# 10.A.6 Combination of Uncertainties

For each scenario, time series of temperature rise and the consequent land ice contributions to sea level are generated using a Monte Carlo simulation (van der Veen, 2002). Temperature rise and thermal expansion have some correlation for a given scenario in AOGCM results (Section 10.6.1). In the Monte Carlo simulation, we assume them to be perfectly correlated; by correlating the uncertainties in the thermal expansion and land ice contributions, this increases the resulting uncertainty in the sea level rise projections. However, the uncertainty in the projections of the land ice contributions is dominated by the various uncertainties in the land ice models themselves (Sections 10.A.2–4) rather than in the temperature projections. We assume the uncertainties in land ice models and temperature projections to be uncorrelated. The procedure used in the TAR, however, effectively assumed the land ice model uncertainty to be correlated with the temperature and expansion projection uncertainty. This is the main reason why the TAR ranges for sea level rise under each of the scenarios are wider than those of Table 10.7. Also, the TAR gave uncertainty ranges of ±2 standard deviations, whereas the present report gives ±1.65 standard deviations (5 to 95%).

## 10.A.7 Change in Surface Air Temperature Over the Major West Antarctic Ice Shelves

The mean surface air temperature change over the area of the Ross and Filchner-Ronne ice shelves in December and January, divided by the mean annual antarctic surface air temperature change, is F_{1} = 0.62 ± 0.48 (one standard deviation) on the basis of the climate change simulations from the four high-resolution GCMs used by Gregory and Huybrechts (2006). From AR4 AOGCMs, the ratio of mean annual antarctic temperature change to global mean temperature change is F_{2} = 1.1 ± 0.2 (one standard deviation) under SRES scenarios with stabilisation beyond 2100 (Gregory and Huybrechts, 2006), while from AR4 AGCMs coupled to mixed-layer ocean models it is F_{2} = 1.4 ± 0.2 (one standard deviation) at equilibrium under doubled CO_{2}. To evaluate the probability of ice shelf mean summer temperature increase exceeding a particular value, given the global temperature rise, a Monte Carlo distribution of F_{1 }× F_{2} is used, generated by assuming the two factors to be normal and independent random variables. Since this procedure is based on a small number of models, and given other caveats noted in Sections 10.6.4.2 and 10.7.4.4, we have low confidence in these probabilities.