The behavior of number concentration tendencies for the continuous collection growth equation using one- and two-moment bulk parameterization schemes

Abstract

This paper presents a mathematical explanation for the nonconservation of total number concentration Nt of hydrometeors for the continuous collection growth process, for which Nt physically should be conserved for selected one- and two-moment bulk parameterization schemes. Where possible, physical explanations are proposed. The assumption of a constant no 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 Nt, conservation and Nt does not come into the derivation. Even scheme F, which perfectly conserves Nt, does not preserve the distribution shape in comparison with a bin model. © 2007 American Meteorological Society.