Parametric representation of the cloud droplet spectra for LES warm bulk microphysical schemes

Parametric functions are currently used to represent droplet spectra in clouds and to develop bulk parameterizations of the microphysical processes and of their interactions with radiation. The most frequently used parametric functions are the Lognormal and the Generalized Gamma which have three and four independent parameters, respectively. In a bulk parameterization, two parameters are constrained by the total droplet number concentration and the liquid water content. In the Generalized Gamma function, one parameter is specified a priori, and the fourth one, like the third parameter of the Lognormal function, shall be tuned, for the parametric function to statistically best fit observed droplet spectra. These parametric functions are evaluated here using droplet spectra collected in non-or slightly precipitating stratocumulus and shallow cumulus. Optimum values of the tuning parameters are derived by minimizing either the absolute or the relative error for successively the first, second, fifth, and sixth moments of the droplet size distribution. A trade-off value is also proposed that minimizes both absolute and relative errors for the four moments concomitantly. Finally, a parameterization is proposed in which the tuning parameter depends on the liquid water content. This approach significantly improves the fit for the smallest and largest values of the moments.