Archive for September, 2007

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Time for sea level to reach equilibrium is not millennia

September 29, 2007

This is part of a series of posts concerning Problems with the Rahmstorf (2007) paper.

Critique #2. The assumption that the time required to arrive at the new equilibrium is “on the order of millennia” is not borne out by the data.

This assumption implies that on a century time scale a temperature rise will result in an increase of the sea level rise rate, and the sea level rise rate will not drop back down unless there is a significant drop in the temperature, as illustrated in figure 1, below.


Figure 1. Illustration of a Rahmstorf type model with a temperature step vs. time, the resulting step in the sea level rise rate (dH/dt) vs. time, and the combination of sea level rise rate vs. temperature. This scenario works under the assumption that the adjustment timescale for the sea level rise rate is on the order of millennia.

If the adjustment time were decades instead of millennia, then a temperature step would result in an increase of the sea level rise rate, quickly followed by a drop. This scenario is shown in figure 2, below.

Figure 2. Illustration of a short adjustment time model. As in figure 1, above, it shows a temperature step vs. time, the resulting step in the sea level rise rate (dH/dt) vs. time, and the combination of sea level rise rate vs. temperature.

The actual temperature (GISS) and sea level data (Church, 2006) is not as clean as the simple models illustrated in figures 1 and 2. However, the best example of a simple temperature step occurs between the years 1890 and 1970. Using the 15 year smoothed temperature ( deviation from the 1951 to 1980 average) and sea level rise data it can be seen that from about 1890 to about 1915 the temperature was quite steady (-0.265 ºC ± 0.015 ºC), followed by a rapid rise of about 0.25 ºC by 1940. Then from 1940 to the mid 70s the temperature stays about 0.0 ºC ± 0.015 ºC.

What does the sea level rise rate do during this same period? When the temperature is flat from 1890 to 1915 the sea level rise rate is dropping. As the temperature rises until 1940, the sea level rise rate also rises. Shortly after that the sea level rise rate stars dropping while the temperature remains flat again. Figure 3, below, shows the temperature and sea level rise rate during this interesting time period.

Figure 3. Temperature anomaly and sea level rise rate from 1890 to 1970. Same data that Rahmsdorf used, 15 year smoothing.

According to Rahmstorf’s model the sea level rise rate should have been constant during the periods when the temperature was constant. The fact that the sea level rise rate was dropping during both of these periods indicates that the adjustment time is not on the order of millennia, but rather on the order of decades. This has a profound impact on his conclusions. According to Rahmstorf’s model, a temperature rise that occurs in the early 1900s would still be contributing to sea level rise in 2100. The data indicates otherwise: the effect of a temperature step on sea level rise diminishes in only decades.

Figure 4. Rahmstorf’s and Moriarty’s smoothed and binned sea level rise rate vs. temperature anomaly, Moriarty’s unbinned version, and Moriarty’s unbinned version with the data from figure 3, above, highlighted showing regions of constant temperature and decreasing sea level rise rate.
Back to series of posts concerning Problems with the Rahmstorf (2007) paper.
2. J. A. Church, N. J. White, Geophys. Res. Lett. 33, L01602 (2006).
3. Rahmstorf, A Semi-Empirical Approach to Projecting Sea Level Rise, Science 315, 368 (2007)
Back to series of posts concerning Problems with the Rahmstorf (2007) paper.
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…

Posted in Rahmstorf, global warming, rise, sea level, temperature | 4 Comments »

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Rahmstorf’s sea level rise rate vs. T does not fit a line

September 28, 2007
This is part of a series of posts concerning Problems with the Rahmstorf (2007) paper.Critique #1. Sea level rise rate vs. temperature is displayed in a way that erroneously implies that it is well fit to a line.

Rahmstorf’s figure 2 shows the sea level rise rate vs. temperature in the form of 24 discreet points. These points are derived by binning the 120 points that represent each individual year from 1880 to 2000 into groups of 5 after smoothing the sea level data (Church, 2006) and temperature data (GISS) with with a nonlinear trend technique. My digitized version of his plot is shown in figure 1, below.

Figure 1. Rahmstorf’s version of sea level rise rate (mm/year) vs. temperature anomaly.

I smoothed the same sea level data and temperature data with a 15 year FWHM Gaussian filter. Note that the difference between smoothing the sea level data with the nonlinear trend line technique and with the Gaussian filter is vanishingly small, as demonstrated by the fact that I derived the same sea level rise rate vs. temperature as Rahmstorf does (sea level =3.375 *(T anomaly + 1.684, r = 0.86). My plot of sea level rise rate vs. temperature anomaly, which is very similar to Rahmstorf’s, is shown below in figure 2. One might plausibly argue that the points in figures 1 and 2 could be reasonably fit to a line. That is precisely the argument that Rahmstorf makes.

Figure 2. Moriarty’s version of sea level rise rate vs. temperature anomaly.
However, if the data is not binned, that is, all 120 data points are shown, then it becomes perfectly clear that fitting this data to a line is entirely inappropriate. Figure 3, below, shows the same data as figure 2, without binning.

Figure 3. When the sea level rise rate vs temperature anomaly data is not binned it appears that fitting it to a line is entirely inappropriate.

Rahmstorf seems to justify fitting this very non-linear data to a line by saying “A highly significant correlation of global temperature and the rate of sea-level rise is found (r = 0.88, P = 1.6 × 10−8) (Fig. 2) with a slope of a = 3.4 mm/year per °C.” It should be understood that this is very poor justification. Section 4.4.4 of the The National Institute of Standards and Technology (NIST) Engineering Statistics Handbook says:

Model validation is possibly the most important step in the model building sequence. It is also one of the most overlooked. Often the validation of a model seems to consist of nothing more than quoting the R^2 statistic from the fit (which measures the fraction of the total variability in the response that is accounted for by the model). Unfortunately, a high R^2 value does not guarantee that the model fits the data well. Use of a model that does not fit the data well cannot provide good answers to the underlying engineering or scientific questions under investigation.

Back to series of posts concerning Problems with the Rahmstorf (2007) paper.

1. GISS: http://data.giss.nasa.gov/gistemp/
2. J. A. Church, N. J. White, Geophys. Res. Lett. 33, L01602 (2006).
3. Rahmstorf, A Semi-Empirical Approach to Projecting Sea Level Rise, Science 315, 368 (2007)

Back to series of posts concerning Problems with the Rahmstorf (2007) paper.

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…

Posted in Rahmstorf, global warming, rise, sea level, temperature | 4 Comments »