# Sea Level Rise Models – II

Picking up where I left off, with model and data assembled, the next step is to calibrate, to see whether the Rahmstorf (R) and Grinsted (G) results can be replicated. I’ll do that the easy way, and the right way.

An easy first step is to try the R approach, assuming that the time constant tau is long and that the rate of sea level rise is proportional to temperature (or the delta against some preindustrial equilibrium).

Rahmstorf estimated the temperature-sea level rise relationship by regressing a smoothed rate of sea level rise against temperature, and found a slope of 3.4 mm/yr/C.

Rahmstorf’s slope corresponds with the ratio a/tau in the Grinsted model, so I picked a large value of a (19,500 mm/C) which yields tau = 19,500/3.4 = 5735 years. If anything, that’s too long, as there wouldn’t be time in the Holocene for sea level to have reached a preindustrial equilbrium. However, it’s right in the middle of R’s 3000-6000 year range based on paleo evidence.

Setting a and tau as above, all that remains is to find T0 and the initial sea level, which determine the intercept of the sea level trajectory. It’s easy enough to hand calibrate, but quicker to turn the optimizer loose on this problem. I specify a calibration payoff (objective function) and optimization control file, with broad ranges to avoid clipping “interesting” regions of the parameter space:

grinsted.vpd
*C
Sea Level Rise|Long Tide Gauge v 2000/Long Tide Gauge Wt
Sea Level Rise|Sat v 2000/Sat Wt

rahmstorf.voc
-400<=init Sea Level<=400
-2<=Sea Level Equil Temp<=2

This tells Vensim to minimize the squared error between model sea level and the two data sources, weighted by their respective standard errors. The minimization is accomplished by varying the initial sea level and equilibrium temperature (T0). The result is T0=-.56 C and initial sea level = -277 mm, with a close fit to the data:

The rate correlation (corresponding with R’s figure 2, but using cruder smoothing) also looks decent:

So far so good, but notice that I’m playing fast & loose here:

• R used Jevrejeva et al. 2006; I’ve used Jevrejeva et al. 2008 plus satellite tide data
• R started in 1880; I started in 1700.