Assimilation of Radar and Cloud-to-Ground Lightning Data Using WRF-3DVar Combined with the Physical Initialization Method—A Case Study of a Mesoscale Convective System

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  • Corresponding author: Yi YANG, yangyi@lzu.edu.cn
  • Funds:

    Supported by the National Key Research and Development Program of China (2017YFC1502102) and National Natural Science Youth Fund of China (41905089)

  • doi: 10.1007/s13351-021-0092-4

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  • Radar data, which have incomparably high temporal and spatial resolution, and lightning data, which are great indicators of severe convection, have been used to improve the initial field and increase the accuracies of nowcasting and short-term forecasting. Physical initialization combined with the three-dimensional variational data assimilation method (PI3DVar_rh) is used in this study to assimilate two kinds of observation data simultaneously, in which radar data are dominant and lightning data are introduced as constraint conditions. In this way, the advantages of dual observations are adopted. To verify the effect of assimilating radar and lightning data using the PI3DVar_rh method, a severe convective activity that occurred on 5 June 2009 is utilized, and five assimilation experiments are designed based on the Weather Research and Forecasting (WRF) model. The assimilation of radar and lightning data results in moister conditions below cloud top, where severe convection occurs; thus, wet forecasts are generated in this study. The results show that the control experiment has poor prediction accuracy. Radar data assimilation using the PI3DVar_rh method improves the location prediction of reflectivity and precipitation, especially in the last 3-h prediction, although the reflectivity and precipitation are notably overestimated. The introduction of lightning data effectively thins the radar data, reduces the overestimates in radar data assimilation, and results in better spatial pattern and intensity predictions. The predicted graupel mixing ratio is closer to the distribution of the observed lightning, which can provide more accurate lightning warning information.
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  • Fig. 1.  Horizontal extension of the two nested domains. Major provinces are marked on the map. The black dots are the locations of the Doppler radars. HF, NJ, and NT represent Hefei, Nanjing, and Nantong stations, respectively.

    Fig. 2.  Distributions of lightning (red spots) and radar composite reflectivity (shaded colors) at (a) 0600, (b) 0700, (c) 0800, and (d) 0900 UTC 5 June 2009.

    Fig. 3.  Analysis increments in d01 for (a1–c1) Exp.PI, (a2–c2) Exp.PIVar_small, (a3–c3) Exp.PIVar, (a4–c4) Exp.PI_lghtn, and (a5–c5) Exp.PIVar_lghtn. The first row shows the qv (g kg−1) increments at 850 hPa, and the second row shows the vertical profile of qv increments along the red line shown in (a1). The third row shows the vertical profile of the rh (%) increments. The red line in (a1) is from 36°N, 115°E to 30°N, 122°E.

    Fig. 4.  Distributions of the maximum reflectivity (dBZ) in d02 for (a1, b1) the observation, (a2, b2) Exp.CTL, (a3, b3) Exp.PI, (a4, b4) Exp.PIVar_small, (a5, b5) Exp.PIVar, (a6, b6) Exp.PI_lghtn, and (a7, b7) Exp.PIVar_lghtn at (a1–a7) 1100 UTC and (b1–b7) 1500 UTC. The blue lines are the isolines of the observed 15-dBZ contour.

    Fig. 5.  (a, b) ETS and (c, d) FBI of the maximum reflectivity at (a, c) 20 dBZ and (b, d) 30 dBZ in d02.

    Fig. 6.  (a) Scatter distributions for lightning at 1500 UTC. The forecasted qg (g kg−1) in d02 at 1500 UTC for (b1, c1) Exp.CTL, (b2, c2) Exp.PI, (b3, c3) Exp.PIVar_small, (b4, c4) Exp.PIVar, (b5, c5) Exp.PI_lghtn, and (b6, c6) Exp.PIVar_lghtn. (b1–b6) Distributions of qg at 600 hPa and (c1–c6) vertical profiles along the black line indicated in Fig. 6a. The red solid lines represent the 0°C isoline and the red dotted lines represent −20°C isoline.

    Fig. 7.  Distributions of accumulated precipitation (mm) in d02 for (a1, b1) the observations, (a2, b2) Exp.CTL, (a3, b3) Exp.PI, (a4, b4) Exp.PIVar_small, (a5, b5) Exp.PIVar, (a6, b6) Exp.PI_lghtn, and (a7, b7) Exp.PIVar_lghtn at (a1–a7) 0900–1200 UTC and (b1–b7) 1200–1500 UTC.

    Fig. 8.  (a, b) ETS and (c, d) FBI of precipitation for (a, c) the 1-mm and (b, d) 5-mm thresholds in d02.

    Fig. 9.  FSS (fractions skill score) for 1-h precipitation at the (a) 1-mm and (b) 5-mm thresholds in d02. The influence radius is approximately 13.5 km (3 × horizontal spacing = 13.545).

    Table 1.  Estimated rh and qv by using the physical initialization method (PI)

    HeightScheme I
    ${\rm{R}\rm{R}'_{\! \rm{o}\rm{b}\rm{s} } }\geqslant 0.1\; \rm{m}\rm{m} \;{\rm{h} }^{-1}$
    Scheme II
    $ \rm{L}\rm{F}\geqslant 1 $ and ${\rm{R}\rm{R}'_{ \! \rm{o}\rm{b}\rm{s} }} \geqslant 0.1 \; \rm{m}\rm{m} \;{\rm{h} }^{-1}$
    $\rm{m}\rm{d}\rm{B}\rm{Z}\geqslant 30\; \rm{d}\rm{B}\rm{Z}$$\rm{m}\rm{d}\rm{B}\rm{Z} < 30\; \rm{d}\rm{B}\rm{Z}$$\rm{m}\rm{d}\rm{B}\rm{Z}\geqslant 30\; \rm{d}\rm{B}\rm{Z}$$\rm{m}\rm{d}\rm{B}\rm{Z} < 30\; \rm{d}\rm{B}\rm{Z}$
    $ z>{z}_{\rm{c}\rm{t}} $$ {\rm{r}\rm{h}}_{\rm{m}\rm{a}\rm{x}}=80{{\text{%}}} $
    ${ {q}_{\rm{v} } }_{\rm{m}\rm{a}\rm{x} }=80{ {\text{%} } }\times { {q}_{\rm{v} }^{*} }$
    $ {\rm{r}\rm{h}}_{\rm{m}\rm{a}\rm{x}}=75{{\text{%}}} $
    ${ {q}_{\rm{v} } }_{\rm{m}\rm{a}\rm{x} }=75{ {\text{%} } }\times { {q}_{\rm{v} }^{*}}$
    $ {\rm{r}\rm{h}}_{\rm{m}\rm{a}\rm{x}}=80{{\text{%}}} $
    ${ {q}_{\rm{v} } }_{\rm{m}\rm{a}\rm{x} }=80{ {\text{%} } }\times { {q}_{\rm{v} }^{*}}$
    $ {\rm{r}\rm{h}}_{\rm{m}\rm{a}\rm{x}}=75{{\text{%}}} $
    ${ {q}_{\rm{v} } }_{\rm{m}\rm{a}\rm{x} }=75{ {\text{%} } }\times { {q}_{\rm{v} }^{*}}$
    $ {z}_{\rm{c}\rm{b}}\leqslant z\leqslant {z}_{\rm{c}\rm{t}} $$ {\rm{r}\rm{h}}_{\rm{m}\rm{i}\rm{n}}=90{{\text{%}}} $
    ${ {q}_{\rm{v} } }_{\rm{m}\rm{i}\rm{n} }={ {q}_{\rm{v} }^{*} }\times 90{ {\text{%} } }$
    $ {\rm{r}\rm{h}}_{\rm{m}\rm{i}\rm{n}}=80{{\text{%}}} $
    ${ {q}_{\rm{v} } }_{\rm{m}\rm{i}\rm{n} }=80{ {\text{%} } }\times { {q}_{\rm{v} }^{*}}$
    $ {\rm{r}\rm{h}}_{\rm{m}\rm{i}\rm{n}}=90{{\text{%}}} $
    ${ {q}_{\rm{v} } }_{\rm{m}\rm{i}\rm{n} }={ {q}_{\rm{v}}^{*} } \times 90{ {\text{%} } }$
    $ {\rm{r}\rm{h}}_{\rm{m}\rm{i}\rm{n}}=80{{\text{%}}} $
    ${ {q}_{\rm{v} } }_{\rm{m}\rm{i}\rm{n} }=80{ {\text{%} } }\times { {q}_{\rm{v} }^{*}}$
    $ z < {z}_{\rm{c}\rm{b}} $${q}_{\rm{v} }={ {q}_{\rm v}^{*}} \left({z}_{\rm{c}\rm{b} }\right),$
    ${\rm{r}\rm{h}}={q}_ {\rm v} / {q}_{\rm v}^{*}$
    ${q}_{\rm{v} }={ {q}_{\rm v}^{*}} \left({z}_{\rm{c}\rm{b} }\right)\times 90{ {\text{%} } },$
    ${\rm{r}\rm{h}}={q}_{\rm{v} }/{ {q}_{\rm v}^{*} }$
    ${q}_{\rm{v} }={ {q}_{\rm v}^{*}} \left({z}_{\rm{c}\rm{b} }\right),$
    ${ \rm{r}\rm{h}}={q}_{\rm{v} }/{ {q}_{\rm v}^{*} }$
    ${q}_{\rm{v} }={ {q}_{\rm v}^{*}} \left({z}_{\rm{c}\rm{b} }\right)\times 90{ {\text{%} } },$
    ${\rm{r}\rm{h}} ={q}_{\rm v} / {q}_{\rm v}^{*}$
    Note: $ {\mathrm{R}\mathrm{R}'}_{\mathrm{o}\mathrm{b}\mathrm{s}} $, rain rate; LF, lightning frequency; $ {{q}_{{\rm v}}^*}$, saturated water vapor mixing ratio; $ {{q}_{\mathrm{v}}^*}\left({z}_{\mathrm{c}\mathrm{b} }\right)$, $ {{q}_{\mathrm{v}}^*} $ at cloud base; and zct, height of cloud top.
    Download: Download as CSV

    Table 2.  Experimental design

    ExperimentSimulation timeAssimilation timeAssimilation methodAssimilation data
    Control experiment (Exp.CTL)From 1800 UTC 4 to 1800 UTC 5 June 2009; the first 12 h is the spin-up period______
    Assimilation experiment I (Exp.PI)As shown above0600, 0700, 0800, and 0900 UTCPI methodRadar data
    Assimilation experiment II (Exp.PIVar_small)As shown above0600, 0700, 0800, and 0900 UTCPI3DVar_rh method; the observation error is the default, and the background error covariance matrix is CV3Radar data
    Assimilation experiment III (Exp.PIVar)As shown above0600, 0700, 0800, and 0900 UTCPI3DVar_rh method; the observation error below 400 hPa is increased by 5%, and the background error covariance matrix is CV3Radar data
    Assimilation experiment IV (Exp.PI_lghtn)As shown above0600, 0700, 0800, and 0900 UTCPI methodRadar and lightning data
    Assimilation experiment V (Exp.PIVar_lghtn)As shown above0600, 0700, 0800, and 0900 UTCPI3DVar_rh method; the observation error below 400 hPa is increased by 5%, and the background error covariance matrix is CV3Radar and lightning data
    Download: Download as CSV
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Assimilation of Radar and Cloud-to-Ground Lightning Data Using WRF-3DVar Combined with the Physical Initialization Method—A Case Study of a Mesoscale Convective System

    Corresponding author: Yi YANG, yangyi@lzu.edu.cn
  • 1. Key Laboratory of Climate Resource Development and Disaster Prevention in Gansu Province, College of Atmospheric Sciences, Lanzhou University, Lanzhou 730000
  • 2. Research Center for the Development of the Earth System Model of Lanzhou University, College of Atmospheric Sciences,Lanzhou University, Lanzhou 730000
  • 3. School of Marine Science, Nanjing University of Information Science & Technology, Nanjing 210044
Funds: Supported by the National Key Research and Development Program of China (2017YFC1502102) and National Natural Science Youth Fund of China (41905089)

Abstract: Radar data, which have incomparably high temporal and spatial resolution, and lightning data, which are great indicators of severe convection, have been used to improve the initial field and increase the accuracies of nowcasting and short-term forecasting. Physical initialization combined with the three-dimensional variational data assimilation method (PI3DVar_rh) is used in this study to assimilate two kinds of observation data simultaneously, in which radar data are dominant and lightning data are introduced as constraint conditions. In this way, the advantages of dual observations are adopted. To verify the effect of assimilating radar and lightning data using the PI3DVar_rh method, a severe convective activity that occurred on 5 June 2009 is utilized, and five assimilation experiments are designed based on the Weather Research and Forecasting (WRF) model. The assimilation of radar and lightning data results in moister conditions below cloud top, where severe convection occurs; thus, wet forecasts are generated in this study. The results show that the control experiment has poor prediction accuracy. Radar data assimilation using the PI3DVar_rh method improves the location prediction of reflectivity and precipitation, especially in the last 3-h prediction, although the reflectivity and precipitation are notably overestimated. The introduction of lightning data effectively thins the radar data, reduces the overestimates in radar data assimilation, and results in better spatial pattern and intensity predictions. The predicted graupel mixing ratio is closer to the distribution of the observed lightning, which can provide more accurate lightning warning information.

1.   Introduction
  • Radar and lightning data are characterized by providing abundant mesoscale or small-scale information. With improved assimilation techniques, the assimilation of Doppler radar and lightning data in numerical weather prediction (NWP) models has recently received increasing attention.

    Doppler radar data have incomparably high temporal and spatial resolution and can provide the location and intensity of precipitation as well as the movement of hydrometeors. At present, many traditional methods have been applied to assimilate radar data into the NWP model to improve the initial field and increase the accuracies of nowcasting and short-term forecasting, including the ensemble Kalman filter (EnKF; Gao et al., 2004; Lindskog et al., 2004; Pu et al., 2009; Sun and Wang, 2013), nudging method (Haase et al., 2000), and empirical methods, such as cloud analysis (Hu et al., 2008; Yang et al., 2015) and the physical initialization method (PI; Haase et al., 2000; Milan et al., 2005). The results of these studies have shown that the prediction of precipitation and reflectivity can be improved. In general, high radar echoes represent severe convective activity except in special situations, such as the existence of a bright band. The bright band is the enhanced radar echo area caused by the melting of hydrometeors in stratiform precipitation (Cha et al., 2009), and it often leads to overestimating precipitation intensity (Rico-Ramirez et al., 2005). The positive impact of radar data assimilation only persists for a few hours, which is considered a problem. Moreover, the use of the small-scale radar information may lead to overestimated forecasts. Therefore, it is necessary to conduct radar data thinning.

    Severe convective weather is usually accompanied by frequent lightning activity (Zhang et al., 2017). The relationship between the stage of convective activity and lightning is apparent, meaning that lightning can be used to monitor the occurrence and development of mesoscale convective systems (Williams et al., 1989; Petersen and Rutledge, 1998; Rudlosky and Fuelberg, 2013). With the development of lightning detection techniques (ground-and space-based systems) as well as their advantages, including a wide detection range, high precision, and resistance to terrain influences, lightning data have the potential to be assimilated in monitoring and early warning systems (Qie, 2012; Qie et al., 2014a). However, an accurate observation operator for lightning data does not exist because the lightning flash rate, electric field, and charge density are not model prognostic variables in most existing models (Marchand and Fuelberg, 2014; Wang et al., 2017; Zhang et al., 2017). In the last two decades, scholars have tried to establish links between lightning and other meteorological variables.

    The first attempts to assimilate lightning data in NWP models occurred in the late 20th and early 21st centuries. Alexander et al. (1999) and Chang et al. (2001) converted lightning data into a convective rainfall rate via an empirical relationship and then transformed it into latent heat, which was assimilated. Stefanescu et al. (2013) used convective available potential energy as a proxy between lightning data and model variables to assimilate lightning data. Mansell et al. (2007) utilized lightning data as an index to control the Kain–Fritsch (KF) parameterization scheme for the presence or absence of deep convection in the Coupled Ocean–Atmosphere Mesoscale Prediction System, although the results were also related to the trigger function formulation and the microphysical processes. Fierro et al. (2012) introduced a methodology to assimilate total lightning at convection-resolving scales by modifying the water vapor mixing ratio simulated by Weather Research and Forecasting (WRF) model according to a function depending on the flash rate and the simulated graupel mixing ratio. Thereafter, many studies based on the Fierro’s method have obtained valuable results (Fierro et al., 2015, 2016; Lynn et al., 2015; Federico et al., 2017a, b, 2019; Lynn, 2017). Moreover, Qie et al. (2014b) established empirical formulas between the total lightning flash rate and ice-phase particle (graupel, ice, and snow) mixing ratios to adjust the mixing ratio of ice-phase particles in the mixed-phase region. Chen et al. (2019) took advantage of the results of Fierro et al. (2012) and Qie et al. (2014b) and nudged the low-level water vapor and graupel mass within the mixed-phase region simultaneously according to the flash rate. Furthermore, the studies by Wang et al. (2014, 2015, 2018) and Yang et al. (2015) converted lightning data to reflectivity using a simple assumed relationship between flash density and reflectivity, and improved the forecasting of the convective events. The assimilation methods are also various and include the ensemble square root filter [EnSRF; three-dimensional variational (3DVar)] data assimilation method (Wang et al., 2017) and cloud analysis (Yang et al., 2015). Lightning data have also been used to indicate the location of deep convection in the simulated region. In the study by Federico et al. (2014), lightning observations were used as a diagnostic tool.

    In summary, radar and lightning data have their own advantages and disadvantages. The efficient combination of radar and lightning data can improve the accuracy of convective weather forecasting. The PI method is a type of assimilation method based on the semiempirical relationship between radar reflectivity and the convective precipitation rate. Data assimilation can be easy to realize if lightning data are introduced as a constraint condition during the PI assimilation process.

    The PI method was first proposed by Krishnamurti et al. (1984) to determine the satellite-based rain rate, thus augmenting the data content at the tropical latitudes. Then, several studies (Krishnamurti et al., 1991, 1993, 1994) have shown an improvement in precipitation forecasting by modifying the initial state via the incorporation and analysis of the rain rate. At the beginning of the 21st century, Haase et al. (2000) and Milan et al. (2005) incorporated precipitation data derived from radar data into the Lokal Model through PI. The use of PI led to very good consistency between the radar observed precipitation field and the precipitation field simulated by the Lokal Model. The work of Wang et al. (2014) subsequently converted lightning data into 3D proxy radar reflectivity and then adjusted model variables using PI. However, the PI method has deficiencies. The forecasting skill of PI is sensitive to the rainfall retrieval algorithm (Krishnamurti et al., 1994). The method does not consider model or observation errors, and several model variables are directly replaced without any constraints, which may lead to an imbalance with other variables. Thus, Yang et al. (2006) first proposed a useful method called PI3DVar, which is a combination of PI and 3DVar. The PI3DVar method takes advantage of the above two assimilation techniques. In the PI3DVar method (Yang et al., 2006, 2009), the vertical velocity, which is derived from radar reflectivity via PI, is assimilated by 3DVar to improve the initial field.

    In this study, we combine 3DVar with PI to assimilate relative humility (rh), which is derived from radar and lightning data (hereafter, this method is called PI3DVar_rh). The objective of this paper is to verify the applicability of the PI3DVar_rh method based on convective activity in Anhui Province on 5 June 2009. This paper is organized as follows. The assimilation and assessment methods are introduced in Section 2. The data and experimental design are described in Section 3. The results are presented in Section 4. Finally, the conclusions and discussion are provided in Section 5.

2.   Methods
  • The PI3DVar_rh method is a composable method. The details of PI3DVar_rh are provided as follows.

    First, the maximum reflectivity factor (Zobs; mm6 m−3) is converted into the rain rate (RR′obs; mm h−1) through the following ZR relationship (Hunter, 1996):

    $$ {\mathrm{R}\mathrm{R}}_{\mathrm{o}\mathrm{b}\mathrm{s}}'={\left(\frac{{Z}_{\mathrm{o}\mathrm{b}\mathrm{s}}}{300}\right)}^{\frac{1}{1.4}}. $$ (1)

    Second, rh (%) and water vapor mixing ratio (qv; kg kg−1) at each model layer are estimated in the areas where the rain rate is higher than 0.1 mm h−1. The water vapor in convective clouds is close to saturated; thus, the minimum rh value inside the cloud is set to 90% (when the maximum reflectivity is higher than 30 dBZ) or 80% (when the maximum reflectivity is less than 30 dBZ). Because rh is relatively low above cloud top, the maximum rh value is set to 80% or 75%. We suppose that there is a dry adiabatic process below cloud base. The variable qv below cloud base is set to qv at cloud base. The cloud top height is assumed to be the echo top of radar reflectivity (18.5 dBZ), while the height of the cloud base is approximated by the lifting condensation level (LCL) of the background as shown in Eq. (2). The water vapor mixing ratio is calculated through Eqs. (3) and (4) (Sheng et al., 2013):

    $$ {z}_{\mathrm{c}\mathrm{b}}\approx \mathrm{L}\mathrm{C}\mathrm{L}=123\times \left({T}_{2}-{T}_{\mathrm{d}2}\right), $$ (2)

    where zcb (m) represents the height of cloud base, and T2 (K) and Td2 (K) are the temperature and dew point temperature at a height of 2 m, respectively.

    $$\begin{split} & {e}_{\mathrm{s}}=\\ & \left\{\!\!\!\!\! \begin{array}{c}6.1078\mathrm{exp}\left[\dfrac{17.2693882\left(T-273.16\right)}{T-35.86}\right], T\! \geqslant \! 273.16\\ 6.1078\mathrm{exp}\left[\dfrac{21.8745584\left(T-273.16\right)}{T-7.66}\right], T\! < \!273.16\end{array},\right. \end{split}$$ (3)
    $$ {q}_{\mathrm{v}}\approx \frac{0.622{e}_{\mathrm{s}}}{p}, $$ (4)

    where p represents atmospheric pressure. When T represents the temperature, es and qv represent vapor pressure and water vapor mixing, respectively. When T represents the dew point temperature, es and qv represent saturated vapor pressure and saturated water vapor mixing, respectively. The detailed adjustment is shown in Table 1. Scheme I retrieves rh and qv using radar data. Lightning data are used as location constraints in Scheme II, and rh and qv are retrieved through radar only when lightning is observed. The introduction of lightning data effectively thins the radar data.

    HeightScheme I
    ${\rm{R}\rm{R}'_{\! \rm{o}\rm{b}\rm{s} } }\geqslant 0.1\; \rm{m}\rm{m} \;{\rm{h} }^{-1}$
    Scheme II
    $ \rm{L}\rm{F}\geqslant 1 $ and ${\rm{R}\rm{R}'_{ \! \rm{o}\rm{b}\rm{s} }} \geqslant 0.1 \; \rm{m}\rm{m} \;{\rm{h} }^{-1}$
    $\rm{m}\rm{d}\rm{B}\rm{Z}\geqslant 30\; \rm{d}\rm{B}\rm{Z}$$\rm{m}\rm{d}\rm{B}\rm{Z} < 30\; \rm{d}\rm{B}\rm{Z}$$\rm{m}\rm{d}\rm{B}\rm{Z}\geqslant 30\; \rm{d}\rm{B}\rm{Z}$$\rm{m}\rm{d}\rm{B}\rm{Z} < 30\; \rm{d}\rm{B}\rm{Z}$
    $ z>{z}_{\rm{c}\rm{t}} $$ {\rm{r}\rm{h}}_{\rm{m}\rm{a}\rm{x}}=80{{\text{%}}} $
    ${ {q}_{\rm{v} } }_{\rm{m}\rm{a}\rm{x} }=80{ {\text{%} } }\times { {q}_{\rm{v} }^{*} }$
    $ {\rm{r}\rm{h}}_{\rm{m}\rm{a}\rm{x}}=75{{\text{%}}} $
    ${ {q}_{\rm{v} } }_{\rm{m}\rm{a}\rm{x} }=75{ {\text{%} } }\times { {q}_{\rm{v} }^{*}}$
    $ {\rm{r}\rm{h}}_{\rm{m}\rm{a}\rm{x}}=80{{\text{%}}} $
    ${ {q}_{\rm{v} } }_{\rm{m}\rm{a}\rm{x} }=80{ {\text{%} } }\times { {q}_{\rm{v} }^{*}}$
    $ {\rm{r}\rm{h}}_{\rm{m}\rm{a}\rm{x}}=75{{\text{%}}} $
    ${ {q}_{\rm{v} } }_{\rm{m}\rm{a}\rm{x} }=75{ {\text{%} } }\times { {q}_{\rm{v} }^{*}}$
    $ {z}_{\rm{c}\rm{b}}\leqslant z\leqslant {z}_{\rm{c}\rm{t}} $$ {\rm{r}\rm{h}}_{\rm{m}\rm{i}\rm{n}}=90{{\text{%}}} $
    ${ {q}_{\rm{v} } }_{\rm{m}\rm{i}\rm{n} }={ {q}_{\rm{v} }^{*} }\times 90{ {\text{%} } }$
    $ {\rm{r}\rm{h}}_{\rm{m}\rm{i}\rm{n}}=80{{\text{%}}} $
    ${ {q}_{\rm{v} } }_{\rm{m}\rm{i}\rm{n} }=80{ {\text{%} } }\times { {q}_{\rm{v} }^{*}}$
    $ {\rm{r}\rm{h}}_{\rm{m}\rm{i}\rm{n}}=90{{\text{%}}} $
    ${ {q}_{\rm{v} } }_{\rm{m}\rm{i}\rm{n} }={ {q}_{\rm{v}}^{*} } \times 90{ {\text{%} } }$
    $ {\rm{r}\rm{h}}_{\rm{m}\rm{i}\rm{n}}=80{{\text{%}}} $
    ${ {q}_{\rm{v} } }_{\rm{m}\rm{i}\rm{n} }=80{ {\text{%} } }\times { {q}_{\rm{v} }^{*}}$
    $ z < {z}_{\rm{c}\rm{b}} $${q}_{\rm{v} }={ {q}_{\rm v}^{*}} \left({z}_{\rm{c}\rm{b} }\right),$
    ${\rm{r}\rm{h}}={q}_ {\rm v} / {q}_{\rm v}^{*}$
    ${q}_{\rm{v} }={ {q}_{\rm v}^{*}} \left({z}_{\rm{c}\rm{b} }\right)\times 90{ {\text{%} } },$
    ${\rm{r}\rm{h}}={q}_{\rm{v} }/{ {q}_{\rm v}^{*} }$
    ${q}_{\rm{v} }={ {q}_{\rm v}^{*}} \left({z}_{\rm{c}\rm{b} }\right),$
    ${ \rm{r}\rm{h}}={q}_{\rm{v} }/{ {q}_{\rm v}^{*} }$
    ${q}_{\rm{v} }={ {q}_{\rm v}^{*}} \left({z}_{\rm{c}\rm{b} }\right)\times 90{ {\text{%} } },$
    ${\rm{r}\rm{h}} ={q}_{\rm v} / {q}_{\rm v}^{*}$
    Note: $ {\mathrm{R}\mathrm{R}'}_{\mathrm{o}\mathrm{b}\mathrm{s}} $, rain rate; LF, lightning frequency; $ {{q}_{{\rm v}}^*}$, saturated water vapor mixing ratio; $ {{q}_{\mathrm{v}}^*}\left({z}_{\mathrm{c}\mathrm{b} }\right)$, $ {{q}_{\mathrm{v}}^*} $ at cloud base; and zct, height of cloud top.

    Table 1.  Estimated rh and qv by using the physical initialization method (PI)

    Then, rh is assimilated by WRFDA-3DVAR in the form of sounding data. The cost function of the 3DVAR method is as follows:

    $$ J\left({{x}}\right)\!=\! \frac{1}{2}\left[{\left({{x}}\!-\!{{{x}}}_\mathrm{b}\right)}^\mathrm{T}{{B}}^{-1}\left({{x}}-{{{x}}}_\mathrm{b}\right)\!+\!{\left[{{H}}\left({{x}}\right)\!-\!{{{y}}}_{0}\right]}^\mathrm{T}{{O}}^{-1}\left[{{H}}\left({{x}}\right)-{{{y}}}_{0}\right]\right], $$ (5)

    where x is the analysis variable, xb is the background of the analysis variable, B is the background error covariance matrix, H is the observation operator, y0 is the observation, and O is the observation error covariance matrix. To find the minimization of the cost function, its gradient is calculated as follows:

    $$ \frac{\partial J}{\partial { x}}={ B}^{-1} \left({ x}-{ x}_{\rm b}\right)-{{ H}}^{\rm{T}}{ O}^{-1} \left[{ y}_{0}-{ H} \left({ x}\right)\right], $$ (6)

    where $ \dfrac{\partial J}{\partial { x}}=0 $ gives the necessary condition for J to be a minimum:

    $$ { x}_{\rm{a}}={ x}_{\rm b}+{\left[{ B}^{-1}+{{ H}}^{\rm{T}}{ O}^{-1}{{ H}}^{-1}\right]}^{-1}{{ H}}^{\rm{T}}{ O}^{-1}\left[{ y}_{0}-{ H}\left({{ x}}_{\rm b}\right)\right]. $$ (7)

    The above xa is the optimal analysis variable. In this study, the background error covariance matrix B is the NCEP background error covariance (CV3), which is estimated in grid space by the National Meteorological Center (NMC) method. The observation data (rh) are pseudo observations in this study. The observation error in Exp.PIVar_small is the default in the 3DVAR system, and the observation error below 400 hPa was increased by 5% in Exp.PIVar and Exp.PIVar_lghtn.

    The traditional PI method is used to modify the initialization field based on a semiempirical relationship between the reflectivity and rainfall rate. In this study, qv values above, in, and below the cloud are derived from the reflectivity and lightning frequency (LF) based on the simple semiempirical relationship shown in Table 1. Then, qv is used to update the qv value in the background field to obtain the analysis field. However, approximations occur when assuming rh and qv in this study. These approximations will affect the results to a certain degree.

    In this study, the equitable threat score (ETS), frequency bias index (FBI), and fractions skill score (FSS) are used to evaluate the reflectivity and precipitation forecasts. The ETS considers the number of hits realized by chance and has the equitable property. An ETS of 1.0 represents a perfect score, although the value can be small as −1/3. Negative values indicate a forecast whose skill is worse than a random forecast. The best FBI is 1. FBI values higher than 1 indicate an overestimation; otherwise, they indicate an underestimation (Goines and Kennedy, 2018). FSS varies with the radius and ranges from 0 to 1.0, with a perfect value equal to 1.0 (Schwartz et al., 2010).

3.   Data and experimental design
  • A severe convective storm occurred from the afternoon to midnight on 5 June 2009, and it was accompanied with lightning, strong wind, hail, and rainstorms in most areas of Anhui, western Jiangsu, and northern Zhejiang provinces. This event resulted in serious economic losses and casualties (Yang et al., 2015). The above severe convective activity is studied in this paper. The horizontal extension of the simulation domains is shown in Fig. 1.

    Figure 1.  Horizontal extension of the two nested domains. Major provinces are marked on the map. The black dots are the locations of the Doppler radars. HF, NJ, and NT represent Hefei, Nanjing, and Nantong stations, respectively.

    The radar data used in this study are from the S-band Doppler weather radars, which have 1° half-power beam width, at Hefei (31.883°N, 117.716°E; 165.5 m), Nanjing (32.19°N, 118.698°E; 138.8 m), and Nantong (32.076°N, 120.976°E; 29.0 m) stations. The data include radar reflectivity, radial velocity, and spectrum width, and they are collected as volume scans, with the elevation progressively increasing from 0.5° to 19.5°. The number of elevation angles and temporal resolution depend on the work pattern of the radar. The reflectivity is recorded at 1-km intervals along the radar beam, and the velocity parameters are recorded at 250-m intervals. Each volume scan lasts approximately 5 min. The most important factor is that radar data from the Hefei radar are for assimilation and the composite reflectivity from Hefei, Nanjing, and Nantong radars are used as references to verify the prediction effect of reflectivity.

    Lightning data are obtained from the LD-II Lightning Detection Network of Anhui Province. At present, the lightning location monitoring network is composed of a main station (Hefei) and 10 substations (Luan, Fuyang, Bozhou, Huaibei, Bengbu, Chuzhou, Anqing, Tongling, Huangshan, and Xuancheng). The maximum detection distance of the main station is 600 km and that of the substations is 300 km. The direction-finding accuracy is ±1°, the time accuracy is 0.1 μs, and the error of lightning positioning is less than 1 km (Chen et al., 2008, 2014; Liu et al., 2015). The network is primarily used to detect cloud-to-ground flashes and differentiate the flash polarity.

    Figure 2 shows the distributions of the radar reflectivity (shaded colors) and lightning (red spots) in the model grid from 0600 to 0900 UTC. The reflectivity is mainly focused on Jiangsu Province (0800 and 0900 UTC). There is a high correlation between lightning and radar reflectivity. The LF is summed over a 40-min period around the analysis time (−30 to +10 min), which is referred to as the selection method of lightning in the cloud analysis system of Grid-point Statistics Interpolation (GSI).

    Figure 2.  Distributions of lightning (red spots) and radar composite reflectivity (shaded colors) at (a) 0600, (b) 0700, (c) 0800, and (d) 0900 UTC 5 June 2009.

  • In this study, numerical simulations are carried out based on WRF-ARW (Advanced Research WRF) version 3.6.1. WRF is driven by the 0.703125° ECMWF reanalysis (ERA)-Interim data. The precipitation observation is from the 0.1° × 0.1° merged precipitation data of the automatic weather stations in China and Climate Prediction Center (CPC) morphing (CMORPH) satellite data. Each experiment is run by using a one-way nesting strategy. D01 is designed with a horizontal 101 × 101 grid in the meridional and zonal directions, and the spacing is 13.545 km. The vertical direction is implemented with 50 nonequidistant levels extending from the surface to 10 hPa. The time step for integration is 60 s. D02 is created by ndown steps using 1-h output from d01, and it is designed with a horizontal 181 × 181 grid and with a horizontal spacing of 4.515 km. The main physical parameterizations include the Thompson microphysical scheme (Thompson et al., 2008), rapid radiative transfer model for general circulation models (RRTMG) longwave radiation scheme, RRTMG shortwave radiation scheme (Iacono et al., 2008), Monin–Obukhov scheme (Chen et al., 1997), rapid update cycle (RUC) land-surface model (Jin et al., 2010), Mellor–Yamada–Janjic TKE (turbulent kinetic energy) planetary boundary layer scheme (Sušelj and Sood, 2010), and Tiedtke cumulus parameterization scheme (Zhang et al., 2011).

    A control experiment (Exp.CTL) and five assimilation experiments are conducted. Each experiment is run from 1800 UTC 4 to 1800 UTC 5 June 2009, and the initial 12 h represents the spin-up time. Each assimilation experiment is circularly assimilated in d01 from 0600 to 0900 UTC. Among all assimilation experiments, Exp.PI and Exp.PI_lghtn are two experiments with the PI method. The other experiments (Exp.PIVar_small, Exp.PIVar, and Exp.PIVar_lghtn) are conducted with the PI3DVar_rh method. The observation error in Exp.PIVar_small is the default in the 3DVAR system, and the observation error below 400 hPa is increased by 5% in Exp.PIVar and Exp.PIVar_lghtn. In the Exp.PI, Exp.PIVar, and Exp.PIVar_small experiments, only the radar reflectivity is assimilated, namely, qv and rh are derived from Scheme I (in Table 1). In Exp.PI_lghtn and Exp.PIVar_lghtn experiments, the radar reflectivity and lightning data are assimilated simultaneously, namely, qv and rh are derived from Scheme II (in Table 1). The detailed experimental design is provided in Table 2.

    ExperimentSimulation timeAssimilation timeAssimilation methodAssimilation data
    Control experiment (Exp.CTL)From 1800 UTC 4 to 1800 UTC 5 June 2009; the first 12 h is the spin-up period______
    Assimilation experiment I (Exp.PI)As shown above0600, 0700, 0800, and 0900 UTCPI methodRadar data
    Assimilation experiment II (Exp.PIVar_small)As shown above0600, 0700, 0800, and 0900 UTCPI3DVar_rh method; the observation error is the default, and the background error covariance matrix is CV3Radar data
    Assimilation experiment III (Exp.PIVar)As shown above0600, 0700, 0800, and 0900 UTCPI3DVar_rh method; the observation error below 400 hPa is increased by 5%, and the background error covariance matrix is CV3Radar data
    Assimilation experiment IV (Exp.PI_lghtn)As shown above0600, 0700, 0800, and 0900 UTCPI methodRadar and lightning data
    Assimilation experiment V (Exp.PIVar_lghtn)As shown above0600, 0700, 0800, and 0900 UTCPI3DVar_rh method; the observation error below 400 hPa is increased by 5%, and the background error covariance matrix is CV3Radar and lightning data

    Table 2.  Experimental design

4.   Results
  • Figure 3 shows the analysis increments of d01 for qv and rh at the last assimilation time (0900 UTC). As shown in Figs. 3a1a5, the qv increments are mainly concentrated in a belt from northwest to southeast, and they are similar to the maximum radar reflectivity distribution. The second row is the vertical profile of the qv increment, and the third row is the vertical profile of the rh increment. The location of the increment corresponds well to the distribution of the radar reflectivity. The qv increments are mainly concentrated below 500 hPa. At 0900 UTC, stronger increments occur in Exp.PI, Exp.PIVar_small, and Exp.PIVar than in Exp.PI_lghtn and Exp.PIVar_lghtn. Namely, lightning data assimilation limits the assimilation of moisture compared to the simulations considering only radar data. In addition, the increments of the experiments using the PI3DVar_rh method (Exp.PIVar_small, Exp.PIVar, and Exp.PIVar_lghtn) are more continuous compared to those of the experiments using the PI method (Exp.PI and Exp.PI_lghtn).

    Figure 3.  Analysis increments in d01 for (a1–c1) Exp.PI, (a2–c2) Exp.PIVar_small, (a3–c3) Exp.PIVar, (a4–c4) Exp.PI_lghtn, and (a5–c5) Exp.PIVar_lghtn. The first row shows the qv (g kg−1) increments at 850 hPa, and the second row shows the vertical profile of qv increments along the red line shown in (a1). The third row shows the vertical profile of the rh (%) increments. The red line in (a1) is from 36°N, 115°E to 30°N, 122°E.

  • Figure 4 shows the distribution of the observed maximum radar reflectivity. At 1100 UTC, strong observed reflectivity was observed in Anhui and Jiangsu provinces, and then, the main body moved slowly to the south. At 1500 UTC, the radar reflectivity was mainly focused on southern Anhui and western Zhejiang provinces. Exp.CTL fails to simulate the main body of reflectivity well, while the data assimilation experiments show distinct improvements. The process of radar reflectivity moving southward is simulated by Exp.PIVar and Exp.PIVar_lghtn experiments. Regarding for assessment result (shown in Fig. 5), the ETS of Exp.CTL is the smallest, and the FBI value of Exp.CTL is less than 1. In contrast, the FBI of Exp.PI_lghtn and Exp.PIVar_lghtn is approximately equal to 1, and the ETS of Exp.PIVar_lghtn is higher when the threshold is 20 dBZ. In general, reflectivity forecasting can be distinctly improved by assimilating radar data or the combination of radar and lightning data, regardless of the PI or PI3DVar_rh method. Furthermore, assimilating both radar and lightning data with the PI3DVar_rh method leads to a more accurate prediction of the reflectivity, especially in the 3–6-h forecasting window.

    Figure 4.  Distributions of the maximum reflectivity (dBZ) in d02 for (a1, b1) the observation, (a2, b2) Exp.CTL, (a3, b3) Exp.PI, (a4, b4) Exp.PIVar_small, (a5, b5) Exp.PIVar, (a6, b6) Exp.PI_lghtn, and (a7, b7) Exp.PIVar_lghtn at (a1–a7) 1100 UTC and (b1–b7) 1500 UTC. The blue lines are the isolines of the observed 15-dBZ contour.

    Figure 5.  (a, b) ETS and (c, d) FBI of the maximum reflectivity at (a, c) 20 dBZ and (b, d) 30 dBZ in d02.

    Lightning activity is another evident characteristic of severe convection and can lead to many disasters. The forecasted graupel pellets can roughly reflect the location of lightning. Figure 6a shows the distribution of lightning at 1500 UTC. Figures 6b1b6 present the distributions of forecasted qg (mixing ratio of graupel; g kg−1) in d02, and Figs. 6c1c6 indicate the vertical profiles of qg. The qg values predicted by Exp.CTL are too small, although the values increase in the assimilation experiments. Among all experiments, the location of qg predicted by Exp.PIVar_lghtn corresponds well with the location of lightning.

    Figure 6.  (a) Scatter distributions for lightning at 1500 UTC. The forecasted qg (g kg−1) in d02 at 1500 UTC for (b1, c1) Exp.CTL, (b2, c2) Exp.PI, (b3, c3) Exp.PIVar_small, (b4, c4) Exp.PIVar, (b5, c5) Exp.PI_lghtn, and (b6, c6) Exp.PIVar_lghtn. (b1–b6) Distributions of qg at 600 hPa and (c1–c6) vertical profiles along the black line indicated in Fig. 6a. The red solid lines represent the 0°C isoline and the red dotted lines represent −20°C isoline.

  • Figure 7 shows the distributions of accumulated precipitation. From 0900 to 1200 UTC (Figs. 7a1a7), the observed precipitation center is mainly located in northern Anhui and Jiangsu provinces. Exp.PI, Exp.PIVar_small, and Exp.PIVar notably overestimate the precipitation intensity in Jiangsu Province. The simulations are significantly improved when the lightning data are introduced as constraints. From 1200 to 1500 UTC (Figs. 7b1b7), the observations are mainly in the center of Anhui and northern Zhejiang provinces. Exp.CTL underestimates the precipitation. Exp.PI and Exp.PIVar_small notably overestimate the precipitation in Anhui and Jiangsu provinces and underestimate the precipitation in Zhejiang Province. However, the precipitation in northern Zhejiang Province is better simulated by Exp.PIVar and Exp.PIVar_lghtn. Exp.PIVar_lghtn performs better considering both the simulation of spatial rainfall pattern and precipitation intensity.

    Figure 7.  Distributions of accumulated precipitation (mm) in d02 for (a1, b1) the observations, (a2, b2) Exp.CTL, (a3, b3) Exp.PI, (a4, b4) Exp.PIVar_small, (a5, b5) Exp.PIVar, (a6, b6) Exp.PI_lghtn, and (a7, b7) Exp.PIVar_lghtn at (a1–a7) 0900–1200 UTC and (b1–b7) 1200–1500 UTC.

    Figure 8 shows the results of the precipitation scores. The ETSs of data assimilation experiments are higher than for Exp.CTL. In addition, the ETSs of experiments using the PI3DVar_rh method are higher than those of the experiments using the PI method. The FBI of Exp.CTL is less than 1, and the FBIs of radar data assimilation experiments are much larger than 1. The FBIs of the data assimilation experiments using the lightning data are closer to 1, indicating that the precipitation forecasting is improved when lightning data are introduced as constraints. The FSS is utilized (shown in Fig. 9) to provide a more effective evaluation of the location of the accumulated precipitation. At different thresholds, all assimilation experiments show higher FSS values than Exp.CTL, indicating that assimilating radar and lightning data can improve the location forecasting of precipitation. Overall, assimilating radar and lightning data simultaneously is better than only assimilating radar data. Moreover, the PI3DVar_rh method performs better than the PI method.

    Figure 8.  (a, b) ETS and (c, d) FBI of precipitation for (a, c) the 1-mm and (b, d) 5-mm thresholds in d02.

    Figure 9.  FSS (fractions skill score) for 1-h precipitation at the (a) 1-mm and (b) 5-mm thresholds in d02. The influence radius is approximately 13.5 km (3 × horizontal spacing = 13.545).

5.   Conclusions and discussion
  • Currently, radar data and lightning data have been used to increase the mesoscale information in the initial field of NWP models. In this study, we use the PI3DVar_rh method to circularly assimilate two types of observations at the same time. In the PI3DVar_rh me-thod, radar data are dominant and lightning data are introduced as constraint conditions.

    A total of five assimilation experiments are designed. Reflectivity and precipitation are underestimated in the control experiment. The assimilation of radar data improves the location prediction of precipitation and reflectivity, although the simulated magnitudes are too large. A somewhat better forecast is obtained when lightning data are assimilated as constraints. The introduction of lightning data in this study effectively thins the radar data and reduces the overestimation of precipitation and reflectivity in radar data assimilation. The experiments using the PI3DVar_rh method effectively simulate the southward shifting of the reflectivity and precipitation from 1200 to 1500 UTC, indicating that the PI3DVar_rh method is better than the PI method, especially in the last three hours of prediction. Moreover, the results show that it is better to increase the observation error appropriately (because the rh values are inverted through a semiempirical relationship) when using the PI3DVar_rh method. In conclusion, cyclic data assimilation of radar and lightning data can improve prediction accuracy and is easy to implement.

    However, there are also shortcomings. In this study, the assumed rh introduces additional approximations that will affect the simulations in a certain degree. Excessive humidity adjustments are the other drawback. In a follow-up study, not only the water vapor in the strong convective area should be increased but the overestimation of the background field should also be weakened. Cloud-to-ground lightning data are used only to filter radar data and for radar data thinning; lighting data still need to be well exploited in data assimilation system. Moreover, flashes are an indicator of deep convection and are absent or very rare in stratiform precipitation. Thus, the PI3DVar_rh method is not suitable for stratiform precipitation.

    Currently, the layout of the radar data observation network is reasonable. Lightning data detection technology has improved considerably in recent decades. Radar and lightning data can be complementary to each other, and both radar and lightning data should be exploited in data assimilation systems in the future.

    Acknowledgments. We thank ECMWF for providing the 0.703125° ERA-Interim dataset (https://rda.ucar.edu/datasets/ds627.0/). We thank the China Meteorological Data Service Center website for providing 0.1° × 0.1° merged precipitation data from automatic weather stations in China and CMORPH satellite data (http://data.cma.cn/data/cdcdetail/dataCode/SEVP_CLI_CHN_MERGE_CMP_PRE_HOUR_GRID_0.10.html). We also thank the Weather Service Forecast Office of China for providing the radar and lightning data.

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