Application of the Local Breeding Growth Mode Method Based on the Gaussian Weight in Convection-permitting Ensemble Forecasts

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  • Corresponding author: Chaohui CHEN, chenchaohui2001@163.com
  • Funds:

    Supported by the Ministry of Science and Technology of China (2017YFC1501803) and National Natural Science Foundation of China (41975128 and 41875060)

  • doi: 10.1007/s13351-021-0173-4
  • Note: This paper has been peer-reviewed and is just accepted by J. Meteor. Res. Professional editing and proof reading are underway. Please use with caution.

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  • The local breeding growth mode (LBGM) method does not consider the difference between the grid points within the local radius. To address this problem, Gaussian weights (GWs) were proposed, which cause the influence of each grid within a local radius to exert an increase in distance with Gaussian decay on the central grid. In this paper, the effects of two different LBGM methods under GWs and equal weights (EWs) in convection-permitting ensemble forecasting are compared and analyzed using two squall line examples. The results showed that the use of the GWs intensified the local characteristics of the initial condition perturbation (ICP) and made the distribution of the ICP more flow-dependent. The result of the kinetic energy spectrum of the ICP indicated that there could be more large-scale information in the ICP using the GWs. In addition, meso-scale information also improved slightly. For nonprecipitation variable forecasting, GWs improved the relationships between the root-mean-square error and the spread and contributed to the forecasting accuracy of wind, temperature, geopotential height, and humidity. For the precipitation forecast, GWs simulated the precipitation structure successfully and provided better probability forecasting during the evolution of two squall line processes than the EWs.
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  • Fig. 1.  (a) a 500-hPa geopotential height field (gpm; the same below) and wind field (m s−1, the same below) (b) a 850-hPa geopotential height field and wind field at 1200 UTC March 30, 2014 and (c) a 500-hPa geopotential height field and wind field (d) a 850-hPa geopotential height field and wind field at 0000 UTC July 30, 2014.

    Fig. 2.  Schematic diagram of LBGM (r=2) and the larger the grid point, the greater the contribution weight.

    Fig. 3.  The ICP distribution of zonal wind speed U (m s−1) at the 200-hPa level under (a) the EWs and (b) the GWs in the outer of model for case 1 and its 200hPa wind field distribution at 0600 March 30, 2014.

    Fig. 4.  As in Fig. 3 but for case 2 at 0000 July 30, 2014.

    Fig. 5.  The kinetic energy spectrum of the ICP of member 5 at (a) 200-hPa, (b) 500-hPa, (c) 700-hPa, (d) 850-hPa levels for case 1. The red line and the blue line represent the results under the GWs and the EWs.

    Fig. 6.  As in Fig. 5 but for case 2.

    Fig. 7.  The low-level (z=12) in case 1. The relationship of RMSE of the EM and the ensemble spread of perturbation variables containing (a) U and (b) V, (c) T, (d) PH and (e) Q with the evolution of the forecast time at the low level (z=12), where the blue and red lines represent EW and GW respectively and the solid and dotted lines represent the RMSE and spread, respectively.

    Fig. 8.  As in Fig. 7 but for the results at the high level (z = 35).

    Fig. 9.  As in Fig. 7 but for case 2.

    Fig. 10.  As in Fig. 8 but for case 2.

    Fig. 11.  The hourly precipitation evolution and corresponding observed precipitation distribution of the EM forecast from 2300 March 30 to 0200 March 31, 2014, in case 1: (a)–(d) is for the observed distribution, (e)–(h) is for the EM result under EWs, and (i)–(l) is the that under GWs.

    Fig. 12.  The forecast result from 0700 to 1000 on July 30, 2014 in case 2.

    Fig. 13.  The NEP (%) distribution of hourly precipitation exceeding 15 mm h−1 from 2300 March 30 to 0200 March 30 in case 1, in which the black solid line represents the contour of the observed precipitation of 15 mm h−1.

    Fig. 14.  The NEP (%) distribution of hourly precipitation exceeding 10 mm h−1 from 0700 to 1000 on July 30 in case 2, in which the black solid line represents the contour of the observed precipitation of 10 mm h−1.

    Table 1.  Physical parameterization setting of two cases

    SchemeCase1[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 schemeSingle-Moment 3-classSingle-Moment 3-classMorrison 2-momentMorrison 2-moment
    Longwave radiation schemeRRTMRRTMRRTMRRTM
    Shortwave radiation schemeDudhiaDudhiaDudhiaDudhia
    Land Surface Process scheme5-layer thermal diffusion5-layer thermal diffusionNoah Land Surfance ModelNoah Land Surfance Model
    Boundary layer schemeYonsei UniversityYonsei UniversityYonsei UniversityYonsei University
    Cumulus parameterization schemeGrell-FreitasBetts-Miller-Janjic
    Near Surface SchemeMonin-ObukhovMonin-ObukhovMonin-ObukhovMonin-Obukhov
    Download: Download as CSV

    Table 2.  Details of the experiments of two cases

    Case 1Case 2
    perturbation variablesThe 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 phase2014/03/29/06-3/30/06(24 h)2014/7/29/00-7/30/00(24 h)
    Perturbation adjustment period6 h6 h
    Start and end time of the forecast phase2014/3/30/06-3/31/06(24 h)2014/7/30/00-7/31/00(24 h)
    LBC update cycle3 h3 h
    Download: Download as CSV
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Application of the Local Breeding Growth Mode Method Based on the Gaussian Weight in Convection-permitting Ensemble Forecasts

    Corresponding author: Chaohui CHEN, chenchaohui2001@163.com
  • 1. College of Meteorology and oceanography, National University of Defense Technology, Changsha 410073
  • 2. PLA Troop 95112, Foshan 528000
Funds: Supported by the Ministry of Science and Technology of China (2017YFC1501803) and National Natural Science Foundation of China (41975128 and 41875060)

Abstract: The local breeding growth mode (LBGM) method does not consider the difference between the grid points within the local radius. To address this problem, Gaussian weights (GWs) were proposed, which cause the influence of each grid within a local radius to exert an increase in distance with Gaussian decay on the central grid. In this paper, the effects of two different LBGM methods under GWs and equal weights (EWs) in convection-permitting ensemble forecasting are compared and analyzed using two squall line examples. The results showed that the use of the GWs intensified the local characteristics of the initial condition perturbation (ICP) and made the distribution of the ICP more flow-dependent. The result of the kinetic energy spectrum of the ICP indicated that there could be more large-scale information in the ICP using the GWs. In addition, meso-scale information also improved slightly. For nonprecipitation variable forecasting, GWs improved the relationships between the root-mean-square error and the spread and contributed to the forecasting accuracy of wind, temperature, geopotential height, and humidity. For the precipitation forecast, GWs simulated the precipitation structure successfully and provided better probability forecasting during the evolution of two squall line processes than the EWs.

1.   Introduction
  • Because of the chaotic nature of the atmosphere (Lorenz, 1963) and errors in the initial conditions and the models, it is inevitable that numerical forecasting results will differ from the actual future situation (Zhang et al., 2006). Thus, the technique of ensemble forecasts has been developed. Currently, the technology of global medium-range ensemble forecasts (with a forecasting period of 3 to 15 days and a resolution of about 16 to 70 km) (Toth and Kalnay, 1993, 1997; Molteni et al., 1996; Bishop and Toth, 1999; Chen et al., 2020) and regional mesoscale ensemble forecasts (with a forecasting period of 1 to 3 days and a resolution of 7 to 30 km) are relatively mature(Du and Tracton, 2001; Torn and Hakim, 2008; Wang et al., 2014; Zhang et al., 2017). With the increasing need to forecast disastrous weather and developments in scientific computation, ensemble forecasts gradually aim to develop their convection-permitting scale (with a forecasting period of less than 24 hours and a resolution of 1 to 4 km) (Kain et al., 2006; Clark et al., 2010; Johnson et al., 2011; Schwartz et al., 2015).

    The design of the initial condition perturbation (ICP) has an important influence on the effect of an ensemble prediction (Raynaud and Bouttier, 2016; Schwartz et al., 2020). Since the birth of ensemble forecasts, there have been some mature perturbation generation methods. Among them, the breeding growth mode (BGM) is typical (Toth and Kalnay, 1993, 1997). In this method, the fastest growing direction in the phase space is obtained using the natural selection of modes. In addition, the process used by the BGM does not rely on highly stable and accurate observational data, and the generated perturbations are well coordinated with the model, including the information for all the scales (Wang et al., 2014)that the model can resolve.

    Previous researchers have conducted more comprehensive studies of the BGM. For example, Cheung (2001) used the BGM to forecast typhoon weather, which showed that the BGM was of value for extreme weather forecasts. Yu and Zhang (2007), Yu et al. (2007), and Zhang and Yu (2007) also explored the effects of the length, superposition, and dynamic and free adjustments of the modes on perturbation generation. All of this research provided a foundation for the application of the BGM to the convection-permitting scale. Gao et al. (2010) attempted to apply the BGM to convection-permitting ensemble prediction for the first time. The experiment was based on the WRFV2.2 model, and the forecast object was a typical supercell storm in the United States. The results showed that the BGM was feasible for use at the convective scale. Li et al. (2017) and Ma et al. (2018a) applied the BGM to forecasts of the squall line, and the results were more skillful than the control prediction at the same resolution. This study, however, also exposed the disadvantage when the BGM was directly applied to the convection-permitting ensemble with low spread. To solve this problem, Chen et al. (2018) proposed a new local breeding growth mode (LBGM). On the basis of the original BGM, the local radius parameter was introduced into the breeding phase to realize the periodic local adjustment of the perturbation. Ma et al. (2019) then showed that the spatial distribution of the LBGM-generated ICP was flow-dependent and contained more local information than the BGM.

    The essence of LBGM localization is that only the grid points within a certain local radius are considered when calculating the adjustment coefficient of the breeding phase. The contributions of these points are the same, which ignores their horizontal differences. The physical field in the atmosphere is continuous, however, and the correlation between two points in a physical field should decrease as the distance increases (Barnes, 1964). Therefore, the relationship between the correlation and the distance between grid points with a local radius also should be considered in the LBGM. By considering the spatial structure of the perturbation that satisfies the Gaussian distribution in deep convection systems (Done et al., 2012), we proposed Gaussian weights (GWs) and compared them with the original equal weights (EWs) to test the effectiveness of the LBGM under GWs and EWs in a convection-permitting ensemble prediction. Section 2 describes the two convection cases and the design of the experiments. Section 3 introduces the LBGM methods under GWs and EWs. Section 4 provides an analysis of the experimental results. Section 5 provides the conclusions.

2.   Individual cases and experimental design
  • 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 large-scale circulation situation at 1200 UTC March 30, 2014. Under the influence of a strong high pressure ridge in a high-latitude area at a 500-hPa 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 500-hPa geopotential height field (gpm; the same below) and wind field (m s−1, the same below) (b) a 850-hPa geopotential height field and wind field at 1200 UTC March 30, 2014 and (c) a 500-hPa geopotential height field and wind field (d) a 850-hPa 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, short-term 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 large-scale circulation situation at 0000 UTC July 30, 2014. Guided by the 200-hPa upper-air jet (figure omitted), the 500-hPa 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 700-hPa 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 850-hPa warm shear line. Therefore, with the cooperation of high- and low-level 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 double-nested 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.

    SchemeCase1[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 schemeSingle-Moment 3-classSingle-Moment 3-classMorrison 2-momentMorrison 2-moment
    Longwave radiation schemeRRTMRRTMRRTMRRTM
    Shortwave radiation schemeDudhiaDudhiaDudhiaDudhia
    Land Surface Process scheme5-layer thermal diffusion5-layer thermal diffusionNoah Land Surfance ModelNoah Land Surfance Model
    Boundary layer schemeYonsei UniversityYonsei UniversityYonsei UniversityYonsei University
    Cumulus parameterization schemeGrell-FreitasBetts-Miller-Janjic
    Near Surface SchemeMonin-ObukhovMonin-ObukhovMonin-ObukhovMonin-Obukhov

    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 1Case 2
    perturbation variablesThe 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 phase2014/03/29/06-3/30/06(24 h)2014/7/29/00-7/30/00(24 h)
    Perturbation adjustment period6 h6 h
    Start and end time of the forecast phase2014/3/30/06-3/31/06(24 h)2014/7/30/00-7/31/00(24 h)
    LBC update cycle3 h3 h

    Table 2.  Details of the experiments of two cases

3.   Methods
  • 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 root-mean-square 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 two-dimensional 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.

4.   Experimental results
  • Figures 3 and 4 show the ICP distribution of the zonal wind speed, U, at the end time point of the breeding stage, and the corresponding reanalysis data wind field of the two cases. In general, the ICP distribution obtained by the LBGM under the two weight methods corresponded to the wind field analysis in both case 1 and case 2. The GW functioned better for local characteristics, however. For example, in case 1, in the rectangular region in Fig. 3, the flow of the ICP distribution obtained by the GWs was more delicate and showed the small trough more clearly. In case 2, in the rectangular region in Fig. 4, the negative center of the ICP was obtained by the GWs, which made the trough’s position in the ICP field more obvious. Therefore, compared with EWs, the GWs increased the local characteristics, thus improving the morphological distribution of the ICP and making the ICP more flow-dependent.

    Figure 3.  The ICP distribution of zonal wind speed U (m s−1) at the 200-hPa level under (a) the EWs and (b) the GWs in the outer of model for case 1 and its 200hPa wind field distribution at 0600 March 30, 2014.

    Figure 4.  As in Fig. 3 but for case 2 at 0000 July 30, 2014.

  • The kinetic energy spectrum can effectively describe the scale information contained in the ICP (Zheng et al., 2008). For a successful ensemble prediction system, the ICP should consider the uncertain information of different scales (Wang et al., 2014). To better understand the scale information of the ICP using the GWs and EWs generated by the LBGM, we adopted the 2-dimensional discrete cosine transform (2D-DCT; Denis et al., 2002) to conduct the kinetic spectrum analysis of the ICP of the two cases.

    Since the kinetic energy spectrum distribution of the ICP obtained by each member was basically similar, only the spectrum results of the ICP of member five at different vertical levels in two cases were given in Figs. 5, 6. Because the minimum resolution scale of the numerical model was 6–10 times the grid spacing (Skamarock, 2004), we could not identify the spectral energy with a wavelength of less than 20 km. Figures 5 and 6 show that in both case 1 and case 2, the peak energy of the spectrum under the two weight methods was concentrated in the large-scale area with a wavelength of approximately 1000 km. Note that, compared with case 2, the spectral energy in case 1 also had a secondary peak at 20–200 km, which may have been related to large-scale forcing. Compared with case 1, the squall line in case 2 not only was affected by the 500-hPa trough and the 850-hPa shear line, but also was influenced by the subtropical height and the typhoon in the western Pacific, and the large-scale forcing was stronger. Compared with the EWs, it was obvious that the GWs’ kinetic energy spectrum had some differences. In case 1, the improvement in the GWs for the energy was primarily in the form of a large-scale region with wavelengths greater than 600 km and a mesoscale region with wavelengths 20–200 km. In case 2, the GWs were higher than the EWs within a scale range that the wavelengths were greater than 100 km. The results of kinetic energy spectrum of the two individual cases showed that the GWs effectively improved the large-scale information in the ICP and slightly increased the mesoscale information.

    Figure 5.  The kinetic energy spectrum of the ICP of member 5 at (a) 200-hPa, (b) 500-hPa, (c) 700-hPa, (d) 850-hPa levels for case 1. The red line and the blue line represent the results under the GWs and the EWs.

    Figure 6.  As in Fig. 5 but for case 2.

  • The relationship between the RMSE of the ensemble mean (EM) and the ensemble spread is often an important evaluation index to evaluate the forecasting capability of an ensemble prediction system. When RMSE is consistent with the spread, it indicates that the ensemble perturbation represents the uncertainty of the analysis field to a certain extent, and the ensemble results most likely cover the future atmospheric real state. Considering that we focused on the ICP, we adopted the hypothesis of the "perfect model"(Johnson and Wang, 2016) when testing the forecast of nonprecipitation variables. More specifically, the set experiment adopted the same model and physical parameterization combination so that the model error was ignored and the control result replaced the real atmospheric state. Therefore, in the perfect mode, the ensemble prediction effect was related only to the ICP, which was helpful to study the influence of the GWs and the EWs on the LBGM-generated ICP.

    Figures 7 and 8 show the evolution relationship of the RMSE and the spread of the perturbation variables with forecast time at different levels for case 1. In the lower atmosphere of the model, the GWs slightly increased the spread of U and V and had little influence on the spread of variables such as T, PH, and Q. Compared with the spread, the RMSE of the GWs was significantly smaller than that of the EWs, which made the ratio of the RMSE to the spread of the GWs closer to 1, which improved the forecasting skill. In the upper atmosphere of the model, the spread and RMSE of each variable were lower than that in the lower atmosphere, and the consistency of the spread and RMSE was also better than that in the lower atmosphere. This indicated that the predictability of the upper atmosphere was higher, which may have been because the upper atmosphere was less affected by the ground. In general, the GWs significantly improved the prediction consistency of each variable, among which PH and Q were the most significant. For variables such as U, V, and T, the GWs increased the spread and reduced the RMSE, which improved the prediction skill at an earlier time. Note that in case 1, the spread was greater than the RMSE. This may have been due to the relatively stable upper atmosphere circulation system, which reduced the forecast uncertainty of U, V, T, and other variables. Therefore, the GWs and EWs consistencies of the RMSE and spread at the upper levels were comparable.

    Figure 7.  The low-level (z=12) in case 1. The relationship of RMSE of the EM and the ensemble spread of perturbation variables containing (a) U and (b) V, (c) T, (d) PH and (e) Q with the evolution of the forecast time at the low level (z=12), where the blue and red lines represent EW and GW respectively and the solid and dotted lines represent the RMSE and spread, respectively.

    Figure 8.  As in Fig. 7 but for the results at the high level (z = 35).

    For case 2 (Figs. 9, 10), whether it was at the high level or the low level, the consistency of the spread and the RMSE under the GWs was better than that of the EWs. The difference from case 1 was that the improvement in the GWs in case 2 was reflected only in the later forecast time, whereas the two weight methods had the same forecast effect at an earlier time. According to the results of Ma et al. (2019), this may have been because in case 2, the uncertainty in the PH was higher. This is also reflected in Fig. 10d.

    Figure 9.  As in Fig. 7 but for case 2.

    Figure 10.  As in Fig. 8 but for case 2.

    By combining the results of these two cases, the GWs improved the consistency of the spread, the RMSE of the perturbation variables, and the ensemble forecasting skills for wind, temperature, geopotential height, and humidity.

  • The squall line process is often accompanied by heavy precipitation. To provide a better comparison between GWs and EWs, we analyzed the results of precipitation forecasts in the two cases.

  • Figure 11 shows the hourly precipitation evolution of the EM forecast from 2300 to 0200 on March 30, 2014, and the corresponding observation of case 1. From Figs. 11ac, the squall line gradually moved from the central portion of Guangdong Province to the southeast, and the intensity gradually increased during this process. Until 0200 March 31, the squall line reached the southeast coast of Guangdong Province before entering the sea. At that time, the range of the squall line was slightly reduced and was about to enter a recession. In terms of the EM results, both the EWs and the GWs generated a precipitation evolution that was consistent with the observation, and the process of the squall line moving to the southeast were both predicted. In addition, the rain belt position also basically agreed with the actual situation. From the structure of precipitation, the rain band range obtained by the EWs was obviously smaller than the actual observation, as shown in Figs. 11fh. The precipitation distribution was relatively fragmented, and the line shape was not very significant. The GWs overcame this shortcoming, and the size of the rain band became more consistent. The rain band was band-shaped with a tight internal structure and a tidy front end, which better represented the movement process and structural characteristics of the squall line, as shown in Figs. 11ik.

    Figure 11.  The hourly precipitation evolution and corresponding observed precipitation distribution of the EM forecast from 2300 March 30 to 0200 March 31, 2014, in case 1: (a)–(d) is for the observed distribution, (e)–(h) is for the EM result under EWs, and (i)–(l) is the that under GWs.

    In case 2, the strong precipitation period began at 0700 and ended at 1000 July 30, 2014. Figures 12ad show that the squall line primarily moved southeast from the northern boundary of Jiangsu and Anhui provinces. At 0900, the main body of the squall line split into two parts. The first part was located north of Jiangsu Province and was directed northeast-southwest. The second part was located in the north of Anhui Province, with an east-west direction. At 1000, the intensity of precipitation weakened and the rain band range shrank. Figures 12eh and il illustrate the EM results under the EWs and GWs, respectively. In general, the position of the squall line obtained by these two weight methods was basically consistent with the observation, and the evolution of the squall line was better predicted. The precipitation intensity and structure obtained by the GWs, however, were slightly better than those obtained by the EWs. For example, in the black rectangular areas in Figs. 12f, j, the internal structure of the rain bands obtained by the GWs was relatively fragmented. Compared with the precipitation center in the EW results, the results of the GW were closer to the actual situation. In addition, in the black rectangular area in Figs. 12g, k, there are three precipitation centers for GW, and the precipitation rate was 15 mm h−1, which was more consistent with the observed rain magnitude, whereas the rate for EW was only 10 mm h−1.

    Figure 12.  The forecast result from 0700 to 1000 on July 30, 2014 in case 2.

  • The outstanding feature of ensemble forecasts is to provide probability guidance for weather forecasts. In particular, for strong convective weather with high uncertainty, it is essential to give reasonable probability forecasts (Stensrud et al., 2009; Snook et al., 2012). Because the object of the convection-permitting ensemble is equivalent to the grid spacing at the spatial scale, this paper adopted the neighborhood approaches (Theis et al., 2005) to generate the neighborhood ensemble probability (NEP). This approach avoided large spatial displacement errors (Schwartz et al., 2010). Following Ma et al. (2018b), the field length chosen in this paper was 60 km.

    Figure 13 illustrates the NEP distribution of precipitation exceeding 15 mm h−1 from 2300 to 0200 March 30, 2014. In general, the NEP distribution under the two weight methods basically covered the observed precipitation area, indicating that the LBGM had a certain predictability for the squall line weather. By comparing these two methods, we obtained two probability centers, as shown in Fig. 13e, which corresponded to the two rain areas in the actual situation. Although the location was slightly offset from the observed centers, the probability prediction effect of the GW was better in the center location relative to the probability shown in Fig. 13a. In addition, in the black rectangular areas in Figs. 13f, 12g, it is clear that the GW covered the zero probability area of EW and more effectively captured the occurrence of heavy precipitation.

    Figure 13.  The NEP (%) distribution of hourly precipitation exceeding 15 mm h−1 from 2300 March 30 to 0200 March 30 in case 1, in which the black solid line represents the contour of the observed precipitation of 15 mm h−1.

    In case 2, the NEP distribution obtained by the GW was closer to the observation than the EW. In the black rectangular area of Figs. 14a, e, the GWs predicted the precipitation center in the northern part of Jiangsu Province well and obtained an 80% probability of precipitation. The probability center given by the EWs was slightly further east than the observed situation, and the effect was not as good as the GWs. In addition, the advantage of the GWs was also reflected in the rain belt in northern Anhui Province, as shown in Figs. 14c, g.

    Figure 14.  The NEP (%) distribution of hourly precipitation exceeding 10 mm h−1 from 0700 to 1000 on July 30 in case 2, in which the black solid line represents the contour of the observed precipitation of 10 mm h−1.

    Therefore, the NEP distribution of the two cases showed that the GWs improved the forecasting skills of a strong squall line. In addition, it provided good probability guidance for the occurrence and development of strong convection compared with traditional EWs.

5.   Summary
  • This paper considered the differences among grid points within the local radius on the basis of the LBGM method and proposed the idea of using the GWs in place of the original EWs. By combining two cases of a squall line process, the morphological distribution of the ICPs and their kinetic spectrum, we then used the relationship between the RMSE and the spread of perturbation variables and the precipitation forecast to examine the results in the convection-permitting ensemble forecast using the LBGM method under these two weighting methods. The primary conclusions are as follows:

    (1) GW intensified the local characteristics in the morphological distribution of the ICPs, thus making the ICPs more flow-dependent compared with the EW.

    (2) The analysis of the kinetic energy spectrum identified the scale information of the initial perturbations. In addition, it was shown in the spectrum at different vertical levels that the GWs could improve large-scale information in the ICPs, as well as slightly increase the meso-scale information.

    (3) As is shown in the result of the forecast of these nonprecipitation variables, the coherence between the RMSE and the spread for the GWs was better than that for EWs, which promoted the forecasting skill for wind, temperature, geopotential height, and humidity.

    (4) The evolution of precipitation during the squall line process using the GWs and EWs both were consistent with the observations. The simulation of the precipitation structure by the GWs was better than that using the EWs. Also, the NEP distribution further demonstrated that the GWs could provide more effective probability guidance for the forecast of the squall line

    Therefore, compared with original EWs in the LBGM, the local characteristics in convective weather were better predicted when using GWs. In addition, GWs did not demand much more computational resources, and thus they were more appropriate for generating ICPs in a convection-permitting ensemble forecast. This paper evaluated the GWs in a basic manner, and a portion of the experiments were based on the assumption of a perfect model. In the future, real observational data and numerous cases of strong convection will be combined to further study the LBGM method under GWs.

    Acknowledgments. The authors thank anonymous reviewers for their constructive comments and suggestions.

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