J. Meteor. Res.  2017, Vol. 31 Issue (5): 955-964 PDF
http://dx.doi.org/10.1007/s13351-017-6695-0
The Chinese Meteorological Society
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#### Article Information

LI, Xiang, Hongrang HE, Chaohui CHEN, et al., 2017.
A Convection-Allowing Ensemble Forecast Based on the Breeding Growth Mode and Associated Optimization of Precipitation Forecast. 2017.
J. Meteor. Res., 31(5): 955-964
http://dx.doi.org/10.1007/s13351-017-6695-0

### Article History

in final form April 30, 2017
A Convection-Allowing Ensemble Forecast Based on the Breeding Growth Mode and Associated Optimization of Precipitation Forecast
Xiang LI1,2, Hongrang HE1,2, Chaohui CHEN1,2, Ziqing MIAO3, Shigang BAI4
1. College of Meteorology and Oceanography, PLA University of Science and Technology, Nanjing 211101;
2. Nanjing Joint Center of Atmospheric Research, Nanjing 210009;
3. PLA Troop 96219, Kunming 650200;
4. PLA Troop 96319, Puning 515347
ABSTRACT: A convection-allowing ensemble forecast experiment on a squall line was conducted based on the breeding growth mode (BGM). Meanwhile, the probability matched mean (PMM) and neighborhood ensemble probability (NEP) methods were used to optimize the associated precipitation forecast. The ensemble forecast predicted the precipitation tendency accurately, which was closer to the observation than in the control forecast. For heavy rainfall, the precipitation center produced by the ensemble forecast was also better. The Fractions Skill Score (FSS) results indicated that the ensemble mean was skillful in light rainfall, while the PMM produced better probability distribution of precipitation for heavy rainfall. Preliminary results demonstrated that convection-allowing ensemble forecast could improve precipitation forecast skill through providing valuable probability forecasts. It is necessary to employ new methods, such as the PMM and NEP, to generate precipitation probability forecasts. Nonetheless, the lack of spread and the overprediction of precipitation by the ensemble members are still problems that need to be solved.
Key words: convection-allowing ensemble forecast     breeding growth mode (BGM)     precipitation optimization     probability matched mean (PMM)     neighborhood ensemble probability (NEP)     Fractions Skill Score (FSS)
1 Introduction

Since chaos theory was proposed by Lorenz (1963), ensemble forecast has been rapidly developed as a forecasting concept that could be distinguished from the traditional single deterministic forecast. Today, the world’s leading numerical forecast centers have all established their own operational ensemble forecast systems. The ensemble forecast was first applied in global long- and middle-term weather forecasts, and its use has gradually expanded to short-term weather forecasts. In terms of spatial scale, the focus of studies has changed from global to regional forecasting. The ensemble forecast adopting varying initial conditions (ICs) is a classical ensemble method. A series of methods to produce IC perturbations has been developed, including the Ensemble Transformation (ET) and the Ensemble Transformation Kalman Filter (ETKF; Bishop and Toth, 1999; Bishop et al., 2001). These methods aim to generate the nonlinear perturbations with the fastest growth rate through a dynamical cycle. In this sense, they are based on the breeding growth mode (BGM; Toth and Kalnay, 1993). The difference is that the ET and ETKF are controlled by the analysis error covariance matrix from the data assimilation system.

Strong convection can bring severe weather, and therefore many countries attach great importance to convective-scale weather forecasting and have developed high-resolution numerical models. Despite this, the forecasting of convective-scale weather is still subject to high levels of uncertainty, due to the high nonlinearity and rapid growth of the errors in convective-scale weather systems. In recent years, the UK Met Office (Tennant, 2015) used three methods, namely, downscaling, large-scale perturbation centering, and short-perturbation rapid cycling, to conduct convective-scale ensemble forecast experiments. In the Consortium for Small Scale Modeling (COSMO) model, investigators conducted a series of convective-scale ensemble forecast experiments (Bentzien and Friederichs, 2012; Kühnlein et al., 2014). In the United States, the National Center for Atmospheric Research (NCAR) and the Center for Analysis and Prediction of Storms (CAPS) at the University of Oklahoma have also conducted a series of convection-allowing ensemble forecast experiments (Xue et al., 2007; Kong et al., 2008, 2009; Clark et al., 2012; Romine et al., 2014; Schwartz et al., 2014, 2015), and made preliminary assessments on the forecast results. These experiments led to an increased interest in the convection-allowing ensemble forecast. Through the perturbation of physical processes, models, and ICs, ensemble members with a 4-km horizontal grid spacing were produced to establish the ensemble forecast system, and then the sensitivity related to physical processes and post-processing techniques was studied (Schwartz et al., 2010; Johnson et al., 2011). With the establishment of a continuously cycling Ensemble Kalman Filter (EnKF) analysis–forecast system, NCAR initialized their ensemble forecast system and conducted continuous operational convection-allowing ensemble forecast experiments and case studies (Schumacher and Clark, 2014; Jones et al., 2015; Weisman et al., 2015). These studies indicated that convection-allowing ensemble forecasts could improve forecast accuracy to a certain extent and provide valuable probability guidance.

Researchers in China have primarily concerned about local mesoscale (rather than convective scale) ensemble forecasts in recent years. The different physical mode method (DPMM) was proposed by Chen et al. (2005) to produce perturbations that reflect mesoscale features, so the generated perturbation can represent the instability of a mesoscale weather system. A regional ensemble forecast experiment was conducted by using China’s Advanced Regional Eta-coordinate Model (AREM; Li et al., 2010). The results indicated that the ensemble forecast performed better than the control, but the ensemble mean (EM) only improved the precipitation forecast under heavy rainfall cases. A multi-model ensemble forecast system was established by combining three mesoscale models: AREM, Mesoscale Model 5 (MM5), and Weather Research and Forecasting (WRF) model (Chen et al., 2009). The system was applied to weather forecasting during the Yangtze River flood season, with the result showing that the ensemble forecast outperformed the control forecast. Three perturbation schemes, that is, ICs, ICs combined with physical processes, and ICs combined with physical processes and lateral conditions, were designed based on the Global and Regional Assimilation and Prediction System (GRAPES; Zhang et al., 2014). The results showed that when considering perturbations of physical processes and lateral conditions, the ensemble spread can be substantially improved. Despite these, there have been few studies on convection-allowing ensemble forecasts.

Compared with traditional ensemble forecast, convection-allowing ensemble forecast has some advantages, but also faces several difficulties. A convective-scale weather system is highly nonlinear, and unlike large- and synoptic-scale weather systems, it can experience a rapid growth of perturbation. It is still uncertain whether the methods presently used to determine perturbation can still be applied to convective-scale weather ensemble forecasts. In addition, a high-resolution numerical model is required for convection-allowing ensemble forecast, which results in considerable computation complexity. How to establish a highly effective ensemble forecast system is also a problem. A convection-allowing ensemble forecast requires a highly localized forecast, and how to advance a perturbation generation method that can reflect such local features has still not been resolved. The traditional method to produce an EM forecast or probability forecast is unsuitable for a convection-allowing ensemble forecast due to the high resolution and more precise forecast requirements. For example, the EM usually under predicts precipitation, and therefore new techniques adapted to convection-allowing ensemble forecasts are needed with appropriate evaluation.

In this study, an ensemble forecast experiment was conducted on a squall line with the IC perturbation initialized by the BGM. To optimize the precipitation forecast, the probability matched mean (PMM) and neighborhood ensemble probability (NEP) were used. The probability forecast was evaluated through the Fractions Skill Score (FSS), which enables the convection-allowing ensemble forecast to be properly considered. Section 2 of this paper describes the convective-scale weather case and some experimental schemes in detail. Section 3 introduces the methods used to produce EM and probability forecasts, as well as the evaluation of the probability forecast. Section 4 analyzes the results of both EM and probabilistic forecasts. Section 5 provides a summary and discussion.

2 Test cases and experimental scheme

From the night of March 29, 2014 to the afternoon of March 31, 2014, a severe convective weather process swept across southern China from the west to the east. It covered a wide area, including the provinces of Yunnan, Guangxi, Guangdong, and Jiangxi, and was accompanied by many short but strong convective processes, which caused severe natural disasters such as gales and hails (e.g., on March 30, Huiyang City observed Level 12 gusts and Yunfu City recorded 50-mm diameter hail). A severe squall line affected most of the area of Guangdong Province from 1200 to 2000 UTC on March 30, and caused a rainstorm with a maximum rainfall of 160 mm.

An experiment was conducted with version 3.6 of the nonhydrostatic WRF model. It started at 0600 UTC 30 March, with a forecast duration of 24 h. As Fig. 1 indicates, the model was run over a nested computational domain, with a two-way feedback. The horizontal grid spacing was 3 km with 279 × 237 grids in the internal nest (D02), and it was 9 km with 288 × 213 grids in the outer domain (D01). Both domains were configured with 35 vertical levels. The same physical parameterization schemes were used for all ensemble members ( Table 1) in order to study the forecast effect of the IC perturbation. The lateral boundary condition of the outer domain was updated every 3 h.

 Figure 1 The computation domain. In the breeding stage, a single domain with a 9-km horizontal grid resolution was used. During the forecast stage, a two-way nested grid was applied.
Table 1 Basic physical parameterization settings
 Physical parameterization Outer domain Inner domain Cumulus Grell–Freitas scheme None Microphysics Lin scheme Longwave radiation RRTM scheme Shortwave radiation Dudhia scheme Planetary boundary layer Yousei University scheme (YSU) Land surface Five-layer thermal diffusion

The BGM method was used to generate IC perturbation members (Fig. 2). The breeding period lasted 3 days, with a 6-h breeding cycle. A single domain with a 15- km grid spacing was used during the breeding stage. To obtain the IC perturbation, a 6-h forecast initialized at 0000 UTC 27 March was run. Then, the root-mean-square error (RMSE) between the forecast and analysis was calculated. Random numbers, which were distributed uniformly between 0 and 1, were added to this forecast RMSE to obtain the initial perturbations. After one breeding cycle was finished, the NCEP Global Forecast System (GFS; 0.5° × 0.5°) analysis in the current moment was introduced as the background field to rescale the perturbation. The specific rescale rule adopted here is to force the perturbation to be equal to the IC perturbation in terms of the RMSE, using the following formula:

 $x t ' x t = e 0 e t ，$

where ${{{x}}_t}$ is the current perturbation field after one breeding cycle; x t ' is the rescaled ${{{x}}_t}$ ; e0 is the initial RMSE value of the perturbation field; and et is the current RMSE value of ${{{x}}_t}$ . The ensemble forecast with IC perturbation members started after the breeding was finished. The control forecast was the forecast initialized by GFS data, without the addition of perturbation.

 Figure 2 The process flow for producing IC perturbation by the BGM. The solid line represents the development of a perturbation forecast. The dashed line represents the perturbation itself. The circles indicate the background field introduced at the beginning of every breeding cycle.

The China Hourly Merged Precipitation Analysis (CHMPA) from the National Meteorological Information Center (NMIC) was used as the observation field for comparison. CHMPA has a resolution of 0.1 degree. Data from the GFS was used to drive the model.

3 Methods

A convection-allowing ensemble forecast produces a regional feature, with a short period of validity, strong uncertainty, and large computation complexity. Here, we used traditional perturbation generation methods, which are relatively simple, to produce preliminary EM and probabilistic forecasts. To reflect the features of convective-scale weather systems, information from each ensemble member should be integrated. Hence, the PMM, NEP, and FSS were used for analysis together with grid precipitation and hourly accumulated precipitation.

3.1 PMM

The EM is the traditional method for producing an ensemble forecast by simply calculating the average of the results from the ensemble members. Although the EM can colligate the information from all members, it tends to eliminate heavy precipitation and induce relatively light rainfall after averaging, due to the different spread directions of ensemble members. The forecast ability of extremely heavy precipitation is consequently degraded. Therefore, the PMM (Ebert, 2001) was adopted here to generate EM precipitation forecast. The PMM procedure consists of the following steps (Fig. 3). In Fig. 3, n is the number of ensemble members, m is the total number of grids, and S is the rainfall amount for a certain grid.

 Figure 3 The probability matched mean (PMM) procedure. Sequence I is composed of the ensemble mean (EM) values of total grids in descending order. Sequence II consists of the precipitation in all grids from n members, and is sorted in descending order. Sequence III is a subset extracted from sequence II, with an interval of n.

Finally, the PMM of all grids is generated. Concrete steps of PMM are as follows:

(a) Calculate the EM value of each grid i:

 ${\rm{E}}{{\rm{M}}_i} = \frac{1}{n}\sum\limits_{k = 1}^n {{S_{k,i}}} .$

Order all grids inside the domain from the largest to the lowest according to their EM values to obtain sequence I.

(b) Arrange the rainfall amount in all grids from all members in a descending order to form sequence II.

(c) Produce a new sequence (sequence III) through extraction from sequence II, with an interval of n, and keep the original sequence. Sequence III will have the same length, with a grid number m.

(d) Determine the PMM value. Start from the grid with the largest EM value in Sequence I, making the PMM of this grid the largest value of Sequence III. Similarly, the PMM value of the grid at the second value of Sequence I should correspond to the second value of Sequence III, and so do the following grids. If the EM equals 0 at grid i, force the PMM of grid i to be zero to retain consistency with the EM field.

The PMM takes the precipitation in all grids from all ensemble members into account and contains information for various types of precipitation. It can ensure the basic structure of the EM field. Compared to the EM method, the PMM will reserve the heavy precipitation value from some ensemble members, which may be beneficial for forecasting extreme precipitation events associated with severe convective weather systems.

3.2 NEP

An ensemble forecast can provide guidance regarding the probability of precipitation. The most common method of achieving this is to transform the precipitation events into a discrete dichotomous number [0/1] and take the average of all ensemble member forecasts. This method regards each grid as an independent individual, without considering the relationship created by the spatial distribution of precipitation. However, the effect of interaction among grids cannot be ignored with respect to the strong nonlinear function of convective-scale weather systems. In addition, for high-resolution numerical modeling, the forecast skill at the grid scale is not accurate enough. Therefore, the NEP method was employed here to combine the results of surrounding grids, reflect the effects of weather systems, and produce more reasonable probability forecasts (Ebert, 2009). A neighborhood circle is specified with a radius of influence r and a center point i (Fig. 4). According to Roberts and Lean (2008), the optimal radius of influence varies within a single model configuration and is a function of lead time. The optimal value of r is unknown, and may vary from model to model. Through experimental trials, 18 km was selected as the radius of influence in this study. Unity was placed where the precipitation at neighboring grids exceeded a certain threshold, whereas zero was placed in another neighboring grid. Then, the precipitation probability of the center grid was the sum of the neighboring grids divided by the grid number, which was referred to as the neighborhood probability (NP). If each ensemble member is equally weighted, NEP is defined by the average of all the ensemble NP values. Because there is a corresponding probability distribution for each precipitation field, the NEP can be employed to the control forecast of all ensemble members as well as the observation to enable a direct comparison.

 Figure 4 The neighborhood ensemble probability (NEP) procedure. Here, r is the radius of influence of the center grid. Grids inside the circle are considered to be in the neighborhood of the center grid. If the precipitation in a grid exceeds a certain threshold, it is recorded as 1; if not, it is recorded as 0.
3.3 FSS

The Brier Skill Score (BSS) is a commonly used method to evaluate the probability forecast. It transforms the observed precipitation into discrete integers, 0 or 1. However, the probability forecast is a continuous fraction located between 0 and 1, and therefore, it is imprecise to compare it with the observation directly. The observed precipitation can be transformed into continuous fractions through the NEP method, as described in the previous subsection, and can then be compared with the probability forecast. Therefore, the FSS method, which was based on the BSS method, was proposed by Roberts (2005). In this method, first, the neighborhood probability of forecast field NPF and observation field NPO is calculated by the NEP, and then the Fractions Brier Score (FBS) is given by:

 ${\rm{FBS}} = \frac{1}{m}\sum\limits_{i = 1}^m {{{({{\rm NP}\!_{{\rm F}(i)}} - {{\rm NP}\!_{{\rm O}(i)}})}^2}} .$

For the BSS, a small FBS value indicates a good probability forecast, while a larger FBS value means that the correlation between forecast and observation fields is smaller. It is obvious that the grids with no precipitation (whether in the observation or forecast field) have a large impact on the FBS. They are influenced by the precipitation event itself and cannot objectively describe the effect of the probability forecast. Therefore, a reference parameter is needed to eliminate the impact of the grids with no rainfall. The parameter is termed FBSworst, and is produced by:

 ${\rm{FB}}{{\rm{S}}_{{\rm{worst}}}} = \frac{1}{m}(\sum\limits_{i = 1}^m {{\rm NP}\!_{{\rm F}(i)}^{\,2} + \sum\limits_{i = 1}^m {{\rm NP}\!_{{\rm O}(i)}^{\,2}} ).}$

In this case, the non-zero fractions of the two fields are not overlapped ( ${{\rm NP}\!_{\rm F}} = 0$ , but ${{\rm NP}\!_{\rm O}} \ne 0$ or ${{\rm NP}\!_{\rm O}} = 0$ , while ${{\rm NP}\!_{\rm F}} \ne 0$ ). Then the FSS can be expressed as:

 ${\rm{FSS}} = 1 - \frac{{{\rm{FBS}}}}{{{\rm{FB}}{{\rm{S}}_{{\rm{worst}}}}}}.$

The FSS ranges continuously between 0 and 1, and therefore it provides a more precise description of forecast skill. When the FSS value reaches 1, the forecast effect is optimal; whereas, when the FSS is zero, the worst forecast effect is achieved. The FSS can evaluate any probability distribution, including the EM, PMM, control, and observation fields, and can therefore be used to compare these fields directly.

4 Results of the analysis 4.1 Ensemble mean forecast

The evolution of hourly precipitation for the whole area (in the internal nest) over time is shown in Fig. 5. The precipitation was less than observed during the first 4 h, because it was in the spinning up stage of the model. The orange and red lines are totally overlapped, which means that the EM and PMM had an equal effect when considering the total precipitation. However, they were better than the control forecast, in which the rainfall was clearly lower than in the observation. The precipitation tendency produced by ensemble forecasts was relatively consistent with the observation, especially at the sixth hour when the second precipitation peak occurred. This occurred 2 h later in the ensemble forecast compared with the largest precipitation peak of the observation (the 14th hour). At the same time, ensemble members can also reflect the precipitation tendency and produce larger rainfall amounts than the control forecast. This indicates that the BGM could identify the direction of fast growing perturbations in the breeding stage and generate a growing perturbation with convective-scale dynamics, which can be transferred from the 9-km horizontal resolution grids in the breeding stage to two-nested areas in the forecast time.

 Figure 5 Evolution of the total hourly precipitation in the forecast area. CONT represents the control forecast and the observed precipitation is fom the China Hourly Merged Precipitation Analysis (CHMPA). The orange, red, green, and blue lines represent the ensemble mean (EM), probability matched mean (PMM), the control forecast, and the observation, respectively. The shadow envelope indicates the forecasts of the ensemble members.

The grid coverage of the precipitation at different thresholds was also calculated to determine the forecast performance for different types of precipitation (Fig. 6). When the threshold was between 0.25 and 5 mm h–1 (Figs. 6ad), both the areal coverage of PMM (red line) and the control forecast were lower and had a large disparity with the observation, while the EM was closer to the observation whether in the precipitation quantity or tendency (orange line). A slight lag in the precipitation peak time forecast was observed. The grid coverage of precipitation of ensemble members was generally smaller than the observation, and therefore they did not contain sufficient information regarding light precipitation. Nonetheless, when the precipitation exceeded 10 mm h–1 (Fig. 6e), the EM performance worsened as a result of the weakening impact of EM on heavy precipitation. As the threshold increased to 16 mm h–1 (Fig. 6f), which is classed as a rainstorm, the EM was almost zero during the 12–20-h period. Here, it was apparent that the EM was unsuitable for large precipitation. However, the PMM was closer to the observation at this time, and could predict the precipitation peak relatively accurately. The forecasts of ensemble members were basically larger than the control forecasts and EM, and the top of the envelope was very close to the precipitation peak, which demonstrates that the perturbation produced by the BGM can effectively reflect the possible development directions of the atmosphere. Therefore, the PMM can be considered to integrate the ensemble member forecasts and overcome the disadvantages of using the EM in extreme precipitation events.

 Figure 6 Evolution of the areal coverage of precipitation exceeding (a) 0.25, (b) 0.5, (c) 1.0, (d) 5.0, (e) 10.0, and (f) 16 mm h–1. The legend is the same as in Fig. 5. The area coverage is the ratio of the number of the grids that exceed a certain threshold to the total grids.

To compare the ensemble and control forecasts, the accumulated precipitation during the 12–20-h period of heavy precipitation was analyzed (Fig. 7). It can be seen that the rainfall amount in Figs. 7c, k, o was clearly higher. Because the values at the top part of the PMM sequence were largely derived from the high precipitation grids, which appear in ensemble members (c), (k), and (o), these members may have a significant influence on the distribution given by the PMM (Fig. 7s), in which the precipitation was larger than the observation. The distribution of the precipitation of the EM and PMM was similar to the observation, but the EM field was much smaller than the observation, while the PMM field was larger. The precipitation center of the control forecast was very different from that of the observation. Compared with the control forecast, the ensemble forecast produced a more accurate distribution of precipitation.

 Figure 7 Distributions of the accumulated precipitation (mm) during 12–20 h. Panels (a)–(p) are ensemble members, and (q)–(t) represent the control forecast, EM, PMM, and the observation, respectively.
4.2 Probability forecast

The evolution of an FSS exceeding different precipitation thresholds is shown in Fig. 8. The highest FSS value was obtained for precipitation greater than 1 mm h–1 (Fig. 8c), followed by 5 and 10 mm h–1 (Figs. 8d, e, respectively). The score of 16 mm h–1 threshold was the lowest (Fig. 8f). Therefore, for moderate intensity precipitation, the probability forecast provides good guidance. Overall, the EM and PMM method results were better than those of the control forecast, especially at precipitation levels greater than 1 mm h–1 and less than 16 mm h–1 (Figs. 8ce). When precipitation exceeded 16 mm h–1, the forecast skill of the EM was nearly 0, while the PMM performed better than the EM and control forecast. It was noticeable that the range of the ensemble member FSS values was relatively large, and the maximum value was larger than the EM and PMM values. At the threshold of 16 mm h–1, the maximum of the ensemble members was more than 0.6, while it was only 0.2 for the PMM. With an increase in forecast time, the FSS of ensemble members tended to spread, which indicated that the difference among ensemble members was more obvious during the late forecast period. This was also observed at the higher precipitation threshold. This phenomenon indicates the forecast capabilities of some ensemble members in heavy rainfall, which should be considered when analyzing the ensemble forecast result. Through the probability forecast results, it can be seen that although relatively lower-resolution grids were applied in the breeding stage, the BGM could determine the fastest growing direction of the perturbations and passed it to the nested grids, and then produced suitable forecasts.

 Figure 8 Evolution of the Fractions Skill Score (FSS) for precipitation exceeding (a) 0.25, (b) 0.5, (c) 1.0, (d) 5.0, (e) 10.0, and (f) 16 mm h–1. The legend is the same as in Fig. 5.

The spatial distribution of probability of two different thresholds when precipitation was largest (the 14th hour) is shown in Fig. 9. For light precipitation, the EM was closer to the observation (Fig. 9b) than PMM, because PMM was strongly affected by the members with large precipitation (see Fig. 7) and the areal coverage of light precipitation diminished. Although its areal coverage was smaller, the PMM could reflect the basic form of the probability distribution (Fig. 9c). A distinct area in the center with a large probability can be observed in the control forecast (Fig. 9a). For heavy precipitation, the probability coverage of EM was very small and deviated considerably from the observation (Fig. 9f). This was due to the elimination effect of the EM method. Compared with the observation field, the PMM could reflect the partial distribution of the probability (Fig. 9g). However, the control forecast had a worse performance.

 Figure 9 The neighborhood ensemble probability (NEP) distribution at the 14th hour. Results from (a, e) the control forecast, (b, f) the ensemble mean (EM), (c, g) probability matched mean (PMM), and (d, h) the observation, are shown for the areas where precipitation exceeded (a–d) 1 mm h–1 or (e–h) 16 mm h–1.
5 Conclusions

A convection-allowing ensemble forecast experiment on a square line was conducted based on the BGM method. The breeding process was run on a single domain to decrease the computation complexity and two-way nested grids were used in the forecast stage. Considering the high-nonlinearity and precise forecast requirements, the PMM and NEP were introduced to optimize the EM and probability precipitation forecast. The FSS was employed to evaluate the probability forecast. Several conclusions have been drawn.

(1) When applied in a convection-allowing ensemble forecast, the BGM could determine the uncertainty in the atmosphere and generate rapidly growing dynamic perturbations through a cyclical breeding process. The ensemble members composed of these perturbations improved precipitation forecasts to a certain extent. A single domain was advisable during the breeding stage to decrease the computation complexity and the results can be interpolated into the inner domain to initialize the forecast process.

(2) The convection-allowing ensemble forecast was more accurate than the control forecast for both the amount and distribution of precipitation, and thus improved the forecast skill.

(3) The EM method produced the basic spatial distribution of precipitation and was more precise in the ensemble mean forecasting and the probability forecasting of light precipitation. However, the ability of ensemble mean forecasting weakened with an increase in precipitation and became poorer for heavy precipitation.

(4) The PMM ensured the basic structure of the EM field and made full use of the information provided by the ensemble members at the same time. It could overcome the disadvantage of the EM in heavy rainfall forecasts, and may improve the forecast skill for extreme weather events caused by convective weather systems.

(5) As a new method to produce probability precipitation forecasts, the NEP was able to reflect the relationship among the grids that were affected by convective-scale weather systems. The observation field was transformed to continuous fractions by the NEP method, and then the FSS could be used to evaluate the probability forecast.

There are still some problems demanding resolutions regarding convection-allowing ensemble forecasts. For example, the spread of the ensemble members is not adequate, and the precipitation forecasts of the ensemble members are generally higher than the observations. More experiments are required to determine the perturbation schemes in various areas because of the localized features of convection-allowing ensemble forecasts. Further studies will focus on these aspects to further the development of convection-allowing ensemble forecasts.

Acknowledgments. We thank the National Meteorological Information Center (NMIC) of the China Meteorological Administration and NCEP for providing the relevant data. We also appreciate Hongsheng Zhang for his enthusiastic help.

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