A Comparison of the Conservation of Number Concentration for the Continuous Collection and Vapor Diffusion Growth Equations Using One- and Two-Moment Schemes

Abstract One- and two-moment parameterizations are integrated over hydrometeor diameters D(0, ∞) for vapor diffusion and the continuous collection growth processes. For the conditions specified, the total number concentration of collector particles should be conserved. To address the problem, the gamma distribution function is used for the spectral density function. Predicted variables can include total mixing ratio q, total number concentration Nt, and characteristic diameter Dn (inverse of the distribution slope λ). In all of the cases, the slope intercept no is diagnosed or specified. The popular one- and two-moment methods that are explored include the one-moment method in which q is predicted, no is specified, and Nt and Dn are diagnosed; the one-moment method in which q is predicted, Dn is specified, and Nt and no are diagnosed; the two-moment method in which q and Dn are predicted and Nt and no are diagnosed; and the two-moment method in which q and Nt are predicted and no and Dn are diagnosed. It ...