Improving,the,Nowcasting,of,Strong,Convection,by,Assimilating,Both,Wind,and,Reflectivity,Observations,of,Phased,Array,Radar:,A,Case,Study

Xiaoxia LIN, Yerong FENG, Daosheng XU*, Yuntao JIAN, Fei HUANG, and Jincan HUANG

1 Guangzhou Institute of Tropical and Marine Meteorology/Guangdong Provincial Key Laboratory of Regional Numerical Weather Prediction,Chinese Meteorological Adminstration, Guangzhou 510641

2 Guy Carpenter Asia–Pacific Climate Impact Centre, School of Energy and Environment, City University of Hong Kong, Hong Kong 999077

3 Zhuhai Meteorological Bureau, Zhuhai 519000

4 Foshan Meteorological Service of Guangdong Province, Foshan 528200

ABSTRACT

Key words: phased array radar, data assimilation, initialization, nudging

In recent years, a cloud-resolving numerical weather prediction (NWP) model named Tropical Regional Assimilation Model for South China Sea_Rapid Update Cycle_1km (TRAMS_RUC_1km) has been running operationally at the Key Laboratory of Regional Numerical Weather Prediction in Guangdong Province (Xu et al.,2020), where there is a need for assimilating high-spatialresolution observations at a frequent update cycle. Compared to other conventional and non-conventional meteorological data, radar observations are a rich source of information regarding the three-dimensional (3D) structure of rainstorms. Many efforts have been made with the aim to extract meteorological information from Doppler radar and assimilate observations into mesoscale NWP models to improve their short-term forecasting capability (Xu et al., 1995, 2001a, b; Gao et al., 1999; Snyder and Zhang, 2003; Xiao et al., 2005). A consensus appears to be emerging on two aspects for radar data assimilation. (1) The combination of both radial velocity and reflectivity observations in data assimilation is critical for the consistency between model dynamics and microphysics (Tong and Xue, 2005; Aksoy et al., 2009; Yang et al.,2009; Zhang et al., 2019). (2) A suitable assimilation frequency of radar data will yield more accurate analyses(Yussouf and Stensrud, 2010; Pan and Wang, 2019).

Phased array radar (PAR) is an emerging technology that can measure precipitation systems more rapidly (1–2 min for a volume scan) and in a more flexible scanning mode. Recent studies show that PAR has great advantages in detecting meso- and micro-scale weather systems (Wu et al., 2014; Ma et al., 2019). PAR can be an important supplement to the traditional Doppler weather radar in severe weather monitoring, making up for the blind observation area of S-band radar in low-altitude areas (Liu et al., 2016; Fu et al., 2020). The benefit of assimilating PAR radar data in high-resolution models has been clearly demonstrated (Yussouf and Stensrud, 2010;Supinie et al., 2017; Stratman et al., 2020), but very few studies have been conducted in China (Zhao et al.,2019).

In recent years, a PAR detection network has been built in the Guangdong–Hong Kong–Macao Greater Bay Area with over 10 X-band dual-polarization radar devices,which can accurately capture rapidly evolving and developing weather phenomena and significantly improve the predictability of severe weather (Cheng et al., 2020).These observations provide an invaluable data source and raise the possibility of improvement in the initialization of convective systems in the TRAMS_RUC_1km model.

The nudging method was chosen for assimilation of PAR data in this study because of its ability to adjust the modeled convection according to the full-physics model dynamical and physical equations for dynamical and physical consistency, and high computational efficiency.Nudging approaches also perform better than traditional ensemble filtering when the model error is large or the estimation of covariance is poor (Lei and Hacker, 2015).Thus, it is suitable for assimilating PAR observations with high temporal and spatial resolution in the rapid update cycle of this operational model system. In fact, the nudging method has been widely adopted in the assimilation of radar reflectivity (Liu et al., 2007; Xu et al., 2013;Huang et al., 2018). In this study, the nudging method was further extended to verify its advantage in the assimilation of the radar radial velocity.

The assimilation of PAR radar data has been widely reported in America and Japan, in which variationalbased methods (Xu et al., 2010) and ensemble-based methods (Lei et al., 2007; Lu and Xu, 2009; Yussouf and Stensrud, 2010; Miyoshi et al., 2016a, Miyoshi et al.,2016b; Maejima, 2017; Supinie et al., 2017; Amemiya et al., 2020; Stratman et al., 2020) are usually adopted. Although these sophisticated methods based on optimal statistical theory can produce more accurate and balanced initial fields, their computational cost is much larger than with the nudging method and cannot satisfy the rigorous computational requirements of the real-time TRAMS_RUC_1km system at present.

In this study, a local rainstorm case that occurred in Foshan city, Guangdong Province, on 26 August 2020,was selected to examine the influence of PAR data assimilation on the precipitation forecast. Following this introduction, Section 2 describes the TRAMS_RUC_1km model, radar dataset, and methods, followed by a case description and a description of the experimental design in Section 3. Section 4 evaluates the precipitation forecast of this rainfall event under different nudging strategies and investigates the possible reason for differences in forecasting performance. Finally, a summary and some further discussion are provided in Section 5.

2.1 Model configuration

Numerical simulations were carried out in this study with the operational TRAMS_RUC_1km model (Xu et al., 2020), which contain the Exner pressure ( Π), potential temperature ( θ), 3D wind field (u,v,w), and water vapor (qv) as prognostic variables in the basic dynamic core(Chen et al., 2008). The microphysics scheme adopted in this study is the WRF single-moment 6-class microphysics scheme (WSM6) developed by Hong et al. (2006),which includes six kinds of prognostic water species: water vapor (qv), cloud water (qc), rain (qr), cloud ice (qi),snow (qs), and graupel (qg). The terrain resolution is the same as the model horizontal resolution [interpolated from the original data with a resolution of 30 s (～900 m)in the Weather Research and Forecasting (WRF) model].

In this study, we used two nested domains with horizontal resolutions of 3 and 1 km, respectively (Fig. 1),with only the inner domain used for PAR data assimilation. The initial fields and lateral boundary conditions of the outer domain (e.g., 3-km model) were provided by the ECMWF analysis field with a horizontal resolution of approximately 9 km.

2.2 Observations

Fig. 1. Model domain setup used for data assimilation experiments.

Observations from the PAR network in Foshan city,Guangdong Province, were used in this study. Figure 2 shows the locations of the seven PAR stations and their coverage. The composite radar reflectivity data at 1000 UTC 26 August 2020 are also displayed in Fig. 2. The PAR data were assimilated via an indirect method in which the forecast variables of the numerical model were first retrieved from radar observations and then ingested into the model via the nudging method as follows:

Fig. 2. The locations (black dots) of the seven PAR stations and the data coverage (red circles) for each radar. The color shading indicates the composite reflectivity at 1000 UTC 26 August 2020. The black frame is the domain in Fig. 3.

whereFdenotes the forecast variable, M represents the dynamical core and physical process of the NWP model,Fobsis the retrieved variable ofF, andδtis the relaxation time of nudging. A series of quality control processes were applied to the PAR data before its retrieval into 3D gridded wind and reflectivity. The quality control system adopted in this study contained the following seven steps: (1) filtering the noise, (2) correction of calibration errors, (3) removal of ground clutter, (4) removal of scatter points for reflectivity, (5) unfolding the velocity ambiguity, (6) refilling the reflectivity and velocity holes,and (7) correction of strong attenuation due to heavy rain. A detailed description of this system will be presented in a separate paper in the future. The nudging approach is a very simple and computationally inexpensive way to assimilate radar data in an operational model. Indeed, it has been used in many operational NWP models(Schroeder et al., 2006; Liu et al., 2008; Dixon et al.,2009; Davolio et al., 2017; Jacques et al., 2018; Zhang et al., 2019) and often shows reasonable performance where increased model error and poor estimation of background error covariance are the problem (Deng and Stauffer, 2006; Lei and Hacker, 2015; Shao et al., 2015).

2.2.1Retrieval of 3D wind fields from PAR observations

As can be seen in Eq. (1), the nudging method can be applied only when the observation (Fobs) and background field (F) are for the same variable. Thus, it is necessary to retrieve the 3D wind field with the observed PAR radial velocity. The retrieved PAR wind field has been proven to be able to capture well the characteristics of small-scale convective systems, such as microburst events (Qiu et al., 2013) and tornadic supercells (Liou et al., 2018). Although the indirect assimilation method has some theoretical drawbacks according to Derber and Wu(1998), the practical effect of the retrieved PAR wind field in nowcasting is still worth pursuing.

In this study, the 3D wind fields were retrieved using the variational dual-Doppler wind analysis method suggested by Gao et al. (1999, 2004) and Potvin et al.(2012). It performs through minimization of the following cost function (Shapiro et al., 2009):

whereJO,JM,JV, andJSare the cost functions associated with the observational, mass, conservation, vorticity,and smoothness constraints, respectively. As the mass continuity equation was applied as a weak constraint to avoid the explicit integration of vertical speedw, the specification ofwboundary conditions was not needed (Gao et al., 1999). In this study, we simply setwas equal to zero in both the top and bottom conditions, as in Gao et al. (1999).

Given the relatively recent emergence of PAR data in China, it was important to first examine their quality before assimilation. The retrieved horizontal wind vectors at the heightZ= 500 and 1500 m are compared with multiple-radar syntheses (Shapiro et al., 2009) in Fig. 3.As can be seen, the wind speed pattern is in close agreement with those obtained from the PAR synthesis, which means that the flow structures can be successfully captured by the retrieved wind field. The root-mean-square error (RMSE) of theu-wind component is around 1 m s−1and changes little with height below 9 km. For thevwind component, the RMSE is around 1.0–2.0 m s−1,with a maximum at about 7.5 km. A similar verification method was adopted by Liou et al. (2018) for the quantitative assessment of single-Doppler velocity retrievals of PAR radar, and their RMSE of the retrieved field was around 2–6 m s−1. Therefore, the quality of the PAR data used in this paper is more accurate, and this can be attributed to the advantage of the dual-Doppler retrieval method compared to the single-Doppler method. The retrieved wind field was further evaluated for 10 other cases with convective or stratiform precipitation in South China, and their RMSEs (figure omitted) were consistent with the case studied in this paper. The retrieved wind was also evaluated with independent observations from wind profile radar data in Foshan (figure omitted), and the results under both stratiform and convective precipitation conditions showed that the retrieved wind was reasonable.

Fig. 3. (a, b) Multiple-radar syntheses of horizontal wind vectors (m s−1) and (c, d) the corresponding retrieved fields at 1000 UTC 26 August 2020 at (a, c) Z = 500 m and (b, d) Z = 1500 m. The color shading indicates the radar reflectivity (dBZ). The red dot indicates Foshan (FS) city.

It should be noted that the coverage of the retrieved wind field (Figs. 3c, d) is not as large as that of the multiple-radar syntheses (Figs. 3a, b), especially in the southwest corner of the domain in Fig. 3. The difference in coverage was caused by the different calculation methods applied for radar syntheses and retrieval. The multiple-radar synthetic wind was calculated within the area covered by three X-band PARs, and the three velocity components (u,v,w) were obtained directly using the different radial velocities from a single X-band PAR.Further details on the method for calculating the synthetic field can be found in many radar meteorology textbooks(Zhang et al., 2001). The synthetic wind field of the three radars has high accuracy and can be regarded as the “true value” to examine the accuracy of the retrieved wind field. As described above, the multiple-radar synthetic wind needs the grid to be observed by three radars at the same time, while the retrieved wind only needs to be observed by two radars (as it is a dual-Doppler wind analysis procedure), so the coverage of the multiple-radar synthetic wind fields was a little smaller than the retrieved wind fields.

Although the multiple-radar synthetic wind fields are more accurate, we still chose the retrieved fields in the data assimilation based on the following two considerations: (1) the spatial coverage of the retrieved wind is usually much larger, which is very helpful in improving the effect of data assimilation, and (2) the computational efficiency will be higher for the retrieval of dual-Doppler radar, as the retrieved wind field can be obtained quickly when the data from two different PARs are received. It will be more feasible in an operational setting because the assimilation period is very short in a nowcasting system.

2.2.2Cloud parameterization adjustment based on reflectivity

As mentioned in Section 2.1, both liquid and ice particles are prognostic variables in the WSM6 microphysical scheme. Therefore, it will be more reasonable to assimilate both liquid and ice hydrometeors for nowcasting. Unfortunately, the retrieval of ice species from PAR radar reflectivity still cannot be realized because it has not been incorporated into the operational cloud analysis system for TRAMS_RUC_1km. For convenience, a simplified microphysical retrieval scheme for radar reflectivity developed by Brewster (1996) was temporarily adopted in this study. The rainwater (qr) can be derived analytically by assuming the Marshal–Palmer distribution of raindrop size (Sun and Crook, 1997):

wherepsis the surface pressure andpis the pressure of each level (hPa) from the background field. Because this retrieval method is derived based on the warm cloud scheme of Kessler (1969), only the rain and cloud water were retrieved and nudged in this study. The quality of the retrieved cloud water (qc) and rain (qr) is difficult to assess, as corresponding observations are still very rare.However, the usability of this simple method in improving short-range forecasts has been examined with the TRAMS model on many occasions (Zhang et al., 2012,2019; Xu et al., 2016).

To improve the thermodynamic balance in the initial field, the temperature accounting for the latent heat (LH)effect resulting from the increments of hydrometeor fields was also considered in this study, using the following equations:

Finally, the moisture field was modified according to the scheme proposed by Zhao et al. (2008). The water vapor was changed by keeping the relative humidity saturated at grid points where the observed reflectivity was not less than 30 dBZ, and adjusting the relative humidity to no more than 80% at grid points where the observed reflectivity indicated that precipitation did not exist (less than 30 dBZ). It is possible that 30 dBZ is too low for saturation; however, according to a sensitivity test (not shown), it was found that too much water vapor will be reduced when it is increased to 40 dBZ, thus leading to an obvious underestimation in the precipitation forecast.Therefore, 30 dBZ was still chosen as the threshold for judgment of saturation in this paper. In terms of the possibility of oversimplicity in the above reflectivityonly-dependent method for humidity adjustment, a certain amount of irrationality in choosing empirical parameters is inevitable. In fact, we noticed that, in the study of Xu et al. (2010), a similar method was adopted for humidity adjustment and their condition of grid saturation was set as the observed reflectivity being larger than 10 dBZ when the analyzed vertical velocity was nonnegative. The obvious uncertainty in this humidity adjustment method indicates the need to adopt more complex schemes for physical rationality. For example, in the case study of Pan et al. (2020), a humidity adjustment scheme based on the relationship between relative humidity and vertical velocity proposed by Tong (2015) exhibited obvious improvement in the forecasting of precipitation.

3.1 Description of the rainstorm case

A rainstorm that occurred on 26 August 2020 in Foshan city, Guangdong Province, was selected for this study. Most of the rainfall occurred during a 3-h period from 0900 to 1200 UTC 26 August. The hourly evolution of composite reflectivity (Figs. 4a–c) indicates that two convective cells—one from the east and another from the west, which then merged together at about 1100 UTC before moving towards the southeast—played a major role during this rainfall event. The corresponding observations of 2-m temperature and 10-m wind from 0900 to 1100 UTC 26 August are shown in Figs. 4d–f. It can be seen that a cold pool was located in the rainstorm area (in this study, the “cold pool” is simply defined as the area with 2-m temperature below 26°C), the front edge of which was an obvious convergence line. At 1100 UTC, the cold pool spread to the southeast, uplifted the warm and humid air from the south, and triggered the release of unstable energy. The convective system propagated southeastwards and eventually moved away from Foshan at about 1300 UTC 26 August 2020.

3.2 Experimental design

As this was the first time that PAR data had been assimilated in the TRAMS_RUC_1km model, and studies on the nudging method for retrieved radar wind fields are still very rare, the influence of several issues should be explored before it is implemented in an operational system. Figure 5 illustrates schematically the data assimilation procedure in different experiments. The TRAMS_RUC_1km model was initialized at 0600 UTC 26 August 2020, while the forecasts started at 1000 UTC 26 August 2020. Eleven parallel experiments were configured to evaluate the performance of PAR reflectivity and retrieved wind data assimilation on the model forecast.

Fig. 4. (a–c) Composite radar reflectivity (dBZ) and (d–f) SYNOP station observations of 2-m temperature (color-shaded; °C) and 10-m wind(black arrows; m s−1) during 0900–1100 UTC 26 August 2020. The red dashed square in (a–c) is the area used for the analysis in Fig. 7. The black dot indicates Foshan (FS) city.

Fig. 5. Illustration of the experimental design.

In this paper, a series of issues are discussed in detail,including: (1) the different behaviors of wind and reflectivity assimilation, (2) the impacts of assimilation frequency, (3) the effect of humidity and temperature adjustment in cloud, and (4) the sensitivity of relaxation time for the nudging method. The control experiment(Cntl) was a model forecast run starting at 0600 UTC 26 August without any data assimilation. The Exp_W and Exp_R experiments used a 4-min relaxation time to nudge the retrieved wind (u,v,w) and water hydrometeors (qc,qr) at 1000 UTC, respectively. Exp_WR was a combination of Exp_W and Exp_R. The results from Exp_WR, Exp_WR_4tim, and Exp_WR_16tim were compared to examine the impact of the assimilation frequency. Exp_WR_4tim assimilated both retrieved wind and reflectivity data at 0900, 0920, 0940, and 1000 UTC,while Exp_WR_16tim was carried out with 16 assimilation times—namely, 0900, 0904, 0908, 0912, 0916,0920, 0924, 0928, 0932, 0936, 0940, 0944, 0948, 0952,0956, and 1000 UTC. Three additional data assimilation experiments were also implemented to investigate the importance of thermodynamics, and they are referred to as Exp_WRT_4tim, Exp_WRQ_4tim, and Exp_WRTQ_4tim. These three experiments used the same assimilation strategies as Exp_WR_4tim but additionally included the adjustment of potential temperature ( θ) and water vapor (qv). Lastly, two other sensitivity experiments were carried out with different relaxation times:Exp_WRTQ_4tim_8min with a nudging time window of 8 min, and Exp_WRTQ_4tim_12min with a nudging time window of 12 min.

4.1 Different behaviors of wind and reflectivity assimilation

The results from Exp_W, Exp_R, and Exp_WR were compared to investigate the separate influence of radar wind and reflectivity. The predictions of 1-h rainfall from Cntl, Exp_W, and Exp_R (from 1100 to 1200 UTC 26 August) are given in Figs. 6c–d, Figs. 6e–f, and Figs.6g–h, respectively. The observed precipitation amounts are also presented in Figs. 6a, b. Cntl almost completely failed to predict the local heavy rain storm around Foshan. The overall improvement in the data assimilation experiments was not particularly significant, but several slight improvements can still be seen, especially for the rain belt in the east of Foshan city in the second hours of the model forecast, albeit the location was a little northwards compared to the observation (Fig. 6b).

In general, the improvements in Exp_W, Exp_R, and Exp_WR were very slight. It is likely that the effect of a single time assimilation was not enough to change the model’s original track during the forecast (Zhao et al.,2006). An interesting phenomenon is that the hourly precipitation forecasts in Exp_W, Exp_R, and Exp_WR were similar to each other, which implies that the behaviors of wind and reflectivity assimilation were similar.This is different from the conclusion of Zhang et al.(2019), who also assimilated retrieved S-band Doppler radar data in TRAMS_RUC_1km for another case. The reason needs to be further explored and is not discussed here, because the influence of nudging the wind field and hydrometeors is much smaller than that of the adjustment of humidity and temperature (see Section 4.3).

4.2 Impacts of assimilation frequency

Exp_WR_4tim and Exp_WR_16tim were designed as an attempt to enhance the impact of data assimilation. As shown in Fig. 5, reflectivity and retrieved wind were nudged into the model every 20 and 4 minutes in Exp_WR_4tim and Exp_WR_16tim, respectively.

Significant changes in the prediction of rainfall location and intensity by Exp_WR_4tim and Exp_WR_16tim can be seen in Figs. 6k–n. From 1000 to 1100 UTC,Exp_WR_4tim underestimated the precipitation in the north of Foshan city (Fig. 6i), but the simulations gradually improved when the nudging time interval was reduced (Figs. 6k, m). From 1100 to 1200 UTC, the rain belt in the east of Foshan city also moved towards the south with an increase in nudging frequency (Figs. 6j, l,n), which was more consistent with the observation (Fig.6b). The enhanced precipitation forecast in the first hour might be attributable to the fact that the background fields (at 1000 UTC) of Exp_WR_4tim and Exp_WR_16tim contained more convective structures than those of Exp_WR.

Fig. 6. Hourly cumulative precipitation (mm) during 1100–1200 UTC 26 August 2020 from (a, b) observation, (c, d) Cntl, (e, f) Exp_W, (g, h)Exp_R, (i, j) Exp_WR, (k, l) Exp_WR_4tim, (m, n) Exp_WR_16tim, (o, p) Exp_WRT_4tim, (q, r) Exp_WRQ_4tim, (s, t) Exp_WRTQ_4tim, (u,v) Exp_WRTQ_4tim_8min, and (w, x) Exp_WRTQ_4tim_12min.

The hydrometeor fields and vertical movement were further examined to address the cumulative effects of the continuous assimilation cycle. The rainwater (qr) and cloud water (qc) over the region (22.5°–23.5°N, 112.5°–113.5°E)—see the red dashed square in Fig. 4 are shown in Fig. 7. It can be seen that more cloud hydrometeors were generated in Exp_WR_4tim and Exp_WR_16tim from 1000 to 1200 UTC, especially in the middle and lower troposphere. It is obvious that the increase in hydrometeors was due to the higher temporal frequency of nudging, especially for the first hour. It should be noted that the difference in hydrometeors between Cntl and Exp_WR was very small during the whole forecast period,and this behavior is consistent with what was observed and reported in Section 4.1. Longitude–pressure crosssections of vertical velocity (averaged from 23.0° to 23.2°N at 1000 UTC 26 August) are shown in Fig. 8 to demonstrate the impact of continuous assimilation on the dynamical field. The convective updraft/downdraft was very weak in Cntl, corresponding to the underestimation of hydrometeors in Fig. 7. The downdraft was slightly enhanced in Exp_WR, while the updraft was still very weak. This indicates that the inclusion of the 3D radar wind field in Exp_WR had a negligible effect owing to their poor consistency with the background field, and the broad downdraft area can be seen as a result of the cooling process caused by the evaporation of added hydrometeors. This is closely consistent with the result of an assimilation test without physical initialization in Yang et al. (2009). This may also indicate that there are inconsistencies in the mass and wind retrievals. It is hard to spinup the model by only nudging the retrievals once if they are not dynamically and physically coherent. In Exp_WR_4tim (Fig. 8c), the updraft began to dominate the convective area, which implies that the dynamical field can be forced towards the observation by increasing the frequency of nudging. This conclusion is further supported by the significantly enhanced updraft/downdraft in Exp_WR_16tim (Fig. 8d).

Fig. 7. Vertical profile of rainwater (qr) and cloud water (qc) over the region (22.5°–23.5°N, 112.5°–113.5°E) at (a) 1000 UTC, (b) 1100 UTC,and (c) 1200 UTC 26 August 2020.

Fig. 8. Longitude–pressure cross-sections of vertical velocity (m s−1) averaged from 23.0° to 23.2°N at 1000 UTC 26 August 2020.

As discussed above, a continuous data assimilation cycle has obvious advantages over a single data assimilation for the spin-up of a convective system, especially for the simple nudging assimilation method used in the present study. In fact, continuous assimilation is also necessary even for more sophisticated methods for radar data assimilation, such as the three-dimensional variational (3Dvar; Zhao et al., 2006) and ensemble Kalman filter (EnKF; Yussouf and Stensrud, 2010) approaches.Considering the lack of consistency between the observation and model forecast, an appropriate time interval is required to attain a new balance (Pan and Wang, 2019)during the assimilation process. If the observations are assimilated with too high a frequency, gravity waves will be stimulated owing to the insufficient balance constraint during the assimilation period (Lin et al., 2021).As shown in Fig. 6m, a large amount of suspicious convective precipitation can be seen as a result of the overly high assimilation frequency, which in fact demonstrates a limitation of the data assimilation method used in this study. These gravity waves are likely excited from the imbalance in the analysis increments imposed on the model. A similar result was found even if both the temperature and moisture were adjusted and nudged 16 times(figures omitted). Therefore, the system cannot take advantage of the more frequent scans of convective systems with PAR. Only a moderate frequency (about once per 20 min) of nudging assimilation could be adopted based on the performance of balance adjustment in the model. In the following test results reported in this paper, Exp_WR_4tim was set as the basis for further investigation.

Although the influence of observation was enhanced by increasing the frequency of nudging assimilation, it should be pointed out that the simulation was still not as good as expected. Test Exp_WR_4tim still underestimate the precipitation obviously in the first hour (Fig. 6k),and the skill aided by radar data assimilation dropped rapidly in the second hour (Fig. 6l). The short-lived benefits of radar data assimilation have been widely reported[e.g., Fig. 15 of Mandapaka et al. (2012) or Fig. 8 of Supinie et al. (2017)]. One possible reason is that it is not enough to initialize the convective system by just adjusting the dynamic and microphysical fields. The thermodynamic balance should also be satisfied with the spin-up and maintenance of convection at the initial forecast time. Therefore, the temperature and moisture fields were adjusted according to the method proposed by Zhao et al.(2008), as reported in the next section.

4.3 Effect of in-cloud humidity and temperature adjustment

To further improve the nowcasting of precipitation,the in-cloud temperature and water vapor were adjusted through the diabatic initialization method (Sun et al.,2014) introduced in Section 2. The increment of potential temperature corresponding to latent heating at 0900 UTC is shown in Fig. 9a. The impact of the latent heating process was obvious in the area where the convection system was observed, and the increment of potential temperature was able to exceed 8 K in the core of the convective cell. The center of the positive temperature increment was located at a height of 6–7 km (about 500–400 hPa), which is consistent with the conclusion of Ding (1989).

The inclusion of LH nudging has been proven to be an effective method to initialize convection and reduce the spin-up time (Zhang et al., 2017; Jacques et al., 2018). A better match of pattern between the observed and modeled hourly precipitation was achieved by the LH nudging in Exp_WRT_4tim (Figs. 6o, p), although the magnitude of precipitation was overestimated.

A series of experiments were also implemented to explore the sensitivity of precipitation to the adjustment of temperature. The spurious precipitation was slightly suppressed by reducing the adjusted temperature, but overestimation was clearly apparent (not shown). This indicates that the overestimated precipitation was not caused by the adjustment of temperature alone. Other thermodynamic issues (such as the humidity) may also play important roles in the precipitation forecast and should be adjusted with the temperature for physical balance.

The analysis increments of specific humidity at 0900 UTC are also shown in Fig. 9b. The humidity was systematically reduced by about 1–1.5 g kg−1between 22.8°and 23.4°N, which indicates that the lower level was too wet in the background field. However, the precipitation forecast was not improved when only the humidity was adjusted, as seen in Exp_WRQ_4tim (Figs. 6q, r), because the precipitation in Exp_WR_4tim (Figs. 6k, l) was underestimated and the reduction in moisture further increased this bias. The combined adjustment of temperature and humidity (Exp_WRTQ_4tim) performed best, as shown in Figs. 6s–t. The improvement can be attributed to both the increased latent heating in the middle levels to trigger the updraft motion and the reduced low-level moisture to avoid the overestimation of precipitation.Therefore, adjusting the temperature and humidity at the same time is critical to the improvement of the forecast in this case.

To validate the reasonability of the improvement in the precipitation forecast through radar data assimilation,the surface fields were further verified with observations.As mentioned in Section 3.1, the convective system was pushed southeastwards by the cold pool after 1100 UTC.The cold pool behind the rain belt (with 2-m temperature below 26°C in Fig. 10a) is successfully simulated in Exp_WRT_4tim (Fig. 10c) and Exp_WRTQ_4tim (Fig.10e), whereas it could not be found in Cntl (Fig. 10b) or Exp_WRQ_4tim (Fig. 10d). It should be noted that the simulation was more consistent with the observation for Exp_WRTQ_4tim, which predicted the area of 26–27°C behind the cold front. Comparison of the 2-m moisture fields also supports a similar conclusion (Figs.10f–j). The surfaces are too warm and wet in Cntl (Fig.10g) and Exp_WRQ_4tim (Fig. 10i), which is consistent with the underestimation of precipitation. In general, the improvement of the precipitation forecast is reasonable according to the comparison with observational surface fields.

Because the adjustment of water and temperature resulted in the most significant change for the X-band PAR assimilation, the different behaviors in vertical cross sections of reflectivity/winds in Exp_WR_4tim, Exp_WRT_4tim, Exp_WRQ_4tim, and Exp_WRTQ_4tim at 1000 UTC are further discussed. As shown in Fig. 11, the adjustment of temperature (Figs. 11b, d) is able to trigger stronger and more convective updrafts at lower levels,which would be helpful in producing and maintaining liquid hydrometeors. This is a key issue for improving the underestimated precipitation in the Cntl forecast (Fig.11a). The precipitation would be further reduced if only the humidity was reduced in Exp_WRQ_4tim (Fig. 11c),while it is important for the weakened strong updraft above 500 hPa in Exp_WRT_4tim and results in a more reasonable magnitude of precipitation in Exp_WRTQ_4tim (Fig. 11d).

4.4 Sensitivity of relaxation time for the nudging method

Fig. 9. Cross-section of analysis increments (along 113.0°E) for nudging at 1100 UTC 26 August: (a) potential temperature (°C) and (b) specific humidity (g kg−1) at z = 1500 m from Exp_WRTQ_4tim.

Fig. 10. Distributions of 2-m (a–e) temperature (°C) and (f–j) specific humidity (g kg−1) at 1100 UTC 26 August from (a, f) observations, (b, g)Cntl, (c, h) Exp_WRT_4tim, (d, i) Exp_WTQ_4tim, and (e, j) Exp_WRTQ_4tim.

As shown in Eq. (1), the relaxation time is an adjustable parameterization in the nudging process. It is a time scale controlling the nudging strength and should be adjusted for different kinds of observations (Skamarock et al., 2008). The sensitivity of the precipitation forecast to the relaxation time is investigated to determine a reasonable for PAR data assimilation in this study. The relaxation time is set to be 4, 8, and 12 min for Exp_WRTQ_4tim, Exp_WRTQ_4tim_8min, and Exp_WRTQ_4tim_12min, respectively. The precipitation forecast gradually deviated from the observation (Fig.6a) when the relaxation time was extended from 4 to 12 min (Figs. 6q, s, u). Comparison of precipitation forecasts during 1100–1200 UTC (Figs. 6r, t, v) leads to a similar conclusion. This indicates that too much meaningful small-scale information in radar observations will be filtered out if it is set to be too long, as pointed out by Lee et al. (2006).

4.5 Objective verification of different experiments

To evaluate the performance quantitatively, the threat score (TS) and bias score (BS) for different experiments are calculated and displayed in Fig. 12. TS and BS are calculated as follows:

where NA is the number of points at which the event is both forecast and observed, NB is the number of points at which the event is forecast but not observed, and NC is the number of points at which the event is forecast but not observed. From Eq. (9), we can see that the precipitation is overestimated (underestimated) when the BS is larger (smaller) than 1.0.

The TS increases obviously after the assimilation of PAR observations (Fig. 12a), and the higher BS (Fig.12b) also indicated an improvement in the underestimation of precipitation in Cntl. It should be pointed out that the benefit of radar assimilation falls rapidly in the second hour (see Figs. 12c, d). This is a common phenomenon in radar data assimilation (Fabry and Meunier,2020), and can be associated with spin-up issues as explained by Kalnay and Yang (2010). According to Kalnay and Yang (2010), the slow spin-up speed of the En-KF method is caused by the unbalanced random perturbation added to the initial fields, and this will lead to a worse analysis than with the 3DVar or 4DVar methods at the initial time. However, when the EnKF system was initialized with the balanced perturbations drawn from a 3DVar error covariance, the spin-up was not a serious problem. This implies that the poor performance of En-KF at the initial time of storm development can be attributed to the imbalance problem caused by initial random perturbations of ensemble members. In Exp_R in this study, the retrieved cloud water and rain from radar reflectivity were nudged into the model without any other variables being adjusted. This violated the physical balance constraint of the initial field and would certainly have caused a spin-up problem. Without the maintenance of updraft motion, the imposed cloud water and rain fell quickly and the improvement caused by radar reflectivity disappeared in the second hour of the forecast.In general, the spin-up problems in both the EnKF system and nudging method are caused by imbalance of the initial field.

Fig. 11. Cross-sections of vertical velocity (contours; m s−1) and liquid hydrometeors (qc + qr, color-shaded; g kg−1) along 23.1°N at 1000 UTC in (a) Exp_WR_4tim, (b) Exp_WRT_4tim, (c) Exp_WRQ_4tim, and (d) Exp_WRTQ_4tim.

Because of the poor consistency between the dynamic and thermodynamic fields, the retrieved 3D wind had little influence on Cntl when it was only nudged once.This problem can be partly alleviated by increasing the frequency of nudging, as shown by the TS of Exp_WR_4tim and Exp_WR_16tim. Another way to improve the consistency in the initial field is to take into account the LH nudging and adjustment of moisture according to radar reflectivities. The added skill caused by adjusting the thermodynamic fields is more obvious in the second hour of the forecast (Figs. 12b, d), which is consistent with the comparison of hourly precipitation fields reported in Section 4.3.

This paper presents a case study in which the impacts of assimilating PAR observations on the forecast of a localized heavy rainfall event were investigated. This research represents a first step towards PAR data assimilation into the TRAMS_RUC_1km model, with the aim to demonstrate the potential for improving nowcasting of local rainstorms by assimilating PAR data. The nudging technique for radar data assimilation used here was an upgraded version of the method proposed by Zhang et al.(2019), by taking into account the nudging of LH and adjustment of temperature.

Fig. 12. (a, b) TS and (c, d) BS as a function of thresholds at (a, c) 1100 UTC and (b, d) 1200 UTC 26 August 2020.

A series of sensitivity tests were carried out to study the individual influence of PAR data assimilation. We have highlighted two factors that significantly improve the forecasting skill: (1) increasing the frequency of radar data nudging, and (2) adjusting the temperature and moisture field to achieve a better thermodynamic balance. The benefit of the first factor could be seen by comparing the results of the Exp_WR, Exp_WR_4tim,and Exp_WR_16tim experiments in Section 4.2. The convective updraft/downdraft was enhanced by reducing the time interval of nudging, and the increased hydrometeors also reflected the cumulative effects of continuous assimilation. Although it is helpful to force the model forecast towards the observation by increasing the frequency of assimilation, drawbacks with such a simple nudging technique are inevitable. For example, the false precipitation that appears in Exp_WR_16tim (Fig. 6m)perhaps can be attributed to the imbalance in the retrievals imposed on the model as a forcing. Therefore, a more sophisticated method such as 3/4DVAR or EnKF will be adopted in the future for PAR data assimilation in the TRAMS_RUC_1km model. The second factor is critical for the skill of nowcasting aided by PAR data assimilation. Temperature and moisture fields were modified for a better match between the observed and modeled precipitation. The precipitation forecast was improved significantly from Exp_WR_4tim to Exp_WRT_4tim, which indicates that LH nudging is important. The sensitivity of the relaxation time in PAR data nudging was also tested,and the results suggested it to be less than 5 min.

In general, the level of improvement reported in this paper is modest, which indicates that more sophisticated methods containing more complete balance constraints should be adopted to alleviate the weakness of the nudging technique. In the future, the assimilation of high-frequency PAR observations will also be compared with traditional S-band radar in severe weather forecasting (Supinie et al., 2017). It may also help to retrieve and assimilate ice species to further improve precipitation forecasts, and in this respect, we are planning to incorporate PAR reflectivity into the Advanced Regional Prediction System (ARPS) Data Analysis System (ADAS;Hu et al., 2006) cloud analysis system to realize this objective. We also noticed that the statistics of the reflectivity–rainfall rate (Z–R) relationship for convective weather can be revised to improve the effect of radar reflectivity assimilation with the 3DVAR method (Fang et al., 2018).However, the influence of a revisedZ–Rrelationship for South China (Feng et al., 2020) on the nudging method adopted in this paper is not obvious, which can be attributed to the weak dependence between different analysis variables in the indirect assimilation method.