Precipitation is a crucial element in the hydrological cycle at regional or global scales. With the characteristics of high intensity, short duration, uneven distribution and sudden occurrence, the precipitation easily causes floods, with a high peak in semi-humid regions, which is tricky for forecasting accurately (Nikolopoulo et al., 2010). The quantitative precipitation forecast (QPF) is an effective method to avoid flood disasters and help flood risk management (Kryza et al., 2013). With the development of computer technology and atmospheric physics, numerical weather prediction (NWP) has become an efficient method for QPF (Yang et al., 2012).

As the latest-generation mesoscale NWP system, the Weather Research and Forecasting (WRF) model can apply to the regions across scales from tens of meters to thousands of kilometers. Not only the rainfall quantity but also the spatial and temporal patterns of rainfall can be captured by the WRF model with high resolution. Though it has been confirmed by many studies that the WRF model performs better than the fifth-generation Penn State/NCAR (National Center for Atmospheric Research) Mesoscale Model (MM5), rainfall is still one of the most difficult variables to simulate and predict (Collischonn et al., 2005; Bruno et al., 2014; Lee et al., 2015). Because of the complicated processes of storm formation and development, the WRF model provides various physical parameterizations to be applied in different cases. Each physical parameterization emphasizes on different physical processes and has its unique structure and complexity, which may have great influence on the rainfall simulations. That is why numerous sensitivity studies of the WRF parameterizations are carried out in different regions of the world (Klein et al., 2015). Three categories of the parameterizations have been mostly discussed and identified as the main influencing factors for rainfall simulation, i.e., microphysics, planetary boundary layer (PBL) and cumulus parameterizations. Different physical parameterizations are found to be efficient for different rainfall events in different regions (Jankov et al., 2011; Madala et al., 2014; Pennelly et al., 2014).

It is an increasingly difficult task to determine the optimal combination of physical parameterizations due to the development of the WRF model with more and more choices of parameterizations. Although many studies show that the best physical parameterization combination can be determined by many simulations for a certain rainfall event, it is difficult to tell the characteristics of the future rainfall events for real-time rainfall prediction. In order to consider the uncertainties associated with the selection of physical parameterizations, it has become a common method to use the ensemble in numerical rainfall prediction (Evans et al., 2011). Flaounas et al. (2011) studied an ensemble with six members over West Africa, which was produced by two PBL and three cumulus parameterizations. An ensemble containing 18 members was investigated in the south-central United States, which was created by three microphysics, three PBL and two cumulus parameterizations (Jankov et al., 2005). And an ensemble with 36 members was tested for a series of rainfall events at the south-east coast of Australia, which contained two PBL, two cumulus, three microphysics and three radiation parameterizations (Flaounas et al., 2011). These studies show that no single physical parameterization combination performs the best for all rainfall events.

In this study, 16 physical parameterization combinations are designed from two microphysics, Purdue–Lin (Lin) and WRF Single-Moment 6 (WSM6), two PBLs, Yonsei University (YSU) and Mellor–Yamada–Janjic (MYJ), and three cumulus parameterizations, Kain–Fritsch (KF), Grell–Devenyi (GD) and Betts–Miller–Janjic (BMJ). Lin is a sophisticated parameterization which contains five classes of hydrometeors, and it is suitable for high-resolution simulations (Lin et al., 1983). WSM6 reveals an improvement in the high cloud amount and surface precipitation, which adds graupel microphysics based on the works of Lin et al. (1983) and Rutledge and Hobbs (1983). MYJ PBL is appropriate for all stable or slightly unstable flows (Janjic, 1994). YSU PBL improves the performance of intense convection based on the Medium Range Forecast (MRF) PBL (Hong et al., 2006). KF is a classic cumulus parameterization and has been used successfully for years in many scientific institutions (Kain, 2004). GD is an ensemble cumulus parameterization and can be used in high resolution models (Grell and Freitas, 2014). BMJ can adjust instabilities in the environment by generating deep convection and has been used extensively throughout the globe (Janjic, 2000).

Two medium sized catchments, the Fuping and Zijingguan, are chosen as the study sites, which are respectively located in the south and the north reaches of the Daqinghe catchment in North China. With the characteristics of high intensity, short duration, uneven distribution and sudden occurrence, the storm events in the study sites are representative for the semi-humid region with temperate continental monsoon climates. The aim of this study is to determine the potential performance of the WRF model for different types of storm events in semi-humid regions. Six storm events are chosen from the study sites and classified into four different types based on the rainfall evenness in the spatial and the temporal dimensions. The 16 designed combinations of physical parameterizations are treated as the ensemble for rainfall simulation, and the results regarding both the cumulative rainfall amounts and the spatiotemporal patterns are verified.

Version 3.6 of the WRF model is used in this study. WRF is a fully compressible, nonhydrostatic, meteorological model, and it features physics, numerics, advanced dynamics and data assimilation. The model manual (Skamarock and Klemp, 2008) shows more detailed information of the WRF model. Two-way nesting is allowed for the communication between multiple domains at different grid resolutions, and three nested domains are centered over the Fuping and Zijingguan catchments respectively. In general, high-resolution rainfall products downscaled by the WRF model are more appropriate to be used as the input of the hydrological models (Cardoso et al., 2013; Chambon et al., 2014). Therefore, horizontal grid spacing of the WRF innermost domain is set to be 1 km, and the downscaling radio is set to be 1:3 (Givati et al., 2012; Yang et al., 2012). The center of the domain is at lat 39∘04′15′′ N and long 113∘59′26′′ E, and the nested domain sizes are 252 × 234, 144 × 126 and 96 × 84  km2 for the Fuping catchments. The center of the domain is lat 39∘ 25′59′′ N and long 114∘ 46′01′′ E, and the nested domain sizes are 216 × 198, 108 × 90 and 72 × 42  km2 for the Zijingguan catchment. The nested domains and the orography of the two catchment are shown in Fig. 1. There are 40 vertical levels for three domains, and the top level is set at 50 hPa (Aligo et al., 2009; Qie et al., 2014). The WRF model is initialized from the six-hourly global analysis data provided by the 1∘ × 1∘ grids of the NCEP (National Centers for Environmental Prediction) Final (FNL) operational model. The integration step of WRF follows the “6 × dx” rule where dx is the grid spacing, and the integration step is 6 s for the innermost domain (Skamarock and Klemp, 2008). The time step of the WRF model output is set to 1 h. The spin-up period is necessary for the WRF model to develop the smaller scale convective features, and the widely used lengths are 6 h (Givati et al., 2012), 12 h (Hu et al., 2010) and 24 h (Wang et al., 2012). Different spin-up lengths were tried for the six storm events in this study, whereas the results did not show obvious differences regarding the simulated rainfall. In order to improve the calculation efficiency for further hydrological use (i.e., flood warning), a 6 h period is chosen to spin up the model. That is to say, the start of the model integration is 6 h earlier than the storm start time, and the end time of the model integration is consistent with the storm end time.

The setting of the WRF model is very important before it is used to simulate the meteorological factors, especially the physical parameterizations. As shown by Table 1, a WRF physical ensemble is constructed by combining different choices of the physical parameterizations to simulate the storm events in the study areas. The selection of the parameterizations is based on their good performance in semi-humid regions of China (Givati et al., 2012; Qie et al., 2014; Di et al., 2015). In order to learn the physical parameterizations more comprehensively, the different complexity and mechanisms are also considered. WSM6 is the most complex in the series of WSM schemes, which is revised based on Lin (Hong and Lim, 2006). YSU is a non-local closure scheme, while MYJ is a local closure scheme (Evans et al., 2011). The KF is a simple cloud model which can be triggered when air parcel temperature at its lifting condensation level is larger than the environmental air (Pennelly et al., 2014). The GD can run effectively within each high resolution grid (Grell and Freitas, 2014). The BMJ scheme is more suitable for convective weather because it can adjust the model profile of temperature and moisture (Janjic, 2000). Some studies have indicated that the cumulus parameterizations may be invalid with fine horizontal resolutions, while the threshold of the resolution is unknown (Argüeso et al., 2011; Evans et al., 2011; Pei et al., 2014). Many studies use cumulus parameterizations with about 1 km resolution for weather simulation. For example, Shepherd et al. (2016) explored the effect of simulation for tropical cyclones by four cumulus parameterizations, including KF, BMJ, G-3 and TD, with the nested domains 1.33, 4 and 12 km. Remesan et al. (2015) studied the WRF model sensitivity to the choice of parameterizations: 4 nested domains (1, 3, 9 and 27 km) are used, and the cumulus parameterizations of GD, BMJ, KF1 and KF2 are investigated. In order to make the study more rigorous, members 13, 14, 15 and 16 are also tested and compared with the members containing cumulus parameterizations. Many studies indicate that the simulation of precipitation is insensitive to the land surface model (LSM) and short- and long-wave radiation parameterizations, so Noah for LSM, the RRTM and Dudhia schemes for long wave and shortwave radiation are used in this study, which are most frequently applied to precipitation simulation (Guo et al., 2014; Chen et al., 2014).

In this study, the performances of 16 WRF physical members are estimated firstly by AREs for cumulative rainfall amounts and then by a two-dimensional verification scheme for spatiotemporal rainfall distributions. According to the spatiotemporal evenness, six storm events are classified into four storm types. Storm type 1 has a two-dimensional evenness of rainfall which is even in the spatiotemporal distribution. The WRF model performs best for simulating this storm type, not only for the cumulative rainfall amounts but also for the spatiotemporal distributions. Storm type 2 is only even in space, and the simulation results from the WRF ensemble are better than storm types 3 and 4. But compared with type 1, the cumulative rainfall amounts of type 2 events are seriously underestimated. Storm types 3 and 4 are both uneven in spatiotemporal distribution, and the unevenness is especially remarkable for type 4 events. The simulations of the WRF model are unsatisfactory for the spatiotemporal patterns of the two storm types. The simulation results of type 4 events are the worst among the four storm types. Some of the members even miss the whole storm duration in space and time. It is interesting to find that the WRF model tends to underestimate the rainfall amounts except for storm type 1. With more events being investigated in the study sites, the general simulation errors of the WRF model can be determined by statistical analysis, which can help build a correction model to further improve the rainfall products of the WRF model.

For rainfall forecast operation, it is hard to identify the storm type before the storm occurs. Therefore it is important to determine the physical parameterizations which generally perform well. According to the REs of the 16 members for the six storm events shown in Table 5, the AREs of the six storm events for one certain member are calculated. It is interesting to find that members containing BMJ have relatively higher AREs, which are 52.49 % (member 9), 48.30 % (member 10), 48.35 % (member 11) and 49.05 % (member 12) respectively. The relative lower AREs (34.02–39.50 %) can be found in members which contain KF. The members containing GD perform better than members with BMJ while worse than members with KF. The range of the AREs is 42.32–44.53 %. The members without cumulus parameterization also perform better than members with BMJ while worse than members with KF, and the range of the AREs is 39.55–49.16 %. That is to say, the cumulus parameterizations have a significant effect on the performance of the WRF model and BMJ performs the worst in the three cumulus parameterizations. Janjic (2000) indicated that BMJ performed poorly in accurately reproducing the range and the intensity of the low-level jet. The strong ability of BMJ in simulating the upward transportation of vapor always results in underestimation of the rainfall amount. That is the main reason why BMJ is not a good choice in the study area. Additionally, it is necessary to use cumulus parameterization for the simulation of the rainfall accumulation and spatiotemporal rainfall distribution in the study area. However, the threshold of the horizontal resolution needs to be further discussed to determine whether to use the cumulus parameterization.

The uncertainties of the rainfall processes affect the choice of the physical parameterizations in a certain area. It is necessary to select the most appropriate physical parameterizations to design the physical ensemble for rainfall simulation and prediction. In this study, the 16 members of the physical ensemble are constituted from two microphysics, two PBL and three cumulus parameterizations, which are proven to be appropriate and widely used in the neighboring areas of the study sites (Hong et al., 2006; Miao et al., 2011; Pan et al., 2014). With the development of the WRF model, more sophisticated and realistic physical parameterizations could be developed and should be tested in the study area.

The verification of the WRF model has always been recognized as a worthy issue to be explored. In this study, a verification method which can estimate the rainfall simulations in both the spatial and the temporal dimension is used. It is assumed that the observations from rain gauges are accurate and representative for the two study sites. However, it brings uncertainties to use point-based observations to evaluate grid-based simulations. More grid-based observational data should be involved to improve the reliability of evaluation, especially those from weather radar and remote sensing.

Ultimately, the main goal of rainfall forecasts is to obtain efficient flood forecasts. The peak flood, flood peak appearance time and flood process are all significantly influenced by the rainfall accumulations and the spatiotemporal distribution of the rainfall (Schellekens et al., 2011; Cane et al., 2013; Fan et al., 2015). Event V, which occurred on 21 July 2012, has caused the greatest flood during the past 10 years in Jing-Jin-Ji (Beijing–Tianjin–Hebei) area and received widespread attention in China. The 24 h rainfall accumulation was 155.43 mm in the Zijingguan catchment, and the peak flow reached 2580 m3 s-1 at the catchment outlet. In such cases, accurate rainfall simulations and predictions can greatly help flood warnings. However, to analyze the usefulness of the WRF simulations to flood warning, the rainfall–runoff transformation processes should be further considered. This will involve many uncertainties, such as the choice of the rainfall–runoff model, the data used for model calibration and the involvement of a real-time updating scheme, which also has a considerable impact on the accuracy of the flood forecasting results. The exploration of different parameterizations for flood warning purposes is an important issue and worth discussing in further study.

In this study, the FNL data from NCAR provide the initial and boundary conditions for the WRF model, which is used for rainfall simulation of six representative storm events with a duration of 24 h in the Fuping and Zijingguan catchments, located in the south and the north reaches of the Daqinghe basin in semi-humid areas of North China. Two microphysics, two PBL and three cumulus parameterizations are selected to develop the 16 members of the physical ensemble of the WRF model. Both the cumulative amount and the spatiotemporal patterns of the simulated rainfall are analyzed and verified. The relative error is used to evaluate the 24 h accumulated areal rainfall. The spatial rainfall distributions and temporal rainfall patterns are verified by a two-dimensional verification scheme including four categorical and three continuous indices. The six storm events are classified into four types based on the spatiotemporal evenness of the rainfall. In general, the ranking of the average model performance for different storm types is type 1 > type 2 > type 3 > type 4, from the best to the worst, depending on both the cumulative rainfall amounts and the spatiotemporal rainfall patterns. A negative correlation is found between the simulation error and the rainfall evenness in both spatial and temporal dimensions. Storm events with more evenly distributed rainfall tend to have better simulation results in space and time. In addition, for the small catchment scale, accumulated areal rainfall is more important than the spatiotemporal rainfall distributions. According to the REs of rainfall accumulations, member 4 is the better choice for storm types 1, 2 and 4, while members 9, 10, 11 and 12 have the worse performance for storm types 1 and 4. For type 3 events, members 5 and 7 are the better choices. It provides a reference for choosing the optimal ensemble in the study area for different storm types.

This study provides a reference for ensemble simulation of different rainfall types in semi-humid areas of China in the WRF model. However, the simulated rainfall has relatively large errors, and the simulation results of the temporal rainfall patterns are always unreliable, especially the results of events III and V, which cannot be used directly in hydrological studies. Data assimilation has been proven to be an effective method in improving the rainfall simulation results of the WRF model by many studies (Ha and Lee, 2012; Liu et al., 2012; Routray et al., 2012). Data assimilation can ingest various sources of observations (surface observed data, radar data, satellite data and sounding data) into the WRF model products and then use the respective error statistics to update and correct the WRF model products (Wan and Xu, 2011; Ha et al., 2014; Xie et al., 2016). More studies should be carried out in the study sites with the assistance of data assimilation so that the rainfall products from the WRF model can be further improved.