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

ADVANCES IN ATMOSPHERIC SCIENCES, VOL. 37, AUGUST 2020, 873–892

• Original Paper •

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

Lu ZHANG1,2, Xiangjun TIAN*1,2,3, Hongqin ZHANG1,2, and Feng CHEN4

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

(Received 20 December 2019; revised 26 April 2020; accepted 26 May 2020)

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 Citation: Zhang, L., X. J. Tian, H. Q. Zhang, and F. Chen, 2020: Impacts of multigrid NLS-4DVar-based Doppler radar observation assimilation on numerical simulations of landfalling Typhoon Haikui (2012). Adv. Atmos. Sci., 37(8), 873−892, https://doi.org/10.1007/s00376-020-9274-8. Article Highlights: • The typhoon prediction accuracy of the MG-NLS4DVar scheme was similar to that of the NLS-4DVar scheme, but had lower computational cost. • Typhoon intensity, track, and precipitation predictions by MG-NLS4DVar analyses were significantly improved by radar data assimilation. • Radar radial velocity data had a large impact on typhoon analysis results obtained using MG-NLS4DVar.

1. Introduction High accuracy in predicting the track and intensity of landfalling typhoons is therefore essential for mitigating damage in China is among the countries most devastated by coastal areas. In recent decades, due to the continuous devel- typhoons worldwide. Typhoons are tropical cyclones (TCs) opment of numerical weather prediction (NWP) models, TC that cause devastating losses in terms of human casualties forecasting technology has steadily improved. NWP is and property losses in coastal cities after making landfall. affected by both the model error and initial error. Model error is mainly caused by inaccurate physical parameters, or * Corresponding author: Xiangjun TIAN errors in the boundary conditions, topography or other for-

Email: [email protected] cing terms (Griffith and Nichols, 2000). Many studies have

874 RADAR ASSIMILATION USING MG-NLS4DVAR VOLUME 37 estimated the model error in the weak-constraint variational with the prediction model. However, the high computa- assimilation method (Zupanski, 1997; Griffith and Nichols, tional cost of the adjoint model and the difficulty of its main- 2000; Trémolet, 2006, 2007), which adds significant computa- tenance make the implementation of 4DVar difficult. Des- tion costs and increases uncertainty. By contrast, the strong- pite these drawbacks, several studies have sought to develop constraint variational assimilation method assumes that 4DVar-based radar data assimilation. Sun and Crook (1997, there is no model error and that all prediction error is attribut- 1998) developed a radar data assimilation system based on able to the errors in the initial conditions. Therefore, accur- 4DVar, called the Variational Doppler Radar Analysis Sys- ate representation of the initial conditions largely determ- tem (VDRAS), and applied it in an initialization and simula- ines the success or failure of NWP and has important tion study of convective systems (Sun, 2005; Sun and impacts on TC numerical prediction. The lack of precise ini- Zhang, 2008). Wang et al. (2013) verified the capability of tial conditions needed to determine the internal structure of radar data assimilation for Weather Research and Forecast- TCs has been identified as a main factor causing intensity pre- ing (WRF) model 4DVar through single-observation experi- diction inaccuracy (Davis et al., 2008). In the numerical simu- ments and real experiments, and demonstrated that an lation of the genesis of Hurricane Diana (1984), Davis and updated version of WRF 4DVar with the incremental formula- Bosart (2002) found that it was sensitive to the specification worked well at the convection-permitting scale for tion of the upper-level trough and ridge in the initial condi- radar radial velocity and reflectivity data assimilation. Sun tions; once the upper-level through and ridge were removed and Wang (2013) assimilated radar radial velocity and from the initial conditions, the simulation of the genesis of reflectivity data and improved short-term quantitative precipit- Diana failed. Nolan (2007) highlighted the important influ- ation forecasting (QPF) in the WRF model. Based on WRF ence of the initial vortex structure on TC simulation, as ini- and the 4DVar system, Li et al. (2014) assimilated airborne tially deeper vortices from the ground to middle levels lead Doppler radar observations to simulate Typhoon Nuri to earlier TC genesis. Raymond and Session (2007) demon- (2008) and found that the enhanced middle level vortex and strated that initial temperature and humidity profiles greatly moisture conditions were conducive to the development of affected TC simulation by changing the vertical distribu- central deep convection. The Ensemble Kalman filter tion of vertical mass fluxes in convection. Kieu and Zhang (EnKF) data assimilation method (Evensen, 1994, 2003; (2010) reported that the specification of a mesoscale vortex Houtekamer and Mitchell, 1998; Houtekamer et al., 2014) is in the initial conditions had an important effect on the simula- also widely used in radar data assimilation because it is eas- tion of the genesis of Tropical Storm Eugene (2005). Many ily implemented without the adjoint model (Snyder and efforts have been made to improve the TC initial condition Zhang, 2003; Tong and Xue, 2005, 2008; Aksoy et al., through data assimilation (Xiao et al., 2000, 2005; Zhao and 2009, 2010). Zhang et al. (2009) and Dong and Xue (2013) Xue, 2009; Li et al., 2014, 2015). Thus, an advanced data effectively improved typhoon track and intensity forecast- assimilation system is required to provide more accurate ini- ing using the EnKF method to assimilate radar data; the lat- tial conditions. ter also improved QPF. However, due to the lack of a tem- Radar data assimilation is essential for improving poral smoothness constraint in the numerical models and NWP, especially in high-resolution models (Xiao et al., the limited number of ensemble samples in the EnKF 2005). Radar observations with high spatial and temporal res- method, its assimilation results inevitably show lower accur- olution have proved to be promising tools that provide essen- acy. tial typhoon structure information. Studies have shown that To maximize the advantages of both variational meth- radial velocity and reflectivity observed by Doppler radar ods (3DVar and 4DVar) and EnKF, the hybrid assimilation can provide important information on the wind field and method has combined their complementary merits and has microphysical properties of typhoons in the vortex and con- become a mainstream data assimilation method. Li et al. vective rainband regions (Weng et al., 2011; Zhang et al., (2012) assimilated WSR-88D radar radial velocity data with 2011). Xiao et al. (2007) assimilated Doppler radar reflectiv- the WRF hybrid ensemble 3DVar system. The hybrid covari- ity data at Jindo, South Korea, to predict the landfalling ance including static and flow-dependent covariance per- Typhoon Rusa (2002) using the three-dimensional vari- formed better than the pure static covariance in the predic- ational (3DVar) data assimilation system of the fifth-genera- tion of Hurricane Ike (2008). Shen et al. (2017) used the tion Pennsylvania State University National Center for Atmo- same assimilation method to predict Typhoon Saomai spheric Research Mesoscale Model. The results showed a sig- (2006) using the Advanced Regional Prediction System. nificant improvement in the short-range precipitation predic- Hybrid covariance also had a significant effect on the 12- tion. However, static background error statistics has no spe- hour accumulated rainfall forecast. However, 3DVar-based cific knowledge about the presence of a typhoon; therefore, assimilation methods can only assimilate the observations at the 3DVar method has limited effectiveness. The four-dimen- a certain moment. The 4DEnVar method combines the advant- sional variational (4DVar) (Lewis and Derber, 1985; Talag- ages of 4DVar and EnKF (Lorenc, 2003, 2013; Lorenc et rand and Courtier, 1987; Courtier et al., 1994) method al., 2015; Tian et al., 2008, 2011; Wang et al., 2010; Tian makes full use of radar data multiple times within the assimila- and Feng, 2015), approximating the tangent model by assum-

tion window to provide initial conditions that are consistent ing a linear relationship between simulated observation per-

AUGUST 2020 ZHANG ET AL. 875 turbations (OPs) and model state perturbations (MPs). Thus, the MG-NLS4DVar method. We also examined the assimila- the solution process is simplified and observation data are tion of radar radial velocity and reflectivity observations assimilated simultaneously at multiple times. Buehner et al. using MG-NLS4DVar, both individually and simultan- (2010a, b) tested 4DEnVar with an NWP model in a series eously. Finally, we explored the effects of NLS-4DVar and of 1-month analysis forecast experiments. Lu et al. (2017) MG-NLS4DVar assimilation of radar data in QPF for assimilated tail Doppler radar data using 4DEnVar and Typhoon Haikui (2012). This study evaluated the applica- found that the analyzed storm intensity forecasts were tion of our newly developed MG-NLS4DVar method for improved compared to hybrid ensemble 3DVar. Shen et al. real radar data assimilation, especially for small- and (2019) compared 3DVar, hybrid ensemble 3DVar and 4DEn- medium-scale weather forecasts. This represents a continu- Var using a WRF 4DEnVar experiment, and obtained a ation and promotion of the work of Zhang and Tian (2018a) more realistic thermal structure of Hurricane Ike (2008), lead- and Zhang et al. (2019). ing to improved intensity and track forecasts. Kay and The remainder of this article is organized as follows. Sec- Wang (2020) developed a multiresolution ensemble method tion 2 briefly reviews the MG-NLS4DVar method and the to resolve a wider range of scales of the background error cov- radar observation operator. Section 3 describes Typhoon ariance in the Gridpoint Statistical Interpolation-based 4DEn- Haikui (2012), the radar observations and verification Var. As a 4DEnVar method, the nonlinear least-squares method used in this study, as well as the numerical experi- four-dimensional variational assimilation method (NLS- ments including the model and experimental configurations. 4DVar) was proposed by Tian and Feng (2015) to convert The impact of radar data assimilation based on a multigrid the cost function of 4DEnVar into a nonlinear least-squares strategy on deterministic forecasts of intensity and track is dis- problem solved using a Gauss–Newton iteration scheme (Den- cussed in section 4. Section 5 shows the results of assimilat- nis and Schnabel, 1996). When solving the cost function, ing radar radial velocity and reflectivity observations, both the NLS-4DVar method is easy to implement without invok- singly and simultaneously. The results of assimilation win- ing the adjoint models and has higher precision than the tradi- dow length sensitivity experiments are shown in section 6. tional 4DEnVar method (Tian et al., 2018). Zhang et al. Finally, a summary is provided in section 7. (2017a) evaluated the assimilation performance of NLS- 4DVar in observing system simulation experiments 2. Methods (OSSEs); the results indicated that the NLS-4DVar method effectively absorbed the radar data and improved the initial 2.1. Brief introduction to NLS-4DVar field. In real experiments, radar data were assimilated with The formulas for the incremental form of the 4DVar the NLS-4DVar method; the intensity and position predic- cost function at the initial time t0 are as follows: tion accuracy of heavy precipitation that occurred in eastern Hubei Province were significantly improved (Zhang et ∑S [ ] ( ′) 1( ′) − ( ′) 1 ′ ′ ( ′) ′ T al., 2017b). To date, the NLS-4DVar method has not been J x = x T(B) 1 x + H M x − y 2 2 k k obs,k k=0 applied to the study of typhoons. [ ( ) ] The multigrid strategy is an efficient method to acceler- × −1 ′ ′ ′ − ′ , Rk Hk Mk x yobs,k (1) ate 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 yobs,k yobs,k Lk (xb) (2) velocity for improved reconstruction of typhoon structure. Zhang and Tian (2018a) applied a multigrid NLS-4DVar = , Lk Hk Mt →t (3) (MG-NLS4DVar) method in OSSEs, concluding that this 0 k approach showed dual advantages of high accuracy and effi- where k is the observation time, S + 1 is the total number of ciency in conventional data assimilation, mainly because it observation times in the assimilation windows, and tk is the corrects background error from large to small scales. MG- kth observation time point. B and Rk are the background ′ NLS4DVar has also shown clear positive effects in radar and observation error covariance matrices, respectively; Hk and M′ (·) are tangential linear models of the nonlinear radial velocity assimilation in OSSEs and has improved the t0→tk accuracy of precipitation prediction (Zhang et al., 2019). observation operator H and forecast model M (·), respect- k t0→tk In this study, we investigated the assimilation of radar ively; M (·) is the nonlinear forecast model integration t0→tk radial velocity and reflectivity observation data from single- from t0 to tk; the superscripts T and −1 represent transpose ′= − Doppler radar using the MG-NLS4DVar method for the and inverse matrices, respectively. x x xb is the perturba- case of Typhoon Haikui (2012) based on the WRF model. tion of the background field, in which xb and x are the state ′ We compared the prediction results for typhoon structure, variables. yobs,k represents the observations at tk. yobs,kis the intensity, and track following assimilation of radar observa- innovation. tions using the NLS-4DVar and MG-NLS4DVar methods, NLS-4DVar uses 4D samples to approximate the tan- and then evaluated the typhoon prediction capability of the gent and minimize the incremental form of the 4DVar cost

radar data assimilation system based on the WRF model and function to obtain the analysis increment (Tian and Feng,

876 RADAR ASSIMILATION USING MG-NLS4DVAR VOLUME 37

∑S ( ) ( ) 2015; Tian et al., 2018). Therefore, NLS-4DVar assumes (l) (l−1) ∗ T ′ ′,(l−1) ′ β =β + γ < e > P L x that the analysis increment x is expressed by the linear com- (i) (i) o,(i) y,k,(i) k,(i) (i) a ( ) k=0 = ′ , ′ ,..., ′ binations of the MPs as Px x1 x2 xN , where N is the ∑S ( ) [ ( )] + γ < > # −1 ′ − ′ ′,(l−1) number of ensemble samples, as follows: o,(i) e Py,k,(i) Rk,(i) yobs,k,(i) Lk,(i) x(i) k=0 ′ = β , xa Px (4) (7)

in which β=(β1,β2,...,βN ). Substituting Eq. (4) into Eq. (1) ( ) ′,(l) = < > γ β(l) , and expressing the cost function in terms of β, β can be x(i) Px,(i) e m,(i) (i) (8) obtained to solve the new cost function using a Gauss–New- where β is the linear combination coefficient vector; ton iterative scheme (Dennis and Schnabel, 1996). The l = 1,..., I is iteration number and I , is the max- detail of the NLS-4DVar method is not described in this max,(i) max (i) imum iteration number at the ith grid level; and I is the N × paper; it can instead be referred to in Tian and Feng (2015) ′ N identity matrix. The analysis increment (x(i) is obtained) by and Tian et al. (2018). Then, we add to the background to = ′ , ′ ,..., ′ multiplying the localized MPs as Px,(i) x1 x2 xN and obtain the analysis xa as follows: β. Px,(i) is( interpolated) from the corresponding data ′ = + . P =Γ → P at the finest grid level, and Γ → (·) rep- xa xb xa (5) x,(i) (n i) x,(n) (i j) resents an interpolation operator from i to j. In this study, an 2.2. Brief review of MG-NLS4DVar efficient local correlation matrix decomposition scheme is adopted for horizontal localization (Zhang and Tian, For any given grid level i, Eq. (1) can be written as fol- 2018b); the vertical localization scheme is consistent( ) with lows: γ =Γ γ that adopted (by Zhang) et al. (2004). o,(i) (n→i) o,(n) and ( ) ( ) ( ) ( ) γ =Γ → γ are matrices related to the localization ′ = 1 ′ T −1 ′ m,(i) (n i) m,(n) J(i) x(i) x(i) B(i) x(i) 2 scheme: ∑S [ ( ) ] ( ) 1 T −1  − ′ ′ ′ ′ ∑S 1 + H , M , x − y , , R ,  ( )  k (i) k (i) (i) obs k (i) k (i) ∗  T −1  2 = P = − (N − 1) P R P + (N − 1) I [ k 0 ( ) ] y,k,(i)  y,k,(i) k,(i) y,k,(i)  = × H′ M′ x′ − y′ , k 0 k,(i) k,(i) (i) obs,k,(i) (6)  −1 ∑S ( )  ( ) ×  T  T , where i = 1,2,...,n is the ith grid level in the brackets and n  Py,k,(i) Py,k,(i) Py,k,(i) (9) k=0 is the total number of levels. A nonlinear optimization algorithm can be used to minim-  −1 ize the cost function [Eq. (6)] of the ith grid level, to obtain ∑S ( )  ( ) # = T −1 + −  T , the analysis increment of each individual level. Further Py,k,(i)  Py,k,(i) Rk,(i) Py,k,(i) (N 1) I Py,k,(i) k=0 details are provided by Xie et al. (2005, 2011) and Zhang (10) and Tian (2018a). MG-NLS4DVar is solved sequentially using NLS-4DVar at each grid level from coarsest to finest ( ) ( ( ( ))) ′ ′,(l−1) = Γ + Γ ′,(l−1) (Zhang and Tian, 2018a). The MG-NLS4DVar assimilation L , x H , (n→i) Mt →t x , (i→n) x k (i) (i) k (i) ( ( 0 k b( (n) ))) (i) method is implemented in the following four steps: − Γ . Hk,(i) (n→i) Mt0→tk xb,(n) (11) Step one: The total number of grid levels n is determined according to the nature of the problem. In this study, the forecast model is WRF; therefore, the , = , ,..., · Step two: The observations yobs,k k 0 1 S and forecast model at each grid level Mt →t ,(i) ( ) is simply set as · 0 k model-simulated data are prepared at the finest grid scale: Mt0→tk ( ). The simulated OPs at the ith grid level are as fol-

= → , lows: the background field is xb,k,(n) Mt0 tk ((n) ()xb), and the = , = , ,..., ( ( ( ))) ensemble simulation is x j,(n) Mt →t ,(n) x j j 1 2 N, 0 k P = H Γ → M → x where N is the number of ensemble samples. To reduce the y,(i) k,(i) (n i) (t0 tk (j,(n) ))) − Γ → → . computational cost, an efficient scheme requires( the) Hk,(i) (n i) Mt0 tk xb,(n) (12) ensemble simulations only on the finest grid, M → , x j ; t0 tk (n) Thus, the analysis increment for each grid level can be these are interpolated from the finest grid to coarser grids to calculated using Eq.( (8)) and interpolated to the finest grid obtain the corresponding data. ′ = Γ ′ level, xa,(i) (i→n) x(i) . The analysis at the ith grid level is Step three: The NLS-4DVar method is used to calcu- ′

the sum of the background fields x and x : late the analysis increment at the ith grid level. The cost func- b a,(i) tion in Eq. (6) is transformed into the following equation to = + ′ . xa,(i) xb xa,(i) (13)

obtain the new variable β:

AUGUST 2020 ZHANG ET AL. 877

= Step four: If i < n, then let xb xa,(i) and return to step 2012, and then migrated to the northwest or north-northw- three to continue the assimilation calculation at the next est. The typhoon intensified to become a tropical storm at higher resolution grid level. The background field (of the) 0900 UTC 5 August and entered the eastern part of the East = → China Sea. Haikui (2012) again intensified at 0900 UTC 6 next grid level should be updated by xb,k,(i+1) Mt0 tk xa,(i) . This process is repeated until i = n. The final analysis of the August, becoming a strong typhoon near the coastal area of MG-NLS4DVar method is Eq. (13). southern Zhejiang Province at 0600 UTC 7 August. The typhoon made landfall at Xiangshan County, Zhejiang 2.3. Observation operators for radar Province, at 1920 UTC 7 August, with a minimum sea level Sun and Crook (1997, 1998) proposed observation operat- pressure (MSLP) of 960 hPa and maximum surface wind ors for radar. VDRAS was constructed based on these operat- speed of 40 m s−1. Haikui (2012) moved westwards across ors, which has been employed in many studies with assimil- Ningbo, Shaoxing, and Hangzhou after landfall, and then ated radar data to predict typhoons and improve precipita- gradually weakened to become a tropical depression at 0400 tion, with positive results (Xiao et al., 2007; Xiao and Sun, UTC 9 August. The best track of Typhoon Haikui (2012) 2007; Pu et al., 2009; Sun and Wang, 2013; Wang et al., between 1400 UTC 7 August to 0800 UTC 8 August, accord- 2013; Zhang et al., 2015, 2017a, b). Therefore, these observa- ing to official best-track data from the China Meteorolo- tion operators for radar were applied in the present study. gical Administration (CMA), is shown in Fig. 1. Typhoon Haikui (2012) brought heavy rains to central and northern The observation operator for radar radial velocity Vradar Zhejiang Province, southern Anhui Province, and southern is Jiangsu Province. In some areas, the 12-h accumulated precip- xobs − xradar yobs − yradar zobs − zradar itation exceeded 140 mm (shown in Fig. 8a). In this study, Vradar = u + v + (w − Vtm) , rdis rdis rdis radial velocity and reflectivity data obtained from Ningbo (14) Doppler radar were assimilated using the MG-NLS4DVar method, and the intensity, track, and precipitation of where r is the distance between the observation location dis Typhoon Haikui (2012) were predicted using the WRF (x ,y ,z ) and the radar location (x ,y ,z ); obs obs obs radar radar radar model. (u,v,w) is the zonal, meridional, and vertical wind velocity, respectively; Vtm is the mass-weighted terminal velocity of 3.2. Prediction model precipitation, which is calculated using the rain water mix- WRF version 3.9 was used as the prediction model in ing ratio qrw: this study. The domain of the numerical simulation was (27°–33°N, 117°–125°E) (Fig. 1). The domain was con- = . ρ 0.125 , Vtm 5 40a( airqrw) (15) figured with 260 × 220 (longitude × latitude) grid points, with 3-km grid spacing and 30 levels in the vertical direc- in which a is the correction factor, defined as tion from the surface to 50 hPa. MG-NLS4DVar experi- ( ) 0.4 ments were conducted over three different meshes (coarse, p0 a = , (16) fine, and finest) in the horizontal direction. The number of p¯

where p0 is the pressure at the ground, and p¯ is the base state pressure. Sun and Crook (1997) proposed a relationship between radar-based reflectivity Zradar and qrw based on the Mar- shall–Parmer hypothesis of raindrop size distribution, as fol-

lows:

Zradar = 43.1 + 17.5lg(ρairqrw) , (17) where the Zradar is expressed in dBZ, ρair is the air density −3 (kg m ), and the rain water mixing ratio qrw is expressed in g kg−1.

3. Typhoon Haikui (2012), prediction model, data and experimental setup Fig. 1. Domain of the numerical simulation at 3-km horizontal 3.1. Typhoon Haikui (2012) resolution, with the best track of Typhoon Haikui (2012) marked at 1-h intervals from 1400 UTC 7 August to 0800 Typhoon Haikui (2012) was one of the most intense UTC 8 August (red lines). The filled star indicates the position typhoons that landed on the east coast of China in 2012; it of the Ningbo radar; the circle indicates the range of the

formed in the Northwest Pacific at 0000 UTC 3 August assimilated Doppler radar data (150 km).

878 RADAR ASSIMILATION USING MG-NLS4DVAR VOLUME 37 v u grid points decreased twofold from the finest grid to the u∑M t 2 coarse grid; thus, the finest, fine, and coarse grid levels had ( fm − ym) = 260 × 220, 130 × 110, and 65 × 55 grid points, respectively. RMSE = m 1 , (18) Parameterization included the WRF Single-moment 6-class M microphysics scheme (Hong and Lim, 2006), the Rapid Radi- ative Transfer Model longwave radiation scheme (Mlawer ∑M ( ) et al., 1997), the Dudhia shortwave radiation scheme (Dud- fm − f¯ (ym − y¯) hia, 1989), the Yonsei University planetary boundary layer m=1 CC = tv tv , (19) scheme (Hong et al., 2006), and the Noah land surface ∑M ( ) ∑M 2 2 model land scheme (Tewari et al., 2004). We excluded the fm − f¯ (ym − y¯) cumulus parameterization scheme. m=1 m=1 Assimilation analysis of the NLS-4DVar method is performed in the model space; thus, the analysis variables are tv ∑M ( ) the model variables. In this study, the analysis variables 2 f − f¯ /M included velocity components u,v and w, perturbation poten- m m=1 tial temperature θ, perturbation pressure P, water vapor mix- SDV = tv , (20) ∑M ing ratio qv, rain water mixing ratio qrw, and cloud water mix- 2 (ym − y¯) /M ing ratio qc. These variables can be increased or decreased m=1 according to the particular assimilation problem. where M is the total number of observation sites used for veri- 3.3. Data and quality control fication; fm and ym are the mth forecast values and observa- National Centers for Environmental Prediction (NCEP) tions, respectively; f¯ is the mean of M forecast values; and Final (FNL) operational global analysis data (1° resolution) y¯ is the mean of M observations. provide first-guess field and boundary conditions. The assimil- The equitable threat score (ETS) and bias score (BS) ation data used in this study were radial velocity and reflectiv- are perhaps the most widely used for model QPF verifica- ity data from Ningbo Doppler radar for Zhejiang Province, tion (Schaefer, 1990; Schwartz et al., 2009). Figure 2 shows China (30.07°N, 121.51°E), at an altitude of 458.4 m. The a schematic diagram of model QPF verification performed maximum Doppler range is 230 km. Considering the qual- in this study. Rain area was defined as the precipitation area ity of the data, only data within the 150 km range were assim- without any missing measured values. For any given precipita- ilated. The radar data coverage is shown in Fig. 1. To avoid tion threshold over an accumulation period, the observed the destruction of observation and analysis results by non-met- rain area is O, the model forecast rain area is F, the intersec- eorological echo, it is necessary to perform quality control tion of O and F indicates a hit (H), and the entire assess- of radar data prior to assimilation. Data preprocessing ment domain is N (Table 1). O − H is an area where precipita- included data de-noising, erasing folded velocity, and remov- tion is observed but not predicted (misses); F − H is an area ing ground clutter and speckle. The innovation vectors (i.e., representing false alarms (predicted but did not occur), and observation minus background) were also used for quality N − (O + F − H) is an area where precipitation is correctly pre- control. All elevation scans (0.5°, 1.5°, 2.4°, 3.4°, 4.3°, 6.0°, dicted to not occur (correct negatives). Accordingly, ETS 9.9°, 14.6°, and 19.5°) were assimilated for reflectivity data, and TS are defined as 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 H − A ETS = , (21) suppress possible spurious convection, negative reflectivity O + F − H − A 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 ran- domly 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−1 and 1 dBZ, respectively, similar to those described by Zhang et al. (2017b). 3.4. Verification methods

We performed verification using the root-mean-square Fig. 2. Schematic diagram of model QPF verification for a error (RMSE), correlation coefficient (CC) and normalized specified threshold during a given accumulation time period

standard deviation (SDV), calculated as follows: within a region.

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Table 1. Precipitation verification criteria. N∑grid [ ] 1 2 FBS = P − P , (25) Observation N Fg Og Precipitation grid g=1 Forecast Yes No where a score of 0 indicates perfect performance and larger Yes H (hits) F − H (false alarms) No O − H (misses) N − (O + F − H) (correct negatives) FBS values show worse correspondence between model forecast and observations. Thus, the worst possible FBS is

defined as: (H + F − H)(H + O − H) A = , (22)   N∑grid N∑grid  N 1   =  2 − 2  . FBSworst  PFg POg  (26) Ngrid = = F g 1 g 1 BS = . (23) O The FSS can be defined by comparing FBS and

Thus, the ETS measures the fraction of observations FBS worst (Roberts, 2005) as follows: that are correctly forecast and penalizes both misses and FBS false alarms. ETS = 1 indicates a perfect forecast; ETS 0 FSS=1 − . (27) ≤ FBS indicates that the model has no forecast skill. BS is the ratio worst of predicted rain area to the observed rain area, and it there- The FSS also ranges from 0 to 1, such that larger val- fore varies from 0 to infinity; however, a score of unity indic- ues indicate a higher number of grid points in which the ates a perfect forecast. model forecast precipitation and observed precipitation both The fractions skill score (FFS) is another metric used exceed the threshold at the same time in every neighbor- for model QPF verification, especially for high-resolution hood within the verification domain, such that model fore- models. In this study, we used FSS following Schwartz et cast precipitation is closer to the observed precipitation. A al. (2009). The precipitation accumulation threshold qrain is score of 1 indicates perfect prediction, whereas a score of 0 selected to define an event, and the observed O and model indicates no predictive skill. forecast F rainfall fields are converted into binary grids. 3.5. Data assimilation setup The grid points with accumulated precipitation ⩾ qrain are assigned a value of 1 and those with accumulated precipita- The analysis time was 1400 UTC 7 August 2012; an < 18-h deterministic forecast was run until 0800 8 August tion qrain are assigned a value of 0, as follows: { { 2012. The baseline control forecast without radar data assimil- 1 if O ⩾ q 1 if F ⩾ q ation (CTRL) was run from 1400 UTC 7 August to 0800 = g rain = g rain , BOg and BFg UTC 8 August, initialized using the first-guess field at 0600 0 if Og < qrain 0 i f Fg < qrain (24) UTC 7 August with NCEP FNL data for 8-h integration, where the 8 h were used as the spin-up period. We conduc- where g represents the accumulated precipitation at the gth ted seven experiments in this study (Table 2); all experi- = , ,..., grid point and g 1 2 Ngrid. Ngrid is the number of grid ments except CTRL assimilated radar data. The first two points on the verification grid within the verification experiments, NLS and MG_All (also called MG_6h), assimil- domain. BOg and BFg are the newly created observation and ated radar radial velocity and reflectivity every 30 min with model binary grids, respectively. A radius of influence an assimilation window of 6 h (from 1400 to 2000 UTC 7 (ROI) is specified to define a neighborhood around each August) using the NLS-4DVar and MG-NLS4DVar meth- grid point. Within the neighborhood of the ith grid point, ods, respectively. To investigate the influence of the multi- = the ratio of the number of grid points with BOg 1 to the total grid strategy on typhoon intensity and track forecasts, we points is defined as POg; PFg is similarly defined. Thus, the compared MG_All (final level, n = 3) with NLS (maximum fractions Brier score (FBS; Roberts, 2005) is determined as iteration number, Imax = 3). Experiments MG_Vr and MG_Z follows: assimilated Vr alone and Z alone, respectively (Table 2).

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

Experiment Observation assimilated Assimilation window (h) Radar assimilation interval (min) Number of grid levels CTRL No radar DA NA NA 1 NLS Vr, Z 6 30 1 MG_All (MG_6h) Vr, Z 6 30 3 MG_Vr Vr 6 30 3 MG_Z Z 6 30 3 MG_1h Vr, Z 1 6 3 MG_3h Vr, Z 3 15 3

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A set of sensitivity experiments, MG_1h and MG_3h (Table and MG_All, with predicted typhoon center positions indic- 2), were the same as MG_All but assimilated data with assim- ated. Typhoon SLP and best-track data were obtained from ilation windows of 1 and 3 h, respectively. To make the Weather China (www.weather.com.cn), a public meteorolo- amount of assimilated radar data equivalent to the experi- gical service portal website maintained by the CMA and hos- ment MG_All, the time intervals for MG_1h and MG_3h ted by the CMA Public Meteorological Service Center. The were 6 and 15 min, respectively. The number of observa- CTRL MSLP was about 3 hPa lower than the observed tions assimilated for MG_All, MG_1h and MG_3h was 1 value. Therefore, Haikui (2012) was stronger in the CTRL 127 620, 862 351 and 1 030 053, respectively. These experi- experiment. The gradient of SLP determined by NLS and ments are illustrated in Fig. 3. MG_All was smaller than that from CTRL, and typhoon The methods used in these experiments employ a 4D intensity was slightly weaker. MSLP increased to 967.286 moving sampling strategy (Wang et al., 2010; Tian et al., and 967.186 hPa in the NLS and MG_All experiments, 2014) to produce MPs (Px) and OPs (Py). In particular, two respectively. Compared with CTRL, the typhoon center posi- 72-h model integrations were initialized from 0000 UTC 6 tions of NLS and MG_All were closer to the observed August and 1200 UTC 6 August, respectively. According to typhoon (Fig. 4). These results indicate that both assimila- the length of the assimilation window, these long-term tion methods effectively absorbed radar observations and sequence forecasting fields intercept two forecasts contain- improved the initial field. We determined the typhoon cen- ing analysis time, each of which contains 106 moving winter position according to MSLP. dows; the sampling window moves back 30 min each time. To better analyze the impact of radar data assimilation, Thus, the size of the ensemble was 212. The 212 ensemble we plotted the increment of horizontal wind vectors and samples were the x j,(n) in step two of section 2.2 (i.e., wind speed at a height of 3 km at 2000 UTC 7 August 2012 N=212). The horizontal localization radius was 90 km. (Fig. 5). In the NLS and MG_All results, horizontal wind increments exhibited a clockwise rotating anticyclonic struc- 4. Verification of typhoon analysis and ture. The weakening effect of this anticyclonic structure on the TC structure was consistent with the weakening effect forecast results of SLP shown in Fig. 4, and brought the assimilated results Analysis and comparison of the results of the NLS and closer to the observed typhoon. Based on the data shown in MG_All experiments are presented as follows. Section 4.1 Figs. 4 and 5, NLS and MG_All similarly improved SLP provides the typhoon structure analysis. Section 4.2 presents and horizontal wind speed. our analysis of the typhoon intensity and track forecast res- Wind and pressure fields from the CTRL, NLS, and ults. Section 4.3 presents the precipitation forecasting evalu- MG_All experiments at 2000 UTC 7 August at a height of 1 ation results. Finally, the computational efficiency of the km and a vertical south–north cross section of the typhoon two methods is compared in section 4.4. through the individual vortex center of each experiment are shown in Fig. 6. Compared with CTRL, wind speeds were 4.1. Typhoon structure analysis lower and pressure at the center was higher in the NLS and Figure 4 shows the sea level pressure (SLP) and sur- MG_All results (Figs. 6a–c). Figures 6d and e show that the face wind speed at the end of the assimilation window maximum wind speed in all experiments occurred north of (2000 UTC 7 August 2012) for experiments CTRL, NLS, the vortex center, i.e., the right front of the typhoon. All

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.

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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. three experiments showed clear vortex and typhoon eye struc- vortex center was larger. Clearly, after assimilating the tures. Compared with the CTRL experiment, the NLS and radar radial velocity and reflectivity, the vortex weakened MG_All experiments showed lower wind speeds in the slightly, which was consistent with the increase in MSLP in typhoon eye. In the CTRL experiment, the height of the the NLS and MG_All experiments shown in Fig. 4. These wind speed exceeding 30 m s−1 reached 200 hPa, whereas adjustments to the vortex structure by assimilation affected those of MG_All and NLS reached only 400 hPa. the predictions. The NLS and MG_All results remained sim- Figures 6g–i show the vertical velocity and temperat- ilar. ure deviation in the vertical south–north cross sections. All Dong and Xue (2013) analyzed the vertical structure of experiments show a clear warm core at low to mid-levels the Hurricane Ike (2008) and reported the changes in the hori- near the typhoon eye, but the warm core was significantly zontal wind speed through the vortex center, vertical velo- weaker in the NLS and MG_All experiments than in the city, and temperature after radar data assimilation, confirm- CTRL experiment. Although the CTRL experiment ing a change in vortex intensity. In their predictions of downdraft was less than 1 m s−1 on both sides of the vertex Typhoon Saomai (2006), Zhao et al. (2012) and Shen et al. center, significantly weaker than those of NLS and (2017) enhanced the weak vortex simulated by CTRL after

MG_All, the range of updrafts in the north gale area of the assimilating radar radial velocity data, and obtained a

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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. warmer core structure in the vertical cross section in assimila- these were clearly closer to the best track than was CTRL. tion experiments. These previous studies corroborate the res- The mean track error of the NLS and MG_All experiments ults obtained in the present study (Fig. 6). was 15.68 and 15.42 km, respectively; MG_All showed a Figures 4–6 show that the pressure of the CTRL vortex slight advantage. These results demonstrate that assimilated center was stronger than the observed pressure, but the differ- radar data had a positive impact on typhoon track forecast- ence was less than 3 hPa. The difference was further ing, reflecting the advantages of the multigrid strategy. reduced, to within 1 hPa, in the NLS and MG_All experi- The MSLP values determined by CTRL, NLS, and ments. Small improvements were also indicated in vortex MG_All are compared in Fig. 7c. Although MSLP was structure, reflecting the positive role of radar data assimila- greatly underestimated, NLS and MG_All showed signific- tion in improving typhoon structure. ant improvement over CTRL in the 13-h forecast, with two The similar assimilation results obtained in the NLS curves almost overlapping. NLS and MG_All reduced the and MG_All experiments demonstrate that both assimila- error by 0.714 and 0.814 hPa, respectively, at 2000 UTC 7 tion methods showed the same degree of improvement in August; these values were lower than the difference typhoon structure and that both had positive effects. between CTRL and the best-track MSLP (2.96 hPa). This MG_All assimilates radar data using a multigrid strategy MSLP error reduction showed about 76% improvement from the coarse to finest grid scale, whereas NLS assimil- over CTRL for NLS and 73% for MG_All. The formula ates data in three iterative processes at the finest grid scale. was defined as (ErrorCTRL − ErrorDA)/ErrorCTRL, where We obtained remarkably higher computational efficiency in error is defined as the difference between the model result the MG_All experiment, as will be described in section 4.4. and best-track data. The observed typhoon weakened due to landfall, and its MSLP continued to increase, from 968 hPa 4.2. Intensity and track forecasts at 2000 UTC 7 August to 982 hPa at 0800 UTC 8 August, Figure 7 shows a comparison of 13-h tracks and MSLP an increase of 14 hPa. In the 13-h forecast, MSLP increased (hPa) values forecast by CTRL, NLS, MG_All for 2000 by 4.26 hPa in the CTRL experiment, whereas those of NLS UTC 7 August to 0800 UTC 8 August 2012, as well as track and MG_All increased by 6.76 and 6.549 hPa, respectively. errors. The typhoon predicted by the CTRL, NLS, and The advantages of the NLS-4DVar method in predict- MG_All experiments advanced in the northwest direction, ing typhoon intensity and track using radar data assimila- consistent with the best track (Fig. 7a). However, the tion are illustrated in Fig. 7, which indicates that MG_All typhoon track predicted by CTRL was mainly located north- slightly outperformed NLS. east of the observed track, which was farthest from the observed track in all experiments. The CTRL track error 4.3. Precipitation forecasts reached 37.6 km at 2100 UTC 7 August (2 h after landfall). Severe inland flooding from local precipitation is a Although track error decreased during the following 2 h, the major hazard associated with typhoon landfall, resulting in error continued to increase after 2300 UTC 7 August, for a the loss of lives and property. Therefore, QPF to allow mean track error of 22.2 km (Fig. 7b). With radar data assimil- timely warning and damage mitigation is an essential compon- ation, the tracks predicted by NLS and MG_All oscillated ent of typhoon prediction. Figures 8a and b show the FFS of

on both sides of the observed track with a small amplitude; every 3-h accumulated precipitation for a threshold of 30

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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. mm with an ROI of 24 km and 48 km, respectively. CTRL (Fig. 9a). However, CTRL also predicted strong precipita- had the lowest score for all thresholds and ROIs during the tion, exceeding 100 mm, in northern and eastern Zhejiang entire forecast period except for the last moment. The FSS Province (Fig. 9b). NLS and MG_All predicted signific- of MG_All was much higher than that of CTRL at the first antly weaker precipitation than the false heavy precipitation moment of both ROIs. The FSS of NLS was very close to areas predicted by CTRL, especially in eastern Zhejiang that of MG_All. The BS of all experiments also indicated Province (Figs. 9b and c). Predicted precipitation results that the rainfall overprediction by CTRL was effectively were similar between NLS and MG_All. weakened after radar data assimilation (Fig. 8c). Figure 9 The Taylor diagram (Taylor, 2001) shown in Fig. S1 shows the 12-h accumulated precipitation for all experi- (in Electronic Supplementary Material, ESM) was used to ments and rainfall measurements from more than 3000 comprehensively evaluate the 12-h accumulated precipita- national and automatic weather stations. Compared with tion predictions of the three experiments in terms of SDV cumulative precipitation observations (Fig. 9a), forecast pre- and CC. The distance between the model point in the Fig. cipitation was greater in all three experiments (Figs. 9b–d). S1 and the observation point (REF point in Fig. S1) is used The maximum observed rainfall occurred in the border area to indicate the effect, where a closer distance indicates bet-

between northwest Zhejiang Province and Anhui Province ter model prediction. Good correlation was observed

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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. between observed and predicted precipitation, with little dif- MG_All was 0.1842 at the 100-mm threshold, slightly ference between experiments; however, the SDV values of higher than that of CTRL (0.1836). However, at the 140- NLS and MG_All were closer to 1 than that of CTRL. Thus, mm threshold, MG_All had a substantially higher ETS. The NLS and MG_All were closer to the REF point, indicating FSS of 12-h accumulated precipitation was calculated (Fig. better prediction in these experiments. S3) for thresholds of 100 and 140 mm, with two ROIs (24 To further quantify the precipitation forecast abilities of km and 48 km). MG_All had the highest scores for all the models, we compared the ETS for 12-h cumulative precip- thresholds and ROIs. NLS and MG_All outperformed itation among CTRL, NLS, and MG_All from 2000 7 CTRL in terms of FSS, as they did in terms of ETS. BS val- August to 0800 UTC 8 August 2012 (Fig. S2). We selected ues corresponding to the two thresholds (Table 3) show a lar- thresholds of 100 and 140 mm to represent heavy precipita- ger difference between CTRL and observations (BS >2) tion. NLS, which incorporates radar data assimilation, had a than between NLS, MG_All and observations, which had

significantly higher ETS at both thresholds. The ETS of BS values closer to 1.

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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 ation was run in parallel using 48 cores; CPU time for each predictions of heavy precipitation (>100 mm) following model run was case- and machine-dependent. Table 4 lists radar data assimilation, showing much lower precipitation the time required for each iteration of NLS and for each grid values in regions for which CTRL falsely predicted heavy pre- scale of MG_All, as well as their respective total CPU cipitation. The results shown in Fig. 9 were confirmed by times. The average time required for each NLS iteration was quantitative analysis using the ETS, FSS and BS, with NLS about 38 min (assimilation process); forecast model runs showing slightly greater improvement than MG_All. 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 4.4. Computational efficiency of multigrid storage by the MG_All method greatly reduced The NLS and MG_All results show the same degree of its calculation cost. The same number of radar observations positive effect. Therefore, we compared the CPU time was assimilated in each iteration and at each grid level: required by both assimilation methods (Table 4). Numer- 1 127 620. ical experiments were conducted on a Lenovo ThinkSys- Thus, radar data assimilation had a positive effect on tem SR650 server comprising 224 CPUs with 1288-G typhoon forecasting and analysis by the NLS-4DVar memory. Assimilation calculations were performed serially method. After assimilating radar radial velocity and reflectiv-

using single nodes and a single core. The forecast model oper- ity data, predictions of Typhoon Haikui (2012)’s structure,

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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 Table 4. CPU times for NLS (Imax = 3) and MG_All (n = 3). 2000 7 August to 0800 UTC 8 August 2012, at thresholds of 100 Ll (l = 1,2,3) is the number of iterations of NLS, and Ii (i = 1,2,3) is and 140 mm for deterministic forecasts by CTRL, NLS, and the ith grid level of MG_All. MG_All. CPU time (min) NLS MG_All Threshold (mm) CTRL NLS MG_All L1/I1 38.2 + 13 24.9 + 13 100 2.1833 1.9791 1.9414 L2/I2 38.4 + 13 27.2 + 13 140 2.9559 1.7761 1.8358 L3/I3 38.6 38.1 Total CPU time 115.2 + 26 90.2 + 26 intensity, track, and precipitation were significantly improved. Our comparison of NLS and MG_All results MG_Vr (assimilation of Vr alone), MG_Z (assimilation of Z demonstrated that, although MG_All was slightly inferior in alone), and MG_All (assimilation of both Vr and Z) using terms of precipitation prediction, it showed considerable the MG-NLS4DVar method. advantages, with a slight improvement in typhoon intensity SLP and surface wind vectors for Typhoon Haikui and track prediction accuracy and substantial improvement (2012) at 2000 UTC 7 August 2012, from CTRL, MG_Vr, in computational efficiency. These advantages can be attrib- MG_Z, and MG_All are plotted in Fig. S4, including pre- uted to the use of grids with different resolution for data dicted typhoon center positions. The assimilation of differ- assimilation, which allows gradual error correction at large ent types of radar data (Vr or Z or both) improved MSLP to to small scales. different extents, as shown by differences in the SLP gradient among the four images (Figs. S4a–d). The largest 5. MG_Vr and MG_Z results increase in MSLP was produced by MG_Vr, slightly exceeding the observed MSLP; however, there was no clear correc-

In this section, we compare assimilation results among tion of the typhoon center location (Fig. S4b). The differ-

AUGUST 2020 ZHANG ET AL. 887 ence in MSLP between MG_Z and CTRL was 0.364 hPa, wind field information within the typhoon structure. Reflectiv- revealing little effect on this variable by MG_Z, although ity is directly related to the microphysical field; therefore, cor- the assimilation of Z alone resulted in effective adjustment relations between reflectivity and wind fields estimated of the typhoon center position (Fig. S4c). MG_All com- from the ensemble may be uncertain (Dong and Xue, 2013). bined the advantages of both models, improving SLP and The FSS results of every 3-h accumulated precipitation modifying the typhoon center position, which is apparently from the experiments CTRL, MG_Vr, MG_Z and MG_All influenced by both Vr and Z (Fig. S4d). are compared in Fig. S7 for a 30-mm threshold and ROIs of The increments of horizontal wind at 3-km height 24 km (Fig. S7a) and 48 km (Fig. S7b). Assimilating radial shown in Fig. S5 further demonstrate the degrees of velocity and reflectivity (MG_ALL) generally resulted in typhoon prediction improvement achieved by MG_Vr, higher FSS than observed in the other experiments, except MG_Z, and MG_All. The increments obtained by assimilat- for the last moment. Assimilation of the radial velocity ing only radial velocity data were greater than that those (MG_Vr) produced higher FSS than did assimilation of the obtained by assimilating reflectivity alone or assimilating reflectivity (MG_Z); however, MG_Z produced a higher both data type. MG_Vr formed more pronounced anticyc- FSS at 0200 UTC, perhaps due to the rainfall overpredic- lonic circulation than did MG_Z, weakening the CTRL circu- tion. The MG_Vr, MG_Z and MG_All experiments all lation field (Fig. S5a). After adding reflectivity information, reduced the BS compared with CTRL (Fig. S7c), especially increments of MG_All near the typhoon center increased, BS of MG_Vr, which was closest to 1. whereas those near the gale decreased. Figure S8 shows the 12-h accumulated precipitation Among MG_Vr, MG_Z, and MG_All, the track fore- from 2000 UTC 7 August to 0800 UTC 8 August 2012, for cast of MG_Z deviated farthest from the best track from all experiments. Precipitation forecast by the assimilation of 2000 UTC 7 August to 0800 UTC 8 August (Fig. S6), and radar radial velocity data alone was closest to the observed was closer to the best track than was CTRL (Fig. S6a). The precipitation. The false heavy precipitation (> 135 mm) in track predicted by assimilation of reflectivity alone showed northern Zhejiang Province was significantly reduced, to 14% improvement in mean track error compared with less than 120 mm, and the range of false heavy precipita- CTRL (Fig. S6b). Tracks predicted by MG_Vr and MG_All tion exceeding 150 mm in eastern Zhejiang Province was were relatively consistent after 0800 UTC 8 August, oscillat- markedly reduced (Fig. S8c). No improvement of precipita- ing to either side of the best track (Fig. S6a). MG_Vr and tion was apparent after assimilating reflectivity data alone MG_All appeared to have produced better tracks than (Fig. S8d). The prediction accuracy of MG_All was shown CTRL and MG_Z. Hourly track error values further demon- to be between those of the other two experiments (Figs. strated the advantages of MG_Vr and MG_All, with S9–S11). Figure S9 shows the SDV and CC of 12-h accumu- MG_All showing the smallest mean error. lated precipitation for CTRL, MG_Vr, _MG_Z and MG_All Figure S6c shows typhoon intensity predictions by experiments as a Taylor diagram. Clearly, MG_Vr provided CTRL, MG_Vr, MG_Z, and MG_All. MSLP was improved the best result, followed by MG_All. All three assimilation to different extents among the three assimilation experi- experiments improved the CTRL results to varying degrees. ments compared with CTRL. As shown in Fig. S4, the inform- The ETS of 12-h cumulative precipitation shown in Fig. S10 quantitatively demonstrates the improvement achieved ation capture capability of reflectivity data for typhoon intens- by assimilation of radar data over the false heavy precipita- ity was weaker than that of radial velocity data, and MSLP tion of CTRL. At the 100- and 140-mm thresholds, MG_Vr was larger in the MG_Z prediction than in those of MG_Vr had the highest score, consistent with the results shown in and MG_All during the 13-h forecasts. Figure S6c also Fig. S8c. MG_Z increased the score by only 0.01 at the shows that the assimilation of V data had the greatest r 140-mm threshold. The advantages of MG_Vr are further con- impact on MSLP in MG_All, with differences between firmed in Fig. S11. There was a large difference in FSS those of MG_Vr and MG_All generally less than 1.1 hPa. between MG_Vr and CTRL at two thresholds. Note that the This result is consistent with that reported by Dong and Xue MG_All also had the higher FSS than CTRL at two (2013), but not by Zhao and Xue (2009); the former study thresholds, whereas MG_Z outperformed CTRL only at the applied direct reflectivity assimilation, as we did in this 140-mm threshold. A comparison of BS among the four study, whereas the latter used a complex cloud analysis experiments shows the largest decrease in bias in MG_Vr, fol- method to adjust the temperature and humidity fields, exert- lowed by MG_All, and MG_Z (Table 5). This result is con- ing a large influence on MSLP. sistent with previous results in the present study and sug- Pu et al. (2009) used WRF 3DVar assimilation radar gest that the influence of radar radial velocity data assimila- data to predict the intensity of Hurricane Dennis (2005); they found that the assimilation of radial velocity alone or Table 5. As in Table 3 but for experiments CTRL, MG_Vr, both radial velocity and reflectivity had a greater effect on MG_Z and MG_All. typhoon intensity and track prediction than did the assimila- Threshold (mm) CTRL MG_Vr MG_Z MG_All tion of reflectivity alone. This finding is consistent with the results of the present study, mainly because typhoons are 100 2.1833 1.6151 2.2542 1.9414 140 2.9559 0.7463 2.6471 1.8358 wind-dominated systems and radial velocity data provides

888 RADAR ASSIMILATION USING MG-NLS4DVAR VOLUME 37 tion was dominant in precipitation forecasts. ments, especially between MG_1h and MG_3h (lines nearly The differences in precipitation forecasts obtained by overlapping) (Fig. S14a). However, as shown in Fig. S14b, assimilating radial velocity alone and assimilating reflectiv- MG_All (MG_6h) was closest to the best track. Track ity alone were further examined using the water vapor field errors were large in MG_1h and MG_3h from 2000 UTC 7 and the dynamic field analyses. Figure S12 illustrates the dif- August to 0100 UTC 8 August 2012, and then declined stead- ferences between MG_Vr, MG_Z, and CTRL at 850 hPa for ily. The mean track errors of MG_1h, MG_3h, and MG_All rain water mixing ratio, water vapor mixing ratio and cloud (MG_6h) were 17.06, 19.20, and 15.42 km, respectively. water mixing ratio at 2000 UTC 7 August 2012. The rain Typhoon intensity predictions associated with MSLP by water mixing ratio around the eyewall and the rainband MG_1h and MG_3h were similar, with MG_6h providing bet- were mainly weakened by the assimilation of radial velo- ter prediction (Fig. S14c). According to the FSS of every 3- city alone, especially on the northwest side of the eyewall h accumulated precipitation at the 30-mm threshold, (Figs. S12a and d). When only the reflectivity was assimil- MG_All had the highest scores at 2300 UTC and 0500 UTC ated, the rain water mixing ratio increased significantly on in all four experiments (Figs. S15a and b). The BS of the northwest and southeast sides of the eyewall, reaching MG_1h was the closest to 1 (Fig. S15c). Figure S16 shows 1.2 g kg−1. The water vapor mixing ratio of MG_Vr around that at the 100-mm threshold, ETS values for 12-h accumu- the eyewall and in northern Zhejiang Province was lated precipitation (from 2000 UTC 7 August to 0800 UTC weakened to a greater extent than in MG_Z (Fig. S12b and 8 August 2012) were similar among the three experiments, e), especially, decreasing by more than 1.2g kg−1 in the at 0.1790, 0.1887, and 0.1842 for MG_1h, MG_3h, and ocean area, which strongly influenced on the source of MG_All (MG_6h), respectively. However, MG_1h and water vapor for future precipitation. The cloud water mix- MG_3h had the higher scores than MG_All at the 140-mm ing ratio also differed in MG_Vr and MG_Z, mainly around threshold. the typhoon eyewall (Figs. S12c and f). Therefore, a 6-h assimilation window (30-min inter- Figure S13a and b compare the vertical velocity of vals) was the most appropriate for intensity, track and precipit- MG_Vr and MG_Z at 850 hPa. The experiment that assimilation forecasts of Typhoon Haikui (2012) in the present ated reflectivity alone (MG_Z) produced faster upward study. One possible reason for this result is that the MG_6h motion than experiment MG_Vr, which was more condu- experiment incorporated longer-term observations. cive to the development of convection. Although the frequency of observation data assimilation The improvement in precipitation forecasting obtained was not high (every 30 min), the background field was adjus- by assimilating radial velocity alone was more obvious than ted continuously for a long period. However, a longer the that obtained by assimilating reflectivity alone. This result assimilation window did not necessarily yield better results; may be due to the greater weakening of the rain mixing an excessively long assimilation window can result in the ratio, water vapor mixing ratio and cloud water mixing ratio introduction of too many model errors, worsening the fore- by MG_Vr compared with CTRL; this effect greatly cast. reduces the amount of water vapor in precipitation. Another possibility is greater weakening of the CTRL cyclone struc- 7. Summary and conclusions ture by radial velocity assimilation (Fig. S5a); the weaker upward motion of MG_Vr may correct the convective In this study, radar radial velocity and reflectivity data motion. Pu et al. (2009) also observed a larger impact on the were assimilated using a multigrid NLS-4DVar method precipitation forecasts of Hurricane Dennis (2005) due to (MG-NLS4DVar), and structure analysis and intensity and the assimilation of radial velocity data; they suggested that track predictions of Typhoon Haikui (2012) were conduc- this phenomenon may result from the improved vortex inner ted using the WRF model. Two sets of comparative experi- convergence and divergence, as well as modified convec- ments were designed to investigate the impact of radar data tion conditions in the initial vortex. assimilation by MG-NLS4DVar on typhoon characteristics. NLS-4DVar and MG-NLS4DVar required three iterations 6. Sensitivity experiments (Imax = 3) and three grid level (n = 3), respectively, to assimilate radial velocity and reflectivity data. Based on the MG- To examine the sensitivity of the typhoon prediction to NLS4DVar method, radial velocity and reflectivity data the length of the radar data assimilation window, radial velo- were assimilated using a 6-h assimilation window, simultan- city and reflectivity data were assimilated with windows of eously and individually. We also explored the effects of 1, 3, and 6 h in MG_1h, MG_3h, and MG_All, respectively. using assimilation windows of 1, 3, and 6 h. The structure Because a 6-h assimilation window was adopted, MG_All is and forecast intensity and track of the typhoon were ana- also referred to as MG_6h in this section (Table 2). lyzed and compared among experiments. This is the first Figure S14 compares typhoon intensity and track fore- study to apply assimilation of radar radial velocity and casts by the three experiments from 2000 UTC 7 August to reflectivity data using MG-NLS4DVar for typhoon analysis 0800 UTC 8 August 2012. The overall direction of the pre- and prediction. The main conclusions of all experiments are

dicted track was relatively consistent among the three experi- as follows.

AUGUST 2020 ZHANG ET AL. 889

The assimilation of radial velocity and reflectivity data the National Key Research and Development Program of China by NLS-4DVar and MG-NLS4DVar weakened the stronger (Grant No. 2016YFA0600203), the National Natural Science Found- CTRL and adjusted the typhoon structure. The adjusted ation of China (Grant No. 41575100), and the Key Research Pro- typhoon vertical structure helped improve the accuracy of gram of Frontier Sciences, Chinese Academy of Sciences (Grant intensity and track predictions for Typhoon Haikui (2012). No. QYZDY-SSW-DQC012). The English in this document has Although MG-NLS4DVar showed little advantage over been checked by at least two professional editors, both native speak- NLS-4DVar in terms of intensity and track prediction, and ers of English. For a certificate, please see: http://www.textcheck. was slightly inferior to NLS-4DVar for 12-h accumulated pre- com/certificate/tY0Tze cipitation prediction, its efficient computing power due to the implementation of a multigrid strategy allowed rapid com- Electronic supplementary material: Supplementary material pletion of the assimilation process while maintaining high pre- is available in the online version of this article at https://doi.org/ diction accuracy. 10.1007/s00376-020-9274-8. The assimilation of radial velocity alone led to much greater improvement in typhoon intensity than did that of REFERENCES reflectivity alone. The assimilation of radial velocity alone provided clear improvement in track prediction, whereas Aksoy, A., D. C. Dowell, and C. Snyder, 2009: A multicase comparative assessment of the ensemble Kalman filter for assimila- assimilation of both radial velocity and reflectivity yielded tion of radar observations. Part I: Storm-scale analyses. similar results to the assimilation of radial velocity alone. Mon. Wea. Rev., 137, 1805−1824, https://doi.org/10.1175/ The assimilation of radial velocity alone substantially 2008MWR2691.1. weakened the false heavy precipitation predicted by CTRL, Aksoy, A., D. C. Dowell, and C. Snyder, 2010: A multicase com- indicating the important role of radial velocity data in parative assessment of the ensemble Kalman filter for assimila- typhoon forecasts produced using the MG-NLS4DVar tion of radar observations. Part II: Short-range ensemble fore- method. The larger impact on the precipitation forecasts due casts. Mon. Wea. Rev., 138, 1273−1292, https://doi.org/10. to the assimilation of radar radial velocity may have been 1175/2009MWR3086.1. caused by weakened water vapor and vertical movement at Buehner, M., P. L. Houtekamer, C. Charette, H. L. Mitchell, and lower levels. In this study, the model variables of the assimila- B. He, 2010a: Intercomparison of variational data assimilation reflectivity update is in a manner similar to radial velo- tion and the ensemble Kalman filter for global deterministic NWP. Part I: Description and single-observation experi- city, as mentioned above. Dong and Xue (2013) used EnKF ments. Mon. Wea. Rev., 138, 1550−1566, https://doi.org/10.11 to analyze Typhoon Ike (2008), updating only pressure and

75/2009MWR3157.1. microphysical variables by reflectivity assimilation; they Buehner, M., P. L. Houtekamer, C. Charette, H. L. Mitchell, and expected reflectivity assimilation to have a negative effect B. He, 2010b: Intercomparison of variational data assimila- on the update of other variables. However, for typhoons, the tion and the ensemble Kalman filter for global deterministic influence of radial velocity is greater than that of reflectiv- NWP. Part II: One-month experiments with real observa- ity; our results are consistent with this phenomenon. We tions. Mon. Wea. Rev., 138, 1567−1586, https://doi.org/10.11 will further investigate the effects of updating different 75/2009MWR3158.1. model variables by assimilating reflectivity in future work. Courtier, P., J. N. Thépaut, and A. Hollingsworth, 1994: A Assimilation experiments with different assimilation win- strategy for operational implementation of 4D-Var, using an dow lengths showed clear typhoon track improvement. incremental approach. Quart. J. Roy. Meteorol. Soc., 120,

1367−1387, https://doi.org/10.1002/qj.49712051912. Typhoon Haikui (2012) intensity and track predictions were Davis, C., and L. F. Bosart, 2002: Numerical simulations of the optimized by a 6-h assimilation window in this study. genesis of Hurricane Diana (1984). Part II: Sensitivity of The contributions of radar data to typhoon forecast track and intensity prediction. Mon. Wea. Rev., 130, were consistently demonstrated in the results of the present 1100−1124, https://doi.org/10.1175/1520-0493(2002)130<11

study. Future work should further explore the applications 00:NSOTGO>2.0.CO;2. of Doppler radar data, especially reflectivity information, to Davis, C., and Coauthors, 2008: Prediction of landfalling hur- derive the maximum benefit from this approach in typhoon ricanes with the Advanced Hurricane WRF model. Mon. prediction. The assimilation of multiple radar data should Wea. Rev., 136, 1990−2005, https://doi.org/10.1175/2007 also be investigated. Background error covariance and obser- MWR2085.1. vation error covariance have important effects on assimila- Dennis, J. E., Jr., and R. B. Schnabel, 1996: Numerical Methods tion results. The coordination of their proportional relation- for Unconstrained Optimization and Nonlinear Equations.

Society for Industrial and Applied Mathematicss, 378 pp. ship (i.e., regularization) will be an important focus in our Dong, J. L., and M. Xue, 2013: Assimilation of radial velocity future work. Application of the results of the present study and reflectivity data from coastal WSR-88D radars using an is dependent, to some extent, on the case and on the data ensemble Kalman filter for the analysis and forecast of land- assimilation system; these experiments should be repeated falling hurricane Ike (2008). Quart. J. Roy. Meteorol. Soc.,

with more cases to obtain more statistically reliable conclu- 139, 467−487, https://doi.org/10.1002/qj.1970. sions. Dudhia, J., 1989: Numerical study of convection observed during the Winter Monsoon Experiment using a mesoscale two-

Acknowledgements. This work was partially supported by dimensional model. J. Atmos. Sci., 46, 3077−3107,

890 RADAR ASSIMILATION USING MG-NLS4DVAR VOLUME 37

https://doi.org/10.1175/1520-0469(1989)046<3077:NSO- Rev., 140, 3507−3524, https://doi.org/10.1175/MWR-D-12-

COD>2.0.CO;2. 00043.1. Evensen, G., 1994: Sequential data assimilation with a nonlinear Li, Z., Z. X. Pu, J. Z. Sun, and W. C. Lee, 2014: Impacts of quasi-geostrophic model using Monte Carlo methods to fore- 4DVAR assimilation of airborne Doppler radar observa- cast error statistics. J. Geophys. Res., 99(C5), 10 143−10 tions on numerical simulations of the genesis of Typhoon

162, https://doi.org/10.1029/94JC00572. Nuri (2008). J. Appl. Meteorol. Climatol., 53, 2325−2343,

Evensen, G., 2003: The ensemble Kalman filter: Theoretical formu- https://doi.org/10.1175/JAMC-D-14-0046.1. lation and practical implementation. Ocean Dynamics, Lorenc, A. C., 2003: The potential of the ensemble Kalman filter

53(4), 343−367, https://doi.org/10.1007/s10236-003-0036-9. for NWP-a comparison with 4D-Var. Quart. J. Roy. Met- Fu, H. L., X. R. Wu, W. Li, Y. F. Xie, G. J. Han, and S. Q. eorol. Soc., 129, 3183−3203, https://doi.org/10.1256/qj.

Zhang, 2016: Reconstruction of typhoon structure using 3- 02.132. dimensional Doppler radar radial velocity data with the multi- Lorenc, A. C., 2013: Recommended Nomenclature for EnVar grid analysis: A case study in an idealized simulation context. Data Assimilation Methods. [Available online from Advances in Meteorology, 2016, 2170746, https://doi.org/ http://www.wcrp-climate.org/WGNE/BlueBook/2013/indi-

10.1155/2016/2170746. vidual-articles/01_Lorenc_Andrew_EnVar_nomenclature.pdf] Griffith, A. K., and N. K. Nichols, 2000: Adjoint methods in data Lorenc, A. C., N. E. Bowler, A. M. Clayton, S. R. Pring, and D. assimilation for estimating model error. Flow, Turbulence Fairbairn, 2015: Comparison of hybrid-4DEnVar and and Combustion, 65(3−4), 469−488, https://doi.org/10.1023/ hybrid-4DVar Data assimilation methods for global NWP.

A:1011454109203. Mon. Wea. Rev., 143, 212−229, https://doi.org/10.1175/

Hong, S. Y., and J. O. J. Lim, 2006: The WRF single-moment 6- MWR-D-14-00195.1. class microphysics scheme (WSM6). Journal of the Korean Lu, X., X. G. Wang, M. J. Tong, and V. Tallapragada, 2017:

Meteorological Society, 42, 129−151. GSI-based, continuously cycled, dual-resolution hybrid Hong, S. Y., Y. Noh, and J. Dudhia, 2006: A new vertical diffu- ensemble-variational data assimilation system for HWRF: Sys- sion package with an explicit treatment of entrainment pro- tem description and experiments with Edouard (2014). Mon. cesses. Mon. Wea. Rev., 134, 2318−2341, https://doi.org/10. Wea. Rev., 145, 4877−4898, https://doi.org/10.1175/MWR-

1175/MWR3199.1. D-17-0068.1. Houtekamer, P. L., and H. L. Mitchell, 1998: Data assimilation Mlawer, E. J., S. J. Taubman, P. D. Brown, M. J. Iacono, and S. using an ensemble Kalman Filter technique. Mon. Wea. A. Clough, 1997: Radiative transfer for inhomogeneous atmo- Rev., 126, 796−811, https://doi.org/10.1175/1520-0493(1998) spheres: RRTM, a validated correlated-k model for the long-

126<0796:DAUAEK>2.0.CO;2. wave. J. Geophys. Res., 102, 16 663−16 682, https://doi.org/10.

Houtekamer, P. L., B. He, and H. L. Mitchell, 2014: Parallel imple- 1029/97JD00237. mentation of an ensemble Kalman filter. Mon. Wea. Rev., Nolan, D. S., 2007: What is the trigger for tropical cyclogenesis?

142(3), 1163−1182, https://doi.org/10.1175/MWR-D-13- Aust Meteorol. Mag., 56, 241−266.

00011.1. Pu, Z. X., X. L. Li, and J. Z. Sun, 2009: Impact of airborne Dop- Kay, J., and X. G. Wang, 2020: A multiresolution ensemble pler radar data assimilation on the numerical simulation of hybrid 4DEnVar for global numerical prediction. Mon. Wea. intensity changes of hurricane Dennis near a landfall. J. Rev., 148, 825−847, https://doi.org/10.1175/MWR-D-19- Atmos. Sci., 66, 3351−3365, https://doi.org/10.1175/2009

0002.1. JAS3121.1. Kieu, C. Q., and D. L. Zhang, 2010: Genesis of Tropical Storm Raymond, D. J., and S. L. Sessions, 2007: Evolution of convec- Eugene (2005) from merging vortices associated with ITCZ tion during tropical cyclogenesis. Geophys. Res. Lett., 34,

breakdowns. Part III: Sensitivity to various genesis paramet- L06811, https://doi.org/10.1029/2006GL028607. ers. J. Atmos. Sci., 67, 1745−1758, https://doi.org/10.1175/ Roberts, 2005: An investigation of the ability of a storm scale con-

2010JAS3227.1. figuration of the Met Office NWP model to predict flood-pro- Lewis, J. M., and J. C. Derber, 1985: The use of adjoint equa- ducing rainfall. Met Office Forecasting Research Technical

tions to solve a variational adjustment problem with advect- Report 455, 80 pp. ive constraints. Tellus A, 37A, 309−322, https://doi.org/10. Schaefer, J. T., 1990: The critical success index as an indicator of

1111/j.1600-0870.1985.tb00430.x. warning skill. Wea. Forecasting, 5, 570−575, https://doi.org/

Li, W., Y. F. Xie, S. M. Deng, and Q. Wang, 2010: Application 10.1175/1520-0434(1990)005<0570:TCSIAA>2.0.CO;2. of the multigrid method to the two-dimensional Doppler Schwartz, C. S., and Coauthors, 2009: Next-day convection-allow- radar radial velocity data assimilation. J. Atmos. Oceanic Tech- ing WRF model guidance: A second look at 2-km versus 4- nol., 27, 319−332, https://doi.org/10.1175/2009JTECHA km grid spacing. Mon. Wea. Rev., 137, 3351−3372,

1271.1. https://doi.org/10.1175/2009MWR2924.1. Li, X., J. Ming, M. Xue, Y. Wang, and K. Zhao, 2015: Implementa- Shen, F. F., D. M. Xu, J. Z. Min, Z. G. Chu, and X. Li, 2019: tion of a dynamic equation constraint based on the steady Assimilation of radar radial velocity data with the WRF state momentum equations within the WRF hybrid Hybrid 4DEnVar system for the prediction of hurricane Ike ensemble-3DVar data assimilation system and test with (2008). Atmospheric Research, 234, 104771, https://doi.org/

radar T-TREC wind assimilation for tropical Cyclone 10.1016/j.atmosres.2019.104771. Chanthu (2010). J. Geophys. Res., 120, 4017−4039, Shen, F. F., M. Xue, and J. Z. Min, 2017: A comparison of lim-

https://doi.org/10.1002/2014JD022706. ited-area 3DVAR and ETKF-En3DVAR data assimilation Li, Y. Z., X. G. Wang, and M. Xue, 2012: Assimilation of radar using radar observations at convective scale for the predic- radial velocity data with the WRF hybrid ensemble-3DVAR tion of Typhoon Saomai (2006). Meteorological Applica-

system for the prediction of hurricane Ike (2008). Mon. Wea. tions, 24, 628−641, https://doi.org/10.1002/met.1663.

AUGUST 2020 ZHANG ET AL. 891

Snyder, C., and F. Q. Zhang, 2003: Assimilation of simulated Dop- tion of Doppler radar data with a compressible nonhydro- pler radar observations with an ensemble Kalman filter. static model: OSS experiments. Mon. Wea. Rev., 133,

Mon. Wea. Rev., 131, 1663−1677, https://doi.org/10.1175// 1789−1807, https://doi.org/10.1175/MWR2898.1.

2555.1. Tong, M. J., and M. Xue, 2008: Simultaneous estimation of micro- Sun, J. Z., 2005: Initialization and numerical forecasting of a super- physical parameters and atmospheric state with simulated cell storm observed during STEPS. Mon. Wea. Rev., 133, radar data and ensemble square root Kalman filter. Part II:

793−813, https://doi.org/10.1175/MWR2887.1. Parameter estimation experiments. Mon. Wea. Rev., 136,

Sun, J. Z., and N. A. Crook, 1997: Dynamical and microphysical 1649−1668, https://doi.org/10.1175/2007MWR2071.1. retrieval from Doppler radar observations using a cloud Trémolet, Y., 2006: Accounting for an imperfect model in 4D- model and its adjoint. Part I: Model development and simu- Var. Quart. J. Roy. Meteorol. Soc., 132(621), 2483−2504,

lated data experiments. J. Atmos. Sci., 54, 1642−1661, https://doi.org/10.1256/qj.05.224. https://doi.org/10.1175/1520-0469(1997)054<1642:DAM- Trémolet, Y., 2007: Model-error estimation in 4D-Var. Quart. J.

RFD>2.0.CO;2. Roy. Meteorol. Soc., 133(626), 1267−1280, https://doi.org/10.

Sun, J. Z., and N. A. Crook, 1998: Dynamical and microphysical 1002/qj.94. retrieval from Doppler radar observations using a cloud Wang, B., J. J. Liu, S. D. Wang, W. Cheng, L. Juan, C. Liu, Q. N. model and its adjoint. Part II: Retrieval experiments of an Xiao, and Y. H. Kuo, 2010: An economical approach to observed Florida convective storm. J. Atmos. Sci., 55, four-dimensional variational data assimilation. Adv. Atmos. 835−852,https://doi.org/10.1175/1520-0469(1998)055<0835: Sci., 27, 715−727, https://doi.org/10.1007/s00376-009-9122-

DAMRFD>2.0.CO;2. 3. Sun, J. Z., and Y. Zhang, 2008: Analysis and prediction of a Wang, H. L., J. Z. Sun, X. Zhang, X. Y. Huang, and T. Auligné, squall line observed during IHOP using multiple WSR-88D 2013: Radar data assimilation with WRF 4D-VAR. Part I: Sys- observations. Mon. Wea. Rev., 136, 2364−2388, tem development and preliminary testing. Mon. Wea. Rev.,

https://doi.org/10.1175/2007MWR2205.1. 141, 2224−2244, https://doi.org/10.1175/MWR-D-12-001

Sun, J. Z., and H. L. Wang, 2013: Radar data assimilation with 68.1. WRF 4D-Var. Part II: Comparison with 3D-Var for a squall Weng, Y. H., M. Zhang, and F. Q. Zhang, 2011: Advanced data line over the U.S. Great Plains. Mon. Wea. Rev., 141, assimilation for cloud-resolving hurricane initialization and

2245−2264, https://doi.org/10.1175/MWR-D-12-00169.1. prediction. Computing in Science & Engineering, 13(1),

Talagrand, O., and P. Courtier, 1987: Variational assimilation of 40−49, https://doi.org/10.1109/MCSE.2011.18. meteorological observations with the adjoint vorticity equa- Xiao, Q. N., and J. Z. Sun, 2007: Multiple-radar data assimilation. I: Theory. Quart. J. Roy. Meteorol. Soc., 113, tion and short-range quantitative precipitation forecasting of

1311−1328, https://doi.org/10.1002/qj.49711347812. a squall line observed during IHOP_2002. Mon. Wea. Rev.,

Taylor, K. E., 2001: Summarizing multiple aspects of model per- 135, 3381−3404, https://doi.org/10.1175/MWR3471.1. formance in a single diagram. J. Geophys. Res., 106(D7), Xiao, Q. N., X. L. Zou, and B. Wang, 2000: Initialization and simu-

7183−7192, https://doi.org/10.1029/2000JD900719. lation of a landfalling hurricane using a variational bogus Tewari, M., and Coauthors, 2004: Implementation and verifica- data assimilation scheme. Mon. Wea. Rev., 128, 2252−2269, tion of the unified NOAH land-surface model in the WRF https://doi.org/10.1175/1520-0493(2000)128<2252:IASOAL>

model. Proc. 20th Conf. on Weather Analysis and Forecast- 2.0.CO;2. ing/16th Conf. on Numerical Weather Prediction, Seattle, Xiao, Q. N., Y. H. Kuo, J. Z. Sun, W. C. Lee, E. Lim, Y. R. Guo,

WA, Amer. Meteor. Soc., 11--15. and D. M. Barker, 2005: Assimilation of Doppler radar obser- Tian, X. J., and X. B. Feng, 2015: A non-linear least squares vations with a regional 3DVAR system: Impact of Doppler enhanced POD-4DVar algorithm for data assimilation. Tel- velocities on forecasts of a heavy rainfall case. J. Appl. Met-

lus A, 67, 25340, https://doi.org/10.3402/tellusa.v67.25340. eorol., 44, 768−788, https://doi.org/10.1175/JAM2248.1. Tian, X. J., Z. H. Xie, and A. G. Dai, 2008: An ensemble-based Xiao, Q. N., Y. H. Kuo, J. Z. Sun, W. C. Lee, D. M. Barker, and explicit four-dimensional variational assimilation method. J. E. Lim, 2007: An approach of radar reflectivity data assimila- Geophys. Res., 113, D21124, https://doi.org/10.1029/2008JD tion and its assessment with the inland QPF of Typhoon

010358. Rusa (2002) at landfall. J. Appl. Meteorol. Climatol., 46,

Tian, X. J., Z. H. Xie, and Q. Sun, 2011: A POD-based ensemble 14−22, https://doi.org/10.1175/JAM2439.1. four-dimensional variational assimilation method. Tellus A, Xie, Y. F., S. E. Koch, J. A. McGinley, S. Albers, and N. Wang, 63, 805−816, https://doi.org/10.1111/j.1600-0870.2011.005 2005: A sequential variational analysis approach for meso-

29.x. scale data assimilation. Preprints, 21st Conf. on Weather Ana- Tian, X., Z. Xie, Y. Liu, Z. Cai, Y. Fu, H. Zhang, and L. Feng, lysis and Forecasting/17th Conf. on Numerical Weather Pre-

2014: A joint data assimilation system (Tan-Tracker) to simul- diction, Washington, DC, Amer. Meteor. Soc. taneously estimate surface CO2 fluxes and 3-D atmospheric Xie, Y., S. Koch, J. McGinley, S. Albers, P. E. Bieringer, M. Wolf- CO2 concentrations from observations. Atmospheric Chem- son, and M. Chan, 2011: A space-time multiscale analysis sys- istry and Physics, 14, 13 281−13 293, https://doi.org/10. tem: A sequential variational analysis approach. Mon. Wea.

5194/acp-14-13281-2014. Rev., 139(4), 1224−1240, https://doi.org/10.1175/2010MWR

Tian, X. J., H. Q. Zhang, X. B. Feng, and Y. F. Xie, 2018: Nonlin- 3338.1. ear least squares En4DVar to 4DEnVar methods for data Zhang, B., X. J. Tian, J. H. Sun, F. Chen, Y. C. Zhang, L. F. assimilation: Formulation, analysis, and preliminary evalu- Zhang, and S. M. Fu, 2015: PODEn4DVar-based radar data ation. Mon. Wea. Rev., 146, 77−93, https://doi.org/10.1175/ assimilation scheme: Formulation and preliminary results

MWR-D-17-0050.1. from real-data experiments with advanced research WRF

Tong, M. J., and M. Xue, 2005: Ensemble Kalman Filter assimila- (ARW). Tellus A, 67, 26045, https://doi.org/10.3402/tellusa.

892 RADAR ASSIMILATION USING MG-NLS4DVAR VOLUME 37

v67.26045. Zhang, H. Q., and X. J. Tian, 2018a: A multigrid NLS-4DVar Zhang, B., X. J. Tian, L. F. Zhang, and J. H. Sun, 2017a: Hand- data assimilation scheme with advanced research WRF ling non-linearity in radar data assimilation using the non-lin- (ARW). J. Geophys. Res., 123, 5116−5129, https://doi.org/

ear least squares enhanced POD-4DVar. Science China 10.1029/2017JD027529. Earth Sciences, 60, 478−490, https://doi.org/10.1007/s114 Zhang, H. Q., and X. J. Tian, 2018b: An efficient local correla-

30-015-0271-4. tion matrix decomposition approach for the localization imple- Zhang, B., X. J. Tian, L. F. Zhang, and J. H. Sun, 2017b: The mentation of ensemble-based assimilation methods. J. Geo- radar data assimilation system based on NLS-4DVar and its phys. Res., 123(7), 3556−3573, https://doi.org/10.1002/2017 application in heavy rain forecast. Chinese Journal of Atmo-

JD027999. spheric Sciences, 41(2), 321−332, https://doi.org/10.3878/j. Zhang, L., X. J. Tian, and H. Q. Zhang, 2019: Application of multi-

issn.1006-9895.1605.16107. (in Chinese) grid NLS-4DVar in radar radial velocity data assimilation Zhang, F. Q., Y. H. Weng, J. A. Sippel, Z. Y. Meng, and C. H. with WRF-ARW. Atmos. Ocean. Sci. Lett., 12(6), 409−416, Bishop, 2009: Cloud-resolving hurricane initialization and pre-

https://doi.org/10.1080/16742834.2019.1671767. diction through assimilation of Doppler radar observations Zhao, K., and M. Xue, 2009: Assimilation of coastal Doppler with an ensemble Kalman filter. Mon. Wea. Rev., 137(7), radar data with the ARPS 3DVAR and cloud analysis for the

2105−2125, https://doi.org/10.1175/2009MWR2645.1. Zhang, F. Q., Y. H. Weng, J. F. Gamache, and F. D. Marks, prediction of Hurricane Ike (2008). Geophys. Res. Lett., 36,

2011: Performance of convection-permitting hurricane initial- L12803, https://doi.org/10.1029/2009GL038658. ization and prediction during 2008-2010 with ensemble data Zhao, K., M. Xue, and W. C. Lee, 2012: Assimilation of assimilation of inner-core airborne Doppler radar observa- GBVTD-retrieved winds from single-Doppler radar for tions. Geophys. Res. Lett., 38, L15810, https://doi.org/10. short-term forecasting of super typhoon Saomai (0608) at landfall. Quart. J. Roy. Meteorol. Soc., 138, 1055−1071, 1029/2011GL048469.

Zhang, H., J. S. Xue, S. Y. Zhuang, G. F. Zhu, and Z. S. Zhu, https://doi.org/10.1002/qj.975. 2004: Idea experiments of GRAPeS three-dimensional vari- Zupanski, D., 1997: A general weak constraint applicable to opera- ational data assimilation system. Acta Meteorologica Sinica, tional 4DVar data assimilation systems. Mon. Wea. Rev., 62, 31−41, https://doi.org/10.3321/j.issn:0577-6619.2004. 125(9), 2274−2292, https://doi.org/10.1175/1520-0493(1997)

01.004. (in Chinese) 125<2274:AGWCAT>2.0.CO;2.