Archive for the ‘IPCC’ Category

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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…

where

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.

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Boston Underwater?

March 24, 2009

Boston, you have been warned. Sea levels are rising , and if one of the IPCC’s five scenarios is correct, the world’s oceans will rise somewhere between 18 and 59 cm (7 to 23 inches) by 2100. If that isn’t terrifying enough for the people living on the New England coast, the Boston Globe now tells us that the ocean near Boston will rise 8 inches more than the world average. How will the hapless rubes of Boston cope with this onslaught of Atlantic water?

I wouldn’t lose to much sleep worrying about the folks in Boston when it comes to pushing back against the ocean. Excerpts from the following maps were used to make an animation of the changing coastline in Boston:

  • A 1775 map showing the Boston area with the rebel military works. Note especially the isthmus, known as Boston Neck< that connects the town of Boston to the mainland.
  • An 1838 George W. Boynton engraving of Boston area from a Thomas G. Bradford atlas.
  • USGS map of Boston area.
  • A 2009 satellite image from Google Earth

The top of the animation shows the maps after photoshopping to make the land and water more obvious. The bottom of the animation shows the unaltered excerpts of the maps or images.

animation-5I

The panic prone will argue that our Bostonian ancestors dealt with a static ocean, not a rising ocean. Not so fast. Check out the NOAA graph below (click inside graph to see it in context at NOAA site). It shows a sea level rise rate of 2.63 mm/yr for the last 100 years in Boston. At that rate it will rise 23.9 cm (9.4 inches) by 2100.

Boston sea level rise

Boston sea level rise data from NOAA. Click in image fro view in context.

Anyone who panics over the IPCCs 100 year projections of rising sea levels does not understand the perseverance and ingenuity of free people. Then there are others, like James Hansen, who enjoy the feeling of panic so much that that they exagerate the probable sea level rise for this century to get their thrills. But that is a story for another day…

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Critique of "A Semi-Empirical Approach to Projecting Future Sea-Level Rise" by Rahmstorf

August 12, 2007

A recent article in Science by Stefan Rahmstorf (2007) predicted extreme sea level rise during the 21st century. Rahmstorf’s predictions went as high as 140 cm (55 inches), far beyond even the high edge of the uncertainty of the IPCC’s unlikely A1Fl scenario (see here, page 820). This high estimate by the IPCC was 59cm (23 inches), with other other scenarios yielding considerably lower estimates. Following is a critique of Rahmstorf’s method and conclusions.

This post has a quick summary of Rahmstorf’s approach to to projecting sea-level rise for this century. Following that summary is a quick list of problems that I have identified in his paper, each with a link to subsequent posts with more detailed information.

Rahmstorf’s Simple Model

Rahmstorf’s simple model of sea level rise consists of a system in equilibrium, where the sea level and the temperature start out as constants. Then an instantaneous step occurs in the temperature, causing the sea level to rise. Eventually the sea level will rise to a new equilibrium, as shown below.

It is very important to note that the time required to arrive at the new equilibrium is, according to Rahmstorf, “to be on the order of millennia.” This long time scale provides the other important point of this simple model. That is, over a short enough time scale the rate of sea level rise can be considered a constant (as illustrated in the above graph during the time where dH/dT is proportional to delta T). Rahmstorf posits that “this linear approximation may be valid for a few centuries.”

Therefore, in this model, a temperature jump in the 1920s, for example, would result in a sea level rising at a constant rate for several hundred years, even without any subsequent temperature increases. Of course, subsequent temperature rises would each result in a greater sea level rise rate, but there would never be any drop in the rise rate for several hundred years, assuming no significant drops in the temperature. The following section puts this model on a mathematical footing.

Rahmstorf’s Mathematical Strategy

1) Assume that the rate of sea level rise rate at any given time is proportional to the deviation form some global equilibrium temperature at that time. He expresses this in the following formula…

where H is the sea level, dH/dt is the sea level rise rate, T is the temperature, To is the the equilibrium temperature, and a is the constant of proportionality.

2) To and a can be derived by simply plotting dH/dt vs T and fitting to a line.

3) Once To and a have been determined, then the sea level for any given time, H(t), can be calculated by integrating equation (I), above, with respect to time…

4) By applying various temperature rise scenarios for the 21st century to equation (II), Rahmstorf predicts the sea level for the hear 2100 (H(2100)).


Problems with this model

1) Sea level rise rate vs. temperature is displayed in a way that erroneously implies that it is well fit to a line, as expressed in equation I, above. More…

2) The assumption that the time required to arrive at the new equilibrium is “on the order or millennia” is not borne out by the data. More…

3)Rahmstorf extrapolates out more than five times the measured temperature domain. More…