Simple climate change refutation challenge

[mhaze]

Its silly to apply correlations and statistics to temperature data......

Knowable unknowns now silly statistical solutions.

 

[Megalodon]

Knowable unknowns now silly statistical solutions.

Ok... You have now been awarded the "The Remedial Reading Classes Voucher", a prestigious award for people that... well, that do what you do, as poorly as you do it...

Congrats

 

[sphenisc]

Ok... You have now been awarded the "The Remedial Reading Classes Voucher", a prestigious award for people that... well, that do what you do, as poorly as you do it...

Congrats

Can I get one as I have no idea what he means?

 

[Geckko]

I see no reason to think the results would be any different. The other measures are lower than GISS, but quite consistently, so you'll get the same contrasts between decades. Each decade warmer than the previous one.

This one hasn't even finished yet; what's passed has been mostly during the down-side of a solar cycle and hasn't seen a sustained El Nino. Then again, it hasn't included a tooled-up volcano either. It has seen some major ice-loss, and the latent heat for that had to come from somewhere. There's less ice to melt now, which implies a reduced heat-sink effect.

All in all, I think this decade's ranking is unlikely to be challenged, absent a seriously tooled-up volcano. Something much bigger than Pinatubo '91.

Just good statistical practice. We have different data collated and adjusted in different ways. Our knowledge and understanding increases as we consider the wider range.

My background in statistics leads me away from thoughts like "I see no reason to think etc.", towards "I wonder what the other data shows?"

 

[Geckko]

Megalodon kindly sent me some output from his temperautre/CO2 regressions so I could run a test on them. I though the results might be of interest here.

I conducted a "Dickey-Fuller" test on the residuals of a regression of temperature anomolies on CO2 concentrations.

For the uninitiated, this is a test to for a "unit root" in a time series of data. The existance of a unit root indicates that the series has a stochastic trend, which means there is serial autocorrelation present. That is important in this instance, because if the residuals of a regerssion of temperautre anomolies in CO2 show the presence of a unit root, it indicates that the two data series can not be used to produce a standard correlation coefficient - "Pearsons R". In econometrics-speak it shows that the two are not "cointegrated", which is a fancy way of saying correlated over time.

The standard (as opposed to augmented) test requires you regress the first difference of the time series of interest against the lagged level of the series of interest and a constant. We then test the resultant estimate for the coefficient of the lagged variable to see if there is evidence that it is non-zero. We need to use special Dickey-Fuller critical vlaues for this as the regression will not exihibit exact gaussian properties.

in algebraic terms I have taken the residuals provided by Megaladon and conducted the following regression:

Rt-Rt-1=A + B Rt-1 + e

A and B are estimated coefficients and B is what we test to see if it might be non-zero. Doing this I obtained the following:

	        Coefficients    Standard Error   t Stat
Intercept	-0.002609364	0.012480168	-0.209080804
X Variable 1	-0.779522839	0.140841828	-5.534739581

The DF critical value at 2% for this sample size is -3.58, which we compare to the t-statistic of the regression which is -5.5 about. So we can reject the hypothesis that B=0 and conclude there is no unit root.

This tends to indicate that the temp anomolies and CO2 are cointegrated (i.e. trend together over time).

This compares with the other test (Durbin Watson) that gave fairly weak evidence of a correlation (which is a different concept).

 

[Megalodon]

Just good statistical practice. We have different data collated and adjusted in different ways. Our knowledge and understanding increases as we consider the wider range.

My background in statistics leads me away from thoughts like "I see no reason to think etc.", towards "I wonder what the other data shows?"

The data is public... knock yourself out! Unfortunately I don't have the time or the inclination to play around with all the datasets. NCDC seems to be one of the less controversial databases.

However, if you follow fsol's link, you'll find a detailed comparison of three of the databases, and also a comparison with the satellite measurments.

I'm sure you'll enjoy it, and I would like to hear your opinion of it as a statistician (or someone with a strong background in it).

 

[mhaze]

Megalodon kindly sent me some output from his temperautre/CO2 regressions so I could run a test on them. I though the results might be of interest here.

I conducted a "Dickey-Fuller" test on the residuals of a regression of temperature anomolies on CO2 concentrations.

For the uninitiated, this is a test to for a "unit root" in a time series of data. The existance of a unit root indicates that the series has a stochastic trend, which means there is serial autocorrelation present. That is important in this instance, because if the residuals of a regerssion of temperautre anomolies in CO2 show the presence of a unit root, it indicates that the two data series can not be used to produce a standard correlation coefficient - "Pearsons R". In econometrics-speak it shows that the two are not "cointegrated", which is a fancy way of saying correlated over time.

The standard (as opposed to augmented) test requires you regress the first difference of the time series of interest against the lagged level of the series of interest and a constant. We then test the resultant estimate for the coefficient of the lagged variable to see if there is evidence that it is non-zero. We need to use special Dickey-Fuller critical vlaues for this as the regression will not exihibit exact gaussian properties.

in algebraic terms I have taken the residuals provided by Megaladon and conducted the following regression:

Rt-Rt-1=A + B Rt-1 + e

A and B are estimated coefficients and B is what we test to see if it might be non-zero. Doing this I obtained the following:

            Coefficients    Standard Error   t Stat
Intercept    -0.002609364    0.012480168    -0.209080804
X Variable 1    -0.779522839    0.140841828    -5.534739581

The DF critical value at 2% for this sample size is -3.58, which we compare to the t-statistic of the regression which is -5.5 about. So we can reject the hypothesis that B=0 and conclude there is no unit root.

This tends to indicate that the temp anomolies and CO2 are cointegrated (i.e. trend together over time).

This compares with the other test (Durbin Watson) that gave fairly weak evidence of a correlation (which is a different concept).

Very clear explanation of fundamental concepts.

Question: I've lost the original graph that this concerned, but I presume it was some yearly temperature series (knowing Meg, GISS), which would be expected to show weak autocorrelation.

Running the two tests with a monthly global temperature series would be instructive, since:

we "think we know" that there is a relation of temperature from one month to the next. But when temperature anomalies are averaged over the globe, and one part is doing winter while the other is doing summer, it's not clear that any such relation remains.

 

[fsol]

Very clear explanation of fundamental concepts.

Question: I've lost the original graph that this concerned, but I presume it was some yearly temperature series (knowing Meg, GISS), which would be expected to show weak autocorrelation.

Running the two tests with a monthly global temperature series would be instructive, since:

we "think we know" that there is a relation of temperature from one month to the next. But when temperature anomalies are averaged over the globe, and one part is doing winter while the other is doing summer, it's not clear that any such relation remains.

If you bothered to read posts or follow links...oh well

 

[Geckko]

Here is an excellent piece on the correlation issue and pushes into thinking about causality. For those stats geeks interested.

http://wmbriggs.com/blog/2008/04/21/co2-and-temperature-which-predicts-which/

 

[a_unique_person]

Here is an excellent piece on the correlation issue and pushes into thinking about causality. For those stats geeks interested.

http://wmbriggs.com/blog/2008/04/21/co2-and-temperature-which-predicts-which/

I have already found some non-excellence .

The source of monthly temperature data is from The University of Alabama in Huntsville, which starts in January 1980.

....


The question we hope to answer is, given the limitations of these data sets, with this small number of years, and ignoring the measurement error of all involved (which might be substantial), does (Hypothesis 1) increasing CO2 now predict positive temperature change later, or does (Hypothesis 2) increasing temperatures now predict positive CO2 change later? Again, this ignores the very real possibility that both of these hypotheses are true (e.g., there is a positive feedback).

There are much longer records, that he ignores unknown reasons .

Another point. CO2 is not the only driver of temperature. Assuming it is, will end up giving you incorrect results.

 

[Geckko]

It strikes me as a resaonble and sensible look at the statistical properties of the data, exactly like the charts posted to this thread (in fact furnished as the OP for this thread). The conclusions seem clear, reasonable and properly caveated.

As mentioned above, what we did not check are all the other possibilities: CO2 might lead or lag temperature by 9.27, or 18.4 months, for example; or, what is more likely, the two variables might describe a non-linear dynamic relationship with each other. All I am confident of saying is, conditional on this data and its limitations etc., that Hypothesis 2 is more probable than Hypothesis 1, but I won’t say how much more probable.

 

[Alric]

Except that straightforward statistics are not suitable for a complex system like climate. We have two variables that we know have a physical correlation but with many known and unknown variables that affect and feedback on the system. Lags are unknown, may change over time and may change in magnitude as well.

I keep going back to biological systems. You can not precisely correlate cholesterol level and incidence of heart disease on an individual basis. Some people have very high cholesterol levels and have no problem and others are the complete opposite. However, looking a a population you can verify higher cholesterol levels are associated with an increased risk of heart disease. Your recommendation thus is to advice EVERYONE to lower their cholesterol level.

In the case of earth climate we only have one patient and we know what the correlation between CO2 concentration and temperature is. Notwithstanding DRs and mhaze denial of basic chemistry.

Finally, I don't believe you will find a real paper attempting a statistical correlation between two variables in a complex system. Only to prove the validation, level of confidence of a method, etc. The equivalent of statistics in an unique complex system is modeling. Examples like the one you provide is why statisticians are not scientists by just looking at the data. They have to understand it as well.