A Reader Question

Part of the joy for me in the blogosphere is how it can expose you to things you would otherwise never see. This came up yesterday when a reader, MikeN, asked me:

Do you think Tamino is justified in his criticism here?

The question wasn't really related to anything I had said, but I like random questions, so I took a look at the link. It didn't take long for me to conclude the answer was "not at all." I told MikeN as much, explaining why, but I thought the subject of the question would make for an interesting post. The blogger Tamino had said this near the beginning of his post:

“… the claim that most of the climate change since 1960 is due to human activities, refers to more than half of a change on the order of only 0.5C …”

I’ve heard claims like this many times, and I always wonder: is this person deliberately misleading his readers, or is he that ignorant? You can’t even get that right?

The rhetoric only gets worse from there, labeling the person he referred to, Richard Lindzen, as "dishonest or astoundingly ignorant (or both)" while his commenters went even further. The problem is Tamino's argument depends almost entirely upon cherry-picking. Had he provided a fair and honest portrayal of things, he'd have never been able to use rhetoric like this.

Tamino's post rests upon him providing this graph:


And saying:

The lower dashed lines mark two estimates of the 1960 value, and the upper dashed lines are 0.5C above those. For an honest definition of the “since 1960” value, we might use the smoothed value of -0.046 deg.C, or we can just use the 1960 average, -0.031 deg.C. They’re not that different.

To define the present value, we can use the smoothed value of 0.75 deg.C, the 2015 annual average so far (based on the first 11 months of the year) of 0.845 deg.C, or the average of the most recent 12 months, 0.839 deg.C.

Whichever honest choice you make, the warming since 1960 has been bigger than 0.5C. You could honestly say 0.8C, or 0.88C, or 0.87C. But you can’t say 0.5C without being either dishonest or astoundingly ignorant (or both).

The problem with this is quite simple. Tamino suggests people might use smoothed values rather than the values of an individual year when trying to figure out how much warming there's been. That makes sense. While Lindzen may have referred to warming "since 1960," odds are he wasn't meaning the specific year 1960. There is always year-to-year variation, and we don't want to run the risk of cherry-picking years that might not be representative.

So naturally, what we're interested in is the warming since the time around 1960. We'd estimate that value by taking data for 1960 and the years around it and combining them in some way to create an estimate. If you repeat that process for every year, what you've done is created a "smoothed" version of the temperature series.

Which is all fine and good. Only, there is no one right way to smooth data. If we compare Tamino's graph of the GISS series to the one posted on the GISS website, we see GISS smooths its data in a different way than he does:


Tamino's version of the smoothed series shows much less variation than GISS's version of it. As a result, GISS gives higher temperatures in 1960 than Tamino gives. This can be confirmed by looking at the data file GISS provides for the graph, which says smoothed temperatures for 1960 were 0.03, not -0.046 like Tamino says.

The most recent smoothed values are different as well. Tamino's smoothed value for the most recent times is 0.75. GISS's smoothed value for the most recent times is 0.67. The result is when you compare Tamino's smoothed values, you find there has been 0.8 degrees of warming, but when you use GISS's smoothed values, you find there has only been 0.64 degrees of warming.

Obviously, nobody would take Tamino seriously if he suggested Richard Lindzen had been dishonest for saying there has been 0.5 degrees of warming when he should have said 0.6. This is clear from his post where he says:

This isn’t just “pretty basic,” it’s as basic as it gets. When you underestimate the warming since 1960 by 60% or more, you’re not telling it like it is. Either you don’t know, or you’re hoping readers don’t look for themselves.

The magnitude of the differences in these numbers is important. Saying a person underestimated "warming since 1960 by 60%" may allow you to justify suggesting the person is dishonest, but change that 60% to 15%, or 20%, and you'd just seem silly.

What this means is any fairminded examination of what Richard Lindzen says requires one to look at how these smoothed numbers were created. You may have noticed Tamino shows smoothed values up to 2015, but GISS only goes up to 2012 with its smoothed series. This is because as you get to 2014, you no longer have as much data on the right side as you do on the left. That means you can't calculate smoothed values in the same way you did for 1960. GISS addresses that issue by simply stopping its series when it no longer has enough data on both sides.

Which approach to handling the lack of data at endpoints is better? That's not clear. GISS's approach effectively reduces the amount of information present in the series, but it's difficult to tell if that would be better or worse than any effect that might be caused Tamino's decision to treat points at the end differently than points in the middle. It's particularly difficult because Tamino didn't say how he smoothed his data.

That's right. GISS's approach to smoothing the data is incredibly simple. It just averages the data for each year with the data for the two years before and after it. There are a number of well-known shortcomings with this sort of approach, but it is one GISS is comfortable enough with to use when publishing results. One could hardly fault a person for choosing to use them.

If the choice is between using the smoothed values published by the people you get the data from or using the smoothed values generated undisclosed, custom-rigged methodology Tamino has created for his personal use... I think the choice is obvious. One could probably get results like Tamino's by using a loess smooth by guessing at what frequency paramater value he used. I don't think they could actually reproduce his results though, as last I heard he uses a custom-modified version of the process (which has some interestingly convenient properties at the endpoints, but that's a subject for another day).

The choice isn't between those two options though. A reasonable person could criticize what Richard Linden said. I'd have no problem with someone arguing the approach GISS uses is sub-optimal and shouldn't be relied on when determining how much warming there has been. I certainly wouldn't rely on it myself.

I just think it's ludicrous to criticize a person for saying there has been 0.5 degrees of warming since 1960 while pointing to NASA GISS's data as proof an "honest" person would say there has been at least 0.8 degrees of warming since 1960. GISS itself publishes results which, following Tamino's suggestion to compare smoothed values, would hold there has only been 0.64 degrees of warming.

When it comes down to it, Lindzen's claim there has been 0.5 degrees of warming is closer to the results published by GISS than Tamino's results are. Pointing to GISS in order to portray Lindzen as dishonest when his answer is closer than yours is absurd.

It's fine to criticize Lindzen if you think he has underestimated the amount of global warming there's been. You just need to acknowledge the fact there is a legitimate reason a person might say something like what he said. Pointing to GISS's data while not addressing the fact GISS publishes results that support what Lindzen said just makes you look, in Tamino's words, "dishonest or astoundingly ignorant (or both)."


  1. An even more basic issue is this:
    'When you underestimate the warming since 1960 by 60% or more'

    Even if you take the 0.5 vs 0.8 values, Lindzen's underestimate is 37.5% not 60%. Duh!

    Now, if this came from average Joe I could assume that he simply mixed things up - it happens a lot that people say something is '100% underestimated' or similar when in fact they mean 50%. From a statistician, it could only happen on purpose.

  2. I'm a little forgiving of that because I don't know of any "right" way to come up with percentages for things like this. 8 is 160% of 5, so I can see where the number comes from. I'm with you in thinking 37.5% would be a more appropriate number to use, but I don't know how harshly I'd criticize someone for using 60%.

    I mean, just look at how common it is for people to claim humans have caused more than 100% of global warming. I think that's absurd and that approach to coming up with percentages is meaningless, but... tons of people do it. It makes me feel like maybe I'm the weird one.

    (That last line is just begging for jokes.)

  3. One should also look at the alternative measures. For example, consider HadCRUT4. Applying the GISS 5-year average approach:
    "1960" temperature (Jan1958-Dec1962) = 0.01 K anomaly
    Current (Last 5 complete years) = 0.50 K anomaly
    Latest 60 months (Nov2010-Oct2015) = 0.53 K anomaly

    "1960" (Jan1958-Dec1962) = 0.07 K anomaly
    Current (Last 5 complete years) = 0.66 K anomaly
    Latest 60 months (Dec2010-Nov2015) = 0.69 K anomaly

    "1960" (average Jan1958-Dec1962) = 0.03 K anomaly
    Current (Last 5 complete years) = 0.67 K anomaly
    Latest 60 months (Dec2010-Nov2015) = 0.69 K anomaly

    It doesn't seem "dishonest or astoundingly ignorant" to describe this as "on the order of only 0.5C". But that's Tamino. Or aTTP, or Dana...

    And there is a "right way" to compute percentages: as a fraction of whatever one is comparing to. Given the phrasing "underestimate the warming since 1960", one should use the (presumed) correct value of warming -- Tamino would say 0.8 K - as the denominator. [Alternatively, Tamino could claim something like "the actual warming is 60% more than Lindzen's 0.5C value".] Think how misleading it would be if a store advertised an item reduced from $100 to $50 as "100% less" than the original price! And yes, I agree with you that it's a common mistake, not worthy of a harsh criticism, but it's a mistake nevertheless. Interesting that none of the 48 comments on Tamino's page mentions this.

  4. I hadn't noticed that Lindzen said 'on the order of'.

    Tamino had a post 'On Smoothing' where he included a description of his preference, and yes it is Lowess.
    By jumping to 2015, is he making assumptions about future temperatures?

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