Study of hail density parametrizations

Abstract

SUMMARYOne aspect of hailstone growth that has received attention over the last twenty years is the importance of low-density riming growth in hail. Density is an important parameter in riming growth because it regulates hail size and is also involved in other atmospheric processes, like crystal multiplication, charge transfer, etc. New numerical dynamic and cinematic models take into account the variability of density with growth parameters (such as size of cloud droplets, impact velocity and surface temperature) in order to attain more realistic results. These kinds of models need to have a function that describes the real low-density riming process.Analysing previous results, it is clear that several different empirical parametrizations are employed to describe density. These parametrizations relate density to growth parameters through the variable X = V o b/T s , where V o is the impact velocity of droplets into the target, b is the droplet size, and T s the hail surface temperature.These empirical expressions give different density values for identical growth conditions. It is important to note that these parametrizations stem from experimental data obtained in very different growth conditions and with different collector geometries.Working with experimental density data, we can show that different parametrizations are equivalent if X is defined in an appropriate way (taking into account correct impact velocity and collector geometry). Different environmental conditions are taken into account by means of Stokes' parameter.Due to this finding, we have aimed at developing a parametrization to be used in cloud models, which satisfactorily represents all experimental results.

A possible influence of the density of ice accretions on their heat transfer coefficient

“…For simplicity, the density was calculated by using the empirical fitting given by Macklin (1962): ρ = 0.11X 0.76 . This fitting is in good agreement with that given by Castellano et al (2002) for the range of interest of N S in the present work. The values of r and T s were experimentally determined, while the values of V o for cylinders were calculated by using the equation given by Castellano et al (2002).…”

“…This fitting is in good agreement with that given by Castellano et al (2002) for the range of interest of N S in the present work. The values of r and T s were experimentally determined, while the values of V o for cylinders were calculated by using the equation given by Castellano et al (2002). Figure 1 shows the values of Nu m /Nu t versus ρ, where Nu m and Nu t are the experimental and theoretical values of Nusselt number, respectively.…”

“…Therefore, the Stokes number seems not be the best choice to parametrize the ventilation effect. Castellano et al (2002) suggested that the Stokes number is a factor in the determination of the mean density of the accreted ice, in addition to the Macklin number, defined as X = rV o (−T s ) −1 , with r the median volume radius of the droplets (µm), V o the impact velocity of droplets on the ice (m s −1 ), and T s the mean temperature of the accreting particle ( • C). The authors found that for a given X, density decreases for decreasing values of N S .…”

Surface temperature distribution on a spherical ice particle growing by accretion in wet growth regime

“…It is important to clarify that the clear ice observed at the stagnation point does not imply wet growth conditions on the ice particle surface. Rime density can be estimated using parametrizations reported in the literature (Macklin, 1962;Pflaum and Pruppacher, 1979;Castellano et al, 2002) and the data reported by Luque et al (2018). In particular, for the expression proposed by Macklin (1962), the estimated rime density varies between 0.7 g/cm 3 and the bulk ice density (0.917 g/cm 3 ), which indicates that partial wet growth conditions could have been reached over the ice particle.…”

“…It is important to clarify that the clear ice observed at the stagnation point does not imply wet growth conditions on the ice particle surface. Rime density can be estimated using parametrizations reported in the literature (Macklin, ; Pflaum and Pruppacher, ; Castellano et al ., ) and the data reported by Luque et al . ().…”