Posts Tagged ‘Church’

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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 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 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.

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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. 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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Rahmstorf (2009): (part 9): Applying three corrections

November 17, 2010

This is part 9 of a series on Vermeer’s and Rahmstorf’s 2009 PNAS paper, “Global sea level linked to global temperature“  (referred to as “VR2009″ in this series of posts).

Naturally, Vermeer’s and Rahmstorf’s  conclusions were scary: oceans rising by as much as 1.8 meters by 2100.  Their results, with the imprimatur or the National Academy of Sciences, have been gleefully touted by those who crave the authority to reshape the economy of the planet to fit their more highly evolved ideals.  A google search for the title of their paper, “Global sea level linked to global temperature” yields thousands of hits.

But they were wrong.

The basic model

VR2009 proposed a model linking sea level rise to global temperature based on the following equation…

where

H is the sea level

T is the temperature

T0 is a constant “equilibrium temperature”

t is the time

a and b are constants 

VR2009 used Church’s and White’s 2006 sea level data  modified with Chao’s correction for artificial reservoir storage for sea level, H.  For temperature, T, they used the GISS global temperature .  They inserted them into the above model equation and found the values of a, b and T0 that yield the best fit.  Then they inserted their values of a, b and T0 back into the model equation and used IPCC temperature scenarios for the 21st century to determine the sea level rise for the 21st century. 

It turns out that the sea level data that VR2009 used was profoundly flawed.

Church and White sea level data update

About the same time that the National Academy of Sciences published VR2009, Church and White updated their sea level data.  The 2009 version of Church’s and White’s sea level data extended the data out to the year 2007, but more importantly, it also incorporated corrections that drastically changed the sea level versus time for the previous 100 years.  I have searched high and low for some acknowledgment of the updated Church and White data by Vermeer or Rahmstorf, but I have found nothing.

Groundwater depletion

VR2009 also gave short shrift to question of groundwater depletion.

VR20009 included the Chao artificial reservoir correction to compensate for water that would have been added to ocean depth but has instead been stored in artificial reservoirs.  They were happy to add this correction to the Church and White sea level data.  I was critical of  Chao for not including the inverse effect of artificial reservoir impoundment: groundwater depletion.  A correction for groundwater depletion would have to be subtracted from the Church and White data.    I have also been critical of VR2009 for brushing this point aside by saying   “No time series of this is available” for groundwater depletion.  It turns out that I was right – in the last part of the 20th century groundwater depletion dominated artificial reservoir impoundment.  And now a time series IS available from 1960 to 2000.

A new Geophysical Research Letters paper (Wada, Y., L. P.H. van Beek, C. M. van Kempen, J. W.T.M. Reckman, S. Vasak, and M.F.P. Bierkens (2010), Global depletion of groundwater resources, Geophysical Research Letters) provides the necessary information.  Wada provides groundwater depletion data covering 1960 to 2000.  That data fits an exponential very nicely, so I have extrapolated it backward and forward along the exponential (see here for details).

Making the corrections

Correcting for either the updated Church and White sea level data or the Wada groundwater depletion data drastically changes the outcome of the VR2009 model.  Taken together they destroy it.

In this post I will use the updated Church and White data,  a groundwater depletion correction based on Wada’s data, and the Chao reservoir correction used by VR2009 to create a superior time series for the sea level.  This more accurate time series will be used to  re-calculate the values for a, b and T0 for the VR2009 model equation.  Figure 1 shows the components of the sea level.

Figure 1. Sea level components.

Figure 2  is an overlay of the sea level data that VR2009 used, and the new, more accurate version created by combining the updated Church and White sea level data, the Wada groundwater depletion correction and the Chao reservoir correction shown in figure 1.

Figure 2. The VR2009 version of sea level data compated to the more accurate version using the updated Church and White data and the Wada groundwater depletion correction.

Look at the difference.  The VR2009 version of the sea level data starts with a lower slope than the more accurate version, but it ends up with a larger slope than the more accurate version.  In fact, the slope for the VR2009 version increases by nearly a factor of 3, while the more realistic version increases by about a factor of 1.6 (see figure 3).

Figure 3. Beginning and ending slopes for VR2009 version of sea level data and the more accurate version used in this post.

VR2009 smoothed their sea level and temperature data with a 15 year smoothing period.  I will smooth them with a 15 year FWHM gaussian filter with end reflection.  The smoothed sea level data is shown in figure 4.

Figure 4. Improved sea level data with 15 year FWHM gaussian smoothing.

Turning the crank

In a previous post I demonstrated that I could reproduce VR2009’s results with my own implementation of their model and the same data sources.  Using the same, less accurate sea level data, my results for the model fit parameters a, b and T0 were nearly identical to VR2009’s results, and easily within their margins of error.  The point is that I have accurately implemented their model, and to gain credibility when I when I make further claims about it.

Vermeer and Rahmstorf found

a = 5.6 ± 0.5 mm/year/K

b= -49 ± 10 mm/K

To = -0.41 ± 0.03 K

I found

a = 5.6  mm/year/K

b= -52 mm/K

To = -0.42 K

What happens when VR2009 is applied to the more accurate sea level data?

The new values for a, b and T0  are

a = 3.1  mm/year/K

b= -52 mm/K

To = -0.71 K

What do these numbers mean?

Everything.  This is huge.  When these numbers are inserted into Vermeer’s and Rahmstorf’s model equation, and 21st century IPCC temperature scenarios are applied, the resulting  sea level predictions are half of what Vermeer and Rahmstorf claimed.  It is just that simple. 

More details coming soon.

Martin and Stefan, I still have a lot more cards to play.  All in good time.

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