Validation and development of a new hailstone formation theory: Numerical simulations of a strong hailstorm occurring over the Qinghai-Tibetan Plateau

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112,, doi: /2005jd006227, 2007 Validation and development of a new hailstone formation theory: Numerical simulations of a strong hailstorm occurring over the Qinghai-Tibetan Plateau Fengqin Kang, 1,2 Qiang Zhang, 2 and Shihua Lu 1 Received 16 May 2005; revised 19 December 2005; accepted 12 July 2006; published 25 January [1] Hailstorms occur frequently over the northeastern border of the Qinghai-Tibetan Plateau and its surroundings because of the combined geographical and meteorological features of this region. Formation and growth of the hailstones in a typical hailstorm are simulated using a three-dimensional (3-D) cloud model with hail-bin microphysics developed by the Institute of Atmospheric Physics of the Chinese Academy of Sciences (IAP/CAS). The information of the large-scale circulations for the cloud model was provided by the MM5V3 model. The results show that (1) the water content of each hailstone bin is significantly large in the cave channels ; (2) at the initial stage of hail formation, there is another high water content region consisting of small ice particles (D < 1 mm), graupel and hail embryos (1 mm < D < 5 mm), as well as small hailstones (5 mm < D < 10 mm), around the altitude of C above the high water content center associated with the cave channels ; between them there is a gap of lower water content, which means that the main mechanisms of hail formation are different in those two regions; (3) as the hail and rain fall, the maximum center at higher level drops until it merges with a lower equivalent; the larger the hail particles are, the earlier the maximum centers merge with each other; (4) during the hailstorm dissipation period the downdraft occurs in the region of cave channels and the cave channels fade; however, it is still the center of high hail water content, even though all updraft airflow turns to downdraft airflow; (5) cave channels are not the only regions of hailstones formation, but are nonetheless effective in the growth of hailstones, so which should be the main region of suppressing hail growth from small to large. Citation: Kang, F., Q. Zhang, and S. Lu (2007), Validation and development of a new hailstone formation theory: Numerical simulations of a strong hailstorm occurring over the Qinghai-Tibetan Plateau, J. Geophys. Res., 112,, doi: /2005jd Introduction [2] Over the last few decades, much effort has been devoted to understanding the physical and dynamic processes taking place in hailstorms, and a number of theoretical models of hailstone formation have been proposed [Barge and Bergwall, 1976; Browning, 1964; Browning and Foote, 1976; Chisholm and Renick, 1972; English, 1986; Krauss and Marwitz, 1984; Lemon and Doswell, 1979; Miller et al., 1988] (see also Cotton and Anthes [1989] for an excellent review). [3] Despite the great progress, our understanding and modeling of relevant physical mechanisms are still far from complete, which seriously limits our ability to mitigate the 1 Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou, Gansu, China. 2 Key Laboratory of Arid Climatic Change and Reducing Disaster of Gansu Province, Lanzhou Institute of Arid Meteorology, Lanzhou, Gansu, China. Copyright 2007 by the American Geophysical Union /07/2005JD destruction caused by such extreme weather phenomena. For example, existing models of hailstone formation and growth cannot explain many observational phenomena [Smith, 2003; Dostalek et al., 2004]. Different models often give inconsistent results [Gilmore et al., 2004; van den Heever and Cotton, 2004]. [4] Over the last decade or so, Xu and his colleagues in China have developed a so-called cave channels theory (hereafter CC theory) on the formation and growth of hailstones [Xu et al., 2000, 2004; Duan and Liu, 1998; Wang and Xu, 1989]. The CC theory has been applied to explain observations successfully [Tian et al., 2005]. However, previous studies regarding the CC theory have been performed by use of a 3-D Lagrangian model that is unable to simulate the growth of all the particles, and as a result, it is unclear if the CC theory can be applied to all the hydrometeors in a hailstorm. [5] In this work, we extend the previous studies using a 3-D cloud model with hail-bin microphysics developed by the Institute of Atmospheric Physics of the Chinese Academy of Sciences (IAP/CAS) with the information of the large-scale circulations provided by the MM5V3 model. 1of13

2 Figure 1. Spatial distribution of annual hail fall day (AHD) over northwestern China. The fine line is the provincial border [from Liu et al., 2004]. We investigate the evolution of various hydrometeors in a typical hailstorm occurring over the northeastern border of the Qinghai-Tibetan Plateau and its surroundings, a region of frequent hailstorms and of weather modification focus in China. In section 2, we first introduce the major region characteristics and statistics of hailstorms over northwest China and then discuss a typical case of strong hailstorms that is chosen for further modeling investigation. Section 3 describes the model framework, the initial data, and model setup. In section 4, we briefly introduce the CC theory and compare the CC theory with simulation results. Section 5 summarizes the major results and important implications for further theoretical development and hail suppression. 2. Statistics of Strong Hailstorms and A Typical Case 2.1. Statistical Analysis [6] The northeastern border of the Qinghai-Tibetan plateau with its surroundings is an intersection of three different climatic regimes (the eastern monsoon area, the northwest arid area, and the high and cold region of the Qinghai-Tibetan plateau). The topography varies widely, with inhomogeneous mixtures of mountains, plateaus, plains, rivers, and deserts. This region is also subject to the influences of the west wind circulation and the monsoons. These factors conspire with the strong thermodynamic and dynamic effects of the Tibetan plateau to generate hailstorms in this place frequently. [7] Figure 1 shows the distribution of the annual hail fall day (AHD) over the northwest of China. The data were collected from 1961 to 2001 at 85 observation stations. As shown in Figure 1, there were 19.6 AHD in Qumajia and 5 to 8 AHD over the southeast of the Tibetan plateau, the Gannan plateau, and east of the Qilianshan mountains, which is the eastward extension of the maximal AHD in China in the middle of the Tibetan plateau. Another center with 1 to 11 AHD is located near the mountainous area of the Tianshan Mountain, the Altai Mountain, and the Kunlun Mountain. The maximum AHD is 22 and is located in Zhaosu [Liu et al., 2004] A Typical Case [8] This section describes a typical case that is chosen for modeling investigation. During the period from 6 8 July 2003, there were two troughs and a ridge from 700 hpa to Figure 2. Thermal advection at 0800, 8 July 2003 (local time (LT)). (left) 400 hpa; (right) 700 hpa. 2of13

3 Figure 3. The 400 hpa weather map and the surface frontal position at 0800, 8 July 2003 (LT). 3of13

4 Figure 4. Vertical shear in the hail fall area (station ID: 53915) from 0800, 7 July to 2000, 8 July 2003 (LT). 300 hpa over the Eurasian continent. The long wave trough was tilted backward from 700 hpa to 300 hpa. The strongest cold thermal advection was at 400 hpa and situated in the hail fall area, the weakest is at 700 hpa (as shown in Figure 2). The warm thermal advection is over the Qinghai- Tibetan plateau, and the cold thermal advection is stronger as the height, which is available to keep and develop the unstable weather. As an illustration, Figure 3 shows the 400 hpa weather map at 0800, 8 July It is clear from this figure that one trough lay over the European plain, and the ridge was over western Siberia and Xinjiang. The northeast edge of the Tibetan plateau and its surroundings were situated on the cold airflow along the southern edge of the frontal region from middle Siberia to Mongolia. Figure 4 shows the vertical shear in the hail fall area at station On 6 9 July 2003, there was a high ( hpa on the surface) from Baikal to Mongolia and a low ( hpa) from Xinjiang to the west parts of Gansu and Qinghai provinces of China. The shearing line was moving eastward over Yongdeng ( E and N). On the afternoon of 8 July 2003, hailstones were falling in Yongdeng, accompanied with flood and strong winds. As a result, acres of plantation were hit by the strong storm, and the grain output was reduced by million kilograms. Observations using a radar with XDR-21X wave band showed that from 1534 to 1646, 8 July 2003 (BJT), there was a strong single cell with classical radar echoes characterized as vault echoes. Figure 5 shows a range height indicator (RHI) image of radar reflectivity taken at 1614:26, 8 July 2003 in the direction of On the basis of these facts, Yongdeng is chosen for further modeling investigation. Observations using a XDR-21X wave band radar show the characteristics of strong hailstorms, which can be used Figure 5. The range height indicator (RHI) image of the radar with XDR-21X wave band taken at 1614:26, 8 July 2003 (LT) in the direction of degrees. 4of13

5 Figure 6. Output of the MM5v3 model and the real-time rawinsonde sounding in Minqing, Gansu, China ( E and N) at 0800, 8 July 2003 (LT). to understand the hail disaster that occurred in the local place. 3. Model and Simulations 3.1. Spectral Bin Microphysical Model [9] The hail-bin microphysical model (HBM), a threedimensional compressible nonhydrostatic cloud model in which hail/graupel is divided into 21 size bins, was used in simulating the water-mixing ratio of five particle classes, i.e., small ice particles, graupel and embryos, small hailstones, typical hailstones, and large hailstones. Details about this model are given by Guo [1997] and Guo and Huang [2002]. The dynamical scheme and microphysical processes in the 3-D hail-bin microphysical model are described in Appendix A Initial Conditions and Simulation Setup [10] The model was integrated to 150 min using a horizontal grid size of 1 km and a vertical grid size of 0.5 km over a km domain. A warm bubble placed in the center of the model domain with a size of 8 8 km in the horizontal and 4 km AGL in the vertical was used to initiate convection in a horizontally homogeneous environment. The maximum temperature perturbation in the center of the thermal bubble was 2.5 C. In this model the model domain is moving so that the center of the storm is in the center of the model domain. [11] The sounding data for the model input was generated using the PSU/NCAR MM5v3 because there is no sounding data for the Yongdeng weather station, and the nearest sounding station is 60 km away. The model has a horizontal grid size of 30 km over a grid domain with Yongdeng at the center. The number of sigma levels in the model is 25 in vertical coordinates. The other model configurations are the Betts-Miller cumulus parameterization for the coarse mesh of 60 km grid size and the Grell cumulus parameterization for the finer mesh of 20 km grid size; the high-resolution Blackadar PBL scheme for the planetary boundary layer/vertical diffusion; the Reisner 1 microphysical parameterizations; the Duhdia radiation scheme; and the surface scheme of the five-layer soil model with 13 land-use categories. The NCEP/NCAR reanalysis data are used as initial and boundary conditions. The model Figure 7. Rawinsonde sounding at 1500, 8 July 2003 (LT) at Yongdeng. 5of13

6 Figure 8. A schematic illustration of the cave channels (CC) theory. (right) Location of CC in a storm. (left) Last positions of various particles in CC when their terminal velocities are equal to the relative updraft velocities [from Xu et al., 2004]. Figure 9. Echo and radial velocity analysis observed by Doppler radar 30 May (a) Plan position indicator (PPI) radial velocity at 1953:42, elevation angle is 2.4 ; (b) PPI echo intensity at 1637:38, elevation angle is 2.4 ; (c) RHI radial velocity at 1953:02, azimuth is ; (d) RHI echo intensity at 1953:02, azimuth is 306.5, distance is 150 km. The dark thick line is velocity zero line [from Liu et al., 2006] 6of13

7 Figure 10. Dependence of the maximal updraft and downdraft of time (unit: ms 1 ). was integrated to 120 hours from 0800 of 5 July 2003 (BJT). According to the development of the hailstorm as observed by the weather radar, we choose the model output at 0300 of 8 July 2003 (BJT) as the sounding input to the 3-D hail cloud model. [12] To provide supports for such an approach, we first use MM5 to generate sounding at the Minqing station ( E and N) where real-time sounding data is available and compare the MM5-generated sounding with real sounding. Figure 6 compares the MM5-generated sounding with the real one at 0800 of 8 July 2003 (BJT). The results suggest that the MM5-generated sounding represents the real sounding reasonably well, providing support for applying the MM5 output at 0300 of 8 July 2003 (BJT) in Yongdeng as the sounding input to the 3-D cloud model with hail-bin microphysics. [13] As shown in Figure 7, the wind reaches its maximum of 38 m s 1 at 200 hpa, and there is a little wind shear in the cloud layer ( hpa). The cloud base temperature is +3.5 C, and the cloud base height is hpa. 4. Simulation Results 4.1. CC Theory [14] We recapitulate the CC theory here because it has not been well known outside China, and it is used to compare and contrast with simulation results. As illustrated by Figure 8 [Xu et al., 2004], this theory has the following main points. First, there is a core of main updrafts (MUD) and an area by this core where the horizontal wind speed relative to the hailstorm equals zero because of the strong convective airflow of the hailstorm. Below this zero line, winds blow toward the core, whereas winds blow away from the core above this zero line. The growth travel trajectories of cloud particles rotate around the zero line. Particles enter the core of MUD circle by circle and grow into hailstones gradually. Second, there is a cave channel (CC) close to the core of MUD and below the zero line. Although the cave channel occupies only about 6% or smaller of the total volume of the hailstorm, it acts as a trap to attract particles. Once a particle enters the CC, it cannot escape the attraction of the CC until it becomes a large hailstone and falls from the CC exit, for it has been growing from small to large in CC until the updrafts cannot bear its weight. Therefore hail embryos form in the entrance end of the CC and grow into large hailstones in the exit end of CC. Finally, the existence of CC and its location depend on the airflow. The rate of hailstone growth and the lengths of the growth trajectories also depend on the field of supercooled water. A 3-D Euler model is used for macrocloud and microcloud fields, and a 3-D Lagrangian growth travel model is used for the behavior of hydrometeor particles [see also Xu et al., 2004]. Until now we cannot find an analytic expression to show these characteristics. Echo and radial velocity analysis observed by Doppler radar can show this theory, one of the observed data on 30 May 2005 in Lanzhou, Gansu, China, as shown in Figure 9, provided by the Lanzhou Doppler radar station, Lanzhou Regional Meteorological Center, Gansu, China. As illustrated by Figure 9, the zero line of horizontal velocity is crossing the middle of the vault echoes, which confirms the CC theory Analysis of the Simulation Results [15] Figure 10 shows the dependence of the maximal updraft and downdraft of time, which shows the lifetime of the storm. At 24 min the solid particles appeared in the hailstorm. The maximal rainfall intensity occurred at 32 min, and the maximal hail fall (graupel fall) occurred at 34 min. So we consider 24 min is the initial stage of cloud and 36 min is the later stage. Figure 11 shows the vertical velocity, and the special water content of various hydrometeors cross X-Z sections at y = 17 km in 26, 30, and 40 min. The hail-bin microphysical model (HBM) has the ability to show weak echo region (WER) as demonstrated by Guo et al. [2002]. However, there is no WER in our model results as shown in the radar imagery. We think the main reason for this disagreement is that the sounding data used as the model input may not represent the reality. Although we are unable to compare the modeled updrafts with observed updrafts, we think that the modeled results of strong winds and hailstones seem reasonably consistent with observation. [16] Figure 12 shows X-Z cross sections of the location of the simulated CC at y = 17 km in 24 min and 36 min, respectively, which is obtained by analyzing the airflow in the simulated storm according to CC theory. Figures 13a and 13b shows the spatial distributions on the X-Z plane at y = 17 km of the water-mixing ratio (g/kg) of each particle class, i.e., small ice particles, graupel and embryos, small hailstones, typical hailstones, large hailstones, and the total hailstones, respectively, from top to bottom. Figure 12 (left) and Figure 12 (right) represent the distributions in 24 min and 36 min, respectively. It is evident that the airflow and the temperature field are almost symmetric, and that the vertical velocity and the temperature reach their maximums at about the same altitude. Over the lifetime of the hailstorm, different particle classes exhibit very different spatial distribution of water contents. At the initial stage, there are two regions of high water content for the first three particle classes: One corresponds to the height of C, and the other is near the 0 C level. There is an obvious gap between two zones of high water content. In two zones of high water content the microphysical processes responsi- 7of13

8 Figure 11. Vertical velocity and the special water content of various hydrometeors X-Z cross sections at y = 17 km in 26, 30, and 40 min from top to bottom. (left) Vertical velocity (unit: m/s). (right) Special water content of various hydrometeors (unit: g/kg) and wind speed. (purple solid line) Hail/graupel; (green long-dashed line) rain; (yellow short-dashed line) cloud; (red short-dashed line) snow; (blue dotted line) ice. 8of13

9 Figure 12. X-Z cross sections of the location of the simulated CC at y = 17 km. Yellow (blue) lines with (without) arrows are the streamlines (vertical velocity in m/s); thicker solid and dotted lines represent the zero values of the zonal and radial velocities, respectively. The thickest lines with arrows are CC. (left) 24 min; (right) 36 min. ble for the formation of hailstones are the same. The difference between them are the dynamics characteristics and flow structure. The high-level water content center corresponds to the convergence zone of updraft velocity, where updraft velocity decreases from its maximum at the middle level of the hailstorm to zero at the top of the storm, and the lower-level water center lies in the region where the CC theory works; its major features have been described in section 4.1. The storm dynamics typically plays an important role in hailstone formation and growth mechanisms. [17] The high-level water content center is primarily for the first three particle classes, whereas the lower-level center is for particles of all sizes, including large hailstones. As for the first four particle classes, the maximal water contents exist in regions outside of the main updraft core where the updrafts are weaker and more in balance with the fall velocities of these particles, rather than in the core where the strength of the updrafts will eject them from the storm. The larger-size particles will be produced here. Once they grow large enough, they fall down into the slant updraft airflow beside the middle updraft of the hailstorm. They will begin moving and growing next time, until hydrometeors are growing into typical hailstones. As for large hail/graupel particles (D > 25 mm), they need enough vertical velocity to support them staying in the storm, so their maximal center is in the center of the hailstorm, where the vertical velocity reaches its maximum, and the horizontal wind speed relative to hailstorm is zero still. The formation and growth mechanism of hail/graupel in this region is connected with the movement of each hailstone/graupel particle class as described in CC theory. [18] At the 36th min it is obvious that the position of the zero value of the horizontal wind speed relative to the hailstorm has been shifting. The small-sized particles (D < 1 mm) are congregating in the vertical convection region, where the updraft is maximal and the temperature is between 0 C and 20 C over the height of km, and also the horizontal wind speed relative to the hailstorm equals zero in this region. Here the cloud water and cloud ice are not abundant except the snow. Thus the main microphysical processes are connected with snow. For the small hail particle, its maximal water content center is not in the middle of the cloud, but in the side of the maximal downdraft. We think that it is related to its growth region. For the classical and large hailstones the water content center is greater and closer to the middle of the cloud. Obviously, in the process of falling, the melting of hail occurs. For the hail/graupel embryo (1 mm < D < 5 mm) the distribution is the same as that of the ice crystal except the height of the maximal water content center is lower. The distribution of the small hail (5 mm < D < 10 mm) has the special feature that the maximal water content center is in the edge of the maximal downdraft, not in the middle of the maximal downdraft, suggesting that the formation and growth of the small hailstones is in the region of slant updrafts, too. For the last two classes of hail/graupel particles, the larger the size, the closer the hail/graupel water content center is to the center of the updraft or downdraft. For particles of all sizes, their water content distribution follows the description by the CC theory. 5. Concluding Remarks [19] Hailstorms that occurred from 1961 to 2001 over northwestern China are statistically analyzed. It is shown that hailstorms occur frequently over the northeastern border of the Qinghai-Tibetan Plateau and its surroundings because of the combined geographical and meteorological features of this region. A typical hailstorm is simulated by coupling a 3-D cloud model with hail-bin microphysics developed by the Institute of Atmospheric Physics of the Chinese Academy of Sciences (IAP/CAS). Simulation results are further analyzed in light of the CC theory that has been recently proposed by Chinese scientists to understand the physical mechanisms for formation and growth of hailstones in hailstorms. The following points can be drawn from this study. 9of13

10 Figure 13a. X-Z cross sections of water content (g/kg) at y = 17 km for each class of hail particles. (top to bottom) Small ice particles, graupel/embryos, and small hailstone. Thick solid and dotted lines denote positive and negative environmental temperature, respectively. (left) 24 min; (right) 36 min. [20] First, the simulation results are largely consistent with the so-called CC theory on hailstone formation. Throughout the lifecycle of a hailstorm, the CC region assumes high water contents of hydrometeors of all sizes, including large hailstones. Furthermore, in the early stage of the hailstorm, there is an additional center of high water contents at high altitude ( C) for smaller particles (first three classes, i.e., small ice particles (D < 1 mm), graupel and hail embryos (1 mm < D < 5 mm), and small hailstones (5 mm < D < 10 mm). There is a gap of lower water contents between the two centers, suggesting different mechanisms for the formation and growth of the particles in these two zones. Although both zones are all important for the formation and growth of particles of the first three classes, the CC region is necessary for further growth of smaller hail/graupel particles into large hailstones. [21] Second, as the hailstorm evolves, the high-level water content center gradually decreases in altitude to merge with the lower one, and an earlier merger leads to the formation of larger hailstones. During the dissipation period, downdraft occurs in the CC region. Nevertheless, the CC region still exhibits high hail water contents. [22] Third, the results show that the accumulation zone of cloud water appears only at the initial stage of the hailstorm, and its maximal cloud water content is below the 10 of 13

11 Figure 13b. As in Figure 13a, but for (top to bottom) typical hailstones, large hailstones, and total hailstones. (left) 24 min; (right) 36 min. 11 of 13

12 level of 0 C. Therefore it seems that the theory of accumulation zone of supercooled water as proposed by Sulakvelidze [Sulakvelidze et al., 1967] does not work in this hailstorm. [23] Finally, for the purpose of hail suppression this study suggests that artificial seeding of particles into the CC area may inhibit the formation of hailstones, especially large ones, because of the competition between the natural and artificial embryos. Appendix A: Spectral Bin Microphysical Model [24] The basic equations in standard Cartesian coordinates (x, y, z) are where dq x dt dn i dt du dt þ 0 pq ¼ D u dv dt þ 0 pq ¼ D v dw dt þ 0 pq ¼ D w þ f w dp 0 dt þ C2 C p rq 2 v ða1þ ða2þ v u j ¼ f p þ D p 0 ða4þ dq dt ¼ Q fm þ Q ce þ Q ds þ D q ða5þ ¼ D qx þ W qx þ I qx 0 V x q x Þ ða6þ 3 ¼ D Ni þ W Ni þ I Ni 0 V x N i Þ ða7þ 3 f p ¼ R d p j þ C2 dq v C j C p q 2 dt v " f w ¼ g q0 q þ 0:608q0 v q c q i q r q s X # q h ðþ I I¼1 ða8þ ða9þ where D u, D v, D w, D q, D q, D Ni and D p are the turbulent fluxes of u, v, w, q, q x, N i and p, respectively. q, q v, and p are potential temperature, virtual potential temperature, and nondimensional pressure, respectively. Q fm, Q ce, and Q ds are the latent heating/cooling terms due to melting/freezing, condensation/evaporation, and deposition/sublimation produced by microphysical processes, respectively. V x is the terminal velocity of a hydrometeor q x, where q x is one of mixing ratio of water vapor q v, cloud water q c, rain water q r, cloud ice q i, snow q s, and hail/graupel bin water content q h (I) (I = 1, 21). W and I are denoted as warm and cold cloud microphysical processes. N i in equation (7) is the ice crystal number concentration. f w is the buoyancy term. f p is the source or the sink term. [25] The model domain is on a standard spatially staggered mesh system. A conventional time-splitting integration technique, the same as that proposed by Klemp and Wilhemson [1978], is also used in this model. The spatial difference terms are of second-order accuracy except for the advection term that has fourth-order accuracy. All other derivatives are evaluated with second-order-centered differences. The radiation boundary conditions of Klemp and Wilhemson [1978] are used for the lateral boundaries while the top and bottom boundaries are assumed as a rigid wall. A Rayleigh friction zone is also used to absorb vertically propagating gravity waves near the top of the domain. The model includes a conventional first-order closure for subgrid turbulence and a diagnostic surface boundary layer based on Monin Obukhov similarity theory. [26] Equations and parameters of microphysics used in the model are given by Lin et al. [1983]. However, in the original microphysics of Lin et al. [1983], the precipitating ice phase is treated in a bulk form. Here, the explicit hail/ graupel bin microphysics proposed by Farley and Orville [1986] and Farley [1987a, 1987b] are also used in order to be compared with each other. The bulk hydrometeor classes in the model are (1) cloud water, (2) cloud ice, (3) snow, (4) rain water, and (5) hail and graupel. The model uses exponential size distributions for rainwater and snow, monodispersed size distributions for cloud water and cloud ice, and a discrete size distribution for graupel and hail. There are 21 size bins of graupel and hail, which are distributed exponentially according to the scheme proposed by Berry [1967], ranging from 100 mm to nearly 7 cm in diameter. [27] The growth in mass of the graupel and hail with diameter D h was calculated on the basis of (1) accretion of bulk cloud water, (2) accretion of bulk cloud ice, (3) accretion of bulk rain water, (4) accretion of bulk snow aggregates, (5) evaporation and condensation from a wet hailstone and graupel, (6) vapor deposition/sublimation onto/from a hailstone and graupel, and (7) wet growth. The densities of graupel and hail are treated to be 0.45 and 0.90 g cm 3, respectively. Whether a fraction of liquid water is allowed to exist on the surface of hail or graupel depends on wet growth or dry growth. Liquid water includes cloud water and rain water in the simulated cloud, so liquid water gets transferred to cloud water and rain immediately following melting. The importance of the improved microphysics is that the hail and graupel size distribution can be allowed to evolve naturally. The actual terminal velocities of each bin are used instead of the mass weighted mean terminal velocities [Wisner et al., 1972], V h ðd h Þ ¼ 4gr 0:5 h D 0:5 h 3C d r a ða10þ where C d is 0.6. r a, r h are the densities of air and graupel/ hail, respectively. This may therefore more realistically reflect the hail growth processes in the hailstorm model. [28] The number concentration of ice crystals is predicted with equation (7) except for its mixing ratio considering its important role in cloud microphysical processes. The initial ice particle number concentration is calculated on the basis of the work of Fletcher [1969]. The initial ice crystal size is set to 16.3 mm and the diffusion growth was also considered. Cloud ice crystals melt 12 of 13

13 instantaneously at temperature warmer than K. A form of heat budget given by Mason [1956] was used to determine the melted mass of snow and hail. Thus the melting of snow and hail depends on the heat budget of (1) conduction of heat from the ambient air, (2) latent heat of condensation supplied by condensation/evaporation of water vapor on snow/hail surface, and (3) conduction of heat from accreted mass. The processes concerning with the depletion of liquid water include the super-cooled liquid water accretion by hail, snow and cloud ice, homogeneous and probabilistic freezing and evaporation. All these processes are realistically treated in the model. The warm microphysical processes are based on Kesslertype parameterizations [Kessler, 1969]. [29] Acknowledgments. The authors would like to thank the reviewers for their critical and constructive comments. The authors thank the Institute of Atmospheric Physics of the Chinese Academy of Sciences for their hail-bin cloud model, especially Xueliang Guo. Thanks are also due to Huiming Ji, Wei Zhou, and Yanzhong Liu for their contributions to this paper. This work is supported under the Ministry of Science and Technology of the People s Republic of China grant 2002dib References Barge, B. L., and F. Bergwall (1976), Fine scale structure of convective storms associated with hail production, Edmonton Rep. 76-2, Atmos. Sci. Div. Alberta Res. Counc., Canada. Berry, E. X. (1967), Cloud droplet growth by collection, J. Atmos. Sci., 24, Browning, K. A. (1964), Airflow and precipitation trajectories within severe local storms which travel to the right of the winds, J. Atmos. Sci., 21, Browning, K. A., and G. B. Foote (1976), Airflow and hail growth in supercell storms and some implications for hail suppression, Q. J. R. Meteorol. Soc., 102, Chisholm, A. J., and J. H. 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