![graphic_esd_cover_homepage[1]](http://wattsupwiththat.files.wordpress.com/2013/01/graphic_esd_cover_homepage1.jpg?w=114&resize=114%2C150)
From the journal Earth System Dynamics billed as “An Interactive Open Access Journal of the European Geosciences Union” comes this paper which suggests that the posited AGW forcing effects simply isn’t statistically significant in the observations, but other natural forcings are.
“…We show that although these anthropogenic forcings share a common stochastic trend, this trend is empirically independent of the stochastic trend in temperature and solar irradiance. Therefore, greenhouse gas forcing, aerosols, solar irradiance and global temperature are not polynomially cointegrated. This implies that recent global warming is not statistically significantly related to anthropogenic forcing. On the other hand, we find that greenhouse gas forcing might have had a temporary effect on global temperature.”
This is a most interesting paper, and potentially a bombshell, because they have taken virtually all of the significant observational datasets (including GISS and BEST) along with solar irradiance from Lean and Rind, and CO2, CH4, N2O, aerosols, and even water vapor data and put them all to statistical tests (including Lucia’s favorite, the unit root test) against forcing equations. Amazingly, it seems that they have almost entirely ruled out anthropogenic forcing in the observational data, but allowing for the possibility they could be wrong, say:
“…our rejection of AGW is not absolute; it might be a false positive, and we cannot rule out the possibility that recent global warming has an anthropogenic footprint. However, this possibility is very small, and is not statistically significant at conventional levels.”
I expect folks like Tamino (aka Grant Foster) and other hotheaded statistics wonks will begin an attack on why their premise and tests are no good, but at the same time I look for other less biased stats folks to weigh in and see how well it holds up. My sense of this is that the authors of Beenstock et al have done a pretty good job of ruling out ways they may have fooled themselves. My thanks to Andre Bijkerk and Joanna Ballard for bringing this paper to my attention on Facebook.
The abstract and excerpts from the paper, along with link to the full PDF follows.
Polynomial cointegration tests of anthropogenic impact on global warming
M. Beenstock1, Y. Reingewertz1, and N. Paldor2
1Department of Economics, the Hebrew University of Jerusalem, Mount Scopus Campus, Jerusalem, Israel
2Fredy and Nadine Institute of Earth Sciences, the Hebrew University of Jerusalem, Edmond J. Safra campus, Givat Ram, Jerusalem, Israel
Abstract.
We use statistical methods for nonstationary time series to test the anthropogenic interpretation of global warming (AGW), according to which an increase in atmospheric greenhouse gas concentrations raised global temperature in the 20th century. Specifically, the methodology of polynomial cointegration is used to test AGW since during the observation period (1880–2007) global temperature and solar irradiance are stationary in 1st differences whereas greenhouse gases and aerosol forcings are stationary in 2nd differences. We show that although these anthropogenic forcings share a common stochastic trend, this trend is empirically independent of the stochastic trend in temperature and solar irradiance. Therefore, greenhouse gas forcing, aerosols, solar irradiance and global temperature are not polynomially cointegrated. This implies that recent global warming is not statistically significantly related to anthropogenic forcing. On the other hand, we find that greenhouse gas forcing might have had a temporary effect on global temperature.
Introduction
Considering the complexity and variety of the processes that affect Earth’s climate, it is not surprising that a completely satisfactory and accepted account of all the changes that oc- curred in the last century (e.g. temperature changes in the vast area of the Tropics, the balance of CO2 input into the atmosphere, changes in aerosol concentration and size and changes in solar radiation) has yet to be reached (IPCC, AR4, 2007). Of particular interest to the present study are those processes involved in the greenhouse effect, whereby some of the longwave radiation emitted by Earth is re-absorbed by some of the molecules that make up the atmosphere, such as (in decreasing order of importance): water vapor, car- bon dioxide, methane and nitrous oxide (IPCC, 2007). Even though the most important greenhouse gas is water vapor, the dynamics of its flux in and out of the atmosphere by evaporation, condensation and subsequent precipitation are not understood well enough to be explicitly and exactly quantified. While much of the scientific research into the causes of global warming has been carried out using calibrated gen- eral circulation models (GCMs), since 1997 a new branch of scientific inquiry has developed in which observations of climate change are tested statistically by the method of cointegration (Kaufmann and Stern, 1997, 2002; Stern and Kauf- mann, 1999, 2000; Kaufmann et al., 2006a,b; Liu and Ro- driguez, 2005; Mills, 2009). The method of cointegration, developed in the closing decades of the 20th century, is intended to test for the spurious regression phenomena in non-stationary time series (Phillips, 1986; Engle and Granger, 1987). Non-stationarity arises when the sample moments of a time series (mean, variance, covariance) depend on time. Regression relationships are spurious1 when unrelated non- stationary time series appear to be significantly correlated be- cause they happen to have time trends.
The method of cointegration has been successful in detecting spurious relationships in economic time series data.
Indeed, cointegration has become the standard econometric tool for testing hypotheses with nonstationary data (Maddala, 2001; Greene, 2012). As noted, climatologists too have used cointegration to analyse nonstationary climate data (Kauf- mann and Stern, 1997). Cointegration theory is based on the simple notion that time series might be highly correlated even though there is no causal relation between them. For the relation to be genuine, the residuals from a regression between these time series must be stationary, in which case the time series are “cointegrated”. Since stationary residuals mean- revert to zero, there must be a genuine long-term relationship between the series, which move together over time because they share a common trend. If on the other hand, the resid- uals are nonstationary, the residuals do not mean-revert to zero, the time series do not share a common trend, and the relationship between them is spurious because the time series are not cointegrated. Indeed, the R2 from a regression between nonstationary time series may be as high as 0.99, yet the relation may nonetheless be spurious.
The method of cointegration originally developed by En- gle and Granger (1987) assumes that the nonstationary data are stationary in changes, or first-differences. For example, temperature might be increasing over time, and is there- fore nonstationary, but the change in temperature is station- ary. In the 1990s cointegration theory was extended to the case in which some of the variables have to be differenced twice (i.e. the time series of the change in the change) be- fore they become stationary. This extension is commonly known as polynomial cointegration. Previous analyses of the non-stationarity of climatic time series (e.g. Kaufmann and Stern, 2002; Kaufmann et al., 2006a; Stern and Kaufmann, 1999) have demonstrated that global temperature and solar irradiance are stationary in first differences, whereas green- house gases (GHG, hereafter) are stationary in second differ- ences. In the present study we apply the method of polyno- mial cointegration to test the hypothesis that global warming since 1850 was caused by various anthropogenic phenom- ena. Our results show that GHG forcings and other anthropogenic phenomena do not polynomially cointegrate with global temperature and solar irradiance. Therefore, despite the high correlation between anthropogenic forcings, solar irradiance and global temperature, AGW is not statistically significant. The perceived statistical relation between tem- perature and anthropogenic forcings is therefore a spurious regression phenomenon.
Data and methods
We use annual data (1850–2007) on greenhouse gas (CO2, CH4 and N2O) concentrations and forcings, as well as on forcings for aerosols (black carbon, reflective tropospheric aerosols). We also use annual data (1880–2007) on solar irradiance, water vapor (1880–2003) and global mean tem- perature (sea and land combined 1880–2007). These widely used secondary data are obtained from NASA-GISS (Hansen et al., 1999, 2001). Details of these data may be found in the Data Appendix.
We carry out robustness checks using new reconstructions for solar irradiance from Lean and Rind (2009), for globally averaged temperature from Mann et al. (2008) and for global land surface temperature (1850–2007) from the Berkeley Earth Surface Temperature Study.
Key time series are shown in Fig. 1 where panels a and b show the radiative forcings for three major GHGs, while panel c shows solar irradiance and global temperature. All these variables display positive time trends. However, the time trends in panels a and b appear more nonlinear than their counterparts in panel c. Indeed, statistical tests reported be- low reveal that the trends in panel c are linear, whereas the trends in panels a and b are quadratic. The trend in solar irradiance weakened since 1970, while the trend in temperature weakened temporarily in the 1950s and 1960s.
The statistical analysis of nonstationary time series, such as those in Fig. 1, has two natural stages. The first consists of unit root tests in which the data are classified by their order and type of nonstationarity. If the data are nonstationary, sample moments such as means, variances and co- variances depend upon when the data are sampled, in which event least squares and maximum likelihood estimates of parameters may be spurious. In the second stage, these nonstationary data are used to test hypotheses using the method of cointegration, which is designed to distinguish between genuine and spurious relationships between time series. Since these methods may be unfamiliar to readers of Earth System Dynamics, we provide an overview of key concepts and tests.
Fig. 1. Time series of the changes that occurred in several variables that affect or represent climate changes during the 20th century. a) Radiative forcings (rf, in units of W m−2) during 1880 to 2007 of CH4 (methane) and CO2 (carbon dioxide); (b) same period as in panel a but for Nitrous-Oxide (N2O); (c) solar irradiance (left ordinate, units of W m−2) and annual global temperature (right ordinate, units of ◦C) during 1880–2003.
[…]
3 Results
3.1 Time series properties of the data
Informal inspection of Fig. 1 suggests that the time series properties of greenhouse gas forcings (panels a and b) are visibly different to those for temperature and solar irradiance (panel c). In panels a and b there is evidence of acceleration, whereas in panel c the two time series appear more stable. In Fig. 2 we plot rfCO2 in first differences, which confirms by eye that rfCO2 is not I (1), particularly since 1940. Similar figures are available for other greenhouse gas forcings. In this section we establish the important result that whereas the first differences of temperature and solar irradiance are trend free, the first differences of the greenhouse gas forcings are not. This is consistent with our central claim that anthropogenic forcings are I (2), whereas temperature and solar irradiance are I (1).
Fig. 2. Time series of the first differences of rfCO2.
What we see informally is born out by the formal statistical tests for the variables in Table 1.
Although the KPSS and DF-type statistics (ADF, PP and DF-GLS) test different null hypotheses, we successively increase d until they concur. If they concur when d = 1, we classify the variable as I (1), or difference stationary. For the anthropogenic variables concurrence occurs when d = 2. Since the DF-type tests and the KPSS tests reject that these variables are I (1) but do not reject that they are I (2), there is no dilemma here. Matters might have been different if according to the DF-type tests these anthropogenic variables are I (1) but according to KPSS they are I (2).
The required number of augmentations for ADF is moot. The frequently used Schwert criterion uses a standard formula based solely on the number of observations, which is inefficient because it may waste degrees of freedom. As mentioned, we prefer instead to augment the ADF test until its residuals become serially independent according to a la- grange multiplier (LM) test. In most cases 4 augmentations are needed, however, in the cases of rfCO2, rfN2O and stratospheric H2O 8 augmentations are needed. In any case, the classification is robust with respect to augmentations in the range of 2–10. Therefore, we do not think that the number of augmentations affects our classifications. The KPSS and Phillips–Perron statistics use the standard nonparametric Newey-West criteria for calculating robust standard errors. In practice we find that these statistics use about 4 autocorrelations, which is similar to our LM procedure for determining the number of augmentations for ADF.
[…]
Discussion
We have shown that anthropogenic forcings do not polynomially cointegrate with global temperature and solar irradiance. Therefore, data for 1880–2007 do not support the anthropogenic interpretation of global warming during this period. This key result is shown graphically in Fig. 3 where the vertical axis measures the component of global temperature that is unexplained by solar irradiance according to our estimates. In panel a the horizontal axis measures the anomaly in the anthropogenic trend when the latter is derived from forcings of carbon dioxide, methane and nitrous oxide. In panel b the horizontal axis measures this anthropogenic anomaly when apart from these greenhouse gas forcings, it includes tropospheric aerosols and black carbon. Panels a and b both show that there is no relationship between temperature and the anthropogenic anomaly, once the warming effect of solar irradiance is taken into consideration.
However, we find that greenhouse gas forcings might have a temporary effect on global temperature. This result is illustrated in panel c of Fig. 3 in which the horizontal axis measures the change in the estimated anthropogenic trend. Panel c clearly shows that there is a positive relationship between temperature and the change in the anthropogenic anomaly once the warming effect of solar irradiance is taken into consideration.
![clip_image002[6]](http://wattsupwiththat.files.wordpress.com/2013/01/clip_image0026.jpg?quality=83 "clip_image002[6]")
Fig. 3. Statistical association between (scatter plot of) anthropogenic anomaly (abscissa), and net temperature effect (i.e. temperature minus the estimated solar irradiance effect; ordinates). Panels (a)–(c) display the results of the models presented in models 1 and 2 in Table 3 and Eq. (13), respectively. The anthropogenic trend anomaly sums the weighted radiative forcings of the greenhouse gases (CO2, CH4 and N2O). The calculation of the net temperature effect (as defined above) change is calculated by subtracting from the observed temperature in a specific year the product of the solar irradiance in that year times the coefficient obtained from the regression of the particular model equation: 1.763 in the case of model 1 (a); 1.806 in the case of model 2 (b); and 1.508 in the case of Eq. (13) (c).
Currently, most of the evidence supporting AGW theory is obtained by calibration methods and the simulation of GCMs. Calibration shows, e.g. Crowley (2000), that to explain the increase in temperature in the 20th century, and especially since 1970, it is necessary to specify a sufficiently strong anthropogenic effect. However, calibrators do not re- port tests for the statistical significance of this effect, nor do they check whether the effect is spurious. The implication of our results is that the permanent effect is not statistically significant. Nevertheless, there seems to be a temporary anthropogenic effect. If the effect is temporary rather than permanent, a doubling, say, of carbon emissions would have no long-run effect on Earth’s temperature, but it would in- crease it temporarily for some decades. Indeed, the increase in temperature during 1975–1995 and its subsequent stability are in our view related in this way to the acceleration in carbon emissions during the second half of the 20th century (Fig. 2). The policy implications of this result are major since an effect which is temporary is less serious than one that is permanent.
The fact that since the mid 19th century Earth’s temperature is unrelated to anthropogenic forcings does not contravene the laws of thermodynamics, greenhouse theory, or any other physical theory. Given the complexity of Earth’s climate, and our incomplete understanding of it, it is difficult to attribute to carbon emissions and other anthropogenic phenomena the main cause for global warming in the 20th century. This is not an argument about physics, but an argument about data interpretation. Do climate developments during the relatively recent past justify the interpretation that global warming was induced by anthropogenics during this period? Had Earth’s temperature not increased in the 20th century despite the increase in anthropogenic forcings (as was the case during the second half of the 19th century), this would not have constituted evidence against greenhouse theory. However, our results challenge the data interpretation that since 1880 global warming was caused by anthropogenic phenomena.
Nor does the fact that during this period anthropogenic forcings are I (2), i.e. stationary in second differences, whereas Earth’s temperature and solar irradiance are I (1), i.e. stationary in first differences, contravene any physical theory. For physical reasons it might be expected that over the millennia these variables should share the same order of integration; they should all be I (1) or all I (2), otherwise there would be persistent energy imbalance. However, during the last 150 yr there is no physical reason why these variables should share the same order of integration. However, the fact that they do not share the same order of integration over this period means that scientists who make strong interpretations about the anthropogenic causes of recent global warming should be cautious. Our polynomial cointegration tests challenge their interpretation of the data.
Finally, all statistical tests are probabilistic and depend on the specification of the model. Type 1 error refers to the probability of rejecting a hypothesis when it is true (false positive) and type 2 error refers to the probability of not rejecting a hypothesis when it is false (false negative). In our case the type 1 error is very small because anthropogenic forcing is I (1) with very low probability, and temperature is polynomially cointegrated with very low probability. Also we have experimented with a variety of model specifications and estimation methodologies. This means, however, that as with all hypotheses, our rejection of AGW is not absolute; it might be a false positive, and we cannot rule out the possibility that recent global warming has an anthropogenic footprint. However, this possibility is very small, and is not statistically significant at conventional levels.
Full paper: http://www.earth-syst-dynam.net/3/173/2012/esd-3-173-2012.pdf
Data Appendix.
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tom curtis,
As I have stated repeatedly: “Anyone who looks at this chart can clearly see that ∆T leads ∆CO2.”
That is my central point, and it is the point that you keep avoiding.
1. The scale is not relevant to my argument: that temperature leads CO2, not vice-versa. Scale is irrelevant.
2. You claim that “proving that temperature has a causal effect on CO2 concentration does not prove that CO2 concentration has no causal effect on temperature.” But you keep avoiding my challenge to produce a chart showing that changes in temperature cause subsequent changes in CO2. That is because there are no such charts; any effect on T from rising CO2 is so minuscule that it is unmeasurable — unlike empirical measurements showing conclusively that ∆T causes ∆CO2.
3. I am evading nothing, because I have read nothing by David Whitehouse, either. I think for myself, and if a growing number of writers agree with me, then they are on the right track.
You say: “You have no basis for evading the question as to why you consider a prediction that two out of five years setting new records, an increased warming trend, and (probably) statistically significant warming from the current cherry picked benchmark constitutes a prediction of no more global warming.”
Of course I have a basis for that fact. And the Met Office has finally agreed with me: global warming has stalled for the past decade and a half. Your argument is based on a prediction, therefore it is nothing but a hopeful conjecture. Such predictions have invariably turned out to be wrong.
None of the alarmist crowd ever predicted sixteen years of no global warming [whether Hadcrut3 or Hadcrut4; they both show the same lack of warming]. That is causing much consternation among the true believers. Rather than going on believing in alarmist pseudo-science, you should really just listen to what the planet is saying. Because Planet Earth is the ultimate Authority. And Planet Earth is disagreeing with the climate alarmist crowd.
D Böehm Stealey says:
January 10, 2013 at 3:25 pm
tom curtis,
…That allows you to avoid the central fact that changes in CO2 are caused by changes in temperature, not vice-versa.”
You are always ready to instantly jump down my throat but there is complete silence when you cannot answer questions from me. (Still unanswered after over a dozen posts of yours to me and after being asked three times – Why can the decrease in temperature from 1940 to 1955 not be taken as representative of the period 1880 to 2007?)
For the sake of argument here I will accept that your graph actually does show what you claim the global temperature Muana Loa data, in spite of your use of the WFT Isolate function which “Does the same running mean as ‘mean’, but then subtracts this from the raw data to leave the ‘noise’”
Since you have specifically claimed that changes in CO2 are caused by changes in temperature I will amend my earlier statement to substitute that for correlation and ask:
Given the complexity of the climate system which involves solar cycles, volacanic eruptions, el nino and la nina events, aerosols and particulates, etc , how does such a near perfect cause and effect relationship between CO2 concentration and temperature operate?
Tom Curtis: thank you for your comments elsewhere. Could you respond to the following here?
Tom Curtis:
Thank you for your explanation. I am still a little confused. According to the Wood For Trees help section:
Mean (Months) Running mean over the given number of months. Keeps the number of samples the same, but smooths them by taking the average of that number of months around each sample.
Isolate (Months) Does the same running mean as ‘mean’, but then subtracts this from the raw data to leave the ‘noise’
I thought the functions you mention were performed by (quoting from WFT help again)
Scale (Scale factor) Multiplies each sample by the given scale factor
Offset (Offset amount) Adds the given offset to each sample (can be negative)
Normalise – Scales and offsets all samples so they fall into the range 0..1
Shehan,
First off, I am not appealing to the authority of the Met. They have none. I simply pointed out that they finally agree with me that global warming has stalled.
Next, you keep trying to corner me into responding to issues that do not address my central concern: there is no acceleration of global warming as you believe. You can stop trying to corner me; as I’ve said before, you just aren’t smart enough to pull it off.
Now that you have finally acknowledged that temperature leads CO2, and that you have no chart showing the opposite, that issue is resolved. Further nitpicking is pointless. I disposed of the scale issue. My only two concerns are the facts that temperature leads CO2, and that there is no acceleration in global warming. The rest is uninteresting to me. I can easily answer the questions, but they are a needless time sink. And you don’t determine which questions I answer; I do.
Next, you are simply complaining when I point out that others do not agree with you. Complaining on the internet won’t get you anywhere. But complain, if you have to be a complainer.
Finally, if/when you admit that there is no current acceleration of global warming, we are done. You will have acknowledged reality, and at that point you can stop posting your mendacious charts showing rapidly accelerating global warming. That just does not exist, and you are about the last person on earth who clings to that anti-science nonsense.
1) Yet again, you wish to draw attention to only that point in the data, and to ignore the implications of the rest of the data. Your bias is duly noted.
2) In fact, images in which rises in CO2 precede rises in temperature are very easy to come by. You just need to plot the rise of both over the twentieth century, as in this example. It is even possible to determine that the best fit between annual CO2 and temperature data (HadCRUT4) is found when the temperature data lags the CO2 data by 18 years.
3) You claim to have made the discovery that the Met Office predicts no ongoing global warming by yourself. Therefore you are guilty not of being hoodwinked by the unscrupulous, but of unscrupulously hoodwinking others by making those claims despite the fact as noted, that prediction on which you made those claims was that “two out of five years setting new records, an increased warming trend, and (probably) statistically significant warming from the current cherry picked benchmark constitutes a prediction of no more global warming”. Please note, it was you who linked to discussions of the prediction when you made your claim. You now try to evade the issue by noting that the evidence you yourself cited was a prediction. Well, yes. But it did not turn from observation to prediction between the time you cited it and the time I looked it up.
tom curtis,
It is hard to know who you are responding to. That said, there are major problems with your comment above.
The most serious is the fact that neither chart that you linked to shows which leads and which lags, CO2 or temperature.
I have shown conclusively with empirical evidence that T leads CO2, and even Philip Shehan has finally acknowledged that fact in his post above. No one has accepted my chalenge to produce a chart showing that CO2 leads T. The reason is clear: there are no such charts, because any warming from CO2 is far too small to measure. The only thing your charts show is correlation, and a fictitious, non-existent acceleration in global warming. There is no such acceleration of global temperatures. Only the deluded true beleivers that inhabit the science fiction blog SkS believe in accelerating global temperatures. In reality, global warming has stalled for the past 16 years.
Even the ultra alarmist Met Office now acknowledges that global warming has stalled. Their predictions mean nothing, since their past predictions were wrong. They certainly failed to predict the current halt in global warming for the past decade and a half.
Your #3 is even more confused than your other points. Do you ever proof read your comments? It would take a mind reader to see what you are trying to communicate.
Face the facts that 1. global warming is not accelerating, 2. that CO2 lags temperature, and 3. that the naturally rising global warming trend since the LIA is unchanged, despite a large increase in harmless, beneficial CO2 — thus deconstructing the failed conjecture that CO2 causes any measurable warming. It does not, no matter how much you wish it were so. Those are all scientific facts, and they destroy your CO2=CAGW belief system.
@ur momisugly JasonB
JasonB, in your example the reason for the false conclusion is the assumption of linearity when the true relationship is non-linear. Assuming there is no prior knowledge of a relationship, one should only conclude that there is no evidence of a relationship as specified by the (linear) test.
I have not suggested this. I have suggested that similar trends can cause (spurious) correlation between unrelated variables.
I have not suggested this either. A detrended correlation should only be interpreted as a failure to reject a hypothesis of causal relationship.
The existence of warming does not rule out all other causes besides CO2. I would also argue that there is plenty of uncertainty surrounding things like ocean response time, feedbacks, and sensitivity to argue that the current rate of warming follows exactly as expected from physical principles.
I have demonstrated that two unrelated variables can be correlated due to existence of similar trends. If you do not detrend you have no way to rule out a spurious correlation – particularly if that relationship does not hold in the detrended case.
Philip Shehan,
As the documentation notes, “Isolate” does an awful lot more than subtract “the trend”.
To illustrate, here is HadCRUT3 with the linear trend for the entire record overlaid:
http://www.woodfortrees.org/plot/hadcrut3vgl/mean:12/plot/hadcrut3vgl/trend
Detrending the data to reveal the residuals from the linear trend shows the familiar “W” shape, and the fact that a linear trend is not a good model for the entire record:
http://www.woodfortrees.org/plot/hadcrut3vgl/mean:12/detrend:0.741532/plot/hadcrut3vgl/trend/detrend:0.741532
Note that a linear trend for the entire record only has two parameters.
Using “Isolate”, however, completely eliminates the “W”:
http://www.woodfortrees.org/plot/hadcrut3vgl/mean:12/detrend:0.741532/plot/hadcrut3vgl/trend/detrend:0.741532/plot/hadcrut3vgl/isolate:60/mean:12
This is because every single sample is being given it’s own five-year trend, which it is then compared to. That’s a whopping 3,766 parameters. Any gradual changes in temperature that are roughly linear on the scale of five years get completelly wiped out, which is why the Isolate plot is completely flat (no “W”) and consists entirely of short-term fluctuations.
Fascinating. A poster is referring to a comment of mine which at the time of reading and typing this response not appeared. I had read elsewhere that this person was in fact a moderator here who has posted under more than one name without disclosing their status. Quoting this source:
“Now, I will note that I feel anonymity on the Web is a good thing. Sock-puppeting, however, is another story entirely – if a moderator on a site misrepresents himself/herself as a rather virulent poster or two (who seem oddly immune to moderation), that is not honest. I don’t care what a posters real name is, or where they work, their posts should make sense on their own. But if they are mixing roles as moderator of a site and an unrestrained sock-puppet poster of distorted information and insults, that’s just downright deceptive. And calls into question the site itself – if there’s deception in an aspect as important as moderation, what else is going on?”
As no evidence was presented to support the assertion, I made no judgement. Now I have the evidence and I make the judgement..
I believe your original point was that in order to analyse the relationship between two trends, the series being compared must not be detrended. You agree that uncorrelated variables can show spurious correlation due to similar trends. How do you establish a causal relationship then when you can’t rule out the spurious case?
Layman Lurker:
Suppose I have two functions; f(x) is a simple linear function of x, while g(x) is actually a simple linear function of f(x).
Their correlation is perfect, and their detrended (i.e. both zero) correlation is perfect.
Now I add a some noise to both. Their correlation is still close to perfect, but their detrended correlation is terrible because I have effectively eliminated the effect of the causal relationship by detrending them. Detrended correlations are highly sensitive to noise and other factors.
In the case of CO2 and temperatures, we expect:
1. The temperature to have a logarithmic relationship with CO2 concentrations, at least in the range of temperatures and concentrations that are relevant to us.
2. The change in CO2 levels to have a lagged effect on temperature.
3. The effect of the change in CO2 levels to be lost in the noise in the short term due to their magnitude relative to other influences in the short term.
If I simply compare the logarithm of annual average CO2 concentrations with annual average temperatures over the period 1958-2012, I get a correlation of about 0.9. If I compare the linearly detrended figures, the correlation drops to about 0.5. What should I conclude?
Indeed not; in fact there are many factors at play, some quite large and highly uncertain (e.g. the direct and especially the indirect effects of aerosols), which makes it difficult to establish climate sensitivity with any real precision using only the instrumental record.
What I believe you showed with your example is that two variables X’ and Y’ related by construction — because you added a linear trend to X and Y in order to create X’ and Y’ — will show correlation, but that if you detrend them, you simply remove again the relationship that you just added. My f() and g() example is similar — g() most definitely depended on f(), but as soon as I added another term to each (some noise) the correlation vanished in the detrended data. If we regard the noise added to f() as X and the noise added to g() as Y, and f() as X’ and g() as Y’, then it’s clear that inferring anything about the relationship between f() and g() from the lack of correlation between X and Y is difficult.
That’s not to say that correlation equals causation, because of course spurious correlation can exist. But in this case the causation is not being inferred by the correlation, it’s inferred from the physics.
JasonB, Thank you for your comment.
I understand the detrend function which shows that a linear fit of the data is inadequate and I beleive simple eyeballing of the data and subtracting the line “in the minds eye” or “informally” so to speak reveals the same information.
If you can point me to where in the documentation there is more explanation of the Isolate function from the WFT help page I was relying on as given in my post (and indeed I find that too brief), It would be helpful in understanding your points fully.
Layman Lurker, correlation is never sufficient by itself to show causation; but as JasonB’s example so, lack of correlation between detrended data does not show correlation of the original data to be spurious. The effect of detrending is that the data no longer contains information about the trend. Ergo, it is impossible from the detrended data to deduce causal relations about the trend. In fact, as Philip Shehan has pointed out, the Isolate function does not remove the trend, but the running mean. That means all data about variations with a period greater than 60 months were removed by Böehm Stealey’s data manipulation, including, of course, any effect of forcing from CO2.
(reply -There are numerous moderators. Speculating about motives is not welcome. ~mod)
Hi Philip,
I wasn’t relying on additional documentation, rather simply the observation that taking the average of the monthly temperatures surrounding a point is the same as finding the midpoint on the linear trend fitted to those same monthly temperatures.
So, in the example with isolate=60, finding the five-year average temperature centred on a point and subtracting it is exactly the same as finding the 5-year linear trend centred on that point, then finding what that trend says the point’s value should be, then subtracting that from the point to leave the residual (i.e. the noise) at that point.
As you can see from the graph, all those parameters give it a lot of freedom to “ride out” longer-term fluctuations and completely remove them from the data, which isn’t terribly surprising.
You are the slippery type, Shehan. I will try once more to pin you down.
GCM’s are, in effect, tinker toy contraptions used to support AGW theory but in fact are no more than that same theory transposed into algorithms. This is all that the global warmers have to offer as support for the unsupportable AGW theory: the cat chasing it’s tail.
What do you say?
I am sure that you are aware that this question is a trap because it puts you in the position of ultimately refuting AGW theory, which projects warming as inevitable, if you deny the premise of the GCM’s, which project inevitable warming .
If you try to finesse the contradiction, you will get tangled up and embarrassed, I can assure you. The world is watching, Shehan. Will you try to wriggle away like last time?
Thank you JasonB.
mpainter:
You have tried this on before, asserting that climate models are designed to only project warming. Further you have claimed that I have agreed with that proposition. Both these claims are nonsense.
@JasonB
As they should be. Failing to reject a null due to a weak S/N ratio is part of science. What is worse though, is rejecting a null because of an artifact of the method.
I would not argue with you on this. I would only point out that appealing to correlation as supportive of causation when the trend is included must consider the null (unrelated variables correlated by chance).
last time?
Philip Shehan says:
January 11, 2013 at 6:19 am
mpainter:
You have tried this on before, asserting that climate models are designed to only project warming. Further you have claimed that I have agreed with that proposition. Both these claims are nonsense.
=====================
From this, I assume that your stand is that GCM’s project other than global warming. Now, suppose you show us one that projects something other than warming, with the important qualifier that it incorporates AGW theory. I have another thread with Joel Shore on this, and he is trying out the idea that the GCM’s do not incorporate AGW theory, so perhaps you two should get together and decide what’s what before I start to quote you two against each other.
@Tom Curtis
Wrong method = right answer is still a spurious result. The null is not that a correlation exists, but rather that a correlation is due to chance. If a trend association cannot distinguish between causative relationships and unrelated variables with common trends, then what is the point of even calculating the correlation in the first place?
tom curtis,
Trying to re-frame the arguments I made is a strawman fallacy. Let me reiterate the only two points I have consistently made here:
1. There has been no acceleration in the long term global warming trend since the LIA, and
2. Empirical evidence shows conclusively that temperature leads CO2, not vice-versa
Respond to those facts instead of going off onto other tangents.
@Tom
Not true. As per Jason’s example it might not be possible to deduce causal relations if the data are too noisy, but then if what we are comparing consists mostly of unrelated noise, there should be no expectation of seeing a relationship. While it is true that trend association might indicate a causal relationship, it means nothing if you cannot reject the null. The basis for statistical inference is rejecting the H0.
What does this have to do with my discussion with you or JasonB? I have not been following the Shehan / Boehm discussion or considering it in any of my comments.
moderator: regarding your comment:
Philip Shehan says:
January 11, 2013 at 1:15 am
(reply -There are numerous moderators. Speculating about motives is not welcome. ~mod)
I am aware there are many moderators. I did not assume or suggest anything else. That said, I apoloogise for any offence caused to moderators who I am sure do their job honestly, diligently and impartially.
I was critical of the behaviour of only one person, who appears to be a moderator.
This person is commenting on the posts of others when those posts have not appeared and that is clearly unnacceptable.
The fact that the suppressed comment was addresed to this person,who may have been acting as moderator at the time, gives rise to the suspicion that the supposedly impartial umpire is in fact a player who is rigging the game. That possibility should be alarming to everyone.
I will represent the post that failed to appear the first time.
D Böehm Stealey says:
January 10, 2013 at 3:25 pm
tom curtis,
…That allows you to avoid the central fact that changes in CO2 are caused by changes in temperature, not vice-versa.”
You are always ready to instantly jump down my throat but there is complete silence when you cannot answer questions from me. (Still unanswered after over a dozen posts of yours to me and after being asked three times – Why can the decrease in temperature from 1940 to 1955 not be taken as representative of the period 1880 to 2007?)
For the sake of argument here I will accept that your graph actually does show what you claim the global temperature Muana Loa data, in spite of your use of the WFT Isolate function which “Does the same running mean as ‘mean’, but then subtracts this from the raw data to leave the ‘noise’”
Since you have specifically claimed that changes in CO2 are caused by changes in temperature I will amend my earlier statement to substitute that for correlation and ask:
Given the complexity of the climate system which involves solar cycles, volacanic eruptions, el nino and la nina events, aerosols and particulates, etc , how does such a near perfect cause and effect relationship between CO2 concentration and temperature operate?
PS
Have to laugh at your criticism of Tom Curtis for his “appeal” to authority (the predictions of the Met office.) You appealed to precisely that authority January 8, 2013 at 10:07 am
“I note that no one else is agreeing with Shehan…In fact, Harrabin and the Met Office admit that…”
(Note the appeal to meta authority – the collective opinion of the committed “skeptics on this blog.) At 3:55 pm January 6 , you individually name two of these authorities:
“Mathew Marler says to Shehan:
Bart says about Shehan:”
You lift your game a little when you later appeal to the authority of the BBC.
mpainter says:
January 11, 2013 at 9:18 am…
Have you stopped beating your wife?
I reject the premise on which your question is based.
Your suggestion that the results of the application of a model shows a particular result means that it is designed to to produce no other result is ludicrous.
Application of models used by the weather bureau here in Australia have been predicting (accurately) extreme high temperatures. That does not mean they are designed to or are only capable of only to producing only that result. They are clearly not. They also accurately predict (here in Melbourne) the arrival of sudden cool changes resulting from the arrival of cooling winds from the southern ocean. Yessterday the temperature dropped at least ten degrees from 37 C in half an hour. Not at all unusual in “four seasons in one day” Melbourne.
Try reviewing this assumption of yours with regard to these comments:
“From this, I assume that your stand is that GCM’s project other than global warming.”
My chuckle of the day in this thread was this from Shehan, when he mistakenly believed that L. Lurker was in agreement with him:
“Thank you from the bottom of my heart… Yours in eternal gratitude…”
LOL! Then LL corrected his mistake, concluding: “Whatever” at Shehan’s sycophantic groveling.
In his next post, Shehan was miffed. Reality wasn’t what he assumed it to be — a recurring fault of his.
It’s the same thing with Shehan’s mistaken belief in ‘accelerating’ global warming. Empirical evidence shows conclusively that there is no acceleration in global warming.
If Shehan would acknowledge that plain fact, we would be done here. But it would be wrong to allow his ‘accelerating’ pseudo-science to go unanswered. New readers might accept Shehan’s false anti-science. Can’t have that nonsense posted here on the internet’s “Best Science” site without being corrected.