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

November 17, 2010This 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

*T _{0}* 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* T _{0}* that yield the best fit. Then they inserted their values of

*a*,

*b*and

*T*back into the model equation and used IPCC temperature scenarios for the 21st century to determine the sea level rise for the 21st century.

_{0}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* T _{0}* for the VR2009 model equation. Figure 1 shows the components of the sea level.

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.

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).

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.

## 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* T _{0}* 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* T _{0}* 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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