The simple climate model MAGICC (Wigley and Raper; 1987, 1992; updated in Raper et al., 1996) was used in the SAR to make temperature projections for various forcing scenarios and for sensitivity analyses. The justification for using the simple model for this purpose was the model’s ability to simulate AOGCM results in controlled comparisons spanning a wide range of forcing cases (for example SAR Figure 6.13). The approach used in this report differs from that in the SAR. Thus the upwelling diffusion-energy balance model (UD/EB) model is not used here as a stand-alone model in its own right but instead it is tuned to individual AOGCMs and is used only as a tool to emulate and extend their results. In this way, a range of results is produced reflecting the range of AOGCM results. The tuning is based on the CMIP2 data analysis of Raper et al. (2001b). The validity of the tuning is tested by comparisons with AOGCM results in the DDC data set and, where available, with recent AOGCM results using the SRES scenarios. By using such simple models, differences between different scenarios can easily be seen without the obscuring effects of natural variability, or the similar variability that occurs in coupled AOGCMs (Harvey et al., 1997). Simple models also allow the effect of uncertainties in the climate sensitivity and the ocean heat uptake to be quantified. Potentially, other simple models (for example, Watterson (2000), Visser et al. (2000)) could be used in a similar way.

The first step in the tuning process is to select appropriate values for the radiative forcing for a CO₂ doubling parameter, F_2x, and the climate sensitivity parameter, T_2x. In the SAR, F_2x= 4.37 Wm^-2 was used, as given in the 1990 IPCC Assessment (Shine et al., 1990). This value, which did not account for stratospheric adjustment and solar absorption by CO₂, is now considered to be too high (Myhre et al., 1998). These authors suggest a best estimate of 3.71 Wm^-2; model-specific values are used here (see Table 9.A1). The effect on global mean temperature and sea level change of using lower values of F_2x has been investigated by Wigley and Smith (1998). The lower F_2x values result in slightly lower temperature projections. Different definitions and methods of calculation of model climate sensitivity are discussed in Section 9.3.4.1. Here the effective climate sensitivities based on the last twenty years of the CMIP2 data are used.

Table 9.A1: Simple climate model parameter values used to simulate AOGCM results. In all cases the mixed-layer depth hm=60m, the sea ice parameter CICE=1.25 and the proportion of the upwelling that is scaled for a collapse of the thermohaline circulation is 0.3, otherwise parameters are as used in the SAR (Kattenberg et al., 1996; Raper et al., 1996).
AOGCM	F2x (Wm -2)	T2x (°C)	T +(°C)	k(cm2s-1)	RLO	LO and NS (Wm-2 °C-1)
GFDL_R15_a	3.71*	4.2	8	2.3	1.2	1.0
CSIRO Mk2	3.45	3.7	5	1.6	1.2	1.0
HadCM3	3.74	3.0	25	1.9	1.4	0.5
HadCM2	3.47	2.5	12	1.7	1.4	0.5
ECHAM4/OPYC	3.8	2.6	20	9.0	1.4	0.5
CSM 1.0	3.60	1.9	-	2.3	1.4	0.5
DOE PCM	3.60	1.7	14	2.3	1.4	0.5
* Here the best estimate from Myhre et al. (1998) is used. F2x – the radiative forcing for double CO2 concentration T2x – climate sensitivity hm – mixed-layer depth CICE – sea ice parameter (see Raper et al., 2001a) T+ – magnitude of warming that would result in a collapse of the THC k – vertical diffusivity RLO – ratio of the equilibrium temperature changes over land versus ocean LO and NS – land/ocean and Northern Hemisphere/Southern Hemisphere exchange coefficients

Having selected the value of F_2x and T_2x appropriate to a specific AOGCM, the simple model tuning process consists of matching the AOGCM net heat flux across the ocean surface by adjusting the simple model ocean parameters following Raper et al. (2001a), using the CMIP2 results analysed in Raper et al. (2001b). Sokolov and Stone (1998) show that when using a pure diffusion model to match the behaviour of different AOGCMs a wide range of diffusion coefficients is needed. The range here is much smaller because a 1-D upwelling diffusion model is used and changes in the strength of the thermohaline circulation are also accounted for. A decrease in the strength of the thermohaline circulation leads to an increased heat flux into the ocean. In the UD/EB model a weakening of the thermohaline circulation is represented by a decline in the upwelling rate (see SAR). The rate of sea level rise from thermal expansion for a collapse in the thermohaline circulation in the UD/EB model is tuned to match that which occurs for an induced collapse in the GFDL model (GFDL_R15_a) control run. An instantaneous 30% decline in the UD/EB model upwelling rate gives rates of sea level rise comparable to that seen in the GFDL model over a period of 500 years. Thus a 30% decline in the UD/EB model upwelling rate represents a collapse in the thermohaline circulation. For the individual models the rate of decline in the strength of the thermohaline circulation relative to the global mean temperature change is based on the CIMP2 data and is specified by the parameter T⁺. It should be pointed out that the processes in the UD/EB model that determine the heat flux into the ocean are not necessarily physically realistic. Raper and Cubasch (1996) as well as Raper et al. (2001a) show that the net heat flux into the ocean in the UD/EB model can be tuned to match that in an AOGCM in several ways, using different sets of parameter values. Nevertheless, if the UD/EB model is carefully tuned to match the results of an AOGCM, and provided the extrapolations are not too far removed from the results used for tuning, the UD/EB model can be used to give reasonably reliable estimates of AOGCM temperature changes for different forcing scenarios. The thermal expansion results are less reliably reproduced because thermal expansion is related to the integrated heat flux into the ocean. Errors therefore tend to accumulate. In addition, the expansion depends on the distribution of warming in the ocean. Nonetheless, the simulation is adequate for comparison of scenarios.

Other parameters in the UD/EB model are adjusted in order to correctly simulate the greater surface temperature change over the land relative to the ocean as shown to a varying degree in different AOGCM results. The land-ocean, Northern-Southern Hemisphere temperature change contrasts are adjusted by parameters that govern the contrast in the land-ocean climate sensitivity and the land-ocean exchange coefficients. The specific parameter values used for the different AOGCMs are given in Table 9.A1.

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