## 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…

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