8.8.2 Simple Climate Models

As in the TAR, a simple climate model is utilised in this report to emulate the projections of future climate change conducted with state-of-the-art AOGCMs, thus allowing the investigation of the temperature and sea level implications of all relevant emission scenarios (see Chapter 10). This model is an updated version of the Model for the Assessment of Greenhouse-Gas Induced Climate Change (MAGICC) model (Wigley and Raper, 1992, 2001; Raper et al., 1996). The calculation of the radiative forcings from emission scenarios closely follows that described in Chapter 2, and the feedback between climate and the carbon cycle is treated consistently with Chapter 7. The atmosphere-ocean module consists of an atmospheric energy balance model coupled to an upwelling-diffusion ocean model. The atmospheric energy balance model has land and ocean boxes in each hemisphere, and the upwelling-diffusion ocean model in each hemisphere has 40 layers with inter-hemispheric heat exchange in the mixed layer.

This simple climate model has been tuned to outputs from 19 of the AOGCMs described in Table 8.1, with resulting parameter values as given in the Supplementary Material, Table S8.1. The applied tuning procedure involves an iterative optimisation to derive least-square optimal fits between the simple model results and the AOGCM outputs for temperature time series and net oceanic heat uptake. This procedure attempts to match not only the global mean temperature but also the hemispheric land and ocean surface temperature changes of the AOGCM results by adjusting the equilibrium land-ocean warming ratio. Where data availability allowed, the tuning procedure took simultaneous account of low-pass filtered AOGCM data for two scenarios, namely a 1% per year compounded increase in atmospheric CO₂ concentration to twice and quadruple the pre-industrial level, with subsequent stabilisation. Before tuning, the AOGCM temperature and heat uptake data was de-drifted by subtracting the respective low-pass filtered pre-industrial control run segments. The three tuned parameters in the simple climate model are the effective climate sensitivity, the ocean effective vertical diffusivity, and the equilibrium land-ocean warming ratio. Values specific to each AOGCM for the radiative forcing for CO₂ doubling were used in the tuning procedure where available (from Forster and Taylor, 2006, supplemented with values provided directly from the modelling groups). Otherwise, a default value of 3.71 W m^–2 was chosen (Myhre et al., 1998). Default values of 1 W m^–2 °C^–1, 1 W m^–2 °C^–1 and 8°C were used for the land-ocean heat exchange coefficient, the inter-hemispheric heat exchange coefficient and the magnitude of the warming that would result in a collapse of the MOC, respectively (see Appendix 9.1 of the TAR).

The obtained best-fit climate sensitivity estimates differ for various reasons from other estimates that were derived with alternative methods. Such alternative methods include, for example, regression estimates that use a global energy balance equation around the year of atmospheric CO₂ doubling or the analysis of slab ocean equilibrium warmings. The resulting differences in climate sensitivity estimates can be partially explained by the non-time constant effective climate sensitivities in many of the AOGCM runs. Furthermore, tuning results of a simple climate model will be affected by the model structure, although simple, and other default parameter settings that affect the simple model transient response.