The Blackboard

For some reason, many in comments seem anxious to find that the IPCC projections and their uncertainty intervals must be consistent with the recent weather pattern. The objections are scatter shot, odd, and unceasingly wrong. I will characterize some, and responde:

1. The current falsification of the 2 C/century based on 6 years and 1 month of data doesn’t count, because one can show that 5 year trends with similar slopes occurred during the previous 30 years.

   Sorry William, but statistically, your funky little graphs tell us practically nothing if we assessing whether or not the recent IPCC claims are sound. The reasons they tell us almost nothing are:
   a) the period you selected has a trend lower than 2C/century, so more zero and negative slope periods are expected during that period rather than the recent one,
   b) the period you selected includes three major volcano eruptions which cause the major excursions from the mean trend. Larger variability, in and of itself resluts in a wider range of slopes than would occur during a period with no major volcanic eruptions. (The effect of the variability that occurred is incorported into the uncertainty intervals for the slope obtained using a regression),
   c) the period you selected has a larger serial autocorrelation in the deviations from the mean trend. This is due in large part to the volcanic eruptions which create an autocorrelation in the anomalous forcing. This serial autocorrelation is a very dramatic anomalous forcing further increases the apparent variability of 5 year trends beyond what would be expected during a period with no volcanic activity and finally,
   d) though this is trivial compared to the other inadequacies in your argument, the fact that it’s a five year trend, means that we expect larger variations in your slopes than in my falsification region.

2. The current falsification doesn’t count because the projections into the future data before projections were made.

   Several people have suggested this. In particular, in comments at Stoat, Atmoz wants to include data from before 2001, and to start by identifying a local minimum in the data. William Connelly wants to ‘prove’ that flat trends are consistent with 2C/century by showing flat 5 year trends occurred during the seventies.

   Logically, if the IPCC made projections they ought to be tested against data that arrived after the projections were made. If we do not restrict ourselves this way, we permit the IPCC to “validate” against data they used to make their projections. This is not reasonable.

   But, even more importantly, both projections into the future and hind-casts of past data are based on an underlying theory. That theory itself says that the trend in the seventies was not supposed to be 2C/century.

   It may be ok to sneak a peak at that data to get a gut feeling about whether or not a single falsification is likely to “stick”.

   However, suggesting one can save “predictions” by including data that came in before the predictions were made is cheating. In anycase, when setting up a hypothesis test, we already assumed the IPCC projections were correct at least in part on the basis of past data. So, we cannot, in some sense “re-prove” their correctness based on that same exact same data we used to assume the correctness for the purpose of a hypothesis test.

3. The current falsification doesn’t count unless it falsifies for every possible cherry picked subset pulled out of the full set.

   If one pulls the maximum out of a set, selecting end points based on looking at the data, limited by no rule, one will often be able to get the result one wishes. This is always true for any data set.

   Boris is suggesting that we should start in 2001, and then pretend it’s 2007, ignoring data afterwards. In which case, he guesses the IPCC will over-predict the trend. Unlike others who wish to use data used to make the projections to falsify them, this one wants to use even less data. However, it turns out that if we pretend it’s 2007 is, the central tendency of the IPCC and the uncertainty bands still fall above the best fit climate trend. However, we can’t falsify the IPCC trend based on that string because the uncertainty intervals are too large.

   To apply statistics, one must select a criterion for both validation and falsification. To deny the validity of a proof, one ought to have some sort of specific criterion to pick an alternate set. Simply picking an endpoint as the worst possible one doesn’t work.

4. This falsification doesn’t count because the trend is too short.

   This falsification says that given the length of the trend and the weather data that actually materialized after the projection was made, the IPCC projections are falsified to a 95% confidence level. That means: Given the weather we have had since the IPCC made the projections, there is a 5% chance their projections for the climate trends are correct.

   So, why can others find strings where the IPCC trends are not to falsified? Well, for short tests, the major difficulty is β error is large. In fact, with less than 10 years data, if the trend were 0C/century, we expect β=50% of all 10 year trends calculated based on annual averages would fail to falsify a hypothesis that the underlying trend is 2 C/century or greater. (After 15 years, that β~5%). I discuss this here.

5. The current falsification doesn’t count because the IPCC climate trends don’t include weather.
   No, the IPCC climate projections don’t include weather noise. That’s what makes the appropriate basis for testing!

   If the weather is thought to decompose into a climate trend and weather noise one might suggest that for short periods of time it follows linear relationship:

   T = m t + e

   Where T is the temperature, “m” is the underlying trend– a climate variable stripped of noise, and “e” is the weather noise.

   The current falsification obtains:
   a) the best fit estimate for a climate trend. This trend is a straight line and does not include “weather noise”. That’s the point of obtaining the trend. and
   b) uncertainties in the estimate for the climate trend.

   So, we obtain m_low < m < m_high. These apply to “m”. The IPCC graphic illustrates projections about the trend, “m” stripped of weather noise. That is: that graphic does not include weather, the analysis I did, obtains “m” which do not include noise.

   (It is also possible to get estimates of the standard devaition of the weather noise. Had the IPCC provided estimates for the magnitude of “weather noise” or made weather predictions, we could test those estimates, by examining the variance in the weather noise obtained from the snippet of weather.

   They did not provide the estimate for weather noise. I don’t need them to test their estimate on “m”.

6. Boris suggested the IPCC trends are ok because the only include 1σ confidence intervals.

   He thinks to disprove the 95% confidence intervals for the IPCC projections, I need to show that the 95% confidence intervals for the IPCC climate projections in now wayoverlap the 95% confidence intervals based on the weather realization.
   This is wrong.

   When testing two means with known variances, one cannot simply draw the 95% confidence intervals for both and conclude that if they overlap, they agree to 95%. In fact, that doesn’t work at all. To the right, I have the distributions of hypothetical trends, that may have occurred somewhere, some time. Assume the sample mean obtained using 10 measurements for the first is -2.16 C/century; the mean for the other is +2.16 per century. Assume the sample standard error for both means is 1 C/century. The 95% confidence intervals are shown.

   Note that the two 95% confidence bands overlap. However, if you perform a t-test, using a traditional method and compared the trends, you would discover that the sample means of +2.16 C/century and -2.16 C/century differ from each other with α < 0.01%. You an find the formula for doing this in most statistics textbooks.

   If you think a short while, it will become obvious why the means disagree to a very high level of confidence. To find the probability that the two means are equal to any particular value, we must multiply the two probabilities that “x” falls bewteen “p(x)dx” together and then perform a double integral over all “x”. It turns out that when means are identical, the two distributions must overlap a lot more than most people would guess. (Exact analyses depend on the number of data, and many details the IPCC did not include in their projections. But, basically, if the IPCC ranges is not in the range permitted by experimental data, it’s falsified.)

I think this covers most of the criticisms.

In reality: This falsification stands as what it is. It is one test, that indicates the IPCC projections are inconsistent with weather data that arrived after the time the IPCC made their projections.

Given the wording of some of the criticisms in comments here and elsewhere do recall what this falsification does not show and what remains possible (and even probablie):

1. It does not falsify AGW. The data are consistent with a range of positive trends and the theory of AGW.
2. It does not falsify the IPCC projections for the trends to absolute certainty. No statistical test can do that.
3. If we include the 95% confidence intervals, calculated including serial autocorrelation, for year trends, the recent data is consistent with those trends. It’s just on the lower end.
4. Any trend, including the recent one, can be an outlier. Things that happen 5% of the time, do happen 5% of the time. It is possible the weather will perk up.