example is the formula for the forcing f(t) for CO2 expressed in units of watts per square meter with a coefficient from IPCC (2001):


where CO2(t) is the atmospheric concentration of CO2 for year t. Such models can relate greenhouse gas emissions to the equilibrium global averaged temperature changes and, using transient oceanic heat uptake models, to transient temperature changes and impacts. For short-lived species, such as aerosols, expressions of the type of Equation 1-4 are not available due to the great spatial variability in concentrations and optical properties.

When linked to socioeconomic models, simple climate models have become a powerful tool for policy analysis, often referred to as “integrated assessment” models (Manne et al., 1995; de Vries et al., 2000; Nordhaus and Boyer, 2000; Roehrl and Riahi, 2000; Matsuoka et al., 2001). They can be linked to an economic “damage” function that simulates the economic impacts and damages of global warming. The system may be further coupled to an optimization scheme to determine optimal investment rates in reductions of greenhouse gas emissions. In these optimization schemes the damage function is dependent on the global averaged surface temperature, while the cost function depends on the level of greenhouse gas emissions abatement (Nordhaus and Boyer, 2000). The simplified “box” approach to climate modeling used in most integrated assessment models is subject to criticism for ignoring regional temperature changes. The current dearth of regionally specific data on damages and their economic costs is a key limitation as well.

Integrated assessment models have been used to evaluate many climate policy questions. Most recently they have been part of the burgeoning suite of studies that evaluated the Kyoto Protocol treaty for greenhouse gas emissions targets for the years 2010-2015 (Kyoto Protocol, 1997). Various emissions pathways were studied in terms of their overall cost-benefit ratios (Nordhaus and Boyer, 2000). The policy targets can be limits on emissions rates as in the Kyoto Protocol; limits on greenhouse gas concentrations, which is the approach for stabilization studies; or limits on the rate of global warming as in the case of environmentally oriented scenarios. These possible policy targets are shown by the shaded boxes in Figure 1-4. Although radiative forcing is inherent to integrated assessment models, radiative forcing per se has not been treated as a climate policy target.

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