Prior to analyzing the diurnal variations of rainfall, we examined the climatological patterns of summer mean rainfall amount, frequency, intensity, and duration as shown in Fig. 2. The rainfall amounts and frequencies have distinct differences for stations with different gauge elevations (Figs. 2a, b). Large rainfall amount (frequency) values, i.e., those above 2.3 mm day–1 (10.0%), appear over the middle and eastern sections of the mountains and the Qinghai Lake areas. The lowest amounts (frequencies) of rainfall are found in the northwestern Hexi Corridor (north of 39.5°N). The average summer rainfall amounts (frequencies) are less than 0.5 mm day–1 (3.0%). The rainfall distribution varies by a large amount (frequency) between the stations over mountainous areas (elevation greater than 2700 m) and the surrounding low lands (with elevation less than 2100 m). The average rainfall amounts and frequencies are more than 2 times greater over the mountainous areas (approximately 2.2 mm day–1, 10.4%) than over the surrounding low lands (approximately 0.9 mm day–1, 5.0%). Additionally, the rainfall amounts and frequencies decrease from the mountains to the northeastern and southeastern low lands. Along the northeastern slope of the mountains, the average rainfall amounts gradually increase from approximately 0.6 mm day–1 over the northwest to 2.1 mm day–1 over the southeast. Rainfall frequency also has a similar increasing trend. Differing from the spatial distributions of the rainfall amounts and frequencies, the stations with relatively low rainfall intensity values (e.g., average value of 0.71 mm h–1) across the entire Hexi Corridor and those with relatively large values are not obviously concentrated (Fig. 2c). However, we can still identify that the mountainous areas have larger average values (0.88 mm h–1) than those observed (0.74 mm h–1) in the surrounding low lands. Differing from the spatial distribution of rainfall amounts, frequencies, and intensities, the region of maximum durations is not located over the mountainous areas but is over the two slope regions [(38.0°–38.8°N, 100.0°–101.5°E) and (37.0°–37.8°N, 102.5°–103.5°E)] (Fig. 2d). The average duration values in the two regions are 4.5 and 4.4 h, respectively. Along the northeastern slope of the mountains and the Hexi Corridor, there is a trend of increasing duration. The duration ranges from below 3.2 h (northwestern Hexi Corridor) to above 4.5 h (38.0°–38.8°N, 100.0°–101.5°E).
Summer mean rainfall (a) amount (colored dots; mm day–1), (b) frequency (colored dots; %), (c) intensity (colored dots; mm h–1), and (d) duration (colored dots; h) averaged over 2009–16. Gray shadings indicate the topography (m).
Notably, the regions with large rainfall amounts (greater than 2.3 mm day–1) comprise 49 stations, and the rainfall frequencies of all 49 stations are greater than 10.0%. In addition, the rainfall intensities at 39 (79.6%) stations are greater than 0.88 mm h–1 (Figs. 2a–c). The spatial correlation coefficient between the rainfall amounts and frequencies (intensities) in large value regions (where rainfall amounts are greater than 2.3 mm day–1) is nearly 1.0 (0.7). This coefficient indicates that most stations with large rainfall amounts also have large rainfall frequencies and intensities. Our findings differ from those obtained from the hourly merged precipitation dataset derived from the national automatic weather stations and the CMORPH (Climate Rainfall Center Morphing) product on a 0.1° × 0.1° resolution, for which the rainfall intensity does not have a large value region and is similar to the amount and frequency values (Liu et al., 2016).
The spatial patterns of the hourly peak over 24 h for the summer rainfall amounts, frequencies, and intensities are shown in Fig. 3. The spatial distribution of the diur-nal peak of rainfall amount has obvious regional characteristics (Fig. 3a). The prevailing late-afternoon peaks [1400–2000 local standard time (LST)] appear over the major mountain ranges, including the southeastern corner (east of 102.2°E) and northeastern slope of the mountains (north of 38°N). In addition, the stations with late-afternoon peaks account for up to 52.8% of all stations. The peak hours of rainfall in the northeastern slope appear approximately 1–2 h later than those in the southeastern corner. The stations with nocturnal peaks (2100–0300 LST) account for the same number (17.4%) of stations as those with an early-morning peak (0400–1000 LST). More than half of the stations (54.3%) with early-morning peaks are concentrated in the northern Hexi Corridor, and the remainder of the stations with early-morning peaks are dispersed across the northern surrounding areas of the mountains. The stations with nocturnal peaks are located around Qinghai Lake on the southern slope of the Qilian Mountains (south of 37.5°N, 98.0°–102.2°E). Rainfalls also have nocturnal peaks over many lakes over the central Tibetan Plateau (Singh and Nakamura, 2009).
Diurnal peaks of summer rainfall (a) amount, (b) frequency, and (c) intensity, averaged across 2009–16. The frames and letters in (b) are the ranges and names of the typical regions.
The pattern of diurnal peaks in rainfall frequencies is very similar to that of the rainfall amount, as shown in Fig. 3b. Three different regions of diurnal peak in rainfall frequency can be clearly identified. A total of 50.6% of the stations have late-afternoon peaks, which are distributed over the major mountain ranges. In contrast, 32.1% of the stations have early-morning peaks and are mainly located in the northeastern plain. Finally, 14.3% of stations have nocturnal peaks and lie around Qinghai Lake.
Compared with the patterns of rainfall amounts, there are three significant features that can be observed in the pattern of the rainfall frequency (Figs. 3a, b). One feature is that the stations with early-morning peaks are more abundant over the northeastern plains of the mountains, and the stations with nocturnal peaks in rainfall amounts have early-morning peaks of frequency to the east of Qinghai Lake (south of 37.0°N, 100.7°–101.7°E). The second feature is that the diurnal peaks at some stations appear at approximately 1900–2000 LST over 38.0°–39.0°N, 100.0°–101.0°E, which is 1–2 h behind the peak of rainfall amount. The last feature is that the peak differences were obvious in the area 36.0°–38.0°N, 101.0°–102.0°E, where the amount shows nocturnal peaks and the frequency is mainly characterized by early-morning peaks.
The diurnal peaks in rainfall intensity mainly appear during two periods (Fig. 3c). Late-afternoon peaks (55.5% stations) appear north of 37.5°N. Nocturnal peaks (24.5%) appear around Qinghai Lake and its eastern areas. Two inverse peaks appear in the southeastern corner of the mountains. One peak is nocturnal and the other is a late-afternoon peak. This finding indicates that heavy rainfall occurs more easily during nighttime and late-afternoon periods in the southeastern corner of the mountains. Compared with the patterns of rainfall amounts and frequencies, one obvious phenomenon is that the number of stations (24.5%) with early-morning peaks is significantly reduced (Figs. 3a–c). This result is consistent with the results for contiguous China (Yu and Li, 2016).
Based on the spatial patterns of the diurnal peaks in rainfall amounts, frequencies, and intensities, we can conclude that the late-afternoon peaks and nocturnal peaks are the main diurnal peaks over the mountains. For rainfall frequency, early-morning peaks also prevail. For 22.3% of stations, the diurnal peaks in the rainfall amounts, frequencies, and intensities have uniform late-afternoon peaks. For 4.2% of stations, the diurnal peaks in the rainfall amounts, frequencies, and intensities show uniform nocturnal peaks. Compared with the spatial patterns of diurnal peaks in rainfall amounts and intensities, the patterns of rainfall frequencies show more obvious differences over different topographies of the Qilian Mountains (Figs. 3a–c).
To illustrate the detailed diurnal cycle features of rainfall in the Qilian Mountains and to facilitate further discussion, we selected three typical regions by considering the patterns of the diurnal peaks in rainfall amounts, frequencies, and intensities and by giving priority to the frequency, as shown in Fig. 3b. These three regions represent the early-morning peak region, late-afternoon peak region, and nocturnal peak region, which are referred to as the N, M, and S region, respectively. In the N region, the percentages of stations with early-morning peaks are 49.1%, 82.6%, and 23.1% for rainfall amount, frequency, and intensity, respectively. In the M region, the percentages of stations with late-afternoon peaks are 87.9%, 89.3%, and 66.4% for rainfall amount, frequency, and intensity, respectively. In the S region, the percentages of stations with nocturnal peaks are 72.2%, 61.1%, and 47.2% for rainfall amount, frequency, and intensity, respectively. The M region contains complex topography with varied mountain tops and different slopes. To verify whether there are differences in diurnal evolutions for different topographies, the M region is divided into three subregions, which are referred to as the M_NE, M_M, and M_SE regions, and these three subregions represent the northeastern slopes, mountain tops, and southeastern slopes, respectively.
Figure 4 shows the standardized diurnal curves of the summer rainfall amounts, frequencies, and intensities averaged over each region/subregion outlined in Fig. 3b. For the N region (Fig. 4a), both the mean rainfall amounts and frequencies reach their diurnal maximum values at approximately 0700 LST, with standardized diurnal amplitudes of approximately 0.1 and 0.2, respectively. The mean rainfall intensity does not show obvious diurnal cycles except for the nocturnal minimum at approximately 2200 LST. For the M region (Fig. 4b), one strong late-afternoon peak occurs at approximately 1800 LST in the rainfall amount, frequency, and intensity, which is the same as the phenomena shown in Fig. 3, and the standardized diurnal amplitudes are approximately 0.3, greater than 0.25 and approximately 0.2, respectively. Additionally, another weaker peak at approximately 0700 LST is observed in the rainfall amount and frequency, while two weaker peaks at approximately 0300 and 0500 LST appear in the rainfall intensity. For the S region, the rainfall amount (intensity) and frequency show single nocturnal peaks at approximately 0000 (0100) LST. The standardized diurnal amplitudes are approximately 0.3, 0.3, and 0.2 for the rainfall amount, frequency, and intensity, respectively. Figures 4d–f show the diurnal variations in rainfall in the M_M, M_SE, and M_NE regions. Although the diurnal peaks of these three regions appear in the late afternoon, the detailed diurnal rainfall cycles are different. Rainfall in the M_M region shows a single peak and its standardized diurnal amplitude is approximately 0.3. The rainfall amount, frequency, and intensity increase rapidly starting at 1300 LST, reaching peaks in the late afternoon (1900 LST) and then decreasing relatively slowly. Additional analysis shows that 83.3% of stations only have a single late-afternoon peak over the M region, which indicates that region M is representative. For the M_NE and M_SE regions, the diurnal cycle of the rainfall amount (frequency and intensity) shows one strong late-afternoon peak and another weak early-morning peak, and the standardized diurnal amplitudes are comparable for the two regions. The dominant late-afternoon peak is consistent with the phenomena over southeastern Tibetan Plateau, wherein the stations have consistent late-afternoon peaks over the slopes (Chen et al., 2012). For the two mountain slopes, there are two obvious differences. One difference is that the late-afternoon rainfall amount (frequency and intensity) peak in the M_SE region appears 2 (3 and 3) h earlier than that in the M_NE region. The other difference is that the weaker peak in the rainfall amount (frequency and intensity) appears in the early morning at approximately 0700 (0800 and 0700) LST for the M_NE region. However, only the weaker frequency peak occurs in the early morning (0700 LST) for the M_SE region, and that of the rainfall intensity (amount) occurs after midnight at approximately 0300 (0200) LST, which causes a weak peak at 0300 LST in the M region (Fig. 4b).
Mean standardized diurnal cycle of the summer precipitation amount (red lines), frequency (black lines), and intensity (blue lines) for (a) N, (b) M, (c) S, (d) M_M, (e) M_NE, and (f) M_SE regions.
For every region, the diurnal variations in rainfall amounts can be attributed by those of both the rainfall frequency and rainfall intensity. This phenomenon is consistent with the conclusions found for most of eastern China (Zhou et al., 2008). In addition, the peak in rainfall intensity precedes the peak in rainfall frequency over every region. This result is consistent with the previous findings that the phase of rainfall intensity (frequency) precedes (lags) the rainfall amount (Yu and Li, 2016). Yu and Li (2016) also indicated that this occurs due to the asymmetry of precipitation processes and the evolution of convective clouds.
The diurnal cycle of rainfall is closely related to the duration of rainfall events (Yu et al., 2007). Over the northeastern and southeastern slopes, the diurnal cycles of rainfall frequency show double peaks, as shown in Figs. 4e, f. To explore the relationships between the double peaks in rainfall frequency and the duration over the two slopes, the rainfall frequency decomposed by duration and diurnal phase for the two slopes is analyzed, and the rainfall frequency is normalized by the daily mean of each duration time (Figs. 5a, c). We also calculated the proportions of rainfall frequency occurring during the two periods (dashed lines in Figs. 5a, c) to the total daily rainfall. Here, the two periods (hereafter referred to as peak periods) were defined as three hours before and after peak hour in Figs. 4e, f, including the late-afternoon period and the early-morning period. Figures 5b, d show the proportions of two peak periods for rainfall events with different durations. For the M_NE region, there is a large value zone during the late-afternoon period, which has a duration of less than 9 h. For these rainfall events, more than 35% of rainfall frequency is from the late-afternoon period. When the duration is between 10 and 12 h, the maximum rainfall occur in the nighttime and the rainfall in the late afternoon is slightly more than the rainfall in the early morning. When the duration is greater than 13 h, the largest value is located in the early-morning period, and rainfall in this period accounts for 30% of daily rainfall. During the early-morning period, several large centers have durations of 4–6 h, 7–8 h, and longer than 13 h, and their proportions show little difference (Figs. 5a, b). Over the southeastern slope, the large value region in the late-afternoon period has the duration shorter than 6 h and has a very large magnitude. The result indicates that the late-afternoon peak mainly comes from rainfall shorter than 6 h. When the duration is greater than 6 h, the large regions appear in the early-morning period and the proportions in this period are obviously greater than those in the late-afternoon period. That is, the late-afternoon peak is characteristic of rainfall shorter than 6 h, while the early-morning peak is contributed by events longer than 6 h. Our results indicate that the strengths of the late-afternoon and early-morning peaks in rainfall frequencies are closely related to the rainfall events with different durations over the two slopes: for rainfall events shorter than 6 h, the proportion in the late-afternoon is greater than that in early-morning, while for events longer than 13 h, the early-morning peak is stronger than the late-afternoon peak. With an increased duration, the occurrence time of rainfall becomes increasingly disperse in a day. There are some distinct characteristics over the two slopes. When the duration is between 7 and 12 h, the proportion in the late-afternoon period is greater than that in the early-morning period for the northeastern slope, but the proportion in the late-afternoon period is less than that in the early-morning period for the southeastern slope.
(a, c) Rainfall frequency with different durations and diurnal phases in regions of (a) M_NE and (c) M_SE. The rainfall frequency is normalized by the daily mean for each duration time. The red (blue) dashed lines denote the late-afternoon (early-morning) period. (b, d) The proportions of rainfall frequency in the late-afternoon (red bars; %) and early-morning (blue bars; %) periods for rainfall events with different durations to their daily rainfall in (b) M_NE and (d) M_SE regions. The y-axis shows the duration.