Application of Gaussian Weight to Improve Perturbation Features of Convection-Permitting Ensemble Forecast Based on Local Breeding of Growing Modes

基于高斯权重的局地增长模培育算法在对流尺度集合预报中的应用

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

    Supported by the National Key Research and Development Program of China (2017YFC1501803) and National Natural Science Foundation of China (41975128 and 41875060)

  • doi: 10.1007/s13351-021-0173-4

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  • Local breeding of growing modes (LBGM) is a method used to generate initial condition perturbation (ICP) for convection-permitting ensemble forecasts. Equal weights (EWs) are usually presumed in LBGM during the localization of ICP, without considering different contributions of the grid points within the local radius. To address this problem, Gaussian weights (GWs) are proposed in this study, which can accommodate the varied influences of the grids inside the local radius on the central grid through a Gaussian function. Specifically, two convection-permitting ensemble forecast experiments based on LBGM with GWs and EWs are compared and analyzed respectively for two squall line cases. The results showed that the use of the GWs intensified the local characteristics of the ICP and made the distribution of the ICP fields more flow-dependent. Kinetic energy spectrum of the ICP indicated that there could be more large-scale information in the ICP by using the GWs. In addition, mesoscale information also improved slightly. For forecast of nonprecipitation variables, GWs improved the relationship 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 the two squall line processes than the EWs.

    针对初始扰动局地增长模培育法(Local Breeding of Growing Modes, LBGM)中未考虑局地半径内格点之间差异性的问题,提出了高斯权重修正,即局地半径内的格点对中心格点的影响随着距离的增加呈高斯函数衰减。结合两次飑线个例,对高斯权重和等权重下的LBGM法在对流尺度集合预报中的效果进行了对比分析。结果发现,高斯权重增加了局地特征,使得初始扰动在形态分布上具有更明显的流依赖性。动能谱分析结果表明,基于高斯权重修正的LBGM能够得到更多的大尺度信息,对中尺度信息也略有改善。对于非降水变量的预报,高斯权重改善了预报均方根误差与离散度的一致性,提高了风场、温度场、位势高度场以及湿度场的预报技巧。对于降水预报,高斯权重成功地模拟出降水结构,能够为飑线降水的演变过程提供更好的概率预报结果。

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  • Fig. 1.  Distributions of (a, c) 500- and (b, d) 850-hPa geopotential height (contour; gpm) and wind (barb; m s−1) at (a, b) 1200 UTC 30 March 2014 and (c, d) 0000 UTC 30 July 2014, respectively. The orange line represents the trough.

    Fig. 2.  Schematic diagrams of (left) equal weights and (right) Gaussian weights used by the local breeding of growing modes (LBGM; r = 2) to generate perturbation for ensemble forecast. The larger the grid point, the greater the contribution weight.

    Fig. 3.  Distributions of (a, b) LBGM-generated ICP of 200-hPa zonal wind speed (U; m s−1) at the end of the breeding stage under (a) equal weights (EWs) and (b) Gaussian weights (GWs) over the outer model domain for case 1, and (c) the corresponding FNL analysis wind field (m s−1) at 200 hPa at 0600 UTC 30 March 2014. Apparent differences in the ICP of U are seen between the boxed regions in (a) and (b), with (b) showing more delicated perturbation texture/structure resembling that in the background wind flow in (c).

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

    Fig. 5.  The kinetic energy spectrum E(k) of the ICP of member 5 at (a) 200-, (b) 500-, (c) 700-, and (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.  Evolution of root-mean-square error (RMSE) of the ensemble mean (EM) and ensemble spread of the perturbation variables including (a) U, (b) V, (c) T, (d) PH, and (e) Q with the forecast time at the low level (z = 12), for case 1. The blue and red lines represent EW and GW, respectively. 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.  Evolution of hourly precipitation (mm) distribution (a–d) from the observation and from the ensemble mean forecast using (e–h) EWs or (e–l) GWs at 2300 UTC 30, 0000 UTC 31, 0100 UTC 31, 0200 UTC 31 March 2014, for case 1.

    Fig. 12.  As in Fig. 11, but at 0700, 0800, 0900, and 1000 UTC 30 July 2014 for case 2. Boxed regions are for detailed comparison.

    Fig. 13.  The neighborhood ensemble probability (NEP; %) distribution of hourly precipitation exceeding 15 mm h−1 from 2300 UTC 30 to 0200 UTC 31 March in case 1, in which the black solid line represents the contour of the observed precipitation of 15 mm h−1. Boxed regions are for detailed comparison.

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

    Table 1.  Physical parameterization settings for the two cases

    SchemeCase 1 [center grid (23.5°N,113.5°E)]Case 2 [center grid (35°N, 115°E)]
    Inner domain
    (310 × 238)
    Outer domain
    (289 × 214)
    Inner domain
    (351 × 351)
    Outer domain
    (301 × 301)
    Microphysics schemeSingle-moment 3-classSingle-moment 3-classMorrison 2-momentMorrison 2-moment
    Longwave radiation schemeRapid Radiative Transfer
    Model (RRTM)
    RRTMRRTMRRTM
    Shortwave radiation schemeDudhiaDudhiaDudhiaDudhia
    Land surface process scheme5-layer thermal diffusion5-layer thermal diffusionNoah land surface modelNoah land surface 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 on perturbation in the experiments for the two cases

    Case 1Case 2
    Perturbation variableHorizontal zonal wind speed U, horizontal meridional wind speed V, perturbation potential temperature T, perturbation geopotential height (PH), and water vapor mixing ratio Q
    Start and end time of the breeding phase2014/3/29/0600–3/30/0600 (24 h)2014/7/29/0000–7/30/0000 (24 h)
    Perturbation adjustment period6 h6 h
    Start and end time of the forecast phase2014/3/30/0600–3/31/0600 (24 h)2014/7/30/0000–7/31/0000 (24 h)
    LBC update cycle3 h3 h
    Download: Download as CSV
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Application of Gaussian Weight to Improve Perturbation Features of Convection-Permitting Ensemble Forecast Based on Local Breeding of Growing Modes

    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 National Key Research and Development Program of China (2017YFC1501803) and National Natural Science Foundation of China (41975128 and 41875060)

Abstract: 

Local breeding of growing modes (LBGM) is a method used to generate initial condition perturbation (ICP) for convection-permitting ensemble forecasts. Equal weights (EWs) are usually presumed in LBGM during the localization of ICP, without considering different contributions of the grid points within the local radius. To address this problem, Gaussian weights (GWs) are proposed in this study, which can accommodate the varied influences of the grids inside the local radius on the central grid through a Gaussian function. Specifically, two convection-permitting ensemble forecast experiments based on LBGM with GWs and EWs are compared and analyzed respectively for two squall line cases. The results showed that the use of the GWs intensified the local characteristics of the ICP and made the distribution of the ICP fields more flow-dependent. Kinetic energy spectrum of the ICP indicated that there could be more large-scale information in the ICP by using the GWs. In addition, mesoscale information also improved slightly. For forecast of nonprecipitation variables, GWs improved the relationship 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 the two squall line processes than the EWs.

基于高斯权重的局地增长模培育算法在对流尺度集合预报中的应用

针对初始扰动局地增长模培育法(Local Breeding of Growing Modes, LBGM)中未考虑局地半径内格点之间差异性的问题,提出了高斯权重修正,即局地半径内的格点对中心格点的影响随着距离的增加呈高斯函数衰减。结合两次飑线个例,对高斯权重和等权重下的LBGM法在对流尺度集合预报中的效果进行了对比分析。结果发现,高斯权重增加了局地特征,使得初始扰动在形态分布上具有更明显的流依赖性。动能谱分析结果表明,基于高斯权重修正的LBGM能够得到更多的大尺度信息,对中尺度信息也略有改善。对于非降水变量的预报,高斯权重改善了预报均方根误差与离散度的一致性,提高了风场、温度场、位势高度场以及湿度场的预报技巧。对于降水预报,高斯权重成功地模拟出降水结构,能够为飑线降水的演变过程提供更好的概率预报结果。

1.   Introduction
  • Because of the chaotic nature of the atmosphere (Lorenz, 1963) and errors in the initial condition 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 3–15 days and a resolution of about 16–70 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 1–3 days and a resolution of 7–30 km) are relatively mature (Du and Tracton, 2001; Torn and Hakim, 2008; Wang et al., 2014; Zhang et al., 2017). With rapid development in scientific computation and the increasing need for forecast of disastrous weather, ensemble forecasts at convection-permitting scale (with a forecasting period of less than 24 h and a resolution of 1–4 km) are gradually being paid much attention (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 emergence of ensemble forecasts, there have been some mature perturbation generation methods. Among them, the breeding of growing modes (BGM) is typical (Toth and Kalnay, 1993, 1997). In this method, the fastest growing direction in the phase space is obtained by 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.

    Comprehensive studies of the BGM have been carried out. For example, Cheung (2001) used the BGM to forecast typhoon weather and 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 these studies provided a base 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 Weather Research and Forecasting Version 2.2 (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 convection 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 of growing modes (LBGM) method. 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, and their horizontal differences are ignored. The physi-cal field in the atmosphere is continuous and the correlation between two points in a physical field normally decreases as the distance increases (Barnes, 1964). Therefore, the relationship between the correlation and the distance between the grid points within a local radius should also be considered in the LBGM. By considering that the spatial structure of the perturbation satisfies Gaussian distribution in deep convection systems (Done et al., 2012), we hereby proposed Gaussian weights (GWs) in this study, and compared them with the original equal weights (EWs) to test the effectiveness of the LBGM under GWs and EWs in 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 is a squall line that occurred in South China in March 2014. From evening of 29 March to the afternoon of 31 March 2014, South China was hit by a severe convective weather process, which affected Guangxi, Guangdong, Yunnan, and other adjacent provinces. From 2000 UTC 30 to 0400 UTC 31 March, a long squall line passed through Guangdong Province from the northwest to southeast. Some cities suffered from severe weather, including hail and gale. Figures 1a and b show the large-scale weather pattern at 1200 UTC 30 March 2014. Under the influence of a strong high pressure ridge at 500 hPa in the high latitude, cold air flowed into South China, providing intermediate cold air conditions for the development of strong convection. At the same time, a small trough appeared over the western Guangdong, which was conducive to the upward air motion there. Under the influence of a warm shear line, a large amount of warm and humid air passed through Guangdong, providing water vapor conditions and aggravating the convective instability in this region. In addition, the entire South China was located in the coupling zone between the upper-level jet and the lower-level jet (figure omitted), favorable for convective weather.

    Figure 1.  Distributions of (a, c) 500- and (b, d) 850-hPa geopotential height (contour; gpm) and wind (barb; m s−1) at (a, b) 1200 UTC 30 March 2014 and (c, d) 0000 UTC 30 July 2014, respectively. The orange line represents the trough.

    Case 2 is a squall line process that occurred in the Yangtze–Huai river basins of China in July 2014. A squall line from north to south swept through central and northern Anhui and Jiangsu provinces from 0600 to 1100 UTC 30 July 2014. The squall line migrated 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. Chuzhou and its affiliated regions had seen thunderstorms and gales above level 7, damaged houses, and some casualties. Figures 1c and d show the large-scale weather situation at 0000 UTC 30 July 2014. Guided by the 200-hPa upper air jet (figure omitted), the 500-hPa trough moved eastward and was blocked by the subtropical high, and thus it eventually stopped in the Jiangsu and Anhui area, thus continuously providing cold air at the middle level. At 700 hPa (figure omitted), under the influence of the low-level jet, a large amount of warm and humid air was transported to Jiangsu and Anhui, and finally accumulated in the south side of the 850-hPa warm shear line. Therefore, with the cooperation of high- and low-level circulations, severe convective weather occurred in the Jiangsu and Anhui area.

  • We based our experiments on the WRFV3.6 model and adopted a double-nested domain. The resolution of the outer domain was 9 km and that of the inner domain (analysis area) was 3 km. The number of vertical layers was 42. The physical parameterization schemes and grid settings of the two individual cases are shown in Table 1. We used NCEP final (FNL) analysis data (available at https://rda.ucar.edu/datasets/ds083.2/) to drive the model and analyze the synoptic weather background. To verify the experiment results, we used precipitation data (0.1° × 0.1°) released by the National Meteorological Information Center of China Meteorological Administration as the observation (available at http://data.cma.cn/data/cdcdetail/dataCode/SEVP_CLI_CHN_MERGE_CMP_PRE_HOUR_GRID_0.10.html).

    SchemeCase 1 [center grid (23.5°N,113.5°E)]Case 2 [center grid (35°N, 115°E)]
    Inner domain
    (310 × 238)
    Outer domain
    (289 × 214)
    Inner domain
    (351 × 351)
    Outer domain
    (301 × 301)
    Microphysics schemeSingle-moment 3-classSingle-moment 3-classMorrison 2-momentMorrison 2-moment
    Longwave radiation schemeRapid Radiative Transfer
    Model (RRTM)
    RRTMRRTMRRTM
    Shortwave radiation schemeDudhiaDudhiaDudhiaDudhia
    Land surface process scheme5-layer thermal diffusion5-layer thermal diffusionNoah land surface modelNoah land surface 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 settings for the 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 perturbation members was 10. To ensure that the experiment results were affected only by the ICPs, configurations of the physical parameterization scheme 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 physics. No observational data were 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 variableHorizontal zonal wind speed U, horizontal meridional wind speed V, perturbation potential temperature T, perturbation geopotential height (PH), and water vapor mixing ratio Q
    Start and end time of the breeding phase2014/3/29/0600–3/30/0600 (24 h)2014/7/29/0000–7/30/0000 (24 h)
    Perturbation adjustment period6 h6 h
    Start and end time of the forecast phase2014/3/30/0600–3/31/0600 (24 h)2014/7/30/0000–7/31/0000 (24 h)
    LBC update cycle3 h3 h

    Table 2.  Details on perturbation in the experiments for the 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:

    $$\begin{aligned} & {x_{a,t}}(i,j,k) = {x_{f,t}}(i,j,k) \times \dfrac{{{e_0}(k)}}{{{e_t}(i,j,k)}}, \\ & {e_t}(i,j,k) =\dfrac{1}{{2r + 1}}\sqrt {\displaystyle\sum\limits_{i - r}^{{{i + r}}} {\displaystyle\sum\limits_{j - r}^{j + r} {{{[{X_{{\rm{per}}_t}}(i,j,k) - {X_{{\rm{ctl}}}}_{_t}(i,j,k)]}^2}} } }, \end{aligned}$$ (1)

    where i, j, and k are the indices of latitude, longitude, and altitude, respectively; ${x_{a,t}}(i,j,k)$ and ${x_{f,t}}(i,j,k)$ are the perturbation fields after and before the adjustment; ${e_0}(k)$ is the root-mean-square error (RMSE) of layer k at the initial time; and ${e_t}(i,j,k)$ is the RMSE at grid point (i, j) of layer k at time t. Their ratio is the perturbation adjustment coefficient. Here, ${X_{{\rm{per}}_t}}(i,j,k)$ and ${X_{{\rm{ctl}}}}_{_t}(i,j,k)$ are the perturbation and control prediction results at time t, respectively. The formula of ${e_t}(i,j,k)$ indicates that introduction of the local radius r makes the adjustment coefficients between the grid points inside and outside the area of the radius of r different during the disturbance adjustment process, thus reflecting the horizontal difference of the physical quantity. Furthermore, however, for the grid points inside the radius, their contributions to the center point are still taken equally rather than differently in Eq. (1), which may need to be remedied.

    As shown in Fig. 2, for the EWs, the RMSE of the red grid considers only the influence of itself and the surrounding 24 black grids, and the contribution weight of each grid point is equal, which is $\dfrac{1}{{{{(2r + 1)}^2}}}$. For the GWs, however, the contribution of the black grid points to the central red grid point decays as a Gaussian function with an increase in their distance, which reflects the difference between the grid points within the local radius. GW realization follows three main steps:

    Figure 2.  Schematic diagrams of (left) equal weights and (right) Gaussian weights used by the local breeding of growing modes (LBGM; r = 2) to generate perturbation for ensemble forecast. 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:

    $$G(x,y) = \frac{1}{{2\pi {r^2}}}{{\rm{e}}^{\dfrac{{ - [{(x \; -\; {x_i})}^2 \;+\; {(y \;-\; {y_i})}^2]}}{{2{r^2}}}}}. \hspace{50pt}$$ (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 RMSE of the forecast field relative to the analysis at each grid point:

    $${e_t}(i,j,k)= \sqrt {\displaystyle\sum\limits_{i - r}^{i + r} {\displaystyle\sum\limits_{j - r}^{j + r} {W(x,y) \times {{[{X_{{\rm{per}}_t}}(i,j,k) - {X_{{\rm{ctl}}}}_{_t}(i,j,k)]}^2}} } } .$$ (4)

    According to investigations of Chen et al. (2018) and Ma et al. (2019), we set 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 distributions of LBGM-generated ICP of zonal wind speed U at the end of the breeding stage, and the corresponding FNL analysis wind field for the two cases. In general, the ICP distributions of U obtained by the LBGM under the two weight methods corresponded to the FNL analysis wind fields in both case 1 and case 2, especially in the boxed regions, where the ripple-like (Figs. 3a, b) and valley-shaped (Figs. 4a, b) fluctuations matching the background wind flow structures (Figs. 3c, 4c) to a certain extent. Obviously, the GW functioned better for local characteristics. For example, in case 1, in the boxed region in Fig. 3, the ICP of U obtained by the LBGM with GWs shows a more delicate structure, with ripples and a shallow trough resembling those of the wind flow more clearly (Fig. 3b), whereas these perturbation features are less salient under the EWs (Fig. 3a). In case 2, in the boxed region in Fig. 4, the ICP shows a negative center under the GWs, making the trough pattern in the ICP field more obvious. Therefore, compared with EWs, the GWs had increased the local characteristics, thus improving the morphological distribution of the ICP and making the ICP more flow-dependent.

    Figure 3.  Distributions of (a, b) LBGM-generated ICP of 200-hPa zonal wind speed (U; m s−1) at the end of the breeding stage under (a) equal weights (EWs) and (b) Gaussian weights (GWs) over the outer model domain for case 1, and (c) the corresponding FNL analysis wind field (m s−1) at 200 hPa at 0600 UTC 30 March 2014. Apparent differences in the ICP of U are seen between the boxed regions in (a) and (b), with (b) showing more delicated perturbation texture/structure resembling that in the background wind flow in (c).

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

  • The kinetic energy spectrum can effectively describe the scale information contained in the ICP (Zheng et al., 2008; Wang et al., 2018). 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 generated by the LBGM using the GWs and EWs, we adopted the two-dimensional discrete cosine transform (2D-DCT; Denis et al., 2002) to conduct the kinetic spectrum analysis of the ICP for the two cases.

    We found that the distribution of kinetic energy spectrum of the ICP for each ensemble member was basically similar, so only the spectra of the ICP of member 5 at different vertical levels in the two cases were given in Figs. 5, 6. Because numerical models can resolve/capture weather events on spatial scales of at least 6–10 times the model 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 is 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 has a secondary peak at 20–200 km, which may be related to mesoscale forcing. Compared with case 1, the squall line in case 2 was affected not only by the 500-hPa trough and the 850-hPa shear line, but also by the subtropical high and a typhoon in the western Pacific, so the large-scale forcing was stronger. Compared with the EWs, it is obvious that the GWs’ kinetic energy spectrum exhibits certain 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 of 20–200 km. In case 2, kinetic energy values with the GWs were higher than those with the EWs within a scale range of wavelengths 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 E(k) of the ICP of member 5 at (a) 200-, (b) 500-, (c) 700-, and (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 RMSE of the ensemble mean (EM) and the ensemble spread is often an important 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 co-ver 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 assessing the forecast of nonprecipitation variables. More specifically, the set of experiments adopted the same model and physical parameterization combination so the model error was ignored and the control experiment 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 of RMSE and the ensemble 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, showing improved forecasting skill. In the upper atmosphere of the model, the spread and RMSE of most variables except T were lower than those in the lower atmosphere, and the consistency of the spread and RMSE was also better than that in the lower atmosphere. This indicates 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, with improved 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 consistency between the RMSE and spread at the upper levels were comparable for GWs and EWs.

    Figure 7.  Evolution of root-mean-square error (RMSE) of the ensemble mean (EM) and ensemble spread of the perturbation variables including (a) U, (b) V, (c) T, (d) PH, and (e) Q with the forecast time at the low level (z = 12), for case 1. The blue and red lines represent EW and GW, respectively. 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), for both the high level and the low level, the consistency between the spread and the RMSE under the GWs was better than that under the EWs. The difference from case 1 is 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, we conclude that the GWs improved the consistency between the spread and the RMSE for the perturbation variables, and obtained higher ensemble forecast skills for wind, temperature, geopotential height, and humidity.

  • Squall lines are 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 evolution of hourly precipitation distribution from the EM forecast during 2300 UTC 30–0200 UTC 31 March 2014 and the corresponding observation for case 1. From Figs. 11ac, it is seen that 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 UTC 31 March, the squall line reached the southeast coast of Guangdong before entering the sea. At that time, the coverage of the squall line was slightly reduced and it was about to enter a recession. In terms of the EM results, precipitation evolution from both the EWs and the GWs was consistent with the observation, and the process of the squall line moving to the southeast were both predicted. In addition, the rainbelt position also basically agreed with the actual situation. From the structure of precipitation, the rain band extension 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.  Evolution of hourly precipitation (mm) distribution (a–d) from the observation and from the ensemble mean forecast using (e–h) EWs or (e–l) GWs at 2300 UTC 30, 0000 UTC 31, 0100 UTC 31, 0200 UTC 31 March 2014, for case 1.

    In case 2, the strong precipitation period began at 0700 and ended at 1000 UTC 30 July 2014. Figures 12ad show that the squall line primarily moved southeast from the northern boundary of Jiangsu and Anhui provinces. At 0900 UTC, 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 UTC, the intensity of precipitation weakened and the rain band 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 EW results, the precipitation center in the GW results was closer to the actual situation. In addition, in the black rectangular area in Figs. 12g, k, there were 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.  As in Fig. 11, but at 0700, 0800, 0900, and 1000 UTC 30 July 2014 for case 2. Boxed regions are for detailed comparison.

  • An outstanding feature of ensemble forecast is that it can provide probability guidance for weather prediction. 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 target of convection-permitting ensemble forecast is of approximately equivalent spatial scale to the ensemble model grid spacing, this paper adopted the neighborhood approach (Theis et al., 2005) to generate the neighborhood ensemble probability (NEP). This approach could avoid 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 UTC 30 to 0200 UTC 31 March 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. Comparing the two methods, we found two probability centers in GW results, as shown in Fig. 13e, which corresponded to the two rain areas in the actual situation. Although the center location slightly deviated from the observed ones, the probability prediction effect of the GWs was better in the center location relative to that of EWs shown in Fig. 13a. In addition, in the black rectangular areas in Figs. 13c, g, it is clear that the GWs method covered the zero probability area of EWs and more effectively captured the occurrence of heavy precipitation there.

    Figure 13.  The neighborhood ensemble probability (NEP; %) distribution of hourly precipitation exceeding 15 mm h−1 from 2300 UTC 30 to 0200 UTC 31 March in case 1, in which the black solid line represents the contour of the observed precipitation of 15 mm h−1. Boxed regions are for detailed comparison.

    In case 2, the NEP distribution obtained by the GWs was closer to the observation than the EWs. 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, and the effect was not as good as the GWs. In addition, the advantage of the GWs was also reflected in the rainbelt 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 UTC 30 July in case 2, in which the black solid line represents the contour of the observed precipitation of 10 mm h−1. Boxed regions are for detailed comparison.

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

5.   Conclusions
  • This paper considered the differences among grid points within the local radius in the LBGM to generate ICP for convection-permitting ensemble prediction, and proposed the idea of using the GWs in place of the original EWs. By examining the effects of GWs and EWs in two squall line cases, the morphological distributions of the ICPs and their kinetic spectra were analyzed. We then verified the consistency between the RMSE and the ensemble spread in the forecasts of perturbation variables and the precipitation under these two weighting methods. The main conclusions are as follows.

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

    (2) 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 mesoscale information.

    (3) As shown in the forecasts of nonprecipitation variables, the consistency between the RMSE and the ensemble spread for the GWs was better than that for EWs, with improved forecast skills for wind, temperature, geopotential height, and humidity.

    (4) Evolution of precipitation during the squall line processes under both the GWs and EWs was consistent with the observation. The simulated precipitation structure by the GWs was better than that by the EWs. Also, the NEP distribution further demonstrated that the GWs could provide more effective probability guidance for the forecast of the squall lines.

    Compared with the 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 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 more cases of strong convection will be employed to further study the LBGM method using the GWs.

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

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