Archive for the ‘PNAS’ Category

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Rahmstorf: Is it OK to call him an “alarmist” now?

May 9, 2012

Some folks never give up.  In the following video Stefan Rahmstorf says…

To me a tipping point in the climate system is like a sweet spot in the climate system, where a small perturbation can have a major, even qualitative effect.  It’s like a small change in temperature moving, for example, the Greenland Ice sheet beyond the point where eventually it will melt down all together…from about 2 degrees global warming there would be a risk of the complete meltdown of the Greenland Ice sheet…I think this two degree limit agreed in Cancun by the politicians may not be enough to prevent a dangerous interference in the climate system.

Now let’s be clear about this: a “complete meltdown” of the Greenland ice sheet would raise the planet’s sea level 7 meters (7000 mm).  The sea level rise rate today is about 3 mm per year and decreasing according to satellite data.  A rational reading the tide gauge data is even less.

I guess in Greenland ice must melt at -25°C.  Here is today’s temperature outlook…

Oh, I know, the scientifically sophomoric sophisticated will tell us all about the rapidly accelerating glaciers.  Well, their favorite journal, Science, throws a little icy cold water on their dreams of catastrophic nirvana.  In 21st-Century Evolution of Greenland Outlet Glacier Velocities ( T. Moon, et. al., Science, 4 May 2012, Vol. 336, pp. 576-578)  Moon et. al. produced “a decade-long (2000 to 2010) record documenting the ongoing velocity evolution of nearly all (200+) of Greenland’s major outlet glaciers.”  They found that in some regions there was a glacier acceleration (SEE! SEE!), but not very consistently over the last 10 years.  Here is their conclusion

Our observations have implications for recent work on sea level rise. Earlier research (33) used a kinematic approach to estimate upper bounds of 0.8 to 2.0 m for 21st-century sea level rise. In Greenland, this work assumed ice-sheet–wide doubling of glacier speeds (low-end scenario) or an order of magnitude increase in speeds (high-end scenario) from 2000 to 2010. Our wide sampling of actual 2000 to 2010 changes shows that glacier acceleration across the ice sheet remains far below these estimates, suggesting that sea level rise associated with Greenland glacier dynamics remains well below the low-end scenario (9.3 cm by 2100) at present. Continued acceleration, however,may cause sea level rise to approach the low-end limit by this century’s end. Our sampling of a large population of glaciers, many of which have sustained considerable thinning and retreat, suggests little potential for the type of widespread extreme (i.e., order of magnitude) acceleration represented in the high-end scenario (46.7 cm by 2100). Our result is consistent with findings from recent numerical flow models (34).

So, Rahmstorf is worried about a “complete meltdown of the Greenland ice sheet” which would lead to 7 meters (7000 mm) of sea level rise, but the data shows “sea level rise associated with Greenland glacier dynamics remains well below the low-end scenario (9.3 cm by 2100)” (93 mm by 2100).  Does being off by a factor of 75 (7000/93) qualify as “alarmist?”

By the way, when Moon says “Earlier research (33) used a kinematic approach to estimate upper bounds of 0.8 to 2.0 m for 21st-century sea level rise” he is talking about Kinematic Constraints on Glacier Contributions to 21st Century Sea-Level Rise (Pfeffer, et. al., Science, 5 September 2008, Vol. 321. no. 5894, pp. 1340 – 1343).  I discussed this paper at length two years ago in my “Reply to John Mashey.” (Still feeling smug, John?) 

And finally,  Moon’s last sentence says “Our result is consistent with findings from recent numerical flow models (34).”  He is talking about Committed sea-level rise for the next century from Greenland ice sheet dynamics during the past decade (Price, et. al., PNAS, 31 May 2011, vol. 108 no. 22 pp. 8978-8983).    Price, et. al. say

The modeling conducted here and some reasonable assumptions can be used to make approximate upper-bound estimates for future SLR from GIS [Greenland Ice Sheet] dynamics, without accounting for future dynamical changes explicitly. As discussed above, numerous observations indicate that the trigger for the majority of dynamic thinning in Greenland during the last decade was episodic in nature, as the result of incursions of relatively warm ocean waters. By assuming that similar perturbations occur at regular intervals over the next century and that the ice sheet responds in a similar manner, we can repeatedly combine (sum) the cumulative SLR [sea level rise] curve from Fig. 4B to arrive at additional estimates for SLR by 2100. For example, if perturbations like those during the last decade recur every 50, 20, or 10 y during the next 100 y, we estimate a cumulative SLR from GIS dynamics by 2100 of approximately 10, 25, and 45 mm, respectively…Addition of the estimated 40 mm of SLR from changes in SMB [surface mass balance] by 2100 would result in a total SLR from Greenland of 85 mm by 2100.

Holy cow! Rahmstorf is telling us to be worried about 7000 mm of sea level rise due to the “complete meltdown of the Greenland ice sheet,” but Price et. al. say maybe 85 mm due to Greenland by 2100.

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“Disbelieving is hard work”

January 19, 2012

Daniel Kahneman

Theory-induced blindness and Vermeer’s and Rahmstorf’s “Global sea level linked to global temperature.”

In one of the many interesting chapters of  Thinking, Fast and Slow, Daniel Kahneman, Princeton University Emeritus Professor of Psychology and winner of the 2002 Nobel Prize in Economics discussed Daniel Bernoulli’s 250-year-old mathematical theory of risk aversion. 

Kahneman points out that “Bernoulli’s essay is a marvel of concise brilliance…

Most impressive, his analysis… has stood the test of time: it is still current in economic analysis almost 300 years later.  The longevity of the theory is all the more remarkable because it is seriously flawed.  The errors of a theory are rarely found in what it asserts explicitly; they hide in what it ignores or tacitly assumes”

Kahneman then goes on to demolish of Bernoulli’s theory.  This demolition is simple and incontrovertible, takes about one page, and is easily understood by anybody of average intelligence. Kahneman says this about the demolition…

“All this is rather obvious, isn’t it?  One could easily imagine Bernoulli himself constructing similar examples and developing a more complex theory to accommodate them; for some reason, he did not.  One could imagine colleagues of his time disagreeing with him, or later scholars objecting as they read his essay; for some reason, they did not either.

The mystery is how a conception … that is vulnerable to such obvious counterexamples survived for so long.  I can explain it only by a weakness of the scholarly mind that I have often observed in myself.  I call it theory-induced blindness: once you have accepted a theory and used it as a tool in your thinking, it is extraordinarily difficult to notice its flaws.  If you come upon an observation that does not seem to fit the model, you assume that there must be a perfectly good explanation that you are somehow missing.  You give the theory the benefit of the doubt, trusting the community of experts who have accepted it.  Many scholars have surely thought at one time or another of stories such as [the examples that Kahneman gives] and casually noted that these stories did not jibe…But they did not pursue the idea to the point of saying ‘this theory is seriously wrong because it ignores the fact[s]‘…As the psychologist Daniel Gilbert observed, disbelieving is hard work…”

What does all this have to do with ClimateSanity?  Simple – it sounds like Vermeer’s and Rahmstorf’s model linking global sea level to global temperature (“Global sea level linked to global temperature,” Proceedings of the National Academy of Science, December 22, 2009 vol. 106 no. 51 21527-21532 ).  It has been incontrovertibly demolished, but the believer’s just can’t let it go.  They must suffer theory-induced blindness.  They seem to have endless capacity to simply overlook the plethora of bizarre, improbable or impossible consequences of the Vermeer and Rahmstorf  model.

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Rahmstorf (2009): Off the mark again (part 13), 21st century projections with gamma = 1

December 16, 2011

Recall the six IPCC families of temperature scenarios, summed up in the following IPCC figure.  VR2009 applied these temperature scenarios to their model to yield corresponding sea level rise rates.  Let’s consider the A1F1 and A1T temperature scenarios.

Figure 1. (top) This is figure 10.26 from the IPCC AR4 Chapter 10, "Global Climate Projections." It shows the temperature projections for each of the six IPCC SRES emission scenarios averaged for the 19 AOGCM models and 3 carbon cycle feed backs and the standard deviations. (bottom) Zoom in on A1F1 and A1t averages.

Here are the resulting VR2009 sea-level rise rates for the A1T and A1F1 scenarios…

Figure 2. Resulting sea level rise rates when the VR2009 model is applied to the A1T and A1F1 temperature scenarios.

Figure 2. Resulting sea level rise rates when the VR2009 model is applied to the A1T and A1F1 temperature scenarios.

Nothing really surprising so far. The sea level rise rates look more or less like the temperatures. 

Now consider some the following hypothetical 21st century scenarios.  Note that they can’t be considered “extreme” when compared the 21st century temperature scenarios already used by VR2009.

Figure 3. The same IPCC temperature scenarios, A1T and A1F1, as in figure 1 and three hypothetical temperature scenarios from Moriarty.

Here are the resulting sea level rise rates…

Figure 4. The sea level rise rates due to the A1T and A1F1 temperature scenarios and three the hypothetical temperature scenarios from Moriarty.

Where are the sea level rise rates for Moriarty’s hypothetical temperature scenarios?  They are perfectly hidden below the sea A1T sea level rise rate.  How can that be?  Because they were designed to be that way to make a point.  See the math here and let γ=1 in equation (VIII) and you will get the idea.  This is not some mistake in my math, but rather a direct consequence of the VR2009 and one more illustration of the bizarre consequences of their model.

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Gordian Knot of Nonsense – Part 3. More Math (Sorry about that.)

September 22, 2011

“Make everything as simple as possible, but not simpler”

Albert Einstein

As usual, I will refer to ”Climate related sea-level variations over the past two millennia” (Andrew C. Kemp, Benjamin P. Horton, Jeffrey P. Donnelly, Michael E. Mann, Martin Vermeer, and Stefan Rahmstorf, PNAS, 2011)  as KMVR2011.

I would like to elaborate on my previous post, in which I presented a simple temperature vs. time function that causes KMVR2011’s model relating sea level rise rate to global temperature behave in a rather peculiar manner.  I am trying to find a balance between simplicity, clarity and thoroughness.  The level of mathematical literacy of my readers may vary widely, but this time around I need to employ some calculus.  If the equations bother you,  just consider the conclusions.

Starting with the conclusions

There exists a simple class of realistic temperature vs. time functions, which when applied to KMVR2011’s model yield results that disqualify it as representing a relationship between global temperature and sea level rise rate.  This class of temperature vs. time functions gives a family of curves for which it is guaranteed that the higher the temperature the lower the sea level rise rate.  This implausible effect is so severe that if forces rejection of the KMVR2011 model.

The Math

Here is the KMVR2011 model


where

Where H is the sea level, T(t) is the global temperature, Too, a1, a2, b and τ are all constants and To(t) is a to-be-determined time varying function related to T(t) as defined by equation Ia.

Now, consider the following temperature evolution.  It is nearly the same as equation II from my previous post, but has an additional unitless constant, γ (a.k.a. “gamma”), in the exponential…

If equation II is inserted into equation I, then…

Rearranging terms in equation III gives…


H is the sea level.  dH/dt, the derivative of the sea level,  is the sea level rise rate.  d2H/dt2, the second derivative of the sea level, is the rate at which the sea level rise rate changes.  That is, d2H/dt2, is the acceleration.  If d2H/dt2, is positive, the sea level rise rate is increasing.  Conversely, if d2H/dt2, is negative, then the sea level rise rate is decreasing.  Taking the time derivative of equation IIIa gives…


Let’s also consider the difference in the sea level rise rates at some time, t, for different values of γ.  We can do this by analyzing the derivative of dH/dt (equation IIIa) with respect to γ.

What does the math tell us?

KMVR2011 does not conclude with specific values for their model constants and their time varying T0(t).  Instead, they present probability density distributions for some constants, or combination of constants.  However, there are some definite constraints that can be noted about the variables and their relationships to each other.  These constraints are key to my conclusions.

Constraints:

  1. a1 + a2 = a, where a1 and a2 are defined in KMVR2011 (see equation I, above) and a is defined in VR2009.  VR2009 found a = 5.6 mm/yr/K.
  2. a1 > 0 mm/yr/K  and a2 > 0 mm/yr/K.  KMVR20011 states that the distribution of a1 for their Bayesian analysis varied between 0.01 and 0.51 mm/yr/K.   Needless to say, if either of these terms were less than zero the KMVR2011 model would make even less sense that it does now.  That would be a road that the KMVR2011 authors do not want to travel.
  3. b < 0 .  VR2009 found b = -49 mm/K.   KMVR2011 varied b about -49 mm/K with σ2 = (10 mm/K)2 for their Bayesian analysis.
  4. C  > 0.  C is a unitless constant that I introduced, and for the purposes of this post I am constraining C to be greater than zero.
  5. γ > 0γ is a unitless constant that I introduced, and for the purposes of this post I am constraining γ to be greater than zero.
  6. Time, t, is restricted to about 1900 and later for my hypothetical temperature (equation II).  This insures that T(t) > T0(t), which in turn insures that dT0(t)/dt > 0.

The equations above, coupled with the listed constraints guarantee the signs of the derivatives shown in table 1, below.

Table 1. Derivatives of temperatures and second derivatives of sea level. Green “up arrows” indicate increasing values and red “down arrows” indicate decreasing values.

As you can see from table 1, it gets little confusing for 0<γ<1.  When a1, a2, b, C, and γ conform to the listed constraints, the signs of the various derivatives are known with certainty as long as…


But when …


at some point in time t- t’ will become large enough that d2H/dγdt will become positive.  When that time occurs depends on the choices of a1, a2, b  and γ.  If we choose a1, a2 and b to agree with VR2009 (recall a+a2 = a = 5.6 mm/yr/K, and b = -49 mm/K) and γ = 0.8, then d2H/dγdt will continue to be negative until t – t’ = 44 years.

The conclusion, again.

Equation 2, above, can be used to build realistic hypothetical temperature evolutions.  See figure 1, here, for some examples.  Remember, KMR2011’s model relates sea level rise to temperature, and when applied to these hypothetical temperatures it must yield realistic sea level rises.  It does not. 

Table 1 shows various aspects of temperature and sea level using my hypothetical temperature evolution and KMVR2011’s resulting sea levels.  Summed up succinctly, the table shows that with this combination the greater temperatures result in lower sea levels.  This implausible situation disqualifies KMVR2011’s model. 

Coming soon

I realize that a bunch of equations and a table do not give visceral understanding of this effect.  A graphical illustration of these points will be coming soon.

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Update (9/30/11)
Table 1 corrected.  Change makes no difference to conclusions.

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Gordian Knot of Nonsense – Part 1. Rahmstorf and company strike again.

August 28, 2011

Rahmstorf and friends are at it again, but this time they have signed on a bigger fish: Michael Mann of hockey stick infamy.  Somehow it does not surprise me that this new serving of dribble comes to us via the Proceedings of the National Academy of Sciences.  Frankly, it grieves me to know that this is the state of the scientific culture in the US. 123

I will refer to “Climate related sea-level variations over the past two millennia” (Andrew C. Kemp, Benjamin P. Horton, Jeffrey P. Donnelly, Michael E. Mann, Martin Vermeer, and Stefan Rahmstorf, PNAS, 2011)  as KMVR2011.  This paper dishes up a third generation model relating sea level rise rate to temperature whose immediate ancestors are Rahmstorf’s 2007 model and Vermeer’s and Rahmstorf’s 2009 model.

With H being sea level and T being global temperature the models have evolved as follows.

Generation 1, form Rahmstorf’s 2007 “A Semi-Empirical Approach to Projecting Future Sea-Level Rise

Generation 2, from Vermeer and Rahmstorf’s 2009 “Global sea level linked to global temperature


And now, Generation 3, from KMVR2011


where


A cursory examination of equation I makes it plain the this new model is simply the cobbling together of  the VR2009 model (with a1 and Too in this model being the same as a and To  respectively in VR2009) with an additional term,  a2[T(t) - T0(t)], taken from Jevrejeva (GRL, 37, 2010).  KMVR2011 sum up the meanings of each term in equation I as follows…

The first term captures a slow response compared to the time scale of interest (now one or two millennia, rather than one or two centuries as in [VR2009]). The second term represents intermediate time scales, where an initial linear rise gradually saturates with time scale τ as the base temperature (T0) catches up with T. In [VR2009], T0 was assumed to be constant. The third term is the immediate response term introduced by [VR2009]; it is of little consequence for the slower sea-level changes considered in this paper.

 In Rahmstorf’s 2007 model linking sea level rise rate to temperature there were only two constants (a and To) that needed to be determined.  The 2009 Vermeer and Rahmstorf (VR2009) model went a step further with three constants (a, To, and b) that needed to be determined.  The new KMVR2011 model advances the science with four constants (a1, a2, Too and b).  Count them!  But even more astonishing: this model requires not just solving for the four constants, but also a time varying function (To(t) )!

Back at the keyboard

I have had a leisurely summer, and have not written any blog posts for several months, but my eyes and ears have been open, and my pencil has scratched out a few equations.   This post represents the beginning of a new series on KMVR2011, which I will call the “Gordian Knot of Nonsense.”

This series will be interspersed with posts on other topics, so please check back occasionally for updates.

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Rahmstorf (2009): Off the mark again (Part 12). A mathematical comedy

February 13, 2011

Here is one more post about the laughably bad PNAS “Global Sea level linked to global temperature” by Vermeer and Rahmstorf.  Will this  fount of absurdity never run dry?

Much has been said about Rahmstorf’s data smoothing techniques.  But the little gem you are about read may make your head spin.

Remember the Chao reservoir correction?  This was the correction that VR2009 applied to the Church and White sea level data to compensate for water that has been impounded in man-made reservoirs.  Never mind the fact that VR2009 paid lip service to, but did not include, a counter-correction for water that has been pumped from the aquifers and has artificially added to the sea level.  Let’s look at some details of how VR2009 handled this correction.

Here is something amazing…

VR2009 had the 2006 Church and White sea level data, which is rather noisy.  They also had the Chao reservoir correction data, which is also noisy.  They correctly saw the need to smooth the noisy data.  It seems that they could have done it one of  two ways: smooth each set separately, then  add the smoothed Chao data to the smoothed Church and White data, or add the unsmoothed Chao data to the unsmoothed Church and White data and then smooth the result.

When I reproduced VR2009’s basic algorithm, I choose the first method.  But VR2009 doubled up on smoothing the Choa reservoir correction.  They smoothed the Chao data, added it to the unsmoothed Church and White data, then smoothed the sum again.  So, the Chao data was effectively smoothed twice.

But here is the really amazing thing:  Look at the overlay of Chao’s data, VR2009’s smooth for the Chao data, and my smooth for the Chao data…

Figure 1. Chao correction to sea level rise rate with VR2009 smooth and Moriarty smooth

Wow! All I can say is “Wow!”  Can you believe how terrible the VR2009 fit for the additional sea level rise rate is?  It’s just amazingly bad! 

How did VR2009 come up with this bizarre data smooth?

In the Matlab program file that VR2009 uses to find the relationship between sea level and temperature (sealevel2.m, get copy here) they first import the unsmoothed Church and White data (church_13221.txt, get copy here) with the following code…

% load the church & white sea level data
load church_13221.txt;
seayear = church_13221(:,1);
sealevel = church_13221(:,2)/10;

Two arrays are created, one with the year, one with the sea level.  The “/10″ in the last line of code converts the sea level data from mm to cm.

Then they apply their Chao reservoir correction.  Instead of importing a time series with the Chao data, they apply a function…

% Apply Chao et al (2008) reservoir correction:
if chao == ‘y’
     sealevel = sealevel + 1.65 + (3.7/3.1415)*atan2(seayear-1978,13);
end

So, VR2009 claims the term “1.65 + (3.7/3.1415)*atan2(seayear-1978,13)” is a representation of the Chao reservoir correction.  Figure 1, above shows the derivative of the Chao reservoir correction (which you can see as figure 3 in Chao’s Science paper).  So the derivative of VR2009’s Chao correction term should at least be close to the derivative provided in Chao’s paper.  Alas, instead it looks like the blue peak in figure 1, above. 

How did VR2009 come up with this strange correction that “fits” the Chao reservoir correction to an inverse tangent (atan2) function?  VR2009 claims to use sophisticated single spectrum analysis (SSA) to smooth its sea level and temperature data.  But their SSA code yields a numerical result, not an analytic one (that is, a time series of numbers, not a formula).  So SSA was NOT used to generate VR2009’s Chao correction term.

If you use my smooth of the Chao data as a baseline, then the VR2009 fit is about 0.2 mm too low around 1960 and about 0.3 mm too high by 1980.  By using their fit to the Chao reservoir sea level rise rate correction, they have effectively increased the sea level rise rate from 1960 to 1980 by an additional 0.5 mm per year.  They have pushed the Chao sea leve rise rate correction to later in the century which, of course, fits their general theme.

The following plot shows the 2006 Church and White sea level data with the questionable VR2009 version of the  Chao reservoir correction data and my version of the Chao reservoir correction.  At first they do not look much different.  But consider this: The VR2009 version causes the average sea level rise rate from 1950 to 1970 to be 1.66 mm/year, and for 1970 to 1990 to be  1.99 mm/year.  That’s a 16% increase.  If my version is used there is an average DECREASE in sea level rise rate, from 1.87 mm/year to 1.78 mm/year.  That is a 5% drop.  Look at figure 1, above, and ask yourself “Whose smooth of the Chao data is better?”

I will not attempt to assign motivation for this laughably bad smooth of the Chao reservoir correction data.  Suffice it to say that it is just one more in long series of blunders and bizarre consequences for VR2009.

Read more about the comedy known as the PNAS “Global Sea level linked to global temperature” by Vermeer and Rahmstorf.

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Rahmstorf (2009): Off the mark again (part 11). VR2009 Matlab code

February 6, 2011

I have written much about Vermeer and Rahmstorf’s 2009 Proceedings of the National Academy of sciences paper “Global sea level linked to global temperature“  (referred to as “VR2009″ in my series of posts).  I have reproduced their algorithm with my own code. 

I thought it would be useful to provide any interested readers easy access to VR2009’s code.  The PDF version of their paper  had a link (which has been long broken) to The National Academy of Sciences website that was supposed to provide the VR2009 code in a zipped file format.  After the original link was broken Kay McLaughlin (PNAS Editorial Staff) kindly sent me this new link.  Just in case that link  breaks, I have archived the zipped file here.  If you unpack the zipped file you will get 24 files: some Matlab code files, some text files, and some .dat files.  Or you can simply look at the list of 24 links at the bottom of this post to download any one of the 24 files individually.

I am not a Matlab programmer, nor was I willing to pay several thousand dollars to buy Matlab.  However, there is a free set of software call GNU Octave, which is highly compatible with Matlab.  With some minor modifications I was able to get VR2009’s “sealevel2.m” file to execute.  The fly in the ointment is that VR2009’s “Sealevel2.m” calls another Matlab file called ‘ssatrend.m,” which is supposed to do single spectrum analysis to smooth the input sea level and temperature data.  VR2009 did not write “ssatrend.m,” but rather reference Aslak Grinsted for this code.  I could not get this version of “ssatrent.m” to work with VR2009’s “sealevel2.m.” 

I had gone down a rabbit hole when I tried to reproduce Rahmstorf’s 2007 results, and I was not going to make the same mistake twice.  So, I simply used LabVIEW to reproduce VR2009’s basic algorithm using my own preferred smoothing method, which I have written about extensively.

It is interesting to note that Rahmstorf’s 2007 science paper also used “ssatrend.m.”  Nicolas Nierenberg at Neirenberg’s Climate Musings pointed out that…

I wrote Dr. Grinsted who wrote me back very promptly, and sent me the source code to ssatrend.m. He also commented that he had no idea how Dr. Rahmstorf had gotten a copy of it, and that he had never meant for it to be distributed. I think that he was just concerned about it being unsupported. My own view is that it is pretty strange to use some random piece of code in a published paper without making the code your own.

Maybe by 2009 Rahmstorf or Vermeer had made contact with Aslak Grinsted and made more conventional arrangements to use his code for VR2009, but I don’s know.

For your reading pleasure, here is an unzipped version of VR2009’s code and results. 
eta_1000y_10be.dat
ipcc_scenarios.dat
sat_1000y_10be.dat
sat_1000y_14c.dat
sat_1750_2100_SRES.dat
ssh_steric_1750_2100_SRES.dat
eta_1000y_14c.dat
chao.m
jack.m
millennium.m
RECE.m
sealevel_predict.m
sealevel2.m
delay_cont.m
autocorr.m
magicc_scenarios.mat
church_13221.txt
giss_landocean.txt
README.TXT
resleft.txt
resright.txt
sl.txt
resid_ab.txt
resid_a.txt

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