Archive for the ‘Vermeer’ Category

h1

Vermeer and Rahmstorf paper rejected

January 31, 2014

Vermeer and Rahmstorf had a paper rejected by the journal “Climate of the Past.” This news is 16 months old, but I just heard about it, and could find very few references about it on the web.

This paper, On the differences between two semi-empirical sea level models for the last two millennia,  promoted their earlier sea level rise models.  They couldn’t seem to get traction with this paper.

Here are some reviewers’ comments…

One of the major problems with this work is the decidedly biased analysis and presentation.

Highly biased analysis and presentation.

It currently takes significant effort to figure out which pairs of models and training data sets the authors use, and whether they have evaluated all the relevant combinations of the same.

No surprise here.  Rahmstorf has a history of alluding to all kinds of data sets and implying that he has taken them into consideration, but only presenting results for those that support his thesis.

And the final blow…

In the light of the two negative reviews and one comment which all require new analyses and point to fundamental flaws in the methodology of the current paper, I regret to inform you that my conclusion is to support rejection. I strongly dissuade the authors from submitting responses and a revised version.

Here is the paper…

Click for full PDF version

Here is the reviewers’ discussion that lead to the the rejection.

Of course, Vermeer and Rahmstorf do not give up that easily, and similar papers have been shopped around to other journals

h1

Library of data for testing “robustness” of Rahmstorf models

September 5, 2012

This is part 3.5 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 have finally published my small library of temperature, sea-level and sea-level modifier (reservoir storage, groundwater depletion, etc.)  data from various sources.

All of these data files have a consistent format which can be read by my code that calculates fit parameters for the Rahmstorf model relating sea level to temperature.  However, not all of the time series are long enough to be useful in that model.

You can see the data files here.

I am open to suggestions for additions to this list.  If you have any criticisms of the files, such as accuracy of the data, format, selection, anything – please leave a comment.  I will give due attention to any legitimate criticism that is aimed at improving the data.

Coming soon…

I am a slow worker, but I try to be thorough.

The first output from my code, using Rahmstorf’s preferred inputs (GISS temperature, Church and White 2006 sea level data, and the Chao reservoir correction) will be presented soon.  The goal of that presentation will be two-fold: to verify that of my model implementation are consistent with Rahmstorfs; to have a simple format for presenting those result.  That format can then be applied to the results of other input data.

h1

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
……..

h1

Pop Quiz!

February 11, 2012

Have you seen the video on my previous post?  Here is a pop quiz (and opinion poll) to see if you were paying attention.   You can review the video (or see it for the first time) here.


h1

“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.

h1

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.

******************

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

h1

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.

Follow

Get every new post delivered to your Inbox.

Join 52 other followers