I was just pointing out that the trend in Tamino’s ARMA example was pre-concluded. It is on a different Tamino post. He could have achieved the same results with a different pre concluded trend i.e temp starts dropping long term.

On entirely different subject from my post, I still believe that the 95% confidence intervals using ARMA are overstated by using short term variation rather than temp uncertainty. We know the temp better than the variation demonstrates. I do understand the reasoning behind the methods.

Unfortunately for me, my position on this mirrors the problem which some people had with my recent post – a post which did not address this issue in any way whatsoever.

Did you notice though that I took the independent RSS – UAH as the worst case in my post? I basically ignored the best fit GISS – UAH

We have 340 or so values by which we can check the SD of the measurement. I would say that because both SD are included we would be looking at a square root of the sum of the square of the SD of GISS and RSS leading to an ‘over estimation’ of the true error in my post.

Still, I appreciate your understanding of my point, it was missed by many people.

What I will show later today is that even with the full variation of temp included we know the slope is basically negative.

Regarding your last paragraph, Tamino just went after a decade temp trend and gave some bad math to prove it. I actually 100% agree with his previous post where he arma models temp trends and shows the ten year cycle doesn’t end the possibility that temps keep rising. Even though his linear model in that post pre-concludes his result.

Thanks.

I’ve looked at those differences too. I think it’s interesting to examine them, but unfortunately, you are likely to under-estimate the measurement uncertainty in that way. Though, who knows? Maybe the uncertainty associated with the algorithms used to calculate GMST from the measurements dominates the basic measurement uncertainties!

If you are saying that once can say the OLS trend from year N to year M is X, yes. You can. I think you’ll even get Briggs on your side on that one. You can certainly say the temperature on day A is greater or less than on day B without doing a any statistical analysis at all.

It’s only when you start comparing to predictions, projections, models, history etc. that you might want to use statistics to state categorically that models are or are not inconsistent with data.

My quibble with Tamino’s post is that he seems to be rebutting a strawman. To rebut what Lomborg actually says, Tamino needs to show the warming this century is worse than projected and that the amount by which it is worse is statistically significant. As far as I can tell, Tamino doesn’t even try to do that.

I don’t make the point that the earth has entered anything sustained. The question from Tamino is, “how well do we know the trend?”. Several posts on my blog missed that point as well.

By subtracting the difference between three different measurements we can establish the “error” in the measurement accuracy – not precision. This is true because they are different methods. It is quite simple and different from the thinking — how well can we predict future trends or is this a long term trend.

The mistake in Taminos blog and others is using the SD of a single measurement to establish trend. I would like to invite you to come back in about 12 hours to my blog because I will use the full and (incorrect) Weather error to make exactly the same point. I planned to do it today anyway but I really thought people would figure this out on their own.

1- We do know the trend to a very high degree of certainty.
2- We also know the trend is slightly downward.
3- It doesn’t mean anything beyond that

I don’t like the term “weather noise” but it’s endemic to blogs. But, subtracting doesn’t give that, as it is simply defined using some sort of set theory where we imagine a set of all possible weather conditions for some “earth”… blah… blah. The reason I say blah…blah…. is the precise definition for similar earths is rarely stated. Does Pinatubo erupt the same year on all these earths? Or are volcanic eruptoins random.

“Measurement uncertainty noise” is more specific. However, you can’t get that by subtracting either. The reason is the measurement groups draw from overlaping station measurements.

Over all, I think Tamino makes a poor case against Lomborg. However, he is correct to observe that you can’t prove the earth has entered a sustained cooling period based on the current 10 year record. But then, Lomborg doesn’t claim you we have.

You might like my post I just did which refutes the confidence intervals reported at tamino regarding the temp measurement trends.

Tamino made the point that the trend is not valid because of statistical uncertainty. I have demonstrated otherwise.

I didn’t know about your post. I got a somewhat different result by taking the difference between the three measurements RSS, GISS and UAH used at Tamino as the true uncertainty. (I believe this is a more accurate method) And I used the uncertainty of each value to demonstrate the 95 % confidence limit of the slope.

http://noconsensus.wordpress.c.....-did-drop/

If you take the temperature trend to be the uncertainty including the short term but real temperature variations you get a much wider confidence interval. I am interested in what you think.

Long term?
Since 1935-1940 (pick 1938 for convenience) we have had 70 years of steadily increasing CO2 concentration at just over 1% per year.
We have had 30 years of decreasing temperatures of about 1/2 of one degree.
We have had 28 years of increasing temperature of 1/2 of one degree: from 1970 to 1998.
We have had nine years of steady, slightly declining temperatures – followed by now two years of rapidly declining temperatures that have lowered averages back to their late 1980’s peaks.

So, any AGW theorist needs to answer: Why is their theory of man-caused, CO2-induced global warming only valid for 1/3 of the time? Why – if it FAILS to predict 45 YEARS of declining temperatures out of 70 – is it considered valid? 1 month? Clearly too short – one month IS “weather” not “climate”.
One year, two or three years? Still too short. But ten years of declining temperatures IS a valid trend. We just don’t know whether that trend is -.1 degree, – 2 degree, or – 3 degree yet.

Solar-magnetic-cosmic ray interactions predict EVERY short term and long term climate change. But these are rejected because the flat-earth societies are too busy eating cake as they grant each other grant money, igNobel Prizes for power point slide shows, and taxing us trillions of dollars.

You write, “I’ve looked through the TAR, and I did already comment that it’s difficult to dig up precise projections.”

That’s putting mildly! I’ve asked a fairly large number of climate scientists to label these assertions as, “true,” “false,” or “don’t know” regarding the projections in the IPCC TAR:

1) The IPCC thinks that there is an approximately 50/50 chance that the warming will be less than 3.6 degrees Celsius.

2) The IPCC thinks that there is an approximately 50/50 chance that the warming will be less than 3.1 degrees Celsius.

3) The IPCC thinks that there is less than a 10 percent chance that the warming will be less than 1.4 degrees Celsius.

4) The IPCC thinks that there is less than a 10 percent chance that the warming will be more than 5.8 degrees Celsius.

5) The IPCC thinks that there is more than a 50/50 chance that the warming will be less than 1.4 degrees Celsius,

6) The IPCC thinks that there is more than a 50/50 chance that the warming will be more than 5.8 degrees Celsius.

7) The IPCC thinks that there is more than a 99 percent chance that the warming will be less than 1.4 degrees Celsius.

The IPCC thinks that there is more than a 99 percent chance that the warming will be more than 5.8 degrees Celsius.

Only John Nielsen-Gammon had the honesty to (correctly) label all the assertions as “don’t know.”

That is, a reader can read everything in the IPCC TAR, and still not know whether the IPCC thinks that there is more than a 99 percent chance that the warming will be LESS than 1.4 deg C, or a more than 99 percent chance that the warming will be MORE than 5.8 deg Celsius.

In other words, the “projections” in the IPCC TAR are completely invalid, as a matter of science. The make no falsifiable predictions.

And the AR4 is no different. The answer would still be “don’t know,” because the IPCC AR4 makes no assessment of the probability of occurrence of any of their scenarios.

I have also offered to debate any climate scientist, in any forum, this assertion: “The IPCC Third Assessment Report’s (TAR’s) projections for methane atmospheric concentrations, carbon dioxide emissions and atmospheric concentrations, and resultant temperature increases constitute the greatest fraud in the history of environmental science.”

None has ever done so, because they’d lose.

Year IPCC Report: e.g., 1990
1. Projected Central Tendency Slope(Deg/Decade): e.g., 0.315
2. Regressed Historical Slope (Deg/Dec): e.g., 0.20
3. Approx. Degrees of Freedom: e.g., 53
4. Standard Deviation of Regressed Slope (Deg/Dec):e.g., 0.035
5. Statistic ( 1 – 2 )/ 4: e.g., 3.2

1. Projected 2. Regressed 3. Approx. 4. Standard 5. Statistic
Central Slope Degrees Deviation ( 1. – 2. )/4.
IPCC Tendency HadCRUT3 of of Slope 2.
Deg./Decade) (Deg/Decade) Freedom (Deg./Decade)
1990 0.315 0.20 53 0.035 3.2
1995 0.17 0.14 38 0.071 0.4
2001 0.20 – 0.16 20 0.105 3.4
2007 0.20 – 5.34 2 2.47 2.2

A few remarks:

1. The table results are essentially Lucia’s analysis for 2001 (but for Hadley only) extended to the other three IPCC projections.

2. Of the four attempts, 1995 does the best, in agreement with visual inspection. The other three lie outside the usual range of statistical uncertainty.

3. The 2001 numbers appear to be very close to Lucia’s values. They should differ slightly because I used only Hadley data vs. her average of four data sets, and I included February 2008.

4. One might be tempted to throw out 2007 because of the small number of DOFs, but that effect is included in the large standard deviation. And it so happens that the r2 for the trend is pretty good (0.76) and correlations for this epoch are small. In any case, as will be seen below, it does not make much difference.

Now the question is, what do these values mean for the class of models? Can one make a statement about the collective accuracy of the models projections over nearly 20 years of records? I take the 4 IPCC projections as independent attempts to project the historical temperature trend in different epochs. This is not strictly true since the four epochs overlap to varying degrees. I use the four values of the statistic in the fifth column of the table to define a best estimate for the mean value of the difference between models and historical actuals, in units of the standard deviation of the historical actuals. Those four values also allow an estimate the standard error of the mean for the four attempts. This gives a mean of 2.3 standard deviations above the set of historical trend lines, with a standard error of the mean of 0.60. Then the statistic for the group of four “measurements” is 2.3 / sqrt ( 1 + 0.6^2) = 2.0. By this reasoning, the class of four attempts by IPCC models to project future climate falls outside statistical uncertainty; p = 0.98 that they are too high. This number drops only slightly to 0.97 if you throw out 2007.

I’ll welcome any comments on the validity of this approach or suggestions for how to deal with the model class problem. Even better I’d be happy if the pros did it. Am sending this to Roger Jr. and Matt Briggs.

1. Projected 2. Regressed 3. Approx. 4. Standard 5. Statistic
Central Slope Degrees Deviation ( 1. – 2. )/4.
IPCC Tendency HadCRUT3 of of Slope 2.
Deg./Decade) (Deg/Decade) Freedom (Deg./Decade)
1990 0.315 0.20 53 0.035 3.2
1995 0.17 0.14 38 0.071 0.4
2001 0.20 – 0.16 20 0.105 3.4
2007 0.20 – 5.34 2 2.47 2.2

A few remarks:

1. The table results are essentially Lucia’s analysis for 2001 (but for Hadley only) extended to the other three IPCC projections.

2. Of the four attempts, 1995 does the best, in agreement with visual inspection. The other three lie outside the usual range of statistical uncertainty.

3. The 2001 numbers appear to be very close to Lucia’s values. They should differ slightly because I used only Hadley data vs. her average of four data sets, and I included February 2008.

4. One might be tempted to throw out 2007 because of the small number of DOFs, but that effect is included in the large standard deviation. And it so happens that the r2 for the trend is pretty good (0.76) and correlations for this epoch are small. In any case, as will be seen below, it does not make much difference.

Now the question is, what do these values mean for the class of models? Can one make a statement about the collective accuracy of the models projections over nearly 20 years of records? I take the 4 IPCC projections as independent attempts to project the historical temperature trend in different epochs. This is not strictly true since the four epochs overlap to varying degrees. I use the four values of the statistic in the fifth column of the table to define a best estimate for the mean value of the difference between models and historical actuals, in units of the standard deviation of the historical actuals. Those four values also allow an estimate the standard error of the mean for the four attempts. This gives a mean of 2.3 standard deviations above the set of historical trend lines, with a standard error of the mean of 0.60. Then the statistic for the group of four “measurements” is 2.3 / sqrt ( 1 + 0.6^2) = 2.0. By this reasoning, the class of four attempts by IPCC models to project future climate falls outside statistical uncertainty; p = 0.98 that they are too high. This number drops only slightly to 0.97 if you throw out 2007.

I’ll welcome any comments on the validity of this approach or suggestions for how to deal with the model class problem. Even better I’d be happy if the pros did it.