Complex terrain has long been regarded as one of the significant factors leading to the inhomogeneous spatial distribution of precipitation, and its influence on precipitation has been extensively studied for several decades (Colle, 2004; Smith and Barstad, 2004; Roe, 2005; Rotunno and Houze, 2007). Tao (1980) pointed out that topography has a strong impact on the distribution of frequency and the amount of heavy rain in summer. Jiang and Smith (2003) also found that under various climatic and synoptic conditions, mountains always increase rainfall to varying degrees. The terrain in China is complex and diverse with various mountain ranges and highlands, and the influence of terrain on precipitation is more complex (Tao, 1980; Peng et al., 1995; Liao et al., 2007). Mountains of different sizes and shapes impact weather and climates in different ways (Houze, 2012). In recent years, considerable analyses have been conducted to reveal the effects of orography on precipitation over large-scale topographic areas such as the Tibetan Plateau (Molnar et al., 2010; Xu and Zipser, 2011; Chen et al., 2012; Li, 2018), Tianshan Mountains (Wang S. J. et al., 2013; Wang T. et al., 2015; Li et al., 2017), and Qilian Mountains (Gou et al., 2005; Jia et al., 2014), and over small-scale topographic areas such as the Dabie Mountains (He et al., 2009; Li et al., 2012; Tang et al., 2012) and Yellow Mountain (Chen and Zhao, 2006; Wang D. et al., 2013). A series of numerical simulation experiments have also been carried out, and important results have been obtained (Fan and Lyu, 1999; Miglietta and Buzzi, 2001; Miglietta and Rotunno, 2009; Wang et al., 2016).

In these studies, the characteristics of cumulative rainfall amount, frequency, and intensity are examined, and several relatively new features are also analyzed (Fujinami et al., 2005; Yu et al., 2007; Bai et al., 2008; Wang et al., 2012). For example, the diurnal variation of precipitation is an important feature associated with the combined effects of atmospheric thermal and dynamic processes on the water cycle of the earth’s climate system (Dai et al., 1999). Diurnal variation of rainfall can not only reflect the physical laws of regional weather and climate evolution, but also indicate the mechanisms of precipitation formation and evolution (Yu et al., 2014; Yu and Li, 2016). Many studies have found that the warm season rainfall often generates over highlands in the afternoon hours and then spreads eastward or southeastward to neighbouring lowlands at night or in the early morning (Wang et al., 2004, 2005; Carbone and Tuttle, 2008; Huang et al., 2010). Yu et al. (2007) combined the diurnal variation with the duration of precipitation and showed that the duration may be a key factor in distinguishing different rainfall events. Furthermore, Yu et al. (2013) studied the evolution process of precipitation, and further improved the understanding of rainfall characteristics. The spatial scale is another significant rainfall feature. The rainfall spatial scale refers to the size of the spatial range covered by rainfall, which represents the extent of precipitation influence and is closely related to formation mechanisms and physical processes of rainfall (Alfieri et al., 2008; Chen et al., 2014). Coverage of rainfall produced by different mechanisms usually varies. Convective precipitation is of high intensity and covers a small area while precipitation generated from stratiform clouds occurs over a longer period and affects large areas (Anagnostou and Kummerow, 1997). A number of methods for calculating the spatial scale of precipitation have been developed (Ebert and McBride, 2000; Liu et al., 2008; Guo et al., 2017; Day et al., 2018).

It is noted that the precipitation characteristics of different regions, even in the same mountainous areas, can vary significantly. For example, Fu et al. (2018) found that across the Qilian Mountains, the average number of rainfall days and rainfall amount are significantly affected by the topography: rainfall on the southern slope is clearly heavier than that observed on the northern slope. Li et al. (2018) pointed out that the diurnal variation of rainfall amount observed over the Qilian Mountains presents completely different regional characteristics: the south of Qinghai Lake presents a single nocturnal peak, while a dominant late afternoon peak occurs on the mountaintop; over the northeastern and southeastern slopes, there exist a dominant late afternoon peak and an early morning secondary peak. Across the central Tibetan Plateau, the hilly region has the strongest rainfall activity in the late afternoon, but the valley and lakes show a late evening maximum (Singh and Nakamura, 2009). For smaller topographic areas, Ding and Wang (2009) found that rainfall hitting windward slopes and funnel-shaped topography is more pronounced for Jiuhua Mountain and that there are remarkable differences in the distribution of rainfall at different heights. Liu et al. (2017) concluded that the spatial distribution of precipitation over Yellow Mountain is closely related to the trends of mountain range and that the spatial distribution of precipitation can be divided into three main types: mid-western, southern, and northeastern. Now it is generally believed that mountains, as obstacles protruding from the earth’s surface, first have the effect of blocking and lifting the airflow, which leads to more rainfall on the windward slope (Maddox et al., 1978; Banta, 1990; Roe, 2005). Discrepancies in topography, landscape slope, and exposure of various mountain ranges can also create regional differences in rainfall characteristics (Ding and Wang, 2009; Wang D. et al., 2013). In addition, Guo et al. (2014) found that local effects such as mountain valley breeze have a great impact on the diurnal variation of precipitation when large-scale dynamic processes are weak, as observed in many other studies (Singh and Nakamura, 2009; Chen et al., 2012). Gravity waves generated by topographic forcing also shape how mountains influence the rainfall diurnal variation in surrounding areas (Barros and Lang, 2003).

Compared to those of large-scale topographic areas, it is more challenging to study regional differences in the precipitation characteristics in small-scale topographic areas. Since the time and spatial scale of precipitation affected by small-scale topography are relatively small, refined requirements must be placed on the datasets used. For example, denser distributions of ground meteorological rain gauges with higher observation quality as well as higher temporal resolution are indispensable for the detailed study of small-scale topographic precipitation. In recent years, with the continuous improvement of precipitation data of high spatial and temporal resolutions, the above requirements have been satisfied to some extent, and detailed features of small-scale complex topographic areas have been identified. Mount Tai is located at approximately 36.2°N, 117.1°E with a peak altitude of 1545 m. It is surrounded by relatively lower hills and plains. Due to the remarkable difference in altitude between Mount Tai and its surrounding area, it is known as an isolated topographic area. Just around the mountain’s summit, Taishan Station serves as an ideal place for examining the impact of isolated terrain on precipitation. Therefore, the present study uses long-term hourly rainfall data from the most up-to-date network of national ground meteorological stations to investigate regional differences in precipitation characteristics over this region.

This paper is organized as follows. Section 2 introduces the data and analysis methods; Section 3 presents the rainfall diurnal variation characteristics over Mount Tai and its surrounding areas. Differences in rainfall spatial scales are investigated in Section 4. Section 5 analyzes differences in rainfall evolution process during stages of the beginning, end, and peak rainfall time, process asymmetry, and the duration features of precipitation. Finally, conclusions and discussion are given in Section 6. The paper intends to enrich our understanding of the precipitation characteristics over Mount Tai from multiple perspectives, which may help facilitate the prediction of mountain precipitation. It also aims to offer new insights on the mechanisms of small-scale terrain influencing precipitation patterns.

The hourly rain gauge observations for the warm season (May to September) of 1996–2015 were used in this study. This rainfall dataset was obtained from the National Meteorological Information Center (NMIC) of the China Meteorological Administration (CMA). It has undergone strict quality control (extreme value, internal consistency, and time consistency checks), rendering it appropriate for studying the effect of small-scale topography on precipitation. For analysis of the circulation background, we used ERA5 (the fifth generation of the ECMWF atmospheric reanalysis of the global climate) hourly reanalysis data with a horizontal resolution of 31 km (Hersbach and Dee, 2016). The study area (35°–37.5°N, 115.85°–118.35°E) is shown in Fig. 1. There are 55 national meteorological stations in this area. Taishan Station, which is located close to the summit of Mount Tai, is one of the oldest alpine stations in China and is positioned at an altitude of 1533.7 m. The other stations are mainly distributed across hilly, mountainous, and plain areas with an average altitude of less than 350 m.

Figure 1 The 1996–2015 warm season mean rainfall (a) amount (colored dots; mm h−1), (b) frequency (colored dots; %), and (c) intensity (colored dots; mm h−1). Surface elevation (m) is shaded. The cross denotes Mount Tai, and the values of its rainfall characteristics are labeled at the upper right corner of each panel.

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In our study, the start time of a precipitation event is defined as the first hour showing measurable precipitation after no precipitation occurs for two hours or more. Similarly, the last measurable hour of rainfall occurring before two or more hours without rainfall is considered to be the last hour of a rainfall event. The duration is the number of hours from the beginning to the end of one event. Some hourly rainfall features are defined as follows:

a. Mean hourly rainfall amount (mm h⁻¹): P_r/N_nm,

b. Rainfall frequency (%): N_r/N_nm,

c. Rainfall intensity (mm h⁻¹): P_r/N_r.

P_r is the accumulated rainfall amount with measurable rainfall (≥ 0.1 mm h⁻¹) during the study period, N_nm is the number of hours with no missing rainfall records, and N_r is the number of hours with measurable rainfall.

As mountains generally enhance precipitation, to examine this effect quantitatively, various definitions have been applied (Peng et al., 1995; Rosenfeld et al., 2007). Similarly, in this paper, we define the ratio of the difference between Mount Tai and its surrounding areas to the corresponding climatic state for the whole study area to describe the enhancement effect, as below:

where E denotes the rainfall enhancement of Mount Tai, P_mnt is the precipitation features of Mount Tai, P_sur and P_ave represent the mean rainfall characteristics of the areas surrounding Mount Tai and of the whole study area, respectively. For a given hour, we use the proportion of rainy sites to represent the spatial scale of precipitation in the study area. When a station detects rainfall at this moment, the proportion is also deemed the spatial scale of rainfall for this station. For example, when there are 55 stations and 10 of which experience rainfall at 1400 local solar time (LST), including Taishan Station, we take 18% (10/55) as the spatial scale of rainfall for Taishan Station at 1400 LST. Similarly, for the other 9 stations at which precipitation has occurred, the spatial scale of rainfall at 1400 LST is also 18%. However, for the other 45 stations without precipitation, the spatial scale of precipitation at this moment is 0.

Prior to detailed analysis, we first examined climatological patterns of the warm season mean hourly rainfall amount, frequency, and intensity as shown in Fig. 1. The cross indicates Mount Tai and in the upper right corner are its rainfall amount, frequency, and intensity. It can be clearly observed from the figure that precipitation amount increases from northwest to southeast. However, in this climate background, the rainfall amount of Mount Tai is still much higher than that in surrounding areas, reaching 0.23 mm h⁻¹, which is 70.2% higher than the average rainfall amount for the surrounding stations (Fig. 1a). The distribution pattern of frequency (Fig. 1b) is consistent with the rainfall amount. The maximum is located on Mount Tai with a value that is 56.2% higher than the mean frequency of the surrounding areas. Although the distribution of intensity (Fig. 1c) is slightly different from that of the previous two with the largest value centered on the south of Mount Tai, the rainfall intensity of Mount Tai is still relatively high, reaching 2.37 mm h⁻¹, which is approximately 10.95% higher than the mean intensity of the surrounding areas. Therefore, despite Mount Tai’s small horizontal scale, a remarkable difference in precipitation characteristics was found between Mount Tai and its surrounding areas. In addition, given that the rainfall amount measured at Taishan Station is much higher than that of the surrounding stations and a large local value center is at Taishan Station, our study mainly focuses on the differences in the precipitation characteristics between the alpine station (Taishan Station) and its surrounding stations. The precipitation characteristics of Mount Tai mentioned in this work refer to those of Taishan Station in particular.

Diurnal variation of the warm season rainfall amount, frequency, and intensity of Mount Tai and the remaining stations are shown in Fig. 2. To describe the phase of the peak time in the diurnal variation more clearly, we divided the 24 h of a day into four time periods: night (2000–0300 LST), early morning (0400–0900 LST), noon (1000–1300 LST), and afternoon (1400–1900 LST). The results show that the peak time periods for diurnal variation of rainfall amount, frequency, and intensity at all stations are relatively consistent: rainfall amount and frequency generally reach their peaks in the early morning, and rainfall intensity has its maximum in the afternoon. Specifically, the diurnal variation in rainfall amount for Mount Tai and surrounding areas (Fig. 2a) presents a dominant early morning peak and a weaker secondary peak in the afternoon. It should be noted that the rainfall amount of Mount Tai is significantly higher than that of surrounding areas. The diurnal variation of the enhancement on the rainfall amount shows remarkable “dual peaks” (red dashed line in Fig. 2a), which reach their maxima at approximately 0400 LST and 1400–1500 LST with a maximum of more than 80%. Meanwhile, the lowest value is observed at 1000 LST, and the enhancement gradually increases when night falls (2100 LST). By further analyzing the diurnal variations of rainfall frequency and intensity (Figs. 2b, c), it is apparent that the enhancement similarly presents a dual-peak feature in early morning and afternoon.

Figure 2 Diurnal variations of the rainfall (a) amount (mm h−1), (b) frequency (%), and (c) intensity (mm h−1). The black solid line denotes Mount Tai; the grey solid line denotes the averaged value for the surrounding stations; the box distribution is for surrounding stations, and the red dashed line denotes the enhancement, which corresponds to the right axis.

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It should not be ignored that, although the enhancement of the rainfall amount is positive at each hour, this does not mean that the maximum value in the study area is always measured from Mount Tai. As is shown in Fig. 2a, there are several hours during which the rainfall amount of Mount Tai is less than that of a few surrounding stations (1–2 stations), and these hours mostly fall at around noon and midnight. The rainfall frequency of Mount Tai at each hour is higher than that of the other stations (Fig. 2b). However, in most hours (16/24), the rainfall intensity of Mount Tai is lower than that of more than 25% of surrounding stations. Therefore, compared with surrounding areas, abundant rainfall observed over Mount Tai is mainly contributed by frequency. In addition, the diurnal phase of the rainfall amount in surrounding areas lags 1 h behind that of Mount Tai. For example, the rainfall amount peaks at 0500 and 1700 LST over Mount Tai while in the surrounding areas, the rainfall reaches its maximum amount at 0600 and 1800 LST (black and grey solid lines in Fig. 2a). The 1-h lag correlation coefficient is 0.95, which is the maximum of all time lag correlation coefficients and surpasses the 99% confidence level.

Diurnal variations of the regional mean spatial scale of rainfall are presented in Fig. 3. The number of stations that recorded rain remains high from the evening to the early morning. A maximum value appears at 0800 LST, covering 13% of the stations in this region. The minimum value appears at 1600 LST, when only 9% of the stations recorded precipitation. That is, rainfall occurring from the night to the early morning covers a relatively larger spatial scale while the coverage of afternoon precipitation is relatively limited. Although the spatial scale of afternoon rainfall is small, high rainfall amount can still be generated due to high intensity and frequency (Fig. 2). Such a kind of rainfall is likely to occur as local convective precipitation. As noted by Liao et al. (2007), due to the diurnal variation of solar heating, the lower atmosphere tends to reach an unstable state in the afternoon so that a little disturbance can trigger convective rainfall.

Figure 3 Diurnal variation in the mean spatial scale (%) of rainfall for the study area.

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Since Fig. 3 gives the mean number of stations recording rain simultaneously at each hour, some large-scale rainfall times may be smoothed out in the statistics. Therefore, to show the detailed diurnal variation characteristics of the rainfall spatial scale and to investigate differences in the rainfall with various spatial scales between Mount Tai and surrounding areas, the distribution of the rainfall amount and frequency with the change of spatial scale and diurnal phase is shown in Fig. 4. The x axis denotes the rainfall spatial scale, and the shaded area denotes the ratio of the cumulative rainfall amount (frequency) at different times and with different spatial scales to the total rainfall amount (frequency) for Mount Tai and surrounding areas. To draw a better comparison, the average of the surrounding stations is used for subsequent analysis. As is observed from the distribution of rainfall amount (Figs. 4a, c) for Mount Tai and surrounding areas, precipitation occurring in the afternoon and early morning can be distinguished by spatial scale: small-scale precipitation (with coverage less than 20%, left dashed line) tends to reach its peak in the afternoon, while large-scale precipitation mainly peaks from the night to early morning. Especially for precipitation with coverage of more than 60% (right dashed line), it usually reaches peak in the early morning. In the surrounding areas, large-scale, early morning precipitation contributes much more to their total rainfall amount than small-scale, afternoon precipitation does. However, for Mount Tai, in addition to rainfall occurring in the early morning, local rainfall occurring in the afternoon also accounts for a large proportion of precipitation. Further from the frequency distribution (Figs. 4b, d), it is seen that differences between Mount Tai and surrounding areas become more obvious. First, compared to surrounding areas, Mount Tai’s rainfall spatial scale is relatively smaller in the early morning when the rainfall coverage is mostly less than 60% while that for the surrounding areas can be more than 70% of the stations. In addition, no matter the proportion or the absolute value (omitted), the frequency of rainfall with small coverage (less than 20%) on Mount Tai is much higher than that of surrounding areas in the afternoon and at night. The unique, small-scale rainfall on Mount Tai has a certain contribution to the dual peaks of enhancement shown in Fig. 2b. Although both of them occur frequently, compared with nocturnal precipitation, the rainfall amount of afternoon precipitation is more significant.

Figure 4 Distributions of (a, c) rainfall amount and (b, d) frequency with change of spatial scale and diurnal phase. The x axis denotes the rainfall spatial scale (note: unequal spacing), and the shaded area denotes the ratio of the cumulative rainfall amount (frequency) at different times and with different spatial scales in relation to the total amount (frequency). The upper row refers to the average for Mount Tai, and the bottom row denotes that for surrounding areas. The dashed lines represent coverage ranges of 20% and 60%, respectively.

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To present more detailed characteristics and differences in rainfall evolution process between Mount Tai and its surrounding areas, we determined the time at which precipitation begins, ends, and peaks based on rainfall events at each station (the mean number of rainfall events is 957). Figure 5 shows the annual mean frequency at each hour of starting, ending, and peak of rainfall events on Mount Tai and in the surrounding areas. It can be observed that precipitation tends to be concentrated in the afternoon and early morning over Mount Tai and in surrounding areas. Specifically, the frequency distribution of the beginning time in surrounding areas (Fig. 5a) presents a smaller diurnal variation from the afternoon to the evening with a maximum at 1700–1800 LST in the afternoon and 0300 LST at night. For Mount Tai, the peak characteristics are clearer in that rainfall tends to start at 1600 and 0300 LST. Regarding the end time (Fig. 5b), both Mount Tai and the surrounding areas present clear peak characteristics. A dominant, early morning peak appears at approximately 0600 LST, and a second peak is found at 1800 LST in the surrounding areas; for Mount Tai, the frequency is roughly equivalent at 1800 and 0700 LST. It should be noted that rainfall over Mount Tai tends to end later in the early morning than rainfall in the surrounding areas. Both Mount Tai and the surrounding areas are prone to reaching their rainfall peak at 1700 LST in the afternoon, but for nocturnal rainfall, Mount Tai tends to reach its maximum 1 h earlier than that of surrounding areas (Fig. 5c).

Figure 5 The mean frequency at each hour of (a) beginning, (b) ending, and (c) peak of rainfall events for Mount Tai and surrounding areas.

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The asymmetry of the precipitation process is an important feature in describing the evolution of precipitation (Yu et al., 2013). Figure 6 presents the ratio of the rainfall frequency at each hour to that at peak time within 12 h before and after the peak of Mount Tai and in the surrounding areas. The rainy period before the peak refers to the number of hours from the beginning to the peak of a rainfall event, while the rainy period after the peak refers to the number of hours from the peak to the end of an event. According to Fig. 5c, rainfall events that reach their peak in the afternoon (1400–1800 LST) and from the evening to the early morning (2400–0700 LST) are centered on the peak time of each event (time zero). It is shown that nocturnal and afternoon rainfall present different degrees of asymmetry, which manifests as the rainfall frequency before the peak being much less than that after the peak. That is, a rainfall event tends to reach its peak over a short period of time and remains for a relatively long time after having reached its maximum. When comparing the asymmetry of these two types of rainfall events, Mount Tai and surrounding areas have roughly comparative asymmetry in the afternoon rainfall, as the frequency measured before the peak to that measured after the peak are 0.647 and 0.630, respectively. However, for the nocturnal rainfall events, Mount Tai shows more significant levels of asymmetry. The rainfall frequency measured before the peak to that measured after the peak is 0.619, while for surrounding areas, it is approximately 0.679. These results correspond with those shown in Fig. 5c, according to which Mount Tai tends to reach its maximum intensity faster, though rain falls at the same time as it does in surrounding areas at night.

Figure 6 The ratio of composed rainfall frequency before and after the rainfall peak to that of the peak time (time zero) for (a) afternoon rainfall events (1400–1800 LST) and (b) early morning rainfall events (2400–0700 LST). The red line with solid circles refers to the average for Mount Tai, and the black line with solid circles denotes that for the surrounding areas. The x axis refers to the 12-h period before (–) and after (+) the peak time.

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Figure 5 also shows that compared to that of the surrounding areas, rainfall of Mount Tai tends to start earlier in the afternoon while rainfall in both areas tends to end at 1800 LST. Nocturnal rainfall events over Mount Tai and in the surrounding areas tend to begin simultaneously while rainfall over Mount Tai ends later, showing that rainfall events over Mount Tai may last longer than those in the surrounding areas. As an important feature of rainfall, the duration is closely related to the nature and physical mechanisms of precipitation. The distributions of annual mean rainfall amount and frequency with change of duration and the diurnal phase are shown in Fig. 7. The results (Figs. 7a, c) show that rainfall occurring in the afternoon and early morning can be distinguished from one another in terms of their durations both for Mount Tai and the surrounding areas. For Mount Tai, rainfall with duration of less than 6 h reaches its peak at roughly 1600 LST in the afternoon, and a less pronounced second peak is observed at 0400 LST in the early morning. Rainfall events lasting more than 6 h tend to peak between 0400 and 0800 LST. In other words, short-duration rainfall events tend to reach a maximum in the afternoon, while long-duration rainfall events tend to peak in the early morning. This is consistent with the conclusion reached by Yu et al. (2007). Similar results are found for the surrounding areas, though the duration separating the rainfall which peaks in the afternoon and in the early morning is 4 h, shorter than that found for Mount Tai. In addition, we must note that nocturnal, long-duration rainfall events of Mount Tai make a larger contribution to total rainfall amount compared to that of surrounding areas (67.1% of the total precipitation over Mount Tai, 49% in surrounding areas).

Figure 7 Distributions of annual mean (a, c) rainfall amount (mm h−1) and (b, d) rainfall frequency with change of rainfall duration and diurnal phases. The upper row refers to Mount Tai and the bottom row refers to the surrounding areas.

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A further analysis of the distribution of rainfall frequency shows that (Figs. 7b, d) rainfall events occurring over Mount Tai and in surrounding areas mostly last less than 6 h (72.37% of the total frequency over Mount Tai, 71.8% in surrounding areas), and the distribution of frequency also presents the peak characteristics of afternoon and early morning. However, compared with surrounding areas, the frequency of rainfall events that last longer than 6 h over Mount Tai is higher, and this kind of rainfall occurs mostly in the early morning. Combined with the rainfall amount analysis, it can be seen that Mount Tai is more prone to having long-duration precipitation than its surrounding areas, especially in the early morning.

This provides us an inspiration to examine the cause of small-scale precipitation that occurs from the evening to the early morning over Mount Tai as shown in Fig. 4b. The raining hours with small coverage (less than 4%) from 2000 to 0700 LST were picked up. Figure 8 shows the distribution of these small-scale rainfall hours in precipitation events of different duration. As shown in Fig. 6, rainfall events are centered at the peak time of each event (time zero). For rainfall events of different durations, shaded values denote the ratio of the frequency at each hour within 12 h before and after the peak to the total frequency of small-scale rainfall in all events of the same duration. We can clearly see that small-scale rainfall tends to occur at the end of a rainfall event, and it becomes more obvious as the duration increases. This means that the precipitation events of Mount Tai tend to end with small coverage rainfall in this period. In addition, we also found that part of these small-scale rainfall hours (57.3%) belong to short-duration precipitation events (lasting 1–3 h), which have small coverage throughout the whole process.

Figure 8 Distribution of the proportion of small-scale rainfall hours in precipitation events of different durations. For rainfall events of different durations, the ratio is the composed frequency at each hour to that of small-scale rainfall in all events of this duration. The x axis is the same as that given in Fig. 6.

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Based on hourly rain gauge records for the warm season (May to September) of 1996–2015, differences in rainfall characteristics between Mount Tai and the surrounding areas are investigated in terms of rainfall diurnal variation, spatial scale, and evolution process. The main results are summarized as follows.

(1) Both Mount Tai and the surrounding areas tend to receive rainfall in the afternoon and early morning. Mount Tai exhibits a remarkable enhancement effect on precipitation. Rainfall amount, frequency, and intensity of Mount Tai are larger than those of the surrounding areas to varying degrees. The enhancement on rainfall amount produces dual peaks at 0400 LST in the early morning and 1400–1500 LST in the afternoon with a maximum of more than 80%. Although the peak time is slightly different, the diurnal variation of the enhancement on frequency and intensity also show dual peaks in the early morning and afternoon. Compared to intensity, abundant rainfall in Mount Tai is mainly affected by frequency. Furthermore, the diurnal phase of the rainfall amount in the surrounding areas lags 1 h behind that of Mount Tai.

(2) In terms of the rainfall spatial scale, the rainfall spatial scale in the afternoon is generally small. While from night to early morning, especially in the early morning, it is larger for both Mount Tai and the surrounding areas. The contributions of early morning, large-scale and afternoon, local precipitation to the respective total rain amount of Mount Tai and the surrounding areas are different. Compared to the surrounding areas, the rainfall spatial scale for Mount Tai is relatively smaller in the early morning (mainly with coverage of less than 60%), while precipitation with coverage of more than 70% accounts for a large proportion in the surrounding areas. In addition, Mount Tai tends to have a kind of unique precipitation at night and in the afternoon, which only covers a quite small range, and this kind of rainfall makes a certain contribution to the dual peak in frequency enhancement.

(3) Rainfall over Mount Tai tends to start at 1600 LST in the afternoon and 0300 LST at night, and tends to end at 1800 and 0700 LST. In comparison, rainfall in the surrounding areas is prone to starting later in the afternoon and ending earlier at night. Regarding peak time, the nocturnal rainfall of Mount Tai tends to reach its peak 1 h earlier than it does in the surrounding area. According to the analysis of the asymmetry of the precipitation process, Mount Tai and its surrounding areas have roughly equivalent asymmetry in the afternoon rainfall. However, for nocturnal rainfall, Mount Tai shows more significant signs of asymmetry than the surrounding areas. The nocturnal and afternoon rainfall can be distinguished in terms of duration for both Mount Tai and its surrounding areas. Short duration precipitation tends to peak in the afternoon, and long duration precipitation tends to peak in the early morning. In addition, rainfall events on Mount Tai are generally longer lasting, especially in the early morning.

This paper furthers our understanding of the precipitation characteristics of Mount Tai from multiple perspectives and reveals some scientific problems for further study. Differences in rainfall features observed between Mount Tai and the surrounding areas should be closely linked with its synoptic circulation. Among the conclusions we have drawn, the most significant difference between Mount Tai and its surroundings is that, the mountain has a remarkable enhancement effect on rainfall amount (higher than surroundings). Therefore, for the night and afternoon, we examined the differences in 850 hPa wind fields between moments at large and small enhancements based on hourly composite analysis. We consider the moment when hourly difference in rainfall amount between Mount Tai and surroundings is greater than 5 mm h⁻¹ as the moment of large enhancement and the moment at which this value is greater than or equal to 0 and less than 0.5 mm h⁻¹ as the moment of small enhancement. Figure 9 presents the preliminary statistical results of the wind field. All of the hours analyzed are the times that Mount Tai has rainfall. At night, when the difference of rainfall amount between the mountain and surrounding areas is not significant (Fig. 9c), compared to the wind field at hours with large rainfall enhancement (Fig. 9a), the proportion and wind speed of southwest winds decrease, and the frequency of other winds increases, especially southerly and southeast winds. In the afternoon, differences of winds between large and small rainfall enhancements are more obvious (Figs. 9b, d). Different from nocturnal situation, at moments when the rainfall enhancement is small in the afternoon, the south winds are replaced with southwest winds to become dominant with a frequency reaching up to 28%, followed by southwest winds. The proportion of southwesterly decreases to 18%, and its mean wind speed also reduces significantly (Fig. 9d). Therefore, in general, when the mountain has a large enhancement effect on rainfall, no matter in the afternoon or at night, the proportion of southwest winds is the highest and its mean wind speed is higher (Figs. 9a, b). However, by comparing these two conditions, we find that although the prevailing wind in the afternoon is still southwesterly, this comes with no absolute advantages due to the relatively higher proportion of southerly winds (Fig. 9b). These results indicate that when precipitation of Mount Tai is significantly enhanced, the corresponding wind field tends to be dominated by stronger southwesterly, while the wind field differs at night and in the afternoon.

Figure 9 The wind rose charts at 850 hPa for Mount Tai at hours of large enhancement (a) at night and (b) in the afternoon, and of small enhancement (c) at night and (d) in the afternoon. Each circle in the wind rose chart represents the percentage of time the wind blows from a particular direction. The mean wind speed is shown at the end of each directional line.

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The above results provide a preliminary background of the synoptic circulation that causes the differences of rainfall amount between Mount Tai and surrounding areas. Due to the small scale of the study area and the limited spatial resolution of the reanalysis data used, to obtain detailed circulation characteristics and to truly understand physical processes behind these differences in the Mount Tai area, high-resolution numerical experiments should be designed and carried out in future work. Furthermore, in addition to the circulation background, locally triggered convective precipitation over the mountain may also constitute an important cause of differences in rainfall characteristics observed in this area. As an isolated area of topography, Mount Tai is prone to severe local convective weather (Chen, 2000). From our results we find a kind of unique precipitation over Mount Tai that occurs in the afternoon with high frequency and intensity, which seems to be closely related to convection. Of course, these preliminary judgements are far from sufficient. It is necessary to examine the properties of this kind of precipitation and to explore the characteristics of triggering, evolution, and propagation of convective precipitation by combining data from radar and regional automatic stations with higher spatial resolutions.

Acknowledgments. The authors wish to thank Dr. Haoming Chen for his suggestions and the anonymous reviewers for their constructive comments.