![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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Thank you Richard for reinforcing my demonstration with a long list of your remarks to me above about your habit of engaging in personal attacks which you claim to have found “false” “untrue” and “egregious”.
You are aso exhibiting your staggering lack of comprehension and reasoning with this gem, commenting on my response to Layman which deserves repeating:
‘Your post at January 8, 2013 at 1:45 pm says
“I did not introduce the term acceleration to the discussion.”
Say what!? Even by your standards that is a ridiculous statement
Your first post to this thread was at January 4, 2013 at 8:43 am and says
“Informal inspection of the temperature data of panel c does show acceleration,”‘
From the very beginning, at my first comment, without rearrangement of the text:
‘Philip Shehan says:
January 4, 2013 at 8:43 am
Quoting from the paper:
“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.”
Informal inspection of the temperature data of panel c does show acceleration, matching…’
So Richard, who introduced the term acceleration into the discussion, the authors of the paper or myself?
And its not as if I did not include the quote from the authors in immediate reference to my statement in the comment to Layman that you take issue with.
Are you completely blind or completely stupid?
In my earlier post I wrote:
“I much prefer and as a scientist am used to, polite respectful and robust disagreement. I recognise that this is (sadly) not the culture of the blogosphere, and have come to the conclusion that there comes a point with the repeated efforts of people like D Boehm and sadly yourself, when turning the other cheek is no longer worth the effort.
Note that Layman knows how to conduct robust discussion without abuse, and I respond to him in kind, but you are getting worse and worse. I no longer bother in your case but return your manner in kind. I will add that I had thought that D. Boehm was the truly obtuse incorrigible abusive idiot in this thread. I have changed my mind.
Philip Shehan:
Having pretended to be a sad, little, lonely and stupid man but being revealed as something else, at January 8, 2013 at 7:55 pm you demonstrate you are a mendacious troll while trying to cause a rift between me and Layman.
You DID introduce temperature “acceleration” into the discussion.
The paper’s authors stated that rise in atmospheric GHG concentrations had accelerated but – as everybody knows – rise in global temperature has not. You joined the discussion at January 4, 2013 at 8:43 am saying you did also observe temperature “acceleration”.
Later, at January 8, 2013 at 1:45 pm, you claimed,
“I did not introduce the term acceleration to the discussion.”
As I said, that claim was “ridiculous”. Please note that I am aware of the tricks of warmunists so I did not say your claim was a literal untruth. The facts are:
1.
The authors mentioned that – as everybody knows – temperature rise has not accelerated.
2.
You joined the thread late and asserted that global temperature rise has accelerated.
3.
You maintained that assertion despite all evidence to the contrary and advice that your stance was making you look foolish.
4.
The UK Met. Office issued a press release admitting that global temperature rise has not accelerated but has decelerated,
5.
Following that press release, you claimed you had not introduced temperature acceleration into the discussion.
6.
I said your claim is “ridiculous”: IT IS.
7.
You have tried to dispute that that your claim is ridiculous and say I am being abusive.
8.
You are a deluded fool whose further comments I shall ignore. And,no, that is also NOT abusive.
Richard
Actually it would be more along the lines of LR08. I don’t see any discussion of their residuals in that paper though.
D Böehm Stealey says:
January 7, 2013 at 3:05 pm
Phil.,
Don’t be silly. This chart shows clearly that T controls CO2, and not just “10%” of it.
[snip.]
Your graph shows nothing of the sort and your refusal to give the scale of the CO2 rate indicates that you know that. In your graph you have subtracted ~2ppm/yr from the rate leaving a fluctuation of ~±0.2 on your graph related to temperature. The 2ppm/yr is the growth due to fossil fuel combustion etc., the slight modulation of sink/source due to temperature is a minor effect.
Your attempt to attach significance to the lag is flawed by your comparison of a global statistic with a local one, why not use the South Pole CO2? Of course it would make more sense to compare two global statistics.
Phil,
Anyone who looks at this chart can clearly see that ∆T leads ∆CO2. You are simply turning yourself into a pretzel trying to argue otherwise. Who should we believe? You?? Or our lyin’ eyes?
And I see that Shehan is still clinging to his preposterous notion of rapidly accelerating global temperatures, even as the rest of his climate alarmist crowd finally admits that global warming has stalled. Incurable cognitive dissonance.
D. Boehm
For the 463rd time (OK slight exageration).
Nowhere, absolutely nowhere, have I argued a causal relationship between temperature and CO2 concentration. I am perfectly happy, for the sake of argument here, to accept that delta CO2 follows delta T. Even that delta T causes delta CO2. (And indeed it does in the case of CO2 produced currently by melting of arctic permafrost with increased temperature and historically following the ice age melts)
The only point I am discussing. The ONLY point I am discussing. Thre ONLY point I am discussing is the claim introduced, that’s introduced, INTRODUCED (for benefit of the other slow learner here) by the authors:
“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.”
To my sad, lonely, stupid but very experienced old eyes in looking at such data, an informal eyeballing af the temperature data shows an acceleration for the temperature data in figure 1, panel c.
And in support of my eyeballing of this 1880 to 2007 global temperature graph (your chart showing short term data trends in central England notwithstanding) I have referred to a non linear accelerating curve of global temperatures for the period under discussion, which shows that my aging experienced eyes did not decieve me. There is a very good match. Superior, but only in the opinion of these ageing experienced eyes in the absence of the availability of an R2 parameter, to a linear fit of the authors data which I have twice provided.
And for the 364th time (OK slight exageration again) the fitting of a line whether linear or non linear is here only a visual aid to an “informal” eyeballing of the data as discussed by the authors. It deos not involve any assumptions of cause and effect, or any other random or non random link to the data on the x and y axes whatsoever.
Hoping that this finally clears up the only point I am making and that you will stop producing irrelevant data and assuming causal or other arguments i have nowhere made. Also hoping for the sudden appearence of a porcine airfleet.
Is Shehan still shoveling his ‘global warming acclerating’ horse manure? Even the most hard core climate alarmists now openly admit that there is no acceleration in global warming, and that global warming has been stalled for many years.
But not Shehan. No, Shehan still believes that global warming is rapidly accelerating. For proof, see the deceptive charts that he is still posting.
Shehan is the last climate alarmist claiming that global temperatures are currently accelerating. That tells us all we need to know about his mental state; pure cognitive dissonance, per psychologist Leon Festinger:
The Seekers have superior knowledge. You must believe their prophets, Mrs. Keech and SkS. The flying saucer will be along very soon to save the Believers. Have faith, Philip. You are right. Everyone else is wrong.
Boehm Stealey @11:37 am, January 9th links to a chart which compares CO2 concentration and temperature after removing all trends, and re-centering at zero. He purports that by removing the trends and showing a correlation, he can show that temperature is responsible for the trend in CO2. That, by itself, is quite an intellectual feat. Most of us would think that if you wish to analyse the relationship between two trends, you do not start by removing both trends from the data.
That, however, is not my primary concern. Taking Boehm Stealey’s chart at face value, I notice that for each 1 degree C fluctuation in temperature, there is a 4 ppmv fluctuation in CO2 concentration (scale factor = 0.25). Ergo, taken at face value, Boehm Stealey shows only that the approximately 1 degree C temperature rise over the course of the last century caused a 4 ppmv rise in CO2 concentration, with the rest of the rise coming from anthropogenic factors. Consequently, he is unable to explain the strong relationship between log CO2 concentration and global temperature.
Tom Curtis,
I deliberately scaled @0.25 to make the T/CO2 relationship clear. It would have been clear enough with, say, a 0.15 scale, but less so. This way, the peaks are about the same amplitude.
The point, however, is that ∆T leads ∆CO2, not vice-versa. If you can produce a similar chart showing that ∆CO2 leads ∆T, I will concede that you are correct. But if you can’t, then I am correct: ∆T causes ∆T. Anyone looking at the chart can see that.
Tom Curtis
As my post replying directly to Boehm’s 11:37 post notes, the major problem with his chart is the use of the isolate function, (See the explanation of this function on the WTF site which means that is neither a plot of CO2 concentration nor temperature but THE NOISE AFTER SUBTRACTION OF THE DATA.
Astonishing but true.
The only ‘astonishing’ thing is that Shehan continues to believe that global warming is accelerating. Even the BBC has now been forced to climb down, and admit that global warming is static.
To understand why Shehan cannot admit that there is no “acceleration” in global warming, and that global warming has in fact stalled for the past 16 years, a famous author has the answer:
OK so my first post may have been a little fruity in expressing my outrage at D Boehm’s conduct and I will accept that as an expalnation if why it has not appeared, but is the failure of my post (to Tom giving further explanation af Boehms analysis and a correct representation of the data to appear with an awaiting cosideration tag) indicative of anything?
Tom, if you want to analyse the relationship between two variables, detrending is often an essential step. If a relationship does not hold after removing the trends, then any correlation prior to detrending is likely spurious. If the cause of the trend is stochastic, then differencing might be necessary. However, differencing may not be necessary if the stochastic series are cointegrated
Here is an example showing how adding a trend creates a spurious correlation between two otherwise uncorrelated series.
Perhaps I was trying to include too many links in my earlier posts. Not sure haow many I used but is there a limit? I shall try 3.
Tom Curtis:
Anyway, it took me a while to track down that the isolate function used in the graph reduces it to a plot of noise.
http://www.woodfortrees.org/plot/esrl-co2/isolate:60/mean:12/scale:0.25/plot/hadcrut3vgl/isolate:60/mean:12/from:1958
An explanation of the functions discussed here is found on the WFT help page:
http://www.woodfortrees.org/help
My suspicions were aroused by informal inspection of the graph (and presentation of another graph from the same source in which extraneous processing had been used which did nothing but iintroduce extraneous lines which flattened the temperature data obscuring the curve of the data which the graph was supposed to be showing did not exist) shows that the match of the data sets is riduculaously good.
Given that temperature is affected by solar cycles, aerosols, volcanic eruptions, el nino and la nina events etc etc, how could there be such a near perfect correlation between temperature and CO2 content alone? Well we now know there isn’t. the graph is fraudulent.
Here is the temperature and Mauna Loa data and Hadcrut3 temperature with the only functions applied being a 12 month smoothing function for the temperature data and the normalise function which applies a scaling and offset adjustment.
http://www.woodfortrees.org/plot/esrl-co2/from:1958/to:2010/normalise/plot/hadcrut3vgl/from:1958/to:2010/mean:12/normalise
Layman Lurker: “Here is an example showing how adding a trend creates a spurious correlation between two otherwise uncorrelated series.”
I’m a little confused by that. If you have two variables X and Y, and you add trends to each, creating new variables X’ and Y’, the correlation between X’ and Y’ can hardly be called spurious, as they are correlated by construction. X and Y could well be uncorrelated but those aren’t the variables being compared, X’ and Y’ are.
Conversely, if I put the kettle on the stove and turn it on, and then I record the temperature and the burner setting every second for a minute or so, and then I detrend the data, I’m going to conclude that the burner has no impact on the temperature of the water (especially since the detrended burner value is zero the entire time). Or, even worse, I’m going to notice that the detrended temperature data starts curving down after a little while — since the water’s rate of warming will slow as it gets closer to equilibrium — and then conclude that the burner actually cools water down.
for Jason
JasonB I presume your burner kettle example is intended to be analagous to CO2 forcing of oceans? It is a great example. If you change the burner setting at defined time steps which do not allow a full temp response then is dT/dt vs dCO2/dt going to be linear? There is a great article and discussion on this at Lucia’s.
Layman Lurker,
The burner kettle example is meant to be literal: If detrending the data would lead us to falsely conclude that the burner is not warming the water, then a negative result in other detrended data could just as easily lead to the same mistake. It’s a question of the validity of the test.
As for correlation vs causation, deciding that causation does not exist because two variables are correlated seems rather perverse, and arguing that the only reason for believing causation to exist is due to the correlation is ignoring an awful lot of theory (and observation) going back quite a long way. In both the kettle/burner example and global temperatures, we have reasons to believe a-priori in both cases that one should cause an effect in the other from basic physical principles, and the predicted warming effect of increased CO2 predates any actual observation of that warming effect by, what, 100 years or so? The way to check that prediction is by comparing the data, not the detrended data.
Thanks for the response JasonB. I will respond later today or this evening.
D Boehm Stealey says:
January 9, 2013 at 11:37 am
Phil,
Anyone who looks at this chart can clearly see that ∆T leads ∆CO2. You are simply turning yourself into a pretzel trying to argue otherwise. Who should we believe? You?? Or our lyin’ eyes?
I’m not turning myself into a pretzel, I’ve been asking you to portray the data honestly but you refuse to do so. Clearly as pointed out below, your graph shows that only a very small fraction of the rate in change in CO2 depends on ∆T. Your “lyin’ eyes” clearly mislead you since they manage not to see most of the change in CO2.
As I pointed out above your graph shows that “CO2 levels rise because of combustion emissions into the atmosphere with a small modulation due to temperature”, so yes you should believe me!
D Böehm Stealey says:
January 7, 2013 at 3:05 pm
Phil.,
Don’t be silly. This chart shows clearly that T controls CO2, and not just “10%” of it.
No it doesn’t because you’ve removed 90% of the change in CO2 (~2ppm/yr) from your plot!
Mr Pretzel,
The chart I posted shows that changes in CO2 follow changes in temperature. You keep tap dancing around that fact. My challenge to you: produce a similar chart that shows that changes in CO2 are caused by changes in temperature. I have repeatedly challenged others to produce such a chart. Their response used up lots of pixels, but… still no chart.
Layman Lurker, your counter example consists of the correlation between to sets of white noise plus trend. Clearly if you eliminate the trends, you will find that there is no correlation between the white noise, but that will not enable you to explain the trend. My point stands.
D Böehm Stealey:
1) Whatever the reasons for your scaling, the fact of similar amplitudes shows the predicted correlation from the relationship you show. That shows unequivocally that global warming is not sufficient to explain any but a tiny fraction of the increase in CO2 concentration over the twentieth century.
2) I grant (because it is true) that year to year fluctuations in global temperature are the primary driver of year to year fluctuations. As shown above (and elsewhere) , the rise in temperature is not the cause of the vast majority of the rise in CO2 concentration over the twentieth century. You, however, wish to infer that because year to year fluctuations in global temperature largely cause the year to year fluctuations in CO2 concentration, that the rise in CO2 concentration cannot cause the rise in global temperatures over the twentieth century. To make that inference, however, it must be the case for all X,Y, that if X causes Y, Y cannot cause X. That is, for example, if the sound from the speaker causes the current in the microphone, the current in the microphone cannot cause the sound in the speaker.
You may be delusional enough to think that there are no feedback loops, but I am not. The essential premise of your argument is simply false, and demonstrated to be false in a host of physical systems.
As it happens, year to year fluctuations in temperature cause changes in CO2 concentration which are large relative to the annual increase in CO2 concentration due to anthropegenic emissions, but small relative to the decadal increase. Hence the short term fluctuations in CO2 concentration are dominated by global temperature, while the long term trend in dominated by anthropogenic emissions. In contrast, the expected equilibrium response to a years increase in CO2 emissions (0.02 C) is very small relative to year to year fluctuations in global temperature, so in the very short term changes in CO2 concentration have no discernible impact on temperature. But the accumulated impact of the accumulated anthropogenic emissions is large, and dominates the decadal trend in global temperatures.
3) I see that you are repeating Delingpole’s latest misrepresentation. The facts (confirmed by digitizing the graph and analyzing the result) is that the new Met Office prediction predicts that 2 out of the next five years will break the current global temperature record; the trend from 1996 to the end of the predicted interval will be approximately double the current trend from 1996 to the end of observations; and the trend from 1996 to the end of the predicted interval is statistically distinguishable from zero. I am sure you will continue to repeat Delingpole’s cannard; but you won’t mention these facts (or any facts) as evidence because that would reveal the claim to be a sham.
tom curtis,
1. You are still stuck on scaling. As I pointed out, the cause-and-effect relationship is the central point. ∆CO2 follows ∆T, and scaling has nothing to do with that fact. I challenge you to produce a similar chart showing the reverse.
2. Thank you for your assertion. It does not, however, change cause-and-effect.
3. I did not read anything by Delingpole regarding this issue. I don’t know what he wrote. So you are using him as a strawman in our debate; you set that strawman up and knocked it right down, you brave strawman slayer. That allows you to avoid the central fact that changes in CO2 are caused by changes in temperature, not vice-versa.
Your citing that the “Met Office prediction predicts” is simply an appeal to an authority that is wrong in it’s predictions far more than it is right. Their credibility is shot. They have now been forced to admit that global warming has stopped. If CO2 has any warming effect, it is negligible, and should be disregarded as trivial.
Wake me when you find a similar graph that shows CO2 causing temperature changes. The global warming hysteria is based on nonsense. There is simply no scientific evidence supporting the CO2=CAGW conjecture.
D Böehm Stealey:
1) Much as you dislike it, the scale is significant and shows the response of CO2 concentration to temperature. I know you like to only look at that part of the data that makes your point, lest you see all of it and be forced to change your opinion. I don’t like such blinkered views, however, and will note what the correlation says about the effect of temperature on CO2 levels.
2) Again, you simply evade the point that proving that temperature has a causal effect on CO2 concentration does not prove that CO2 concentration has no causal effect on temperature. That CO2 does indeed have a causal effect on temperature has been demonstrated beyond reasonable doubt, and is acknowledged by all AGW skeptics with a skerrick of scientific credibility (and quite a few without).
3) First, I apologize. It was David Whitehouse, not Delingpole, who started the deceptive spin on this story. You, apparently got the story second hand, but that in no way improves the basis of the story, and does not justify your ignoring the evidence that shows Whitehouse’s spin to be deceptive. 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. (Note that my original analysis used HadCRUT4 data along with a digitized version of the prediction. I have since discovered that the Met Office used the HadCRUT3 data set for the prediction. This will change the detailed results of my analysis, but is unlikely to overturn the main points.)
Lets separate out what we know from what are guesses.
1) the greenhouse effect is real and can be shown by looking at the temperature of the earth without greenhouse gases. The physics for this is well established.
2) we know that temperatures have gone up and down over thousands of years. There are what appear to be cyclic patterns to thse movements. We’ve also clearly demonstrated a shorter term cyclic movement related to ENSO/amo/pdo
3) we know other things can have powerful effects on temperature including small movements in the earths gravity and changing it from the sun.
4) there is a relationship between co2 and temperature and historically we have seen that co2 does indeed rise as temperature rises due to outgassing from the oceans. Similarly co2 has declined as temperatures go down.
5) we don’t know what percentage of the temperature increases or decreases in the past are actually due to whatever forcing caused the initial temperature change and how much is related to changing gas concentrations. Several lines of analysis show that the feedback could be one ( null) to 9 times the original forcing. This is based on our understanding of what the conditions that caused the forcing and how the forcing effected the environment. It is clear that our understanding of solar forcing at this time does not allow it to account for the entire temperature change we’ve seen in the past. Therefore paleo methods for determining how much co2 effects temp are not reliable due to lack of sufficient proxies for all parameters, error in the proxies we have and a basic lack of understanding how the environment reacts to changing co2 or solar or other forcings.
6) a good part of the energy balance for the system is tied up in the oceans which represent 1000 times the heat capacity of the atmosphere. Without knowing precisely the movement of energy in and out of the ocean it is difficult to understand where energy may be coming from or going to. Satellites can measure numerous things in the atmosphere but only Argo has been able to give us the first accurate information about the top 3000 meters of the ocean. Unfortunately the ocean is so large that even Argo doesn’t really tell us everything we need to know to be sure what’s happening to energy in the system
7) models have been created with assumptions about how the earth oceans and atmosphere react to each other and we don’t know if the assumptions in these models are correct. Wellnwenknow they are wrong because in fact the models have been seen to be poor predictors of any variable including temperature.
8) fitting the models to the proxies and data we have produces numerous fits that sometimes look good and sometimes look bad. We know that when predicting the next year or 10 years that none of the models (23 or so) is any better than the other (papers available). So a mean is calculared but a mean implies that none of the models is correct and also that there is a big cicular element to the models that the scientists building the models know the data and are constantly trying to make the models better but since they all use the same data and there is common knowledge of what the models consist of with similar assumptions in all the models and common ideas the models could all be easily wrong and even predicting higher temperatures in 2100 from the models is poppycock. Error analysis of the models demonstrates that there is no way the models could produce a fixed prediction with small error. The error bars are so enormous that in 2100 a temperature +10 or -10 is possible.
9) we know that the models have consistently predicted higher temps and more effects from co2 than we’ve seen.
10) we know that a good fraction of the co2 increase is due to man burning fossil fuels. However the rate of increase in co2 is below projections of the ipcc. Apparently the environment can absorb the co2 better than we think. Further we assume that the oceans and other means of absorbing the co2 naturally will not work as well. We don’t know if that is really true.
11) nobody has tested the assumptions in the models about how water vapor will change and how other things will react. These are assumptions that are untested and can make a huge difference on rhe result
12) the models to this point have assumed a hockey stick as a base assumption of the temperature record. They cannot explain variations in temperature because of cyclical phenomenon except if co2’changes. Yet we know now that’s there have been variations in the past and these cycles absolutely seem to exist
13) while co2 has been correlated with temperature change so has cosmic rays and sunspot number. We can’t explain these relationships with our understanding of climate.
14) the last ipcc thought that the models were so good that taking them and adding effects of Enso and volcanoes we had largely been able to show a tight fit to the data. We therefore thought we had a good handle on natural variability and its causes. We therefore issues a statement that with 95% certainty the temp change from 1979-1998 was caused mostly by co2. However since 1995 there is no statistically observable trend in temperature which means the natural variability that we assumed we had a tight leash on in ipcc ar4 has proven to be wrong. That is a central failure that is not talked about. We now cannot say that we understand the level of other factors affecting the environment and how long such effects would dominate any co2 effect. However the fact that the entire release of co2 since 1995 has been neutralized by a “natural variability” that we cannot explain means that our “certainty abut the cause of the heating between 1079-1998 is now up in the air completely. Given how much variability has been observed its now clear that a similar level of variability could in fact be the entire cause of the 1979-1998 warmup meaning that the presumed fit of high sesitivity to co2 in the models could be completely wrong. This is a central point that is not understood. The global warming hypothesis rested on the idea we could ascribe within controlled ranges the effects of other forcings. Now that its clear we don’t have a good handle on these other forcings or natural variability we are forced to go back and rejustify the oft assumed now position that we know that co2 is the cause. It’s clear in fact that other factors such as El Niño could have been a large part of the warming from 1979-1998 or other unknown phenomenon related to longer cycles in the system. Since we don’t fully understand the cause of the 18 year hiatus in temperature we also dont know where that effect is going go in the future. It could as some have speculated actually drive temperatures colder for any period of time or make them warmer.
15) there is a high variability in the estimates from the paleo record on the climate sensitivity. We lost the assurance we had that the 1979-1998 period was “clean” and we could understand what caused that heating. The models are way too inaccurate and circular to be able to add credence to the assumed 3.0 climate sensitivity in the most widely publicized predictions of the ipcc.
16) the historical record of the us temperature has been fiddled with based on “in homogenous inconsistencies”. This algorithm which is used to blindly adjust our historic temperatures to make them mores accurate seems to have a strong bias to adding z0.3-0.5c to the temperature rise in the last century. This widespread and massive change in the historical record without being thoroughly vetted is a sore point. Nonetheless nobody would argue temperatures haven’t gone up. We simply don’t know with certainty why they have or what the real magnitude of the increase is.
17). While glaciers are melting they have been doing so for hundreds and hundreds of years. Satellite measurements clearly are showing that we overestimated the melting. We calculated 3 feet gain with one foot coming from Antarctica one foot from inland glaciers and one foot from warming water. Newest data shows that Antarctica is probably neutral or gaining ice mass. Inland glaciers are losing 1/4 the ice we assumed and 1/12 what some predicted. Further there is very little warming of the oceans since we have an accurate thermometer in argo that has been observed in the ocean. The result of this is that we understand why sea level has risen very little in the last 10 years. For whatever reason this is way less of a problem than people anticipated and is probably going to produce the same amount of sea level rise we’ve seen for hundreds of years which is about 6″ of rise not 3′. This is a miss of factor of 6. Huge error.
18) numerous other things predicted have proven wrong. There is no deonstrable increase in storms as has been predicted. We don’t see higher variability in rainfall but decreasing variability. We don’t see higher humidity in the atmosphere a critical important prediction that has failed. This tells us that key assumptions may be wrong.
What’s my conclusion after studying all this?
A) over the next 10 years some of the parameters in alternate theories show a declining trend in temperature. For the first time sincemthensatellite era we will be able to observe if these alternate causes of climates change play a larger role than co2 or lesser. Co2 is unmistakably climbing. The sun is unmistakably less intense and has lower sunspots. The oceans are in a negative pdo /amo phase. All of these were during the 1979-1998 period in sync and rising. Therefore ascribing the temperature change reliably to one or the other was difficult. In the nextn10 years if temperatures resume a 1979-1998 type rise or higher as cagw theory requires then its will show conclusively that co2 rules. If temperatures stays flat or goes down it means the assumptions that co2 was the lord of temperature change will be disproven. If temperatures go down a lot then coz2 probably has almost no effect on the atmosphere and all the research and assumptions will look ridiculous in their certainty. If temperatures stay the same it similarly means that co2 isn’t lord. Other things can overwhelm co2. It’s also possible temperatures go up modestly and this would mean that the climate sensitivity is weak but there is some effect of co2. All things are possible. It’s occurred to me that maybe co2 is powerful but so is solar and oceans. That a complex adding and subtracting of large effects has resulted in a more muted temp change. We need to observe more to conclude what the real CS for all these things are but happily nature over the next 10 years is going to give us that experiment to observe.