| Abstract: | A general parameterization for solid and liquid hydrometeors is presented. hydrometeors basically are viewed as porous spheroids with the following variable parameters: diameter, axial ratio, mass, and porosity. Based on this parameterization a functional dependence on the Reynolds number of the drag of hydrometeors is derived, which is based on boundary layer theory. The basic form of this functional dependence is consistent with viscous theory and the inertial drag at low Reynolds numbers is predicted with good accuracy by matching the results from the boundary layer theory with Oseen's theory of creeping motion. Based on this solution a general semi-empirical expression for the Reynolds number and fall speed of particles is found. The results from the present theory are in remarkable agreement with experiments: The errors generally are < 5–10% for a wide variety of hydrometeors in the range of Reynolds numbers 0<NRe<5×105, including columnar and variously branched planar ice crystals, rimed and unrimed aggregates, lump, conical, and hexagonal graupel, hail, and rain drops. The present parameterisation aims far beyond the limits of the conventional methods since it is suitable for mixed-phase models of the microphysics of precipitation with continuously varying particle mass and shape characteristics and including processes such as depositional growth of ice crystals under varying environmental conditions, collisional growth of particles, and melting. |
