Precipitation Formation in Warm Clouds

The influences of precipitation and drizzle processes on cloud lifetime, cloud water content, and cloud radiative properties discussed above cannot be simulated well in current GCM cloud parameterization schemes. For example, the autoconversion rate, which is the rate at which cloud droplets collide and coalesce with each other to form precipitation size drops, is a nonlinear function of the total water condensate. Thus, the mean LWC from a GCM model grid box is essentially meaningless for the representation of precipitation production (e.g., Pincus and Klein 2000). Since the autoconversion bias attributable to horizontal heterogeneity has been found to scale strongly with cloud fractional coverage (Wood et al. 2002), it may be overcome using a parameterization that takes this bias into account. Alternatively, a PDF approach to subgrid modeling may be better in resolving these deficiencies. PDFs of subgrid quantities, such as vertical velocity and liquid water path, are determined from prescribed basis functions in which various moments of the basis functions are calculated in the models (e.g., Pincus and Klein 2000).

Autoconversion of cloud droplets to rain drops is a key process governing the amount and lifetime of clouds in the atmosphere, and must be represented accurately in models from the cloud-resolving to global scale. Even though the mass transfer rate of cloud drops to rain is dominated by accretion in most clouds (Wood 2005), autoconversion is the dominant process in most GCMs because rain is assumed to reach the surface within one model time step. Thus, developing parameterizations for autoconversion suitable for incorporation in large-scale models is an active area of research. Traditional parameterizations are either empirically or intuitively obtained (e.g., Kessler 1969 and Sundqvist 1978) or are derived by curve-fitting detailed microphysical models with simple functions, such as a power law (e.g., Berry 1968; Beheng 1994). These parameterizations lack, however, clear physical bases and have arbitrarily tunable parameters. Furthermore, parameterizations that calculate at least the cloud droplet number concentration in addition to the LWC would be expected to provide much better representation of cloud radiative influences and aerosol effects than existing one-moment schemes.

One promising scheme, which has been derived from theoretical considerations (see Liu et al. 2007 and earlier papers referenced therein), represents the autoconversion rate as the product of a rate function based on the collection efficiency of falling rain drops that describes the conversion rate after the onset of the autoconversion process times a threshold function. The threshold function, unlike that of earlier parameterizations such as the widely used Kessler (1969) parameterization, does not increase abruptly at a critical value of mean droplet mass but instead increases gradually over a range of mean droplet masses that is dependent on the relative dispersion of the cloud droplet size distribution (ratio of standard deviation to mean radius). This dependence captures initiation of the autoconversion by large drops at the high end of the size distribution; its variation for differing values of relative dispersion encompasses prior empirical representations of threshold behavior. This approach yields a strong dependence of autoconversion rate on relative dispersion; for example, for liquid water volume content 0.3 g m-3 and cloud droplet number concentration 50 cm-3, as the relative dispersion increases from 0.33 to 1 the characteristic time of autoconversion decreases from 10 hours to 0.1 hour. This parameterization has found application in modeling on regional (Gustafson et al. 2007) and global scales (Rotstayn and Liu 2005), modeling scavenging of soluble gases by precipitation (Garrett et al. 2006), and remote sensing of precipitation (Berg et al. 2006).

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