4.3.2. Radar-Based Quantitative Precipitation Estimation (QPE)

In this part, a set of various radar rainfall algorithms including the "adapted algorithm" [36], the localized blended algorithm, the localized relation and WSR-88D Z-R relation [13], were applied to quantify the precipitation intensity and amounts during this event. After estimating the instantaneous rainfall rates using various radar rainfall algorithms, the rainfall accumulations were computed at hourly scale. To quantify the performances of different algorithms, a set of metrics was computed, including the bias (*BIAS*), normalized mean bias (*NMB*), normalized mean absolute error (*NMAE*), Pearson's correlation coefficients (*CC*), which are defined as follows:

$$BIAS = \frac{\sum\_{N=1}^{M} (R\_N - G\_N)}{M}\_{} \tag{13}$$

$$NMB = \frac{\left[\sum\_{N=1}^{M} (R\_N - G\_N)\right] / M}{\left(\sum\_{N=1}^{M} G\_N\right) / M} \times 100\% \tag{14}$$

$$\text{NMAE} = \frac{(\sum\_{N=1}^{M} \left| \mathbf{R}\_{N} - \mathbf{G}\_{N} \right|) / M}{(\sum\_{N=1}^{M} \mathbf{G}\_{N}) / M} \times 100\% \tag{15}$$

$$\text{CC} = \frac{\sum\_{N=1}^{M} (R\_N - \overline{R\_N})(G\_N - \overline{G\_N})}{\sqrt{\sum\_{N=1}^{M} \left(R\_N - \overline{R\_N}\right)^2 \sum\_{N=1}^{M} \left(G\_N - \overline{G\_N}\right)^2}} \tag{16}$$

where *RN* and *GN* represent the radar estimates of different algorithms and the rain gauge measurements at time frame *N*, respectively. *M* is the total sample number.

The comparison of estimates from different rainfall algorithms and rain gauge measurements at Gaotan and Doumen station is shown in Figure 13 and the evaluation results are shown in Table 4. As shown in Figure 13, all the algorithms have similar patterns to the rain gauge measurements, while QPE results of the "adapted algorithm" is better than other algorithms with lowest *BIAS*, *NMB*, *NMAE* and the highest *CC* (Table 4). This is in line with the findings during typhoon case studies [36]. Nevertheless, we should note that all the algorithms are underestimating the rain rates and accumulations during this flood event and the results still need to be optimized.

**Figure 13.** The rain gauge measurements (red line) and estimates computed by various radar algorithms. (**a**) Gaotan station, (**b**) Doumen station.


**Table 4.** Evaluation results of the various radar algorithms at Gaotan station and Doumen station.

To further analyze the QPE results of various radar rainfall algorithms, the scatter plots of radar rainfall estimates versus gauge measurements at all rain gauge stations less than 100 km from the radars are shown in Figure 14 and the evaluation results are shown in Table 5. Most of the hourly rainfall rates are from 0 to 40 mm hr<sup>−</sup>1. Again, the adapted algorithm has the best performance, while all the rainfall algorithms show underestimation compared to the gauge measurements, especially during heavy rain periods.

**Figure 14.** The scatter plots of radar estimated rainfall versus gauge measurements at gauge locations less than 100 km from the radar: (**a**) the "adapted algorithm" [36]; (**b**) localized blended rainfall algorithm; (**c**) localized Z–R relation; (**d**) WSR-88D Z-R relation [13]. The color density represents the observation sample numbers in logarithmic unit.



#### **5. Discussion**

Although the analysis of DSD and polarimetric radar signatures shows similar results, the relatively long distances between disdrometers and the extreme rain centers might induce some uncertainty in the representation of extreme rainfall DSD characteristics. As mentioned, the polarimetric radar signatures at the two rainfall centers are quite different, even for the same precipitation system, which is likely due to the complex falling processes as a result of orographic enhancement and dynamic cloud microphysics involved in this extreme event [44]. More disdrometers and in situ measurements would be required to fully resolve the three-dimensional structure of precipitation in such complex terrains.

In addition, although the polarimetric radars could provide more insights into the two extreme rain regions, the precipitation estimated by the current radar algorithms underestimate the rainfall compared to the ground gauges. The differences of sample areas between radars and gauges may be one reason, especially when the gauges are far from the radars. In such cases, a network of short-range X-band polarimetric radars would be useful for better QPE. Additionally, the adapted algorithms have relatively better performance mainly because they are derived using DSD and gauge data collected during many storm events in Southern China [36]. However, at the same time, the DSD observed at both Huidong and Zhuhai stations during this event showed a lower number concentration compared with previous long-term studies in Yangjiang [43]. This reminds us that the rainfall algorithms should be appropriately developed based on local rainfall characteristics, which is still under investigation.
