*2.3. Precipitation Types and Quality Control (QC)*

In this study, in order to analyze the characteristics of raindrop spectra in different precipitation types, the precipitation data is classified into convective and stratiform rain based on the rainfall intensity [14]. Quality control is carried out in this study because there are errors in the measurement of large diameters of raindrops using the disdrometer. In this study, raindrops larger than 6 mm in diameter were considered to have crushed during falling [33]. Therefore, raindrops larger than 6 mm in diameter are excluded in this study

Figure 3 illustrates the principle of classifying stratiform, convective, mixed-cloud rain and non-rainfall events. In this study, the effective observation range of raindrop diameter is 0.25–6 mm. Raindrop spectrum data with the total number of raindrops less than 10 or rain intensity less than 0.5 mm/h is regarded as noise [34,35].

**Figure 3.** Classifying stratiform, convective rain and non-rainfall events. This classification method is derived by Li et al. [36] and used in Mt. Huangshan (118◦10 E, 30◦07 N, 1351 m a.s.l.), and is considered valid in this study to classify stratiform/convective rain.

The quality control principle is similar to the method used by Li et al. [36]. For an instantaneous moment *tn* during a rainfall event, if the rain intensity *R* within the time range [*tn* − *Ns*, *tn* + *Ns*] is > 5 mm/h and the standard deviation is >1.5 mm/h, the event is classified as a convective rainfall event; if the rain intensity *R* within the time range [*tn* − *Ns*, *tn* + *Ns*] satisfies 0.5 < *R* < 5 mm/h and the standard deviation is <1.5 mm/h, then the event is classified as a stratiform rainfall event. Other rainfall events are classified as mixed-cloud rain [37].

#### *2.4. Derivation of KE-R Relationships*

Rainfall kinetic energy (KE) can be calculated from the raindrop disdrometer, rainfall terminal velocity and raindrop size distribution. The total kinetic energy KE (J/(m3·s)) can be derived as [25,38]:

$$\text{KE} = \frac{1}{12} \rho \pi a^3 N\_0 \int\_0^\infty D^{\mu+3+3b} e^{-\Lambda D} dD \tag{12}$$

where *a* = 3.78 and *b* = 0.67 are constant parameters [39]. In arid or semi-arid areas, most of the precipitation is of weak or moderate levels and Marshall et al. [40] concluded that *N*<sup>0</sup> in the expression of *N*(*D*) is almost fixed to 0.08 cm<sup>−</sup>4. The parameter *x* is defined as:

$$
\mu = \mu + 4 + 3b = \mu + 6.01\tag{13}
$$

From Equations (12) and (13), the KE can be further expressed as:

$$\text{KE} = \frac{\rho \pi a^3 N\_0}{12\Lambda^x} \int\_0^\infty t^{x-1} e^{-t} dt = \frac{\rho \pi a^3 N\_0 \Gamma(\mathbf{x})}{12\Lambda^x} \tag{14}$$

The expression of Λ is:

$$
\Lambda = 4.1R^{-0.21} \tag{15}
$$

which is commonly used in the calculation of KE-*R* relationships in many studies [41–43], and:

$$\text{KE} = \frac{\rho \pi a^3 N\_0 \Gamma(\mathbf{x})}{12 \cdot \mathbf{4.1^x}} \cdot R^{0.21 \mathbf{x}} \tag{16}$$

The parameter η is defined as:

$$
\eta = \frac{\rho \pi a^3 N\_0}{12} \tag{17}
$$

and is constant. Then:

$$\text{KE} = \frac{\eta \Gamma(\mathbf{x})}{4.1^{\text{x}}} \cdot \text{R}^{0.21x} \tag{18}$$

Therefore, the empirical formula of the relationship between KE and *R* with the variable parameter *x* for the semi-arid area is derived.
