#### 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.

#### 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 *T*_{o} for their model…

#### Rahmstorf and company figured that once *a*, *b*, and *T*_{o} 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 *T*_{o}, 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 *T*_{o}); 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 *T*_{o}, 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

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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] 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