**1. Introduction**

Characteristics of precipitation show the impact of meteorological conditions [1], and the measurement of quantitative distribution of precipitation is important for studying the mechanism of global climate and environmental change [2]. Raindrop size distributions (DSDs) show the microphysical properties of a rainfall event and vary with precipitation both in time and space. The DSDs are of importance to enhance the accuracy of quantitative precipitation estimation (QPE) by weather radar, and raindrop spectra have been used to calculate radar reflectivity factors in many studies [3–6]. Thus, investigating the raindrop spectra is essential for providing information on the

microphysical characteristics of different precipitation types, and improving the parameterizations of different rainfall processes.

Raindrop spectra can be measured by many methods, e.g., as done by Das et al., Waldvogel et al., Schönhuber et al. and Liu et al. [3,7–9], and these different methods vary in measurement principles and precision of data. In recent years, the raindrop disdrometer has been widely used to measure raindrop spectra because of its high measurement accuracy and small-time interval for data acquisition. Liu et al. [9] measured the precipitation in Nanjing, China and compared four different methods of rainfall to conclude that the disdrometer and other methods are consistent within the range of medium particle size. However, Zhang et al. [10] used three different methods to analyze the DSD characteristics in Zhuhai, China and found that the disdrometer had limitations in measuring small raindrops when compared to other methods. Raupach et al. [11] used a 2DVD device to correct the DSDs measured by three disdrometers and the correction showed its general applicability under different climate types. However, the study on the seasonal variation of rainfall characteristics in semi-arid areas of China using a raindrop disdrometer is very limited.

The measured raindrop spectra can be used to calibrate and validate the parameters in radar reflectivity-rainfall intensity (*Z-R*) relationships (quantitative estimate precipitation, QPE). Variability of DSDs in different forms of precipitation impact the radar reflectivity-rainfall intensity relationships (*Z-R* relationships, normally in the form of power function *Z* = *aRb*, in which *a* and *b* are parameters derived from data fitting) [12,13], and the quantitative estimation of rainfall intensity (*R*) by *Z-R* relationships can be further modified. Sulochana et al. [14] investigated the *Z-R* relationships over a tropical station and concluded that the prefactor of *Z-R* relationships is larger for stratiform rain than for convective rain, which was in agreement with the results reported from two other tropical stations. Sulochana et al. also found that there were large variations in *Z-R* relationships in different seasons. Das et al. [3] analyzed the impact of different precipitation types on *Z-R* relationships in a hill station with a pronounced monsoon climate, and the results showed that the *Z* values of the shallow-convective system are the lowest, compared to other precipitation types. Das et al. concluded that the coefficient *a* is larger for stratiform rain than for convective and shallow-convective rain. However, there remains very limited research on using disdrometers to investigate raindrop spectra in semi-arid areas [15], and further research on the parameters in *Z-R* relationships is needed.

In addition, the measured raindrop spectra can be used to explore the mechanism of precipitation erosivity. The relationship between rainfall kinetic energy (KE) and intensity (*R*) is a significant approach to study the impact of precipitation on soil erosion [16], and a disdrometer can be deployed to measure the rainfall kinetic energy and intensity [17]. Angulo-Martínez et al. [18] measured and analyzed the uncertainty in KE-*R* relationships with five Parsivel disdrometers among three locations, and found that the types, accuracy and location of the disdrometers and precipitation types influence the estimation results of KE. Overestimation of the midsize raindrops led to a high estimation result of KE. Moreover, Carollo et al. [19] concluded that KE/*R* depends on the median volume diameter of precipitation events strictly, and this relationship does not rely on the locations of disdrometers. There have also been studies investigating the KE-*R* relationships in arid and semi-arid areas, e.g., Meshesha et al. and Abd Elbasit et al. [20,21], and many KE-*R* relationships were derived with this approach [22]. Nevertheless, many of the relationships vary greatly because of the different climate conditions, and a general formula for KE-*R* relationships needs to be derived to be suitably utilized in arid and semi-arid areas.

Yulin (in the northern region of Shaanxi Province, China) has a semi-arid climate, and the precipitation in this area is not evenly distributed throughout different seasons of the year [23]. The analysis of DSDs in different seasons is helpful to understand the variability of precipitation in this semi-arid area. The objectives of this paper are: (1) to analyze the detailed statistical data of DSDs based on the observation of a raindrop disdrometer located in Yulin, and collect data on the variability of microphysical characteristics of precipitation in different seasons; (2) to investigate the *Z-R* relationships in different seasons, and analyze the variability of the parameters in the *Z-R* relationships across different precipitation types; (3) to derive a theoretical formula for KE-*R* relationships and further analyze the calculated results.

The following sections are organized below. Section 2 describes the research method, the datasets of the research area, and the derivation processes of theoretical formula. Section 3 analyzes the observed results statistically and presents the comparison of different precipitation periods in different seasons. Section 4 presents a further discussion of the comparison of disdrometer- and gauges-measured rainfall data, the comparison of different *Z-R* relationships and the theoretical formula of KE-*R* relationships through sensitivity analysis. Section 5 gives the conclusion.

### **2. Materials and Methods**
