Sea Level Rise: What the Data Actually Shows

Someone recently pointed to a post by Norman G. Purves at “Climategate Country Club” about sea level rise.

Purves compares statements from the Univ. of Colorado at Boulder sea level change website to his own “analysis” of the “data.” He concludes:

… the difference between a straightforward line-fit to these data, and the results of the UColo group, strongly suggests that Climate Researchers have done some fishy things with this data.

Finally, these results should stand as positive proof that anthropogenic global warming is having no measureable effect on sea-level. At least in regard to sea-level, the current assertions of the “Climate Change Researchers” are without any scientific foundation.

He begins by showing this graph from the U. of Colo website:

He objects, saying

There were some things about this chart that bothered me; first, the “60-day smoothing” of this data suggests a cyclic trend in the sea-level measurements that is simply not evident in the actual data; second, the line-fit to these data simply didn’t look right to me.

Then with a hearty “So, I obtained the actual data from TOPEX/Jason and did my own analysis,” he shows us his own graph:

What he fails to mention is that his graph isn’t of the same data.

The minor point is that his graph is of data with the inverse-barometer correction applied, whereas the U.Colo. graph he shows does not have the inverse-barometer correction applied. But really, that’s minor compared to the fact that the U.Colo. graph is of global sea level, Purves’s graph is for the Pacific Ocean only.

Even accounting for using different data, Purves still can’t get the analysis right. He says “the “60-day smoothing” of this data suggests a cyclic trend in the sea-level measurements that is simply not evident in the actual data,” and “Note that any periodic variation in sea-level (such as suggested by the “60-day smoothing” done by UColo) is not at all evident in the data,” and “The tolerance of the spacecraft’s orbital position renders UColo’s “60-day smoothing” absurd. There simply is no cyle to be measured here. The blue curve in UColo’s graph is, therefore, complete nonsense.”

Let’s take the data he uses, subtract a linear trend, and do a Fourier spectrum of the residuals to look for periodic variation. Here ’tis:

Well well! There’s quite a peak in the periodogram, at period P=1 year. That’s periodic variation. We can even do a close-up of the frequency range from 0 to 4 cycles/yr:

Not only do we see the undeniable peak at period 1 yr, we also see two higher harmonics of that period. There’s no doubt about it: these data (yes, the data shown by Purves) show a periodic variation. How could he have missed that? Maybe … when it comes to time series analysis, he doesn’t know what he’s doing.

As for the 60-day smoothing applied by U.Colo., that turns out to be an especially good choice. Look at the periodogram from frequencies 4 to 8 cycyles/yr:

There’s a clear peak at frequency 6.197 cycle/yr, corresponding to period P=0.1614 year. That’s 58.94 days, which is suggestively close to twice the lunar month. So, there appears to be another periodic variation in the data, which may be related to the lunar month (and to the tidal cycle). By smoothing on a 60-day time scale the U.Colo. smooth actually removes that cyclic variation, which emphasizes the long-term trend over the short-term cycle.

In fact for the best picture of the long-term trend, you’d want to remove the 1-year periodic variation as well. I guess that’s why U.Colo. also supplies data with the seasonal cycle removed, to further emphasize the long-term trend over the short-term cycle.

Purves makes other, rather silly mistakes. For instance the comment about how “The tolerance of the spacecraft’s orbital position renders UColo’s “60-day smoothing” absurd,” is itself absurd. The spacecraft tolerance has nothing whatever to do with the appropriateness of a 60-day smooth.

But, pointing out all of Purves’s absurdities is hardly necessary. After all, not only did he not get the analysis right, he didn’t even show the right data. Besides, it would take too long.

Maybe some interested reader should post a comment at that site. I wonder whether it’ll be allowed through?

30 responses to “Sea Level Rise: What the Data Actually Shows

  1. I checked out his post at the CCC site and noted right away 3 interesting items:
    -He just had to bring Gore into the post.
    -Even though his own work shows sea level rising (at a much lower rate), he twists that into a “…very strong downward trend.”
    -And finally, he decribes himself as an astronomer by training.

    What is it with these guys?
    The Al Gore obsession, twisting the facts and somehow thinking that since they have training in one field of science that makes them experts in other fields of knowledge??

  2. Can you tell us something about those freq. below 1 cycle/year? First two peaks have more power than the one corresponding to the lunar cycle, especially first one.

    [Response: They’re not indicative of genuine periodic behavior. Instead they’re low-frequency response to the combination of the nonlinear part of the trend, and the strong autocorrelation between the data series. The lowest frequency, e.g., corresponds to a “period” of 12.3 years, but it can’t be considered demonstrative of periodic behavior in a time series only 17.3 years long — there hasn’t even been enough time for such a putative “cycle” to repeat (and repetition is the hallmark of periodicity).

    You’d get similar low-frequency response from red noise, or from a low-order polynomial, or their combination. Not periodic.]

  3. arch stanton

    >”post a comment”

    Posting to CCC requires registration at Ning ID social networking platform.

    Although their privacy policy starts out with: “We value your privacy,” if you read the details they are not so reassuring considering the discclaimer they provide considering third party data collection.

    More from Wikipedia:

    “On May 4, 2010, Ning Network sent official email to all members saying:
    “ We want to provide a new level of innovation to Network Creators — and build all the valuable features Network Creators have asked us to. To get there, we need to focus 100% on paid Ning Networks. This phasing out of free services won’t happen until July, so you’ll have plenty of time to weigh your options. We’ll do our best to provide you with a migration path if you don’t wish to continue with Ning, but we’d love to have you come along for all of the exciting future developments””

    I know it sounds lame but I promised my wife that I would avoid places like this, along with providing the personal data they require.

    [Response: Very wise too. How very “country club” of them. I was unaware of the requirements for commenting. Don’t go there!]

  4. Tony O'Brien

    60 day smoothing, 2 lunar cycles smooth out the monthly tidal movement. No?

  5. The 60-day cycle in this data is related to the precession of the orbital plane of the TOPEX/Poseidon, Jason-01 and Jason-2 satellites. The orbital plane rotates (precesses) around the Earth every 60 days.

    Neil White

  6. Watching the Deniers

    Thanks, great dissection of the tricks used by such climate “auditors”.

    I call this the “Google Galileo” phenomenon:

    “Google Galileo: an individual whose knowledge of a scientific discipline is restricted to information sourced from Google, Wikipedia or other online sources (i.e. blogs). Within a period of a few weeks/months the feel confident to not only dismiss an entire discipline of science, but have gained the ability to “practice science” by commenting on online forums and constructing alternative theories using raw data obtained freely from public sources.

    When confronted with evidence or arguments that contradict their position, they retreated into the “Galileo was persecuted for his beliefs!” defence, imagining the gales of laughter emanating from the scientific community is a form of persecution. “

  7. Thanks, Watching the Deniers.
    Your Google Galileo post should be required reading for anyone using the net.
    You have given me much to think about.

  8. Enjoyed that, Tamino; thanks. One small typo:

    “4 to 8 cycyles/yr:”

    That’s cycles, of course.

  9. As a tidal and sea-level specialist I am frankly amazed by you use of Fourier Analysis to discern tidal signals.

    Why are you not using the very well established tidal harmonic analysis techniques?

    Fourier analysis has a very small place in tidal analysis – but only on analysis of residuals after tidal harmonic analysis has been performed.

    [Response: The subject was periodic variation in sea level data. Fourier analysis is a perfectly good way to detect and quantify it. Please don’t embarrass yourself by claiming it isn’t.]

  10. carrot eater

    “Climategate country club”? Whatever will the internet send up next?

  11. Jerry: “As a tidal and sea-level specialist I am frankly amazed by you use of Fourier Analysis to discern tidal signals.”

    As a graduate of grade school, I am frankly amazed by you(r) reading comprehension.

    Which part of

    “Note that any periodic variation in sea-level (such as suggested by the “60-day smoothing” done by UColo) is not at all evident in the data,”

    did you fail to parse?

  12. The rate of increase is also increasing. If you are lucky enough to find older U Colo graphs on The Interwebs, you will see that the rates in the past were less than they are today.



  13. John Mashey

    Climategate Country Club:
    I think this is an effort by Mark Gillar, aka Dash Riprock III, creator of Hooterville Gazette. He is a big fan of Monckton’s, and although he lives a few miles from Texas A&M (which Monckton visited), he seems unable to get over there to talk to real climate scientists there. I tried, a while back, then gave up. Climate anti-science now appears to be his career.

  14. AndrewAdams

    That Google Galileo piece is great, although I guess those of us without any serious scientific qualifications who argue the case for AGW should be wary of falling into some of the same traps.

  15. Ray Ladbury

    Andrew, there is a huge difference between an amateur attempting to learn and elucidate the consensus of experts and an amateur thinking that they’ve overturned the consensus of experts. The former is autodidactic, while the latter is Dunning-Kruger.

  16. Can someone help me out here?

    Purves is saying the UColo graph, showing a clear trend in sea level rise, is nonsense.

    Even allowing for him being totally wrong as demonstrated by Tamino, he puts up his own interpretation of the sea level data, showing a clear trend in sea level rise, and says “now this is what’s really happening”.

    Then he further picks another section of his data to demonstrate the scandalous bit of all this – a continuing (albeit lesser) trend in sea level rise.

    “I have re-analysed the data and am about to demonstrate to you the obvious fraud of global warming: as you can see here, my new data clearly shows global warming effects which are slightly different to the global warming effects shown by the scientists! HA!!! How’s that?”

    Very clever indeed. I never would’ve thought of this tactic myself.

    • What help did you need? You sound like you’ve pretty much grasped it.

      • OK, no probs. I just wanted to be sure I wasn’t misunderstanding the crux of his argument: that demonstrating that one of the scientists’ basic predictions of global warming is correct (ie, sea levels are continuing to rise), shows it’s all a big fraud. ;)

        No doubt about it – these sceptics have really helped me deeply explore my inner rationality.

      • I know. It’s all so “Alice-through-the-looking-glass,” isn’t it?

        I think of Steve Goddard, who tells us implicitly (by writing a commentary on it) that the return of sea-ice extent to near-average numbers is important, but two months later describes the crash of the same numbers as “not interesting.”

        I do believe that such a lack of logic or even simple coherence must become evident to a larger percentage of people (and maybe is even doing so to some extent now.) But it’s still pretty disturbing on some level to watch.

        Maybe that’s one reason some (including me) tend to mock the worst examples: laughter is better than some of the alternate emotional responses. And the levels of divorce from basic sense, from proportion, from reality, can be deeply sad and frightening.

        To come clean, I should say that for me at least, they ARE deeply sad and deeply frightening–as well as funny. Call it tragicomedy.

  17. Kevin McKinney // May 27, 2010 at 11:49 am

    PIOMAS has dropped the current [May 24] estimated negative anomaly of sea ice volume by another 500 cubic kilometers since their previous update on May 13.

    It Ain’t True They Say [which is no surprise].

    • I’m not surprised. The maps on CT have been suggesting to me that there’s a lot of thin ice, and the IJIS value for the 27th was within (IIRC) a few thousand square kilometers of the lowest value for that date in that data. (Ie., May 27, 2006.) Looks like a very real chance exists that the track could cross below 2006 values.

  18. Well, that didn’t take long: today’s IJIS value:

    11,162,188 km2 (May 28, 2010)

    May 28, 2006:

    11,199,844 km2

    IOW, today’s IJIS sea ice extent is the lowest in that record.

  19. Of course, I meant “lowest May 28 in that record.”

  20. IJIS adjusted it up to 11,211,719 – there’s almost always a small upwards adjustment some hours after they put up their first number.

  21. One or two more days should do it for IJIS. My question is why the non-trivial discrepancies between Bremen and IJIS?

  22. Jacob Mack

    Great job Tamino.

  23. > discrepancies
    It’s been discussed before, this may help:

  24. OK, now IJIS is at a record low for the date (ie., May 31)–11,059,688 km2.