Numerical simulation of the accumulation zones and hail growth in hailstorms

ABSTRACT

In China, nowadays, with the great help of radar observation and numerical modeling, various research results show that there exist accumulation zones in some hailstorms with warm base, and this situation can last for several minutes. However, the amount of the supercooled water in this region is time-dependent which does not accord with the classical theory of Sulakvelidze. Further approaches have found most hail embryos in this kind of hailstorms are frozen drops. There are also some interesting findings about the motion of drops during their growth, about the problem that embryos form in which part can rapidly grow into largest and about their trajectories during growth. However, in these simulations particles were sent out into parts of the storms, covering some regions where there might be no embryos forming in real cases.

Calculation of the trajectories of particles growing in a time-dependent field which is similar to real cases, might give further and more accurate understanding of the hail growth. Firstly, to get further study of the accumulation zone and the formation of hail embryos, a rawinsonde sounding was used to initiate a three-dimensional, nonhydrostatic, and fully compressible hailstorm model with two-moment bulk microphysics scheme. Simulations were integrated to 3600 s using a horizontal grid spacing of 1 km over an 80km multiplies 80km domain and a vertical grid spacing of 0.5 km over a 18.5km depth. Secondly, A three-dimensional Lagrangian hail growth model was used to calculate the three-dimensional trajectories. All modeling has the same simulation space and grid spacing as that of the first step modeling. Series of time-dependent data such as the wind fields, liquid water contents, and temperatures used in this model to give a real case background were obtained from the three-dimensional convective cloud modeling in the first step. And at the 13^th minute, particles are sent out into a certain cubic space, from 20~40km horizontally and from 4~10km vertically until the accumulation zone disappeared (actually, the time and the certain space where the particles were introduced were determined from the results of the first step). Eight experiments have been done; in each experiment drops had a specific and unified origin size: 1, 2, 3, 4, 5, 6, 7 and 8 mm respectively. Then the 3D trajectories and the time-dependent growth rate of drops with different origin size and origin place were calculated. 

The results of showed: 1) that a relatively stable accumulation zone is found above the level of greatest updraft velocity before 16 min and this situation last for 7-8 minutes. Moreover, it was the place where the embryos were formed and where they grew large in their early stages, however, not the main area where stones got quick accretion; 2) that the final size of large stones are sensitive to the original size of drops according to the results of this study, the larger original size the drops have, the larger the drops will grow, and the more large stones were formed; 3) that according to the calculation of trajectories of numbers of drops originally from certain space, of great interest, particles moved simply in a down-up-down manner, but no further recirculation growth have been found. And the motion of stones with larger origin sizes present similarity with that of the stones in supercell, which, however, were originally from a area called ¡°embryo curtain¡±; 

Table 1  Growth parameters of the maximum-sized hailstones

	D0 mm	N1	N2	Dmax cm	K0	X0 km	Y0 km	Z0 km	tm min	dD/dt mm/min
R1	1	0	0	0.72	2862	35	40	7.0	20.7	0.299
R2	2	18	0	1.27	217	36	40	4.0	18.6	0.578
R3	3	58	0	1.54	2865	38	40	7.0	18.7	0.665
R4	4	100	0	1.73	2865	38	40	7.0	16.9	0.788
R5	5	161	0	1.98	3306	38	40	7.5	16.6	0.892
R6	6	206	2	2.12	3747	38	40	8.0	15.5	0.981
R7	7	234	4	2.25	3747	38	40	8.0	15.1	1.027
R8	8	273	7	2.33	3747	38	40	8.0	14.7	1.043

 D₀: the original size; K₀: the No. of the particles which grew largest in each experiment; (X₀,Y₀,Z₀): the original location of the drop;  N₁,N_1.5,N₂: the total number of drops whose final diameter are larger than 1cm and 2cm respectively.

     

Fig.1  Representative maximum-sized hailstone growth trajectories for eight experiments projected on the x-z plane, y-z plane and x-y plane.

Fig. 2  Time vs. distance in X (a), height(c) sections of the growthrate for particle No.3747 with initial diameter 6mm. The solid curves show the growthrate in each time and at its corresponding location.

Fig. 3   Detail 3D trajectories for particle No.3747 in R6.