3.1. Rainfall Events with and without Single Tip Events (STE)
The average rainfall characteristics (
Table 1) varied with the minimum inter-event time (MIET) and when STE were included (
Table 3 and
Figure 2). The dynamics of the rainfall events indicate that careful attention should be given to studies that adopt data analysis based on the scale of events [
21,
22,
24,
28,
42], considering that these characteristics influence the assessment of interception [
3,
4,
5,
6,
7,
8], water infiltration in the soil [
9], runoff [
10,
11,
12], soil loss [
13,
14,
15], kinetic energy [
43], soil moisture content [
16,
17,
18], and ecosystem services [
19,
20].
The database shows that the impact of STE on rainfall characterization depends on the MIET defined for the analysis (
Figure 3). Adopting a MIET of 15 min, the frequency of occurrence of STE is corresponds to 41% of a total of 199 mm (2.3% of the total precipitation), and decreases to two STE events out of 307 total events for a MIET of 24 h (0.03% of the total precipitation) (
Figure 3).
The increase of MIET for event separation implies a decrease in the number of STE and, consequently, the precipitation associated with single-tip events [
21]. The Wilcoxon non-parametric test indicated a significant difference in the variables for a MIET equal to or less than 3 h (
Table 4), as the medians of the events with or without STE do not correspond to the same distribution with a 99% confidence level. The total rainfall expected by STE, assuming a MIET of 6 h (when there is no more statistical difference), is 10.7 mm for the entire study period (2009 to 2020). Therefore, these results suggest that the best MIET to characterize statistically independent rainfall events in the region must be equal to or greater than 6 h, since the STE no longer interferes with the choice of MIET (
Table 4)—with a level of confidence of 99%.
A power curve best fits the relationship between the number of events and MIET with and without STEs (
Figure 4). Both expressed high correlations, with an R² of 0.98 and 0.97 for events with STE without STE, respectively. For lower values of MIET, more rainfall is separated into STE, which is contrary to higher values of MIET that will include these STE in longer events [
21,
22,
26,
27].
Results show a smaller difference in the total number of rainfall events for MIET values above 6 h (
Figure 4) in both tested conditions, which represent approximately 96% of the total rainfall events (
Figure 3)—characterizing the occurrence of a higher number of smaller events. The derivative of the number of events by MIET decreases significantly with the increase in MIET (
Figure 4), with a hundredfold decrease in value between 6 and 9 h. For MIETs greater than 6 h, the two curves of the number of events with and without STE are similar (
Figure 4) and the derivative is in a slowing decreasing pattern.
Studies carried out in arid and semi-arid environments did not use the STE to evaluate the average rainfall characteristics, as they considered this data uncertain [
21,
22,
51]. However, STE can be crucial for studies in tropical dry forests focusing, for instance, on canopy interception [
3,
7], soil moisture dynamics [
17], soil cracking, and runoff generation—particularly in vertisols [
11]—as well as water fluxes in the soil–atmosphere interface [
52] and ecological processes such as root shrinkage and expansion [
53]. Therefore, it is important that STE be investigated in studies of rainfall characterization to better define MIET in semi-arid regions with high temporal [
13,
38] and spatial variability [
24,
34,
35].
3.2. Characteristics of Rainfall Events
Descriptive statistics of events with and without STEs are presented in
Table 3 and the variability of the average rainfall event characteristics as a function of MIET is in
Figure 2. For all rainfall events, the average total rainfall ranged from 5.1 to 28.2 mm for 15-min and 24-h MIETs, respectively (
Table 3)—which is a fivefold difference. The average duration of rainfall events ranged from 0.5 h (MIET = 15 min) to 16.4 h (MIET = 24 h), i.e., an increase of over 32 times (
Table 3). The highest coefficients of variation were recorded at the 15-min MIET.
Rainfall duration tends to increase as the MIET value increases, with the highest values at MIET above 6 h (
Figure 2). The greatest range for rainfall duration occurs for a larger rainfall separation time of approximately one day [
26]. However, the average rainfall intensity is reduced by 24.3% at a MIET of 24 h (
Table 3;
Figure 2). The average values of intensity and CV remain almost constant, regardless of the MIET value, as also shown by [
26].
In general, rainfall events have a longer duration, higher total precipitation and lower average intensity for higher MIETs (
Table 3;
Figure 2) due to the larger number of continuous records incorporated into the events [
32]. For higher MIETs, the average intensity of the rainfall events shows greater intra-event variability (
Table 3) because increasingly larger time intervals are included in the events [
22].
For the maximum rainfall intensities at different time intervals (I5 to I60), the maximum intensity at 5 min (I5 max) was the most variable (higher values of CV, asymmetry, and kurtosis), as also shown by [
21], and with greater amplitudes, as observed in the study by [
7]. As the time interval increases, the maximum intensities decrease, with lower variability for different MIETs, indicating an attenuation of the rainfall intensity at larger intervals and less variation in the CV (
Table 3;
Figure 2).
In all the analyzed variables (
Table 3), the highest and most positive values of the kurtosis and skewness coefficient recorded in the lowest MIETs indicate a higher concentration of intermediate values. These characteristics define a higher coefficient of variation of the data and a non-normal distribution, since the values are not close to zero, indicating that the data are not distributed equally around the mean [
47].
For longer MIETs, for example 24 h, the characteristics of rainfall events present greater intra-event variability [
22] and, with this, an ecohydrological processes analysis may differ. For example, in studies of soil erosion that use average rainfall intensity to represent the ability of rain to cause erosion through empirical relationships [
12,
13,
14,
15,
43,
54] and obtain the erosivity index, careful attention is essential, and it should be taken into account that the results generated for each MIET are different.
3.3. Minimum Inter-Event Time (MIET)
The probability distribution functions were adjusted for the event variables: total rainfall, duration, average intensity and inter-event time (IET) at each MIET (
Appendix A Table A1). Lower MIETs are farther from the 95% confidence interval of the variable’s frequency distribution (
Appendix A Table A1) because STE occurs more frequently up to a MIET of 3 h (
Figure 3;
Table 4) [
21]. As the MIET increases from 6 to 24 h, STE events decrease, presenting a lower coefficient of variation (
Table 3). Both series show a similar distribution pattern (
Figure 4) with statistically equal median values (
Table 4), which were detected by the Wilcoxon non-parametric test with a 99% confidence level.
Among the tested distributions (Normal, Log-Normal, Gamma, Exponential, and Weibull), the Weibull distribution was the one that best fit the data on total rainfall, duration, and IET, and the Log-Normal distribution on the average rainfall intensity (
Figure 5), as also showed in recent studies [
45,
46,
47,
48].
According to the Anderson–Darling (AD) goodness of fit test, the 6 h MIET (
Appendix A Table A1;
Figure 5) was the one with the best fit (AD = 0.69 and
p = 0.07) for rainfall depth, implying that a MIET of 6 h is the most suitable to characterize the distribution of rainfall in the study region. For the other variables analyzed and for a 6-h MIET, the curves were well adjusted by the AD test, with significance levels ranging between 95% and 99% (
Appendix A Table A1;
Figure 5).
Research in different parts of the globe highlight that a 6-h MIET is widely adopted in hydrological studies [
22,
29,
54,
55,
56]. As in this study, changing the MIET value substantially alters the number and properties of rainfall events in an arid region of Australia [
22]. However, there is still not a consensus on the best MIET to characterize rainfall events in arid and semi-arid environments, and hydrological criteria have been used. In the semi-arid region of Spain, studies show that the optimum MIET is 1 h, as it is the minimum period necessary for water in larger macropores to drain and sufficiently modify the effect of soil moisture on the runoff generation process [
21]. For the semi-arid region of northeast Brazil, studies indicate that the 30-min MIET is the most representative and characterizes the main properties of rain by type of hietogram [
28].
Inter-event dry periods (IET) increase with MIET. For the 6-h MIET, the average IET was 187.3 h (fiftyfold of the average event duration). In all cases, the largest gap between events was a 248-day rainless interval (
Figure 5); this long period of continuous dry days is expected for this location, with more than 80% of the rains concentrated in the rainy season (January-April) [
36], showing the high temporal variability of precipitation [
6,
35,
38].
3.4. Rainfall Characterization for a 6-h Minimum Inter-Event Time (MIET)
After identifying the 6-h MIET as the most adequate to characterize the distribution of rainfall in the region, the events were clustered based on total rainfall (mm), duration (hours), and average intensity (mm h
−1), resulting in three statistically different classes (
Table 5;
Figure 6). The class represented by group I, Class I was composed of events with lower rainfall depth, intermediate durations, and lower than average rainfall intensity (
Table 5,
Figure 6). This class is composed of a high frequency of small events (88.7% of the events registered a rainfall below 20 mm) with low average intensity (
Table 5) and represents 77.4% of the total events and 42.4% of the total rainfall. The high occurrence of small events and high temporal variability is a common feature of rainfall events in this tropical semi-arid region [
6,
12].
Class II is represented by 14 short duration events (median 0.3 h) (
Table 5) and high rainfall intensities (average 45.9 mm h
−1) (
Table 5). These results are attributed to the convective rains, with high intensity and short durations [
12,
43] that are common in semi-arid regions. For the tropical semi-arid study region, short-duration rainfall events with high intensities play an important role in hydrological processes [
12,
13,
42], particularly on the generation of Hortonian-type runoff [
9] and on the onset of the rainy season where vertisols prevail [
11].
Class III has the events with the highest rainfall depths, with a maximum of 161.9 mm, average of 45.1 mm, and median of 43.2 mm (
Table 5,
Figure 6). Longer rainfall events (approximately 1 day) with an average of 8.1 h (
Table 5,
Figure 6) were also observed for this class. The higher magnitude rainfall events during the rainy season are due to the atmospheric systems in the region, where the rainfall distribution is mainly related to the displacement of the Intertropical Convergence Zone (ITCZ) to the south during the months of February to May [
35] and the frontal rainfall systems [
57]. For the study area, high magnitude rainfall events are hydrologically important so that the vegetation canopy exceeds its interception capacity and saturates, generating a redistribution of rainfall to the soil, favoring infiltration, increasing soil moisture, and contributing to other ecohydrological processes [
6,
7,
19]. We highlight the importance of this study, as previous works in the region classified rainfall events differently [
6,
12] and were supported by daily records of rainfall (total rainfall within 24 h intervals) for their characterization. The present work verified significant differences in events characteristics based on MIET values, and, therefore, the importance of defining adequately the MIET for event separation for the hydrologic processes assessment based on rainfall events.