Archive for the ‘rise’ Category


What is RealClimate afraid of?

December 10, 2010

I left a comment over at RealClimate on December 4th 6th and they deleted it.   I expected them to delete it, since that is what they have done before.  I had the foresight to take a screen shot of their page with the comment and you can read it by clicking on the following image.  Yes it was off-topic, but they don’t seem to delete other off-topic (sycophantic) comments.   You can make your own judgement about why they deleted it.   

My comment dealt with a very serious issue that needs to be addressed by Stefan Rahmstorf – he can only ignore it for so long.

The issues pointed out in the comment are covered in more depth here, here, and here.

If you have read the three above links, then please answer the following poll…

I’m sorry that I spelled “Rahmstorf” incorrectly in the salutation of my comment.  My name is also frequently spelled wrong, but I’m used to it.


Rahmstorf (2009): Off the mark again (part 10). Sea level projections exaggerated by factor of 2

November 28, 2010

This is part 10 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).

In my last post I pointed out that VR2009 used out-date sea-level data from Church and White, and did not include a correction for groundwater depletion.  Even if  you believe the validity of their very dubious model, these two flaws cause VR2009’s projections of sea level rise for the 21st century to be overstated by a factor of two.

VR2009 proposed a model linking sea level rise to global temperature based on the following equation…

When Vermeer and Rahmstorf used inadequate sea level data they found

a = 5.6 mm/year/K
b = -49 mm/K
To = -0.41 K

When I used the superior sea level data that included the Church and White sea level update and the Wada groundwater depletion correction I found

a = 3.1 mm/year/K
b = -52 mm/K
To = -0.71 K

VR2009 said that they applied their model with their fit parameters to 342 temperature scenarios.  How did they come up with 342?  They borrowed them from the IPCC, who applied six IPCC SRES emission scenarios to nineteen Atmosphere-Ocean General Circulation Models (AOGCM) with high, medium and low-carbon cycle feedbacks (6 x 19 x 3 = 342).

IPCC SRES emission scenarios

The six emission scenarios are the inventions of the IPCC and are summarized in the IPCC  SRES (Special Report on Emission scenarios).  Their differences lie in their assumptions about global economic, technological and social changes during the coming decades.  Each set of assumptions results in different levels of CO2 emissions.  Under some assumptions the use of fossil fuels will increase dramatically, but under others the use of fossil fuels will reach a peak in mid-century and then start to drop off.

Carbon Cycle feedbacks

The amount of predicted CO2 in the air during the 21st century depends on more than just the CO2 emissions. It also depends on carbon cycle feedbacks. For example, warmer oceans would remove CO2 from the atmosphere slower than colder oceans, everything else being equal. The possible feedbacks are not necessarily well understood or well quantified, and each AOGCM model handles them differently.

 Atmosphere-Ocean General Circulation Models (AOGCM)

There are about 2 dozen prominent Atmosphere-Ocean General Circulation Models (AOGCM) made by various groups around the world.  Each AOGCM purports to simulate the flow of energy and matter through atmosphere and oceans and therefore yield their evolution into the future.   The SRES emission scenarios and carbon cycle feedbacks can be plugged into each AOGCM, which calculate various parameters, including temperature, for each year of the 21st century. 

Combining IPCC SRES & Carbon Cycle feedbacks & AOGCMs

The IPCC 4th Assessment Report used 19 AOGCMs, three carbon cycle feedback schemes with six families of temperature scenarios, one for each SRES emission scenario (19 x 3 x 6 = 342).  These are the temperature scenarios used by VR2009.  These families of temperature scenarios are summed up in the following IPCC figure.

This is figure 10.26 from the IPCC AR4 Chapter 10, "Global Climate Projections." It shows the temperature projections for each of the six IPCC SRES emission scenarios averaged for the 19 AOGCM models and 3 carbon cycle feed backs and the standard deviations.

Figure 1. This is figure 10.26 from the IPCC AR4 Chapter 10, "Global Climate Projections." It shows the temperature projections for each of the six IPCC SRES emission scenarios averaged for the 19 AOGCM models and 3 carbon cycle feed backs and the standard deviations.

I do not have the 342 temperature  scenarios used to construct figure 1 and used by VR2009, but I am working on it.  The most extreme of these 342 temperature scenarios falls under the A1F1 emission scenario, and yields Vermeer’s and Rahmstorf’s widely echoed 1.8 meter sea level rise for the 21st century.  If I had the temperature data for that particular AOGCM/SRES emission scenario/carbon cycle feed back scenario, I would simply insert it into VR2009’s model using their fit parameters and then again using my fit parameters.  Their fit parameters would  yield 180 cm, and mine would yield about half of that.

Instead I have digitized the IPCC temperature data shown in figure 1, above.  My digitized version of the data is shown in figure 2, below.  Note that I have translated the temperatures about 0.25° higher than in figure 1 because the IPCC used the 1980-1999 temperature average for their zero point (see IPCC AR4, chapter 10, section 3.1), but VR2009 and I used the 1950 to 1980 temperature average as the zero point. The following image is a reproduction of the IPCC temperature data shown in figure 1, and the data can be downloaded here

Figure 2. Reproduction of IPCC AR4 figure 10.26 from data digitized from IPCC figure. I have added about 0.25 degrees to change the zero baseline from 1980-1999 to 1950-1980.

If VR2009’s model with their fit parameters (using the  out-dated Church and White sea level data without the Wada groundwater depletion correction) and my fit parameters (using updated Church and White sea level data and the Wada groundwater depletion correction) is applied to the average temperatures  (dark central curves) from the six scenarios in figures 1 or 2, then the difference in projected sea level rise is quite stark.

Figure 3. Sea level rises from averge temperatures in the six SRES scenarios.

Similarly, both sets of fit parameters can be used to calculate sea levels for the higher temperature scenarios that match the upper edge of the shaded areas in figures 1 and 2.

Figure 4. Sea level rises for higher temerature scenarios.

The Difference

This is pretty easy to see.  Figures 4 & 5 show that when the updated Church and White data are used and the Wada groundwater depletion correction is added the sea level rise rates are cut almost exactly in half…

Figure 5. Using the proper sea level data cuts VR2009's sea level rise projections in half.

It can be shown that this approximately 50% difference will occur for any of the 342 temperature scenarios the VR2009 used.


Vermeer’s and Rahmstorf’s model is bogus for the many reasons that I have explained in previous posts.  But even if the concept of their model were valid, it would still yield sea level rises that are two times too large when it starts with the out-dated version of Church and White sea data and neglects the correction for groundwater depletion.

Surely Vermeer and Rahmstorf are aware of the updated Church and White data.  That update occurred about the same time that VR2009 was published, and possibly before.  It would be a simple exercise for Vermeer and Rahmstorf  to update their fit parameters based on the updated Church and White data.  It would be instantly obvious to them that their extreme sea level rise projections are far too large.  Then they could write letters to the editors of the multiple publications that quoted their 1.8 meter projection and tell them about the lower numbers.  Or they could post some comments about the corrections on the endless list of blogs and websites that have repeated their extreme numbers. 

Heck, Stefan Rahmstorf even has the keys to the control panel over at  RealClimate is seen by at least a hundred times as many readers than my humble ClimateSanity.  Martin Vermeer has even held forth as a guest commentator at RealClimate with a self congradulatory love-fest over the publication of VR2009.   (Despite the all-star cast over at RealClimate, they do seem to have a slight problem handling non-sycophantic comments.)

You would think that Stefan and Martin could get together and post an article at RealClimate with corrected fit parameters for their profound dubious model.  They could bill it as “Good News:” maybe the world is not coming to an end after all. 

Nah, that wouldn’t be any fun.


Update 1/29/11

I realized that I inadvertently made my sea level calculations for the above for figures 3, 4, and 5 using To=-0.44 K.  I actually calculated To to be -0.71 K.  Mea culpa.   As of today, the graphs in figures 3 and 4, and the ratios in figure 5 are corrected to my calculated value of  To=-0.71 K.  It makes very little difference to the conclusions. (Tom Moriarty)


Rahmstorf (2009): Off the mark again (Part 6 and a half). Gory details

June 11, 2010

This is to fill in some of the details of the math used to reverse Vermeer’s and Rahmstorf’s model ( Global sea level linked to global temperature, 2009, PNAS) to give temperature as a function of sea level.  In my previous post I skipped over these details for the sake of brevity.

In various posts I have used Vermeer’s and Rahmsorf’s (VR2009 for rest of this post) model that relates sea level rise rate to global temperature to see how different temperature scenarios would result in sea level rise rates, according to VR2009.  In my previous post I inverted their model to calculate the temperature from satellite sea level data.  Here are the details of that inversion…

The Math

Starting with VR2009’s model…

Re-arranging equation 1 gives…

If we assume that dH/dt is a known function of t, then equation 2 is a first order linear differential equation.  So, multiplying both sides of equation 2 by exp(at/b) gives..

The left side of equation 3 can be re-written…

If both sides of equation 4 are integrated, then…

Solving for T….

Remember, we are assuming that dH/dt is a known function of t.   We will get that function by taking the derivative of a quadratic fit of satellite derived sea level data.   That is, the satellite sea level data will be fit to…

So, substituting equation 7 into equation 6 gives….

We can solve the integral on the right side of equation 8 as follows…

Substituting equation 9 into equation 8 gives…

So far, so good.

a, b, and T0 are given by VR2009.  c1 and c2 are determined from the best fit of H to a quadratic.  That leaves only c4 as an unknown.  If initial conditions (that is, the temperature, T’,  at time, t’) are known, then equation 10 can be solved for c4

Initial conditions

There are a variety of sources for getting initial conditions (temperature, T’,  at time, t’) to calculate c4 in equation 11.  However, the final results of the temperature that comes from equation 10 is highly sensitive to c4, which is in turn highly sensitive to the chosen initial conditions.  VR2009 used the GISS global temperature to derive their model, so we will first consider the GISS Monthly Mean Surface Land/Ocean Temperature Anomaly (which covers 1996 to the present).

For example, we could choose t’ = 1998.12 with T’ = 0.8 °C during the peak of an extreme El Nino.  In this case equation 10 would give a temperature rise of about 2 °C between 1996 and 2010.  Or we could choose t’ = 1999.38, when the global temperature was 0.21 °C  (according to GISS).  For this choice the temperature drops from about 1996 to 2001, and then rises about 0.5 °C by 2010.

These extreme initial condition choices seem to yield extreme results.  Perhaps it would be better to choose smoothed temperature data.  The following plot shows an overlay of the plain GISS Monthly Mean Surface Land/Ocean Temperature Anomaly, and with a 7 month running average (generated by me), as well as the GISS Annual Mean Land/Ocean Surface temperature anomaly.  It seems prudent to select an initial time where the monthly data, the 7 month smoothed data, and the annual mean data are all about the same, as marked in the image, below.

I decided to pick T’ = 2001.5 and t’ = 0.44 °C (GISS monthly T = 0.51 °C, GISS monthly T with 7 month average = 0.46 °C, GISS yearly average t = 0.48 °C, and GISS 5-year mean T = 0.44 °C).

Applying my choice of initial conditions to equation 11 to determining c4, inserting the result into equation 10, and plotting T vs. t from equation 10 for 1996 to the present gives the following result.

So, Vermeer’s and Rahmstorf’s model requires an unrealistic temperature rise from 1996 to the present to reproduce the sea level rise rate over that period.  The decade from 2000 to 2010 (during which the GISS data shows a more or less constant) would have required a temperature increase of almost 0.7 °C, according to VR2009.

This is just another reason to reject VR2009.

Try it yourself.

I have given any interested person with a basic understanding of calculus and differential equations everything needed to reproduce my results.  My conclusions are sound.  VR2009 is unrealistic.