In a previous post, I showed the Lower Stratospheric Temperature Anomaly (TLS) Trends (link). A reader submitted the following comment:
“The lower stratosphere temperature profile is essentially flat from ca. 1995 to the present. This approximately mirrors the temperature trend for the surface temperature. From 1980 to about 1995, the surface temperature increased while the lower stratospheric temperature decreased. After that both went flat.” tony
In the words of Edwards Deming:
In God we Trust, All Others Must Bring Data”
Since tony didn’t bring any data to back up his claims, I’ll do the analysis for him.
First, here’s the trend chart tony discussed.
Tony’s Claims
- The lower stratosphere temperature profile is essentially flat from ca. 1995 to the present.
- After that [1995] both [TLS & TLT] went flat.
Tony apparently eyeballed his findings after looking at my chart. Eyeballing climate trends is not wise, climate trends usually have a lot of variability that can fool the eyes, regression is a much more effective method.
Assessing Trends: Eyeball versus Regression
tony focused on post 1995, so I’ll chart data after 1995. tony says the TLS and TLT data went flat. I’ll use the 1995 – 2011 (so far) mean to represent the flat trend (green line) and I’ll use a gls regression trend (red) line for the regression based trend. The chart below shows the results for both TLS and TLT:
Let’s see how tony did:
- “The lower stratosphere temperature profile is essentially flat from ca. 1995 to the present. “Wrong – The TLS actually had a slight positive trend of 0.006/year. To be precise, this slope is not significant @ 95%, so tony would have been correct if he said “statistically flat” .
- “After that [1995] both [TLS & TLT] went flat.” Wrong. The TLT had a 0.012/year trend. This slope is statistically significant @95%, so tony has no wiggle room here.
tony got claim 2 completely wrong and a partial credit on claim 1 if he meant to say “statistically flat”.
My Conclusion
Deming was right! In God we trust, tony and everyone else must bring data! Eyeballing climate trends is not reliable. While time series regression has problems (link), it is wiser to show a moving average or regression rather than rely on eyeball interpretation of trend lines.
Here is my RClimate script (link) if tony or anyone else wants to check my analysis.
Amazing work, well done.
I introduced your blog on my Farsi/Persian Climate Change website and hope more people from Iran will come here and enjoy your interesting material. I would also try to come here time to time and translate some of your new content and link back to the original posts.
Remember that “statistical significance at the 95% level” is arbitrary. If done classically, need to impose a loss function of some kind. If want to be more modern, need to compare the likelihood of the Red Line model versus the Green Line model.
Hey Kelly, I’ve gotten a little off track with my learning R stuff. Need to get back on the go with it! I was wondering if you could possibly at some point do a small post on regression/multiple regression with the GLS model.
I was also wondering whether you had ever ran a Shapiro Wilk test for normality before
http://en.wikipedia.org/wiki/Shapiro%E2%80%93Wilk_test
Tamino mentioned to me that it would be appropriate for some datasets I was working on.
I would take issue with your distinction between “flat” and “statistically flat,” as there can be no trend that is not statistically significant (though some statistically significant trends may not be of practical significance).
It seems to me that there is a bigger problem with the use of regression to analyze the TLT data. Regression assumes that you have a homogeneous population from which you’re sampling; that the data represents a single population and so can be modeled by a single regression. The TLT data appears to have several different things going on, as though conditions changed (statistically) significantly in the 1995 – 2010 period (e.g. the bumps in 1997 – 1998 and 2008 – 2009). While a simple regression would seem to address the question of flatness over the period, nonhomogeneity in the data would make such analysis questionable.
Regarding Tony’s observations, it seems to me that there is another view of this data. Rather than a drop in temperature anomalies in the 1980 – 1995 period that has “flattened out” post-1995, it looks like several “flat-ish” periods punctuated by the El Chichon and Pinatubo events, which include longer-term decreases in temperature anomaly.
Both ts exhibit significant autocorrelation that must be considered. As a first estimate of possible influence I used
gls(…, correlation=corARMA(p=1))
Looks like a tightrope walk to me.
Hmm, your models don’t even come close to fitting the data well, and so fail the major assumption of linear regression that the postulated model correctly describes the relationship between the response and the predictor(s). I no more trust your statistical models than Tony’s eyeballing of the data.
Furthermore, you make the mistake of attaching exactness to “lower stratosphere temperature profile” trend and that it has meaning. It would be highly unlikely to get any trend that was perfectly, exactly zero. Following your line of argument, if you’d achieved anything other that a true zero slope you’d have claimed Tony was only partially right. This make no sense. Are the data consistent with the hypothesis of no trend in this case? Yes, therefore we must conclude that there is no trend that we can determine from the inherent uncertainty in the model and the stochasticity of the process being modelled.
You note correctly that I “didn’t bring any data to back up [my] claims” and that I merely eyeballed data provided by RSS through your website. Datasets such as this one, which monitor some climatic measurable (e.g., temperature) as a function of time, have, to my knowledge, no theoretical basis for any specific functionality whether linear, polynomial, exponential, etc. To see a big fat linearly regressed line through the data often tends to obscure some interesting features as, I believe, it does in this case. In your new graph for TLS covering 1995 to the present, you get a slope of +0.00636 K/yr (relatively flat) compared to -0.0305 K/yr (about 5x the previous magnitude with the opposite sign) for the entire time period. This is possibly a feature of note.
With regard to the TLT data, my memory failed me and I was too busy (to be read “lazy”) to look up the data prior to contacting you.