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The averaged FSS and BIAS values derived from ExpNoDA, Exp3DVar and ExpE3DA for the thresholds of 25, 35 and 45 dBZ over the entire domain are shown in Fig. 1. The FSS generally deceases with time in all experiments and the highest scores are at the threshold of 25 dBZ. The FSS values for the threshold of 45 dBZ decline quickly, indicating a less skillful forecast for very intense reflectivity cores. When compared with ExpNoDA, the radar DA experiments result in improved FSS values for all thresholds over the entire forecast period. In both Exp3DVar and ExpE3DA, the improvements are most evident between t = 3.5–4 h and t = 0.5 h for the thresholds of 25 and 45 dBZ. In addition, the FSS values of ExpE3DA are consistently higher than those of Exp3DVar at all forecast periods, and the differences are larger for the 25 and 35 dBZ thresholds in the final 2 h. Meanwhile, as shown in Figs. 1d–f, ExpNoDA has the smallest BIAS for all thresholds, indicating underestimation of the reflectivity. In Exp3DVar, the underestimation is reduced with the BIAS closer to 1.0 at the threshold of 25 dBZ. For the thresholds of 25 and 35 dBZ, ExpE3DA has the highest BIAS scores (closest to 1.0) at the initial time, and these are maintained throughout the forecast period. For the threshold of 45 dBZ, the BIAS is smaller than 1.0 in all experiments, and ExpE3DA has the largest BIAS at all forecast periods.
Figure 1. The (a–c) FSS and (d–f) BIAS of the ExpNoDA (dashed gray curve), Exp3DVar (solid gray curve) and ExpE3DA (solid black curve) experiments for reflectivity thresholds of 25, 35 and 45 dBZ. The x-axis is the time starting at 0930 UTC 5 June 2009.
The 2-h reflectivity forecasts from each of the above three experiments at 1130 UTC 5 June 2009 are shown in Fig. 2. At 1130 UTC, a strong convective cluster was initialized in Anhui and a well-organized bow echo was evident in observation (Fig. 2a). ExpNoDA mainly forecasts a weak bow echo and misses the convective cluster in Anhui, resulting in large underestimation of reflectivity exceeding 35 dBZ. Exp3DVar captures the general appearance of the bow-shaped echo, although it extends too broadly in the northeastern direction. Similar bow echo features are also found in ExpE3DA but with a stronger reflectivity center collocated with the observation. In addition, ExpE3DA is able to capture moderate–intense reflectivity around the border of Jiangsu and Anhui and in southern Jiangsu, whereas the same convection is scattered in Exp3DVar. For the vertical cross section of reflectivity (Fig. 3), the observation shows an extensive strong convective system of 500 km in length and extending over a vertical range of 15 km, as well as some separate convections ahead of it. These features are not captured in ExpNoDA, except for some narrow and weak cells at the range of 150–300 km. Exp3DVar yields slight improvements over ExpNoDA, manifest as a large increase in the areal coverage of reflectivity smaller than 45 dBZ. In the region of 50–300 km, ExpE3DA forecasts a well-organized convective system that closely matches the observed reflectivity exceeding 30 dBZ, although with some underestimation of the high reflectivity above 45 dBZ. ExpE3DA also outperforms both ExpNoDA and Exp3DVar by producing more convection in the region of 300–500 km.
Figure 2. Radar reflectivity (units: dBZ) from (a) observation, (b) ExpNoDA, (c) Exp3DVar and (d) ExpE3DA at 1130 UTC 5 June 2009.
Figure 3. Vertical cross sections of the radar reflectivity (units: dBZ) along line AB in Fig. 2a from (a) observation, (b) ExpNoDA, (c) Exp3DVar and (d) ExpE3DA at 1130 UTC 5 June 2009.
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The averaged root-mean-square errors (RMSEs) of the forecast radial velocity for the three experiments verified against the radar observations are shown in Fig. 4a. It is found that Exp3DVar consistently and significantly outperforms ExpNoDA at all forecast hours, with an RMSE reduction of 1.2–2.5 m s−1. ExpE3DA further reduces the RMSE relative to Exp3DVar by 25%–35%, sufficient to ensure the best performance among the experiments during the entire forecast period. The smaller RMSE in ExpE3DA in comparison with both ExpNoDA and Exp3DVar suggests superiority of E3DA in predicting radial velocity.
Figure 4. (a) RMSEs for radial velocity (units: m s−1) against the radar observations (the x-axis is the time starting at 0930 UTC 5 June 2009), and (b–e) the radial velocity (units: m s−1) from (b) observation, (c) ExpNoDA, (d) Exp3DVar and (e) ExpE3DA at the 0.5° elevation angle from HFRD at 1300 UTC 5 June 2009.
The radial velocity at 0.5° elevation angle from HFRD and the corresponding 3.5-h forecast radial velocity from the three experiments at 1300 UTC 5 June 2009 are presented in Figs. 4b–e. A strong eastern surface wind with peak radial velocity exceeding 24 m s−1 is clearly visible in central Anhui in the observation (Fig. 4a). This feature is not captured in ExpNoDA and the wind speed is clearly weaker. Instead, a southwestern wind is incorrectly forecast in central Anhui. In Exp3DVar, the negative radial velocity is maintained better to the east of HFRD, while the positive velocity is absent to the west of HFRD. ExpE3DA successfully forecasts the positive and negative velocity structures with a maximum wind speed of 22 m s−1 that is similar to the observation. These results indicate the importance of radar DA using E3DA in this case for capturing important circulation features that lead to surface radial velocity intensification during the forecast.
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Quantitative verification was also performed for the hourly precipitation forecast. Figure 5 presents the averaged FSS and BIAS of the three experiments at precipitation thresholds of 1, 2.5 and 5 mm. In Figs. 5a–c, it can be seen that Exp3DVar results in higher FSS values than ExpNoDA during the 6-h forecast period, particularly for the threshold of 1.0 mm at t = 2 h and for the threshold of 2.5 mm during the final 2 h. ExpE3DA further improves the forecast skill in comparison with Exp3DVar, increasing the FSS by 0.1 on average for all thresholds. The FSS differences between ExpE3DA and Exp3DVar are smaller than that between Exp3DVar and ExpNoDA, except for the threshold of 2.5 mm in the first 4 h. The BIAS (Figs. 5d–f) indicates that ExpNoDA largely underpredicts the rainfall, with the lowest BIAS values smaller than 1.0, especially for the threshold of 5.0 mm. The dry bias values are reduced by Exp3DVar and their differences can be as large as 0.35 for the threshold of 1.0 mm during the first 3 h. For all thresholds, the highest BIAS values from ExpE3DA are closer to 1.0 than from Exp3DVar, with average BIAS enhancement of 0.2–0.4.
Figure 5. The (a–c) FSS and (d–f) BIAS of the ExpNoDA (dashed gray curve), Exp3DVar (solid gray curve) and ExpE3DA (solid black curve) experiments for precipitation thresholds of 1, 2.5 and 5 mm. The x-axis is the time starting at 1000 UTC 5 June 2009.
The 6-h accumulated precipitation forecast patterns from the observations and the three experiments starting from 1000 UTC are shown in Fig. 6. The observed precipitation is characterized by two major rainbands covering northern Zhejiang and large parts of Anhui and Jiangsu with a maximum value of 12.8 mm (Fig. 6a). ExpNoDA fails to distinguish these two organized rainbands, producing scattered precipitation over the entire region. Again, both Exp3DVar and ExpE3DA show more skillful precipitation forecasts, indicating that radar DA is effective for producing satisfactory initial representation of the storm. Exp3DVar captures the bow-shaped rainband well but with some dry bias values of 1.6–4.8 mm. It also largely underpredicts the rainband in Anhui and western Jiangsu and overpredicts the precipitation intensity in central Jiangsu. In contrast, ExpE3DA realistically reproduces the two rainband features in terms of intensity and spatial extent, and it has greatly reduced dry biases in comparison with Exp3DVar.
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The domain-averaged RMSEs of the horizontal wind components, temperature, and water vapor forecasts against radiosonde and surface METAR observations in the inner 3-km domain are presented in Fig. 7. As shown in Figs. 7a–d, ExpE3DA significantly outperforms ExpNoDA, and it is generally better than Exp3DVar for all variables, except in the upper levels where the errors are similar. Water vapor appears to have the largest error reduction from ExpE3DA compared with Exp3DVar and ExpNoDA between 350 and 700 hPa. The reductions for wind and temperature are smaller but are evident in the low and middle levels. In comparison with the RMSEs against the surface observations, the errors of ExpE3DA are the lowest, while the errors of ExpNoDA are the greatest and worse than those of Exp3DVar for all variables.
Figure 7. Averaged RMSEs of the forecast from ExpNoDA, Exp3DVar and ExpE3DA against all the (a–d) radiosondes and (e) METAR stations in the 3-km domain for the
${u_{\rm{h}}}$ component (units: m s−1),${v_{\rm{h}}}$ component (unit: m s−1), T (units: °C), and Q (units: g kg−1) at 1200 UTC 5 June 2009.To reveal the reasons for the improved forecast, diagnosis of the analysis fields was performed. Figure 8 presents the vertical cross sections of first-guess and analyzed radar reflectivity and relative humidity, and vertical velocity and temperature during the fifth assimilation cycles along the line from (33.6°N, 117.5°E) to (31.7°N, 120.6°E). It can be seen that both Exp3DVar and ExpE3DA are able to increase reflectivity associated with the convections at x = 100 and 300 km (Figs. 8a–d). ExpE3DA also adjusts other fields, such as vertical velocity, temperature and humidity, to create a stronger updraft, warmer and more saturated environment corresponding to the added reflectivity (Figs. 8c and d, 8g and h). The temperature and vertical velocity in ExpE3DA can be increased by 3°C and 4 m s−1, respectively. However, the added reflectivity of Exp3DVar shown in Figs. 8a and b does not correspond to these adjustments. Further examination reveals that both experiments perform similarly for the other assimilation cycles (figure not shown). This indicates that ExpE3DA has reasonable cross-variable correlations for convective-scale reflectivity assimilation.
Figure 8. Vertical cross sections of the (a–d) radar reflectivity (shaded; units: dBZ) and relative humidity (solid blue line; units: %), and (e–h) vertical velocity (shaded; units: m s−1) and temperature (solid black line; units: °C) along the line from (33.6°N, 117.5°E) to (31.7°N, 120.6°E) from the (a, c, e, g) first guess and (b, d, f, h) analysis of Exp3DVar and ExpE3DA during the fifth assimilation cycle.
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To generalize the conclusions of this study, we further applied E3DA to two additional convective cases: one that occurred over southern China on 23 April 2007 and the other that affected southeastern China on 14 June 2009. A summary of the experimental setup is listed in Table 1. Figure 9 shows the averaged FSS and BIAS of these two cases for ExpNoDA, Exp3DVar and ExpE3DA using thresholds of 25, 35 and 45 dBZ. It confirms the finding that ExpE3DA has the highest FSS for all thresholds during the entire forecast period, followed by Exp3DVar. The largest differences in FSS between Exp3DVar and ExpE3DA are in the first 3 h. The BIAS of the three experiments shows that ExpE3DA has the highest bias for all hours, and that both Exp3DVar and ExpNoDA underpredict the BIAS for all thresholds.
The 14 June 2009 case The 23–24 April 2007 case Domain center 33.5°N, 118.5°E 24°N, 114°E Domain size D01: 161 × 161 × 51 (9 km)
D02: 501 × 501 × 51 (3 km)D01: 161 × 161 × 51 (9 km)
D02: 501 × 501 × 51 (3 km)Assimilation period 0400–0900 UTC 14 June
(every 1 h)1900 UTC 23 April–0000 UTC
24 April (every 1 h)Forecast period 0900–1500 UTC 14 June 0000–0600 UTC 24 April Physics parameterization schemes Same as the 5 June 2009 case Same as the 5 June 2009 case Radar sites used Shangqiu, Fuyang, Hefei, Xuzhou,
Lianyungang, Yancheng, Nanjing
and NantongXiamen, Fuzhou, Jianyang, Guangzhou,
Shenzhen, Shantou, Yangjiang,
Shaoguan and GuilinTable 1. List of model configurations, and the radar sites used for the additional two convective cases.
Figure 9. Averaged (a–c) FSS and (d–f) BIAS from the two convective cases of the ExpNoDA (dashed gray curve), Exp3DVar (solid gray curve) and ExpE3DA (solid black curve) experiments for reflectivity thresholds of 25, 35 and 45 dBZ. The x-axis is the forecast time length.
Figure 10 shows the 2.5-h reflectivity forecasts for an example (1130 UTC) of the convective case that occurred on 14 June 2009. At this time, the observed reflectivity showed two major convective clusters in eastern Anhui and eastern Jiangsu provinces, with maximum reflectivity exceeding 60 dBZ. The two convective clusters in ExpNoDA were weaker and displaced to the northeast. This location error was corrected by both ExpE3DA and Exp3DVar; however, the intensity and coverage of the two areas of convections in ExpE3DA were much closer to the observations than in Exp3DVar, especially for the convection at the border of Anhui and Jiangsu provinces.
Figure 10. As in Fig. 2 but at 1130 UTC 14 June 2009.