Xin LI，Mingjian ZENG，Yuan WANG，Wenlan WANG，Haiying WU，and Haixia MEI0009

2Key Laboratory of Mesoscale Severe Weather/MOE，and School of Atmospheric Sciences，Nanjing University，Nanjing210023，China

3Jiangsu Provincial Observatory，Nanjing210008，China

Evaluation of Two Momentum Control Variable Schemes and Their Impact on the Variational Assimilation of Radar Wind Data: Case Study of a Squall Line

Xin LI1，2，Mingjian ZENG*1，Yuan WANG2，Wenlan WANG1，Haiying WU3，and Haixia MEI1
1Jiangsu Research Institute of Meteorological Sciences，Nanjing210009，China

2Key Laboratory of Mesoscale Severe Weather/MOE，and School of Atmospheric Sciences，Nanjing University，Nanjing210023，China

3Jiangsu Provincial Observatory，Nanjing210008，China

（Received 3 December 2015；revised 29 April 2016；accepted 4 May 2016）

Di ff erent choices of control variables in variational assimilation can bring about di ff erent in fl uences on the analyzed atmospheric state.Based on the WRF model’s three-dimensional variational assimilation system，this study compares the behavior of two momentum control variable options—streamfunction velocity potential（ψ—χ）and horizontal wind components（U—V）—in radar wind data assimilation for a squall line case that occurred in Jiangsu Province on 24 August 2014.The wind increment from the single observation test shows that the ψ—χ control variable scheme produces negative increments in the neighborhood around the observation point because streamfunction and velocity potential preserve integrals of velocity. On the contrary，theU—Vcontrol variable scheme objectively re fl ects the information of the observation itself.Furthermore，radial velocity data from 17 Doppler radars in eastern China are assimilated.As compared to the impact of conventional observation，the assimilation of radar radial velocity based on theU—Vcontrol variable scheme signi fi cantly improves the mesoscale dynamic fi eld in the initial condition.The enhanced low-level jet stream，water vapor convergence and low-level wind shear result in better squall line forecasting.However，the ψ—χ control variable scheme generates a discontinuous wind fi eld and unrealistic convergence/divergence in the analyzed fi eld，which lead to a degraded precipitation forecast.

three-dimensional variational assimilation，momentum control variable，Doppler radar data，squall line

1. Introduction

Severe convection is among the most common natural hazards in Jiangsu Province，China.Accurate prediction of severe convective weather is crucial for the protection of lives and property.Apart from good prediction models，an accurate initial condition is also a vital factor for improving forecasts，which requires well-performed data assimilation methods.Based on some well-known regional prediction models，such as the WRF model（Skamarock et al.，2008），APRS（Advanced Regional Prediction）（Xue et al.，2003）and GRAPES（Global and Regional Assimilation and Prediction System）（Chen et al.，2008），conventional observations are widely appliedinregionaloperations.Forinstance，thereal-timeWRFRUC（Rapid Update Cycle）（Benjamin et al.，2004）analysis—forecast system is currently used at Jiangsu Meteorological Bureau to assimilate surface synoptic observations，as well as automatic station，radiosonde and wind pro fi ler data.In addition，GPS/MET precipitable water data have been evaluated and introduced into the WRF model for the Jiangsu region（Zeng et al.，2014）.However，for the forecasting of severe convection，a better description of three-dimensional dynamic and thermodynamic structures in the initial condition is crucial，which greatly depends on radar data assimilation.

Many studies have been conducted on radar data assimilation into numerical models.For example，based on the WRF forecasting model，an observation operator for Doppler radial velocity（Sun and Crook，1997，1998）was developed within WRF’s three-dimensional variational system（WRF-3DVAR）by Xiao et al.（2005）.With the implementation of thisoperatoritwasfoundthatradialvelocityassimilationwas e ff ective in improving the quantitative precipitation forecast for a heavy rainfall case.In addition，a radar re fl ectivity data assimilation scheme was developed，and the capability of refl ectivity assimilation during the landfall of typhoon Rusa（2002）was assessed，in Xiao and Sun（2007）.Meanwhile，Puetal.（2009）exploredtheimpactofairborneDopplerradar wind and re fl ectivity assimilation using WRF-3DVAR on the forecasting of hurricane Dennis（2005）.Broadly speaking，much e ff ort has been applied during the last 10 years in research on various weather systems，including tropical cyclones，heavy rainfall and squall lines（Sheng et al.，2006；Yang et al.，2006；Shi et al.，2009；Zhang et al.，2009；Zhao and Xue，2009；Zhao et al.，2012；Sun and Wang，2013a；Wang et al.，2013；Dong and Xue，2013）；and these results suggest—as compared to re fl ectivity data，which mainly adjust the moisture fi eld—that radial velocity is more e ff ective in improving initial dynamic structures，which are important for the prediction of severe convection.

Among the various data assimilation methods，3DVAR is computationally efficient and suitable for operational use. However，the quality of the 3DVAR analyzed fi eld depends on the reasonable construction of the background error covariance（BBB）matrix used in the variational method.It is well recognized that theBBBmatrix can be approximately generated via the so-called“NMC（National Meteorological Center）method”（Parrish and Derber，1992）from the statistics of di ff erences between 24-h and 12-h forecasts，typically.Owing to the extremely large dimensions（in excess of 106×106） of the B matrix，control variable preconditioning is usually applied to avoid the explicit computation of theBBBmatrix. Since di ff erent control variables can lead to di ff erentBBBstructures，the assimilation results are a ff ected by the choice of control variables.For radar wind assimilation，the behavior of the horizontal wind analysis is mainly determined by the momentum control variables.Two di ff erent options are commonly used in regional models（e.g.WRF-3DVAR，ARPS-3DVAR）:（1）streamfunction（ψ）and velocity potential（χ）；（2）eastward wind（U）and northward wind（V）.The former preserves the wind integral values due to the fact that streamfunction and velocity potential are essentially the integration ofUandV，while the latter preserves the wind itself（Xie and MacDonald，2012）.In WRF-3DVAR（Barker et al.，2004），before version 3.7 was released，ψ—χ was the only option for momentum control.By contrast，ARPS-3DVAR（Gao et al.，2004）has the ability to use either ψ—χ orU—Vas momentum control variables，and theU—Voption is used in most ARPS-3DVAR applications（Gao et al.，2004；Hu et al.，2006；Zhao and Xue，2009）.

Although the ψ—χ control variable option is a popular choice for operational models，recent studies suggest that it may not be suitable for small-scale analysis and forecasts in regional models.Through theoretical investigation，Xie and MacDonald（2012）demonstrated that，due to the property of preserving wind integral values possessed by streamfunction andvelocitypotential，a3DVARsystemusingstreamfunction and velocity potential（ψ—χ 3DVAR，hereafter）tends to produce nonphysical wind increments with opposite direction to the observed wind in the neighborhood around the observation point.Sun and Wang（2013b）reported the same discovery in a review article，and proposed that a 3DVAR system using horizontal wind components（U—V3DVAR，hereafter） can solve this problem in cases of convective-scale wind assimilation.Besides，in a tropical cyclonecase，Li et al.（2015）described ψ—χ 3DVAR as producing unreasonable circulation around the vortex inner core after radar wind assimilation，and thus the subsequent track forecast was degraded.All these results indicate that comparing ψ—χ 3DVAR andU—V3DVAR in analyses and forecasts would be useful in identifying the most suitable momentum control variable option for convective-scale wind data assimilation.

In a recent study，Sun et al.（2016）compared in detail the behavior of ψ—χ andU—Vmomentum control in WRF-3DVAR through real-data experiments on seven convective events.In addition to the issues addressed by Xie and Mac-Donald（2012），the characteristics of background error statistics of the two momentum control variable options，which can also impact the quality of the analysis and forecast results，were discussed.It was found that the ψ—χ control variable option tends to increase the length scale and decrease the variance forUandV，which causes a negative impact on the small-scalefeaturesofanalyzedwind fi elds，andonprecipitation predictions.The assimilation of Doppler radar data was also examined for one of the seven cases in their study.The results suggested thatU—V3DVAR allows a closer fi t to radar radial velocity observations，which leads to better short-term precipitation prediction，as compared to ψ—χ 3DVAR.

The present study examines the behavior of ψ—χ 3DVAR andU—V3DVAR in the assimilation of radial velocity data from 17 Doppler radars around Jiangsu Province，China，for a squall line case that occurred on 24 August 2014.Based on the WRF-3DVAR data assimilation system，this study focuses on the impact of the two sets of control variables on the dynamic structures of the squall line analyses.Furthermore，the impacts of radar data assimilation on the formation and development of the squall line are also investigated and compared between ψ—χ 3DVAR andU—V3DVAR.Following this introduction，section 2 describes the WRF-3DVAR system and the modeling process of the two momentum control variable options，the localized Jiangsu WRF-RUC analysis—forecast system，and the radar radial velocity assimilation method.Section 3 examines the squall line case，including an overview of the synoptic situation，a description of the experimental con fi guration，the performance of the single observation test，the impact of radar data assimilation，and the forecast results.A summary and conclusions are presented in section 4.

2. Method and model description

2.1. Theψ-χandU-Vmomentum control variable schemes in WRF-3DVAR

In WRF-3DVAR，the analysis fi eld is obtained via minimizing the cost function as

In this study，the background error covarianceis derived from a forecast di ff erence ensemble generated by the WRF forecasts during June 2014 using the“NMC method”（Parrish and Derber，1992），which averages the forecast differences between two forecasts（24-h minus 12-h）valid at the same time over a period of time（one month）:

Here，the overbar denotes an average over time and geographical areaandare the true atmospheric state and background state，respectively；stands for the background error；andandare the 24-h and 12-h forecasts valid at the same time，respectively.In the WRF-3DVAR system，the background error covariance matrixcan be decomposed as，with，whereis a horizontal transform，is a vertical transform，andis a physical variable transform（Barker et al.，2004）.By applying the decomposed background matrix，the analysis incrementis obtainedthroughacontrolvariabletransformδ xxx =，where vvv stands for the control variable.

In WRFDA v3.7（DA:data assimilation），two sets of momentum control variables are available，which are named as the CV5 and CV7 options，respectively.The CV5 option employs ψ—χ as the momentum control variables.The fi ve control variables are streamfunction（ψ），unbalanced velocity potential（χu），unbalanced temperature（Tu），relative humidity（RH）and unbalanced surface pressure（Ps，u）.Through a statistical balance transform，the full variables of χ，T and P are represented by the sum of the balanced parts，which are related to ψ and the unbalanced parts of χu，Tuand Ps，u，respectively.The full fi elds of control variables are then converted to analysis variable increments in the model space through Eq.（3）:

The new option，CV7，employs U—V as momentum control variables，and uses a di ff erent set of control variables:U，V，temperature（T），RH，and surface pressure（Ps）.Since the momentum variables have no change through the conversion from control variable space to model space，the transform is more straightforward，as follows in Eq.（4）:

Note that，in the U—V control variable option，the wind components U and V，the temperature T，and the surface pressure Ps，are full variables.These variables are assumed to be analyzed independently.As pointed out by Sun et al.（2016），the correlation between U and V is not signi fi cant，as compared to that between ψ and χ.Therefore，no multivariate correlation between U and V is considered for the U—V control variables in this study.It should also be pointed out that other e ff orts（e.g.incorporating equation constraint in the cost function）can be made to represent the correlation between wind components.In the ARPS 3DVAR system，a mass continuity constraint is included to couple the three wind components together（Gao et al.，2004；Hu et al.，2006）.

2.2. The Jiangsu WRF-RUC analysis-forecast system

The operational Jiangsu WRF-RUC analysis—forecast system is used in this study，which includes the WRF model and WRFDA for forecasting and analyzing，respectively. Two one-way nested domains are employed.The domains have horizontal dimensions of 449×353 and 271×241，and grid spacings of 15 km and 3 km，respectively.All model domains have 45 vertical levels from the surface to 50 hPa. GFS analyses with 0.5°spacings are used to provide the initial conditions for all DA experiments.The boundary conditions for the coarse domain（D01）and the fi ne domain（D02）are provided by GFS forecasts and the WRF forecasts from D01，respectively.In real-time forecasting，four cold-start forecasts are conducted every day in D01 with 6-h time intervals.Besides，eight forecasts are carried out in D02 with 3-h time intervals，including six warm-start forecasts and two cold-start forecasts，which start at 0000 UTC and 1200 UTC，respectively（Fig.1）.ThephysicsoptionsincludetheThompson microphysics，RRTM longwave radiation，Noah land surface，YSU（Yonsei University）planetary boundary layer，and Kain—Fritsch cumulus（15-km domain only）schemes（Skamarock et al.，2008）.

2.3. Radar radial velocity assimilation in WRF-3DVAR

Doppler radar data used in this study come from 17 S-band CINRAD WSR-98D（Chinese Next Generation Weather Surveillance Radar 1998 Doppler）radars in Jiangsu Provinceandsurroundingareas（Fig.2a）.Duringtheobservation period，all radars used the VCP21（volume coverage pattern 21），where a volume scan consists of nine elevation angles（0.5°，1.5°，2.4°，3.3°，4.3°，6.0°，9.9°，14.6°，and 19.5°）and is completed in about 6 min.The maximum Doppler radial velocity range is about 230 km，and the gate spacings and azimuth resolution are 0.25 km and 1°，respectively.After quality control that includes unfolding aliased Doppler velocity and removing noise，the edited data are thinned and interpolated onto WRF grids before assimilation.

Fig.1.Flow chart illustrating the Jiangsu WRF-RUC operational system.

Doppler radial velocity data assimilation in WRF-3DVAR was developed by Xiao et al.（2005）；the observation operator for radial velocity（Vr）is

Here，（u，v，w）represent wind components；（x，y，z）are the radar location；（xi，yi，zi）are the location of radar observations；riisthe distancebetween theradarsiteandtheobservation；andvTis the terminal velocity，which can be estimated by the rainwater mixing ratio（Sun and Crook，1997）.Since the vertical velocitywis not a control variable，Richardson’s equation is used in the WRF-3DVAR physical transformto produce the vertical velocity increment（Xiao et al.，2005）. The linear and adjoint models of this equation also serve as a bridge between dynamic and thermodynamic fi elds.A detailed description of WRF-3DVAR radial velocitydata assimilation can be found in Xiao et al.（2005）and Xiao and Sun（2007）.

3. The 24 August 2014 squall line case

3.1. Synoptic overview

On 24 August 2014，under the combined e ff ects of a high-level trough，low-level vortex and surface cyclone，a squalllineformedneartheborderbetweenAnhuiandJiangsu provinces.At 0000 UTC 24 August 2014，Jiangsu Province was a ff ected by southwest fl ow in front of the westerly trough at 500 hPa（Fig.2b）.In the lower troposphere，a vortex developed near Anhui and Shandong provinces，accompanied by a wind shear line at 850 hPa.An intense southwest jet stream was present to the south of the low-level vortex（Fig.2c）.At the same time，a frontal cyclone occurred（Fig.2d）and then moved into Jiangsu Province.During the eastward propagation of the surface cyclone，an intense and narrow squall line formed around the cold front and then moved eastward quickly.The maximum hourly rainfall in Jiangsu Province reached 25.1 mm h-1，27.9 mm h-1，20.9 mm h-1and 28.5 mm h-1，respectively，from 0700 UTC to 1000 UTC.

3.2. Experimental design

In order to evaluate the in fl uence of di ff erent momentum control variable schemes on the analysis and forecast of the squall line，three experiments are conducted.A control forecast（CTL），whichonlyassimilatesconventionaldata（surface observations and radiosondes）is performed fi rst.In addition to the conventional data，the experiment RADAR-psichi assimilates radial velocity data from 17 Doppler radar around Jiangsu Province（Fig.2a）using ψ—χ 3DVAR.For comparison purposes，RADAR uv assimilates the same data as RADAR psichi except it usesU—V3DVAR.In order to make the comparison more clearly，we exclude the re fl ectivity data assimilation.Furthermore，WRF-RUC analyzed fi elds valid at 0000 UTC，0300 UTC and 0600 UTC 24 August（Fig.1）are chosen as the initial fi elds for forecasting，respectively，to investigate the impact of a di ff erent initial time on the squall line forecast.To better re fl ect reasonable increments associatedwithsmall-scaleconvection，thedefaulthorizontalcorrelation scales in CV5 and CV7 background error covariances are reduced by a factor of 0.2 and 0.3，respectively，following Xiao et al.（2005），Pu et al.（2009）and Li et al.（2013），resulting in a decorrelation scale of approximate 20 km.

3.3. Characteristics of analysis increments inψ-χ3DVAR andU-V3DVAR

Fig.2.（a）S-band Doppler radar observation network in Jiangsu Province and surrounding areas.（b，c）Geopotential height（blue solid lines；units:gpm），temperature（red solid lines；units:°C）and wind fi elds（wind barbs）at 500 hPa and 850 hPa，respectively，at 0000 UTC 24 August 2014.（d）Surface pressure（blue solid lines；units:hPa），surface temperature（red solid lines；units:°C），and surface wind fi elds（wind barbs），at 0000 UTC 24 August 2014，and the accumulated precipitation（shaded；units:mm）during 0700—1000 UTC 24 August 2014.In all panels，the borders of Anhui Province and Jiangsu Province are highlighted with thick lines.

In this section，we examine the wind increments using the single observation test in order to clearly understand the infl uence of di ff erent momentum control variable schemes on the wind analysis.Choosing the GFS global analysis fi eld at 0000 UTC 24 August as the background fi eld，a pseudo eastward wind（U wind）observation at the grid point of（i=130，j=130，k=10）［approximately（33°N，118.8°E），850 hPa］is assimilated.The innovation（observation minus background）of the single U wind is assigned to be 20 m s-1.Figures 3a and b compare the analysis increments of U wind between ψ—χ 3DVAR and U—V 3DVAR.In Fig.3a，apart from the eastward wind increments around the observation site，the ψ—χ control variable scheme produces negative increments（westward wind）in the north and south neighboring areas of the observation site，which leads to cyclonic and anticyclonic increments in these areas，respectively.Since streamfunction and velocity potential are essentially the integration of U and V，they possess the property of maintaining the horizontal wind integral values.Therefore，when the velocity changes around the observation site，the velocity adjustment of the opposite direction takes place in its near neighborhood.Owing to the property of streamfunction and velocity potential，this phenomenon cannot be completely avoided in 3DVAR even if the horizontal scale factor of the background error covariance is tuned（Xie and MacDonald，2012）.On the contrary，as shown in Fig.4b，when the U—V control variable scheme is used，the analysis increments show consistent eastward winds，which re fl ect the observed wind itself more objectively.

Fig.3.The increments of U wind（shaded；units:m s-1）and wind vector at 850 hPa from single observation experiments using the（a）ψ—χ control variable and（b）U—V control variable，and the increments of wind speed（shaded；units: m s-1）and wind vector at 850 hPa after the assimilation of NJRD radial velocity using the（c）ψ—χ control variable and（d）U—V control variable.

For further comparing the di ff erent behavior of ψ—χ 3DVAR and U—V 3DVAR in wind assimilation，real radial velocity data from Nanjing Doppler radar（NJRD）are assimilated.The background fi eld is also from the GFS global analysis at 0000 UTC 24 August.Figures 3c and d show the increments of wind speed and wind vector after NJRD data assimilation.Remarkable di ff erences can be found between the wind increments from the two momentum control variable schemes.ψ—χ 3DVAR generates some local convergence/divergence and small-scale cyclonic/anticyclonic incremental structures（Fig.3c）outside the observation region of NJRD，which are nonphysical.This result can be explained by the unrealistic negative wind increments shown by the single observation test（Fig.3a）when ψ—χ 3DVAR is used.In comparison，the wind increments from U—V 3DVAR re fl ect the radar observation more objectively.The nonphysical local convergence/divergence increments are avoided（Fig.4d）.

3.4. Analysis and forecast results for the squall line

The above comparison of wind analysis increments illustrates a signi fi cant di ff erence between ψ—χ 3DVAR and U—V 3DVAR in wind assimilation.In this section，the impact of radial velocity data assimilation from 17 radars（Fig.2）on the forecasting of the squall line is investigated by verifying the analysis and forecast results from WRF-RUC（Fig.1）.

Fig.4.Analyzed wind speed（shaded；units:m s-1）and wind vector at 700 hPa at 0600 UTC 24 August:（a）CTL；（b）RADAR psichi；（c）RADAR-uv.

Figure 4 shows the horizontal wind analyzed fi elds at 700 hPa for experiments CTL，RADAR psichi and RADAR uv at 0600 UTC 24 August.As illustrated in Fig.1，the analyzed fi eld at 0600 UTC is the fi nal analysis of the three assimilation cycles starting from GFS 0000 UTC with a 3-h time interval.In the analyzed fi elds at 700 hPa，a low-level vortex can be found in the northern region of Anhui and Jiangsu provinces for each experiment.In CTL，the center of the southwest low-level jet stream is located at approximately（33°N，118°E），with maximum wind speed of 20 m s-1（Fig.4a）.In comparison，the two radar assimilation experiments exhibit stronger low-level jet streams with maximum speeds of about 25 m s-1（Figs.4b and c），which are also located farther east than in CTL.Comparing the wind analyzed fi elds between RADAR-psichi and RADAR-uv，it is obvious that the horizontal winds are more continuous（Fig.4c）whenusingU—V 3DVAR.Besides，consistentsouthwest winds appear in the southern area of Jiangsu Province，and northwest fl ows are found in the northern part of Anhui Province.The con fl uence of northwest cold fl ows and southwest warm fl ows provides potentially favorable conditions for the severe convection.However，when the ψ—χ 3DVAR is employed，the southwest low-level jet is narrower and less well-organized.The wind speeds and wind directions are discontinuous in some areas.The investigations of analyzed horizontal winds show that the assimilation of radar radial velocity data results in enhancement and location adjustment of the low-level jet stream.Similar to the results of analysis increments from single radar assimilation（Fig.3c），RADAR-psichi generates small-scale convergence/divergence and discontinuous analyzed wind structures.

To assess the impact of radar data assimilation on the analyzed and predicted structures of the squall line，Fig.5 displays the analyzed and predicted composite radar re fl ectivity starting from the WRF-RUC analyzed fi elds at 0600 UTC in each experiment，together with the corresponding observed re fl ectivity fi elds.At 0600 UTC，observed re fl ectivity echoes are found near the border between Anhui and Jiangsu provinces.The structure shows an organized line of multi-cell convections along the southwest—northeast direction，with a maximum re fl ectivity of about 50 dBZ（Fig. 5a）.In CTL（Fig.5d），the structures of the convective line are captured to some extent.However，the analyzed squall line takes place farther west than observed，with a bias of approximately 0.5°longitude.By contrast，the analyzed squall lines in the other two radar assimilation experiments are better located，matching observations well，and better organized，especially in RADAR uv（Fig.5j）.However，in RADAR psichi，an unrealistic rainfall band occurs ahead of the squall line.The echoes of this rainfall band are as large as that of the squall line，while the intensity is relatively weak（Fig.5g）.At 0800 UTC，the observed squall line moves eastward to about 119°E，showing better organized convectiveline structures（Fig.5b）.In CTL，the system structure is not well-organized，with scattered convective cells.The location of the predicted squall line still shows westward bias（Fig. 5e），suggesting it moves slower than observed.The unrealistic precipitation band also appears ahead of the predicted squall line in RADAR-psichi（Fig.5h），the same as that at 0600 UTC.Compared with the other experiments，the squall line in RADAR-uv still shows an organized convective line with better intensity and location，though slightly wider（Fig. 5k）than observed.At 1200 UTC，the observed squall line moves out of Jiangsu Province（Fig.5c）.In CTL（Fig.5f）and RADAR psichi（Fig.5i），the organized structures of squall lines disappear and the eastern region of Jiangsu Province is covered by large-area rainfall.In contrast，although the predicted precipitation appears slightly farther west than observed，RADAR-uv still exhibits the organized structures of the convective line clearly（Fig.5l）.

Fig.5.Composite re fl ectivity（shadedunitsdBZ）predicted by experiment（d—f）CTL，（g—i）RADAR psichi，and（j—l）RADAR-uv，as compared to（a—c）observed composite re fl ectivity.The corresponding times are 0600 UTC，0800 UTC，and 1200 UTC 24 August 2014.The thick solid line in（d，g，j）indicates the vertical cross section location in Fig.9.

To investigate the water vapor condition，the water vapor fl ux divergences at 700 hPa for all experiments are shown in Fig.6，along with the horizontal wind vectors.In the analyzed fi elds at 0600 UTC 24 August，it is obvious that the convergence of the northwest fl ow associated with the lowlevel vortex and the southwest warm fl ow on the south side form a strong moisture convergence zone.The water vapor convergence area in CTL is located near（33.5°N，117.5°E）（Fig.6a），matching the precipitation region（Fig.5d）well. The suggestion，therefore，is that the position bias of the predicted squall line in CTL is mainly caused by the incorrect moisture convergence in the analyzed fi eld.In RADAR-uv，the strong water vapor convergence zone is located near the border between Anhui and Jiangsu provinces，to the east of 118°E，and exhibits several independent structures arranged in a southwest—northeast oriented line（Fig.6c）.The large negative values of water vapor fl ux divergence re fl ect the convective precipitation（Fig.5j）well.In comparison，in RADAR-psichi，apart from the moisture convergence zone that corresponds to the squall line echoes，there is a distinct band of water vapor convergence near 118.2°，from 31.5°N to 32.5°N，caused by the signi fi cant horizontal wind shear（Fig. 6b）.This unexpected moisture convergence zone is considered to be the main factor for the unrealistic rainfall band ahead of the squall line.The investigation of water vapor fl ux divergence demonstrates that the assimilation of radarradial velocity through U—V 3DVAR corrects the position of the convergence area by correctly adjusting the wind fi elds，andthus bene fi ts theforecasting ofthesubsequentsquall line. However，RADAR-psichi produces a problematic analyzed wind fi eld that leads to unexpected moisture convergence.

Fig.6.Horizontal wind vector and water vapor fl ux divergence（shaded；units:10-6g cm-1hPa-1s-1）at 700 hPa at 0600 UTC 24 August 2014:（a）CTL；（b）RADAR psichi；（c）RADAR-uv.

To evaluate the forecasting skill for the heavy rain associated with the squall line，we present in Fig.7 the equitable threat score（ETS）of the hourly accumulated precipitation for the 5 mm h-1threshold from 0700 UTC to 1200 UTC.All of the experiments，with their di ff erent initial times，are veri fi ed against CMORPH analyses（Joyce et al.，2004；Xie and Xiong，2011）with a resolution of 0.1°×0.1°. For the forecasts launched at 0000 UTC，the ETSs in the three experiments are all below 0.2，declining as the forecasting time goes on.Since 0000 UTC is four hours earlier than the observed genesis time of the squall line，the improvement brought by radar data assimilation is actually limited.For the forecasts launched at 0300 UTC，the impacts of radar radial velocity data assimilation are obvious. As compared to CTL，RADAR-psichi and RADAR-uv substantially improve the heavy rain forecasting，with ETSs of 0.3 and 0.32 at 0700 UTC，respectively.However，the ETS in RADAR-psichi drops dramatically after 0800 UTC.For the forecasts launched at 0600 UTC，the ETSs in RADAR psichi and RADAR uv are much higher than those in CTL throughout the forecasting period.Similar to the results from 0300 UTC，RADAR-uv performs better，with an initial ETS of 0.38 at 0700 UTC—much higher than the value of 0.29 in RADAR-psichi.Overall，it is found that radar data assimilation is able to improve the forecasting of heavy precipitation associated with the squall line；and the forecasting skill improves further with more analysis cycles.Meanwhile，the relatively lower ETSs in RADAR-psichi，as compared to those in RADAR-uv，are probably a result of the unrealistic precipitation forecast（Figs.5g and h）.

3.5. Impactofradarassimilationontheformationanddevelopment of the squall line

In the previous section，the in fl uences of radar data assimilation on the squall line forecasts are compared between ψ—χ 3DVAR and U—V 3DVAR.To further illustrate the e ff ects of radar data assimilation on squall line formation and development，this section discusses the dynamic and thermodynamic structures in three experiments in the developing stages.

Figure 8 shows the predicted wind fi elds at the lowest model level and the corresponding composite re fl ectivity at the approximate genesis time of the squall line（0400 UTC 24 August），together with the observed re fl ectivity fi elds. All the experiments veri fi ed are from the WRF-RUC forecasts initialized from 0300 UTC 24 August.The squall line initially forms in eastern Anhui Province（Fig.8d）.Unlike CTL，which only shows scattered convective cells（Fig.8a），RADAR-uv preliminarily re fl ects the convective line to some extent（Fig.8c），although less well-organized，in the same region as observed.As shown by the predicted winds at the lowest model level，an obvious north—south oriented convergence zone is found in the eastern region of Anhui Province，which provides an important lifting condition for triggering the severe convection.However，RADAR-psichi exhibits an extraconvectiveregionnear117°E，tothesouthof31.5°（Fig. 8b），as compared with observed radar echoes.The unrealistic convection is probably triggered by the long and nar-row convergence line at the low level（Fig.8b），which has greater north—south span than that in RADAR uv.This result suggests that the unrealistic convective rainfall band in RADAR-psichi（Figs.5g and h），which occurs throughout the lifespan of the squall line forecast，is partly attributable to the inaccurate wind fi elds that lead to incorrect convergence in the near-surface layer during the formation of the squall line.

Fig.7.One-hour ETSs of predicted hourly accumulated precipitation at the 5 mm h-1threshold for experiment CTL（green lines），RADAR-psichi（blue lines）and RADAR uv（red lines），from di ff erent initial times.

Fig.8.Wind fi eld（vectors）at the lowest model level and composite re fl ectivity（shaded；units:dBZ）at 0400 UTC 24 August 2014 in（a）CTL，（b）RADAR-psichi and（c）RADAR-uv，as compared to（d）observed composite re fl ectivity. The blue curved line in（a—c）indicates the wind convergence line.

To investigate the dynamic and thermodynamic characteristics of the squall line system，we display the vertical cross section of the environmental pseudo-equivalent potential temperature，horizontal wind vectors and re fl ectivity at 0600 UTC 24 August in Figs.9a—c，respectively.Besides，the vertical structure of temperature anomalies and velocity vectors along the cross section are presented in Figs.9d—f. The chosen cross sections of all the experiments are shown in Figs.5d，g and j.In all three experiments，the environmental pseudo-equivalent potential temperature in the lower levels（below 850 hPa）is higher than that in the middle levels（850—700 hPa）in front of the predicted squall lines.The obvious thermodynamic instability（∂θ/∂p＞0）ahead of the squall line below 700 hPa is conducive to the initiation of single-cell thunderstorms within the squall line，as well as the maintenance of the whole squall line system.Furthermore，low-level wind shear is regarded as a key factor for the maintenance and development of squall lines（Newton，1950，1966；Fujita，1955；Bluestein and Jain，1985）.In front of the squall line in CTL，southeast wind exists near the surface；however，it turns to southwest wind at 850 hPa（Fig.9a），re fl ecting wind direction shear at lower levels.In comparison，in RADAR-uv，with the help of radar wind data assimilation，the southwest winds between 850 hPa and 600 hPa are distinctly enhanced in front of the squall line（Fig.9c），such that the lower-level wind shear is enlarged.Furthermore，the cold pool behind the squall line in RADAR-uv（Fig.9f）is found to be stronger than that in RADAR psichi（Fig.9e），and the lower-level vertical shear ahead of the squall line is also more obvious（Fig.9f）.According to Rotunno—Klemp—Weisman（RKW）theory（Rotunno et al.，1988），the interaction of the cold pool and lower-level vertical shear can produce much deeper and non-inhibited lifting.Thus，the environmental conditions in RADAR-uv are more favorable for the development of the squall line.Nevertheless，note that the minimum temperature anomaly is-4 K and the isoline of-1 K extends to only 850 hPa in RADAR-uv，suggesting the strength of the cold pool is not strong enough at this stage.Therefore，the positive vorticity induced by the wind shear dominates over the negative vorticity caused by the cold pool，and the air ahead of the cold pool is preferentially dragged up and tilted downshear（Fig.9f）.It can be concluded that the successful subsequent forecast for the squall line in RADAR uv（Figs.5k and l）relies on the improvement of lower-level wind structures，which leads to a stronger vertical wind shear condition.Besides，note that the upper-level wind speeds of the southwest fl ows in RADAR-psichi（Fig. 9b）are much larger ahead of the squall line than those in RADAR-uv.The upper-level horizontal wind speed gradient in RADAR-psichi leads to divergence above 300 hPa，which is favorable for the maintenance and development of convective systems.As a result，the vertical cross section of re fl ectivity in RADAR psichi shows a broader convective rainfall band than that in RADAR-uv，especially at the high levels above 500 hPa in front of the squall line（Fig.9b）.

The maintenance and development of squall line sys-tems largely rely on the vorticity transports from.As the storm-relative helicity（SRH）［SRH= wheredenotes wind speed，represents the moving speed of the storm，ωHis vertical vorticity，and z is the height］can re fl ect the degree of rotation in the environmental fl ow and the environmental vorticity transported into convective cells（Brandes et al.，1988；Davies-Jones et al.，1990），SRH is considered to be a measure of the potential for updraft rotation in thunderstorm cells.Figure 10 shows the 0—3 km SRH for the three experiments at 0600 UTC 24 August.Large SRH values are obvious in the north—central region of Jiangsu Province in all experiments，corresponding to the convective precipitation（Fig.5）on the north side of the squall line.Besides，as compared to CTL，RADAR psichi and RADAR-uv clearly show southwest—northeast oriented large values（in excess of 250 m2s-2）of SRH to the east of 118°E，from 31°N to 33°N（Figs.10b and c），indicating the moving trend of the squall line more correctly.Within the region of large SRH values，the horizontal vorticity resulting from vertical wind shear transforms to the vertical vorticity，with the contribution of tilting e ff ects brought by the lowerlevel in fl ow.As a result，sustained vertical vorticity ahead of the storm line provides favorable conditions for the development of the squall line system and convective precipitation. Meanwhile，in CTL，the region of large SRH values，which is located to the west of 118°E（Fig.10a），also explains why the predicted squall line is situated farther west（Fig.5d）than observed.Through the investigation of the SRH distribution in all experiments，it can be concluded that，as the SRH is diagnosed by lower-level wind structures，the improvement in wind fi elds brought about by radar wind data assimilation can be ascribed as a main factor for better predicting the squall line.

4. Summary and conclusions

This study compares the behavior of two momentum control variable options of 3DVAR［stream function—velocity potential（ψ—χ）and horizontal wind components（U—V）］in radar wind data assimilation for a convective case.Based on the Jiangsu WRF-RUC analysis—forecast system，the assimilation of Doppler radar radial velocity data using WRF-3DVAR is explored for the analysis and prediction of a squall line that a ff ected Jiangsu Province and surrounding areas on 24 August 2014.The main conclusions can be summarized as follows:

Fig.9.Cross sections of the pseudo-equivalent temperature（shaded；units:K），re fl ectivity（contours；units:dBZ）and horizontal wind（vectors）at 0600 UTC 24 August in（a）CTL，（b）RADAR-psichi and（c）RADAR-uv.Cross sections of temperature anomalies（shaded；units:K），re fl ectivity（contours；units:dBZ）and velocity vectors（U，W）（U stands for the wind component along the horizontal axis of the cross section；W is the vertical wind component）in（d）CTL，（e）RADAR-psichi and（f）RADAR-uv at 0600 UTC 24 August 2014.

Fig.10.Storm-relative helicity（shaded；units:m2s-2）in the 0—3 km layer at 0600 UTC 24 August 2014 in（a）CTL，（b）RADAR psichi and（c）RADARuv.

A single observation test is performed to evaluate the characteristics of the two momentum control variable options in wind data assimilation.The wind increments show that the ψ—χ control variable scheme produces nonphysical negative increments in the neighborhood around the observation point because streamfunction and velocity potential preserve integrals of velocity.This property results in unrealistic local convergence and divergence when radar wind data is assimilated.On the contrary，the U—V control variable scheme produces consistent wind increments with the same direction as observed，which objectively re fl ects the observation itself.As a result，the analysis increments from radar wind data assimilation realistically reveal the information of radar observations.

Three experiments are conducted to evaluate the impact of radar wind data assimilation on the squall line forecast. In addition to CTL，which only assimilates conventional observations，RADAR-psichi and RADAR-uv further assimilate 17 Doppler radars around Jiangsu Province using ψ—χ 3DVAR and U—V 3DVAR，respectively.Compared to the conventional data，the assimilation of Doppler radar winds signi fi cantly improves the mesoscale dynamic fi elds，in terms of enhancing the southwest low-level jet stream and the water vapor convergence.These lead to better location and structure prediction of the squall line，as well as preferable forecasting skill with respect to strong precipitation.Besides，bene fi ting from the improvement of lower-level wind structures brought about by radar data assimilation，the nearsurface wind convergence triggers the convection more effectively，and the enhanced lower-level wind shear provides more favorable conditions for the maintenance of convective cells in the squall line system.During the developing stage，both of the two radar data assimilation experiments（RADAR-psichi and RADAR uv）exhibit large values of SRH arranged in a line ahead of the moving direction of the squall line，suggesting strong vorticity enters the updraft fl ow along the storm streamline.The improved wind fi eld caused by radar wind data assimilation is considered to be a key factor for a better squall line forecast.

The di ff erent impacts on the analyzed fi elds and subsequent squall line predictions are compared between the ψ—χ and U—V momentum control variable options in 3DVAR.When the ψ—χ control variable scheme is applied，RADAR-psichi shows discontinuous wind analyzed fi elds that generate obvious convergence/divergence in some regions.The strong water vapor convergence resulting from the unrealistic wind fi elds leads to an unexpected rainfall band forecast，and thus degrades the precipitation forecasting skill. In comparison，using U—V as momentum control variables，RADAR-uv avoids the unrealistic wind convergence in the analyzed fi elds and more objectively re fl ects the radar observation itself.The subsequent forecasts of squall line structures and strong precipitation are signi fi cantly improved.

In this study，the appropriate selection of momentum control variables in variational data assimilation is evaluated through numerical research on a squall line case that occurred on 24 August 2014.The impacts of radar wind data assimilation in the regional model are distinctly in fl uenced by the chosen momentum control variables.Consistent with Sun et al.（2016），our results demonstrate that U—V is more suitable than ψ—χ for small-scale wind assimilation in convectiveweather cases.The dynamic structures in the analyzed fi elds ofU—V3DVAR are found to provide more favorable conditions for the development of severe convection.Although the results are encouraging，to make the conclusions more general，investigationsintoothersevereweathersystems（e.g. tropical cyclones）should be conducted in future studies.

Acknowledgements.This work was jointly supported by the National Fundamental Research（973）Program of China（Grant Nos.2015CB452801 and 2013CB430100），the Jiangsu Meteorological Bureau Research Fund Project for the Youth（Grant Nos. Q201514 and Q201407），the Shandong Institute of Meteorological Sciences Research Fund Project（Grant No.SDQXKF2015M10），the Jiangsu Provincial Key Technology R&D Program（Grant No. BE2013730），the Jiangsu Meteorological Bureau Key Research Fund Project（Grant No.KZ201502），and the National Key Technology R&D Program（Grant No.2014BAG01B01）.We also thank the editor and the anonymous reviewers who provided valuable suggestions for improving our manuscript.

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*Corresponding author:Mingjian ZENG

Email:swordzmj@qq.com