|Working Group I: The Scientific Basis|
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5.4.2 Overall Uncertainty in Direct Forcing Estimates
To illustrate how the uncertainty associated with each of the factors determining
aerosol direct forcing contribute to the overall uncertainty in forcing, we
adopt a simple box-model of the overall change in planetary albedo. This approach
follows that presented in Penner et al. (1994a), but is updated in several respects.
For this model, the change in global average planetary albedo associated with
anthropogenic aerosols is described as (Chylek and Wong, 1995):
Ta = atmospheric transmissivity above the main aerosol layer
The key quantities that enter into the calculation of uncertainties are listed in Table 5.10, together with estimates of their 2/3 uncertainty range. Given these central values and uncertainties, the variance (and thus uncertainty) associated with the planetary albedo change (Dap) is determined by standard Taylor expansion of the function around the central values for the change in planetary albedo. Thus, with variances given by Si2:
where the function cov(xi,xj) is the covariance of the variables in the argument and a variable subscript (i.e., i or j) implicitly requires summation from 1 to n where n is the number of variables. Significant covariances are found between b and as, b and fb, as and f(RH), and w0 and f(RH). For these variable pairs, Bravais-Pearson (linear) correlation coefficients were found to be -0.9, -0.9, 0.9 and 0.9, respectively. These were determined by sampling the probability distribution associated with each pair of variables to generate a large set of corresponding pairs of values. Linear regression analysis was then performed on these corresponding pairs to determine the linear correlation coefficient between the paired variables. The burden estimates in Table 5.10 are based on model calculations from the IPCC workshop. The uncertainty range was taken from the range in burdens from the models (assumed here to be a 2/3 uncertainty range) which may be a reasonable estimate for some of the “structural uncertainty” associated with different parametrization choices in the models (Pan et al., 1997). It includes both “chemical” quantities such as the fraction of emitted SO2 that is converted to sulphate aerosol and the mean residence time of the aerosol. The central emissions estimates are those specified in the model workshop (except where noted) and the uncertainties are those estimated in Section 5.2. The uncertainty range for the burden, M, used in evaluating the change in planetary albedo was calculated from the uncertainty in emissions together with the uncertainty in burden utilising the geometric concatenation procedure of Penner et al. (1994a).
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