1 Introduction

As one of the most devastating natural disasters, tropical cyclones (TC) have drawn lots of attention by meteorologists (Emanuel 2005). Accurate forecasts of TC track, intensity, as well as induced torrential rainfall are crucial for issuing early warning to the public society and therefore preventing/reducing TC-induced losses of lives and properties. Though a substantial improvement has been made over the past decades (Goerss et al. 2004; Yu et al. 2012), considerable track forecast errors still exist. The intensity forecasting skill has even lagged that of the track (DeMaria et al. 2007; Emanuel et al. 2004), despite many efforts and progresses that have been made (Rogers et al. 2013). Therefore, accurate prediction of TC track and intensity still remains a significant challenge to the forecasters all over the world (Lai et al. 2014).

To progress the forecast skill, one needs to upgrade the initial conditions of the atmospheric state using finer observations, as the forecast accuracy depends highly on how well the initial state is prescribed (e.g., Peng et al. 2007). Great efforts have been made to improve TC forecasts by assimilating observations into numerical models, including traditional (e.g., wind, temperature and humidity from ground stations) observations (e.g., Srinivas et al. 2010) as well as non-conventional observations such as satellite-derived observations (e.g., Pu et al. 2002; Sandeep et al. 2006; Wu and Zou 2008) and targeted observations from field campaign (e.g., Chou et al. 2011; Wu et al. 2007). While traditional observations can well capture the information of large-scale synoptic fields, satellite-derived observations with a resolution of a few kilometers have more advantages in representing the meso- to small-scale features of weather events such as tropical cyclones, which makes satellite data assimilation important for the accuracy of initial conditions for TC forecasts (Andersson et al. 1991; Eyre et al. 1993; Reale et al. 2009; Zhu and Zhang 2002).

With the development of radio techniques, Doppler radar becomes one of the most effective tools to probe the state of the atmosphere in a consecutive and high-resolution senses. Doppler radar emits electromagnetic wave and obtains weather information (precipitation and wind) based upon the energy and frequency changes of returned echo (Doviak and Zrnić 2006). Nowadays, an observational network of Doppler radar has been developed in China and has gathered a large amount of atmospheric data for meteorologists (Xu 2003). These real-time data have been utilized to detect/estimate precipitation, water vapor and horizontal wind components in mesoscale thunderstorms (Yang et al. 2014), squall lines (Qin et al. 2014), tornadoes (Zhao et al. 2017), and those TCs very close to land (Xiao et al. 2007).

To improve the prediction of landfalling TCs, an efficient way is to assimilate near-shore radar observations into numerical models and improve the depiction of TC-scale structure at initial times. Case studies are found over the Atlantic basin (Li et al. 2012; Pu et al. 2009; Zhang et al. 2009; Zhao and Jin 2008) and over the western North Pacific (Xiao et al. 2007; Zhao et al. 2012; Zhu et al. 2016). The assimilated quantities included reflectivity and radial velocity or both and the data assimilation methods included 3D variational (3DVAR) approach (Pu et al. 2009; Zhao et al. 2012; Zhao and Jin 2008), ensemble Kalman filter (Zhang et al. 2009; Zhu et al. 2016), and a hybrid system of both (Li et al. 2012). These studies demonstrated that the assimilation of radar reflectivity can upgrade the model representation of cloud water and rainwater mixing ratio within TC, result in a notable influence on its thermal and hydrometeor structures, and thus improve the forecast of precipitation induced by TC (e.g., Pu et al. 2009; Xiao et al. 2007; Zhao et al. 2012). The assimilation of radar radial velocity, on the other hand, can improve the wind structure (convergence/divergence) and associated thermal field, resulting in significant improvement in TC’s intensity and track forecasts (e.g., Zhang et al. 2009; Zhao et al. 2012; Zhao and Jin 2008; Zhu et al. 2016).

Up to now, however, studies concerning the utilization of Doppler radar data (especially radial velocity) for improving the forecasts of landfalling TCs, which are the major threat to the coastal region of China, are still relatively limited. Besides, the efficiencies of different assimilation methods still need to be assessed in different situations. Therefore, in the present study, wind observations from two radar stations in Sanya and Haikou will be used to examine the effect of assimilating radial winds on the prediction of a TC using gridpoint statistical interpolation assimilation system. The selected TC for this study is Supertyphoon Rammasun (2014), which is found to be much stronger than those cases listed above when it was about to make landfall on the coast of South China.

The rest of this paper is organized as follows. Section 2 gives a brief description of the numerical model and relevant data. Section 3 shows the basic information of the selected tropical cyclone case of Supertyphoon Rammasun in 2014. The results of both the processing of radar data and data assimilation are presented in Sect. 4. Finally, the summary is given in Sect. 5.

2 Numerical model and data

The Weather Research and Forecasting (WRF) model (Skamarock et al. 2008) of version 3.4 is employed in this study to numerically simulate a real typhoon case. This numerical model, developed by the National Center for the Atmosphere Research (NCAR) and the National Centers for Environmental Prediction (NCEP) of the USA, is a next-generation mesoscale model for advancing the prediction of mesoscale phenomena using a fully compressible, non-hydrostatic dynamical equation set in a terrain-following hydrostatic-pressure vertical coordinate system. It also includes various parameterizations schemes for different physical processes, including cloud microphysics, cumulus precipitation, planetary boundary layer (PBL), surface layer, land surface, and longwave/shortwave radiations.

In the present simulation, the WRF model is used to simulate the landfall process of Supertyphoon Rammasun (2014). Dynamical downscaling techniques are commonly used for a regional atmospheric model to obtain higher-resolution output with small-and mesoscale features from the lower-resolution output of a global atmospheric model. To do this, a single-domain configuration is used (see Fig. 1), covering the northern half of the South China Sea as well as southern China and the eastern part of Indo-China Peninsula with a horizontal grid of ~ 6 km. The Kain–Fritsch cumulus scheme (Kain and Fritsch 1990), Dudhia shortwave (Dudhia 1989) and RRTM longwave (Mlawer et al. 1997) radiation scheme are chosen in the simulation. The Global Forecast System (GFS) product, maintained by the NCEP with horizontal grid resolution of 1° × 1°, is used to provide initial and lateral boundary conditions for the numerical simulation. The outputs of the simulation are stored at 1-h intervals up to 48 h for the subsequent analysis.

Fig. 1
figure 1

a Best track and b minimum sea-level pressure (hPa) and maximum sustained wind speed (m s−1) of Typhoon Rammasun (2014) obtained from Regional Specialized Meteorological Center (RSMC), Japan Meteorological Agency (JMA). Red arrow in a and red line in b indicate the position and time when radar observations are available. The model domain is also indicated by the thick black box in a

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The next-generation analysis system, which is based on the 3D variational data assimilation (3DVAR) technique and named as Gridpoint Statistical Interpolation (GSI) system of version 3.3 (Hu et al. 2017), is used to assimilate radar observations in the present study. GSI was developed by the National Oceanic and Atmospheric Administration (NOAA) NCEP. Instead of being constructed in spectral space like the Spectral Statistical Interpolation analysis system, GSI is constructed in physical space and is designed to be a flexible, state-of-art system that is efficient on available parallel computing platforms.

Radar observations are obtained from Haikou and Sanya radar observatories (see Table 1) in Hainan Province. Radar at Haikou station is of CINRAD SA/SB type (WSR-98D) and has an elevation of 127.2 m above the sea level. The one at Sanya station is of CINRAD SC type and elevated 443 meters above the sea level. Both data have the same azimuthal resolution of approximate one degree (Table 2). The radial resolution for SA/SB-type radar is 1 km for reflectivity and 250 m for radial velocity. Therefore, the outermost observable distance is different for SA/SB radar: 460 km for reflectivity and 230 km for radial velocity. For SC-type radar, both quantities cover the same distance of 300 km. Besides, the Nyquist (aliasing) velocity varies slightly in different elevation scans (ranging from 27.82 to 35.34 m s−1) for SA/SB-type radar. For SC radar, however, it is fixed at 24.4 m s−1 for all the elevation scans.

Table 1 Parameters of two radar stations used in the present study
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Table 2 Parameters of the radar observations in Haikou and Sanya stations
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The TC “best track” data are obtained from the Regional Specialized Meteorological Centre (RSMC), Tokyo. Six-hourly TC positions, near-center maximum surface wind speed, and minimum sea-level pressure, are used in the present study.

The Tropical Rainfall Measuring Mission (TRMM)-merged high-quality (HQ)/infrared (IR) precipitation product 3B42 (https://trmm.gsfc.nasa.gov/3b42.html) is used to validate the simulation of rainfall in the present study. This product is on a 3-h temporal resolution and a 0.25° × 0.25° spatial resolution in a global belt extending from 50 degrees South to 50 degrees North latitude.

3 Supertyphoon Rammasun (2014)

Supertyphoon Rammasun (2014) was the most intense TC over the western North Pacific in 2014, and the strongest TC that landed on China mainland since 1949 (Zhang et al. 2017). From Fig. 1, we can see that prior to 0600 UTC 12 July, Rammasun (2014) was identified by RSMC as a tropical depression. Later, it reached the minimum strength of tropical storm (maximum wind speed above 17.2 m s−1) and moved westwards along the southern edge of the subtropical high toward the Philippines. Before crossing the central Philippines, Rammasun intensified to a severe typhoon and thus brought gale force winds and heavy rains to Philippines. Although slightly weakened after crossing the Philippines, Rammasun intensified for the second time over the SCS from 0000 UTC 16 July. This re-intensification was identified as a rapid intensification (RI) process due to high SST and other favorable environmental conditions (Zhang et al. 2017). At 0600 UTC 18 July, very close to the eastern coast of the Hainan Island, Rammasun reached a peak intensity of 46.3 m s−1 wind speed and 935 hPa sea-level pressure shortly before it struck Hainan as the most destructive TC since 1949. This intensity measurement was based on the satellite observations but it was still found to be substantially underestimated. A minimum sea-level pressure of 899.2 hPa was recorded by a barometer located at Qizhou island before it was destroyed by the approaching Rammasun (Cai and Xu 2016). Based on this observation and further analysis, the peak intensity of Rammasun in the Best Track data of China Meteorological Administration has been updated to 888 hPa, which makes Rammasun the strongest typhoon that has ever made landfall in China’s recorded history. After sweeping over the whole island, Rammasun moved across the Qiongzhou Strait and then hit the mainland, causing great losses of lives and properties along its path. It eventually weakened near the border between China and Vietnam on 20 July (Fig. 1a).

In the present study, we focus on the re-intensification when Rammasun was about to make a landfall on Hainan Island. At 0000 UTC 18 July (see the red arrow and red line in Fig. 1), just prior to reaching the peak intensity, the radars at both Haikou and Sanya stations in Hainan Province had a clear visual covering the core region of Rammasun (Fig. 2). The structure of the core region is more complete in the lowest reflectivity scan (~ 0.53° elevation angle) at Haikou station shown in Fig. 1a, due to the relatively longer observing range (~ 460 km) of the SA/SB-type radar. The eye region, characterized by a blank region of reflectivity with a diameter of ~ 50 km, was surrounded by the intense upward convection indicated by the yellow-to-orange colors. The spiral structure of the rainband emanating from the core region is also clear, especially the southwest and northeast branches (Fig. 1a).

Fig. 2
figure 2

Radar reflectivity (dBZ) observations from a Haikou station and b Sanya station at the first elevation angle (~ 0.5°) valid at 0000 UTC July 18, 2014. The cylindrical grids are shown with a 30° interval in azimuthal direction and a 50-km interval in radial direction

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As we have the direct radar observations of the TC core at this time, just prior to the peak intensity and subsequently landfall to the mainland, it is worth knowing whether these radar observations can be used to promote better numerical forecasts of Rammasun’s track and intensity.

4 Results

4.1 Radial velocity preprocessing

The decoded radial velocity observed by radar cannot be directly assimilated by GSI into the numerical model due to several reasons. First, these raw velocity data are generally aliased (folded) as all Doppler radar has a Nyquist velocity \( V_{\text{Ny}} \). If the radial component of wind \( V_{\text{R}} \) is larger (smaller) than \( V_{\text{Ny}} \) (\( - V_{\text{Ny}} \)), the observed velocity will be folded as \( V^{\prime}_{\text{R}} = V_{\text{R}} - 2V_{\text{Ny}} \) (\( V^{\prime}_{\text{R}} = V_{\text{R}} + 2V_{\text{Ny}} \)). That is, \( V^{\prime}_{\text{R}} \) will always be confined between 0 and \( V_{\text{Ny}} \). Second, the resolution of the observation (~ 300 m) is inconsistent with that (~ 6 km) of the present numerical model. Such a large discrepancy (an order of magnitude) in resolution between observation and model grid could induce large imbalance to the model at grid-scale or alias small-scale variations into synthetic large-scale pattern, once the finer observations were assimilated into a coarse-resolution model. Therefore, a series of preprocessing are necessary before data assimilation.

To correct the raw velocity data, a simple de-aliasing algorithm is used to unfold those aliased data. First, the region of aliased velocity data is determined visually based on the plot of the raw data. In these regions, the radial gradient of velocity is checked to identify discontinuity (neighboring differences are close to or larger than ~ 2\( V_{\text{Ny}} \)) where velocity folding occurs and the true value is obtained as \( V_{\text{R}} = V^{\prime}_{\text{R}} + 2V_{\text{Ny}} \) (James and Houze 2001). This procedure is repeated three times in case the velocity is folded more than once. Second, there are many spikes in the plot of raw data, especially not far away from the center of the radar. This is probably due to the topography (ground clutters), flying birds and other non-meteorological noises that reflect radar beams at low altitudes. Regions of these spikes are also identified visually from the raw plot, and then, the gradient-check method is used to locate them. These spikes are filled in by interpolation based on the information of nearby bins. Finally, the above procedure, served as a simple quality-control (QC) step, is applied to all elevation scans, except for the highest three scans in which there are very little useful information but full of noise, before inserting into the model.

Figure 3 shows the radar-observed radial velocities at the lowest elevation angle (~ 0.5°) before and after applying the above de-aliasing algorithm. Velocity observations by both radars did not completely cover the core region of Rammasun, only the halves closer to the radars are scanned. The most obvious feature is that large area of velocity near the center of Rammasun is folded, indicating a velocity magnitude larger than the Nyquist velocity there. Besides, a lot of velocity spikes appeared near the center of Haikou station (Fig. 3a), as well as the northwest quadrant of Sanya scan (Fig. 3c). After the QC procedure, the aliased velocity is unfolded into a clear, continuous and intense-rotating dipole pattern near the center of Rammasun. The observed inner-core maximum wind speed (~ 45 m s−1) is close to that obtained from the RSMC best track data. Those velocity spikes in both plots are greatly removed, leading to relatively smoothed noise-free velocity observations.

Fig. 3
figure 3

Original observed radial component of velocity (m s−1, positive indicates outward flow) at a Haikou and c Sanya stations at the first elevation angle (~ 0.5°), valid at 0000 UTC July 18, 2014. The corresponding velocities after de-aliasing are shown, respectively, in b, d. Red typhoon symbols indicate the centers of Typhoon Rammasun (2014). The cylindrical grids are shown with a 30° interval in azimuthal direction and a 50-km interval in radial direction

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After the QC step, the model output wind field can be compared with the radar-observed field. First, the initial wind field on model grids is interpolated into the radar-cylindrical grids horizontally. Then they are interpolated vertically to the elevation according to the elevation angle and radial distance, assuming no refraction of radar beam by the nonuniform atmosphere. Finally, the horizontal winds in lat/lon grids is re-projected onto the cylindrical components and only the radial component is retained. After the interpolation, both data are on the same cylindrical grids that facilitate the comparison. Generally, the model outputs are in good agreement with the radar observations (figure not shown) and hence it is much clear to show their differences (Fig. 4). From Fig. 4, we can see that both panels are primarily filled with green color, indicating that the overall differences between radar observations and model outputs are small. Only at the region near the core of Rammasun are the differences quite large. This is caused by underestimate of maximum rotating winds by the model even after 6-h spinup, as well as the slightly displaced location of Rammasun’s center. Without any vortex modification, it is unavoidable to underestimate the TC strength as the initial conditions are obtained from 1°-resolution (~ 100 km) GFS analysis. Another possible factor is that exact location of Rammasun in the model was slightly different from the observed one, which may cause a dipole-pattern difference shown in Fig. 4. Notice that there are also many spikes which may outstand when taking the difference calculation. Completely removing these spikes is not easy as real observations always contain a certain portion of noise. It is significantly reduced in the QC step as shown in Fig. 3.

Fig. 4
figure 4

Observational increments of radial velocity (m s−1) at a Haikou and b Sanya stations at the first elevation angle (~ 0.5°) valid at 0000 UTC July 18, 2014. The cylindrical grids are shown with a 30° interval in azimuthal direction and a 50-km interval in radial direction

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After the QC step, the inconsistent resolution between observation and model simulation is resolved by subsampling radar observations (data thinning). This is to re-sample the data at every 5 grids in the azimuth direction and every 20 grids in the radial direction, which yields approximately 6-km resolution in the radial direction, in consistent with that of the model simulation. Figure 5a shows all the radial velocity observations inputted to the GSI assimilation system after QC and data thinning. In order to guarantee the consistency between model resolution and observation density, many of the velocity observations were discarded, including those precious near-core ones. During the analysis process by the GSI system, certain observations could be further rejected if the difference between initial guess and observations meet certain criterions (e.g., larger than a prescribed threshold). Figure 5b shows all the rejected observations which are indicated by the analysis usage flag (value of − 1) in the GSI system. It is found that no more than 0.19% of all radial velocity observations were rejected by the assimilation system, proving the efficiency of the QC preprocess as well as the GSI system. However, as shown in Fig. 5b, some key observations near the center of Rammasun that survived the data thinning were also rejected. The reason for these rejections can be found in Fig. 4a that the observational increment at the same location was largest (negatively). Since both radars only scanned half of the core region of Rammasun, these rejections may further degrade the representation of the core structure of the TC, as will be shown later.

Fig. 5
figure 5

a All the radial velocity (m s−1) observations input to the GSI assimilation system. Quality control and data thinning are applied. Observations at different elevation angles are all plot together which may yield overlapping in the plot. b The same as a except for those observations rejected by the assimilation system, as indicated by the analysis usage flag in the system

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Whether an observation is assimilated or rejected by the assimilation system is controlled by a parameter called observation error. Larger observation errors will tolerate larger differences between observation and background field, and thus less rejection to those observations. Several studies used a constant observation error of, for example, 2 m s−1 (Pu et al. 2009) or 3 m s−1 (Zhang et al. 2009) for radial velocity observations. Others also used varying observation errors with a standard deviation of 1.5 m s−1 (Zhao et al. 2012) or 2 m s−1 (Li et al. 2012). This parameter used in the present study is also not a constant, changing between 1 and 5 m s−1, consistent with these studies.

4.2 Numerical simulation with data assimilation

After the QC and data thinning, the radar observations can be readily assimilated into the numerical model using the GSI assimilating module. In the GSI module, there is an option for choosing the background error covariance matrix that determines the horizontal and vertical influencing scales. In order to assess the influence of this choice on the assimilation, three numerical experiments are carried out (Table 3). The first is control experiment (CTRL), in which radar-observed radial velocity is not assimilated into the model. The remaining two experiments, denoted as RWGLB and RWLCL, refer to using different (global and local) background error covariance matrices for radial wind assimilation.

Table 3 List of numerical experiments
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Initialized with relatively coarse (1°) GFS analysis product, the WRF model may require some time to adjust the dynamical field and generating small-scale features (called model spinup). Therefore, in CTRL, we initialize the simulation at 1800 UTC 17 July, 6 h before radar observations. After 6-h spinup, the radar observations are assimilated at 0000 UTC 18 July and the model integration is continued up to 2 days to 20 July.

Figure 6 compares the tracks and intensity (minimum sea-level pressure) of the simulated Supertyphoon Rammasun (2014) to those obtained from RSMC best track data. Generally, the simulated northwestward track and the “V”-shape minimum sea-level pressure are all reproduced by the three numerical experiments. However, there are also obvious differences. The track in CTRL (red line in Fig. 6a) originates the same as the observations (black line in Fig. 6a); it seesaws during the 6-h spinup and deviates northeastward from the observed track slightly (~ 50 km). From this slightly offset location, the tracks in both data assimilation experiments start but disperse owning to different choices of background error covariance matrices in the next 2 days. During the first day, the track of CTRL goes across the Leizhou Peninsula and does not deviate much from the observation. In the second day, the CTRL track still keeps relatively straight line to the northwest, while the observed track turned much westward, producing larger and larger errors (Fig. 7a). This situation is more pronounced for the RWLCL track which almost overlaps with the observations in the first day and then merge with CTRL track in the second day, leading to small track errors in the first day and large errors in the second day (Fig. 7a). The RWGLB track is better in the sense that it never deviates significantly in both days as compared with CTRL and RWLCL tracks (Fig. 7a). The mean track error for RWGLB is 69.4 km, whereas those for CTRL (95.1 km) and RWLCL (72.7 km) are somewhat larger.

Fig. 6
figure 6

Observed and simulated a tracks and b minimum sea-level pressure (hPa) of Typhoon Rammasun (2014)

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Fig. 7
figure 7

a Track (km) and b intensity (hPa) errors between simulated and observed Typhoon Rammasun (2014). The vertical black lines indicate the time of radial wind assimilation

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Due to the better track simulation, the minimum sea-level pressure for the RWGLB is also the best among the three, reaching minimum value at about 0600 UTC 18 July, while those of CTRL and RWLCL are too low after landfall (Fig. 6b). Although the SLP by CTRL has a minimum value close to the observed one, it is delayed for several hours, probably due to the relatively longtime stay over the ocean. The track of RWLCL, very close to the observed one, encountered Hainan Island several hours after data assimilation and thus did not have enough time to intensify to the strength of CTRL. The overall mean intensity error of simulation (measured by minimum sea-level pressure) for RWGLB is 7.1 hPa, which is also the lowest among the three. The intensity error for RWLCL (8.7 hPa) is even slightly larger than that for CTRL (8.4 hPa), indicating no improvement during the 2-day simulation.

Simulated reflectivity in Fig. 8 demonstrates the structural changes in Rammasun. In CTRL, the simulated eye of Rammasun is coarse and broad which is due to the improper representation of Rammasun’s inner structure by the coarse GSF products. However, the large-scale spiral rainbands are well reproduced, especially the one located south and southeast to the Hainan Island, corresponding to that of observations shown in Fig. 2. Once the radial winds are assimilated, the relatively circular form of Rammasun’s eye is distorted and squeezed into elliptical form. Therefore, the modification induced by assimilating radial winds alter its inner structure. This can also be seen in the cross section between the radar station and the center of Rammasun (Fig. 9). In the CTRL (Fig. 9b), Rammasun’s eye embedded in two reflectivity towers is broad and large (~ 60 km). However, after assimilating the radial winds (Fig. 9c, d), the eye becomes compact and small (~ 30 km), close to that of observed one (Fig. 9a). The relatively low extend of the reflectivity towers is probably due to the parameterization scheme used in the present study.

Fig. 8
figure 8

Simulated reflectivity (dBZ) in a CTRL, b RWGLB, and c RWLCL experiments at 0100 UTC 18 July, 1 h after assimilating radar-observed radial velocity

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Fig. 9
figure 9

Vertical-radial cross section of a observed and b–d simulated reflectivity (dBZ) in different experiments at 0100 UTC 18 July. The cross-sectional originates from Haikou station and passes through Rammasun’s center, as indicated by the red typhoon symbol

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The simulated rainfall amount is also compared with the TRMM observations. Figure 10 shows the spatial pattern of accumulated precipitation for each day of simulation. The overall magnitude of simulated rainfall amount is comparable to that of the TRMM, while the spatial distributions are somewhat different. During the first day, TRMM observations show that the rainfall was concentrated around Hainan Island and maximized at the Qiongzhou Strait (Fig. 10a). This is broadly reproduced by CTRL (Fig. 10b) and RWGLB (Fig. 10c) experiments, while the RWLCL (Fig. 10d) tended to shift the maximum center to the southwest of observations. More specifically, the maximum center (as indicated by the red areas) in CTRL (Fig. 10b) is much larger and broader than that of observations, probably due to the relatively large eye structure in CTRL. The spatial pattern of rainfall in RWGLB (Fig. 10c) seems to be reasonable as the red maxima are narrowly laid out following the track of Rammasun, taking into account the fact that TRMM observations tend to underestimate the total rainfall amount when precipitation is intense (> 50 mm h−1, Islam and Uyeda 2005).

Fig. 10
figure 10

a Observed and b–d simulated 24-h accumulated rainfall amount (mm) in different experiments on July 18, 2014. e–h are the same as a–d except for 19 July. Observed rainfall is obtained from TRMM 3B42 3-h dataset

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4.2.1 Dynamical analyses

To assess the influence of assimilating radar radial velocity on TC’s track and structure, diagnostics are calculated at the time of data assimilation in the cylindrical coordinates following the motion of Rammasun. The cylindrical coordinates contain 180 azimuth grids (2° increment) and 150 radial grids (~ 3.33 km increment). The horizontal wind vector is then re-projected onto the coordinates as tangential and radial components.

Figure 11 shows the deep-layer (0–12 km) mean wind increments in both RWGLB and RWLCL, with respect to the CTRL experiment. It is clear that the assimilation brought strong onshore wind toward Hainan Island, indicating relatively uniform inflow toward Haikou station. This is in accordance with the negative radial increment in the fourth quadrant shown in Fig. 4a. However, due to different horizontal influencing scales, the increment is generally broad in RWGLB, while the magnitudes in both experiments are similar. This onshore wind would lead to more westward motion of modeled Rammasun, especially for the RWLCL case as Rammasun is located within the maximum center of the increment (slightly northeast to the big black dot in Fig. 11, see Fig. 5a) and the increment near the center of Rammasun has a larger westward component. Therefore, Rammasun in RWLCL moves more westward and then coincides with the observed track. In the second day after Rammasun was landed, there is also westward wind increment over China mainland in RWGLB (around 22°N in Fig. 11a). If these increments could persist longer than one day, then they could affect the track in the second day, which partially explains the more westward track of Rammasun in RWGLB than in RWLCL (see Fig. 6a).

Fig. 11
figure 11

Deep-layer mean (12 km below) wind increments (m s−1) in a RWGLB and b RWLCL with respect to CTRL at 0000 UTC July 18, 2014 when Rammasun was located at the big black dot. Differences larger than 2 m s−1 are shown. Best track starting from 1800 UTC July 17, 2014 is also shown

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Although the overall pattern of the radar-observed wind increment is reproduced, it is worth noting that the eyewall-related strong dipole feature is not correctly reproduced by assimilation, as there is no strong-rotating wind shear in Fig. 11 (also obvious in Fig. 4). Several reasons may account to this problem. First, the eyewall of Rammasun was not completely observed by radar scans. Although the reflectivity scan in Haikou station covers the whole core region (Fig. 2a), velocity scans of both radars only sampled halves of Rammasun’s inner-core structure (Fig. 3). Second, these observations are coarsened to fit the current model resolution so that the remaining information for the core region becomes insufficient. Third, some key observations near the core region are found to be rejected by the GSI assimilation system (Fig. 5b), probably due to the large observational increment (Fig. 4a). Therefore, very little information of the strong wind shear in the core region was effectively assimilated, yielding little dipole-feature wind increment in Fig. 11. These lead to a wind increment somewhat different from those in previous studies (e.g., Li et al. 2012; Zhang et al. 2009; Zhao et al. 2012), in which cyclonic rotating wind centered at the TC core is quite obvious after assimilation. The improper representation of Rammasun’s inner-core circulation urges us to use much higher resolution of the model in the future study. Altering the default rejection criterion (observation error) of the assimilation system may also be required, as for a TC as intense as the present case (with a minimum SLP below 900 hPa as identified by a barometer at Qizhou Island), observations near the core region could be significantly different from the initial guess.

Figure 12 shows the basic azimuthal-mean structure of TC Rammasun (2014) in CTRL experiment (left column), including tangential, radial and vertical velocities as well as potential temperature. Differences in Rammasun’s structure between assimilation and non-assimilation experiments (middle and right columns in Fig. 12) are also shown accordingly. All these features of Rammasun’s structure are typical of a mature typhoon: strong cyclonic rotating winds extending to ~ 18 km height with the maximum located approximately above the boundary layer (~ 1 km height) (Fig. 12a), strong inflow within the boundary layer and deep outflow with a maximum at 14–16 km (Fig. 12d), intense upward motion forming the eyewall (Fig. 12d), and obvious warm core structure centered at 8–10 km height (Fig. 12g). The maximum surface wind speed (~ 40–45 m s−1) is close to the radar observations as shown in Fig. 3. The assimilation of radar-observed radial winds is expected to produce some differences in the wind structure, both azimuthal and radial components. This is indeed found in the differences between assimilating and non-assimilating experiments. The assimilation in RWGLB causes a large increment of cyclonic rotation at mid-troposphere between 8 and 14 km and a moderate decrement of cyclonic winds between 4 km (Fig. 12b). This may be caused by the fact that radar-observed information is located at mid-troposphere (Fig. 9a). The assimilation in RWLCL produces a similar increment pattern, with weak cyclonic rotation at mid-levels and stronger anticyclonic winds at lower levels, as compared with that of RWGLB. Since the wind information is assimilated without any mass innovation, to retain in geostrophic balance, the increased cyclonic wind will be deflected to the right on the Northern Hemisphere under the Coriolis effect. Such a deflected wind then produces strong outflow at mid-troposphere and inflow at lower levels (Fig. 12e, f).

Fig. 12
figure 12

Radius-height cross sections of a azimuthal-averaged tangential wind (m s−1) for CTRL and differences of b RWGLB and c RWLCL with respect to CTRL at 0000 UTC July 20, 2014. d–f are the same as a–c except for azimuthal-averaged radial wind (m s −1, positive for outflow). Shading in d indicates vertical velocity (m s−1). g–i are the same as a–c except for potential temperature (K). Shading in g indicates anomalies of potential temperature with respect to the averaged values at 500 km

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The corresponding adjustment of thermodynamic field is not obvious, indicating that the assimilation of radial winds has limited influence on the thermodynamic structure. This result is not surprising because the GSI assimilation system is based on the 3DVAR method. Li et al. (2012) found that 3DVAR produced a temperature increment of no more than 1 °C when wind increment reached ~ 25 m s−1. They also pointed out that the cold-core temperature increment produced by the 3DVAR approach was improper in the core region and a hybrid ensemble-3DVAR could remedy this as the ensemble could provide flow-dependent covariance between different model quantities (e.g., velocity and temperature).

Although the innovation of assimilating the radial winds was most dramatic in the wind field rather than the mass field or thermodynamic field, it will also propagate throughout the region of simulation and to other quantities of atmospheric state. However, the persistent influence of such innovation cannot be easily identified. Thus, we have investigated the temporal evolution of azimuthal-mean tangential wind at 1 km height where the maximum swirling wind occurred. In Fig. 13, it is clear that at the level of 1 km and outside the core region (50 km outward), the cyclonic wind is reduced in both RWGLB and RWLCL. This is also clearly shown in Fig. 13b, c at the very beginning, except that within the core region the swirling flow is strengthened. The strengthening of the core circulation can be identified by the inward-protruding dense contours within 50 km and is much clear (characterized by positive increments) in the difference plots (Fig. 13d, e). Although there is a shrink in the eyewall swirling wind, it does not make Rammasun intensify dramatically as in CTRL. In contrast, at subsequent time Rammasun struggles in intensifying (Fig. 13b, c) and never reaches the peak intensity as in CTRL. The assimilation of radial winds brings in some asymmetries (Fig. 8b, c) that eventually excite vortex-Rossby waves propagating azimuthally along the eyewall region and consuming much of the azimuthal-mean kinetic energy, preventing Rammasun from axisymmetrization and thus intensification (Fig. 13d, e) (e.g., Montgomery and Kallenbach 1997). Such process could be viewed from the jigsaw-like contours within 100 km (Fig. 13b, c).

Fig. 13
figure 13

Time–radius plots of azimuthal-mean tangential wind (m s −1) for a CTRL, b RWGLB, and c RWLCL experiments at the height of 1 km. d–e show the corresponding differences between b–c and a

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5 Summary

The present study has tried to incorporate the radar-based direct observations into a numerical model (WRF) to promote the simulation of an intense tropical cyclone case—Supertyphoon Rammasun (2014) just prior to its landfall on China coast. This TC case was found to be the strongest typhoon ever made landfall in China’s recorded history (Cai and Xu 2016). After a series of simple but effective QC steps, including de-aliasing and subsampling, radar-observed radial velocity data are assimilated into the model after a 6-h spinup run using a 6-km horizontal grid. The incorporation of radial velocity into the model brings considerable modifications of track, intensity, eyewall structure and precipitation to the simulation of Rammasun. Compared with the CTRL experiment (no-assimilation), the RWGLB experiment (using the global error covariance matrix) reproduces the best track simulation, compact eyewall structure, as well as better accumulated rainfall pattern. The RWLCL experiment (using the local error covariance matrix), on the other hand, reproduces satisfactory results at the beginning but not lasting long, primarily due to the relatively small influencing scale chosen for assimilation.

In RWGLB experiment, the large-scale background wind field is corrected by assimilating the radar observations, while the small-scale strong-rotating core feature of Supertyphoon Rammasun is not effectively incorporated into the model. This is primarily due to that the core region was not fully scanned by both radars and that radar observations need to be thinned before assimilated into a 6-km numerical model. Data thinning as well as the rejection of some near-core observations by GSI system eventually lead to a poor representation of the inner-core circulation structure of Rammasun. To make assimilation more effective, higher-resolution (~ 1 km) simulation is needed. Moreover, sine the assimilation of the radar observations is only performed at one timestep, more persisting improvements in TC track and intensity forecasts are expected if the assimilation is continuously performed at multi-time levels. Besides, although the incorporation of radar-based radial velocity could improve the short-time simulation of intense TC, the influence of assimilation parameters cannot be overlooked. Optimization of these parameters is worth further investigation in the future study.