Posts Tagged ‘Global sea level linked to global temperature’

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Rahmstorf (2011): Robust or Just Busted (Part 7): The Irony of Jevrejeva’s Data.

January 7, 2013

This is part 7 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.

Let’s talk a little more about the irony of using the Jevrejeva’s 2008 sea level data, which I will refer to as JE08[1], to confirm Rahmstorf’s sea level projections for the 21st century.

As I have already explained, Rahmstorf claims in his 2011 paper (which I will refer to as R2011[2]), that his model is “robust,” meaning that variations of historical 20th century input sea level data yield essentially the same sea level rise projections for the 21st century.  R2011 graphically presents seven sources of sea level data  (while ignoring others) and implies their similarity by overlaying the same quadratic fit for all of them.  R2011 leads us to believe that the model is robust with, specifically, the input of these various sea level data sets.

R2011 presents the results of the model using only three of the seven sea level rise inputs.  Two of the three are by the same authors, Church and White[3][4],  who clearly believe their later version of the sea level data (CW11[4]) is an improvement over their earlier version (CW06[3]).  Then, R2011 cynically rejects the model results from Church’s and White’s better set of data because those results testify against R2011’s desired conclusion of extremely high sea level rises for the 21st century. 

Which brings us to Jevrejeva

The third data set that R2011 used is Jevrejeva’s.  So after all the blathering about the “robustness” of their model under a broad variety of inputs, R2011 is left with just two sea level data sets that they are satisfied with: Church’s and White’s earlier data set, CW06; and Jevrejeva’s 2008 data, JE08.   Figure 1, below shows R2011’s figures 1 and 9, with my annotation.

Figure 1.  R2011's figures 1 & 9 showing Rahmstorf's judgement about the quality of sea level sets.

Figure 1. R2011’s figures 1 & 9 showing Rahmstorf’s judgement about the quality of sea level sets.

Keep in mind that R2011’s objective in their claim of robustness was to prove that their earlier results [5], based on the CW06 were realistic.  So, in effect, after all the hand waving JE08 is the only one of the seven sea level data sources that fulfills that purpose.  That is why we are taking a little closer look at JE08.

Let’s start by looking at an overlay of JE08, CW06 and CW11 in figure 2.  If Rahmstorf’s model were “robust,” as R2011 claims, then all three of these data sets as input to the model should yield very similar sea level rise projections for the 21st century.  But one of them yields much lower results than the other two. The amazing thing is that the outlier is CW11, which  is nearly a twin to CW06, at least compared to JE08.  How can that be?

Figure 2
Figure 2

Let’s suspend our higher cognitive functions for the moment and agree with R2011’s reasoning.   That is, we will agree that the sea level rise projections for the 21st century based on CW11 input data must be rejected because they are much lower than the projections based on CW06 input data.  Inversely, we will agree that sea level rise projections for the 20th century based on JE08 input data must be accepted because they give high 21st century projections, just like the projections based on CW06 input data.

A closer look at JE08 sea level data

Since we have decided to mindlessly accept the usefulness of JE08 to back up Rahmstorf’s high sea level rise projections for the 21st century, then we should also accept some other interesting features of JE08.  So let’s take a closer look.

JE08 says their version of sea level data was in “good agreement with estimates of sea level rise during the period 1993–2003 from TOPEX/Poseidon satellite altimeter measurements.”  Figure 3, below, shows an overlay JE08 and the satellite altimeter data[6],…

Figure 3
Figure 3

It is quite striking that according to JE08 and the satellite data that the sea level rise rate for the middle third of the 20th century (1933 to 1966) is exactly the same as the sea level rise rate at the end of the 20th century and beginning of the 21st century.  How can this possibly be!?  How can this data that indicates no increase in the sea level rise rate for 80 years cause tremendous increases in the sea level rise rate for the 21st century when used as input to Rahmstorf’s model?

Stefan the Dart Thrower

Consider Stefan Rahmstorf the Dart Thrower.  He holds forth at the pub as the best thrower in the kingdom.  He brags about his precision, claiming “I can hit high numbers every time! My talent is robust!” Challenged by another annoyed pub patron to “put up or shut up,” Stefan grabs a handful of darts and goes to work.  He throws seven, but only three hit the board.  Two are on high numbers and one is on a low number, the rest are stuck in the wall.  “See!” he says triumphantly, pointing at the two darts on the high numbers.

The other patron points out the projectiles stuck in the wall.  “Bad darts” Stefan replies.

“What about this dart on the low number – it is identical to one of the darts on a high number” the incredulous patron points out. “Same length, same material, same weight, same manufacturer.”

“Obviously a bad dart, nevertheless” sniffs Stefan.  “If if were a good dart it would have landed on a high number.”

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

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

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

[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] See “Critique of “Global sea level linked to global temperature, by Vermeer and Rahmstorf

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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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