The impact of CCN on the cloud droplet number concentration (N_d) can be non-linear. One consequence of this is that the number of natural CCN can strongly influence the way that CCN from anthropogenic emissions affect the indirect radiative forcing. For example, Ghan et al. (1998) have shown that the presence of relatively high concentrations of sea salt particles can lead to increased N_d at lower sulphate concentrations and higher updraught speeds. Conversely, the N_d are lowered by high salt concentrations if sulphate concentrations are higher and updraught speeds are weaker (see also O’Dowd et al. (1999)). However, it is not clear whether these processes significantly affect the radiative forcing.

There are two general methods that have been used to relate changes in N_d to changes in aerosol concentrations. The first and simplest approach uses an empirical relationship that directly connects some aerosol quantity to N_d. Two such empirical treatments have been derived. Jones et al. (1994b) used a relationship between N_d and the number concentration of aerosol particles (N_a) above a certain size. This method is appropriate for the particles that serve as nuclei for cloud droplets in stratiform cloud, but it can be ambiguous for cumuliform cloud because of the activation of particles smaller than the threshold of the N_a (Isaac et al., 1990; Gillani et al., 1995). Boucher and Lohmann (1995) used observations of N_d and of CCN versus particulate or cloudwater sulphate to devise relationships between N_d and particulate sulphate. This approach has the advantage that it circumvents the assumptions required in deriving the aerosol number concentration N_a from sulphate mass. The use of sulphate as a surrogate for N_d implicitly accounts for other particulate species in the aerosol, but only as long as relationships are used that take into account the potential regional and seasonal differences in the chemical mixture of the aerosol (e.g., Van Dingenen et al., 1995; Menon and Saxena, 1998). Thus, the empirical relationships derived for regions with high industrial sulphate loading may not be appropriate for biomass aerosols. A new empirical approach relates N_d to the particle mass concentration and mean volume diameter in the accumulation mode aerosol. It is based on mass scavenging efficiencies of the accumulation-mode aerosol by stratiform clouds (Glantz and Noone, 2000). When deriving empirical relationships, it is important to be aware of the effects of the averaging scale (Gultepe and Isaac, 1998). An advantage of the empirical methods is that they may account for the effects on N_d that are associated with cloud dynamics in an average sense. Variance in the cloud updraught velocities is one of the main reasons for the large scatter in the observations from which these empirical relationships are derived (Leaitch et al., 1996b; Feingold et al., 1999b).

The second method that has been used to relate changes inN_dto changes in aerosol concentrations is based on a prognostic parametrization of the cloud droplet formation process (Ghan et al., 1993, 1995, 1997; Chuang and Penner, 1995; Abdul-Razzak et al., 1998; Abdul-Razzak and Ghan, 2000). This type of approach requires a representation of the CCN activity of the particles and a representation of the dynamic and thermodynamic properties of the cloud. At present, some of the aerosol properties necessary to describe the CCN spectrum must be assumed in order to apply this approach.

A comparison of the empirical and prognostic methods currently in use for determining the N_d is shown in Figure 5.7. The empirical relationships are taken from Jones et al. (1994b) and Boucher and Lohmann (1995) and represent stratiform cloud. The curves labelled PROG follow the prognostic parametrization used by Chuang and Penner (1995). There is some relative general agreement between the empirical curves and the prognostic curves for low updraught velocity. The prognostic curves for the higher updraught velocity, i.e. more convective cloud, give much higher N_d than the empirical results for stratiform cloud. The relatively close agreement of the 10 cms^-1 updraught curve with the empirical scheme for the ocean is somewhat fortuitous. Further work comparing both the empirical and prognostic schemes with observations is needed, especially for the climatologically important marine stratocumulus, to better understand the reasons for the agreements and differences in Figure 5.7.

There are also atmospheric dynamic factors that affect the prediction of N_d. Trajectories of air parcels through strato-cumulus are highly variable (e.g., Feingold et al., 1998). For the prognostic methods with their explicit representation of the updraught velocity, there is a need to understand not just the probability distribution function (PDF) of updraughts in these clouds, but the PDF of those that actually nucleate droplets. No satisfactory method of parametrizing the local updraught has yet been devised. The prognostic methods also produce an adiabatic N_d, which leads to the problem of how to represent the mean N_d in the cloud in the presence of the entrainment of dry air. Entrainment can even result from changes in N_d (Boers and Mitchell, 1994). These issues are critical for the prognostic prediction of N_d and deserve continued study to determine how best to take their effects into account.

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