Posts Tagged ‘artificial reservoir’


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.


“Impact of Artificial Reservoir Water Impoundment on Global Sea Level” by Chao, et. al.: Useful but flawed

May 9, 2010

B. F. Chao, et. al., made a useful but flawed contribution to the question of sea level rise with their Science article “Impact of Artificial Reservoir Water Impoundment on Global Sea Level.”  The gist of their paper was that all the water captured by man-made reservoirs is water that would otherwise be contributing to higher sea levels.  This is an important point, they say, when considering global warming induced sea level rise.

They correctly point out that the sea level would be higher if this impounded water had been allowed to naturally flow to the sea.  Therefore, they conclude, global warming induced sea level rise is even worse than thought.  Read on, and I think you will agree with me that, amazingly, they missed one obvious point.


Chao, et. al., did an inventory of reservoirs, their creation dates and their capacities for the 20th century.  Their online supplementary material includes an exhaustive 600 page list of over 29,000 reservoirs.  They add up the total impounded water in these reservoirs to be 10,800 cubic kilometers.  They point out that this would have contributed another 30 mm to the sea level during the 20th century.  (See simple conversion factor here.)

They find that the vast majority of the water impoundment happened in the second half of the 20th century.  So, the amount of uncounted sea-level rise in the second half of the century was greater than the fist half of the century.  This confirms the alarmist point of view about dangerously accelerating sea level rise rates.

Here is Chao’s plot of the Church and White observed sea level with and without the Chao reservoir correction…

…but fatally flawed

What about the opposite effect: depleted natural reservoirs, such as lakes and aquifers?  Water that is pumped from an aquifer or lake, but not recharged, ultimately adds to the sea level.  This water would mistakenly be considered to be part the sea level rise due to global warming.

Ground water depletion has a host of serious ramifications apart from sea level rise.  For example the Indian states of Rajasthan, Punjab and Haryana (114, million people, or less than 2% of the world’s population) are depleting their aquifers by about 20 cubic kilometers per year, which may have devastating effects to these important agricultural regions.  In the United States (5% of the world’s population) as much as 800 cubic kilometers of water have been overdrawn from the aquifers in the 20th century.

In just 40 years the Aral Sea in central Asia has shrunk by nearly 1000 cubic kilometers (as this very nice interactive web page illustrates).

The University of Wisconsin’s Professor J. Van Klump estimates that the yearly global ground water overdraft is 200 cubic kilometers per year!!  This would account for over half a millimeter of sea level rise per year (“200 cubic kilometers” x “2.78 microns sea level rise per cubic kilometer“), and entirely counteract the effect of artificial reservoirs.

So, Chao made a useful contribution to the understanding of sea level, but his sea level correction was fatally flawed because he neglected the counter-effect of ground water depletion.

My question

Why wasn’t this point obvious to Chao, et. al.?  My guess is that I am not the only one who thought about ground water depletion when reading about Chao’s artificial reservoir water impoundment and its effect on sea level.  It is hard to believe that it did not occur to Chao, et. al.  It seems quite simple and obvious.  Their paper would have been more scientifically accurate and useful if it had not neglected ground water depletion.

The only conclusion I can draw is that the prevailing alarmist view of the day makes it easier to get a paper that inflates sea level rise rates published than a more complete paper that does not.

Update 10/24/10
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).  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.