climate reached radiative equilibrium around the late 80's (give or take a decade). So how has our planet's radiative imbalance evolved over the latter 20th century?

Figure 1: net radiation flux at the top of the atmosphere (Hansen 2005).

Hansen 2005 finds that the net radiative imbalance has steadily increased over the 20th century. There is no indication that the climate is heading towards equilibrium - quite the contrary. This is confirmed by satellite measurements of energy flux at the top of the atmosphere:

Figure 2: Global ocean heat storage (blue) against global net flux anomalies (Wong 2005).

The climate is not heading towards equilibrium. Rather, the radiative imbalance is increasing with the climate steadily receiving more energy than it is radiating back out into space. And this is where the true significance of climate time lag lies. Even if the radiative imbalance were to level off at its current rate of around 0.85W/m2, it would take several decades for the climate to return to radiative equilibrium. Based on this climate lag, Hansen 2005 calculates there is still 0.6°C warming still "in the pipeline".

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Comments 151 to 200 out of 288:

1. I think it might be the ideology of ocean acidification is 10 times worse than calculated, the ideology of an ice free Arctic by 2010, the ideology of 7m sea level rise by the end of the century, the ideology of a few pairs of breeding humans surviving in Antarctica by 2100. It is an ideology that not even a failure of the oceans to continue to warm (at a minimum) and falling surface temperatures cannot dent. It is the ideology that argues that the planet is still warming. It is an ideology that prefers GISSTEMP over HADCRU because GISSTEMP includes some marginal arctic stations but refuses to countenance the independent UAH or RSS satellite methods because they are showing less warming.

It is an ideology that says that any exaggeration is responsible if it scares people into acting, any action is moral if it advances the cause and any opposition is evil and corrupt.

This is an ideology that fails to recognise obvious 50 year climate cycles in global temperature, fisheries, sea surface temperature, Arctic temperature, rainfall, North American temperature etc. Not even last week’s effort on realclimate can put a dent in their confidence. Let me repeat the message of realclimate – no warming trend for 20 to 30 years (i.e. a 25 year cooling phase) from 2001/2002 and a background warming of 0.1 degree C/decade from all other factors.

We are in a cooling trend and it will continue for a decade or 2 more. There is a trend of temperature increase of bugger all (an Australian technical term) in the UAH globally and depth average lower troposphere temperature.

A value judgement – a trend of 0.10C/decade in temperature rature is insufficient to justify all of the present silliness and outright perverse self righteousness of Co2 ideology.
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2. When I first came across his website, I was excited. "Finally, I've found someplace that really examined the "skeptic arguement", I.E,the tactics they used to maintain the illusion of a debate. What I ended up finding was a place where a bunch of psuedo eggheads congregate to impress themselves and each other with how smart they sound. What a waste of cyberspace!
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3. Get a life for crying out loud!!!!
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4. It's actually 9:00 PM on July 21st. I know, non relevant.
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5. Pseudo egghead? I resent the implication that I'm not a real egghead.

You really should spend some time on the science before leaping into the fray. The realclimate dicussion is here:

And the Swanson and Tsonis paper is here.

http://www.uwm.edu/~kswanson/publications/2008GL037022_all.pdf
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6. Pseudo egghead? I resent the implication that I'm not a real egghead.

You really should spend some time on the science before leaping into the fray. The realclimate dicussion is here:

And the Swanson and Tsonis paper is here.

http://www.uwm.edu/~kswanson/publications/2008GL037022_all.pdf
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7. #151 Silly me, so it's the CO2 ideology that says you can burn all of the carbon sequestered underground for millions of years and pump all that extra CO2 into the air while having no effect on the climate, while minor changes, up and down, in the sun, and which, conveniently, we can do nothing about, account for whatever climate change we have seen in the last 50 years.

Oh and you might want to re-read the RC paper on "warming interrupted", and the discussion which follows. It doesn't say what you think it says, and in any case you do know it's an hypothesis and has nothing to do with solar variation, don't you? You did read the sentence "it’s important to note that we are not talking about global cooling, just a pause in warming" didn't you? You do know that this is just a variation on the already well known effect of El NIno-La NIna variation on the long term rise and rise in emissions-caused general global warming, don't you?

I certainly wouldn't call you an egghead.
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8. Boy that Yobbo is a horse that can talk. And that carbonic snow cone, you'll have it chocolate or vanilla? LOL.
Oh, I forget, it's so darn cold in Vostok.

That people like you or thinga with his obsession on transposing the diurnal "heat lag" to a larger scale would try to give lessons in assessing the science is, well, ironic.
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9. re150:
Ideology attempts to place everything within the same set of related ideas and reduce inherant uncertainty, chaos and variation; it always takes the same side where there is fundamental ambiguity, and it usually suits vested interests-call them banks, academics, greens or whatever. Another feature of ideology is over-confidence, another suppression of valid dissent etc etc.

To not even examine solar effects and solar heat lag on the 'energy imbalance' in Hansen 2005 reveals an ideological stance. Or even better, an 'ideological imbalance'. You could argue that I have a solar ideological bent, but with good reason, the sun tends to completely dominate earth climate variation historically/geologically, there is no reason this should suddenly cease in the last few centuries.

Your c02 and general greenie-rant is a good example of an ideological stance. Pity you can't see it, but that's the nature of extreme ideology-it denies its own existance, or in Dawkins words-the ideology/meme complex secures its own perpuation by discouraging rational inquiry.

But getting back to the topic, because the earth is not warming quite fast enough, 'realclimate' are now saying T will level off over the next decade or so. (Perhaps they have secretly taken a look at the sun lately-like KGB agents secretly trying to figure out why the capitalist system works so well).
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10. "That people like you or thinga with his obsession on transposing the diurnal "heat lag" to a larger scale would try to give lessons in assessing the science is, well, ironic".

Transposing scale in natural systems is very common-eg from atomic to mesoscopic (eg crystal structure), eg fractal geometry, eg diurnal to annual, annual to decadal, and so on. In my field we use the term 'bonzai'-when comparing features of the very small to the very large. It is a very common scientific practice. But of course my field isn't strictly 'climate science', so it isn't relevant...

There are numerous examples of scale correlations, and lag effects in nature, so I don't know what bee is in your bonnet about it, but one of the reasons I bring lag effects up is because some academics/ideologists tend to hate/miss the idea of a lag effect, because they can't directly 'match' causes and effects, which means they can't easily reduce innate variation down to their preferred mantra. It is the same reason historically that various ideologists tended to hate the idea of Einsteins relativity when it came out -it produces a mismatch between ideology, causes-effects, and general perspective.
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11. #159 Look thingy, that kind of stuff goes down well in talk back radio, or on the letters page of "The Australian", or at a branch meeting of the National Party, but your in the wrong venue here.

"not even examine solar effects and solar heat lag" - two different things, as you must know. Solar effects (and I assume you are including Milankovitch cycles here) are well known, taken seriously, included in all models, account for some climatic changes in the past and present. never any dispute about that, much as you might try to mislead people. "Solar heat lag" as an explanation of current warming is, on the other hand, nonsense. John's original post points this out, and a number of us have responded on this thread. But I'll bet you keep saying it and keep writing it endlessly into the future, each time pretending it is a new idea never considered, Nobel Prize winning research.

"'realclimate' are now saying T will level off over the next decade or so". Um, no, they are not. One guest paper by two academics have suggested that the well known El NIn-La Nina cycling might, in 1998 have caused an even bigger jump than predicted from CO2 alone, and that there will be a discontinuity until the effects of greenhouse essentially catch up to where they would have been anyway. It's just a hypothesis, considering the very big jump in 1998. I don't think it's correct, nor do many of the posters on the very long thread that follows (read that have you, thought about it?), but in any case it has absolutely no bearing, as the authors say, on the inevitable CO2 induced warming. To pretend that it does (or that warming has somehow stopped in the last decade) is denialist dishonesty of the most obvious kind. You might say it is "discouraging rational inquiry".

And a concern for the future of the planet (last time I looked, the only one for miles around suitable for my grandchildren to live on) is a "greenie rant"? So be it.
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12. Sorry - is it the squid that are getting bigger because of global warming or the sheep that are getting smaller? Must be all that CO2 snow.

I think the Swanson and Tsonis paper says that the recent rate of warming (between 1977 and 1997) is 0.1 degrees centigrade per decade from all other causes when the points of rapid climate shift are excluded – and that there will be no warming trend for the next decade or so.

I made no other argument – simply that in my value judgement, 0.1 of warming between 1977 and 1997 from whatever cause, and there are many, is insufficient justification for continued global warming silliness.

The 50 year modulation of ENSO is involved but so are modes of major climate variability. The Swanson and Tsonis paper uses coupled climate parameters - ENSO,
the Pacific Decadal Oscillation, the North Atlantic Oscillation, and the North Pacific Index – and postulates that when these modes of major climate variability resonate, or are ‘synchonised’, the ‘character of ENSO variability’ is changed for 2 or 3 decades with a break in the ‘the global mean temperature trend’.

They say that clouds may be involved. Acknowledging the limited cloud data available from the ISCCP – it is a possibility for the latest climate shift in 2001/2002.

Swanson and Tsonis are recognising an underlying physical reality. The ‘modes of climate variability’ are real, quantified and, as I say, not simply the 2 to 7 year ENSO variation.

‘Extension of this analysis to the entire 20th century as shown in the bottom panel of Figure 1 reveals three climate shifts marked by breaks in the temperature trend with respect to time, superimposed upon an overall warming presumably due to increasing
greenhouse gasses. Global mean temperature decreased prior to World War I, increased during the 1920s and 1930s, decreased from the 1940s to 1976/77, and as noted above increased from that point to the end of the century. Insofar as the global mean temperature is controlled by the net top-of-the-atmosphere radiative budget [IPCC 2007], such breaks in temperature trends imply discontinuities in that budget. Such discontinuities are difficult to reconcile with the presumed smooth evolution of anthropogenic greenhouse gas and aerosol radiative forcing with respect to time [Hansen et al. 2005]. This suggests that an internal reorganization of the climate system may underlie such shifts [Zhang et al. 2007].

And

‘However, the nature of these past shifts in climate state suggests the possibility of near constant temperature lasting a decade or more into the future must at least be entertained. The apparent lack of a proximate cause behind the halt in warming post 2001/02 challenges our understanding of the climate system, specifically the physical reasoning and causal links between longer time-scale modes of internal climate variability and the impact of such modes upon global temperature.’

I take it you will entertain the idea, reject it and accuse me of being psychologically aberrant.

You might try these for a little background – I suggest that you take your time because real understanding comes from a considered and balanced approach.

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13. I was obviously optimistic to think that people would read the paper before rejecting it.

It's OK David, just read the 'guest blog' and the posts - it won't challenge your preconceptions.
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14. Which part of "superimposed upon an overall warming presumably due to increasing
greenhouse gasses" did you not understand? And yes, I did read the guest blog, written, as you know, by Kyle Swanson, as a summary and explanation of the Swanson-Tsonis paper. And the thread. Did you?
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15. No - I gave up on the thread - it was appallingly silly.

"'realclimate' are now saying T will level off over the next decade or so". Um, no, they are not. One guest paper by two academics have suggested that the well known El NIn-La Nina cycling might, in 1998 have caused an even bigger jump than predicted from CO2 alone, and that there will be a discontinuity until the effects of greenhouse essentially catch up to where they would have been anyway."

Perhaps not - because the level of understanding exhibited is entirely inadequate.

The paper excluded sudden climate shifts and calculated a residual warming from all other causes of 0.1 degrees centigrade/decade.

To my knowledge, no one has ever claimed that temperature didn't increase in the 20th century. There may be a farmer in Woop Woop - but look at it this way - he is still as right as you.
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16. No - I gave up on the thread - it was appallingly silly.

"'realclimate' are now saying T will level off over the next decade or so". Um, no, they are not. One guest paper by two academics have suggested that the well known El NIn-La Nina cycling might, in 1998 have caused an even bigger jump than predicted from CO2 alone, and that there will be a discontinuity until the effects of greenhouse essentially catch up to where they would have been anyway."

Perhaps not - because the level of understanding exhibited is entirely inadequate.

The paper excluded sudden climate shifts and calculated a residual warming from all other causes of 0.1 degrees centigrade/decade.

To my knowledge, no one has ever claimed that temperature didn't increase in the 20th century. There may be a farmer in Woop Woop - but look at it this way - he is still as right as you.
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17. Oh I remember - I got to:

save gaia says:
12 Jul 2009 at 5:27 pm

Maybe this annomaly you speak of has something todo with the montreal protocol?
http://en.m.wikipedia.org/wiki/File:Ozone_cfc_trends.png

and gave up.
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18. All I can suugest is that you take on the advice below.

'Thanks for the post Kyle. I hope you’re wrong though, because the thought of 10 more years of the deniers screaming (increasingly loudly) about how global warming is a bunch of not happening BS is a bit more than I for one can take. They could really use this to very damaging political advantage, weakening proactive action just when it’s most needed.'

[Response: When the Keenlyside paper came out, Andy Revkin had a nice blog article on whether the drive for carbon mitigation action could survive (another) decadal interruption in warming. It's a good question, but one I wouldn't presume to know how to answer. Our best armory for the arguments you fear quite rightly is to build up our understanding of decadal variability and the extent to which it can cloud the long term trend. It's too soon to say whether the current "pause" in warming is anything more than statistics being clouded by one unusual El Nino event, but we should be thinking now about possible explanations just in case something more interesting is going on. --raypierre]
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19. All I can suugest is that you take on the advice below.

'Thanks for the post Kyle. I hope you’re wrong though, because the thought of 10 more years of the deniers screaming (increasingly loudly) about how global warming is a bunch of not happening BS is a bit more than I for one can take. They could really use this to very damaging political advantage, weakening proactive action just when it’s most needed.'

[Response: When the Keenlyside paper came out, Andy Revkin had a nice blog article on whether the drive for carbon mitigation action could survive (another) decadal interruption in warming. It's a good question, but one I wouldn't presume to know how to answer. Our best armory for the arguments you fear quite rightly is to build up our understanding of decadal variability and the extent to which it can cloud the long term trend. It's too soon to say whether the current "pause" in warming is anything more than statistics being clouded by one unusual El Nino event, but we should be thinking now about possible explanations just in case something more interesting is going on. --raypierre]
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20. re #148

"Also, be advised that there are yet other lines of evidence(that we haven't talked about yet) for CRF-climate links which detail climate fluctuations for periods when the relationship btw CRF and solar irradiance is known to be altered."

I doubt that shawnet. So far when we examine in detail whatever is raised for discussion, we find that the evidence for CRF-climate links is dubious. That applies to the contemporary periods in which the relationships can be examined in detail and the periods encompassing the LIA/MWP, for which we also have a reasonably good estimate of the solar outputs. Solar influences are understandable in terms of solar irradiance changes as indicated for example by recent simulations of temperature through the last 1000 years [*]. These indicate that the lower estimates of solar irradiance reconstructions, with volcanic and greenhouse forcings, fit the hemispheric temperature data rather well. Neither is there evidence for the CRF – climate hypothesis, nor is this required to understand solar contributions over this period. Kirkby makes a pseudoscience case for a CRF contribution based on misrepresentation of the science and innuendo (he misrepresents the solar irradiance contribution and pretends that volcanic and greenhouse contributions don't exist!). I suspect if we look at Kirkby's other examples in detail we'll find these similarly deficient.

"Yes, I think that if you agree that there is some form of solar amplification, we aren't that far apart. You are missing the point of the Kirkby paper, though. It is saying that the CRF-climate interaction is worth studying precisely because it appears such an unknown amplification that CRF can help fill."

No. That's another illogical argument The solar effects may be amplifed by ocean current effects or may (with volcanic forcing) trigger circulation state changes. There so far isn't a requirement for internal solar amplification of the sort that you suggest. There is neither evidence for a CRF-climate link nor is there a requirement for one. Solar and volcanic forcings may well trigger or be amplified by ocean/atmosphere current effects but that has got nothing necessarily to do with any CRF effects. The evidence simply isn't there. That doesn't mean that it doesn't exist…however one can't pretend that evidence exists by misrepresenting the science and using false logic.

I don't think I'm missing the point of Kirkby's review at all. He's proselytizing wildly for CRF influences, and in doing so giving a false account of the science. I don't have a particular problem with that, but if we want to understand the science we may as well recognise second-rate arguments. We are simply not going to learn anything about paleoclimate from Kirkby. Happily there's a huge wealth of good science out there. If we want to understand the difficult subject of Holocene climate variability, far better to read authoritative sources that consider the subject in its entirety. A very good source is a recent review by a large group of experts in all the relevant aspects of the subject which was published last year [**]. This review doesn't cheat the reader by pretending that the well characterised influences on Holocene climate variability don't exist!

As you say the climate is complex. That complexity is represented in all its diversity in the scientific literature and in excellent reviews, such as the one by Wanner et al This is highly recommended if you feel it's worth learning about these subjects.

[*] C. M. Ammann et al (2007) Solar influence on climate during the past millennium: Results from transient simulations with the NCAR Climate System Model, Proc. Natl. Acad. Sci. USA 104, 3713-3718

The potential role of solar variations in modulating recent climate has been debated for many decades and recent papers suggest that solar forcing may be less than previously believed. Because solar variability before the satellite period must be scaled from proxy data, large uncertainty exists about phase and magnitude of the forcing. We used a coupled climate system model to determine whether proxy-based irradiance series are capable of inducing climatic variations that resemble variations found in climate reconstructions, and if part of the previously estimated large range of past solar irradiance changes could be excluded. Transient simulations, covering the published range of solar irradiance estimates, were integrated from 850 AD to the present. Solar forcing as well as volcanic and anthropogenic forcing are detectable in the model results despite internal variability. The resulting climates are generally consistent with temperature reconstructions. Smaller, rather than larger, long-term trends in solar irradiance appear more plausible and produced modeled climates in better agreement with the range of Northern Hemisphere temperature proxy records both with respect to phase and magnitude. Despite the direct response of the model to solar forcing, even large solar irradiance change combined with realistic volcanic forcing over past centuries could not explain the late 20th century warming without inclusion of greenhouse gas forcing. Although solar and volcanic effects appear to dominate most of the slow climate variations within the past thousand years, the impacts of greenhouse gases have dominated since the second half of the last century.

[**] Wanner H, Beer J,, Butikofer J,, Crowley TJ, Cubasch U, Fluckiger J, Goosse H, Grosjean M, Joos F, Kaplan JO, Kuttel M, Muller SA, Prentice IC, Solomina O, Stocker TF, Tarasov P, Wagner M, Widmann M. (2008) Mid- to Late Holocene climate change: an overview, Quaternary Sci. Rev. 27, 1791-1828

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21. "They could really use this to very damaging political advantage, weakening proactive action just when it’s most needed." Well, yes, and that is precisely what is happening, on this thread and others.

Swanson-Tsonis are not on the side of deniers, give you no comfort. They are simply looking at the precise nature of the period from 1998 - does it represent a stepwise upward shift, or is it simply part of the variability within error ranges, of the steady climb of GHG-induced temp rise of the last 50 years or so. So don't pretend there is some other weird and unproven mechanism lurking in there that turns the whole climate change analysis on its head and allows everybody to take bat and ball home and pretend the game never happened. Business as usual eh Yobbo, that's the name of this game is it not? And to hell with the planet.
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22. So, thinga, what is the mechanism behind the diurnal temperature heat lag?
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23. "I doubt that shawnet. So far when we examine in detail whatever is raised for discussion, we find that the evidence for CRF-climate links is dubious. That applies to the contemporary periods in which the relationships can be examined in detail and the periods encompassing the LIA/MWP, for which we also have a reasonably good estimate of the solar outputs. Solar influences are understandable in terms of solar irradiance changes as indicated for example by recent simulations of temperature through the last 1000 years [*]. These indicate that the lower estimates of solar irradiance reconstructions, with volcanic and greenhouse forcings, fit the hemispheric temperature data rather well. Neither is there evidence for the CRF – climate hypothesis, nor is this required to understand solar contributions over this period. Kirkby makes a pseudoscience case for a CRF contribution based on misrepresentation of the science and innuendo (he misrepresents the solar irradiance contribution and pretends that volcanic and greenhouse contributions don't exist!). I suspect if we look at Kirkby's other examples in detail we'll find these similarly deficient. "

The only case were the CRF climate correlation is weak is for the short term, which I've already discussed. Your explanations of LIA/MWP are not fundamental, you don't know what causes THC to vary(if that's what's actually happening). Further, the climate is a lot more than 1000 years old. The long-term correlation btw CRF and climate makes no sense without some form of solar amplification.

Frankly, it is a little silly the way you keep claiming that everyone who disagrees with you is performing bad science or pseudoscience in some way. Scientific hypotheses don't get falsified by hand-waving and name calling. BTW, even if GCMs could explain the climate changes we have observed over the past 1000 years based on lower solar forcing, they wouldn't be able to explain the extent of the correlation btw solar proxies and climate changes without such an amplification.
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24. "the sun tends to completely dominate earth climate variation historically/geologically, there is no reason this should suddenly cease in the last few centuries."

"No reason?" Really? You mean no reason other than Man's contribution to atmospheric CO2 levels? I'm not sure I'm following correctly. Are you arguing that modern civilization hasn't radically altered atmospheric CO2 levels from historically/geological norms, or that CO2 isn't a greenhouse gas, or we have and it is but the sun is so dominant that it just doesn't matter?
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25. I don't think so, shawnet. Again you're ignoring the fundamental element of science which is evidence. I'm generally agreeing with the evidence-based science. You seem to be rather uninterested in this. What I'm disagreeing with is bogus arguments and misrepresentation in the two sources you have introduced to this thread (I have no problem with the Harrison work you've referred to – he seems to be doing solid science without the fatuous hyperbole of your main sources). You're happy to cheerlead for dodgy "science". Fine....but you should expect that skeptical individuals are very likely to point out its flaws.

We've examined those sources and arguments in detail, in the light of 30-40 scientific papers and data resources together on this thread (i.e. not "hand-waving"). It's tedious to go through this all again, but your two sources are simply objectively deficient as science. If we consider the MWP/LIA, your Kirkby misrepresents the science on solar irradiance reconstructions, takes the misrepresented value (0.06 oC), substracts this from the LIA to mid 20th century warming (around 0.6 oC), pretends that there has been no enhanced greenhouse or volcanic contribution, and insinuates that there must have been a major CRF contribution.

That's clearly bogus isn't it. We can make that conclusion objctively in the light of the science – we don't have to beat around the bush. It's not a question of agreeing or disagreeing.

Now perhaps you're suggesting that while these analyses are bogus, maybe some other arguments are more convincing. Fine. Let's have a look at them. You say "the long term correlation btw CRF and climate makes no sense without some form of solar amplification.". Which long term correlation? Why, exactly, does this make "no sense without some form of solar amplification"?

No one is saying that there might not be a contribution of CRF to climate. There simply isn't compelling evidence that this is of any significance whatsoever. There are lots of good scientists working on all elements of these subjects, and if evidence for a CRF-climate link of any significance arises, that will be just dandy. In the meantime let's not be suckered by tedious "catch all fill-in-the-blanks type mechanisms" that do nothing to inform our understanding.
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26. David - denying the reality of decadal climate variability is, well, denying reality.

Swanson and Tsonis -

‘The subject of decadal to inter-decadal climate variability is of intrinsic importance not only scientifically but also for society as a whole. Interpreting past such variability and making informed projections about potential future variability requires (i) identifying the dynamical processes internal to the climate system that underlie such variability (seee.g. Mantua et al. [1997]; Zhang et al. [1997]; Zhang et al. [2007]; Knight et al. [2005]; Dima and Lohmann [2007]), and (ii) recognizing the chain of events that mark the onset of large amplitude variability events, i.e., shifts in the climate state. Such shifts mark changes in the qualitative behavior of climate modes of variability, as well as breaks in trends of hemispheric and global mean temperature. The most celebrated of these shifts in the instrumental record occurred in 1976/77. That particular winter ushered in an extended period in which the tropical Pacific Ocean was warmer than normal, with strong El Niño-Southern Oscillation (ENSO) events occurring after that time, contrasting with the weaker ENSO variability in the decades before (Hoerling et al. [2004]; Huang et al. [2005]). Global mean surface temperature also experienced a trend break, transitioning from cooling in the decades prior to 1976/77 to the strong warming that characterized the remainder of the century.’
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27. "I don't think so, shawnet. Again you're ignoring the fundamental element of science which is evidence. I'm generally agreeing with the evidence-based science. You seem to be rather uninterested in this. What I'm disagreeing with is bogus arguments and misrepresentation in the two sources you have introduced to this thread (I have no problem with the Harrison work you've referred to – he seems to be doing solid science without the fatuous hyperbole of your main sources). You're happy to cheerlead for dodgy "science". Fine....but you should expect that skeptical individuals are very likely to point out its flaws."

It is fairly tedious to talk to someone who interprets any disagreement with themselves as dodgy science or whatever. The fact is, differences of opinion don't make either side of a scientific debate dodgy or whatever pejorative you wish to use. Calling something dodgy isn't pointing out its flaws.

It is pretty obvious that there is much more detailed examination of the CRF-climate link in the Kirkby review than you have taken time to acquaint yourself with. However, rather than look at the totality of the evidence, it is much simpler to call it pseudoscience(when the worst you can offer is that he uses a different TSI reconstruction than you).

You have offered no coherent objection to the central point of the Kirkby review which is that there appears to have been an amplification of solar effects on climate operating at various time schemes in Earth's history and that one way to see that connection working is by some sort of connection btw CRF and climate phenomena. Kirkby isn't saying the link is established, just laying out the reasons why he thinks it is worth exploring.

""Now perhaps you're suggesting that while these analyses are bogus, maybe some other arguments are more convincing. Fine. Let's have a look at them. You say "the long term correlation btw CRF and climate makes no sense without some form of solar amplification.". Which long term correlation? Why, exactly, does this make "no sense without some form of solar amplification"? "

This paragraph makes me think that you aren't even reading what I write. There must be at least a dozen papers delineating the long term correlation btw solar proxies and climate events in the Kirkby review and I know we discussed the Bond paper already. The fact is, these papers lay out climate events whose magnitude is much greater than can be explained by variation in solar irradiance alone, but that are still well correlated to CRF.

And, as I have said before, it is not that your papers are bogus, it is that, by and large, they don't deal with fundamental causes (for instance, they say THC is responsible without saying why THC changes happen). There is no contradiction btw saying both that a climate-CRF link and a THC change are responsible(if the climate CRF is indirectly responsible for THC changes).
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28. RE: 174: "the sun is so dominant that it just doesn't matter".

Yes, this is my position.

I think the relative effect of increasing C02 on T in the atmosphere, ie by ~0.01% (ie ~280-390ppm) is very small.

EG 1:
C02 rise only 'correlates' with 2/4 T step changes since the 19th century (~1900-1940, 1978-1998), whereas the solar increase correlates with 3/4 (1900-1940, 1940-1978, 2000s-2009), so the sun is at least as dominant. Its ideology, not data, to claim that c02 is more dominant, from this simple correlation alone.

The problem humans have, is to disentangle the relative effects between the sun and c02 on recent T-I wish it wasnt like this, I wish the sun had cooled or stayed the same in the last few hundred years so we would know the relative contribution, but because of various forcings and so on, nobody really knows or sure. IPCC's '90% certainty' is ideological bureacuratic convenience, nothing more.

EG2.
To discount changes in the sun as only having a very minor effect on T is not valid, because similar 'very minor' effects have produced large-scale T changes before, so the earth MUST be very sensitive to minor solar changes. However similar changes in c02 in the past have not driven T changes, so it is precarious at best to assert that C02 rise is dominating recent T changes.

Th physics of c02 on heat in the amosphere is not incorrect, it is the relative contribution to recent changes that is the issue. I personally think, like the NIPCC, that the IPCC have got it backwards, c02 has less than 10% effect on recent T changes, and the sun dominates.

EG3.
Have a look at human history- a mountain pass in Europe recently (2003) became free of ice/snow revealing 4 previous times it has been open in the last 5,000 years. None of these previous openings were driven by c02, all by very small changes in the sun (the 1500 years solar cycle-in which we are currenly in a warming trend). So, we know small changes in the sun can do it, whether c02 can singnificantly drive T is not supported by previous times c02 was high (such as in previous interglacials-no 'runaway greenhouse', and during previous geological periods).

Ref: "Unstoppable global warming evey 1500 years", F. Singer and D.Avery.

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29. "So, thinga, what is the mechanism behind the diurnal temperature heat lag? "

There are multiple 'mechanisms', aren't there?. A few might include thermal inertia and heat transfer; proportions of land-ocean-ice, land use, and localised winds and clouds also play a role; longer time scales would also include eg ocean currents, atmospheric wind systems, and probably numerous other things. You tell me?
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30. I thought I would go directly to the 4AR. Unlike some tryhards on this site - even the IPCC entertains the notion of cosmic rays and clouds - and cites some of the 'dodgy' science.

The estimates of long-term solar irradiance changes used in the TAR (e.g., Hoyt and Schatten, 1993; Lean et al., 1995) have been revised downwards, based on new studies indicating that bright solar faculae likely contributed a smaller irradiance increase since the Maunder Minimum than was originally suggested by the range of brightness in Sun-like stars (Hall and Lockwood, 2004; M. Wang et al., 2005). However, empirical results since the TAR have strengthened the evidence for solar forcing of climate change by identifying detectable tropospheric changes associated with solar variability, including during the solar cycle (Section 9.2; van Loon and Shea, 2000; Douglass and Clader, 2002; Gleisner and Thejll, 2003; Haigh, 2003; Stott et al., 2003; White et al., 2003; Coughlin and Tung, 2004; Labitzke, 2004; Crooks and Gray, 2005). The most likely mechanism is considered to be some combination of direct forcing by changes in total solar irradiance, and indirect effects of ultraviolet (UV) radiation on the stratosphere. Least certain, and under ongoing debate as discussed in the TAR, are indirect effects induced by galactic cosmic rays (e.g., Marsh and Svensmark, 2000a,b; Kristjánsson et al., 2002; Sun and Bradley, 2002).

Table 2.11 indicates that there is now stronger evidence for most of the RFs discussed in this chapter. Some effects are not quantified, either because they do not have enough evidence or because their quantification lacks consensus. These include certain mechanisms associated with land use, stratospheric water vapour and cosmic rays.
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31. I thought I would go directly to the 4AR. Unlike some tryhards on this site - even the IPCC entertains the notion of cosmic rays and clouds - and cites some of the 'dodgy' science.

The estimates of long-term solar irradiance changes used in the TAR (e.g., Hoyt and Schatten, 1993; Lean et al., 1995) have been revised downwards, based on new studies indicating that bright solar faculae likely contributed a smaller irradiance increase since the Maunder Minimum than was originally suggested by the range of brightness in Sun-like stars (Hall and Lockwood, 2004; M. Wang et al., 2005). However, empirical results since the TAR have strengthened the evidence for solar forcing of climate change by identifying detectable tropospheric changes associated with solar variability, including during the solar cycle (Section 9.2; van Loon and Shea, 2000; Douglass and Clader, 2002; Gleisner and Thejll, 2003; Haigh, 2003; Stott et al., 2003; White et al., 2003; Coughlin and Tung, 2004; Labitzke, 2004; Crooks and Gray, 2005). The most likely mechanism is considered to be some combination of direct forcing by changes in total solar irradiance, and indirect effects of ultraviolet (UV) radiation on the stratosphere. Least certain, and under ongoing debate as discussed in the TAR, are indirect effects induced by galactic cosmic rays (e.g., Marsh and Svensmark, 2000a,b; Kristjánsson et al., 2002; Sun and Bradley, 2002).

Table 2.11 indicates that there is now stronger evidence for most of the RFs discussed in this chapter. Some effects are not quantified, either because they do not have enough evidence or because their quantification lacks consensus. These include certain mechanisms associated with land use, stratospheric water vapour and cosmic rays.
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32. What? You want ME to tell YOU? Considering how you have already convicted climate scientists with ignoring/suppressing the issue, I would assume you are quite knowledgeable about at least the basis of your comparison. But you're not. Interesting.

This is extremely basic meteorology stuff. Blabbing about advanced research if you don't even know that kind of basics is pointless.

Try this: the surface radiates heat out. The Sun radiates energy in. In the morning, the balance becomes positive, in exceeds out, surface starts warming (immediately). Surface continues to warm as long as in exceeds out. The moment out exceeds in (anywhere between 3 and 5 depending on the type of surface), surface stops warming and starts cooling.

This is somewhat complicated by the fact that what is considered is not the surface temp itself but that of the adjacent air. Stratification, convection, moisture, lapse rate also come in to complicate things. Yet, the basic principle is there.

There is no real delay. The reason why surface temp continues to increase in the afternoon is not that it's, somehow, catching up because of some mysterious "lag." Energy in remains higher than energy out until some time in the afternoon. There is no real "lag" in diurnal temperature variations, only the appearance of one. The temperature increases as long as the radiative imbalance is positive.

Between the Yobbo and his carbonic snow, giving lessons on atmospheric physics, and you, we're getting some serious expertise here. And guys like you have no problem yelling that the scientists have it all wrong. Great.
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33. Mr Donta,

I would suggest that the energy flux/energy content concept is an obvious candidate.

I don't often use analogies - they are too often imprecise. But consider he humble pot on the stove - it neither toils nor spins - no that's the wrong metaphor.

The energy flux is constant - it is the W/m2 transferred to the pot and the water from the stovetop - but the water keeps getting warmer. The energy content of the water keeps increasing due to the accumulating Joules (W/s).

The hot afternoon is also a reasonable analogy. The ground keeps accumulating energy until it is radiating more than the declining afternoon insolation.

These guys are just thrashing about in the dark with not the slightest love of science and misuse peer reviewed literature to stubbornly insist on the wildest and most improbable points. They have no sense of humour at all and insist that they and their secular humanist and socialist minions are the annointed ones to secure the future of humanity and the planet.

It is only most amusing because they never had a hope of winning the battle for hearts and minds.

Cheers
Robbo
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34. Oh Phillipe - I am saddened - but you are right. I quote the 4AR and realclimate. I must be woefully muddle headed.
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35. RE182:

The radiative description you have given is correct (ie there is no 'offset' or 'lag' with regards to radiative balance etc), but I would say just not quite the right 'take' on the main issue.

Your 'radiative balance' explanation doesn't emphasise the time difference between max incoming heat energy (noon) and highest T (3pm), which is the CRUCIAL point. Incoming heat energy actually drops, but T keeps rising-a 20-25% offset. (ie until your 'radiative imbalance' is restored) The physical reason for this time-offset is, 'basically', thermal inertia and heat transfer.

Max energy in occurs when the sun is highest overhead, when incoming rays are at the lowest angle of incidence to the ground (around noon). The angle of incidence is the key-the area of ground that the rays have to heat is less with a lower angle of incidence. This is largely why the tropics are warmer than the poles.

But one main argument used by 'global warming by humans' against the sun as the driver of warming in the late 20th century states that there has been no increase in solar activity since the mid 20th century, therefore the sun can't be responsible for late 20th century warming. But if there is a long time heat-lag effect-just as happens during any day-and air keeps warming after peak solar incoming activity (eg 40-60 years-which is valid if the earth land-ocean system is very sensitive to changes in the sun-which history tells us is the case) it is obvious this 'basic' argument against the sun as a driver of more recent late 20th century warming is invalid.

John Cook states above however, that the earth's radiative imbalance shows that the earth-land-ocean system is not approaching equilibrium, therefore invalidating this idea of a long ~40-60 year solar heat lag.

However even if the 'energy imbalance' of the early 2000s itself is real (and I'm not sure it is), the 'cause' itself is contentious-it is modelled/explained using c02/greenhouse gas forcing in the Hansen 2005 paper-however it actually may be a confirmation of the solar heat lag itself- which would ALSO produce an apparent mismatch between 1955-1998 stored ocean heat and incoming/outgoing energy-however NO attempt is made to examine long term solar heat lag as an explanation for this apparent 'imbalance'. The imbalance is simply assumed/modelled to be greenhouse gas related.

Moreover, Hansen et al then predict continuing increasing imbalances, high ocean T, and high T in coming years, which HASN'T happened, the ocean has actually cooled, which shows he may have got the whole issue as to 'cause' completely wrong-ie the sun's solar ?40-60 year heat lag may actually be the cause of his apparent 'energy imbalance', which, as the sun is now waning and lag effects are subsiding (ie its after 3pm), explains the non-rise in T since early 2000s.

C02 doesnt explain this non-rise in T since early 2000s at all, however long term solar heat lag does, very nicely.
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36. You're still not getting it on the diurnal variation. The physical reason for the lag is not "thermal inertia." It is what I just explained above. Peak incoming energy is meaningless, unless taken in the context of the radiative imbalance.

If you examine the variation more closely, you will see that the fastest increase in temp happens around noon, i.e. the time at which the radiative imbalance is the highest. If, for some reason, ground radiation would suddenly exceed incoming energy at that moment, the surface would stop warming. No lag.

There is no crucial point here, you're trying to cling to an idea that has no real existence. Find a better idea to transpose to climate lag. Stop saying that the oceans have cooled, when John has recently examined this and showed that it's not the case.

Yobbo, sorry I hurt your feelings mate. For one capable of cramming so many empty right-wing talk show adjectives in a paragraph, you're quite sensitive.
Perhaps another snow cone will make you feel better, although I doubt that it will help you understand what you quote better.
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37. The next test happens in the boreal spring - will there be a strong El Nino?

Very unlikely given the statistical correlation between the PDO and ENSO modulation over decades.
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38. The oceans are cooling. The metric more telling than any other is the state of Earth albedo. Figure 3 on the Project Earthshine site shows an increase in earth albedo of 1% since 1999 – a decrease in shortwave radiative forcing of 2 W/m2. While this persists – the cooling progresses. It is a proximate cause of the recent lack of ocean and atmospheric warming.

As Swanso says in the paper I have apparently understood - the lack of warming in the past should challenge the current understanding of climate. It is not sufficient to say that the variability is chaotic and warming will return worse than ever soon time soon.

Nor is it sufficient to suggest that I am a liberal humanist and a theist and therefore stupid and irrelavant. I could try and persuade with a passionate and flowery discussion of the nuances of liberal humanism - but it seems to be pearls before swine.

You really need to integrate new data into your thinking even if it does challenge. Of the insults - in the vernacular - I don't give a rat's arse.
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39. The oceans are cooling. The metric more telling than any other is the state of Earth albedo. Figure 3 on the Project Earthshine site shows an increase in earth albedo of 1% since 1999 – a decrease in shortwave radiative forcing of 2 W/m2. While this persists – the cooling progresses. It is a proximate cause of the recent lack of ocean and atmospheric warming.

As Swanso says in the paper I have apparently understood - the lack of warming in the past should challenge the current understanding of climate. It is not sufficient to say that the variability is chaotic and warming will return worse than ever soon time soon.

Nor is it sufficient to suggest that I am a liberal humanist and a theist and therefore stupid and irrelavant. I could try and persuade with a passionate and flowery discussion of the nuances of liberal humanism - but it seems to be pearls before swine.

You really need to integrate new data into your thinking even if it does challenge. Of the insults - in the vernacular - I don't give a rat's arse.
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40. This should be - as Swanson says in he paper I have apparently misunderstood - the lack of warming in the last decade should challenge..
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41. This one just in – the SOI is of course intimately related to ENSO and varies with the multi-decadal modulation of the ENSO states. It shows that most of the warming in recent times is associated with the warm ENSO phase from 1976 to 1998.

And it is simply not good enough to call this dodgy science by dodgy scientists and go on your merry way.

Influence of the Southern Oscillation on tropospheric temperature

J. D. McLean
Applied Science Consultants, Croydon, Victoria, Australia
C. R. de Freitas
School of Geography, Geology and Environmental Science, University of Auckland, Auckland, New Zealand
R. M. Carter
Marine Geophysical Laboratory, James Cook University, Townsville, Queensland, Australia

Time series for the Southern Oscillation Index (SOI) and global tropospheric temperature anomalies (GTTA) are compared for the 1958−2008 period. GTTA are represented by data from satellite microwave sensing units (MSU) for the period 1980–2008 and from radiosondes (RATPAC) for 1958–2008. After the removal from the data set of short periods of temperature perturbation that relate to near-equator volcanic eruption, we use derivatives to document the presence of a 5- to 7-month delayed close relationship between SOI and GTTA. Change in SOI accounts for 72% of the variance in GTTA for the 29-year-long MSU record and 68% of the variance in GTTA for the longer 50-year RATPAC record. Because El Niño−Southern Oscillation is known to exercise a particularly strong influence in the tropics, we also compared the SOI with tropical temperature anomalies between 20°S and 20°N. The results showed that SOI accounted for 81% of the variance in tropospheric temperature anomalies in the tropics. Overall the results suggest that the Southern Oscillation exercises a consistently dominant influence on mean global temperature, with a maximum effect in the tropics, except for periods when equatorial volcanism causes ad hoc cooling. That mean global tropospheric temperature has for the last 50 years fallen and risen in close accord with the SOI of 5–7 months earlier shows the potential of natural forcing mechanisms to account for most of the temperature variation.
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42. Nature not man responsible for recent global warming

Three Australasian researchers have shown that natural forces are the dominant influence on climate, in a study just published in the highly-regarded Journal of Geophysical Research. According to this study little or none of the late 20th century global warming and cooling can be attributed to human activity.

The research, by Chris de Freitas, a climate scientist at the University of Auckland in New Zealand, John McLean (Melbourne) and Bob Carter (James Cook University), finds that the El Niño-Southern Oscillation (ENSO) is a key indicator of global atmospheric temperatures seven months later. As an additional influence, intermittent volcanic activity injects cooling aerosols into the atmosphere and produces significant cooling.

"The surge in global temperatures since 1977 can be attributed to a 1976 climate shift in the Pacific Ocean that made warming El Niño conditions more likely than they were over the previous 30 years and cooling La Niña conditions less likely" says corresponding author de Freitas.

"We have shown that internal global climate-system variability accounts for at least 80% of the observed global climate variation over the past half-century. It may even be more if the period of influence of major volcanoes can be more clearly identified and the corresponding data excluded from the analysis.”

Climate researchers have long been aware that ENSO events influence global temperature, for example causing a high temperature spike in 1998 and a subsequent fall as conditions moved to La Niña. It is also well known that volcanic activity has a cooling influence, and as is well documented by the effects of the 1991 Mount Pinatubo volcanic eruption.

The new paper draws these two strands of climate control together and shows, by demonstrating a strong relationship between the Southern Oscillation and lower-atmospheric temperature, that ENSO has been a major temperature influence since continuous measurement of lower-atmospheric temperature first began in 1958.

According to the three researchers, ENSO-related warming during El Niño conditions is caused by a stronger Hadley Cell circulation moving warm tropical air into the mid-latitudes. During La Niña conditions the Pacific Ocean is cooler and the Walker circulation, west to east in the upper atmosphere along the equator, dominates.

"When climate models failed to retrospectively produce the temperatures since 1950 the modellers added some estimated influences of carbon dioxide to make up the shortfall," says McLean.

"The IPCC acknowledges in its 4th Assessment Report that ENSO conditions cannot be predicted more than about 12 months ahead, so the output of climate models that could not predict ENSO conditions were being compared to temperatures during a period that was dominated by those influences. It's no wonder that model outputs have been so inaccurate, and it is clear that future modelling must incorporate the ENSO effect if it is to be meaningful."

Bob Carter, one of four scientists who has recently questioned the justification for the proposed Australian emissions trading scheme, says that this paper has significant consequences for public climate policy.

"The close relationship between ENSO and global temperature, as described in the paper, leaves little room for any warming driven by human carbon dioxide emissions. The available data indicate that future global temperatures will continue to change primarily in response to ENSO cycling, volcanic activity and solar changes.”

“Our paper confirms what many scientists already know: which is that no scientific justification exists for emissions regulation, and that, irrespective of the severity of the cuts proposed, ETS will exert no measurable effect on future climate.”
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43. I do not recall calling you stupid or irrelevant. Your personal philosopy and ideology would certainly not qualify to categorize you as such. Your "broadly feasible" carbonic snow, however, is an indication of your competence in basic science. The fact that you even had to look up wiki before making that statement does nothing to let me believe that I can learn much from you. Nothing personal and nothing about your ideology either.
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44. #192 Ah Mr Yobbo, your eager acceptance of any piece of denialosphere rubbish tells us all we need to know about both your ideology and your scientific competence. Did the name of Bob Carter on the paper you quote not ring any warning bells? Did you not then look at who the other authors were? Did you not smell a rat, wonder if this might not be quite what it seems?

Check out the explanation of what Carter and friends have done here http://tamino.wordpress.com/2009/07/24/old-news/. It is roughly equivalent to discovering that a+b = b+a.

Why so much fervor in trying to trying to defend the indefensible Yobbo? Why so much effort to prefer rubbish over the simple truth that Blind Freddy could see?
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45. I understand that you are ideologically inclined to take Carter and al's paper as biblical truth.

So I won't put pearls of mathematical precision before you. For others who are interested in what's in the paper, there is a look at the methodology here:
http://tamino.wordpress.com/2009/07/24/old-news/#more-1737

Nothing especially new or interesting there.

Let's see, if this was happening the other way around, with an AGW confirming paper, and I were a skeptic, what would I do? Hmmm
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46. Phillipe - you insist on repeatedly going back to a single silly remark on Vostok made because I had my dander up from some gratuitous insult of a respected elder scientist. Proper respect is due. It was never intended to be serious - as I think I made very clear - and it never had any relevance to the discussion - as I also made clear.

Although it may indeed have some interesting implications for CO2 in ice cores.

'One of these processes is formation of gas hydrates or clathrates. In the highly compressed deep ice all air bubbles disappear, as under the influence of pressure the gases change into the solid clathrates, which are tiny crystals formed by interaction of gas with water molecules.'

And lest I be accused of taking this less than seriously - absolutely, science is play.
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47. Tamino

'Their only justification for the claim that ENSO has affected trends is to point out that “For the 30 years prior to the 1976 shift (i.e., 1946–1975) the SOI averaged +1.93 but in the 30 years after 1976 (i.e., 1977–2006) the average was -3.06, which represents a shift from a La Nina inclination to an El Nino inclination.” While a shift from la Nina to el Nino can cause a shift in temperature, there’s no evidence at all (nor do the authors provide any) that it can introduce a trend. This argument is nothing more than hand-waving, and is only apparently supported by the strong correlation they estimate using a methodology which eliminates all effect of trends.'

But we have already seen in Swanson and other papers I have referenced the modulation of ENSO
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48. from a warm mode in 1976 to 1998 and a cool mode since. A physical reality stemming from the the "Great Pacifc Climate Shift' of 1976/1977.

Tamino simply continues to ignore oceanographic reality.
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49. What does the peer reviewed science say? As opposed to a blog?

I give up.
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50. Less than seriously is accurate. For example, how did you scrutinize the Carter/Freitas piece? Less than seriously.

But how does that square with your claim of being concerned about the welfare of all your fellow humans, plunged into paleolithic chaos by restrictions on fossil fuel use? You seemed to take that very seriously when you made the argument.

I don't see anything new in your clathrate quote. Did you just discover this? At least now you realize the role of pressure.

As for the "elder" scientist involved, I'll post the link again for those readers who want to better appreciate what he puts out on the internet:

http://tamino.wordpress.com/2009/01/19/a-bag-of-hammers/

The mathematical analysis is indeed similar to the Carter/Freitas piece.

Same old same old.
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