A few weeks ago, we’ve argued in a paper in Nature that the Atlantic overturning circulation (sometimes popularly dubbed the Gulf Stream System) has weakened significantly since the late 19th Century, with most of the decline happening since the mid-20th Century. We have since received much praise for our study from colleagues around the world (thanks for that). But there were also some questions and criticisms in the media, so I’d like to present a forum here for discussing these questions and hope that others (particularly those with a different view) will weigh in in the comments section below.
Exhibit #1, and the prime observational finding, is a long-term cooling trend in the subpolar Atlantic – the only region in the world which has cooled while the rest of the planet has warmed. This ‘cold blob’ or ‘warming hole’ has been shown in IPCC reports since the 3rd assessment of 2001; it is shown in Fig. 1 in a version from the last (5th) IPCC report. In fact it is Figure 1 of the Summary for Policy Makers there – you can’t get more prominent than that.
Fig. 1 Observed temperature trends since the beginning of the 20th Century (Figure SPM1 of the last IPCC report).
I think there is a consensus that this is a real phenomenon and can’t be explained away as a data problem. According to NOAA, 2015 was the coldest year in this region since record-keeping began in 1880, while it was the hottest year globally. The key question thus is: what explains this cold blob?
In 2010, my colleagues Dima and Lohmann from Bremen were the first (as far as I know – let me know if you find an earlier source) to suggest, using sea surface temperature (SST) pattern analyses, that the cold blob is a tell-tale sign of a weakening AMOC. They wrote that
“the decreasing trend over the last seven decades is associated to the weakening of the conveyor, possibly in response to increased CO2 concentrations in the atmosphere”
(with ‘conveyor’ they refer to the AMOC). One of several arguments for this was the strong anti-correlation pattern between north and south Atlantic which they found using canonical correlation analysis and which is the well-known see-saw effect of AMOC changes.
I have since become convinced that Dima and Lohman were right. Let me list my main arguments upfront before discussing them further.
- The cold blob is a prediction come true. Climate models have long predicted that such a warming hole would appear in the subpolar Atlantic in response to global warming, due to an AMOC slowdown. This is seen e.g. in the IPCC model projections.
- There is no other convincing explanation for the cold blob. There is strong evidence that it is neither driven by internal atmospheric variability (such as the North Atlantic Oscillation, NAO) nor by aerosol forcing.
- A range of different data sets and analyses suggest a long-term AMOC slowdown.
- Claims that the slowdown is contradicted by current measurements generally turn out to be false. Such claims have presented apples-to-oranges comparisons. To the contrary, what we know from other sources about the AMOC evolution is largely consistent with the AMOC reconstruction we presented in Nature.
Let us look at these four points in turn.
A climate prediction come true
The following graph shows climate projections graph from the last IPCC report.
Fig. 2 Global warming from the late 20th Century to the late 21st Century (average over 32 models, RCP2.6 scenario) – Figure SPM8a of the IPCC AR5.
The IPCC writes that “hatching indicates regions where the multi-model mean is small compared to natural internal variability (i.e., less than one standard deviation of natural internal variability in 20-year means.)” The subpolar North Atlantic stands out as the only region lacking significant predicted warming even by the late 21st Century. The 4th IPCC report included a similar graph (Fig. TS28).
In our paper we have analysed the ‘historic’ runs of the CMIP5 climate models (i.e. those from preindustrial condition to the present) and found that the observed ‘cold blob’ in this region is consistent with what the models predicted, with the amount of cooling in the models depending mainly on how much the AMOC declines (see below). In the mean of the 13 models we examined (Fig. 5 of our paper), the downward trend of the AMOC index is -0.33 °C per century, in the observations we found -0.44 °C per century. (Our AMOC index simply consists of the difference between the surface temperatures of the subpolar Atlantic and the global ocean). The models on average thus predicted three quarters of the decline that the observational data indicate. (In fact most models cluster around the observed decline, but three models with almost zero AMOC decline cause the underestimation in the mean.)
Is there an alternative explanation?
If the ocean temperature in any region changes, this can only be due to a change in heat supply or loss. That can either be a change in heat flow via ocean currents or through the sea surface. Thus the subpolar Atlantic can either have cooled because the ocean currents are bringing less heat into this region, or alternatively because more heat is being lost to the atmosphere. So how do we know which of these two it is?
First, we can analyze the heat flux from ocean to atmosphere, which can be calculated with standard formula from the sea surface temperature and weather data. Halldór Björnsson of the Icelandic weather service has done this and presented the results at the Arctic Circle conference 2016 (they are not published yet). He showed that the short-term temperature fluctuations from year to year correlate with the heat exchange through the sea surface, but that this does not explain the longer-term development of the ‘cold blob’ over decades. His conclusion slide stated:
Surface heat fluxes did not cause the long term changes and are only implicated in the SST variations in the last two decades. Long term variations are likely to be oceanic transport but not due to local atmospheric forcing.
That’s exactly what one expects. Weather dominates the short-term fluctuations, but the ocean currents dominate the long-term development because of the longer response time scale and “memory” of the ocean.
Nevertheless some have suggested that the main mode of atmospheric variability in the north Atlantic, the North Atlantic Oscillation or NAO, might have caused the “cold blob”. In our paper we present a standard lagged correlation analysis of the NAO with the “cold blob” temperature (in form of our AMOC index). The result: there is indeed a significant correlation of the NAO with subpolar Atlantic surface temperatures. But on the longer time scales of interest to us (for 20-year smoothed data), changes in the sea surface temperature lead the NAO changes by three years. We conclude that changes in sea surface temperatures cause the changes in NAO and not vice versa. (And we’re certainly not the first to come to this conclusion.)
And a third point: in summer, the effect of heat flow through the sea surface should dominate, in winter the effect of ocean currents. That is because the well-mixed surface layer of the ocean is thin, so only the uppermost part of the ocean heat transport gets to affect the surface temperature. But the thin surface layer still feels the full brunt of atmospheric changes, and even stronger than in winter, because the thermal inertia of the thin summer surface layer is small. In our paper we analysed the seasonal cycle of the temperature changes in the subpolar Atlantic. The cooling in the “cold blob” is most pronounced in winter – both in the climate model (where we know it’s due to an AMOC slowdown) and in the observations. That yet again suggests the ‘cold blob’ is driven from the ocean and not the atmosphere.
There is another well-known mode of Atlantic temperature variability known as AMO, which correlates strongly with our AMOC index. Its established standard explanation in the scientific literature is… variations in the AMOC. (The NAO and AMO connections are discussed in more detail in the Extended Data section of our paper.)
There may be the possibility that some ocean heat transport change other than an AMOC change could be responsible for the ‘cold blob’ in the subpolar Atlantic, and I wouldn’t argue that we understand the ocean current changes in detail. But if you take a ‘big picture’ view, it is a fact that the AMOC is the dominant mechanism of heat transport into the high-latitude Atlantic, and the region that has cooled is exactly the region that cools in climate models when you slow down the AMOC. We have analysed the ensemble of CMIP5 “historic” model simulations for the past climate change from 1870 to 2016. For each of these model runs, we computed the AMOC slowdown over this time as diagnosed by our AMOC index (i.e. based on subpolar ocean surface temperatures) as well as the actual AMOC slowdown (which we know in the models, unlike in the real world.) The two correlate with a correlation coefficient R=0.95. Thus across the different models, differences in the amount of AMOC slowdown nearly completely explain the differences in subpolar Atlantic temperatures. If you doubt that what the temperatures in the Atlantic are telling us is a story of a slowing AMOC, you doubt not only that the high-resolution CM2.6 climate model is correct, but also the entire CMIP5 model ensemble.
A range of different data sets and analyses suggest a long-term AMOC slowdown
A number of different SST data sets and analyses support the idea of the AMOC slowdown. That is not just the existence of the subpolar cooling trend in the instrumental SST data. It is the cross-correlation with the South Atlantic performed by Dima and Lohmann. It is the fact that land-based proxy data for surface temperature suggest the cold blob is unprecedented for over a millennium. It is the exceptional SST warming off the North American coast, an expected dynamical effect of an AMOC slowdown, and strong warming off the west coast of southern Africa (see Fig. 1 in my previous post).
In addition we have the conclusion by Kanzow et al. from hydrographic sections that the AMOC has weakened by ~ 10% since the 1950s (see below). And the Nitrogen-15 data of Sherwood et al. indicating a water mass change that matches what is predicted by the CM2.6 model for an AMOC slowdown. And the subsurface Atlantic temperature proxy data published recently by Thornalley et al. Plus there is work suggesting a weakening open-ocean convection. And finally, our time evolution of the AMOC that we proposed based on our AMOC index, i.e. based on the temperatures in the cold blob region, for the past decades matches evidence from ocean reanalysis and the RAPID project. Some of these other data are shown together with our AMOC index below (for more discussion of this, see my previous post).
Fig. 3 Time evolution of the Atlantic overturning circulation reconstructed from different data types since 1700. The scales on the left and right indicate the units of the different data types. The lighter blue curve was shifted to the right by 12 years since Thornalley found the best correlation with temperature with this lag. Our index is the dark blue line starting in 1870. Graph: Levke Caesar.
Do measurements contradict our reconstruction?
Measuring the AMOC at a particular latitude in principle requires measuring a cross-section across the entire Atlantic, from surface to bottom. There are only two data sets that aspire to measure AMOC changes in this way. First, the RAPID project which has deployed 226 moored measuring instruments at 26.5 ° North for that purpose since 2004. It shows a downward trend since then, which closely matches what we find with our temperature-based AMOC index. Second is the work by Kanzow et al. (2010) using results of five research expeditions across the Atlantic between 1957 and 2004, correcting an earlier paper by Bryden et al. for seasonal effects and finding a roughly 10% decline over this period (in terms of the linear trend of these five data points).
Some other measurements cover parts of the overturning circulation, and generally for short periods only. For 1994-2013, Rossby et al. (2013) – at the Oleander line between 32° and 40° North – found a decrease in the upper 2000m transport of the Gulf Stream by 0.8 Sverdrup (a Sverdrup is a flow of a million cubic meters per second). It is important to realize that the AMOC is not the same as the Gulf Stream. The latter, as measured by Rossby, has a volume flow of ~90 Sverdrup, while the AMOC has a volume flow of only 15-20 Sverdrup. While the upper northward branch of the AMOC does flow via the Gulf Stream, it thus only contributes about one fifth to the Gulf Stream flow. Any change in Gulf Stream strength could thus be due to a change in the other 80% of Gulf Stream flow, which are wind-driven. The AMOC does however provide the major northward heat transport which affects the northern Atlantic climate, because its return flow is cold and deep. Most of the Gulf Stream flow, in contrast, returns toward the south near the sea surface at a similar temperature as it flowed north, thus leaving little heat behind in the north.
Likewise for 1994-2013, Roessler et al. (2015) found an increase of 1.6 Sv in the transport of the North Atlantic Current between 47° and 53° North. This is a current with a mean transport of ~27 Sverdrup, 60% of which is subtropical waters (i.e., stemming from the south via the Gulf Stream). For this period, our reconstruction yields an AMOC increase by 1.3 Sv.
For 1994-2009, using sea-level data, Willis et al. (2010) reconstructed an increase in the upper AMOC limb at 41°N by 2.8 Sv. For this period, our reconstruction yields an AMOC increase by 2.1 Sv.
Finally, the MOVE project measures the deep southward flow at 15° North. This is a flow of ~20 Sverdrup which can be considered the sum of the north Atlantic overturning circulation plus a small component of returning Antarctic Bottom Water (see Fig. 1 in Send et al. 2011). The following graph shows all these measurements together with our own AMOC index (Caesar et al 2018).
Fig 4. Our AMOC index in black, compared to five different measurement series related more or less strongly to the AMOC. The dashed and dotted linear trends of our index can be directly compared to the linear trends over corresponding data intervals. The solid black line shows our standard smoothed index as shown in our paper and in Fig. 3. Graph by Levke Caesar.
First of all, it is clear that these data contain a lot of year-to-year variability – which doesn’t correlate between the different measurements and for our purposes is just ‘noise’ and not a climate signal. That is why for our index we generally only consider the long-term (multidecadal) changes in SST to reflect changes in the AMOC. Thus, we need to look at the trend lines in Fig. 4.
Given that even these trends cover short periods of noisy data sets and thus are sensitive to the exact start and end years, and that lags between the various parts of the system may be expected, all these trends are surprisingly consistent! At least I don’t see any significant differences or inconsistencies between these various trends. Generally, the earlier trends in the left part of the graph are upward and the later trends going up to the present are downward. That is fully consistent with our reconstruction showing a low around 1990, an AMOC increase up the early 2000s and then a decline up to the present (compare Fig. 3).
Claims that any of these measurements are at odds with our index or even disprove the long-term AMOC decline are thus baseless (and thus rightly fit into Breitbart News where they were raised by the notorious James Delingpole).
One interesting question for further research is how the AMOC in the Atlantic is linked to the exchange with the Nordic Seas across a line between Greenland, Iceland and Scotland. In our 2015 paper we showed a model result suggesting an anti-correlation of these overflows with the AMOC, and our new paper suggests a similar thing: a warm anomaly off Norway coinciding with the cold anomaly in the subpolar Atlantic, both in the high-resolution CM2.6 model and the observations.
So, while there is obviously the need to understand the ocean circulation changes in the North Atlantic in more detail, I personally have no more doubts that the conspicuous ‘cold blob’ in the subpolar Atlantic is indeed due to a long-term decline of the northward heat transport by the AMOC. If you still have doubts, we’d love to hear your arguments!
Looking at ice melt today 4 June in Greenland there was a huge spike in melting- and many weather stations across Greenland had temperatures above freezing with warm temperatures to continue through the week
Are there any specific observations that should be made to discover information that would support, or contradict, the models?
I know the modeling budgets probably don’t include funding expeditions, but perhaps supporting specific instrumental observations?
Victor @96
Your rather rambling claim appears to be that atlantic ocean warming doesn’t correlate exactly with the decline of the amoc, so theres allegedly a ‘problem’. Using the graph in your link shows an atlantic ocean warming trend from 1900 until 2010 which is the end point on the graph, with a cooling trend from 1960 – 1975 embedded within this. The amoc slowed from about 1900 until presently, with most of the decline after 1975.
Remember the system has a lot of intertia, so the amoc could continue to slow for a decade or so even if temperatures dropped for a period. And remember the slowing of the amoc prior to 1975 was modest, most of the slowing happened after 1975 when warming commenced in earnest. And the amoc didn’t slow as a nice smooth line, it was pretty bumpy.
Oddly enough you are far more pedantic than MAR. For example, anyone with any scientific sense looks at various climate hockey sticks, and sees the urgent and obvious message. The fact that the trends are so bumpy over decadal levels of time is not surprising to me given the ammount of noise in the system.
It sounds characteristic of North Pole warming…
Victor the Troll @97,
Okay. My mistake. Your grabled comment @87 does not “insist” AMO = AMOC because you tell us @97 that your message “has nothing to do with the relation, if any, between AMO and AMOC” adding “I could[n’t] care less about the relation between AMO and AMOC. That was Rahmstorf’s claim, not mine.”. This leaves the question as to why you would introduce AMO into this discussion. This was one of the points I raised @85 after you evidently were incorrectly using AMO=AMOC @80.
☻ Why do you troll AMO into this discussion?
☻ In what way is AMO “inconsistent with Rahmstorf’s claims”? And perhaps you should be clear as to which “Rahmstorf’s claims” you are considering when you describe this mysterious ‘inconsistency’.
100 Kevin McKinney says: “Victor, #92– ‘No one says [early 20th-C CO2 increase] was unreal — only insignificant.’
Ah, but you invariably go on from asserting its “insignificance” to the assumptions that it therefore doesn’t matter and that it can safely be disregarded, which are pretty much the same the same things, IMHO, as saying that it is ‘unreal’ or ‘immaterial.’”
Kevin goes on and on, offering one nit-pick after another in a futile attempt to undermine the notion, endorsed by just about everyone who’s ever studied this matter in any depth, that CO2 levels could not have been a significant factor in the precipitous temperature rise from ca. 1910 through ca. 1940. And as we can see, he’s not the only one trying desperately to shore up a crumbling hypothesis.
I am more than willing to concede that, yes, CO2 MAY have played SOME role in that rising temperature trend, though I must insist that there is absolutely no evidence it played any role at all, ever. What really matters, however, from a scientific viewpoint, is the question of whether or not a correlation exists.
To this end, let’s take a close look at the following (very typical) graph: https://static.skepticalscience.com/images/co2_temp_1900_2008.gif
Now: beginning at the start of the 20th century and continuing until approximately 1979, does anyone here see anything remotely like a correlation between the red line (temperature) and the green one (CO2)? If so, I feel sorry for you. Maybe you should get your eyes (or your head) examined.
Then, out of the blue, beginning ca. 1979 and continuing to almost the beginning of the 20th century, what looks like a very strong correlation appears, followed, in the 21st century by a period in which CO2 levels continue to soar while temperatures rise only slightly.
So, over a period of roughly 116 years we see 96 years of no correlation and 20 years of strong correlation. Put them all together and what do we have? Well, the word “inconclusive” would, in my opinion, be a huge understatement. You can’t establish a correlation on the basis of 20 years out of 116, sorry. Not to mention that correlation in itself does not imply cause, a basic dictum of scientific method. Even if there were a correlation (which there definitely is not), there would still be no evidence, aside from some far from conclusive thought experiments based on questionable physics, that the sensitivity of climate to CO2 has any significant affect on temperature at all.
So, may I ask, what is the basis for Rahmstorf’s assumption that “the AMOC decline since the 1950s is very likely to be largely anthropogenic, given that it is a feature predicted by climate models in response to rising CO2 levels”?
RE: Hank Roberts says:
4 Jun 2018 at 2:33 PM
“. . . Someone is wrong on the Internet….”
No way! Are you suggesting I rely entirely on Twitter? Oh, wait a sec . . . I’ve got something coming in from TrumpTwitterhHouse . . .
Victor, #106–
Hallelujah! My desperate (and of course impeccably-intended) effort to save the world through carbon mitigation by convincing Victor of the errors of his ways succeeds!
But as the Victor giveth, so also the Victor taketh. Blessed be the name of the Victor!
Dude, that’s another one of your really, really silly moments.
Victor @106 asks us to trust our eyes as to whether we can ‘see’ a correlation between two lines – and asserts his sympathy if we can.
Well I accept my eyesight is a bit dodgy – so I prefer cold hard statistics.
Lets calculate the correlation coefficient between the COD data and global temperaturesa (I may not have the exact numbers from his example graph – I downloaded CO2 and temperature data off NASA).
For data from 1900 to 2014 – Correlation coefficient .93 using annual temperature data. But we know annual data are noisy (volcanos, El Ninos etc) so we can smooth the data I used a Loess smoother – that gives a .97 correlation coefficient. Both of these correlation coefficients are statistically significant using an alpha of 0.05.
But he invites us to look at the data 1900 to 1979 – for the raw data that drops us to .7 – not so good, but it’s still a correlation, and if we use the Loess smoother its .84. I checked my statistics for dummies – and a correlation coefficient of .7 is defined as a ‘strong’ correlation. (Both correlations are statistically significant).
Now Victor suggests we have correlated rise between 1979 and 2000 – a bit too short for really valid stats, but lets do the maths (my ‘eyes’ are still a bit tired). Hmm – actually while the data may ‘look’ more correlated the actual coefficient is only .88 for the unsmoothed yearly values- slightly more than the early period (though .98 with the Loess smoother!).
@106/109
Victor doesn’t do calculations to figure correlations. His eyes are ever so much better than calculated numbers.
V 106: So, over a period of roughly 116 years we see 96 years of no correlation and 20 years of strong correlation.
BPL: And that statement shows you still have no idea what “correlation” means, and have attached a purely private meaning to the word which you expect everyone else to accept. Surprise! It doesn’t work that way.
I, and others, have attempted to teach you about the correlation coefficient, but you resolutely refuse to learn. If there is such a thing as intellectual sin, you’re giving us a pretty clear example.
#109 Well well well. Looks like I’ve been bested. Guess Victor the Troll should just pack up his little carpet bag and get out of Dodge while he can. Are my cheeks red.
Why? Because our friend Astringent stuck in his thumb and pulled a plum out of his little black box: the number .7 — and what do you know, when he looked that up in his statistics for dummies book (no comment) it came up as a “strong” correlation. Can’t argue with that. You just can’t beat “the science” now can you? I already knew the answer to the meaning of life the universe and everything was 42, but this .7 came as a huge surprise.
Now really folks. Seriously! If the statistics tells us the two lines depicted on that graph from 1900 through 1979 are “strongly correlated” or correlated in any sense, then sorry but there is something wrong with the statistics, because MY eyes are perfectly fine and I can see very clearly that there is no meaningful relation whatsoever between them. Maybe the operant word here is “meaningful,” a concept unknown to statistics. The basis for all science is observation. The math is of course extremely important in helping us understand what we’ve observed, and relate it to other observations, but no amount of math is going to convince us that a raven is a writing desk, when we can easily see the difference with our own two eyes.
And yes, of course, there are instances where our eyes can deceive us. But this is not one of them, OK? It’s pretty straightforward, folks, and if you can’t “see” it then you have no right to dabble in scientific issues. It’s the difference between real science and scientism. Real science goes beyond simple answers pulled out of a hat to critically examine and evaluate the evidence. And it looks to me that this is where so many climate scientists have gone wrong, especially in the realm of statistics, where you can “prove” just about anything by adjusting your inputs and your methods until you get what you want.
#106, 108, 109–
Tamino synchronistically weighs in on a related pronunciamento by Roy Spencer:
https://tamino.wordpress.com/2018/06/02/sea-level-rise-denial-by-bullshit/
Hmm, where have I heard or read something like that before?
But there’s more, if you read the link.
Victor,
You’ve been here long enough to know about studies related to variation. Thus, to present an argument that ignores said studies is tossing an airball on purpose. Grow up.
V 112: If the statistics tells us the two lines depicted on that graph from 1900 through 1979 are “strongly correlated” or correlated in any sense, then sorry but there is something wrong with the statistics, because MY eyes are perfectly fine and I can see very clearly that there is no meaningful relation whatsoever between them.
BPL: A perfect example of militant ignorance.
So Victor the Troll wishes to convert this thread from a discussion of proxy data for identifying AMOC strength and instead wants us to discussn of his grand theory that AGW doesn’t exist. He even has the audacity to suggest that the OP’s author (one of our hosts) makes “dubious assumptions.”
Of course, today may not be the best for Victor’s silly theorising as yesterday saw the publication of a MLR analysis running back to 1890. We are probably familiar with Foster & Rahmstorf (2011) which used MLR to demonstrate the impact of Sol, Vol & ENSO on global temperature, straightening the wobbles and, goodness, disappearing the so-called ‘hiatus’. Braving the less-precise data of earlier years, Folland et al (2018) ‘Causes of irregularities in trends of global mean surface temperature since the late 19th century’ runs a similar analysis to demonstrate an attribution of all those wobbles that Victor’s grand theory relies and thus demonstrating the underlying anthropogenic forcings driving AGW. “Most of the warming since 1891 is found to be attributable to the net influence of increasing greenhouse gases and anthropogenic aerosols.”
Victor, one with no formal training in the hard sciences, not only knows climate science better than climate scientists, he knows statistics better than statisticians! Seriously folks!
@112
A stats 101 first quiz question (about 5th week into a first year course) for vic:
A .7 correlation means that approximately _____ of the variance in the two distributions is in common.
a. 10%
b. 25%
c. 50%
d. 66%
e. 75%
Of course you can use your own idiosyncratic definition of correlation to come to some different conclusion, but that is your problem, not the problem of anyone conversant with stats.
BTW, the correct answer here is true _deductively_ NOT inferentially through any scientific process of reasoning. That is, it is universally true regardless of what anyone ignorant of stats thinks. It is equally true on Earth, on Jupiter, or on a planet in the Andromeda galaxy.
111
Barton Paul Levenson says:
“V 106: So, over a period of roughly 116 years we see 96 years of no correlation and 20 years of strong correlation.
BPL: And that statement shows you still have no idea what “correlation” means, and have attached a purely private meaning to the word which you expect everyone else to accept. Surprise! It doesn’t work that way.
I, and others, have attempted to teach you about the correlation coefficient, but you resolutely refuse to learn. If there is such a thing as intellectual sin, you’re giving us a pretty clear example.”
Bart, you are confusing “correlation” with “statistical correlation,” which is not the same. The basic concept has been defined as a “mutual relation of two or more things, parts, etc.” (http://www.dictionary.com/browse/correlation) The correlation coefficient is an attempt to quantify that relation by applying a mathematical formula to the data. As with the notion of “trend” (as discussed earlier on this blog), a statistical analysis can be a valid tool IF a correlation already exists. But if there is no correlation, then the same method can be extremely deceptive. This is how (pseudo) scientists can deceive themselves. For example, two datasets produced purely from chance operations could, in principle, produce a positive correlation coefficient.
Another type of error can be seen in the following graphic, from a Wikipedia article on correlation and dependence: https://upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Anscombe%27s_quartet_3.svg/650px-Anscombe%27s_quartet_3.svg.png
As indicated in the caption, all four data sets have the same (statistically determined) correlation (.816). From the text:
“. . . the fourth example (bottom right) shows another example when one outlier is enough to produce a high correlation coefficient, even though the relationship between the two variables is not linear.
These examples indicate that the correlation coefficient, as a summary statistic, cannot replace visual examination of the data.”
General comment re. vic’s “correlation” pronouncements and Spencer’s first effects” argument as tackled by tamino:
Cancer cannot be detected reliably at the earliest stages even though we can find out later it really was there and developing. Does a person have a cancer problem when a tumor is only a few cells in volume? According to vic/Roy apparently not. One only has a cancer problem once the tumor is fully detected later. There was never any cancer problem prior to that, apparently.
That said, we are long beyond the initial detection stage for warming now. Further, as tamino points out, it is straightforward to look into the prior record to see where the problem (cancer/CO2) first started affecting things.
Victor, 112–
No, Victor, you can’t.
Mark I eyeball has its uses, but precise assessment of correlation is not one of them.
What you CAN do, and in point of fact ARE DOING, is telling yourself (and subsequently everyone else) that that there is no correlation.
But your methodology is grossly insufficient for making that determination. If it weren’t, no-one ever would have bothered with t-tests, and values of r, and auto-correlation and all the other complications used to try and avoid fooling one’s self.
Sadly, you don’t *want* to avoid fooling yourself. You like your reality arranged neatly the way you wish it to be–that is to say, with you the ultimate arbiter, and those refusing to worship your little idols of the mind as benighted fools, whom you can contemplate with satisfaction from the Parnassian heights of your imagined superiority.
Or at least, that is how it appears to this benighted fool.
@112 – Victor
I guess we all know that you don’t actually care in any way about the science, and this is just a little game of rhetoric. If scientists were solely taking lines on graphs and saying – “ohh look – those lines are correlated” [btw correlation is defined as a mutual relationship or connection between two or more things], then they ought to be criticised. But they aren’t and don’t. They look at the physics and chemistry of the atmosphere. They look for evidence of change in driving variables (energy from the sun, landuse, CO2, Methane etc). They construct models using the physics and chemistry and those models predict certain responses in the atmosphere.The effectiveness of these models has been repeatedly demonstrated, and the paper we are discussing shows that not only are their temperature predictions correct, but they can resolve some relatively localised and possibly counter-intuitive, variations, like AMOC weakening.
And I really do recommend that you read an elementary statistical text book. You will find there are whole chapters on ‘meaningful’ , although the term used tends to be ‘significance’. In the case of 1900-1979 CO2/Temperature correlation, the maths tells us that there is a (considerably) less than 1 in 20 chance that the relationship between the two variables is down to chance. If we had no plausible physical mechanism to link the two variables, that correlation could still be challenged, but we do have a physical mechanism, which has been explained to you more than once.
BPL: Bet his eyes “see” a “pause” too. Equally bad math there too.
#121 & #122 Once again I see a tendency to confuse correlation with statistical correlation. If your notion of a correlation is based solely on the result of a mathematical procedure, then a correlation (or lack of same) produced by any other means (such as direct observation) is going to be suspect. To me this is the difference between science (based on observation and critical analysis) and scientism (based on a blind faith in formulae).
Our posts overlapped so I’m assuming neither of you had a chance to absorb the lesson provided in the Wikipedia article I referenced: https://en.wikipedia.org/wiki/Correlation_and_dependence If you look under the heading “Correlation and linearity” you will find a display with “Four sets of data with the same correlation of 0.816.” There is obviously a problem with the dataset on the lower right, where very clearly no real correlation exists, yet the “correlation coefficient” has been calculated as 0.816. As the author explains, “one outlier is enough to produce a high correlation coefficient, even though the relationship between the two variables is not linear.” He (she?) then adds: “These examples indicate that the correlation coefficient, as a summary statistic, cannot replace visual examination of the data.”
Considerable confusion can be eliminated (I would hope) if we drop the term “correlation” altogether, as so many here find it so difficult to understand in non-statistical terms. So, returning to the aforementioned graph depicting both CO2 levels and temperature, let’s just ask ourselves if we can see a clear relationship between the two lines. Forget about whether or not they are “correlated” in any technical sense — just examine the lines directly and ask yourself if it looks like the steadily rising line representing CO2 is related in any way to the continually shifting line representing global temperatures. And if not, then we have good reason to believe that the correlation coefficient produced by our friend Astringent is nothing more than an artefact. As in “the correlation coefficient, as a summary statistic, cannot replace visual examination of the data.”
[Response: Let’s close this discussion, which is leading nowhere and is off topic. We covered the link between CO2 and temperature years ago here: https://www.realclimate.org/index.php/archives/2014/12/the-most-popular-deceptive-climate-graph/ ]
Victor entertains resp occupied the complete discussion about this article, while Stefan Rahmstorf is long gone :’D Keep on entertaining, doesn’t matter anymore anyway. I keep on being amused :)
So Victor the Troll, you link to a graphic of Anscombe’s Quartet @119. If this is how you wish to play your little game of non-AMOC blather, where is your graph of CO2 v temp? This is important, so where is it? You know, the graph that Anscombe says should be an initial step in any statistical (or other) analysis (and Anscombe is not alone with such a message).
In past years, your ineptitude has led to others providing such a graph for you but like-as-not you have blanked it all from your memory because it rather stuffs your grand theory, diminishing the wobbles your beady eye cannot resist staring at to the point of their irrelevance.
Read Victors recent comments in the borehole. This character clearly has a huge anti environmental bias, and this may be a large part of his motivation. He will deny it, but its plain in his recent post there. This explains his relentless deliberate stupidity.
Please consider creating focused threads in which scientists can have discussions, and the rest of us can watch (and make our comments in the open thread, to avoid overlarding the scientific conversation by accumulation of beliefs and bogosity
It seems to me that the AMOC Can be thought of asa kind of thermal pump driven by the difference in thermal potential between the polar regions and the warmer mid regions. When the thermal difference between the two is large this would Inssume tend to drive the pump harder and so the AMOC would be stronger. Reduce the thermal difference and you have less potential to drive the pump and the AMOC weakens. With global warming pushing polar and northern temperatures higher faster this reduces the thermal potential between northern and mid latitudes and the pump weakens. Chuck in ever increasing flows of cold freshwater to that from massive Greenland melts and it seems to me you must have a great recipe for creating a cool blob just exactly where we see it.
Is that a reasonable understanding of what is going on?
I haven’t read all the responses yet so I hope I’m not repeating anything earlier.
Victor claims that since a correlation based solely on math but without a mechanism or support in the physical world is flawed, then scientists by definition have no mechanism or physical data. He points to a Wiki page’s fourth example with nary an attempt to show that that example even slightly resembles the data he’s deriding. If his point were valid he’d explain why the first graph didn’t apply.
Dude, YOU’RE the one with no data, link, or mechanism. You’re the one who is insisting that having a mechanism is irrelevant (for you) and that the mounds of studies scientists have dropped on your desk are irrelevant because in some distant galaxy those studies don’t locally exist.
Pot calling the snowflake black
Quit tossing airballs on purpose. I can’t believe you’re as dumb as donald drumpf. (But you might be as dishonest)
[Response: Let’s close this discussion, which is leading nowhere and is off topic. We covered the link between CO2 and temperature years ago here: https://www.realclimate.org/index.php/archives/2014/12/the-most-popular-deceptive-climate-graph/ ]
Yes, the discussion appears to have moved a bit off topic, but the correlation issue came up as a direct result of our discussion of Rahmstorf’s paper and is indeed relevant. My assertion that CO2 emissions had only a minor influence on temperatures from the early 20th century through ca. 1940, based on what appears to be a clear consensus, was challenged by someone who argued otherwise and offered evidence that the influence in question was indeed significant. Rather than continuing to quibble over different interpretations of the evidence, I decided that the most effective way to settle the matter was to see if a correlation could be found.
Here is my reasoning. If CO2 emissions were indeed insignificant, then my assertion regarding the period 1900 – 1940 was correct — and since the years from 1940 through 1979 did not display any significant warming (also based on a general consensus) then Rahnstorf’s assumption that the AMOC slowdown was based on some “long term” warming due to CO2 must be wrong.
Now: If CO2 emissions were in fact significant after all, then we have to wonder why we see no meaningful correlation between CO2 levels and temperature during the 80 year period from 1900 through 1979. In other words, if no meaningful correlation can be found in all that time then, once again, it becomes very difficult to see any evidentiary basis for Rahmstorf’s assumption.
“Astringent” helpfully provided a “correlation coefficient” of .7, which seems to have settled the matter for others posting here. But as I demonstrated, this result could easily have been an artefact of the methodology he used. As noted by the statistician who wrote the article I cited, “the correlation coefficient, as a summary statistic, cannot replace visual examination of the data.” And as anyone can plainly see, a visual examination reveals NO correlation. This is where things stand at this point and additional discussion and debate is certainly in order.
The blog post you referenced has little bearing on the current discussion. The first graph you displayed begins in 1979, whereas the period in question here is 1900-1979. Moreover, solar activity plays no part in my argument. The second graph begins a bit earlier, in 1950, where a portion of the uncorrelated evidence can be clearly seen until 1979 is reached. The attempt to interpret this as evidence of a correlation is therefor misleading, since the only time the two lines “agree very well” is from 1979 through 1998.
Oh and by the way, the author of this post (stefan) seems to have no problem basing a claim of correlation on purely visual evidence.
I see Judy Curry is examining her own N Atlantic SST pattern which she has named the “Atlantic ARC Pattern.”
The northern part of the arc that makes up this pattern (tenth gaphic in Curry post linked above) is the “cold blob” discussed in the OP, creating an arc by cool anomalies extending down the African coast and expanding across the ocean in the northern tropics.
The OP here sets out reason to see the “cold blob” as a proxy for AMOC strength and wobbles in the AMOC strength (as opposed to longer-term trends) as appearing as the wobbly AMO signal.
Yet Curry appears to be suggesting that her “Atlantic ARC Pattern” can be used to predict impending AMO wobbles, as in her eleventh graphic she appears to be showing the very recent appearance of the “Atlantic ARC Pattern” as a possible less-than-momentary event and thus possibly presaging a new dip beginning in the AMO. Of course, as an inveterate wobblologist, Curry has been predicting that impending dip in the AMO as “in the ~mid 2020’s” as part of her advocacy of Wyatt’s Unified Wave Theory although ever happy to mention she is “prepared to be surprised.”
This from Victor caught my eye in the comments above –
” Now really folks. Seriously! If the statistics tells us the two lines depicted on that graph from 1900 through 1979 are “strongly correlated” or correlated in any sense, then sorry but there is something wrong with the statistics, because MY eyes are perfectly fine and I can see very clearly that there is no meaningful relation whatsoever between them. Maybe the operant word here is “meaningful,” a concept unknown to statistics. The basis for all science is observation. The math is of course extremely important in helping us understand what we’ve observed, and relate it to other observations, but no amount of math is going to convince us that a raven is a writing desk, when we can easily see the difference with our own two eyes.”
If I see a strong statistical correlation between the number of icebergs and the numbers of elephants killed by poachers I would have reason to say that the statistic was simply a non meaningful correlation. I have no mechanism where I can causally link one to the other. If on the other hand I see a strong correlation between say the volume of water falling in a mountain range with the volume of water running from rivers in those countries then I take this to be an extremely meaningful correlation because I have mechanisms of all sorts that form a strong explanation as to why this correlation is pointing to a causally connected chain of events.
More importantly good science works in two directions at the same time. It moves from observations to models but it also moves from models to observations of things suggested by those models. I see this going on across an enormous range of evidence sources and it’s all pointing in the same direction. Anthropogenic Global Warming seems (sadly) to be supported by tremendous consilient weight and range of evidence. Only fools and those with an agenda now deny it.
Ultimately people like Victor are pissing in the wind as they try to misrepresent science. Why? Because reality is overtaking them.
http://tylervigen.com/spurious-correlations
OK, Victor, let’s try a little test. What does your eye tell you about the correlation or lack thereof in the linked ‘mystery quantities’?
http://i1108.photobucket.com/albums/h402/brassdoc/Mystery%20quantities.png
V 131: we have to wonder why we see no meaningful correlation between CO2 levels and temperature during the 80 year period from 1900 through 1979.
BPL: No matter how many times you say this, it still won’t be true.
Al Bundy @130, Victor is indeed throwing curved air balls, with maybe some deliberate ignorance and some real ignorance mixed together in a horrible mash.
Read Victors recent comments in the borehole. This guy is driven by an anti environmental agenda of some sort. He will deny it, but its plain to see.
Victor thinks anything that’s not an exact correlation, as in two identical and perfectly synchronised wavy lines, is no correlation at all. In other words he is just really bad at science. Must have skipped too many classes.
I was recently directed to the following RC blog post (https://www.realclimate.org/index.php/archives/2014/12/the-most-popular-deceptive-climate-graph/), in which Stefan very convincingly debunks a graph purporting to support the notion that global temperatures over the last 60 years or so were largely influenced by fluctuations in solar activity. If you scroll down far enough you’ll find a second graph, comparing CO2, temperature and solar activity. In this graph, according to Stefan, “The trends in the CO2 and temperature anomaly curves agree very well with each other.” (Actually, this is somewhat misleading, as, imo, the agreement begins only after 1975 — but we can let that pass for now.)
Note that Stefan saw no need to produce a “correlation coefficient” or perform any other statistical procedure to make this point, relying solely on our ability to interpret the data visually. I haven’t had time to read through all the comments, but I’m wondering whether anyone took the trouble to check Stefan’s claim by producing a correlation coefficient. Looks to me as though everyone was perfectly willing to accept his assessment based purely on an “eyeball” based view of the graph.
116 MA Rodger: “Braving the less-precise data of earlier years, Folland et al (2018) ‘Causes of irregularities in trends of global mean surface temperature since the late 19th century’ [http://advances.sciencemag.org/content/4/6/eaao5297.full] runs a similar analysis to demonstrate an attribution of all those wobbles that Victor’s grand theory relies and thus demonstrating the underlying anthropogenic forcings driving AGW.”
Thanks, MA, for the link to this very interesting (but seriously misguided) paper.
My response:
OK first of all: this paper is totally irrelevant as far as the current topic (Rahmstorf’s AMOC theory) is concerned. My critique of Rahmstorf is based on his assumption that CO2 driven temperature rise was responsible for the AMOC slowdown he sees, despite the fact that there was NO such temperature rise during the period he’s identified as initiating the process (mid-century) and, moreover, there is no evidence that CO2 could have been a major factor in the earlier rise, from 1910 – 1940. The reason why temperatures failed to rise after 1940 has no bearing on the issue at hand. Absence of the rising temperature trend assumed by Rahmstorf remains absence of a rising temperature trend, regardless of whatever it is that’s responsible for that absence. So all the various forcings brought into play by Folland have no bearing on the issue at hand.
Now secondly, as I’ve reminded you countless times (but you refuse to listen, naturally) there is a reason why Occam’s Razor has been such an important guide in assessing scientific evidence from the Middle Ages to the present. You can get any result you desire by introducing a host of complicating factors as a hedge against falsification. This has already been done countless times in a long list of studies, mostly directed at the “hiatus,” but nevertheless using equally questionable methods. The only difference now is that Folland et al. have made things even more complicated by attempting to consolidate an even greater number of factors to “explain” away all the very clear bodies of evidence, from the late 19th century to the present, that tell us the prevailing theory (AGW) must be wrong.
It’s almost pathetically obvious that the object all along was to carefully pick and choose any and all “forcings” that would, when considered in toto, elicit the desired, pre-ordained, result. At every step of the way, decisions are made to include whatever will work to that end and exclude whatever won’t. I’m not suggesting that any dishonesty was involved — I have no reason to believe these people were not sincere. But confirmation bias is an ever present danger in all scientific research and self criticism in that regard is by no means an easy task.
From https://en.wikipedia.org/wiki/Occam%27s_razor
“. . . consider that for each accepted explanation of a phenomenon, there is always an infinite number of possible, more complex, and ultimately incorrect, alternatives. This is so because one can always burden a failing explanation with an ad hoc hypothesis. . .
Put another way, any new, and even more complex, theory can still possibly be true. For example, if an individual makes supernatural claims that leprechauns were responsible for breaking a vase, the simpler explanation would be that he is mistaken, but ongoing ad hoc justifications (e.g. “… and that’s not me on the film; they tampered with that, too”) successfully prevent outright falsification. This endless supply of elaborate competing explanations, called saving hypotheses, cannot be ruled out—except by using Occam’s razor.”
@134
If I read the graphic titles in the link correctly, it appears that the author is confusing r with r^2 re. percentage of common variance or just doesn’t know the definitions.
Delete or borehole if considered too off topic…
All victor needs to know (and clearly doesn’t): A small, undergrad level R script showing how (truly) uncorrelated data becomes (highly) correlated if a trend is added. This is not “cheating”. It is the very basis of the term.
set.seed(12345)
# Function to create an n by 2 matrix with a specified column correlation
corr_data <- function (n, correlation) {
x <- rnorm(n)
y <- rnorm(n)
z <- correlation * scale(x)[,1] + sqrt(1 – correlation^2) *
scale(resid(lm(y ~ x)))[,1]
xresult <- scale(x)[,1]
yresult <- z
return(cbind(xresult,yresult))
}
# Create a matrix, then find r and plot
r <- corr_data(n = 50, correlation = 0)
cor(r)
matplot(r, type='l', lty='solid')
# Create function to add the same specified trend to each column
f <- function(x,trend) {
idx <- 1:length(x)*trend
x <- x+idx
}
# Create a matrix adding column trends (here defined as .1/step), then find r and plot
trendcor <- apply(r,2,f,trend=.1)
cor(trendcor)
matplot(trendcor, type='l', lty='solid')
The original .00 correlation becomes a .69 correlation by virtue of both series following the same .1/step trend regardless of the fact that year-by-year correlations are constructed to be zero. This is not cheating. The correlation is "seeing" that the two series trend together now. And they really do.
” Let’s close this discussion, which is leading nowhere and is off topic.”
This is a simple enough request but apparently not for Victor the Troll @131 who resorts to the award-winning Vikki Pollard repost – “Yeah but no but…” Of course Victor is an award winner himself having been awarded membership of Tamino’s “Proud to be Stupid Club”. And“Yeah-but-No-but” Vic (or Docgee as he were masquerading-as when he gained that award), may remember that was also the point when he was provided with a CO2-v-SAT graph (usually two clicks to ‘download your attachment’), the one he should be waving to demonstrate any lack of correlation, that assuming it supports his bold assertion that there is a ‘lack of correlation’
@142
The blog appears to be adding invisible junk of some sort in line 5. To make the script work, on my machine anyway, you need to delete “sqrt(1 – correlation^2)” within line 5 and then type the very same text “sqrt(1 – correlation^2)” in by hand (presumably without any junk). Then the script works fine for me at least.
Alternatively, get the working script here: http://www.nfgarland.ca/CorrTrend.r
127 nigelj says: “Read Victors recent comments in the borehole.”
Yes, by all means read it. It’s not intended to be taken literally, of course, though most posting here are so eager to take offense — and so literal minded — they probably won’t notice. Basically what it is is a reductio absurdum argument, exposing the insanity of the notion now being spread just about everywhere that we HAVE to do something drastic NOW or civilization as we know it is doomed. I modeled it on Swift’s “Modest Proposal,” another pointed response to the insanity of his own day.
If anyone here has a better proposal to satisfy the demand for radical changes to world civilization that we need to implement RIGHT NOW, in order to forestall total disaster, by all means post it.
Hank Roberts:
John Nielsen-Gammon, Bart Verheegen and a couple of other guys tried that a while back. Their website sure looks good, but there doesn’t seem to be much current activity on it. Nice idea, though.
Victor @140
“My critique of Rahmstorf is based on his assumption that CO2 driven temperature rise was responsible for the AMOC slowdown he sees, despite the fact that there was NO such temperature rise during the period he’s identified as initiating the process (mid-century) and, moreover, there is no evidence that CO2 could have been a major factor in the earlier rise, from 1910 – 1940.”
The initiating process was not mid century. The article discusses slowdown of the amoc from approximately 1900 onwards, and this is apparent in the graph. Most of the slowdown was after 1975 as pointed out to Victor by the author. So yet again Victor is badly mistaken.
Look at the full period of the amoc slowdown under consideration, from 1900 – 2018. CO2 emissions and global warming started in earnest over approximately this same period. These are the famous hockey sticks comparing warming and emissions to previous centuries.
CO2 emissions were still a factor early last century even if they were not a large factor.
I see an obvious correlation by eye between all three quantities over this period of 1900 – 2018, and a statistical test finds correlations between all three variables. The correlation is not very high, because of the flat period of temperatures mid century, but its very significant. Correlations exist on a scale, something beyond Victors apparent knowledge.
The amoc has some intertia and could have continued to slow even during mid century flat temperatures.
Of course the correlation is stronger from 1975 onwards as agw global warming became more significant and the amoc slowed down more dramatically and CO2 emissions were greater.
Aerosols in the middle of last century are not as Victor claims some “complicating factor”. They HAPPENED, and so have to be evaluated scientifically. We have extremely good evidence aerosols like this cause a temporary cooling effect. Victors commentary is worse than useless.
Victor @139
So what? Correlation CAN be obvious. But that does not mean ALL correlation is obvious. Victor’s point is moronic. Not a surprise.
Victor’s argument appears to be that correlation means tracing all the jags up and down, and if you can’t do that with a single factor, adding in other factors that DO do that is the same as adding UNNECESSARY complexity. He doesn’t get that Occam’s Razor means “Choose the simplest hypothesis that covers all the facts,” NOT “Choose the simplest hypothesis.” As with “correlation,” his understanding of “Occam’s Razor” is an idiosyncratic private definition which he criticizes everyone else for not following.
Victor @140
Victor must believe that climate is simple because using complexity to explain it is in his simple mind a violation of Occam’s Razor. But then when presented with a simple explanation as to how science actually works, Victor invokes *climate is complicated*…can’t have it both ways.
Of course, when it comes to Occam’s Razor, Victor has not provided the *alternative simpler* theory. A simpler theory that explains why nights are warming faster than days, winters faster than summers, and the arctic faster than the rest of the planet. Nor has he explained why CO2 is not doing what physics says it will do. To him these questions are not science.
With Victor it is lather, rinse, repeat ad nauseam. It is tiresome and a waste of time.