*4.1. Uncertainty Analysis of Disdrometer-Measured Data*

Figure 10 shows the relationship between two different measurements on a daily scale. Each point represents the total rainfall of a given day during the 1-year observation period. The abscissa is the total measured rainfall of Parsivel-2, and the ordinate is the averaged total rainfall measured by four TE525MM Gauges (data with both daily total rainfall greater than 1mm are taken for analysis). The results show that the disdrometer-measured data demonstrates a good correlation with the average rainfall gauge-measured data, and the deviation is mainly caused by the instrument theoretical error in measurement of disdrometer and gauges (e.g., sampling error), which was concluded by Tokay et al. [29]. The measured rainfall data of the disdrometer is suitable for this semi-arid area.

**Figure 10.** Scatter plot of gauge- and disdrometer-measured total rainfall on a daily scale. The results obtained by the two measurement methods are compared with the scatter plot. The solid green line is the fitted result.

Figure 11 shows the precipitation process of three rainfall events, with the calculated average of the data measured by four rainfall gauges. The determinate coefficient *R*<sup>2</sup> of a linear relationship between Parsivel Disdrometer and TE525MM Gauges is 0.68 for (a), 0.83 for (b) and 0.96 for (c). The standard deviations of disdrometer-measured (gauge-measured) rainfall intensity in (a), (b) and (c) are 1.37 mm/h (2.90 mm/h), 1.02 mm/h (1.43 mm/h) and 1.43 mm/h (2.46 mm/h), respectively. The standard deviation of the disdrometer-measured data in each season is less than the gauge-measured data in the corresponding season. In order to further compare the difference between disdrometer-measured and gauges-measured data, the mean absolute error(MAE) and the root mean square error(RMSE) of the events are also given. Event 3 has the smallest MAE (0.69 mm·h<sup>−</sup>1) and smallest RMSE (0.99 mm·h<sup>−</sup>1) among the three events. This indicates that the disdrometer can potentially estimate the precipitation with better performance during Event 3, according to the comparison with gauge-measured data.

**Figure 11.** The comparison of measurement results of OTT Parsivel-2 (orange solid lines) and four TE525MM gauges (green dotted lines, averaged) in 3 rainfall events. (**a**) a rainfall event in spring, from 19–20 April 2019; (**b**) a rainfall event in summer, on 3 August 2019; (**c**) a rainfall event in autumn, on 1 September 2018.

The measuring range of Parsivel-2 is 0.25–6 mm, and it has been proved that the disdrometer has errors in measuring both smaller and larger diameters of raindrops in many studies [53,54], which have more accuracy in measuring mid-level raindrops in the spectra. Liu et al. [54] further explained the algorithm of the disdrometer and concluded that the differences can be attributed to a certain error of rainfall amount accumulation. In all three measured events, when the TE525MM Gauges-measured data reaches its peak (at 0:30 in (a), 19:00 in (b), and 18:30 in (c)), the data measured by gauges are all more than the disdrometer-measured data; and when the TE525MM Gauges-measured data reaches its minimum of the event (at 23:30 in (a), at 11:30 in (b) and 15:00 in (c)), the data measured by gauges are all no more than the disdrometer-measured data. As raindrop spectra data larger than 6 mm are treated as solid rainfall and eliminated, the peak value of the disdrometer is lessened. This is consistent with the results in Section 3.3 that in Event 1 the disdrometer- and gauge-measured *R* data indicates a significant gap (2.94 and 3.51 mm·h<sup>−</sup>1, respectively). Since the measured raindrop spectra data larger than 6 mm have been removed, and raindrops of large diameter are often accompanied by heavy rain [25], it is speculated that this is the reason why the peak of rainfall intensity obtained by the raindrop disdrometer is smaller than the value measured by rain gauges.
