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All the data used in this paper are provided by the OPACC project. In June and July 2013 and 2014, about 20 IOPs focusing on the lower Yangtze and Huaihe River basins in Jiangsu and Anhui provinces were carried out (Xue, 2016). We processed the observations from 6 IOPs between 23 June and 21 July 2013 (Table 1), in which the last five IOPs were used to recalculate the Z–R relationship and the IOP of 23 June 2013 was used in reflectivity data assimilation experiments.
IOP Time span Description Weather phenomenon 1 0000 UTC 22 to 1502 UTC 23 June 2013 Frontal convection Heavy rainfall 2 0000 UTC to 1459 UTC 25 June 2013 Frontal convection Heavy rainfall 3 0004:00 UTC 26 to 1456:37 UTC 27 June 2013 Frontal convection Heavy rainfall 4 0000 UTC 4 to 1500 UTC 5 July 2013 Frontal convection Heavy rainfall, gales 5 0001 UTC 6 to 1502 UTC 7 July 2013 Frontal convection Heavy rainfall, tornados 6 0002 UTC 20 to 1500 UTC 21 July 2013 Frontal convection Gales, heavy rainfall Table 1. Information of the six intensive observing periods (IOPs) in 2013
In the lower reaches of the Yangtze and Huaihe River basins, 10 Chinese Next Generation Weather Radars (CINRADSA/SB) are deployed in the cities of Shangqiu, Hefei, Fuyang, Nanjing, Nantong, Xuzhou, Lianyungang, Hangzhou, Ningbo, and Jiujiang (Fig. 1). Each radar provides volume scan data with nine elevation angles (0.5°, 1.45°, 2.4°, 3.35°, 4.3°, 6.0°, 9.9°, 14.6°, and 19.5°) every six minutes. Within the areas covered by these radars, there are 6529 AWSs providing hourly precipitation data (Fig. 1).
Figure 1. Distribution of the 10 radars and automatic weather stations in the Yangtze–Huaihe River basin, in which ten radars are located in the cities Shangqiu (SQ), Hefei (HF), Fuyang (FY), Nanjing (NJ), Nantong (NT), Xuzhou (XZ), Lianyungang (LYG), Hangzhou (HZ), Ningbo (NB), and Jiujiang (JJ), respectively.
First of all, we select the radar reflectivity and rainfall data from the five IOPs at times when both reflectivity and rainfall data are available. The rainfall measurements are subjected to quality control processes, such as inspection revisions (Ren et al., 2010). The reflectivity data are processed by using the quality control method in the Weather Surveillance Radar1988 Doppler precipitation estimation algorithm (Fulton et al., 1998), which includes the removal of superrefraction echoes and isolated points, and the detection of singular echoes. A scanning composite plane is then generated in which the reflectivity data are extracted from the fourth tilt (3.35°) within 20 km, from the third tilt (2.4°) between 20 and 35 km, from the second tilt (1.5°) between 35 and 50 km, and from the first tilt (0.5°) between 50 and 230 km.
Through the quality control procedure and the generation of the scanning composite plane, a total of 1386 samples are obtained. Each sample consists of scanning composite planes and the available hourly precipitation data that are valid at the same time. Considering that the 1386 samples cover multiple stages of severe precipitation events—such as occurrence, development, and disappearance—we reselected samples for the statistics of the Z–R relationship to exclude interference from weaker phases during severe weather processes. The proportion of reflectivity ≥ 30 dBZ (dBZ30) of a single sample is simply used as the screening standard. For all 1386 samples, the value of dBZ30 ranges from 0.004 to 0.373 and the sample size varies with different values of dBZ30. For example, the number of samples is 969 when dBZ30 = 0.1, but only 396 samples for dBZ30 = 0.2 and 28 samples for dBZ30 = 0.3. We select 891 samples (64.3% of the total number of samples, when dBZ30 = 0.12) for the statistics of the Z–R relationship.

The radar reflectivity factor (Z; mm^{6} m^{–3}) is commonly converted to an estimated precipitation rate (R; mm h^{–1}) through a power law relationship:
$$ Z = {{A}}{{{R}}^b}, $$ (1) where A and b are parameters related to the raindrop spectrum, which are in the ranges of 31–500 and 1.1–1.9, respectively (Chumchean, 2004).
The Z–R relationship is calculated with a widely used optimization method, in which the discriminant function is given as
$$ {C_{{\rm{TF}}}} = \min \left\{ {\sum\limits_{i = 1}^n {[{{({R_i}  {I_i})}^2} + ({R_i}  {I_i})]} } \right\}, $$ (2) where R_{i} is the rainfall estimated from radar reflectivity and I_{i} is the hourly rainfall measured by the AWSs. The optimum values of A and b in the Z–R relationship are determined by adjusting the values of A and b to find a minimum value for C_{TF}. Based on data from the 891 samples described in Section 2, we obtained new statistics for the Z–R relationship for severe convective weather over the Yangtze–Huaihe River basin:
$$ Z = 109{R^{1.74}}. $$ (3) To preliminarily evaluate the applicability of this new Z–R relationship over the Yangtze–Huaihe River basin, two Z–R relationships are used as a comparison. One is the classic Marshall–Palmer relationship, Z = 200R^{1.6} (Marshall and Palmer, 1948; Marshall et al., 1955), and the other is Z = 300R^{1.4}, which is used by the National Weather Service for convective rainfall (Fulton et al., 1998) and the new generation of weather radar precipitation series in China (Yao et al., 2007). Table 2 shows the values of C_{TF} from the three Z–R relationships. It can be seen that the C_{TF} value calculated from the new Z–R relationship decreases by 18.3% and 16.4%, compared with the existing Z–R relationships of Z = 300R^{1.4} and Z = 200R^{1.6}, respectively. This implies that the new Z–R relationship gives an improved estimation of precipitation from radar observations.
Z–R relationship C_{TF} Z = 109R^{1.74} 690,578 Z = 300R^{1.4} 845,217 Z = 200R^{1.6} 825,638 Table 2. Three Z–R relationships and their values of C_{TF}
To further illustrate the role of new Z–R relationship, Fig. 2 shows these three Z–R relationships and the scattered pairs of Z and R. Compared with the existing relationship of Z = 300R^{1.4} for convective rainfall (Fig. 2, dotted line), the new Z–R relationship (Fig. 2, dashed line) produces a larger value of R for Z < 42.9 dBZ, but a smaller R for Z > 42.9 dBZ when this difference increases significantly with increasing Z. The rainfall rate derived from the new Z–R relationship is larger for values of Z between 25 and 50 dBZ relative to the relationship of Z = 200R^{1.6}. For example, the rainfall rate calculated from the new Z–R relationship increases by 16.43% when Z = 40 dBZ. From the value of C_{TF} in Table 2 and the distribution of scattered data shown in Fig. 2, the new Z–R relationship should be more reasonable for severe convective weather over the Yangtze–Huaihe River basin than the other two Z–R relationships.
Figure 2. Scattered pairs of radar reflectivity Z (dBZ) and corresponding rainfall rate R (mm h^{–1}) over the Yangtze–Huaihe River basin from five IOPs in 2013 (gray crosses), as well as the Z–R relationships from Marshall–Palmer (solid line), Fulton et al. (1998) (dotted line), and new statistics in this study (dashed line).

In the WRF 3DVar system, radar reflectivity data are assimilated through the relationship between the radar reflectivity (Z) and the rainwater mixing ratio (q_{r}), which is expressed by
$$ Z = 43.1 + 17.5\log (\rho {q_{\rm{r}}}), $$ (4) where ρ (kg m^{–3}) is the density of the atmosphere and q_{r} (g kg^{–1}) is the rainwater mixing ratio. It should be noted that Eq. (4) is derived analytically by assuming the Marshall–Palmer distribution for raindrop size (Sun and Crook, 1997).
The Z–q_{r} relationship can be obtained by eliminating the rainfall rate between the Marshall–Palmer expressions for the Z–R and q_{r}–R relationships (Battan, 1973), as described in Sun and Crook (1997). Therefore, we obtain a new Z–q_{r} relationship according to the recounted Z–R relationship in Section 2.2:
$$ Z = 43.0 + 19.77\log (\rho {q_{\rm{r}}}). $$ (5) The Z–q_{r} relation in Eq. (5) is used to update Eq. (4) as a correction of the observational operator for the reflectivity data in the WRF 3DVar system. The two Z–q_{r} relationships are shown in Fig. 3. In addition, the Z–q_{r} relationship derived from Z = 200R^{1.6} is plotted in Fig. 3 as a reference, i.e., Z = 43.78 + 18.2 log(ρq_{r}). It can be found that the variations of q_{r} with Z are consistent with the corresponding Z–R relationships in Fig. 2, such as the recounted Z–R relationship and Z = 200R^{1.6} (Fig. 3, dashed and dotted lines, respectively). Compared with two Z–q_{r} relationships derived from the recounted Z–R relationship and used in the WRF 3DVar system, we can see that the new Z–q_{r} relationship produces a larger value of q_{r} than that used in the WRF 3DVar system (Fig. 3, solid line) for Z < 43.87 dBZ. However, the opposite is seen for Z > 43.87 dBZ.
Figure 3. Three Z–q_{r} plots, from the WRF 3DVar system (solid line), the Marshall–Palmer (dotted line), and the recounted Z–R relationship in this study (dashed line). The inset graph shows an enlargement of the Z–q_{r} curves between 30 and 50 dBZ.
In the following section, a set of numerical experiments were performed with the IOP on 23 June 2013 to test the effect of the corrected operator [Eq. (5)] on the analysis and forecast of severe precipitation.