Continued from previous page
Several issues arise that deserve some discussion. The first such issue is
the concatenation of uncertainties in the empirical relationship between the
concentration of SO_{4}^{2} andN_{d}. The uncertainty
in SO_{4}^{2} is straightforward and is based on the assessment
of uncertainty in burden and the uncertainty in emissions as used in Section
5.4.2. The uncertainty in the relationship between SO_{4}^{2}
andN_{d}, equation (3), requires an evaluation
of the uncertainties in the coefficients A and B. Based on a comparison of the
parametrization of Boucher and Lohmann (1995) with that of Jones et al. (1994b)
(Figure 5.7), we assign an ad hoc contribution of
the functional relationship to the uncertainty inN_{d}of 40% of the
central value. We then further assume that the uncertainties in A and B contribute
equally to the total uncertainty (i.e., 40%) and, with these constraints, derived
the uncertainties in A and B. This allows us to use Taylor expansions for both
the perturbed and unperturbed atmosphere. Due largely to the form of the functional
relationship, this procedure yields uncertainties whose major components in
both the perturbed and unperturbed cases are attributable to the uncertainty
in the parametrization (61% for the unperturbed case and 64% for the perturbed
case) rather than the uncertainty in burden or emissions.
In order to assess the overall uncertainty in forcing, the covariance between
the base parametersN_{d}, LWC and h must be evaluated. But both LWC
and h are assumed to be constant in the first indirect effect, and therefore
the covariance is assumed to be zero. Certainly, the limited observations available
(cf., Hegg et al., 1996b) do not show any covariance. Nevertheless, it is important
to note this potential effect and the possible impact of the second indirect
effect (precipitation modulation effects by aerosols) on the uncertainty in
the first.
Another covariance which cannot be neglected arises in the evaluation of the
uncertainty in DAp from the possible covariance between A_{c} and A_{c}'.
This covariance arises because of the dependence of the perturbation in cloud
albedo on both the unperturbed aerosol concentration and the unperturbed albedo.
We assessed this covariance by using equations (4)
and (3) to generate a set of corresponding values
of the perturbed and unperturbed albedos for different values ofN_{d}.
Then a linear fit to the parameters DN_{d}
and A_{c}' was used to derive the correlation coefficient and then the
covariance. Various sample sizes and incremental values of the aerosol perturbation
were generated to test the stability of the correlation. This procedure resulted
in a stable correlation coefficient between A_{c} and A_{c}'
of 0.74.
A final issue arises as to the choice of susceptible cloud fraction (f_{c})
in the basic forcing equation. Here, we follow the analysis of Charlson et al.
(1987) and use the estimates in the cloud atlas of Warren et al. (1988). The
total fractional cover of low and mid level clouds is not used since midlevel
clouds can be mixed phase and the relationship of these clouds to anthropogenic
aerosol is still unclear (Section 5.3.6). Instead, we
use the estimates of Charlson et al. (1987) for nonoverlapped low marine cloud
as a lower bound (2/3 bound) for the susceptible cloud fraction and the sum
(correcting for overlap) of the low and middle marine stratiform cloud as an
upper limit for fc. The central value is taken as midway between these extremes.
The above assumptions, together with the parameter values given in Table
5.13, yield a central value for the indirect forcing over marine areas of
1.4 Wm^{–2} together with an uncertainty of ±1.4 Wm^{–2}.
Hence, the forcing lies in the range between zero and 2.8 Wm^{–2}.
This range is in reasonable agreement with that given in Chapter
6, based on GCM assessments. Nearly all of the uncertainty in the forcing
is associated with that in the planetary albedo which, in turn, is dominated
by the uncertainties in the perturbed and unperturbed cloud albedos, and thus
in the cloud optical depths. However, it is interesting to note that most of
the uncertainty in the optical depths for both perturbed and unperturbed clouds
arises from the uncertainties in the cloud LWC and cloud thickness, and not
from the uncertainties in the CDNC. This is not actually particularly surprising
and is simply due to the stronger functional dependence of the optical depth
on the LWC and thickness, h. This allocation of uncertainty may be slightly
misleading because the 1st indirect effect depends on an assumption of fixed
h and LWC. Yet here we are concerned with evaluating both the central estimate
as well as its uncertainty. Hence, knowledge of h and LWC are needed. Indeed,
consideration of these parameters and the accuracy of their representation in
GCMs must certainly contribute to any uncertainty in the estimates of forcing
from GCMs. Thus, it seems clear that progress in reducing the uncertainty in
the indirect forcing of the first kind will be at least as dependent on acquiring
better data on cloud LWC and thickness as on better quantifying anthropogenic
aerosol concentrations and their effects on N_{d}. At a somewhat lower
priority, it is clearly quite important to better understand the relationship
between cloud drop number concentration and sulphate concentration. The total
uncertainty is clearly dependent on this relationship. If it were significantly
different in form, a somewhat different order of contribution to total uncertainty
might have arisen. On the other hand, the uncertainty in the magnitude of the
emissions of sulphur gases as well as the uncertainty in the burden of sulphate
played only a minor role in the determination of the overall uncertainty.
