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Case 1 was a squall line in south China in March 2014. From the evening of March 29 to the afternoon of March 31, 2014, south China was hit by a severe convective weather process, which affected Guangxi, Guangdong, Yunnan, and other provinces. From 2000 UTC March 30 to 0400 UTC March 31, a long squall line passed through Guangdong Province from the northwest to the southeast. Some cities suffered from severe weather, including hail and gale. Figures 1a and b show the largescale circulation situation at 1200 UTC March 30, 2014. Under the influence of a strong high pressure ridge in a highlatitude area at a 500hPa level, cold air flows into south China, which provides intermediate cold air conditions for the development of strong convection. At the same time, the western part of Guangdong Province had a small trough, which was conducive to the upward movement of air. Under the influence of the warm shear line, a large amount of warm and humid air passed through Guangdong Province, providing water vapor conditions and aggravating the convective instability in this region. In addition, the entire south China area is located in the coupling zone between the upper jet and the lower jet (figure omitted), which is helpful for convective weather.
Figure 1. (a) a 500hPa geopotential height field (gpm; the same below) and wind field (m s^{−1}, the same below) (b) a 850hPa geopotential height field and wind field at 1200 UTC March 30, 2014 and (c) a 500hPa geopotential height field and wind field (d) a 850hPa geopotential height field and wind field at 0000 UTC July 30, 2014.
Case 2 was a squall line process that occurred in the Jianghuai region of China in July 2014. A squall line from north to south swept through the central and northern provinces of Anhui and Jiangsu from 0600 to 1100 UTC July 30, 2014. The squall line shifted from north to south and moved eastward at 1600 UTC 30, dissipating in Jiangsu Province at approximately 1900 UTC 30. Affected by this squall line, shortterm heavy precipitation occurred in Yancheng and other cities, with hourly rainfall reaching 20–50 mm, causing serious waterlogging disasters. Chuzhou and its affiliated regions have seen thunderstorm gales above level 7, damaged houses, and casualties. Figures 1c and d show the largescale circulation situation at 0000 UTC July 30, 2014. Guided by the 200hPa upperair jet (figure omitted), the 500hPa trough moved eastward over the Jiangsu and Anhui regions and was blocked by the subtropical high so that the trough line eventually stopped in the Jiangsu and Anhui regions, thus continuously providing cold air in the middle level for the development of strong convection. At a 700hPa level (figure omitted) and under the influence of the jet stream, a large amount of warm and humid air was transported to the Jiangsu and Anhui regions, and finally accumulated in the south side of the 850hPa warm shear line. Therefore, with the cooperation of high and lowlevel circulation, the possibility of severe convective weather in the Jiangsu and Anhui area increased significantly.

We based our experiments on the WRF V3.6 model and adopted the doublenested scheme. The resolution of the outer area was 9 km and that of the inner area (analysis area) was 3 km. The number of the vertical layers was 42. The physical parameterization schemes and grid setting of the two individual cases are shown in Table 1. We used NCEP (National Centers for Environmental Prediction) FNL reanalysis data to drive the model and analyze the weather situation. To verify the experimental results, we used precipitation data (0.1° × 0.1°) released by the Meteorological Data Center of China Meteorological Administration as the observed field.
Scheme Case1[Center Grid (23.5°N,113.5°E)] Case 2[Center Grid (35°N, 115°E)] Inner Region(310 × 238) Outer Region(289 × 214) Inner Region(351 × 351) Outer Region(301 × 301) Microphysical process scheme SingleMoment 3class SingleMoment 3class Morrison 2moment Morrison 2moment Longwave radiation scheme RRTM RRTM RRTM RRTM Shortwave radiation scheme Dudhia Dudhia Dudhia Dudhia Land Surface Process scheme 5layer thermal diffusion 5layer thermal diffusion Noah Land Surfance Model Noah Land Surfance Model Boundary layer scheme Yonsei University Yonsei University Yonsei University Yonsei University Cumulus parameterization scheme – GrellFreitas – BettsMillerJanjic Near Surface Scheme MoninObukhov MoninObukhov MoninObukhov MoninObukhov Table 1. Physical parameterization setting of two cases
For each case, we used the LBGM (details in Section 3) under GWs and EWs to generate the ICPs, and the number of members was ten. To ensure that the experimental results were affected only by the ICPs, the physical parameterization scheme configurations of each member in the two experiments were consistent with the control experiment without any perturbations, and we did not consider perturbations on the lateral boundary conditions (LBCs) and the model. No observational data was assimilated. We divided all of the ensemble experiments into a breeding stage and a prediction stage. See Table 2 for details.
Case 1 Case 2 perturbation variables The horizontal zonal wind speed U, the horizontal meridional wind speed V, the perturbation potential temperature T, the perturbation geopotential height (PH), and the water vapor mixing ratio Q Start and end time of the breeding phase 2014/03/29/063/30/06(24 h) 2014/7/29/007/30/00(24 h) Perturbation adjustment period 6 h 6 h Start and end time of the forecast phase 2014/3/30/063/31/06(24 h) 2014/7/30/007/31/00(24 h) LBC update cycle 3 h 3 h Table 2. Details of the experiments of two cases
2.1. Case studies introduction
2.2. Experimental design

Considering the local characteristics of strong convective weather, Chen et al. (2018) proposed the LBGM method. In LBGM, the perturbation adjustment formula is as follows:
$$\begin{array}{l} \begin{array}{*{20}{l}} {\begin{array}{*{20}{l}} {}&{}&{} \end{array}}&{} \end{array}{x_{a,t}}(i,j,k) = {x_{f,t}}(i,j,k) \times \dfrac{{{e_0}(k)}}{{{e_t}(i,j,k)}} \\ {e_t}(i,j,k) =\dfrac{1}{{(2r + 1)}}\sqrt {\displaystyle\sum\limits_{i  r}^{{\rm{i + r}}} {\displaystyle\sum\limits_{j  r}^{j + r} {{{[{X_{pe{r_t}}}(i,j,k)  {X_{ctl}}_{_t}(i,j,k)]}^2}} } } \\ \end{array},$$ (1) where i and j are the indices of latitude and longitude, respectively;
${x_{a,t}}(i,j,k)$ and${x_{f,t}}(i,j,k)$ are the perturbation before and after the adjustment;${e_0}(k)$ is the rootmeansquare error (RMSE) of layer k at the initial time point; and${e_t}(i,j,k)$ is the RMSE at grid point (i, j) of layer k at the corresponding time point. Their ratio is the perturbation adjustment coefficient.${X_{pe{r_t}}}(i,j,k)$ and${X_{ctl}}_{_t}(i,j,k)$ are the results of the perturbation and control prediction results at time t, respectively. The formula of${e_t}(i,j,k)$ indicates that the introduction of the local radius parameter, r, makes the adjustment coefficients between the grid points different during the disturbance adjustment process, thus reflecting the horizontal difference of the physical quantity.As shown in Fig. 2, for the EWs, the RMSE of the red grid considered only the influence of itself and the surrounding 24 black grids, and the contribution weight of each grid point was equal, which was
$\dfrac{1}{{{{(2r + 1)}^2}}}$ . For the GWs, however, the contribution of the black grid pointed to the red grid point decays as a Gaussian function with an increase in their distance, which reflected the difference between the grid points within the local radius. GW realization followed three main steps:Figure 2. Schematic diagram of LBGM (r=2) and the larger the grid point, the greater the contribution weight.
Step 1: Calculate the contribution value of each grid point in the local area according to the twodimensional Gaussian function:
$$G(x,y){\rm{ = }}\frac{1}{{2\pi {r^2}}}{e^{\frac{{  [{{(x  {x_i})}^2} + {{(y  {y_i})}^2}]}}{{2{r^2}}}}}. \hspace{102pt}$$ (2) Step 2: Use the contribution value in the local area to obtain the GW of each grid point:
$$W(x,y) = \frac{{G(x,y)}}{{\displaystyle\sum\limits_{i  r}^{i + r} {\displaystyle\sum\limits_{j  r}^{j + r} {G(x,y)} } }}. \hspace{120pt}$$ (3) Step 3: Calculate the forecast RMSE of the analysis grid:
$${e_t}(i,j,k)= \sqrt {\displaystyle\sum\limits_{i  r}^{i + r} {\displaystyle\sum\limits_{j  r}^{j + r} {W(x,y) \times {{[{X_{pe{r_t}}}(i,j,k)  {X_{ctl}}_{_t}(i,j,k)]}^2}} } } .$$ (4) According to the research of Chen et al. (2018) and Ma et al. (2019), we determined the local radius parameter, r, of this experiment to be 13 to ensure that the results were affected only by the weighting method in the LBGM for comparison.