Simulation study of a Squall line hailstorm using High-Resolution GRAPES-Meso with a modified Double-Moment Microphysics scheme

This study uses the high-resolution GRAPES_Meso (the mesoscale version of the Global/Regional Assimilation and Prediction System) to simulate a severe squall line hailstorm in Shandong province. The accumulated precipitation, radar 10 reflectivity, and cloud hydrometeor properties simulated using a modified double-moment microphysics scheme are compared with observation. Results show that simulations captured the basic character of this squall line hailstorm. The simulated accumulation precipitation and radar reflectivity are comparable with the observation. The cross-section of the dynamic, microphysical, and radar reflectivity structures of the simulated hailstorm was analyzed. The simulated hailstorm has shown a reasonable result in both macrostructure and micro hail production rates. The development of the simulated 15 hailstorm is consistent with the conceptual model of hailstorm evolution. Results imply the ability of high-resolution GRAPES_Meso on forecasting hailstorm.

. Distinguished by the surface temperature of a hailstone, the growth of hail can be separated 30 into dry and wet growth (Lesins and List 1986;Garcia-Garcia and List 1992). In wet growth, the hail nucleus is in a region where the air temperature is closed to the hail surface. Therefore, the supercooled water droplet does not immediately freeze around the nucleus. In dry growth, the air temperature is well below freezing, and the water droplet immediately freezes as it collides with the hail nucleus. Graupel can convert to hail inappropriate situations (Ilotoviz et al. 2016;Vié et al. 2016). Note that as mentioned by Hu and He (1988), the conversion rate of graupel to hail is the most important source for hail formation, 35 compared to other processes. Meanwhile, researchers pointed out that strong vertical wind shear is favorable for hail formation (Das, 1962;Dennis and Matthew, 2017).
However, as the absence of observation and the sophisticated microphysical processes during hail formation and growth, the accurate forecasting of the position and time of hailstorm forecasting is extremely challenging (Knight and Knight 2015;Luo et al. 2017). Therefore, hail is not a common forecaster in most operational numerical weather prediction (NWP) models (e.g. 40 Sokol et al. 2014). Despite the above difficulties, the efforts of improving hail simulation never stopped. Moore and Pino (1990) use a diagnostic/prognostic sounding analysis package to add operational forecasters and found that this method helps estimate the maximum hail diameter. Jewell and Brimelow (2009) use a one-dimensional model to predict hail size and coupled the one-dimensional model to a regional model (Brimelow and Reuter, 2009). Adams-Selln and Zeigler (2016) use the same approach to successfully forecast a reasonable hail size. Chatterjee et al. (2008) modified a cloud microphysics 45 scheme in the regional model for simulating hailstorms. Yang et al. (2011) study the aerosol effects on hailstorms and found that increasing aerosol might decrease surface accumulated precipitation. Luo et al. (2014) use multimoment microphysics schemes to predict hailstorm explicitly. Labriola et al. (2019) adopt an explicit ensemble method to predict hail and analysis hail growth with different microphysics schemes.
The Global/Regional Assimilation and Prediction System (GRAPES) is an operational numerical weather prediction system 50 that has been developed in the China Meteorological Administration since 2000(Chen et al., 2012Ma et al., 2018Ma et al., , 2020Chen et al., 2020). The mesoscale version of GRAPES (GRAPES_Meso) is an important component of the GRAPES.
GRAPES_Meso was first put into operational application in the National Meteorological Center in 2006 and has been continuously developed since then. The operational products of GRAPES_Meso are provided to meteorological agencies at all levels in China ever since. Not only being used as an operational model since 2006 (Xu et al. 2017), GRAPES_Meso is 55 also a suitable tool for scientific investigation (e.g., Deng et al; Huang et al. 2012;Wang et al. 2014;Wan et al. 2015;Wang et al. 2017). The high-resolution version of GRAPES_Meso (horizontal resolution of 3km) has been developed in 2015.
The purpose of this study is to test the ability to forecast a hailstorm using high-resolution GRAPES_Meso with a modified double-moment and to evaluate the performance based on comparisons of simulation results and observational data. The modified double-moment microphysical scheme is described in Section 2. A brief overview of the squall line hailstorm and 60 experimental design are shown in Section 3. Results are shown in Section 4. Summary and discussion are provided in Section 5. https://doi.org/10.5194/gmd-2020-439 Preprint. Discussion started: 8 February 2021 c Author(s) 2021. CC BY 4.0 License.

Brief description of the double-moment microphysics scheme
The double-moment mixed-phase scheme developed from the convective and stratus cloud (Hu and He, 1988;Hu and Yan, 1986) using a box model. It was embedded in regional and global scale models for weather forecasting and scientific 65 research (e.g., Zhang and Liu 2006;Shi et al. 2015;Ma et al. 2018Ma et al. , 2020. Li et al. (2018Li et al. ( , 2019aLi et al. ( , 2019b tested the performance of this double-moment microphysics scheme in multi-scale models and improved its mixed-phase microphysical processes. The basic version of the double-moment microphysics scheme predicts the mass mixing ratios of cloud ( ), rain ( ), ice ( ), snow ( ), graupel ( ) and the number concentrations of rain ( ), ice ( ), snow ( ) and graupel ( ). Detailed descriptions of this double-moment microphysics scheme can be seen in Hu and Yan (1986), 70 He (1988), Chen et al. (2007).
A modified version of this double-moment microphysics scheme which contains the prediction of hail mixing ratio ( ℎ ), hail number concentration ( ℎ ), and associated microphysical processes are developed to investigate hailstorm in this study.
Related equations are shown below: (1) 75 Where ℎ (cm) is the slope parameter for hail, * (cm) is the minimum diameter of hail, which is 0.5, q is a temporary variable calculated in Eq. (2): Where ℎ is the fall speed parameter of group hail particles, which is 0.471 g cm -3 .
Where V ℎ (cm s -1 ) is the mean fall speed of hail, 0 (g cm -3 ) is air density at the freezing point, (g cm -3 ) is the air density, ℎ is fall speed parameter of single hail particle, which is 810 cm 0.2 s -1 , ℎ is a temporary variable ( ℎ = ℎ * ). Collision, autoconversion, melting and sublimation processes of hail are considered in this modified double-moment scheme.
Autoconversion, melting, and sublimation processes of hail are list below: 100 Where ℎ (g kg -1 s -1 ) and ℎ (kg -1 s -1 ) are mass and number autoconversion rates of graupel to hail, A is the conversion parameter, which is 0.01 s -1 , * (cm) is the diameter of graupel, which is 0.97.
[( ℎ * ) 1.9 + 1.8274(0.9 ℎ * + 1)] + ( ℎ + ℎ ) 105 Where ℎ (g kg -1 s -1 ) and ℎ (kg -1 s -1 ) are mass and number melting rates of hail, , and are the latent heat of freezing and evaporation, is the specific heat capacity of water, , , and are thermal conductivity, diffusion coefficient, and dynamic viscosity of water vapor, respectively. (K) is temperature, (g kg -1 ) is the mass mixing ratio of 110 water vapor, while 0 and 0 are the temperature and saturated specific humidity of the freezing point.
Where ℎ (g kg -1 s -1 ) is the sublimation rate of hail, is the saturated specific humidity over ice, R is the universal gas province from 0000 UTC 13 June 2018 to 0000 UTC 14 June 2018. This process reported a wicked wind speed around 20 m s-1 , and a maximum wind speed of 34.8 m s -1 in Qingdao city, along with hourly rainfall rates even over 50 mm h -1 . The blue triangles indicate the locations where hailstones were observed, the typical hailstone diameter in this process is around 5-20 mm in this hailstorm, and even higher than 20 mm were recorded. The associated hailstorm caused significant casualties and economic losses. Nearly 860,000 people were affected, 2 deaths and 1 missing, more than 4100 houses were damaged. The 125 damaged area of crops is 105, 800 m 2 , and the direct economic loss is almost 1 billion yuan.
The synoptic-scale background associated with this squall line hailstorm is shown in Fig. 2. At 0600 UTC on 13 June 2018, the atmospheric circulation at 500 hPa was characterized by a cold vortex that came from the northeast over the north China plain, as shown in Fig. 2b. Shandong province was located at the bottom of the cold vortex and in the region ahead of the East Asian trough (EAT), where is favorable for upward vertical motion, as shown in Fig. 2a A Skew-T plot with hodograph was used to analyze the stratification of the atmosphere at Qingdao Station at 0000 UTC on 13 June 2018 (9 h before the hailstorm passed by), as shown in Fig. 3. The sounding of radiosonde data is from the 135 University of Wyoming. Relatively cold air between 250 and 650 hPa contributes to convective available potential energy (CAPE) of 1022.59 J kg -1 , with convective inhibition (CIN) of 541.02 J kg -1 in this sounding. The CAPE is suitable for the formation of deep convection. CIN was quite big compared to other hailstorms (Luo et al., 2014;Yin et al., 2019), this might because it needed 9 hours before the hailstorm passed. From surface to 850 hPa, horizontal wind changes from southeasterly to westerly. There is a wind shear above the free convection level (LFC, around 3000 m), which provided a suitable 140 condition for hail growth (Dennis and Matthew, 2017). The wind speed increased with height and can be 20 m s -1 at around 8000 m. Meanwhile, the dew point profile shows a clear mixing of the wet and dry layers in the middle troposphere, which is favorable for the growth of hail (Luo et al., 2014;Costa et al., 2001;Webb and Muirhead, 2002).

Experimental design
This study uses GRAPES_Meso (version 4.4) to simulate the squall line hailstorm. The modified double-moment 145 microphysics scheme is used to simulate the cloud microphysical processes. The Medium-Range Forecast (MRF) scheme (Hong and Pan, 1996) is used to parameterize the boundary-layer processes. The rapid radiative transfer model (RRTM) https://doi.org/10.5194/gmd-2020-439 Preprint. Discussion started: 8 February 2021 c Author(s) 2021. CC BY 4.0 License.
scheme (Mlawer et al. 1997) and Dudhia scheme (Dudhia 1989) are adopted to parameterize the longwave and shortwave radiative transfer process, respectively. The cumulus process is closed in this study. Fig. 1 also implies the simulation domain, which covers the Shandong province. The initial and boundary conditions are supplied by the 0.5º National Centers 150 for Environmental Prediction (NCEP) 6-h reanalysis data. The horizontal resolution is 0.03º, and the vertical resolution increases toward the model top at 35000 m. The simulation period starts at 1800 UTC on June 12 2018 and runs for 24 hours to simulate the squall line hailstorm. This period covers the lifetime of this squall line hailstorm. As clearly in Fig. 4, rain belts in both observation and simulation show a southeast-northwest orientation with the maximum at around 40-100 mm. The narrow rain belt pattern also indicates that this simulation captured this squall line successfully. However, the maximum precipitation area located east southward than the observation, as shown in Fig. 4b. 160

Evolution of the squall line hailstorm
Composite reflectivity of four moments with 1h interval from 0080 to 1100 UTC 13 June 2018 is shown in Fig. 5a, c, e, g, which implies the evolution of the squall line hailstorm. During the four hours, the squall line hailstorm formatted and moved from southern to northern of Shandong province, with a southeast-northwest orientation. The squall line has a high composite reflectivity. Most of its eastern part is at around 50 -60 dBZ, the maximum composite reflectivity of this squall 165 line can even up to 70 dBZ. Simulated composite reflectivity also shows a southeast-northwest orientation and northern movement, as shown in Fig. 5b, d, f, h. The high composite reflectivity region is at around 50 -60 dBZ, locates at the eastern part, and the simulated maximum composite reflectivity is up to 70 dBZ as well. Although the specific location of the squall line is northern than that of the observation, results can still imply that this squall line is well captured by simulation with GRAPES_Meso. The detail of the evolution of this squall line hailstorm is analyzed below. 170 As discussed in Yin et al. (2019) and Luo et al. (2014), hailstorm evolution can be separated into the stages of developing, mature, and dissipating. Fig. 6, 7 show the cross-sections of microphysical and dynamical properties of the simulated squall line hailstorm along the dashed lines in Fig. 5. Fig. 6 shows the mixing ratios of hail and rain shaded contours of radar reflectivity. Fig. 7 shows the wind vector over the shaded contours of vertical velocity.
The radar reflectivity evolves quickly from 0800 to 0900 UTC 13 June 2018 during the developing stages of the squall line 175 hailstorm. As shown in Fig. 6a, the cross-section of radar reflectivity shows a convective storm with a maximum value of over 45 dBZ at the right convective core right below 600 hPa with the temperature around 0 ℃. At this time, the mixing ratio of hail and rain mixing ratio is up to 1 g kg -1 at the convective storm, as shown in Fig. 6a. This convective storm has a https://doi.org/10.5194/gmd-2020-439 Preprint. Discussion started: 8 February 2021 c Author(s) 2021. CC BY 4.0 License. strong updraft above the convective core, with a maximum vertical velocity up to 8 m s -1 at the cloud top. The convergence and divergence of wind vector can be seen at the convective core and the top of the cloud, respectively. The convective 180 storm has a large anvil at around 200-400 hPa, and the mixing ratio of total cloud hydrometeors in the convective storm is around 2 g kg -1 at the convective core, as shown in Fig. 7a.
As the squall line hailstorm developed, the convective storm enhanced with a maximum radar reflectivity of 60 dBZ, the maximum mixing ratio of hail increased to 4 g kg -1 at the convective core, the mixing ratio of rain also increased, as shown in Fig. 6b. The vertical velocity increased to over 12 m s -1 at the convective core. The region of high vertical velocity (> 4 m 185 s -1 ) thickened, from near ground to the top of the cloud. Downdraft also enhanced at the convective core from 600-800 hPa.
The convergence of the wind vector is clear at this time, and the mixing ratio of total cloud hydrometeors is more than 4 g kg -1 in the convective core, as shown in Fig. 7b.
The mature stage of the squall line hailstorm can be seen at 1000 UTC 13 June 2018. The convective storm continued enhanced with a maximum radar reflectivity near 70 dBZ. The mixing ratio of hail is over 8 g kg -1 in the convective core. 190 The high radar reflectivity and large mixing ratio of hail near the ground imply large hailstones are falling to the ground at this stage of the hailstorm, as also mentioned by Luo et al. (2014). The mixing ratio of rain near the ground increased implies that there was heavy precipitation at this time as well, as shown in Fig. 6c. The dynamic field also shows a strong updraft with a maximum value of over 12 m s -1 in the convective core. The convergence of wind vector is still clear, and the total cloud hydrometeors mixing ratio is more than 8 g kg -1 in the convective core, as shown in Fig. 7c. 195 The squall line hailstorm dissipated rapidly with a decreasing maximum radar reflectivity of only 40 dBZ in the convective core. The mixing ratio of rain at the bottom of the cloud is small at this time, as shown in Fig. 6d. The mixing ratio of total cloud hydrometeors is down to 2 g kg -1 . No noticeable updraft and downdraft at this stage, convergence, and divergence are also decreasing, as can be seen in Fig. 7d.
To be more specific, the profiles of cloud hydrometeors are shown in Fig. 8. Those profiles are plotted at the red cross along 200 the dashed line in the right column. As already mentioned above, the simulated squall line hailstorm evolved from 0800 -1100 UTC 13 June 2018. The squall line hailstorm started to produce hail at around 0800 UTC 13 June 2018. The maximum mixing ratio of hail is around 1 g kg -1 at around 600 hPa at this time. Rain fell to the ground, with a maximum mixing ratio over 2 g kg -1 near the surface, as shown in Fig. 8b. The mixing ratio of hail increases as the storm is enhanced. At 0900 UTC 13 June 2018, the maximum mixing ratio of hail is 2 g kg -1 , other mixing ratios of cloud hydrometeors also increased, as well 205 as the mixing ratio of rain near the surface, as shown in Fig. 8d. The mixing ratio of hail and rain reach their maximum at 1000 UTC 13 June 2018, with a maximum of 4 and 7 g kg -1 respectively. A large amount of hail and rain hit the ground at this time, as shown in Fig. 8f. The squall line hailstorm passes and dissipated at 1100 UTC 13 June 2018. The mixing ratio of rain near the surface weakened as well, as shown in Fig. 8h.
The basic characteristics of the development of a hailstorm are consistent with previous studies (Luo et al. 2014;Ying et al. 210 2019). Those results point out that the squall line hailstorm is well captured using the modified double-moment microphysical scheme in GRAPES_Meso.

Hail microphysical processes and cloud properties in the hailstorm
Two hailstorms are chosen to investigate the validity of the modified double-moment microphysics scheme in detail, despite the location and time error between observation and simulation. Fig. 9a shows the cross-section of operational radar 215 reflectivity of a deep convective cloud at 1000 UTC 13 June 2018 at Qingdao city. The maximum reflectivity can be over 70 dBZ at around 500 hPa. There is a thick high-value area of reflectivity (>40 dBZ) from the surface to around 200 hPa in this deep convective cloud, such high reflectivity implies heavy precipitation at this time. Note that the blank area below 930 hPa is because of the lack of data. The large area of radar reflectivity around 30 dBZ at 200-600 hPa also implies the large cloud anvil of this deep convective cloud. Fig. 9b shows the cross-section of simulated radar reflectivity of a deep convective 220 cloud at 0940 UTC 13 June 2018 at around (38.25 ºS, 120.8 ºN). The maximum reflectivity is near 70 dBZ at around 600 hPa, which is slightly lower than that of the observation. The high-value area of reflectivity (>40 dBZ) is from the surface to around 200 hPa as well. The maximum mixing ratio of hail is over 4 g kg -1 at the convective core. It can be seen at this time, simulated hail fell to the ground, and this deep convective cloud produces a large amount of precipitation. The simulated convective cloud also contains a large cloud anvil, as shown in Fig. 9b. Results show that the basic characteristic of the deep 225 convective cloud is well captured using the modified double-moment microphysical scheme in GRAPES_Meso, compare to the observation.
To be more specific, the hail production rate of the simulated deep convective cloud is analyzed in Fig. 10. The hail production rate of collision processes, autoconversion, melting, and sublimation are shown in Fig. 10a, b, c, d, respectively.
It can be seen that autoconversion and melting processes are the dominant source and sink terms in hail production. The 230 maximum hail production rate can be over 1e-5 g kg -1 s -1 for these two terms, which is consistent with a previous study (Hu and He et al., 1989). The collision and autoconversion processes are much active below 0 ℃, as shown in Fig. 10a, b. It can be seen that graupel is the most important source of hail production in this modified double-moment scheme. The melting process is also very active, the falling hailstones melted to rain above 0 ℃, as shown in Fig. 10c. The results are consistent with Fig. 9e, f, which shows a hailstorm in its mature stage. Moreover, it can be seen that the sublimation process evaporated 235 hail to water vapor, and moistures the environment, as shown in Fig. 10d.

Summary and Discussion
A severe squall line hailstorm is simulated using a modified double-moment microphysics scheme in high-resolution GRAPES_Meso that occurred on 13 June 2018. This squall line hailstorm caused strong wind, heavy precipitation, and hail reported on most of the Shandong province. Simulation results of accumulated precipitation, radar reflectivity, and cloud 240 hydrometeor properties were compared to observation. The detailed mechanism of hail production in the modified doublemoment microphysics scheme was analyzed. The major points of this study are noted as follows: The squall line hailstorm occurred in a synoptic environment with a strong midlevel cold air advection from the north and was superimposed on low-level warm advection from the south, leading to destabilization of the atmosphere in Shandong https://doi.org/10.5194/gmd-2020-439 Preprint. Discussion started: 8 February 2021 c Author(s) 2021. CC BY 4.0 License.
province. The CAPE is quite high at 1022 J kg -1 . There is a mixing of the wet and dry layers in the middle troposphere, 245 which is favorable for hail formation.
Compared to the observed accumulated precipitation and radar reflectivity, simulation results of GRAPES_Meso with the modified double-moment microphysical scheme generally reproduced the development of this squall line hailstorm, although there might be time and location errors.
The cross-section of the dynamic, microphysical, and radar reflectivity structures of the simulated hailstorm was analyzed. 250 The development of this hailstorm is consistent with previous studies of hailstorms (Luo et al., 2014;Ying et al., 2019). The profiles of cloud hydrometeors in the hailstorm are analyzed, the distribution is also reasonable.
Detailed analysis of hail production rate shows that the formation and growth of hail are reasonable and consistent with the previous study (Hu and He, 1989), which implies the modified double-moment microphysical can successfully predict hailstorm in GRAPES_Meso. 255 Code and data availability. The model simulation data used in this study is available at https://pan.baidu.com/s/1fxfk4f8OgMy9MQKRVZ6wrA with access code fhoh; the model code is only available by request via liz@cma.gov.cn due to the confidential requirement.          Fig. 9. but for the hail production rate (1e-5 g kg -1 s -1 ), cloud hydrometeors mixing ratio, and specific humidity. Shaded colors represent hail production rate from collision (a, cch, crh, cih, csh, and cgh), autoconvesion (b, agh), melting (c, rhqh), and 410 sublimation (d, svh) respectively. Black contours (g kg -1 ) represent the mixing ratio of ice and snow (a), graupel (b), rain (c), and specific humidity (d). The purple lines represent the 0 and -20 isotherms.          Fig. 9. but for the hail production rate (1e-5 g kg -1 s -1 ), cloud hydrometeors mixing ratio, and specific humidity. Shaded colors represent hail production rate from collision (a, cch, crh, cih, csh, and cgh), autoconvesion (b, agh), melting (c,