*2.2. Processing Microphysical Datasets from Disdrometer*

In order to process the calculation of the characteristic variables of precipitation, the formulas are derived as follows:

$$\text{IN}(D\_i) = \sum\_{j=1}^{32} \frac{n\_{ij}}{V\_j \cdot \Delta D\_i} = \sum\_{j=1}^{32} \frac{n\_{ij}}{A \cdot \Delta t \cdot v\_j \cdot \Delta D\_i} \tag{1}$$

where <sup>N</sup>(*Di*) (mm−<sup>1</sup> · m−3) is the number concentration of raindrops per unit diameter interval for raindrops per unit volume with the diameter equal to *Di* (the *i*th-bin of diameters of the spectra); *<sup>A</sup>* = 5.4 <sup>×</sup> 10−<sup>4</sup> m2 is the sampling area scanned by the laser beam; <sup>Δ</sup>*<sup>t</sup>* = 60 s is the sampling time interval; *vj* is the raindrop terminal velocity of the *j*th-bin of velocities of the spectra; Δ*Di* is the class spread of the *i*th-bin of diameters of the spectra.

**Figure 1.** (**a**) The location of Yulin Ecohydrological Station (green point) and the location of Yulin Meteorological Station (blue point) and the DEM (Digital Elevation Model) characteristics around the sites. The red rectangle in the China map highlights the location of Mu Us Sandy Land; (**b**) the OTT Parsivel-2 disdrometer and the surrounding 4 TE525MM rain gauges in Yulin Ecohydrological Station; (**c**) vegetation cover situation in Yulin Ecohydrological Station.

**Figure 2.** Schematic of the research technical route in this study.

The *n*th-moment of the DSD can be calculated as:

$$M\_{\rm II} = \int\_0^\infty D^\eta N(D) dD \tag{2}$$

Moreover the 6th-moment of the DSD is equal to the radar reflectivity *<sup>Z</sup>* (mm6·m−3):

$$Z = M\_6 = \int\_0^\infty D^6 N(D) dD = \sum\_{i=3}^{32} D\_i^6 N(D\_i) \Delta D\_i \tag{3}$$

where the 1st-bin and the 2nd-bin of diameters are not evaluated in the measurements of the OTT Parsivel-2 because these two bins are out of the measurement range of the disdrometer, thus *i* starts from 3 to 32.

The *<sup>R</sup>*total(i,j) (mm·h−1) is the total rainfall per unit time in the *nij* grid:

$$R\_{\text{total}(i,j)} = v\_j \cdot N(D\_i) \cdot \Delta D\_i \cdot \frac{1}{6} \pi D\_i^3 \cdot 3600 \cdot 10^{-6} = \frac{3\pi}{5000} v\_j D\_i^3 N(D\_i) \Delta D\_i \tag{4}$$

The rainfall intensity *<sup>R</sup>* (mm·h−1) is the summation of *<sup>R</sup>*total(i,j), and thus, can be calculated as:

$$R = \frac{3\pi}{5000} \sum\_{i=3}^{32} (\sum\_{j=1}^{32} v\_j D\_i^3 N(D\_i) \Delta D\_i) \tag{5}$$

The content of liquid raindrop *<sup>W</sup>* (g·m−3) is the mass of liquid raindrops per unit volume:

$$\mathcal{W} = \frac{\pi}{6} \cdot 10^{-3} \cdot \int\_0^\infty D^3 \mathcal{N}(D) dD = \frac{\pi}{6} \cdot 10^{-3} \cdot \sum\_{i=3}^{32} D\_i^3 \mathcal{N}(D\_i) \Delta D\_i \tag{6}$$

The gamma distribution of raindrop spectra is derived as:

$$N(D) = N\_0 D^\mu \exp\left(-\Lambda D\right) \tag{7}$$

where *<sup>N</sup>*<sup>0</sup> (mm−1−μ·m<sup>−</sup>3) is the intercept parameter and varies in dozens of orders of magnitudes [26]. Thus, the normalized intercept parameter *Nw* (mm−1·m−3) is used by Testud et al. [27] to represent *<sup>N</sup>*0, in order for the characteristics of the parameter of distribution of raindrop spectra can be calculated without any assumption about the DSD shapes:

$$N\_{\rm w} = \frac{4^4 M\_3^5}{6 \rho\_{\rm w} M\_4^4} \tag{8}$$

*Nw* is better than *N*<sup>0</sup> for representing the raindrop concentration with certain raindrop sizes, as is not dependent on parameter μ. The mass-weighted mean diameter *D*m(mm), and the rainfall shape parameter μ (dimensionless, related to rainfall types [28]), can be expressed as [29,30]:

$$D\mathbf{m} = \frac{4 + \mu}{\Lambda} \tag{9}$$

$$\mu = \frac{1}{2\left(1 - \frac{M\_4^3}{M\_3^2 M\_6}\right)} \left\{ 11 \frac{M\_4^3}{M\_3^2 M\_6} + \left[ \frac{M\_4^3}{M\_3^2 M\_6} \left(\frac{M\_4^3}{M\_3^2 M\_6} + 8\right) \right]^{\frac{1}{2}} - 8 \right\} \tag{10}$$

The slope parameter of gamma distribution Λ (mm <sup>−</sup>1) is dependent on parameter μ, and Seela et al. [31] concluded that μ-Λ relationships vary with different precipitation types in different areas. In this study, the Λ is expressed as a function of the 2nd and 4th-moment of the DSD and parameter μ [32]:

$$\Lambda = \left[\frac{M\_2 \Gamma(\mu + 5)}{M\_4 \Gamma(\mu + 3)}\right]^{\frac{1}{2}} \tag{11}$$
