Posts Tagged ‘A 20th century acceleration in global sea-level rise’

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Rahmstorf (2011): Robust or Just Busted (Part 6): Holgate’s sea level data

November 11, 2012

This is part 6 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.

Recall figure 1 from R2011[1]…

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

One of the primary points of this graphic is the quadratic fit of one data set (CW06) overlaid on all the other data sets.  The message that you are to receive is that these various sets of sea level data all tell the same essential story.  The falseness of this claim was discussed in “Quadratic fits of laughter.”

But let’s take Rahmstorf at his word.  Let’s agree with him that these sea level data sets all tell essentially the same story.  R2011’s big point is that the Rahmstorf model is “robust” given a variety of different historical data sources.  So it seems a tad bit strange that after going to all the trouble to point out these various sea level data sources and their similarities, he only gives the projection results of his model for three of them (CW06[2], CW11[3], and JE08[4]).

Of those three input sea level data sets, only two of them give similar sea level projections for the 21st century.  The outlier which results from CW11 shows significantly lower sea level projections.  Because of this, the outlier must be rejected (according to R2011), even though Church and White, the authors of both CW06 and CW11, clearly think the CW11 data is an improvement over their Cw06 data.

What about some of the other sea level rise data sets shown in R2011’s figure 1?  What type of 21st century sea level projections do they yield when inserted into Rahmstorf’s model?

Holgate’s sea level data

Let’s consider the sea level rise data of Simon Holgate.    The above image shows Holgate’s 2004 data[5], labeled HW04.  As I have previously pointed out, R2011 oddly includes Holgate’s 2004 data but ignores his 2007 data[6], H07.  I will consider both.  In my previous post I showed the results of Rahmstorf’s model when either CW06 and CW11 are input with six different combinations of reservoir storage and ground water depletion inputs.  The following two graphs show the results in the same format using HW04 and H07 (instead of CWo6 and CW11) with the same combination of reservoir storage and ground water depletion inputs.  I have kept the horizontal axis scaling the same as in the previous post to highlight the different results when Church and White data is used and when Holgate data is used.  Data files with all the specifics of this data are at the bottom of the post.

FIGURE 2. Sea level rise projections for the 21st century based on my implementation of Rahmstorf’s model under the RCP45 emissions scenario (Moss, 2010)[7] for Holgate sea level data coupled with various combinations of reservoir storage and groundwater depletion data inputs.
FIGURE 3. Sea level rise projections for the 21st century based on my implementation of Rahmstorf’s model under the RCP85 emissions scenario (Moss, 2010)[7] for Holgate sea level data coupled with various combinations of reservoir storage and groundwater depletion data inputs.

For comparison, here are the previously posted results using Church and White sea level data…

 RCP45

 RCP85

Hmmm…

Didn’t R2011 imply that those various sea level data sets shown if figure 1, above, told the same essential story?  Yes, I believe he did!  That is why they overlaid the same quadratic fit onto all of them.

And didn’t R2011 say that their model was “robust?”  Yes, I am quite certain that they did!  In fact the word “robust” was in the title of their paper, and they said…

“We determine the parameters of the semiempirical link between global temperature and global sea level in a wide variety of ways…We then compare projections of all these different model versions (over 30) for a moderate global warming scenario for the period 2000–2100. We find the projections are robust

and

“we will systematically explore how robust semi-empirical sea level projections are with respect  to the choice of data sets”

So, they claim to use “a wide variety of ways” to look at “all these different model versions (over 30).”  They show plots of seven different sea level data sets and imply their similarity.  But they only show projections based on three of them.  Then they reject the projections based on one of the three, even though it is arguably the best sea level data of the bunch.

What do they say about their model’s projections based on the “wide variety” other sea level data sets that look so good overlaid with the same quadratic fit…?

Cricket. Cricket.

How would R2011 reject the projections based on the Holgate data?

How would R2011 reject the projections based on the Holgate data that I have shown above in figures 2 and 3?  Well they would undoubtedly point out that the fit parameter, To (the so called baseline temperature, is way too low.  Recall, R2011 finds To to be on the order of -0.4 °C (below the 1950 to 1980 global average).  When Holgate’s sea level data is used, To is on the order of -4.0 °C.  Hey Rahmstorf, don’t blame me, its your model!

Maybe one of these days I will write a justification for a large negative To.  It is really quite simple.  But I am going to conclude for today.

Which of the many projections do I endorse?

Which projections are better – the ones based on CW06, CW11, JE08, HW04, or H07?  None of them.  As I have pointed out over and over, the Rahmstorf model is bogus, bogus, bogus.  I have now shown, again, that it is also not robust.  It is only marginally better than a random number generator.  HIgher temperatures would likely lead to higher sea levels, but Rahmstorf’s model is useless in determining how much.

Data files with specifics of of my implementation of Rahmstorf’s model using Holgate sea level data

Sea level data: Holgate and Woodworth 2004
Reservoir storage: Chao 2oo8
Ground water depletion: none
Result files…
Summary: vr-summary-121110-165152.doc
Inputs: vr-input-image-121110-165152.png
Fit: vr-fit-image-121110-165152.png
Projections: vr-projections-image-121110-165152.png

Sea level data: Holgate and Woodworth 2004
Reservoir storage: Chao 2oo8
Ground water depletion: Wada 2010 extrapolated to 1880
Result files…
Summary: vr-summary-121029-132349.doc
Inputs: vr-input-image-121029-132349.png
Fit: vr-fit-image-121029-132349.png
Projections: vr-projections-image-121029-132349.png

Sea level data: Holgate and Woodworth 2004
Reservoir storage: Chao 2oo8
Ground water depletion: Wada 2010
Result files…
Summary: vr-summary-121029-132148.doc
Inputs: vr-input-image-121029-132148.png
Fit: vr-fit-image-121029-132148.png
Projections: vr-projections-image-121029-132148.png

Sea level data: Holgate and Woodworth 2004
Reservoir storage: Chao 2oo8
Ground water depletion: Wada 2012
Result files…
Summary: vr-summary-121105-230616.doc
Inputs: vr-input-image-121105-230616.png
Fit: vr-fit-image-121105-230616.png
Projections: vr-projections-image-121105-230616.png

Sea level data: Holgate and Woodworth 2004
Reservoir storage: Pokhrel 2012 extrapolated back to 1900
Ground water depletion: Pokhrel 2012 extrapolated back to 1900
Result files…
Summary: vr-summary-121029-133403.doc
Inputs: vr-input-image-121029-133403.png
Fit: vr-fit-image-121029-133403.png
Projections: vr-projections-image-121029-133403.png

Sea level data: Holgate and Woodworth 2004
Reservoir storage: Pokhrel 2012
Ground water depletion: Pokhrel 2012
Result files…
Summary: vr-summary-121029-132906.doc
Inputs: vr-input-image-121029-132906.png
Fit: vr-fit-image-121029-132906.png
Projections: vr-projections-image-121029-132906.png

Sea level data: Holgate 2007
Reservoir storage: Chao 2008
Ground water depletion: none
Result files…
Summary: vr-summary-121029-133753.doc
Inputs: vr-input-image-121029-133753.png
Fit: vr-fit-image-121029-133753.png
Projections: vr-projections-image-121029-133753.png

Sea level data: Holgate 2007
Reservoir storage: Chao 2008
Ground water depletion: Wada 2010 extrapolated to 1880
Result files…
Summary: vr-summary-121029-135519.doc
Inputs: vr-input-image-121029-135519.png
Fit: vr-fit-image-121029-135519.png
Projections: vr-projections-image-121029-135519.png

Sea level data: Holgate 2007
Reservoir storage: Chao 2008
Ground water depletion: Wada 2010
Result files…
Summary: vr-summary-121029-134334.doc
Inputs: vr-input-image-121029-134334.png
Fit: vr-fit-image-1209121029-134334.png
Projections: vr-projections-image-121029-134334.png

Sea level data: Holgate 2007
Reservoir storage: Chao 2008
Ground water depletion: Wada 2012
Result files…
Summary: vr-summary-121029-135834.doc
Inputs: vr-input-image-121029-135834.png
Fit: vr-fit-image-121029-135834.png
Projections: vr-projections-image-121029-135834.png

Sea level data: Holgate 2007
Reservoir storage: Pokhrel 2012 extrapolated to 1900
Ground water depletion: Pokhrel 2012 extrapolated to 1900
Result files…
Summary: vr-summary-121029-175833.doc
Inputs: vr-input-image-121029-175833.png
Fit: vr-fit-image-121029-175833.png
Projections: vr-projections-image-121029-175833.png

Sea level data: Holgate 2007
Reservoir storage: Pokhrel 2012
Ground water depletion: Pokhrel 2012
Result files…
Summary: vr-summary-121029-140159.doc
Inputs: vr-input-image-121029-140159.png
Fit: vr-fit-image-121029-140159.png
Projections: vr-projections-image-121029-140159.png

_________________________________

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[1]  Rahmstorf, S., et. al., “Testing the robustness of semi-empirical sea level projections” Climate Dynamics, 2011

[2] Church, J. A., and N. J. White, “A 20th century acceleration in global sea-level rise“,  Geophys. Res. Lett., 33, 2006

[3] Church, J. A. and N.J. White, “Sea-level rise from the late 19th to  the early 21st Century“, Surveys in Geophysics, 2011

[4] Jevrejeva, S., et. al. “Recent global sea level acceleration started over 200 years ago? ,”  Geophys. Res. Lett., 35, 2008

[5] Holgate, S. J. and Woodworth, P.L., “Evidence for enhanced coastal sea level rise during the 1990s,” Geophys. Res. Lett., 31, 2004

[6] Holgate, S.J., “On the decadal rates of sea level change during the twentieth century,” Geophys. Res. Lett., 34, 2007

[7] Moss, et. al., “The next generation of scenarios for climate change research and assessment,” Nature, 463, 2010

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Rahmstorf (2011): Robust or Just Busted (Part 5): Why a paper about “robustness”

September 29, 2012

This is part 5 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].

What does R2011 mean by “robust?”

What does Rahmstorf mean when he says his model linking sea level to temperature is “robust?”  Simply this: when the inputs that he deems acceptable are inserted into his model, he gets the results he likes.

How does he decide which inputs are acceptable?  Easy – if they yield the results he likes, then they are acceptable.  It is a very simple and efficient system of logic!

Why a paper about “robustness?”

Rahmstorf and his associates have a pressing need to defend their sea level rise projections.  I have presented a host of reasons why his model is bogus.  One of the most embarrassing is that one of his fit parameters, that he expected to be positive, is in fact negative for every combination of input tried.  This leads to all kinds of bizarre results (see here, here and here , for example).  The other is that his sea level projections dropped dramatically when his preferred source of 20th century historical input data updated their data set.

This “robustness” paper (R2011) is a stumbling attempt to dismiss the revised sea level data from the source that he had previously enthusiastically used.

A quick recap

Rahmstorf’s model, which I will refer to as the VR2009[2] model, attempts to relate global sea level rise to global temperature through the following formula…

where H is sea level and T is temperature.  Insert historical data for H and T,  and solve to a, b, and To.  Then insert projected temperatures for the 21st century and calculate projected sea level rises for the 21st century.  The VR2009 model and approach have an amazing number of problems and the list just keeps getting longer.  There is a whole family of realistic temperature scenarios for the 21st century that cause this model to yield ridiculous results (see here).  The root of most of these problems comes from the fact that every set of historical sea level inputs and temperatures that Rahmstorf and associates have tried result in a negative b.  That includes every set of input data considered in R2011 (see figure 1, below).

Model inputs and projections in R2011

(click to enlarge) …

FIGURE 1. R2011’s projections of 21st century sea level rise and baseline temperatures under the RCP45 emissions senario (Moss, 2010)[3] for various temperature and sea level input data sets.

I have circled the results R2011 likes.  As you can see, nothing involving the Church’s and White’s 2011 sea level data (CW11)[4] meets R2011’s  quality standard.  R2011 has determined that Church’s and  White’s 2006 sea level data (CW06)[5] is better than Church’s and White’s 2011 data, despite the fact that Church and White obviously think their updated 2011 data is better.

It comes down to To

Why does R2011 think the 2006 sea level data is better than the improved 2011 sea level data?  Well, I have already explained that – the 2006 Church and White sea level data gives the results that R2011 wants – higher sea level rise projections for the 21st century!

But they can’t really say that.  Instead they say that the 2011 Church and White data leads to a baseline temperature, To, that they insist is too low.  To is the steady-state temperature deviation from the 1950-1980 average temperature at which Rahmstorf’s model says the sea level would be unchanging.

Look at the right side of figure 1.  It shows the baseline temperature that R2011 derived with the various sets of input data.  The values of To that meet with R2011’s approval average out to about -0.43 degrees.  But those based on CW11 average out to about -0.62 degrees C.  A difference of less than two tenths of a degree.

If you were to ask the authors of R2011 what other evidence do they have that To must be about -0.43 degrees, they will refer you to “Climate related sea-level variations over the past two millennia[6],” which used evidence from two salt marshes in North Carolina to corroborate this global value.  And they have great confidence in this independent confirmation (because two out of three of the R2011 authors were also authors on this paper).  Hmmm.

I will have more to say about R2011’s preference for To in a later post.

A few input combinations that R2011 did not show you

R2011 implies that it has tried some vast universe of input sea level and temperature data combinations in their model. They say “We then compare projections of all these different model versions (over 30)…”  Wow! Count them – over 30!

But there are many more possible combinations than that.  R2011 has picked a few cherries from a very prolific tree.

In figures 2 and 3, below, I have run several temperature and sea level input data sets in my implementation of Rahmstorf’s model.  In some cases my input combinations are the same as some found in figure 1.  In some cases they are different.  I have arranged the input combinations in chronological order, with older versions of input data on the bottom.  Notice a trend?  Figure 2 and figure 3 give projections based on the RCP45  and RCP85 emission scenarios, respectively.

FIGURE 2. Sea level rise projections for the 21st century based on my implementation of Rahmstorf’s model under the RCP45 emissions scenario (Moss, 2010) for various temperature and sea level input data sets.
FIGURE 3. Sea level rise projections for the 21st century based on my implementation of Rahmstorf’s model under the RCP85 emissions scenario (Moss, 2010) for various temperature and sea level input data sets.

As you can see, newer sea level data (whether it is actually sea level (CW06 vs CH11, or reservoir storage (RS) or ground water depletion (GWD)  modifiers) tends to lead to lower 21st century projections when inserted into Rahmstorf’s model.

Which projection do I endorse? None of them.  Make no mistake – the Rahmstorf model is bogus, no matter what the inputs are.  I am just playing games with it.  The Rahmstorf model is an illusion that hooks you with a simple truth: It is a pretty good bet that higher temperatures lead to higher sea levels.  But the Rahmstorf model is not much better than a Ouija board for quantifying how much.

There is much to be said about the results in figures 2 and 3.  The 48 files below give the long story that is summarized in figures 2 and 3.

Much more to come in later posts

Sea level data: Church and White 2006
Reservoir storage: Chao 2oo8
Ground water depletion: none
Result files…
Summary: vr-summary-120923-091214.doc
Inputs: vr-input-image-120923-091214.png
Fit: vr-fit-image-120923-091214.png
Projections: vr-projections-image-120923-091214.png

Sea level data: Church and White 2006
Reservoir storage: Chao 2oo8
Ground water depletion: Wada 2010 extrapolated to 1880
Result files…
Summary: vr-summary-120923-091326.doc
Inputs: vr-input-image-120923-091326.png
Fit: vr-fit-image-120923-091326.png
Projections: vr-projections-image-120923-091326.png

Sea level data: Church and White 2006
Reservoir storage: Chao 2oo8
Ground water depletion: Wada 2010
Result files…
Summary: vr-summary-120923-091413.doc
Inputs: vr-input-image-120923-091413.png
Fit: vr-fit-image-120923-091413.png
Projections: vr-projections-image-120923-091413.png

Sea level data: Church and White 2006
Reservoir storage: Chao 2oo8
Ground water depletion: Wada 2012
Result files…
Summary: vr-summary-120923-091517.doc
Inputs: vr-input-image-120923-091517.png
Fit: vr-fit-image-120923-091517.png
Projections: vr-projections-image-120923-091517.png

Sea level data: Church and White 2006
Reservoir storage: Pokhrel 2012 extrapolated back to 1900
Ground water depletion: Pokhrel 2012 extrapolated back to 1900
Result files…
Summary: vr-summary-120923-091643.doc
Inputs: vr-input-image-120923-091643.png
Fit: vr-fit-image-120923-091643.png
Projections: vr-projections-image-120923-091643.png

Sea level data: Church and White 2006
Reservoir storage: Pokhrel 2012
Ground water depletion: Pokhrel 2012
Result files…
Summary: vr-summary-120923-091727.doc
Inputs: vr-input-image-120923-091727.png
Fit: vr-fit-image-120923-091727.png
Projections: vr-projections-image-120923-091727.png

Sea level data: Church and White 2011
Reservoir storage: Chao 2008
Ground water depletion: none
Result files…
Summary: vr-summary-120923-091904.doc
Inputs: vr-input-image-120923-091904.png
Fit: vr-fit-image-120923-091904.png
Projections: vr-projections-image-120923-091904.png

Sea level data: Church and White 2011
Reservoir storage: Chao 2008
Ground water depletion: Wada 2010 extrapolated to 1880
Result files…
Summary: vr-summary-120923-091956.doc
Inputs: vr-input-image-120923-091956.png
Fit: vr-fit-image-120923-091956.png
Projections: vr-projections-image-120923-091956.png

Sea level data: Church and White 2011
Reservoir storage: Chao 2008
Ground water depletion: Wada 2010
Result files…
Summary: vr-summary-120923-092105.doc
Inputs: vr-input-image-120923-092105.png
Fit: vr-fit-image-120923-092105.png
Projections: vr-projections-image-120923-092105.png

Sea level data: Church and White 2011
Reservoir storage: Chao 2008
Ground water depletion: Wada 2012
Result files…
Summary: vr-summary-120923-092202.doc
Inputs: vr-input-image-120923-092202.png
Fit: vr-fit-image-120923-092202.png
Projections: vr-projections-image-120923-092202.png

Sea level data: Church and White 2011
Reservoir storage: Pokhrel 2012 extrapolated to 1900
Ground water depletion: Pokhrel 2012 extrapolated to 1900
Result files…
Summary: vr-summary-120923-092330.doc
Inputs: vr-input-image-120923-092330.png
Fit: vr-fit-image-120923-092330.png
Projections: vr-projections-image-120923-092330.png

Sea level data: Church and White 2011
Reservoir storage: Pokhrel 2012
Ground water depletion: Pokhrel 2012
Result files…
Summary: vr-summary-120923-094501.doc
Inputs: vr-input-image-120923-094501.png
Fit: vr-fit-image-120923-094501.png
Projections: vr-projections-image-120923-094501.png

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

[2] Vermeer, M., Rahmstorf, S., “Global sea level linked to global temperature,” PNAS, 2009

[3] Moss, et. al., “The next generation of scenarios for climate change research and assessment,” Nature, 463, 2010

[4] Church, J. A. and N.J. White, “Sea-level rise from the late 19th to  the early 21st Century“, Surveys in Geophysics, 2011

[5] Church, J. A., and N. J. White, “A 20th century acceleration in global sea-level rise“,  Geophys. Res. Lett., 33, 2006

[6] Kemp, Horton, Donnelly, Mann, Vermeer & Rahmstorf,  “Climate related sea-level variations over the past two millennia,” PNAS, 2011

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Rahmstorf (2011): Robust or Just Busted (Part 4): First results from new code

September 14, 2012

This is part 4 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].

The new code for consistent processing of temperature and sea level data according to the predominant Vermeer and Rahmstorf 2009 model (VR2009)[2] is complete.

It is written LabView V7.1.  There have been several upgrades to LabView since V7.1, but I believe my code will open in any of them.  I prefer this older version of LabView for a variety of reasons that I will not go into here.  But one advantage is that anyone who is interested in running this code can find a used student version of LabView on Ebay at a very reasonable cost.

My code can be downloaded here.

VR2009 input the GISS temperature, Church’s and White’s 2006 sea level data, and modified the sea level data with a correction for reservoir storage from Chao and determined the fit parameters, a, b, and To  for their model…

Rahmstorf and company figured that once a, b, and To were found they could insert hypothesized temperature scenarios for the 21st century into equation 1 and calculate the resulting sea levels.  I have provided a long list of criticisms of their logic.  One of the most devastating observations is that their own source of 20th century sea level data(Church and White, 2006[3]) had revised their data, and the new version of data (Church and White 2009[4] or Church and White 2011[5]) resulted in much lower sea levels by the end of the 21st century when inserted in to equation 1.

Two years ago I reproduced the VR2009 fit parameters, a, b, and To, to demonstrate that I could accurately reproduce their model.

In R2011 Rahmstorf re-works the numbers with the same inputs used in VR2009, and I have reworked the numbers with this new code.  And for the same inputs used back on VR2009, everything lines up within Rahmstorf’s stated uncertainties.  But that is a minor point.  Rahmstorf’s primary objective in R2011 is to defuse my observation that Church’s and White’s newer, more accurate sea level data causes Rahmstorf’s model to yield much lower sea level projections for the 21st century.  Plenty of time to deal with that issue later.

But for now and for the record: in VR2009 Vermeer and Rahmstorf found

a = 5.6 ± 0.5 mm/year/K

b= -49 ± 10 mm/K

To = -0.41 ± 0.03 K

In 2010, using my implementation of their model, I found

a = 5.6  mm/year/K

b= -52 mm/K

To = -0.42 K

In R2011 Rahmstorf presents slightly different numbers than he did in VR2009 for the same input conditions.  Similarly, with my new code I now get slightly different numbers for the same input conditions.

With the new code I found

a = 5.8  mm/year/K

b= -54 mm/K

To = -0.41 K

Presentation of my results

In R2011 Rahmstorf makes some claims based the same model as equation 1, but with various combinations of temperature and sea level data from different sources.  His claim is that he gets essentially the same results – no matter what inputs he uses – indicting that his model is “robust.”

I will also be presenting a lot of results for different possible inputs in the days to come.   But my results will be very detailed, complete, and entirely open for your examination.  You also have access to my complete code.

My code will always generate four files for any set of inputs.  Three of those files are images of: graphs of the input data;  graphs of the model fits to the input data (used to derive a, b, and To); and graphs of sea level projections based on various temperature scenarios for the 21st century, including the SRES emission scenarios used in VR2009 and the RCP45 and RCP85 scenarios used in R2011.  The fourth file is a tab delimited text file with all setup parameters, fit plots and results, and projections.

Note that the graph images of the 21st century sea level projections will not be autoscaled.  That is, the Y axis of the projection graphs will all have the same scaling.  This will make many of the graphs look crowded, but it will also be easy to make a qualitative comparison of the projections from different input data.   You can always open the tab delimited text file in the spreadsheet of your choice and replot the data as you see fit.

Below you can see an example of the graph images and the corresponding tab delimited text file that is generated by my code with the same input data used to find the model fit parameters listed above.  That is, I will use the  GISS temperature, Church and White’s 2006 sea level data and the Chao reservoir correction, which result in my values of a, b, and To, shown above.

The tab delimited text file is shown below.  I have truncated the columns of data (which could be thousands of rows long).   The headers and columns would line up better if you opened the file in a spreadsheet.

INPUTS
Temperature filename: T GISS Land Ocean.txt
Original source: http://data.giss.nasa.gov/gistemp/graphs_v3/Fig.A2.txt		

http://data.giss.nasa.gov/gistemp/graphs_v3/

Sea level filename: SL CW06.txt
Original source: http://www.psmsl.org/products/reconstructions/church_white_grl_gmsl.lis

Modifier filename: RS Chao 2008.txt
Original source: “Impact of Artificial Reservoir Water Impoundment on Global Sea Level”		
Chao, et al., Science 320, 212 (2008)

SETUP PARAMETERS
Minimizing residual: dH/dt
Extension (years): 15.0
Smoothing Gaussian FWHM (years): 15.0
input years used: 1880.0 - 2000.0

FIT PARAMETERS
a: 5.8
b: -54
To: -0.41
H mse: 1.986
dH/dt mse: 0.250

FIT CURVES
date	model H (mm)	data H (mm)	H residuals (mm)	model dH/dt (mm/year)	data dH/dt (mm/year)	dH/dt residuals (mm/year)
1880.050000	-76.997238	-76.648275	0.348963	1.252341	0.699570	-0.552771
1880.150000	-76.873236	-76.577572	0.295664	1.240020	0.714500	-0.525521
1880.250000	-76.750402	-76.505711	0.244692	1.228336	0.722720	-0.505615
    |               |                |              |              |                |                |      
    |               |                |              |              |                |                |    
PROJECTIONS
year	RCP45	RCP85	A1B max	A1B mid	A1B min	A1F1 max	A1F1 mid	A1F1 min	A1T max	A1T mid	A1T min	A2 max	A2 mid	A2 min	B1 max	B1 mid	B1 min	B2 max	B2 mid	B2 min
2000.500000	3.564485	3.462285	4.177685	4.330985	4.330985	4.841985	4.688685	4.586485	4.279885	4.228785	4.688685	4.126585	4.382085	4.790885	4.126585	4.841985	4.688685	4.841985	4.841985	4.790885
2001.500000	7.325070	7.132270	8.226370	8.413370	8.668870	8.815270	8.679370	8.997570	7.908170	8.169470	8.730470	8.181070	8.458670	9.178770	8.181070	9.019670	9.037070	8.917470	8.917470	8.923270
2002.500000	11.429255	11.515155	12.424755	12.588555	13.019455	12.938255	12.819755	13.511955	11.681455	12.169255	12.916155	12.283055	12.628055	13.567755	12.334155	13.170555	13.392355	12.568955	12.875555	13.085755
   |               |                |              |              |                |                |      |               |                |              |              |                |                |

Tab delimited text: VR summary 120913-212735.doc

The three associated graph images…

Input data image: http://climatesanity.files.wordpress.com/2012/09/vr-input-image-120913-212735.png

Fit image: http://climatesanity.files.wordpress.com/2012/09/vr-fit-image-120913-212735.png

projections image: http://climatesanity.files.wordpress.com/2012/09/vr-projections-image-120913-212735.png

___________________________________

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

[2] Vermeer, M., Rahmstorf, S., “Global sea level linked to global temperature,” PNAS, 2009

[3] Church, J. A., and N. J. White, “A 20th century acceleration in global sea-level rise“,  Geophys. Res. Lett., 33, 2006

[4] www.psmsl.org/products/reconstructions/church_white_new_gmsl.lis

[5] Church, J. A. and N.J. White, “Sea-level rise from the late 19th to  the early 21st Century“, Surveys in Geophysics, 2011

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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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Links to Church and White sea level data

May 9, 2011

I have written several posts about Church and White Sea level data and how it pertains t Rahmstorf sea level models. 

It seems the Permanent Site for Mean Sea Level (PSMSL) page for Church and White has eliminated the link for the 2009 version of Church and White data when it added the link for the 2011 version of their data.  As of today, the PSMSL still archives the 2009 data, but does not provide the link.

Just so there will be no confusion, I will provide several links for each of the 2006, 2009, and 2011 versions of the Church and White data.

2006 version

  • Abstract for associated paper: “A 20th century acceleration in global sea-level rise,” GEOPHYSICAL RESEARCH LETTERS, VOL. 33, L01602, 4 PP., 2006  doi:10.1029/2005GL024826
  • Full PDF version of associated paper: “A 20th century acceleration in global sea-level rise,” GEOPHYSICAL RESEARCH LETTERS, VOL. 33, L01602, 4 PP., 2006 doi:10.1029/2005GL024826
  • Sea level data archived at PSMSL (Columns: time, Global Mean Sea Level in mm, One-sigma error in mm)
  • Sea level data archived at Commonwealth Scientific and Industrial Research Organisation (CSIRO).  This is a Zip file containing “church_white_grl_gmsl.txt” (Columns: time, Global Mean Sea Level in mm, One-sigma error in mm)
  • Sea level data archived by me on 4/27/11. 

The above three archives of the 2006 version of Church and White sea level data were identical as of 4/27/11. 

2009 version

  • This version did not have an associated paper.  There used to be a link and a short explanation at the PSMSL page for Church and White, but both are now gone.  But the data still exists as of 4/27/11.
  • Sea level data archived at PSMSL (Columns: time, Global Mean Sea Level in mm, One-sigma error in mm)
  • Sea level data archived by me on 4/27/11.

The above two archives of the 2009 version of Church and White sea level data were identical as of 4/27/11.

2011 version

  • Full PDF version of associated paper: “Sea-level rise from the late 19th to the early 21st Century.” Surveys in Geophysics, (2011)
  • Sea level data archived at Commonwealth Scientific and Industrial Research Organisation (CSIRO). This is a Zip file containing 9 files.  “aa_read_me.txt” explains the contents of the other 8 files, which include text and comma separated value files of satellite altimeter monthly and yearly data and monthly and yearly versions Church’s and White’s reconstruction.
  • Sea level data in the form of the same Zip file as above, but archived by me.
  • The 9 individual files from the Zip file

If any of these links break, please alert me by leaving a comment.

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