# Appendix 10.A: Methods for Sea Level Projections for the 21st Century

## 10.A.1 Scaling MAGICC Results

The MAGICC SCM was tuned to emulate global average surface air temperature change and radiative flux at the top of the atmosphere (assumed equal to ocean heat uptake on decadal time scales; Section 5.2.2.3 and Figure 5.4) simulated by each of 19 AOGCMs in scenarios with CO_{2} increasing at 1% yr^{–1} (Section 10.5.3). Under SRES scenarios for which AOGCMs have been run (B1, A1B and A2), the ensemble average of the tuned versions of MAGICC gives about 10% greater temperature rise and 25% more thermal expansion over the 21st century (2090 to 2099 minus 1980 to 1999) than the average of the corresponding AOGCMs. The MAGICC radiative forcing is close to that of the AOGCMs (as estimated for A1B by Forster and Taylor, 2006), so the mismatch suggests there may be structural limitations on the accurate emulation of AOGCMs by the SCM. We therefore do not use the tuned SCM results directly to make projections, unlike in the TAR. The TAR model means for thermal expansion were 0.06–0.10 m larger than the central estimates in Table 10.7, probably because the simple climate model used in the TAR overestimated the TAR AOGCM results.

The SCM may nonetheless be used to estimate results for scenarios that have not been run in AOGCMs, by calculating time-dependent ratios between pairs of scenarios (Section 10.5.4.6). This procedure is supported by the close match between the ratios derived from the AOGCM and MAGICC ensemble averages under the scenarios for which AOGCMs are available. Applying the MAGICC ratios to the A1B AOGCM results yields estimates of temperature rise and thermal expansion for B1 and A2 differing by less than 5% from the AOGCM ensemble averages. We have high confidence that the procedure will yield similarly accurate estimates for the results that the AOGCMs would give under scenarios B2, A1T and A1FI.

The spread of MAGICC models is much narrower than the AOGCM ensemble because the AOGCMs have internally generated climate variability and a wider range of forcings. We assume inter-model standard deviations of 20% of the model average for temperature rise and 25% for thermal expansion, since these proportions are found to be fairly time and scenario independent in the AOGCM ensemble.