The Behavior of Number Concentration Tendencies for the Continuous Collection Growth Equation Using One-and Two-Moment Bulk Parameterization Schemes

摘要

This paper presents a mathematical explanation for the nonconservation of total number concentration N_t of hydrometeors for the continuous collection growth process, for which N_t physically should be conserved for selected one- and two-moment bulk parameterization schemes. Where possible, physical explanations are proposed. The assumption of a constant n_o in scheme A is physically inconsistent with the continuous collection growth process, as is the assumption of a constant D_n for scheme B. Scheme E also is nonconservative, but it seems this result is not because of a physically inconsistent specification; rather the solution scheme's equations simply do not satisfy N_t conservation and N_t does not come into the derivation. Even scheme F, which perfectly conserves N_t, does not preserve the distribution shape in comparison with a bin model.