*2.2. Raindrop Size Distribution*

In order to understand the microphysics of the extreme rain, two disdrometers nearest to Doumen and Gaotan gauge stations are used to provide the DSD observation. These two disdrometers are located at Zhuhai and Huidong, collocated with rain gauges within 20 m. Both disdrometers are optical disdrometers with a 54 cm2 horizontal sample area and are configured with 1-min sampling resolution to measure the DSD and fall velocity of raindrops [23,24]. The disdrometer performance has been assessed and improved since it was invented, and many previous studies have been conducted with this device [25–28]. In particular, the velocity and particle sizes are divided into 32 non-uniform bins, varying from 0.05 to 20.8 m s−<sup>1</sup> for bin-center velocity and 0.062–24.5 mm for bin-center diameter (for detailed information in the user manual, https://www.manualslib.com/products/Ott-Parsivel2- 5889584.html). The direct measurements from disdrometer are the number of raindrops at each velocity (*i*) and diameter (*j*) bin. Here, we take the bin-center value of each bin as the corresponding value. Several parameters used to describe the characteristics of DSD are calculated in the following.

The total number of raindrops can be calculated as follows:

$$Td = \sum\_{i=1}^{32} \sum\_{j=1}^{32} n\_{i,j} \tag{1}$$

where *ni*,*<sup>j</sup>* is the number of drops at each bin.

The number concentration of raindrops per unit volume for the *j*th diameter bin *N*(*Dj*) can be calculated as follows:

$$N(D\_{\dot{\cdot}}) = \sum\_{i=1}^{32} \frac{n\_{i,\dot{\cdot}}}{A \cdot \Delta t \cdot V\_{i} \cdot \Delta D\_{\dot{\cdot}}} \, \, \, \, \tag{2}$$

where *N*(*Dj*) is in m−<sup>3</sup> mm<sup>−</sup>1; *A* is the sampling area in m2; Δ*t* is the sampling time interval in s; *A* and Δ*t* are, respectively, 0.0054 m<sup>2</sup> and 60 s in this study; Δ*Dj* (mm) is the diameter interval from *Dj* to *Dj*+<sup>1</sup> for the jth diameter bin; *Vi* (m s<sup>−</sup>1) is the fall speed for the *i*th velocity class. Due to the measurement error, especially for larger size drops [23], the empirical terminal velocity–diameter (*V* – *D*) relation in Atlas et al. [29] is adopted in this study:

$$V(D\_{\dot{j}}) = 9.65 - 10.3 \exp\left(-0.6 D\_{\dot{j}}\right),\tag{3}$$

The drops with velocity out the range of ±60% *V*(*Dj*) are removed from the analysis [30].

The total number concentration *Nt* (m<sup>−</sup>3), the mass weighted diameter *Dm* (mm), and normalized intercept parameter *Nw* (m−<sup>3</sup> mm<sup>−</sup>1) [14] are derived as:

$$N\_t = \sum\_{i=i}^{32} \sum\_{j=1}^{32} \frac{m\_{i,j}}{A \cdot \Delta t \cdot V\_i} \tag{4}$$

$$D\_{\mathfrak{M}} = \frac{\sum\_{j=1}^{32} N(D\_j) \cdot D\_j^4 \cdot \Delta D\_j}{\sum\_{j=1}^{32} N(D\_j) \cdot D\_j^3 \cdot \Delta D\_j},\tag{5}$$

$$N\_{\text{i}\sigma} = \frac{4^4}{\pi \rho\_{\text{i}\sigma}} \left(\frac{10^3 \text{W}}{D\_{\text{m}}^4}\right) \tag{6}$$

*Dm* is closely related to the drop size; *Nt* and *Nw* are related to the number of raindrops. All these parameters are important in representing the DSD characteristics.

The integral rainfall parameters including rain rate *R* (mm h<sup>−</sup>1) and liquid water content *W* (g m<sup>−</sup>3) are calculated based on the following equations:

$$R = \frac{6\pi}{10^4 \rho\_{\rm uv}} \sum\_{j=1}^{32} V(D\_j) D\_j^{-3} N(D\_j) \Delta D\_j \tag{7}$$

$$W = \frac{\pi \rho\_w}{6 \times 10^3} \sum\_{j=1}^{32} D\_j^{\;3} N(D\_j) \Delta D\_{j\prime} \tag{8}$$

where ρ*<sup>w</sup>* is the water density (1.0 g cm<sup>−</sup>3).

Meanwhile, a series of polarimetric radar variables are simulated at S-band frequency based on the DSD measurements using the T-matrix method [31–33], including horizontal reflectivity Z*<sup>h</sup>* (mm6 m<sup>−</sup>3, or Z*<sup>H</sup>* in dBZ), differential reflectivity Z*dr* (dB), and specific differential phase *Kdp*(degree km−1). The drop shape model used in the simulation is the one proposed by Thurai et al. [34] and temperature is 20 °C. The canting angle is not taken into account (i.e., canting angle is 0) as the DSD measurements are near ground.

We also want to note that to minimize the measurement errors and improve data reliability, several quality control procedures were applied on the 1-min DSD data. First, because of the low signal-to-noise ratios, the first two diameter bins are always empty, so the data in first two bins are eliminated in the analysis [23]. Second, the 1-min sample data with total raindrop number smaller than 10 or the derived rain rate less than 0.1 mm h−<sup>1</sup> are considered noise and removed [23]. Then, if the continuous data satisfying the above conditions last less than 5 min, they will be ignored to avoid the spurious and erratic measurements [25,35]. Additionally, threshold on simulated radar parameter (i.e., Z*<sup>H</sup>* < 55 dBZ) is used to further guarantee the creditability of the measured DSD data. The DSDs with the radar parameters out of the range are deleted to avoid mixed phase hydrometeors.

#### *2.3. Radar Quantitative Precipitation Estimation*

The two S-band radars are located at Guangzhou (hereafter referred as GZRD, 23.004◦ N, 113.355◦ E, 179 m) and Meizhou (MZRD, 24.256◦ N, 115.975◦ E, 423 m). Both radars are configured with a 6-min time resolution and 250-m range gate spacing, and have undergone rigorous quality control to ensure the data quality [36]. These two radars are used to monitor the evolution of the storm system and associated microphysical signatures. Moreover, these two radars are applied to estimate the rainfall to show the great potential of radar quantitative precipitation estimation.

For polarimetric radar, *R*(*ZH*), *R*(*Kdp*), *R*(*ZH*,*Zdr*), *R*(*Zdr*,*Kdp*) are the four relations commonly used to estimate rainfall [14]. The parameters (i.e., coefficients and exponents) in these relations are determined by the local precipitation microphysics, and are usually derived from the in situ DSD data. The representative of these parameters and how to combine different relations are the key issue in deriving radar QPE [14].

In this study, four rainfall algorithms are applied to quantify the precipitation intensity and amounts during this event. These algorithms belong to two categories: one is *R*(*ZH*) relation, i.e., WRS-88D Z-R relationship [13] and localized Z-R relationship; another is a combination of the four rainfall relations (i.e., *R*(*ZH*), *R*(*Kdp*), *R*(*ZH*,*Zdr*), *R*(*Zdr*,*Kdp*)), i.e., the "adapted algorithm" described by Xia et al. [36] and the localized blended relation. Both Z-R relations are commonly used for single-polarized radar. The "adapted algorithm" is derived from DSD data and adjusted based on gauge observation and it has been demonstrated during several typhoon events in Southern China, which showed great performance [36].

Based on the nonlinear least-square method with the DSD data from two stations, the localized relations are fitted as follows:

*<sup>R</sup>*(*ZH*) = 0.06082 <sup>×</sup> 100.05709*ZH* , (9)

$$R(K\_{dp}) \;=\; 40.4615 K\_{dp}^{0.7703} \tag{10}$$

$$R(Z\_{H\prime}Z\_{dr}) = 0.00632 \times 10^{0.09134Z\_H} 10^{-0.3325Z\_{dr}} \tag{11}$$

$$R(Z\_{dr}K\_{dp}) = \; \text{84.43} \; \text{18K}\_{\text{DP}}^{0.9377} \; \text{10}^{-0.1588Z\_{dr}} \tag{12}$$

where Equation (9) is referred to as the localized Z-R relation, and the localized blended relation is a combination of Equations (10)–(12), using the same logic described by Xia et al. [36].
