model calculates the emission of CO2 that would lead to a given concentration. Since fossil fuel energy production relates directly to emission of CO2, and atmospheric concentration of CO2 relates to global warming, these models can be used to relate fossil fuel energy production to global warming. The forward model can thus be used to predict the globally averaged temperature change that would result from a given emissions (or energy) profile. The inverse model can be used to give an emissions (or energy) profile that would cause a given temperature change. Wigley's work is based on earlier work by Maier-Reimer and Hasselmann.9 Atmospheric concentration of CO2 is given by the following convolution integral: C(t) = atmospheric CO2 concentration E(t) = Rate of CO2 emissions G(t) = impulse response (Green's) function t = time u = variable of integration. Maier-Reimerand Hasselmann calculated G(t) for three different pulse injections of CO2. Wigley's models interpolate between these three impulse functions as the total CO2 emissions range between the values of the three impulse injections. Total CO2 emission is given by: In this integral, t = 0 refers to the beginning of anthropogenic CO2 emissions (in the year 1770). The impulse response functions are of the form: where aj are numerical coefficients and tj are decay times. The fraction of emissions that remains permanently in the atmosphere is given by a0. Note that Equation 3 represents the form of each of the three impulse response functions. Thus, the models use a total of 15 different a's and 12 different t's. The impulse response function represents the ability of the oceans to take up CO2 from the atmosphere. Primary electricity was subtracted from the total energy requirement in conventional fuel equivalent to obtain fossil fuel use for the year 1986 (Reference 10). The total CO2 emissions for 1986 were then considered and the small contribution from where
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