Although the resolution of numerical weather prediction (NWP) systems is increasing with the improvement of computational efficiency and abundance of observation data, rainfall is still one of the most difficult meteorological factors to forecast (Lu et al., 2017; Avolio and Federico, 2018). A typhoon always comes with heavy rainfall which leads to great loss. However, due to the uncertainty of the rainfall and the imperfect generation of NWP systems, rainfall forecast with severe convection is unsatisfactory in medium and small catchment scales (Tian et al., 2017a). Data assimilation plays an important role in NWP and is always applied to correct the initial and lateral boundary condition of NWP systems, which can effectively improve the rainfall forecast (Mohan et al., 2015; Liu et al., 2018).

Various kinds of observation data have been tested and assimilated by different assimilation methods. Wan and Xu (2011) simulated a heavy rainstorm using the Weather Research and Forecasting (WRF) model with the Gridpoint Statistical Interpolation (GSI) data assimilation (DA) system in the central Guangdong Province of southeast China. The rainfall simulation error was reduced at 4 km grid scale by assimilating satellite radiance data, which helped to analyze rainfall causes accurately. Giannaros et al. (2016) evaluated a lightning data assimilation (LTNGDA) technique over eight rainfall events occurring in Greece. The verification scores of the rainfall simulations were significantly improved by the employment of the WRF-LTNGDA scheme, especially for heavy rainfall. Zhang et al. (2013) presented a regional ensemble data assimilation system that assimilated microwave radiances into the WRF model for hydrological applications. The rainfall simulations were improved in terms of the accumulated rainfall and spatial rainfall distribution in the southeastern United States. Yucel et al. (2015) assimilated conventional meteorological data by a three-dimensional variational data assimilation (3-DVar) model into the coupled atmospheric–hydrological system. The rainfall simulations, as well as the runoff simulations, improve significantly in large basins in the western Black Sea region of Turkey.

Due to their high spatiotemporal resolution, radar data are assimilated to correct the NWP system for mesoscale and microscale weather prediction (Milan et al., 2008; Zhao and Jin, 2008). Wang et al. (2013) tested the four-dimensional variational data assimilation (4-DVar) system by simulating a midlatitude squall-line case in the US Great Plains, and the results indicated that radar data assimilation was able to improve rainfall forecasts from the WRF model at the convective scale. Liu et al. (2013) selected four storm events in a small catchment (135.2 km2) located in southwest England to explore the effect of data assimilation for rainfall forecasts based on the WRF model, and assimilating radar reflectivity by the 3-DVar model can significantly improve the forecasting accuracy for the events with one-dimensional evenness in either space or time. By using the WRF model and Advanced Regional Prediction System (ARPS) 3-Dvar, Hou et al. (2015) improved the short-term forecast skill by up to 9 h by assimilating radar data in southern China.

Most studies focus on the assimilation algorithm and data selection. However, consistent conclusions have not been obtained for the option of radar reflectivity and radial velocity, and few studies pay attention to the time interval setting of data assimilation. Based on the WRF and 3-DVar models, Tian et al. (2017b) found that radar reflectivity assimilation led to better rainfall simulations than radial velocity assimilation at the time interval of 6 h. Maiello et al. (2014) assimilated both radar reflectivity and radial velocity by the 3-DVar model with a 3 h assimilation cycle to improve the WRF high-resolution initial conditions, and the rainfall forecast became more accurate for several experiments in the urban area of Rome. Bauer et al. (2015) used the WRF model in combination with the 3-DVar scheme to estimate the rainfall simulations, and the results showed that radar data assimilation significantly improved the rainfall simulations by a 1 h Rapid Update Cycle at the high resolution of 3 km in Germany.

In reality, the operational forecasts from meteorological departments are guidance forecasts with a large forecasting area. It is impossible to focus on the accuracy of the rainfall in small and medium catchment scales. Limited computing power means that the number of restarting times for the forecasting system is only 2–4 times per day (Xie et al., 2016). The forecasting accuracy descends gradually as the run time goes on because the data assimilation is not in real time. Due to the poor accuracy at small scales and low resolutions, the rainfall forecasting from the meteorological department cannot be used directly as the input for hydrological forecasting in small and medium catchments (Tian et al., 2019). The local meteorological observations are necessary to be assimilated to improve the high-resolution rainfall forecast. The NWP model may not be corrected in a timely manner at a long time interval of data assimilation, while shortening the time interval needs a lot of computational resources, and the observation errors in local meteorological observations may also be amplified with high assimilation frequency in the NWP model.

China suffers approximately nine tropical cyclones (TCs) each year on average (Shen et al., 2017). Most TCs develop into typhoons which always bring huge economic losses and a great number of casualties. Fujian is one of the most regularly affected provinces on the coastline of southeast China, and heavy rainfall caused by the interaction of typhoons and complex terrain leads to severe flood disasters. Accurate rainfall forecasting is of great significance to flood control and disaster mitigation. However, typhoon rainstorms are still difficult to predict (Li et al., 2019). There are eight Doppler radar stations to obtain full coverage for meteorological monitoring in Fujian Province. The plentiful radar data provide convenience and a basis for the exploration of radar data assimilation at catchment scale.

In this study, Meixi catchment located in Fujian Province is chosen as the study area. Due to the frequent heavy rainfall, flood disasters are up more than 20 times since 1949. On 9 July 2016, heavy rainfall caused by typhoon Nepartak led to severe flooding and attracted strong interest from the public, academics, and government. Accurate rainfall simulations have a great practical significance in the study area. In order to explore the reasonable use of Doppler radar data assimilation to correct the initial and lateral boundary conditions of the NWP systems, the WRF model is applied to simulate three typhoon storm events affecting the Meixi catchment, and the 3-DVar model is used to assimilate the radar data to improve the typhoon rainstorm simulations. Nine assimilation modes are designed by three kinds of radar data (radar reflectivity, radial velocity, and radar reflectivity and radial velocity) and at three assimilation time intervals (1, 3, and 6 h). The rainfall simulations are evaluated by three indices, including relative error (RE), critical success index (CSI), and root mean square error (RMSE).

The Meixi catchment lies in central-eastern Fujian Province with a subtropical monsoon climate (Fig. 1). The drainage area is 956 km2, and the average annual rainfall is approximately 1560 mm. There are eight rain gauges and one hydrologic station (Fig. 2). In order to investigate the radar data assimilation effects on rainfall simulations, different kinds of rainfall processes caused by different stages of the typhoons are chosen in Meixi catchment. Three rainfall storms are shown in Table 1. Saola formed on 28 July 2012 and landed at Fuding, Fujian, by 3 August. Then Saola weakened into a tropical storm at Jiangxi. With the movement of Saola, Meixi catchment was not directly affected, and the accumulated 24 h rainfall was only 84 mm. Hagibis landed at Shantou, Guangdong, on 15 June 2014 and then moved toward the north at a fast-moving speed. Fortunately, Hagibis weakened into a tropical depression quickly while moving to northeastern Fujian on 17 June. Event II occurred after the typhoon passed Meixi catchment, and the accumulated 24 h rainfall was only 66 mm. Nepartak reached Fujian on 9 July 2016 and strengthened at Putian. Then Nepartak moved towards the northwest at a fast-moving speed, and event III occurred when Nepartak was close to Meixi catchment. During the period, Nepartak reached its peak intensity. The 24 h accumulated rainfall was 242 mm, which led to a high peak flow of 4710 m3s-1 in Meixi catchment. The most destructive flood caused water and power outages in 11 villages and towns. Official figures stand at 74 dead and 15 missing from the flood, which also caused a direct economic loss of CNY 5.234 billion. Accurate rainfall forecasts appeared to be particularly important for Meixi catchment.

In this study, the observation of areal rainfall in Meixi catchment is averaged by the eight stations with the Thiessen polygon method (Sivapalan and Blöschl, 1998), while the simulation of areal rainfall is averaged from all grids of the WRF model inside the Meixi catchment. The relative error (RE) is used to evaluate the total rainfall amount simulation: 6RE=P′-PP×100%, where P′ is the simulation of 24 h accumulated areal rainfall, and P is the observation of 24 h accumulated areal rainfall.

The spatiotemporal patterns of the rainfall simulations are evaluated by the critical success index (CSI) and modified root mean square error (m-RMSE), which is defined as the ratio of root mean square error (RMSE) to the mean values of the corresponding observations (Liu et al., 2012; Prakash et al., 2014; Agnihotri and Dimri, 2015): 7CSI=1N∑i=1NNAiNAi+NBi+NCi, 8m-RMSE=1M∑j=1MPj′-Pj21M∑j=1MPj. The CSI is calculated based on the rain or no rain contingency table (Dai et al., 2019). Table 4 shows that rainfall<0.1 mmh-1 as the threshold is regarded as no rain. In order to evaluate the simulation of spatial rainfall distribution by CSI, NAi, NBi, and NCi at each time step i (i=1 h) are calculated by comparing the rainfall observation with the simulation extracted at eight rain gauge locations, and then the values of NAi, NBi, and NCi at all time steps are averaged to produce the final verification results. Therefore, N refers to the total time steps (N=24). For temporal dimension evaluation, NAi, NBi, and NCi are first calculated using the time series data of simulations and observations at each rain gauge i (i=1), then the averaged index values of all rain gauges are regarded as the final verification results. Thus instead of the simulation time steps, N represents the total number of the rainfall gauges (N=8) for temporal dimension evaluation. The perfect score of CSI is 1.

The m-RMSE is calculated using Eq. (). For spatial dimension evaluation, Pj′ and Pj refer to the simulation and observation of 24 h accumulated rainfall at rain gauge j, respectively. M is the total number of rain gauges (M=8). For temporal dimension evaluation, Pj′ and Pj are the simulation and observation of areal rainfall at each time j, respectively. M represents the total amount of time (M=24). The perfect score of RMSE is 0.

In order to prove the accuracy of the assimilation results, typhoon paths for different assimilation modes are also simulated (Fig. 10). According to the simulations of Saola and Nepartak, the accurate typhoon path simulations always lead to accurate rainfall simulations. However, for typhoon Hagibis, the actual typhoon center is far away from the Meixi catchment during the assimilation process. Hence, only the actual typhoon path for Hagibis is added in Fig. 10. Comparing the nine radar data assimilation modes, assimilating radial velocity at a time interval of 6 h always performs the worst in rainfall simulations, while the rainfall simulations can be significantly improved by shortening the time interval of data assimilation. According to Eq. (), although the physical process of the rainfall formation cannot be influenced by the radial velocity assimilation directly, the wind field and the water vapor transportation in initial and lateral boundary conditions can be changed with the wind information in radial velocity. However, the wind field is quite variable, especially for stormy weather. As the time interval becomes longer, the WRF model cannot be corrected by the radial velocity in time, whereas compared to the simulations without data assimilation, the inevitable observation errors caused by atmospheric refractivity in the radial velocity might lead to worse performance in the WRF model as the running time goes on (Montmerle and Faccani, 2009). That is the main reason that assimilating radial velocity at a time interval of 6 h cannot obtain satisfactory simulations. Increasing the frequency of data assimilation, the effective information in radial velocity can correct the wind field and the water vapor transportation in the background field of the WRF model timely, which is helpful to improve the rainfall simulations (Kawabata et al., 2014).

The water vapor transportation increments and wind field for different modes at the rainfall concentrating time are used to show how assimilating radial velocity and radar reflectivity affects the WRF model's initial and boundary conditions (Figs. 11–13). The shadows in Figs. 11–13 mean that water vapor transportation in the analysis field is more than in the background field. The darker the shadow in the figures is, the more the water vapor transportation increment is, which is one of the most important factors that affects the amount of rainfall. For event I, counterclockwise wind field has contributed to the water vapor transportation from ocean to inland at 12:00 on 3 August 2012. Modes 1, 2, 5, 7, 8, and 9 all obtain the shadow area with the obvious water vapor transportation increment. However, according to the coverage area of the shadow, only modes 5 and 8 influence Meixi catchment directly, which is consistent with the result that rainfall simulations with modes 5 and 8 are higher than simulations with no data assimilation at 12:00, while the increment of simulated rainfall is quite obvious for mode 8. The differences of nine modes can be easily found in both the wind field and water vapor transportation increments for event II. The water vapor transportation increases significantly in modes 2, 3, 8, and 9 at 18:00 on 18 June 2014, which has a direct impact on the rainfall simulations in Meixi catchment. That is the main reason why simulated rainfalls with modes 2, 3, 8, and 9 are higher than the simulated rainfall with no data assimilation. However, the wind fields in these modes indicate a lack of warm and wet flow supply, and the rainfall weakening is almost inevitable after 18:00. Considering the wind field and the range of water vapor transportation increments, the rainfalls may continue for a period of time after 18:00 in modes 3, 8, and 9, which can also be reflected by hourly simulated rainfall shown in Fig. 8. For event III, the water vapor transportation increases significantly in modes 2, 3, 5, 6, 7, 8, and 9 at 06:00 on 9 July 2016, while only modes 8 and 9 affect Meixi catchment directly. The range of shadows in Fig. 13 is also consistent with the rainfall simulations. The wind field indicates that water vapor transportation is sufficient for mode 8 at a later time, which leads to a significant increase in simulated rainfall.

Does further shortening the assimilation interval obtain better rainfall simulations? In terms of theory, the answer is yes because improving the assimilation frequency can correct the initial and lateral boundary conditions in a timely manner. However, the observation errors of radial velocity may be amplified with the high assimilation frequency in the WRF model. There may be an “inverted u” relationship between the accuracy of the rainfall simulations and the assimilation time interval (Myung et al., 2000). Further study should be carried out to investigate the optimal assimilation time interval.

On the contrary, assimilating radar reflectivity offers little help for improving rainfall simulations except for accumulated rainfall. Furthermore, rainfall simulations become even worse as the time interval of radar reflectivity assimilation shortens from 6 to 1 h. The background field of the WRF model has large differences from the actual weather situation, which can be reflected in the rainfall simulations without data assimilation against the rainfall observations for the three storm events. As shown in Eq. (), radar reflectivity is closely related to the humidity field and contains the information of rainfall hydrometeors (Wattrelot et al., 2014). That is to say the humidity information in radar reflectivity is quite different from the actual weather situation, which makes it difficult for the 3-DVar data assimilation to produce an optimal estimate of the true atmospheric state by the iterative solution of a prescribed cost function. It should also be mentioned that due to its unchangeability, the matrix of CV3 has wide applicability but is not practical for all cases (Kong et al., 2017). The inadaptability of CV3 in the typhoon synoptic system and the large differences between the humidity information in radar reflectivity and the actual weather situation might be the main reasons for the poor performance of radar reflectivity assimilation (Sun, 2005). The more frequent the radar reflectivity assimilation is, the greater the pressure on the 3-DVar data assimilation model is. Other data assimilation models with variable background error covariance, such as the hybrid ensemble transform Kalman filter–three-dimensional variational data assimilation (ETKF-3DVAR) (Wang et al., 2012; Shen et al., 2016), should be tested for radar reflectivity assimilation in future studies.

For the even rainfall events in space and time, such as storm event I, data assimilation should be used carefully. The WRF model has good performance in rainfall simulations, especially for accumulated rainfall. The errors in the assimilated data may have a negative effect on the rainfall simulations. Additionally, assimilating other kinds of data and radar data together may help to improve the rainfall simulations. Though the conventional observations, such as upper-air and surface observations from meteorological stations and sounding balloons, have low spatiotemporal resolution, the kinds of data are various and have wide coverage, which can help to improve the atmospheric motion in the WRF model at large scales (Li et al., 2018). Yesubabu et al. (2016) indicate that assimilating the satellite observation also has a positive effect on the rainfall simulations. Assimilating different data sources, together with the radar data, may further improve the rainfall simulations at catchment scale. In reality, ECMWF was also tested for the data assimilation before FNL was used in this study (Zhang et al., 2018; Zhao et al., 2012). Although the rainfall simulations show some differences based on the two kinds of boundary conditions, the patterns of improvements from different data assimilation modes are quite similar, and the same conclusions can be obtained.

Data assimilation is an efficient technique for improving rainfall simulations. In order to explore the reasonable use of Doppler radar data assimilation to correct the initial and lateral boundary conditions of the NWP systems, three typhoon storm events, including Saola, Hagibis, and Nepartak, are chosen to be simulated by the WRF model with nine modes in Meixi catchment located on the southeast coast of China. The FNL analysis data with 1∘×1∘ grids are used to drive the WRF model, and radar data from the Changle Doppler radar station are applied to correct the initial and lateral boundary conditions. Three evaluating indices, RE, CSI, and RMSE, are used to evaluate the nine radar data assimilation modes, which are designed by three kinds of radar data (radar reflectivity, radial velocity, and radar reflectivity and radial velocity) and at three assimilation time intervals (1, 3, and 6 h).

Contrastive analyses of the nine modes are carried out from three aspects: accumulated rainfall simulations, spatial rainfall distribution, and temporal rainfall distribution. Four main conclusions are obtained: (1) in the nine radar data assimilation modes, assimilating radial velocity at a time interval of 1 h can significantly improve the rainfall simulations and outperform the other modes for all the three storm events; (2) shortening the assimilation time interval can improve the rainfall simulations in most cases, while assimilating radar reflectivity always leads to worse simulations as the time interval shortens; (3) radar reflectivity is the best choice for the data assimilation at a time interval of 6 h, while radial velocity performs best for the data assimilation at a time interval of 1 h; and (4) data assimilation can improve the rainfall simulations as a whole, especially for the heavy rainfall with strong convection, whereas the improvement for evenly distributed rainfall in space and time is limited. More numerical simulation experiments should be tested in other catchments in different climate conditions. Further studies also should be carried out to investigate the data assimilation techniques to improve the ability of the simulations of heavy rainfall in the study areas.