Impacts of Multigrid NLS-4DVar-based Doppler Radar Observation Assimilation on Numerical Simulations of Landfalling Typhoon Haikui (2012)

Lu ZHANG, Xiangjun TIAN*,3, Hongqin ZHANG, and Feng CHEN

1International Center for Climate and Environment Sciences, Institute of Atmospheric Physics,Chinese Academy of Sciences, Beijing 100029, China

2University of Chinese Academy of Sciences, Beijing 100049, China

3Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters,Nanjing University of Information Science and Technology, Nanjing 210044, China

4Zhejiang Institute of Meteorological Sciences, Hangzhou 310008, China

ABSTRACT We applied the multigrid nonlinear least-squares four-dimensional variational assimilation (MG-NLS4DVar) method in data assimilation and prediction experiments for Typhoon Haikui (2012) using the Weather Research and Forecasting(WRF) model. Observation data included radial velocity (Vr) and reflectivity (Z) data from a single Doppler radar, quality controlled prior to assimilation. Typhoon prediction results were evaluated and compared between the NLS-4DVar and MG-NLS4DVar methods. Compared with a forecast that began with NCEP analysis data, our radar data assimilation results were clearly improved in terms of structure, intensity, track, and precipitation prediction for Typhoon Haikui (2012). The results showed that the assimilation accuracy of the NLS-4DVar method was similar to that of the MG-NLS4DVar method,but that the latter was more efficient. The assimilation of Vr alone and Z alone each improved predictions of typhoon intensity, track, and precipitation; however, the impacts of Vr data were significantly greater that those of Z data.Assimilation window-length sensitivity experiments showed that a 6-h assimilation window with 30-min assimilation intervals produced slightly better results than either a 3-h assimilation window with 15-min assimilation intervals or a 1-h assimilation window with 6-min assimilation intervals.

Key words:MG-NLS4DVar,NLS-4DVar,radar data assimilation,typhoon forecast

1.Introduction

China is among the countries most devastated by typhoons worldwide. Typhoons are tropical cyclones (TCs)that cause devastating losses in terms of human casualties and property losses in coastal cities after making landfall.High accuracy in predicting the track and intensity of landfalling typhoons is therefore essential for mitigating damage in coastal areas. In recent decades, due to the continuous development of numerical weather prediction (NWP) models, TC forecasting technology has steadily improved. NWP is affected by both the model error and initial error. Model error is mainly caused by inaccurate physical parameters, or errors in the boundary conditions, topography or other forcing terms (Griffith and Nichols, 2000). Many studies have estimated the model error in the weak-constraint variational assimilation method (Zupanski, 1997; Griffith and Nichols,2000; Trémolet, 2006, 2007), which adds significant computation costs and increases uncertainty. By contrast, the strongconstraint variational assimilation method assumes that there is no model error and that all prediction error is attributable to the errors in the initial conditions. Therefore, accurate representation of the initial conditions largely determines the success or failure of NWP and has important impacts on TC numerical prediction. The lack of precise initial conditions needed to determine the internal structure of TCs has been identified as a main factor causing intensity prediction inaccuracy (Davis et al., 2008). In the numerical simulation of the genesis of Hurricane Diana (1984), Davis and Bosart (2002) found that it was sensitive to the specification of the upper-level trough and ridge in the initial conditions; once the upper-level through and ridge were removed from the initial conditions, the simulation of the genesis of Diana failed. Nolan (2007) highlighted the important influence of the initial vortex structure on TC simulation, as initially deeper vortices from the ground to middle levels lead to earlier TC genesis. Raymond and Session (2007) demonstrated that initial temperature and humidity profiles greatly affected TC simulation by changing the vertical distribution of vertical mass fluxes in convection. Kieu and Zhang(2010) reported that the specification of a mesoscale vortex in the initial conditions had an important effect on the simulation of the genesis of Tropical Storm Eugene (2005). Many efforts have been made to improve the TC initial condition through data assimilation (Xiao et al., 2000, 2005; Zhao and Xue, 2009; Li et al., 2014, 2015). Thus, an advanced data assimilation system is required to provide more accurate initial conditions.

Radar data assimilation is essential for improving NWP, especially in high-resolution models (Xiao et al.,2005). Radar observations with high spatial and temporal resolution have proved to be promising tools that provide essential typhoon structure information. Studies have shown that radial velocity and reflectivity observed by Doppler radar can provide important information on the wind field and microphysical properties of typhoons in the vortex and convective rainband regions (Weng et al., 2011; Zhang et al.,2011). Xiao et al. (2007) assimilated Doppler radar reflectivity data at Jindo, South Korea, to predict the landfalling Typhoon Rusa (2002) using the three-dimensional variational (3DVar) data assimilation system of the fifth-generation Pennsylvania State University National Center for Atmospheric Research Mesoscale Model. The results showed a significant improvement in the short-range precipitation prediction. However, static background error statistics has no specific knowledge about the presence of a typhoon; therefore,the 3DVar method has limited effectiveness. The four-dimensional variational (4DVar) (Lewis and Derber, 1985; Talagrand and Courtier, 1987; Courtier et al., 1994) method makes full use of radar data multiple times within the assimilation window to provide initial conditions that are consistent with the prediction model. However, the high computational cost of the adjoint model and the difficulty of its maintenance make the implementation of 4DVar difficult. Despite these drawbacks, several studies have sought to develop 4DVar-based radar data assimilation. Sun and Crook (1997,1998) developed a radar data assimilation system based on 4DVar, called the Variational Doppler Radar Analysis System (VDRAS), and applied it in an initialization and simulation study of convective systems (Sun, 2005; Sun and Zhang, 2008). Wang et al. (2013) verified the capability of radar data assimilation for Weather Research and Forecasting (WRF) model 4DVar through single-observation experiments and real experiments, and demonstrated that an updated version of WRF 4DVar with the incremental formulation worked well at the convection-permitting scale for radar radial velocity and reflectivity data assimilation. Sun and Wang (2013) assimilated radar radial velocity and reflectivity data and improved short-term quantitative precipitation forecasting (QPF) in the WRF model. Based on WRF and the 4DVar system, Li et al. (2014) assimilated airborne Doppler radar observations to simulate Typhoon Nuri(2008) and found that the enhanced middle level vortex and moisture conditions were conducive to the development of central deep convection. The Ensemble Kalman filter(EnKF) data assimilation method (Evensen, 1994, 2003;Houtekamer and Mitchell, 1998; Houtekamer et al., 2014) is also widely used in radar data assimilation because it is easily implemented without the adjoint model (Snyder and Zhang, 2003; Tong and Xue, 2005, 2008; Aksoy et al.,2009, 2010). Zhang et al. (2009) and Dong and Xue (2013)effectively improved typhoon track and intensity forecasting using the EnKF method to assimilate radar data; the latter also improved QPF. However, due to the lack of a temporal smoothness constraint in the numerical models and the limited number of ensemble samples in the EnKF method, its assimilation results inevitably show lower accuracy.

To maximize the advantages of both variational methods (3DVar and 4DVar) and EnKF, the hybrid assimilation method has combined their complementary merits and has become a mainstream data assimilation method. Li et al.(2012) assimilated WSR-88D radar radial velocity data with the WRF hybrid ensemble 3DVar system. The hybrid covariance including static and flow-dependent covariance performed better than the pure static covariance in the prediction of Hurricane Ike (2008). Shen et al. (2017) used the same assimilation method to predict Typhoon Saomai(2006) using the Advanced Regional Prediction System.Hybrid covariance also had a significant effect on the 12-hour accumulated rainfall forecast. However, 3DVar-based assimilation methods can only assimilate the observations at a certain moment. The 4DEnVar method combines the advantages of 4DVar and EnKF (Lorenc, 2003, 2013; Lorenc et al., 2015; Tian et al., 2008, 2011; Wang et al., 2010; Tian and Feng, 2015), approximating the tangent model by assuming a linear relationship between simulated observation per-turbations (OPs) and model state perturbations (MPs). Thus,the solution process is simplified and observation data are assimilated simultaneously at multiple times. Buehner et al.(2010a, b) tested 4DEnVar with an NWP model in a series of 1-month analysis forecast experiments. Lu et al. (2017)assimilated tail Doppler radar data using 4DEnVar and found that the analyzed storm intensity forecasts were improved compared to hybrid ensemble 3DVar. Shen et al.(2019) compared 3DVar, hybrid ensemble 3DVar and 4DEn-Var using a WRF 4DEnVar experiment, and obtained a more realistic thermal structure of Hurricane Ike (2008), leading to improved intensity and track forecasts. Kay and Wang (2020) developed a multiresolution ensemble method to resolve a wider range of scales of the background error covariance in the Gridpoint Statistical Interpolation-based 4DEn-Var. As a 4DEnVar method, the nonlinear least-squares four-dimensional variational assimilation method (NLS-4DVar) was proposed by Tian and Feng (2015) to convert the cost function of 4DEnVar into a nonlinear least-squares problem solved using a Gauss-Newton iteration scheme (Dennis and Schnabel, 1996). When solving the cost function,the NLS-4DVar method is easy to implement without invoking the adjoint models and has higher precision than the traditional 4DEnVar method (Tian et al., 2018). Zhang et al.(2017a) evaluated the assimilation performance of NLS-4DVar in observing system simulation experiments(OSSEs); the results indicated that the NLS-4DVar method effectively absorbed the radar data and improved the initial field. In real experiments, radar data were assimilated with the NLS-4DVar method; the intensity and position prediction accuracy of heavy precipitation that occurred in eastern Hubei Province were significantly improved (Zhang et al., 2017b). To date, the NLS-4DVar method has not been applied to the study of typhoons.

The multigrid strategy is an efficient method to accelerate iterative convergence. Li et al. (2010) and Fu et al.(2016) adopted a multigrid strategy using the Space and Time Mesoscale Analysis System to assimilate radar radial velocity for improved reconstruction of typhoon structure.Zhang and Tian (2018a) applied a multigrid NLS-4DVar(MG-NLS4DVar) method in OSSEs, concluding that this approach showed dual advantages of high accuracy and efficiency in conventional data assimilation, mainly because it corrects background error from large to small scales. MGNLS4DVar has also shown clear positive effects in radar radial velocity assimilation in OSSEs and has improved the accuracy of precipitation prediction (Zhang et al., 2019).

In this study, we investigated the assimilation of radar radial velocity and reflectivity observation data from single-Doppler radar using the MG-NLS4DVar method for the case of Typhoon Haikui (2012) based on the WRF model.We compared the prediction results for typhoon structure,intensity, and track following assimilation of radar observations using the NLS-4DVar and MG-NLS4DVar methods,and then evaluated the typhoon prediction capability of the radar data assimilation system based on the WRF model and the MG-NLS4DVar method. We also examined the assimilation of radar radial velocity and reflectivity observations using MG-NLS4DVar, both individually and simultaneously. Finally, we explored the effects of NLS-4DVar and MG-NLS4DVar assimilation of radar data in QPF for Typhoon Haikui (2012). This study evaluated the application of our newly developed MG-NLS4DVar method for real radar data assimilation, especially for small- and medium-scale weather forecasts. This represents a continuation and promotion of the work of Zhang and Tian (2018a)and Zhang et al. (2019).

The remainder of this article is organized as follows. Section 2 briefly reviews the MG-NLS4DVar method and the radar observation operator. Section 3 describes Typhoon Haikui (2012), the radar observations and verification method used in this study, as well as the numerical experiments including the model and experimental configurations.The impact of radar data assimilation based on a multigrid strategy on deterministic forecasts of intensity and track is discussed in section 4. Section 5 shows the results of assimilating radar radial velocity and reflectivity observations, both singly and simultaneously. The results of assimilation window length sensitivity experiments are shown in section 6.Finally, a summary is provided in section 7.

2.Methods

2.1.Brief introduction to NLS-4DVar

The formulas for the incremental form of the 4DVar cost function at the initial timeare as follows:

NLS-4DVar uses 4D samples to approximate the tangent and minimize the incremental form of the 4DVar cost function to obtain the analysis increment (Tian and Feng,

Step four: Ifi

2.3.Observation operators for radar

Sun and Crook (1997, 1998) proposed observation operators for radar. VDRAS was constructed based on these operators, which has been employed in many studies with assimilated radar data to predict typhoons and improve precipitation, with positive results (Xiao et al., 2007; Xiao and Sun,2007; Pu et al., 2009; Sun and Wang, 2013; Wang et al.,2013; Zhang et al., 2015, 2017a, b). Therefore, these observation operators for radar were applied in the present study.

3.Typhoon Haikui (2012), prediction model,data and experimental setup

3.1.Typhoon Haikui (2012)

Typhoon Haikui (2012) was one of the most intense typhoons that landed on the east coast of China in 2012; it formed in the Northwest Pacific at 0000 UTC 3 August 2012, and then migrated to the northwest or north-northwest. The typhoon intensified to become a tropical storm at 0900 UTC 5 August and entered the eastern part of the East China Sea. Haikui (2012) again intensified at 0900 UTC 6 August, becoming a strong typhoon near the coastal area of southern Zhejiang Province at 0600 UTC 7 August. The typhoon made landfall at Xiangshan County, Zhejiang Province, at 1920 UTC 7 August, with a minimum sea level pressure (MSLP) of 960 hPa and maximum surface wind speed of 40 m s?1. Haikui (2012) moved westwards across Ningbo, Shaoxing, and Hangzhou after landfall, and then gradually weakened to become a tropical depression at 0400 UTC 9 August. The best track of Typhoon Haikui (2012)between 1400 UTC 7 August to 0800 UTC 8 August, according to official best-track data from the China Meteorological Administration (CMA), is shown in Fig. 1. Typhoon Haikui (2012) brought heavy rains to central and northern Zhejiang Province, southern Anhui Province, and southern Jiangsu Province. In some areas, the 12-h accumulated precipitation exceeded 140 mm (shown in Fig. 8a). In this study,radial velocity and reflectivity data obtained from Ningbo Doppler radar were assimilated using the MG-NLS4DVar method, and the intensity, track, and precipitation of Typhoon Haikui (2012) were predicted using the WRF model.

3.2.Prediction model

Fig. 1. Domain of the numerical simulation at 3-km horizontal resolution, with the best track of Typhoon Haikui (2012)marked at 1-h intervals from 1400 UTC 7 August to 0800 UTC 8 August (red lines). The filled star indicates the position of the Ningbo radar; the circle indicates the range of the assimilated Doppler radar data (150 km).

WRF version 3.9 was used as the prediction model in this study. The domain of the numerical simulation was(27°-33°N, 117°-125°E) (Fig. 1). The domain was configured with 260 × 220 (longitude × latitude) grid points,with 3-km grid spacing and 30 levels in the vertical direction from the surface to 50 hPa. MG-NLS4DVar experiments were conducted over three different meshes (coarse,fine, and finest) in the horizontal direction. The number of grid points decreased twofold from the finest grid to the coarse grid; thus, the finest, fine, and coarse grid levels had 260 × 220, 130 × 110, and 65 × 55 grid points, respectively.Parameterization included the WRF Single-moment 6-class microphysics scheme (Hong and Lim, 2006), the Rapid Radiative Transfer Model longwave radiation scheme (Mlawer et al., 1997), the Dudhia shortwave radiation scheme (Dudhia, 1989), the Yonsei University planetary boundary layer scheme (Hong et al., 2006), and the Noah land surface model land scheme (Tewari et al., 2004). We excluded the cumulus parameterization scheme.

Assimilation analysis of the NLS-4DVar method is performed in the model space; thus, the analysis variables are the model variables. In this study, the analysis variables included velocity componentsand, perturbation potential temperature, perturbation pressure, water vapor mixing ratio, rain water mixing ratio, and cloud water mixing ratio. These variables can be increased or decreased according to the particular assimilation problem.

3.3.Data and quality control

National Centers for Environmental Prediction (NCEP)Final (FNL) operational global analysis data (1° resolution)provide first-guess field and boundary conditions. The assimilation data used in this study were radial velocity and reflectivity data from Ningbo Doppler radar for Zhejiang Province,China (30.07°N, 121.51°E), at an altitude of 458.4 m. The maximum Doppler range is 230 km. Considering the quality of the data, only data within the 150 km range were assimilated. The radar data coverage is shown in Fig. 1. To avoid the destruction of observation and analysis results by non-meteorological echo, it is necessary to perform quality control of radar data prior to assimilation. Data preprocessing included data de-noising, erasing folded velocity, and removing ground clutter and speckle. The innovation vectors (i.e.,observation minus background) were also used for quality control. All elevation scans (0.5°, 1.5°, 2.4°, 3.4°, 4.3°, 6.0°,9.9°, 14.6°, and 19.5°) were assimilated for reflectivity data,but the lower seven elevation scans (0.5°, 1.5°, 2.4°, 3.4°,4.3°, 6.0°, and 9.9°) were assimilated for radial velocity. To suppress possible spurious convection, negative reflectivity values were set to zero and still assimilated, in an approach similar to that of Dong and Xue (2013). Raw Doppler radar data have substantially high resolution: 250 m for radial velocity and 1 km for reflectivity. The mismatch in resolutions between raw observation and model-simulated data imposes a burden on the assimilation system. Therefore, we randomly retained only one observation of the same type in each model grid cube as a form of data thinning. The observation error of radial velocity and reflectivity were 1 m s?1and 1 dBZ, respectively, similar to those described by Zhang et al. (2017b).

3.4.Verification methods

We performed verification using the root-mean-square error (RMSE), correlation coefficient (CC) and normalized standard deviation (SDV), calculated as follows:

whereMis the total number of observation sites used for verification;andare theth forecast values and observations, respectively;is the mean ofMforecast values; andis the mean ofMobservations.

The equitable threat score (ETS) and bias score (BS)are perhaps the most widely used for model QPF verification (Schaefer, 1990; Schwartz et al., 2009). Figure 2 shows a schematic diagram of model QPF verification performed in this study. Rain area was defined as the precipitation area without any missing measured values. For any given precipitation threshold over an accumulation period, the observed rain area isO, the model forecast rain area isF, the intersection ofOandFindicates a hit (H), and the entire assessment domain isN(Table 1).O?His an area where precipitation is observed but not predicted (misses);F?His an area representing false alarms (predicted but did not occur), andN? (O+F?H) is an area where precipitation is correctly predicted to not occur (correct negatives). Accordingly, ETS and TS are defined as

Fig. 2. Schematic diagram of model QPF verification for a specified threshold during a given accumulation time period within a region.

Table 1. Precipitation verification criteria.

Thus, the ETS measures the fraction of observations that are correctly forecast and penalizes both misses and false alarms. ETS = 1 indicates a perfect forecast; ETS ≤ 0 indicates that the model has no forecast skill. BS is the ratio of predicted rain area to the observed rain area, and it therefore varies from 0 to infinity; however, a score of unity indicates a perfect forecast.

The fractions skill score (FFS) is another metric used for model QPF verification, especially for high-resolution models. In this study, we used FSS following Schwartz et al. (2009). The precipitation accumulation thresholdis selected to define an event, and the observedand model forecastrainfall fields are converted into binary grids.The grid points with accumulated precipitationare assigned a value of 1 and those with accumulated precipitationare assigned a value of 0, as follows:

where a score of 0 indicates perfect performance and larger FBS values show worse correspondence between model forecast and observations. Thus, the worst possible FBS is defined as:

The FSS can be defined by comparing FBS and FBSworst (Roberts, 2005) as follows:

The FSS also ranges from 0 to 1, such that larger values indicate a higher number of grid points in which the model forecast precipitation and observed precipitation both exceed the threshold at the same time in every neighborhood within the verification domain, such that model forecast precipitation is closer to the observed precipitation. A score of 1 indicates perfect prediction, whereas a score of 0 indicates no predictive skill.

3.5.Data assimilation setup

The analysis time was 1400 UTC 7 August 2012; an 18-h deterministic forecast was run until 0800 8 August 2012. The baseline control forecast without radar data assimilation (CTRL) was run from 1400 UTC 7 August to 0800 UTC 8 August, initialized using the first-guess field at 0600 UTC 7 August with NCEP FNL data for 8-h integration,where the 8 h were used as the spin-up period. We conducted seven experiments in this study (Table 2); all experiments except CTRL assimilated radar data. The first two experiments, NLS and MG_All (also called MG_6h), assimilated radar radial velocity and reflectivity every 30 min with an assimilation window of 6 h (from 1400 to 2000 UTC 7 August) using the NLS-4DVar and MG-NLS4DVar methods, respectively. To investigate the influence of the multigrid strategy on typhoon intensity and track forecasts, we compared MG_All (final level,n= 3) with NLS (maximum iteration number,Imax= 3). Experiments MG_Vr and MG_Z assimilatedVralone andZalone, respectively (Table 2).A set of sensitivity experiments, MG_1h and MG_3h (Table 2), were the same as MG_All but assimilated data with assimilation windows of 1 and 3 h, respectively. To make the amount of assimilated radar data equivalent to the experiment MG_All, the time intervals for MG_1h and MG_3h were 6 and 15 min, respectively. The number of observations assimilated for MG_All, MG_1h and MG_3h was 1 127 620, 862 351 and 1 030 053, respectively. These experiments are illustrated in Fig. 3.

Table 2. List of experiments. DA, data assimilation; Vr, radial velocity; Z, reflectivity; NA, not applicable.

The methods used in these experiments employ a 4D moving sampling strategy (Wang et al., 2010; Tian et al.,2014) to produce MPs () and OPs () . In particular, two 72-h model integrations were initialized from 0000 UTC 6 August and 1200 UTC 6 August, respectively. According to the length of the assimilation window, these long-term sequence forecasting fields intercept two forecasts containing analysis time, each of which contains 106 moving windows; the sampling window moves back 30 min each time.Thus, the size of the ensemble was 212. The 212 ensemble samples were thein step two of section 2.2 (i.e.,). The horizontal localization radius was 90 km.

4.Verification of typhoon analysis and forecast results

Analysis and comparison of the results of the NLS and MG_All experiments are presented as follows. Section 4.1 provides the typhoon structure analysis. Section 4.2 presents our analysis of the typhoon intensity and track forecast results. Section 4.3 presents the precipitation forecasting evaluation results. Finally, the computational efficiency of the two methods is compared in section 4.4.

4.1.Typhoon structure analysis

Figure 4 shows the sea level pressure (SLP) and surface wind speed at the end of the assimilation window(2000 UTC 7 August 2012) for experiments CTRL, NLS,and MG_All, with predicted typhoon center positions indicated. Typhoon SLP and best-track data were obtained from Weather China (www.weather.com.cn), a public meteorological service portal website maintained by the CMA and hosted by the CMA Public Meteorological Service Center. The CTRL MSLP was about 3 hPa lower than the observed value. Therefore, Haikui (2012) was stronger in the CTRL experiment. The gradient of SLP determined by NLS and MG_All was smaller than that from CTRL, and typhoon intensity was slightly weaker. MSLP increased to 967.286 and 967.186 hPa in the NLS and MG_All experiments,respectively. Compared with CTRL, the typhoon center positions of NLS and MG_All were closer to the observed typhoon (Fig. 4). These results indicate that both assimilation methods effectively absorbed radar observations and improved the initial field. We determined the typhoon center position according to MSLP.

To better analyze the impact of radar data assimilation,we plotted the increment of horizontal wind vectors and wind speed at a height of 3 km at 2000 UTC 7 August 2012(Fig. 5). In the NLS and MG_All results, horizontal wind increments exhibited a clockwise rotating anticyclonic structure. The weakening effect of this anticyclonic structure on the TC structure was consistent with the weakening effect of SLP shown in Fig. 4, and brought the assimilated results closer to the observed typhoon. Based on the data shown in Figs. 4 and 5, NLS and MG_All similarly improved SLP and horizontal wind speed.

Wind and pressure fields from the CTRL, NLS, and MG_All experiments at 2000 UTC 7 August at a height of 1 km and a vertical south-north cross section of the typhoon through the individual vortex center of each experiment are shown in Fig. 6. Compared with CTRL, wind speeds were lower and pressure at the center was higher in the NLS and MG_All results (Figs. 6a-c). Figures 6d and e show that the maximum wind speed in all experiments occurred north of the vortex center, i.e., the right front of the typhoon. All three experiments showed clear vortex and typhoon eye structures. Compared with the CTRL experiment, the NLS and MG_All experiments showed lower wind speeds in the typhoon eye. In the CTRL experiment, the height of the wind speed exceeding 30 m s?1reached 200 hPa, whereas those of MG_All and NLS reached only 400 hPa.

Fig. 3. Flowchart of the data assimilation experiments and the CTRL experiment.Each upward arrow indicates the amount of time required to assimilate the radar data.

Fig. 4. Analyzed SLP (solid contours; units: hPa) and surface wind (vectors) for Typhoon Haikui (2012) at 2000 UTC 7 August 2012, derived in the (a) CTRL, (b) NLS, and (c) MG_All experiments. Approximate center positions of the typhoon determined by observed typhoon (blue dot), CTRL (purple dot), NLS (green dot), and MG_All (red dot) are indicated.

Figures 6g-i show the vertical velocity and temperature deviation in the vertical south-north cross sections. All experiments show a clear warm core at low to mid-levels near the typhoon eye, but the warm core was significantly weaker in the NLS and MG_All experiments than in the CTRL experiment. Although the CTRL experiment downdraft was less than 1 m s?1on both sides of the vertex center, significantly weaker than those of NLS and MG_All, the range of updrafts in the north gale area of the vortex center was larger. Clearly, after assimilating the radar radial velocity and reflectivity, the vortex weakened slightly, which was consistent with the increase in MSLP in the NLS and MG_All experiments shown in Fig. 4. These adjustments to the vortex structure by assimilation affected the predictions. The NLS and MG_All results remained similar.

Dong and Xue (2013) analyzed the vertical structure of the Hurricane Ike (2008) and reported the changes in the horizontal wind speed through the vortex center, vertical velocity, and temperature after radar data assimilation, confirming a change in vortex intensity. In their predictions of Typhoon Saomai (2006), Zhao et al. (2012) and Shen et al.(2017) enhanced the weak vortex simulated by CTRL after assimilating radar radial velocity data, and obtained a warmer core structure in the vertical cross section in assimilation experiments. These previous studies corroborate the results obtained in the present study (Fig. 6).

Rather than look at helplessly her two babies die in succession, the female eagle thought she should do something. She pulled apart her own chest with the sharp beaks5, the feathers that fell off her body being blowed here and there by the icy wind. With feeble strength, she told her last baby who was still at the verge6 of death: Eat me… . Outside, the male eagle, who stood for a long time keeping close watch on the food, shook out the snow accumulated in her wings. After making a yowl, he made his best efforts to unfold two wings, flinging into the sky. He overlooked the land, which was still a vast expanse of whiteness. Suddenly, a leaden object jumped into his eyes.

Fig. 5. Increments of horizontal wind (vectors) and wind speed (shaded; units: m s?1) at z = 3 km for the (a) NLS and(b) MG_All experiments at 2000 UTC 7 August 2012.

Figures 4-6 show that the pressure of the CTRL vortex center was stronger than the observed pressure, but the difference was less than 3 hPa. The difference was further reduced, to within 1 hPa, in the NLS and MG_All experiments. Small improvements were also indicated in vortex structure, reflecting the positive role of radar data assimilation in improving typhoon structure.

The similar assimilation results obtained in the NLS and MG_All experiments demonstrate that both assimilation methods showed the same degree of improvement in typhoon structure and that both had positive effects.MG_All assimilates radar data using a multigrid strategy from the coarse to finest grid scale, whereas NLS assimilates data in three iterative processes at the finest grid scale.We obtained remarkably higher computational efficiency in the MG_All experiment, as will be described in section 4.4.

4.2.Intensity and track forecasts

Figure 7 shows a comparison of 13-h tracks and MSLP(hPa) values forecast by CTRL, NLS, MG_All for 2000 UTC 7 August to 0800 UTC 8 August 2012, as well as track errors. The typhoon predicted by the CTRL, NLS, and MG_All experiments advanced in the northwest direction,consistent with the best track (Fig. 7a). However, the typhoon track predicted by CTRL was mainly located northeast of the observed track, which was farthest from the observed track in all experiments. The CTRL track error reached 37.6 km at 2100 UTC 7 August (2 h after landfall).Although track error decreased during the following 2 h, the error continued to increase after 2300 UTC 7 August, for a mean track error of 22.2 km (Fig. 7b). With radar data assimilation, the tracks predicted by NLS and MG_All oscillated on both sides of the observed track with a small amplitude;these were clearly closer to the best track than was CTRL.The mean track error of the NLS and MG_All experiments was 15.68 and 15.42 km, respectively; MG_All showed a slight advantage. These results demonstrate that assimilated radar data had a positive impact on typhoon track forecasting, reflecting the advantages of the multigrid strategy.

The MSLP values determined by CTRL, NLS, and MG_All are compared in Fig. 7c. Although MSLP was greatly underestimated, NLS and MG_All showed significant improvement over CTRL in the 13-h forecast, with two curves almost overlapping. NLS and MG_All reduced the error by 0.714 and 0.814 hPa, respectively, at 2000 UTC 7 August; these values were lower than the difference between CTRL and the best-track MSLP (2.96 hPa). This MSLP error reduction showed about 76% improvement over CTRL for NLS and 73% for MG_All. The formula was defined as, where error is defined as the difference between the model result and best-track data. The observed typhoon weakened due to landfall, and its MSLP continued to increase, from 968 hPa at 2000 UTC 7 August to 982 hPa at 0800 UTC 8 August,an increase of 14 hPa. In the 13-h forecast, MSLP increased by 4.26 hPa in the CTRL experiment, whereas those of NLS and MG_All increased by 6.76 and 6.549 hPa, respectively.

The advantages of the NLS-4DVar method in predicting typhoon intensity and track using radar data assimilation are illustrated in Fig. 7, which indicates that MG_All slightly outperformed NLS.

4.3.Precipitation forecasts

Fig. 6. (a-c) Horizontal wind (vectors) and pressure (contours, 3-hPa intervals) at a height of 1 km at 2000 UTC 7 August derived from the (a) CTRL, (b) NLS, and (c) MG_All experiments. Purple, green, and red dots indicate vortex centers for CTRL, NLS, and MG_All, respectively. (d-f) South-north vertical cross section of horizontal wind speed (shaded; units: m s?1) through the vortex center for (d) CTRL, (e) NLS, and (f) MG_All (black dotted lines in a-c). (g-i) Temperature deviation (contours, 1°C intervals) and vertical velocity (shaded; units: m s-1) for the three corresponding cases in the same vertical south-north section.

Severe inland flooding from local precipitation is a major hazard associated with typhoon landfall, resulting in the loss of lives and property. Therefore, QPF to allow timely warning and damage mitigation is an essential component of typhoon prediction. Figures 8a and b show the FFS of every 3-h accumulated precipitation for a threshold of 30 mm with an ROI of 24 km and 48 km, respectively. CTRL had the lowest score for all thresholds and ROIs during the entire forecast period except for the last moment. The FSS of MG_All was much higher than that of CTRL at the first moment of both ROIs. The FSS of NLS was very close to that of MG_All. The BS of all experiments also indicated that the rainfall overprediction by CTRL was effectively weakened after radar data assimilation (Fig. 8c). Figure 9 shows the 12-h accumulated precipitation for all experiments and rainfall measurements from more than 3000 national and automatic weather stations. Compared with cumulative precipitation observations (Fig. 9a), forecast precipitation was greater in all three experiments (Figs. 9b-d).The maximum observed rainfall occurred in the border area between northwest Zhejiang Province and Anhui Province(Fig. 9a). However, CTRL also predicted strong precipitation, exceeding 100 mm, in northern and eastern Zhejiang Province (Fig. 9b). NLS and MG_All predicted significantly weaker precipitation than the false heavy precipitation areas predicted by CTRL, especially in eastern Zhejiang Province (Figs. 9b and c). Predicted precipitation results were similar between NLS and MG_All.

The Taylor diagram (Taylor, 2001) shown in Fig. S1(in Electronic Supplementary Material, ESM) was used to comprehensively evaluate the 12-h accumulated precipitation predictions of the three experiments in terms of SDV and CC. The distance between the model point in the Fig.S1 and the observation point (REF point in Fig. S1) is used to indicate the effect, where a closer distance indicates better model prediction. Good correlation was observed between observed and predicted precipitation, with little difference between experiments; however, the SDV values of NLS and MG_All were closer to 1 than that of CTRL. Thus,NLS and MG_All were closer to the REF point, indicating better prediction in these experiments.

Fig. 7. Typhoon Haikui (2012) track and MSLP during the 13-h forecast period from 2000 UTC 7 August to 0800 UTC 7 August 2012. Predicted (a)track, (b) track error (km), and (c) MSLP (hPa) determined in the CTRL (blue lines), NLS (green lines), and MG_All (red lines) experiments. Best-track data (black lines) are shown for comparison.

To further quantify the precipitation forecast abilities of the models, we compared the ETS for 12-h cumulative precipitation among CTRL, NLS, and MG_All from 2000 7 August to 0800 UTC 8 August 2012 (Fig. S2). We selected thresholds of 100 and 140 mm to represent heavy precipitation. NLS, which incorporates radar data assimilation, had a significantly higher ETS at both thresholds. The ETS of MG_All was 0.1842 at the 100-mm threshold, slightly higher than that of CTRL (0.1836). However, at the 140-mm threshold, MG_All had a substantially higher ETS. The FSS of 12-h accumulated precipitation was calculated (Fig.S3) for thresholds of 100 and 140 mm, with two ROIs (24 km and 48 km). MG_All had the highest scores for all thresholds and ROIs. NLS and MG_All outperformed CTRL in terms of FSS, as they did in terms of ETS. BS values corresponding to the two thresholds (Table 3) show a larger difference between CTRL and observations (BS >2)than between NLS, MG_All and observations, which had BS values closer to 1.

Fig. 8. FSS of every 3-h accumulated precipitation for a threshold of 30 mm and ROIs of (a) 24 km and (b) 48 km. (c) Bias for deterministic forecasts by CTRL, MG_All, and NLS.

Thus, the NLS-4DVar method significantly improved predictions of heavy precipitation (>100 mm) following radar data assimilation, showing much lower precipitation values in regions for which CTRL falsely predicted heavy precipitation. The results shown in Fig. 9 were confirmed by quantitative analysis using the ETS, FSS and BS, with NLS showing slightly greater improvement than MG_All.

4.4.Computational efficiency

The NLS and MG_All results show the same degree of positive effect. Therefore, we compared the CPU time required by both assimilation methods (Table 4). Numerical experiments were conducted on a Lenovo ThinkSystem SR650 server comprising 224 CPUs with 1288-G memory. Assimilation calculations were performed serially using single nodes and a single core. The forecast model operation was run in parallel using 48 cores; CPU time for each model run was case- and machine-dependent. Table 4 lists the time required for each iteration of NLS and for each grid scale of MG_All, as well as their respective total CPU times. The average time required for each NLS iteration was about 38 min (assimilation process); forecast model runs required 26 min. The CPU times required for the three MG_All grid levels were 24.9, 27.2, and 38.1 min. The use of multigrid storage by the MG_All method greatly reduced its calculation cost. The same number of radar observations was assimilated in each iteration and at each grid level:1 127 620.

Thus, radar data assimilation had a positive effect on typhoon forecasting and analysis by the NLS-4DVar method. After assimilating radar radial velocity and reflectivity data, predictions of Typhoon Haikui (2012)’s structure,intensity, track, and precipitation were significantly improved. Our comparison of NLS and MG_All results demonstrated that, although MG_All was slightly inferior in terms of precipitation prediction, it showed considerable advantages, with a slight improvement in typhoon intensity and track prediction accuracy and substantial improvement in computational efficiency. These advantages can be attributed to the use of grids with different resolution for data assimilation, which allows gradual error correction at large to small scales.

Fig. 9. Accumulated precipitation (units: mm) during the 12-h period from 2000 UTC 7 August to 0800 UTC 8 August 2012, determined by (a) observation and the (b) CTRL, (c) NLS, and (d) MG_All experiments.

Table 3. Bias scores of 12-h accumulated precipitation from 2000 7 August to 0800 UTC 8 August 2012, at thresholds of 100 and 140 mm for deterministic forecasts by CTRL, NLS, and MG_All.

5.MG_Vr and MG_Z results

In this section, we compare assimilation results amongMG_Vr (assimilation ofVralone), MG_Z (assimilation ofZalone), and MG_All (assimilation of bothVrandZ) using the MG-NLS4DVar method.

Table 4. CPU times for NLS (Imax = 3) and MG_All (n = 3). is the number of iterations of NLS, and is the ith grid level of MG_All.

Table 4. CPU times for NLS (Imax = 3) and MG_All (n = 3). is the number of iterations of NLS, and is the ith grid level of MG_All.

CPU time (min) NLS MG_All L1/I1 38.2 + 13 24.9 + 13 L2/I2 38.4 + 13 27.2 + 13 L3/I3 38.6 38.1 Total CPU time 115.2 + 26 90.2 + 26

SLP and surface wind vectors for Typhoon Haikui(2012) at 2000 UTC 7 August 2012, from CTRL, MG_Vr,MG_Z, and MG_All are plotted in Fig. S4, including predicted typhoon center positions. The assimilation of different types of radar data (VrorZor both) improved MSLP to different extents, as shown by differences in the SLP gradient among the four images (Figs. S4a-d). The largest increase in MSLP was produced by MG_Vr, slightly exceeding the observed MSLP; however, there was no clear correction of the typhoon center location (Fig. S4b). The differ-ence in MSLP between MG_Z and CTRL was 0.364 hPa,revealing little effect on this variable by MG_Z, although the assimilation ofZalone resulted in effective adjustment of the typhoon center position (Fig. S4c). MG_All combined the advantages of both models, improving SLP and modifying the typhoon center position, which is apparently influenced by bothVrandZ(Fig. S4d).

The increments of horizontal wind at 3-km height shown in Fig. S5 further demonstrate the degrees of typhoon prediction improvement achieved by MG_Vr,MG_Z, and MG_All. The increments obtained by assimilating only radial velocity data were greater than that those obtained by assimilating reflectivity alone or assimilating both data type. MG_Vr formed more pronounced anticyclonic circulation than did MG_Z, weakening the CTRL circulation field (Fig. S5a). After adding reflectivity information,increments of MG_All near the typhoon center increased,whereas those near the gale decreased.

Among MG_Vr, MG_Z, and MG_All, the track forecast of MG_Z deviated farthest from the best track from 2000 UTC 7 August to 0800 UTC 8 August (Fig. S6), and was closer to the best track than was CTRL (Fig. S6a). The track predicted by assimilation of reflectivity alone showed 14% improvement in mean track error compared with CTRL (Fig. S6b). Tracks predicted by MG_Vr and MG_All were relatively consistent after 0800 UTC 8 August, oscillating to either side of the best track (Fig. S6a). MG_Vr and MG_All appeared to have produced better tracks than CTRL and MG_Z. Hourly track error values further demonstrated the advantages of MG_Vr and MG_All, with MG_All showing the smallest mean error.

Figure S6c shows typhoon intensity predictions by CTRL, MG_Vr, MG_Z, and MG_All. MSLP was improved to different extents among the three assimilation experiments compared with CTRL. As shown in Fig. S4, the information capture capability of reflectivity data for typhoon intensity was weaker than that of radial velocity data, and MSLP was larger in the MG_Z prediction than in those of MG_Vr and MG_All during the 13-h forecasts. Figure S6c also shows that the assimilation ofVrdata had the greatest impact on MSLP in MG_All, with differences between those of MG_Vr and MG_All generally less than 1.1 hPa.This result is consistent with that reported by Dong and Xue(2013), but not by Zhao and Xue (2009); the former study applied direct reflectivity assimilation, as we did in this study, whereas the latter used a complex cloud analysis method to adjust the temperature and humidity fields, exerting a large influence on MSLP.

Pu et al. (2009) used WRF 3DVar assimilation radar data to predict the intensity of Hurricane Dennis (2005);they found that the assimilation of radial velocity alone or both radial velocity and reflectivity had a greater effect on typhoon intensity and track prediction than did the assimilation of reflectivity alone. This finding is consistent with the results of the present study, mainly because typhoons are wind-dominated systems and radial velocity data provides wind field information within the typhoon structure. Reflectivity is directly related to the microphysical field; therefore, correlations between reflectivity and wind fields estimated from the ensemble may be uncertain (Dong and Xue, 2013).

The FSS results of every 3-h accumulated precipitation from the experiments CTRL, MG_Vr, MG_Z and MG_All are compared in Fig. S7 for a 30-mm threshold and ROIs of 24 km (Fig. S7a) and 48 km (Fig. S7b). Assimilating radial velocity and reflectivity (MG_ALL) generally resulted in higher FSS than observed in the other experiments, except for the last moment. Assimilation of the radial velocity(MG_Vr) produced higher FSS than did assimilation of the reflectivity (MG_Z); however, MG_Z produced a higher FSS at 0200 UTC, perhaps due to the rainfall overprediction. The MG_Vr, MG_Z and MG_All experiments all reduced the BS compared with CTRL (Fig. S7c), especially BS of MG_Vr, which was closest to 1.

Figure S8 shows the 12-h accumulated precipitation from 2000 UTC 7 August to 0800 UTC 8 August 2012, for all experiments. Precipitation forecast by the assimilation of radar radial velocity data alone was closest to the observed precipitation. The false heavy precipitation (> 135 mm) in northern Zhejiang Province was significantly reduced, to less than 120 mm, and the range of false heavy precipitation exceeding 150 mm in eastern Zhejiang Province was markedly reduced (Fig. S8c). No improvement of precipitation was apparent after assimilating reflectivity data alone(Fig. S8d). The prediction accuracy of MG_All was shown to be between those of the other two experiments (Figs.S9-S11). Figure S9 shows the SDV and CC of 12-h accumulated precipitation for CTRL, MG_Vr, _MG_Z and MG_All experiments as a Taylor diagram. Clearly, MG_Vr provided the best result, followed by MG_All. All three assimilation experiments improved the CTRL results to varying degrees.The ETS of 12-h cumulative precipitation shown in Fig.S10 quantitatively demonstrates the improvement achieved by assimilation of radar data over the false heavy precipitation of CTRL. At the 100- and 140-mm thresholds, MG_Vr had the highest score, consistent with the results shown in Fig. S8c. MG_Z increased the score by only 0.01 at the 140-mm threshold. The advantages of MG_Vr are further confirmed in Fig. S11. There was a large difference in FSS between MG_Vr and CTRL at two thresholds. Note that the MG_All also had the higher FSS than CTRL at two thresholds, whereas MG_Z outperformed CTRL only at the 140-mm threshold. A comparison of BS among the four experiments shows the largest decrease in bias in MG_Vr, followed by MG_All, and MG_Z (Table 5). This result is consistent with previous results in the present study and suggest that the influence of radar radial velocity data assimila-tion was dominant in precipitation forecasts.

Table 5. As in Table 3 but for experiments CTRL, MG_Vr,MG_Z and MG_All.

The differences in precipitation forecasts obtained by assimilating radial velocity alone and assimilating reflectivity alone were further examined using the water vapor field and the dynamic field analyses. Figure S12 illustrates the differences between MG_Vr, MG_Z, and CTRL at 850 hPa for rain water mixing ratio, water vapor mixing ratio and cloud water mixing ratio at 2000 UTC 7 August 2012. The rain water mixing ratio around the eyewall and the rainband were mainly weakened by the assimilation of radial velocity alone, especially on the northwest side of the eyewall(Figs. S12a and d). When only the reflectivity was assimilated, the rain water mixing ratio increased significantly on the northwest and southeast sides of the eyewall, reaching 1.2 g kg?1. The water vapor mixing ratio of MG_Vr around the eyewall and in northern Zhejiang Province was weakened to a greater extent than in MG_Z (Fig. S12b and e), especially, decreasing by more than 1.2g kg?1in the ocean area, which strongly influenced on the source of water vapor for future precipitation. The cloud water mixing ratio also differed in MG_Vr and MG_Z, mainly around the typhoon eyewall (Figs. S12c and f).

Figure S13a and b compare the vertical velocity of MG_Vr and MG_Z at 850 hPa. The experiment that assimilated reflectivity alone (MG_Z) produced faster upward motion than experiment MG_Vr, which was more conducive to the development of convection.

The improvement in precipitation forecasting obtained by assimilating radial velocity alone was more obvious than that obtained by assimilating reflectivity alone. This result may be due to the greater weakening of the rain mixing ratio, water vapor mixing ratio and cloud water mixing ratio by MG_Vr compared with CTRL; this effect greatly reduces the amount of water vapor in precipitation. Another possibility is greater weakening of the CTRL cyclone structure by radial velocity assimilation (Fig. S5a); the weaker upward motion of MG_Vr may correct the convective motion. Pu et al. (2009) also observed a larger impact on the precipitation forecasts of Hurricane Dennis (2005) due to the assimilation of radial velocity data; they suggested that this phenomenon may result from the improved vortex inner convergence and divergence, as well as modified convection conditions in the initial vortex.

6.Sensitivity experiments

To examine the sensitivity of the typhoon prediction to the length of the radar data assimilation window, radial velocity and reflectivity data were assimilated with windows of 1, 3, and 6 h in MG_1h, MG_3h, and MG_All, respectively.Because a 6-h assimilation window was adopted, MG_All is also referred to as MG_6h in this section (Table 2).

Figure S14 compares typhoon intensity and track forecasts by the three experiments from 2000 UTC 7 August to 0800 UTC 8 August 2012. The overall direction of the predicted track was relatively consistent among the three experiments, especially between MG_1h and MG_3h (lines nearly overlapping) (Fig. S14a). However, as shown in Fig. S14b,MG_All (MG_6h) was closest to the best track. Track errors were large in MG_1h and MG_3h from 2000 UTC 7 August to 0100 UTC 8 August 2012, and then declined steadily. The mean track errors of MG_1h, MG_3h, and MG_All(MG_6h) were 17.06, 19.20, and 15.42 km, respectively.Typhoon intensity predictions associated with MSLP by MG_1h and MG_3h were similar, with MG_6h providing better prediction (Fig. S14c). According to the FSS of every 3-h accumulated precipitation at the 30-mm threshold,MG_All had the highest scores at 2300 UTC and 0500 UTC in all four experiments (Figs. S15a and b). The BS of MG_1h was the closest to 1 (Fig. S15c). Figure S16 shows that at the 100-mm threshold, ETS values for 12-h accumulated precipitation (from 2000 UTC 7 August to 0800 UTC 8 August 2012) were similar among the three experiments,at 0.1790, 0.1887, and 0.1842 for MG_1h, MG_3h, and MG_All (MG_6h), respectively. However, MG_1h and MG_3h had the higher scores than MG_All at the 140-mm threshold.

Therefore, a 6-h assimilation window (30-min intervals) was the most appropriate for intensity, track and precipitation forecasts of Typhoon Haikui (2012) in the present study. One possible reason for this result is that the MG_6h experiment incorporated longer-term observations.Although the frequency of observation data assimilation was not high (every 30 min), the background field was adjusted continuously for a long period. However, a longer the assimilation window did not necessarily yield better results;an excessively long assimilation window can result in the introduction of too many model errors, worsening the forecast.

7.Summary and conclusions

In this study, radar radial velocity and reflectivity data were assimilated using a multigrid NLS-4DVar method(MG-NLS4DVar), and structure analysis and intensity and track predictions of Typhoon Haikui (2012) were conducted using the WRF model. Two sets of comparative experiments were designed to investigate the impact of radar data assimilation by MG-NLS4DVar on typhoon characteristics.NLS-4DVar and MG-NLS4DVar required three iterations(Imax= 3) and three grid level (n= 3), respectively, to assimilate radial velocity and reflectivity data. Based on the MGNLS4DVar method, radial velocity and reflectivity data were assimilated using a 6-h assimilation window, simultaneously and individually. We also explored the effects of using assimilation windows of 1, 3, and 6 h. The structure and forecast intensity and track of the typhoon were analyzed and compared among experiments. This is the first study to apply assimilation of radar radial velocity and reflectivity data using MG-NLS4DVar for typhoon analysis and prediction. The main conclusions of all experiments are as follows.

The assimilation of radial velocity and reflectivity data by NLS-4DVar and MG-NLS4DVar weakened the stronger CTRL and adjusted the typhoon structure. The adjusted typhoon vertical structure helped improve the accuracy of intensity and track predictions for Typhoon Haikui (2012).Although MG-NLS4DVar showed little advantage over NLS-4DVar in terms of intensity and track prediction, and was slightly inferior to NLS-4DVar for 12-h accumulated precipitation prediction, its efficient computing power due to the implementation of a multigrid strategy allowed rapid completion of the assimilation process while maintaining high prediction accuracy.

The assimilation of radial velocity alone led to much greater improvement in typhoon intensity than did that of reflectivity alone. The assimilation of radial velocity alone provided clear improvement in track prediction, whereas assimilation of both radial velocity and reflectivity yielded similar results to the assimilation of radial velocity alone.The assimilation of radial velocity alone substantially weakened the false heavy precipitation predicted by CTRL,indicating the important role of radial velocity data in typhoon forecasts produced using the MG-NLS4DVar method. The larger impact on the precipitation forecasts due to the assimilation of radar radial velocity may have been caused by weakened water vapor and vertical movement at lower levels. In this study, the model variables of the assimilation reflectivity update is in a manner similar to radial velocity, as mentioned above. Dong and Xue (2013) used EnKF to analyze Typhoon Ike (2008), updating only pressure and microphysical variables by reflectivity assimilation; they expected reflectivity assimilation to have a negative effect on the update of other variables. However, for typhoons, the influence of radial velocity is greater than that of reflectivity; our results are consistent with this phenomenon. We will further investigate the effects of updating different model variables by assimilating reflectivity in future work.

Assimilation experiments with different assimilation window lengths showed clear typhoon track improvement.Typhoon Haikui (2012) intensity and track predictions were optimized by a 6-h assimilation window in this study.

The contributions of radar data to typhoon forecast were consistently demonstrated in the results of the present study. Future work should further explore the applications of Doppler radar data, especially reflectivity information, to derive the maximum benefit from this approach in typhoon prediction. The assimilation of multiple radar data should also be investigated. Background error covariance and observation error covariance have important effects on assimilation results. The coordination of their proportional relationship (i.e., regularization) will be an important focus in our future work. Application of the results of the present study is dependent, to some extent, on the case and on the data assimilation system; these experiments should be repeated with more cases to obtain more statistically reliable conclusions.

Acknowledgements. This work was partially supported by the National Key Research and Development Program of China(Grant No. 2016YFA0600203), the National Natural Science Foundation of China (Grant No. 41575100), and the Key Research Program of Frontier Sciences, Chinese Academy of Sciences (Grant No. QYZDY-SSW-DQC012). The English in this document has been checked by at least two professional editors, both native speakers of English. For a certificate, please see: http://www.textcheck.com/certificate/tY0Tze

Electronic supplementary material:Supplementary material is available in the online version of this article at https://doi.org/10.1007/s00376-020-9274-8.