Let’s consider the equation that relates sea level rise rate to temperature from Vermeer’s and Rahmstorf’s 2009 PNAS paper, “Global sea level linked to global temperature” (referred to as VR2009 for the rest of the post) again.

where *H* is the sea level and *T* is the global temperature. VR2009 has already told us the values for a, b, and To (* a = 05.6 mm*a^{-1}K^{-1}*,

*b*= -49 mm*K

^{-1}, and

*T*= -0.41 K).

_{o}Some of the bizarre consequences of this formula have already been discussed extensively.

## Applying VR2009 to satellite sea level data.

Here I apply their formula to the best sea level data available, from the Topex and Jason-1 satellites.

The graph below shows the result of using the GISS monthly temperature data, covering 1996 to the present, to calculate the sea level from VR2009’s equation. It also shows the actual satellite sea level data covering the same time period, and a version of the sea level data that has a reservoir “correction” applied. Click on the image to enlarge.

The thing that should jump out at you is that the calculated sea level shows an increasing rise rate, while the actual satellite derived data for the same time period shows a decreasing sea level rise rate. This may look like a subtle point, but predictions of sea level rise in the 21st century are extremely sensitive to these types of differences. A model that is applied to the best data of the last one and a half decades and cannot even get the sign of the change of the sea level rise rate (*d ^{2}H/dt^{2}*) correct cannot possibly be trusted to draw conclusions about the remainder of the 21st century.

## Reversed look: getting temperature from the sea level data

In my previous posts I have used VR2009’s equation on various temperature scenarios to generate sea levels. We can reverse this process by re-arranging VR2009’s equation to use sea levels to generate temperature….

Fitting the satellite sea level data, H, to a function, inserting the function’s derivative (dH/dt) into equation 2, and solving the differential equation will give an analytical solution for the temperature. Reasonable initial conditions can be extracted from the GISS temperature data.*****

The graph of temperature vs. time, below, shows the result of this process. It shows the GISS 5-year mean temperature, the GISS monthly land+ocean temperature (which covers 1996 to present), and the 7-month running average of the GISS monthly land+ocean temperature. Contrasted to these three versions of the GISS temperature data is the temperature that the VR2009 model (equation 1, above) would require to yield a sea level that looks like the actual satellite measured sea level (from 1996 to present).

So, VR2009 would require a ridiculously rising temperature to generate the measured sea level rise of the last decade and a half. This bizarre result is one more reason that VR2009 should be rejected

________________________

* In my example, the satellite sea level data from 1996 to the present was fit to a quadratic, as shown in figure 1…

The initial condition was chosen as 0.44 degress in the year 2001.5, as indicated by the GISS 5-year mean.