Posts Tagged ‘Climate related sea-level variations over the past two millennia’

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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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Gordian Knot of Nonsense – Part 6. Irrelevance of Baysian Analysis

May 28, 2012

It has been a while since I wrote about ”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), which I will refer to as KMVR2011.

Please see this index of my posts concerning KMVR2011.

I want to sew up one loose end here.  Last time around I showed that this latest incarnation of the Rahmstorf model relating sea level to temperature was just as bogus at the previous versions. But I did not talk about one of their interesting (but ultimately irrelevant) new twists. Another layer of complexity was added by the application of Bayesian analysis, or in KMVR2011 nomenclature: “Bayesian multiple change-point regression.”

Bayesian analysis is a useful, but often counter intuitive, statistical method to tease out an underlying distribution from an observed distribution. That being said, the KMVR2011 application of Bayesian analysis starts out with a bogus model, which has been demonstrated ad nauseam. (See here and here.)  This added layer of complexity simply obfuscates the failures of the starting model, rather that addressing those failures.

My next series of posts will move on to another recent outing by Rahmstorf and company – Testing the robustness of semi-empirical sea level projections  (Rahmstrof, et. al., Climate Dynamics, November 2011)

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Gordian Knot of Nonsense – Part 5. Resulting sea-level rise rates

November 20, 2011

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.

Please see this index of my posts concerning KMVR2011. Check back occasionally because the list of posts is slowly growing.

I will keep things almost entirely graphical this time around (no equations, YEAH!).

Figure 1. Figure 4c from KMVR2011. Global EIV land and ocean temperature and KMVR2011 equilibrium temperature.

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Figure 2. Same as figure 1 from digitized data.

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Figure 3. Same as figure 2 overlaid with GISS temperature (raw and smoothed) and with five hypothetical temperature scenarios starting around 1950

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Figure 4. Same as figure 3, zoomed in to 20th century

Consider the temperature scenarios shown in figure 4.  Which one do you think would lead to higher sea-level rise rates, γ=0.9 or γ=1.1?  Take a look at figure 5, and you may be surprised!

Figure 5. Resulting Sea-Level rise rates when the KMVR20011 model is applied to my hypothetical temperature scenarios compared to the results when the model is applied to GISS temperature.

No Mistake

This not a result of some outrageous error in my calculations.  This is a direct consequence of the KMVR2011 model.  Like VR2009, this bizarre result comes from choosing b to be negative (their choice, not mine).

Some may argue that KMVR2011 uses a wide range of values for the variables in their Bayesian updating.  True enough.  But they kept b negative.  ALL combinations of variables that they used would give qualitatively the same results that I have shown.

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