Posts Tagged ‘Chao’


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): (part 9): Applying three corrections

November 17, 2010

This 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…


H is the sea level

T is the temperature

T0 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 T0 that yield the best fit.  Then they inserted their values of a, b and T0 back into the model equation and used IPCC temperature scenarios for the 21st century to determine the sea level rise for the 21st century. 

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 T0 for the VR2009 model equation.  Figure 1 shows the components of the sea level.

Figure 1. Sea level components.

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.

Figure 2. The VR2009 version of sea level data compated to the more accurate version using the updated Church and White data and the Wada groundwater depletion correction.

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).

Figure 3. Beginning and ending slopes for VR2009 version of sea level data and the more accurate version used in this post.

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.

Figure 4. Improved sea level data with 15 year FWHM gaussian smoothing.

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 T0 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 T0  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.


25% of sea-level rise is due to groundwater depletion

October 24, 2010

We are told that sea level rise is one of the more dire consequences of global warming.  It is posited as a bellwether to the fate of the planet.  So it may come as a surprise to learn that about 25% of the yearly sea level rise comes from pumping water from the ground and adding it to the oceans, not from melting ice.  And this percentage has been rapidly increasing since 1950.  Mistaking this groundwater as ice-melt-water in calculations designed to ferret out the effects of global temperature on sea level greatly prejudices the calculations toward higher sea levels in the future.

Remember the “correction” to the sea level from Chao that made the sea level rise rate for the second half of the 20th century appear to be higher  (surprise, surprise) than the commonly referred to Church and White sea level data (Church, J. A., and N. J. White , “A 20th century acceleration in global sea-level rise”, Geophys. Res. Lett., 33, 2006)?  I wrote about it back in May.  Martin Vermeer and Stefan Rahmstorf were all too happy to include this “correction” in their model relating sea level to temperature, of which I have written about extensively.

Chao’s idea was that water stored in the increasing number of artificial reservoirs built around the world in the last half of the 20th century is water that would otherwise be in the oceans.  Therefore, he said, the effect of global warming on sea levels was underestimated, and needed to be corrected by adding the stored water to the sea level.    I pointed out that his analysis was both useful and flawed.  Useful because he did a nice job of researching the construction of reservoirs around the world and their total capacity.  Flawed because he neglected to consider the balancing effect of groundwater depletion.

Figure 1. Groundwater extraction cartoon from Environment Canada. Note the "groundwater discharge into the sea" on the far right side of the cartoon.

I argued that water pumped out of the planet’s aquifers ultimately makes its way to the oceans, and raises the sea level.  This results in an overestimation of the effect of global warming on sea levels.   My quick calculation showed that the depleted groundwater could “entirely counteract the effect of artificial reservoirs.”

This effect of groundwater depletion was briefly mentioned and quickly dismissed by Vermeer and Rahmstorf as they drew a very different conclusion than mine.   They said…

We have corrected the sea-level data for the reservoir storage component, but a further non-climatic effect of relevant magnitude is the mining of groundwater for human uses in arid regions. No time series of this is available, so it cannot be included in the above analysis…but in recent decades groundwater mining could have contributed 0.2–0.3 mm/year to sea level.

Lo and behold!  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, in press) confirms my estimate (and more) and shows that Vermeer and Rahmstorf were low-balling the effect of groundwater depletion.  In fact, Wada’s data shows the effect of ground water depletion at the present time to be GREATER than the effect of artificial reservoir storage. They say…

We estimate that since the 1960s groundwater abstraction has more than doubled (from 312 ± 37 to 734 ± 84 km3 a-1) resulting in an increase in groundwater depletion of from 126 ± 32 to 283 ± 40 km3 a-1. Most of the groundwater released from storage due to groundwater depletion will end up in the ocean, partly by runoff and, as most of the groundwater use is for irrigation purposes, predominantly through evaporation and then precipitation…We estimate the contribution of groundwater depletion to sea level rise to be 0.8 (±0.1) mm a-1, which is 25 (±3) % of the current rate of sea level rise of 3.1 mm a-1… and the same order of magnitude as the contribution from glaciers and ice caps.

It seems preposterous not to include a correction for groundwater depletion when its effect is “the same order of magnitude as the contribution from glaciers and ice caps.”

The following plot (figure 2) from Wada shows the total number of km3 of water removed from the ground each year (top plot) and the depleted fraction (bottom plot) each year from 1960 to 2000.   The depleted ground water is the fraction of the removed water that is not naturally recharged by rain, snow, etc. 

Figure 2. Groundwater abstraction and depletion (km3/year). (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, in press)

 The depletion rate fits an exponential very nicely. In figure 3 I have digitized the groundwater depletion data from figure 2,  converted it to sea level rise rate in mm ( one km3 of water yields 2.78 x 10-3 mm of sea level rise), and fit it to an exponential (R2= 0.98). 

Figure 3. Wada groundwater depletion (mm/year) with an exponential fit

 The Wada groundwater depletion data only covers 1960 to 2000.   However, it is reasonable to assume that prior to 1960 (and after 2000) the groundwater depletion approximates an exponential.  As Wada says…

“Increasing population numbers, expanding areas of irrigated agriculture and economic development are drivers for an ever-increasing demand for water worldwide.”

and these drivers have all been moving along more or less exponential trajectories for the last century.  So, in figure 4 I have extrapolated the Wada groundwater depletion back to 1880 along its exponential fit, and overlaid it with the Chao reservoir correction.

Figure 4. The Chao reservoir correction and the Wada groundwater depletion correction. The Chao correction is added to the Church and White sea level data, and the Wata correction is subtracted.

Figure 5 shows the uncorrected Church and White sea rise rate, as well as the Chao reservoir corrected version, and the Chao reservoir plus Wada groundwater depletion versions.  Vermeer and Rahmstorf used only the Chao reservoir corrected version.  The version that has both the reservoir and groundwater depletion corrections is further divided into two parts: prior to 1960 and after 1960.  The pre-1960 data is based on the exponential extrapolation of the 1960 to 2000 data.  Those who feel incredulous about this extrapolation can simply ignore it – it has no effect on the groundwater delpletion correction after 1960.

figure 5. The effect of sea level rise rate corrections.

Does it make any difference?

Does the Wada groundwater correction make any difference?  Look at figure 4 and notice that around 1985 the groundwater depletion correction overtakes the reservoir correction.  Before 1985 the combination of the two corrections yield a sea level rise rate that is greater than the plain Church and White data, but after that the sea level rise rate is lower.  The groundwater depletion data only goes to the year 2000, but if the exponential extrapolation holds, then by 2010 the reduced sea level rise rate will be even more pronounced.

This difference is huge in the scheme of things.  It takes brutal mathematical contortions to turn this…

figure 6. Church and White sea level with Chao reservoir correction, compare to figure 7, below, by clicking both to enlarge.

…into this…

Figure 7. (This is figure 6 from VR2009) The red curve at the lower left corner is exactly the same as the data in figure 6, above, but it is cut off below 1950. Click on each image to enlarge to inspect the details.

The following animation gives some idea of the effect of going from figure 6 to figure 7.

Figure 8. transformation of figure 6 into figure 7


What do you lying eyes tell you about the sea level from about 1930 to the 2000 in figure 6?  Here is what I see: a sea-level rise rate that does not change much, with a pretty good fit to a line, despite changes to the global temperature.  Any significant increase in the future sea level rise rate that can be divined from it must arise from obscure effects that only the most powerful mathematical minds (like Vermeer’s and Rahmstorf’s) can discern.  From figure 5 it can be seen that the inclusion of the Wada groundwater depletion correction decreases the sea level rise rate by a not so obscure 20% at the end of the 20th century, compared to Vermeer’s and Rahmstorf’s calculations.

Let’s face it, Vermeer’s and Rahmstorf’s sea-level rise predictions come from the forced confession of innocent data.  Every effort is made, no stone unturned, in a quest to wring out as much sea level rise as the most gullible audience will believe.  The review and publication of their model by the National Academy of Science stands as a monument to the supreme reign of the global warming dogma.

Figure 10. Data analysis - Vermeer and Rahmstorf style.