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Rahmstorf (2011): Robust or Just Busted (Part 2) – Quadratic Fits of Laughter

July 6, 2012

This is part 2 of a multi-part series about “Testing the robustness of semi-empirical sea level projections,” Rahmstorf, et. al., Climate Dynamics, 2011. You can see an index of all parts here. I frequently refer to this paper as R2011.

I will refer to Stefan Rahmstorf’s “Testing the robustness of semi-empirical sea level projections”  as R2011 [1].

This post is all about fitting sea level data to a quadratic.

There is only one reason to fit sea level vs. time data to a quadratic: to highlight an acceleration trend.  It only makes sense to do so if you think that the trend is more or less uniform over time.  I have warned against reading too much into a quadratic fit, and especially against using a quadratic fit to imply a future trend in sea level.

I have seen something in R2011 that I have never seen before.  The use of a quadratic fit as a kind of “optical delusion.”

Consider the image at the right.  Do you see the triangle?  Sure you do.  Of course, it is not really there.  But what would you say if I insisted that the triangle really was there and said “The circles are shown merely to help the eye find the triangle?”

R2011 has done much the same thing with a quadratic data fit in their figure 1.   I would think what they have done was just a joke, if it weren’t such an obvious attempt to convince readers that the data says something that it does not say.  Take a look…

Figure 1 from "Testing the robustness of semi-empirical sea level projections" (Rahmstorf, et. al., Climate Dynamics, 2011)

Note the dashed grey lines through each data set.  As R2011 explains in their caption, these dashed  grey lines which pass through all the data sets, are actually the quadratic fit to just one of the data sets (CW06)[2].  They say

“The dashed grey line is a quadratic fit to the CW06 data, shown here merely to help the eye in the comparison of the data sets.”

The point the R2011 wants to make, of course, is that all of these data sets have the same acceleration trend as R2011’s preferred sea level data, CW06.

But that is not true.  In fact, if you fit any of the other data sets to a quadratic you will see that every single one of them has a lower trend than CW06 when projected through the 21st century. Every single one of them.

The following figure shows proper quadratic fits to all the sea level data sets used by R2011 in their figure 1.  The legend shows the sea level rise that would result for the period 2000 to 2100 if these quadratics were extrapolated to 2100.

Quadratic fits for all sea level data sets used by R2011 in their figure 1. The legend shows the sea level rise that would result for the period 2000 to 2100 if these quadratics were extrapolated to 2100
Quadratic fits for all sea level data sets used by R2011 in their figure 1. The legend shows the sea level rise that would result for the period 2000 to 2100 if these quadratics were extrapolated to 2100

Updated Holgate data

Science is about constant refinement of theories and data.  When Rahmstorf is faced with old data and new data from the same authors, he has a special method for deciding which data set is better.  The version that points to higher sea level rise in the 21st century is always considered to be better.  Thus his insistence that the 2006 Chuch and White sea level data is  better than the 2009 or 2011 Church and White data that incorporated Church’s and White’s data reduction improvements.

The same is true for Holgate’s sea level data.  Look at HW04 [3] plots in the above graphs.  This Holgate sea level data covers the mid-1950s to the mid-1990s.  It is a curious thing (not really curious if you understand Rahmstorf’s modus operandi) that R2011 chose this data over Holgate’s updated data from 2007 [4], which covers the entire 20th century.  What would happen if we replaced the HW04 data with the 2007 Holgate data (H07)?  Take a look…

Holgate data from 2004 has been replaces with Holgates updated data from 2007.
Holgate data from 2004 has been replaces with Holgates updated data from 2007.

Let me stress again, I do not recommend extrapolating sea level data with quadratic fit, and I am not endorsing any of the extrapolations shown above.  I am simply guffawing at Rahmstorf’s chuzpa in his figure 1.

______________________

1.  Rahmstorf, S., Perrette, M., and Vermeer, M., “Testing the robustness of semi-empirical sea level projections” Climate Dynamics, 2011

2. Church, J. A.,, and White,  N. J., “A 20th century acceleration in global sea-level rise,” Geophysical Research Letters, 33, 2006

3. Holgate, S. J., Woodworth, P.L., “Evidence for enhanced coastal sea level rise during the 1990s,” Geophysical Research Letters, 31, 2004

4. Holgate S., “On the decadal rates of sea level change during the twentieth century,” Geophysical Research Letters, 34, 2007
……..

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9 comments

  1. After I read your post, my first thought (about Rahmstorf) was ‘what a fool’.


  2. What is the quadratic fit for Church and White 2009 and 2011?

    What are the extrapolations if you do a quadratic fit using just the most recent 50 or 75 years?

    I played around with sea level data a few years ago and if I recall correctly, the best fit (lowest rms residuals) to CW06 was two straight line segments with the breakpoint around 1930.


  3. Analysis of the data using a quadratic equation isn’t a bad idea, just the imposition of a desired one, and justifying the departures as variances due to error bars (which, in essece, what R did). Your analysis shows 4 of the 6 do generate a decent trend of increasing sea-level rise. Which is interesting, HOWEVER ….

    The data is supposed to reflect the world, not remake it. If we take the trends of the 4 to reflect reality, then let us not focus on the end result, but the near result. I cannot determine what the current trend is, but I see that the four indicate that the average rise over the next 88 years lies between 2.5 and 3.7 mm/yr. Without including isostatic rebound (a cheap term to make flooding look worse than it should), the current rate is about 2.7 mm/yr as claimed in the alarmist literature. So the average projection of 2.5 – 3.7 over the next 88 years is actually good, saying that today must be LESS than 2.7 (or 3.1) mm/yr. Which is kinda interesting, right?

    But let us consider the end-result. Hmm. I’m not sure I’m worried by any of R’s stuff. Even a 3.7 mm/yr average to 2100 is only 0.322 m, or 1.06 feet or 12.6 inches. Not one meter, let alone six. This should make Gore roll over on his massage table.

    How does CAGW fit into any of this?

    Perhaps I’m missing your point; R’s work, I thought, meant a lot to the warmists’ narrative. This discussion about trends would therefore be more than pointing out anacademic, though correct errort. But R’s work, and yours, seems to show that R is showing that CAGW has no basis in observational data on sea-level rise!

    Since sea-level rise is seen to be directly related to temperature rises in Greenland and Antarctica (for melt) plus sea-water expansion, the low trends suggest the temperatures are not rising at a rate sufficient to INITIATE the melting of significant ice mass. For an additional 1m rise by 2100, we’d have to have 11.4 mm/yr average, or 3.0 -4.5X the current rate. This isn’t going to happen in the next two years (though I would love it if they would predict it will!). Which means that even the beginning of CAGW is still in the future despite the claims of Hansen et al that we are in the process already.


  4. Holgate 07 is hardly an update of HW04.

    HW04 is a global series with 177 stations, while H07 consists of 9 stations.


    • Dear Anonymous,

      Thank you for the comment. I am sorry that you do not like the word “update.”

      However, your statement “HW04 is a global series with 177 stations, while H07 consists of 9 stations” is a partial truth that downplays the significance of H07.

      HW04 covered the years 1955 to 1998. H07 extended that coverage from 1904 to 2003. Here is what Holgate says in H07…

      In a previous paper, Holgate and Woodworth [2004] (hereinafter referred to as HW04), rates of mean ‘‘global’’ sea level change (i.e., global coastal sea level change) were calculated from a large number of tide gauge records (177) for the period 1955–1998. HW04 found that the highest and lowest rates of change in the 1955–1998 period occurred in the last 20 years of the record. In this paper it is examined whether a few high quality tide gauge records can replace the many used by HW04. On the basis of these high quality records the work of HW04 is then extended back to the early twentieth century to examine whether the rates of sea level change experienced in recent decades are unusual.

      and

      The nine stations selected here as high quality records capture the mean decadal rates of change described by the larger set of stations used in HW04 and also have a similar global mean rate over the common period of the two analyses (1953–1997). This provides confidence that the nine station set can be used to study decadal rates of global mean sea level change throughout the twentieth century.

      Best regards,
      ClimateSanity


      • Thanks for your reply.

        When you use the word “updated”, you are implying that H07 contains more information than HW04, and it is overall a better data set. In your post you are suggesting that Rahmstorf et al. decided to use an inferior data set because it gave them the answer that they’ve wanted.

        Now, there is no doubt that the H07 record captures the decadal variability seen in HW04 quite well. However the crucial question in the context of R2011 is whether the sea-level change is accelerating or decelerating. From your fitted curves clearly HW04 and H07 give different answer (perhaps statistically significant?).

        On what basis can you argue that we should trust that 9 station gives a better characterisation of global sea level then a record with 177 stations?

        Suppose there are two studies
        1) longer 9 station record that gives an accelerating trend
        2) shorter 177 station record that gives a decelerating trend.
        If Rahmstorf et al. had used study 1, will that be a defensible position?


      • Dear Anonymous,

        Thank you for you comment.

        You asked “On what basis can you argue that we should trust that 9 station gives a better characterisation of global sea level then a record with 177 stations?” My concern with this post was the wisdom of fitting this data to quadratics. Please re-read the last paragraph where I say “I do not recommend extrapolating sea level data with quadratic fit, and I am not endorsing any of the extrapolations shown above.”

        We have an iteresting situation: two “competing” sea level reconstructions from the same author. What does Holgate say?

        “On a decadal timescale, the length scales of sea level change are very large (O(1000) km) though not necessarily global. As a result, many tide gauges in a given region are highly correlated with each other. This paper demonstrates that a few high quality records from around the world can be used to examine large spatial-scale decadal variability as well as many gauges from each region are able to.”

        That is, those 177 stations tend to be bunched together. Those within a 1000 km of each other tend to say the same thing. But those stations do not have records extending back to the beginning of the 20th century. For example, north and western Europe are vastly over-represented in those 177 stations.

        He says…

        “When it comes to calculating long term global sea level means from tide gauge data, there are a number of problems. Firstly there is a bias in the distribution of tide gauges towards certain regions, notably Northern Europe and North America [Douglas, 1991]. Secondly there is the problem that not all tide gauge records are of equivalent quality…As a result of these two problems, there are very few high quality, long tide gauge records in different regions suitable for calculating global mean sea level change…

        In order to test whether a few high quality records could provide similar information to the composites, nine tide gauge records were carefully selected from the database of the Permanent Service for Mean Sea Level…The nine long records thus enable the study of HW04 into variability of decadal rates of sea level change to be extended over a much longer period…the tide gauge data presented here is of the very highest quality available.”

        Comparing the results of the two methods, Holgate says…

        “the two curves have overlapping error bars (based on one standard error). The global mean rates are similar for the second half of the 20th century (1953–97), 1.47 mm/yr and 1.41 mm/yr for the 177 and 9 stations respectively…

        The nine stations selected here as high quality records capture the mean decadal rates of change described by the larger set of stations used in HW04 and also have a similar global mean rate over the common period of the two analyses (1953–1997). This provides confidence that the nine station set can be used to study decadal rates of global mean sea level change throughout the twentieth century.”

        So I think Holgate prefers the 9 station method becuase it extends the record back to the beginning of the 20th century with little or no loss of quality for the last half of the century.

        But there is a more important point, aside from which reconstruction is better. Holgate also says of the longer (9 station) reconstruction..

        “The decadal rates of sea level change shown in Figure 2 are qualitatively similar to the corresponding rates in Figure 2 of Church and White [2006], with the exception of the period 1930–1940 which shows lower variability in the work of Church and White [2006].”

        “Church and White [2006]” is Rahmstorf’s preferred sea level data. So if Rahmstorf’s model is “robust” then we should expect that Holgate’s 2007 data should give similar results as the Church and White 2006 data when inserted into Rahmstorf’s model. Does it? Well, it just so happens that I know the answer to this question, and it is the subject of my upcoming post.

        Stay tuned. I think you will find it interesting.

        Best regards,
        ClimateSanity


  5. You can spin the paper however you want, but you cannot escape from the fact that they give different characterization of sea level change during the overlapping period (HW04 shows acceleration, H07 shows deceleration). Please note that Holgate said the agreement is qualitative, NOT quantitative.

    When you fit a model to data you are doing quantitative work, so you can’t argue that the data sets are interchangeable because they are not for your purpose.

    You yourself have confirmed that they give very different results.

    You said, “So I think Holgate prefers the 9 station method becuase it extends the record back to the beginning of the 20th century with little or no loss of quality for the last half of the century.”

    The second half of your claim is problematic:
    1) They give conflicting results when it comes to acceleration vs deceleration
    2) If you look at fig 2 of H07, the rates between 1950 to 1960, rate recorded in H07 is twice the rate of HW04. For the 1990-2000, HW04 is 50% higher. Not trivial differences for your purpose here.
    3) Satellite data shows that the highest rate of sea level increase is over the western pacific. HW04 has more than 15 stations. H07 has 0.

    All this boils down to, is which is a better data set for characterizing global sea level change.

    Let me repeat this again. Suppose that there are two studies
    1) longer 9 station record that gives an accelerating trend
    2) shorter 177 station record that gives a decelerating trend.
    If Rahmstorf et al. had used study 1, will that be a defensible position?



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