The explicit microphysics model

The explicit bin-resolving microphysics model is an accurate moment-conserving scheme, described in detail in Tzivion et al. [1987, 1989] and Stevens et al. [1996a]. A brief description of the explicit microphysics model is given below. In this scheme, both the mass and the number mixing ratios are predicted for each bin. A total of 25 bins cover a drop spectrum ranging from 1.56-504 $\mu m$ (radius), with mass doubling from one bin to the next. Predictive equations for both the mass and the number mixing ratios in each bin require an additional 50 scalars for the liquid cloud related processes: condensation/evaporation, collision-coalescence, droplet activation from CCN, and sedimentation.

In some of our prior studies [Stevens et al., 1996a] a rather simple drop activation scheme was implemented whereby CCN were assumed to have a constant (in time and space) size distribution and activation was calculated such that the the number of cloud drops was based on the model-derived supersaturation but could not exceed the number concentration of CCN. Thus, at each time step the drop concentration N_d was incremented by an amount

$$\Delta N_d = {\rm max} [0, ~ N_{ccn} \int_{r_{cut}}^\infty f(r; r_g, \sigma_g) dr - \sum_{k=1}^{25} N_k ]$$ (1)

where N_ccn is the total CCN concentration, r_cut is the smallest radius of CCN activated at the ambient supersaturation S, r_gis the median radius of CCN, $\sigma_g$ is the geometric standard deviation of the CCN radii, and N_k is the number concentration of drops in size bin k. In order to explore aerosol-cloud interactions one would ideally like to model the size resolved aerosol spectrum [e.g., Feingold et al., 1996b] as well as the drop size distribution response to the aerosol spectrum. Due to the large computational expense of these simulations we opted for a more simplified droplet activation scheme based on equation(1). We assume that the CCN size distribution is constant throughout the model domain (i.e., r_g and $\sigma_g$ are constant), and that only N_ccn varies as one passes from the clean boundary layer to the rather polluted air aloft. The representation of the aerosol is reduced to prognosing N_ccn, rather than a set of parameters that describe the full distribution of CCN particles. For the goals of our study, we feel that this representation is sufficient, although we recognize that variations in both the size distribution and chemical composition of the particles may have significant impact under certain circumstances [Feingold et al., 1999]. Note that outside of cloud the prognosed field N_ccn is the number concentration of CCN in cm^-3 whereas within the cloud, it represents the potential number of drops that can be activated, and not the number concentration of unscavenged CCN. The latter can easily be calculated as

N_unscavenged = N_ccn - N_d (2)

Unlike Feingold et al. [1996b], CCN particles are not tracked within drops and the current simplified treatment has an inherent assumption that the CCN concentration would be unmodified (in both number and size) on complete evaporation of drops. For clouds with very weak collision-coalescence such as the cases examined here, this is quite reasonable.