by Ross McKitrick
I recently published an op-ed inside financial articles describe the findings of new JGR paper by NOAA’s Zou et al. NOAA’s STAR series of troposphere temperatures based on the MSU satellite is used to show more warming than mid-tropospheric UAH or RSS. Chau et al. recently rebuilt their dataset and now STAR tends to be slightly lower than UAH. This is a big deal because it adds evidence that the GCMs are warming up far too much from the observations, which suggests there is a problem with their climate sensitivity (ECS) values.
In subsequent discussion on Twitter and elsewhere, some have criticized me for not heeding Zou et al’s observation that the rate of warming appears to be accelerating, with a trend after 2001 is twice that of the entire series. Aside from the space limitation in an op-ed, there are two reasons why I’m not discussing that topic.
First, not too long ago, many skeptics pointed to the slowing warming after 2001 as evidence that the models were unreliable. The modelers’ response was emphatic that we must look at the entire data set to get the right long-term picture. In short, small timescales, natural variability can cause deviations above or below the trend, the argument goes, but this does not detract from the reality of steady warming rates over the long term. Perhaps the same logic still applies. This was especially the case when there was a pair of strong El Niño events after 2015 that pushed the troposphere average temperature above the trend. Of course, you’ll get a clear acceleration if you compare a short sub-period ending in 2020 with a trend using an earlier pattern.
Second, if we want to check if the heating rate changes, it needs to be done properly. Zo and associates. presents some suggested calculations but does not test the official statistics. Suppose we have a data series Y
Y
Where a0 ARRIVE a3 are the regression coefficients, Y
This form of regression allows us to check if the trend changes after the date g. in the previous periodg about D(g) = 0 so the intersection is given by a0 and the trend is given by the coefficient a2. in post-g about D(g) = 1 so the intercept is given by the sum of a0 + a1 and the trend is given by the sum of a2+a3. So a1 measures if there is a step change and a3 measures if there is a change in trend between before and afterg Cycle. To check if there is a significant change in the trend, we use a F (or t) limit test a3 =0. If P-the value in this test is higher than 0.05, we do not reject the null model and we can conclude that there is no significant acceleration (or deceleration). Note that this allows for the possibility that there is a single step change at gbut no trend change.
To do the test properly, two other problems need to be solved, I’m only addressing one of them here. First, the error terms e
[Digression: This further assumes that Y
The second problem concerns how g is choice. It is tempting to treat it as an unknown parameter and estimate it using informal grid search. You can do it, but then you need to take into account the fact that you have estimated it. It is common to experiment with values of g based on looking at the data series itself. This is the total tropospheric temperature (TTT)-Global series from Zou et al.
If you insert breakpoints at different points to see what happens, this is equivalent to processing g as an unknown parameter is evaluated, but then inferences about other parameters are conditional based on the value of g. we we carry normally F check without taking into account the fact that g has been estimated, we will use imprecise significant values and exaggerate the significance of the test scores. Tim Vogelsang and I discussed this in a paper 2014 IN environmental measurement.
I’ll ignore this for now but I’ll comment on it as we move on. I received from John Christy new NOAA data showing monthly TTT-Global and TTT-Tropics data (TTT=Total Troposphere Temperature) from 1979:1 to 2022:12. i allow g varies from month to month from 1990:1 to 2012:12, so always allow at least a decade before and after the holiday. For each position of the breakpoint, I estimate the regression model described above and calculate F-limit test a3 = 0 using the Hypothesis Linear command in R with a Newey-West covariance matrix.
The chart below shows P-the value of the test is plotted during the assumed holiday. The dotted line represents the 5% significance level. Whenever the green or red line is below the dotted line, we reject the null hypothesis; in other words, we have evidence of a significant change in the conditional trend on that breakout day.
Looking at the global series (green), which places the break point on most samples, there is no evidence of an acceleration but there is a short period from late 2005 to mid 2006 where if you put the breaking point there, you can ask for proof of a significant acceleration in warming. But then the tests go back to the non-rejection region, meaning the apparent acceleration is only temporary. Also, we need to take into account the fact that we have chosen the date and since P-values are too close to 0.05, any upward correction to critical values will mean that the rejection is no longer strong. Overall, the TTT-global chain does not support the claim of an accelerating trend. More evidence is provided by the red line. If global warming in the troposphere is accelerating, this will probably happen in the tropics as well. However, looking at the red line, we see very clearly that there is no evidence of an acceleration regardless of the selected holiday.
The next figure shows similar results for the global LT (lower troposphere) and MT (middle troposphere) sequences. There’s a bit more evidence of acceleration, especially in the MT class. But again, you have to choose a day off, and even then, the tests will roll back to the non-rejected zone if it’s set after mid-2011. Therefore, for most records, we will conclude that there is no solid evidence of trend acceleration, even without adjusting the critical values for the fact that g is not known.
Regarding the mid-troposphere sequence, we can say that there is preliminary evidence of acceleration, but the checkpoint reverses after 2010 so this is not a permanent feature of the data yet. Here is the global MT time series from NOAA v5.0. The linear trend is 0.092 degrees Celsius per decade. On the surface, it looks like the record spiked in 2015 and has been back on trend ever since. It will take another 5 years of data or more to determine the permanent acceleration.
In conclusion, based on preliminary analysis, the new NOAA data do not support the claim that tropospheric warming has experienced a statistically significant change in trend. The global and tropical TTT series shows no support for the claim. The Global MT line seems to show support but only when the interrupt data is set to a specific time period early in the last decade and more recently, the tests do not support acceleration. Ultimately, all of these results are biased towards finding evidence of a trend break due to processing g. Strong critical values can be created, which I might achieve someday if no one else does it first.
