1. Introduction
Understanding the characteristics of precipitation is fundamental in meteorology and hydrology. The temporal and spatial variation of rainfall could be important in deciding both the timing and the volume of rain transformed into runoff (Castro et al. 2009; Faurès et al. 1995; Obled et al. 1994). As one of the most fundamental modes of variability of the global climate system, the diurnal variation of rainfall allows us to better understand the characteristics of precipitation (Trenberth et al. 2003). In recent decades, with the appearance of multiyear hourly rainfall data, an increasing number of studies have focused on the diurnal cycle from which to improve the understanding of water cycle forcings and to serve as a benchmark for new representations in models (e.g., Carbone et al. 2002; Dai and Trenberth 2004; Sato et al. 2009; Wang et al. 2012; Xu and Zipser 2011; Yang and Slingo 2001; Yang and Smith 2008). As revealed by Yu et al. (2007b), diurnal variation of precipitation presents a distinctive geographical pattern during summer over contiguous China. Numerous studies have further investigated the diurnal variation of precipitation and its related features such as frequency, intensity, and duration over contiguous China, which have extended our understanding of the phenomena that underlie the diurnal cycle of rainfall in East Asia (Chen et al. 2012; He and Zhang 2010; Li et al. 2008b; Yin et al. 2011; Yu et al. 2007b, 2010; Zhou et al. 2008).
Despite the climatic features of rainfall diurnal patterns, it is essential to understand the characteristics of hourly rainfall events in detail. Yu et al. (2007a) discriminated the rainfall events with the duration time and proposed that the duration time can explain the inhomogeneous spatial variation of the diurnal cycle of dominant mechanisms. The short-duration rainfall events are dominated by afternoon peaks due to the development of the atmospheric boundary layer or the increasing sensible and latent heat flux from the surface induced by the solar heating. Factors behind the nocturnal peak of long-duration rainfall events are multiple, and the large-scale circulation is considered to play an important role (Chen et al. 2013; Chen et al. 2010; Huang and Chan 2011; Yuan et al. 2010, 2012). The classification of rainfall events also provides new insights for exploring the mechanisms of the decadal rainfall shifts over eastern China (Li et al. 2011).
Previous studies mainly focused on the spatial or temporal variability of hourly precipitation recorded by individual stations at a fixed location, while the space–time coherence of precipitation patterns is a heretofore unrecognized feature. Rainfall is an evolving process, and a recent study by Yu et al. (2013) found that evolution of most rainfall events is asymmetric, which means rainfall events usually reach the intensity maximum in a short period and then experience a relatively longer retreat to the end of the event. Since the variability of rainfall events in space and time are not independent of each other (Moron et al. 2010; Moseley et al. 2013; Soltani and Modarres 2006; Toews et al. 2009; Venugopal et al. 1999), for example, local rainfall (LR) events and regional rainfall (RR) events could show different characteristics, it is more valuable to investigate the coherent spatiotemporal evolution of different rainfall events.
LR events can be regarded as being from convective clouds with limited spatial and temporal scales, while RR events are regarded as being from frontal systems with larger spatial and temporal scales (Toews et al. 2009). Several methods have been applied to separate regional (stratiform) precipitation events from local (convective) precipitation and to investigate their effects on the hydrologic cycle as well as local weather and climate (Alfieri et al. 2008; McGinley et al. 1991). Venugopal et al. (1999) explored the existence of relationships that connect the rate of rainfall pattern evolution at small space and time scales to that at larger scales and pointed out that results are important for water management studies. By classifying the rainfall events into local and regional precipitation, Toews et al. (2009) suggested the different contributions of local and regional precipitation events to groundwater processes and mentioned the poor ability in predicting local precipitation in global climate models. However, the organizations and evolution of rainfall events in a given region have not been thoroughly studied before.
Understanding the spatiotemporal organization and evolution of rainfall at a certain scale is essential to comprehend the physical processes of precipitation and clouds. Physically, the local convection may occur randomly in a given area, and observations at an individual station may not catch the lifetime of the convection. The regional rainfall is usually in close relationship with the mesoscale systems or large-scale frontal systems. The longest reported duration of organized convective systems over the continent is associated with mesoscale convective complexes (MCCs; e.g., Laing and Fritsch 1997; Maddox 1980, 1983). Based on radar product data, Carbone et al. (2002) discovered a larger scale of dynamical organization marked by the coherent regeneration of rainfall systems and their systematic propagation eastward over distances of 500–2000 km and durations of 10–60 h over North America. They identified a coherence of warm season, continental precipitation on time and space scales greatly exceeding those of individual convective systems. Nevertheless, the detailed spatial–temporal evolution of the rainfall events related with MCCs or large-scale systems is not clear.
In this study, quality-controlled hourly rainfall records at eight well-distributed stations over the Beijing plain are used to analyze the spatial–temporal evolution of the regional rainfall events (RREs). The dataset resolves 50-km features at 1-h intervals, which provides both a detailed view of diurnal pattern of mesoscale rainfall systems and reliable statistics of events underlying these patterns. The rest of the paper is organized as follows. Section 2 describes the datasets and analysis methods. The intensity, duration characteristics of RREs, and the diurnal variation and evolution processes of intense long-duration RREs are presented in section 3. The concluding remarks are given in section 4.
2. Data and methods
Hourly rainfall records of eight stations over the Beijing plain (Fig. 1) in the warm seasons (May–October) of 2005–12 are used in this study. The hourly rain gauge data were obtained from the national climatic reference network and the national weather surface network. Hourly precipitation was automatically recorded by tipping-bucket rain gauges. The dataset was collected and quality controlled by the National Meteorological Information Center of the China Meteorological Administration.
The location of eight automatic stations (solid circles) in the Beijing plain. The color of the circles denotes the warm season (May–October) mean rainfall intensity at each station from 2005 to 2012 (bottom color bar; mm h−1). The shading indicates the height of topography (right color bar; m). The black contours are the borders of city of Beijing.
Citation: Journal of Hydrometeorology 16, 1; 10.1175/JHM-D-14-0086.1
The hourly rainfall records from N = 8 stations over the Beijing plain are composited to define the RRE. Universally, the composite should be suitable to any limited region with N ≥ 3 stations. For each hour t, the maximum record 
A regional rainfall coefficient (RRC) is defined to quantify the rainfall temporal variability in space. Both the 
The definition of RRE and RRC is further illustrated by a rainfall case from 2100 local solar time (LST) 19 July to 0900 LST 20 July 2011 (Fig. 2). The markers with different colors show the rainfall amount 
The observed hourly rainfall amount for a rainfall event from 2100 LST 19 Jul to 0900 LST 20 Jul 2011. The markers with different colors denote the rainfall intensity observed by each station. The red and purple dashed lines indicate Px and Pm, respectively; and the blue dotted line indicates the RRC (right y axis) at each hour in this event.
Citation: Journal of Hydrometeorology 16, 1; 10.1175/JHM-D-14-0086.1
The 
3. Results
a. The intensity, duration, and regional characteristics of RREs
The intensity and duration are two of the most important features of a rain event. The mean intensity and frequency of RREs as a function of hourly intensities are given in Fig. 3. The mean intensity of RREs, as calculated by the accumulated rainfall amount at all stations, increases with the hourly intensity distribution (Fig. 3a). The warm season mean frequency, as counted by occurrence time of the RREs, decreases with the increase in hourly rainfall intensity. For frequently occurring RREs with intensity no larger than the warm season mean of about 2 mm h−1 (Fig. 1), the 
The mean hourly intensity (line with solid circles) of RREs as a function of rainfall intensity (x axis; mm h−1) in the warm seasons during 2005–12. (b) As in (a), but for the mean frequency (line with solid circles, left y axis) and RRC (dotted line with open circles, right y axis) of rainfall events. The gray vertical sliver divides the rainfall events with intensity less than and greater than the warm season mean intensity as shown in Fig. 1.
Citation: Journal of Hydrometeorology 16, 1; 10.1175/JHM-D-14-0086.1
The mean intensity and maximum intensity of event (maximum rainfall between the beginning and the end of an RRE) with different duration hours are shown in Fig. 4a. The two lines show similar trends with the increase of duration. The warm season mean duration of RRE over the Beijing plain is 4.12 h. For the events with duration shorter than the mean duration hours, both of the mean and maximum rainfall amounts of the events increase with the prolonging of duration hours. For longer-lasting events, there is still an increasing trend but with a relatively large fluctuation, which is partly caused by the lower frequency of these events. As shown in Fig. 4b, the frequency of RREs decreases while the duration becomes longer. The 
(a) The mean (line with solid circles) and maximum (dotted line with open circles) rainfall intensity (mm) as a function of duration hours (x axis) in the warm seasons during 2005–12. (b) As in (a), but for the frequency of rainfall events (line with solid circles, left y axis) and the RRC (dotted line with open circles, right y axis). The gray vertical sliver divides the rainfall events with duration hour less than and greater than the warm season mean duration time.
Citation: Journal of Hydrometeorology 16, 1; 10.1175/JHM-D-14-0086.1
To further investigate the climatic characteristics of RREs with different 
The warm season mean frequency (line with solid circles, left y axis), intensity (dotted line with open circles, right y axis), and duration hours (dashed line with open squares, rightmost y axis) of RREs as a function of RRC. The x axis denotes RRC.
Citation: Journal of Hydrometeorology 16, 1; 10.1175/JHM-D-14-0086.1
The regional characteristics of RREs with different duration times are demonstrated by histograms of the frequencies and intensities in Fig. 6. The short-duration LR occurs more frequently while the long-duration RR contributes more to the total rainfall amount. Most of the RREs with duration shorter than 4 h show an LR feature with the 
Histograms of the warm season maximum rainfall intensity (color shaded), mean intensity (black contours), and frequency (blue dotted contours) of RREs for different duration hours (x axis) and RRCs (y axis).
Citation: Journal of Hydrometeorology 16, 1; 10.1175/JHM-D-14-0086.1
b. Diurnal variation and evolution of intense long-duration RREs
The diurnal variation of rainfall events at a single station has been extensively examined as it is an important aspect of regional climate. The normalized diurnal variations of rainfall frequency and intensity for RREs with different duration hours are shown in Fig. 7. To eliminate the influences of frequently occurring events with smaller intensities, only the intense RREs with peak amount larger than the warm season mean of 2 mm h−1 are analyzed in the following text. Consistent with previous studies using single-station records (Li et al. 2008a; Yu et al. 2007a), the rainfall occurring in late afternoon (1500–1900 LST) and overnight (2100–0600 LST) dominates the total rainfall over the Beijing plain. The late afternoon diurnal peaks are primarily caused by the rainfall lasting less than or equal to 8 h, and the late night to early morning peaks are primarily contributed by the rainfall lasting longer than 8 h. As the total rainfall amount is mainly caused by RR events with long duration (Fig. 6), the diurnal variation and evolution of RREs with duration longer than 8 h and intensity larger than 2 mm h−1 (hereafter referred to as intense long-duration RR) are further investigated in the subsequent discussions.
The diurnal variation of normalized rainfall intensity (shaded) and frequency (contours) of RREs with different duration hours. The x axis denotes the LST, while the y axis is duration hour.
Citation: Journal of Hydrometeorology 16, 1; 10.1175/JHM-D-14-0086.1
The diurnal variations of rainfall intensity and frequency of the intense long-duration RR are shown in Fig. 8. The rainfall amount shows two diurnal peaks, one peak at 2000 LST and a comparable peak at 0200 LST. The frequency is dominated by a midnight peak at 0200 LST, indicating that the early evening peak is mainly contributed by the intensity, while the midnight peak is largely contributed by the frequency. The diurnal curves of frequency of the peak hour, the beginning hour, and the ending hour of RREs are also shown to illustrate more details in the diurnal variations of these events. Similar to the diurnal variation of rainfall frequency, the occurrence frequency of peak hours also has a maximum in the midnight. The frequency of starting hour has two diurnal maxima. The most frequent time of occurrence for when the RREs start is in the early evening at 2100 LST, while a secondary peak occurs in the late afternoon at 1700 LST. It is also interesting that the ending hour occurs most frequently in the morning at 0700 LST, with the largest amplitude among these variables.
The diurnal variation of the normalized rainfall amount (black line with solid circles) and frequency (blue dashed line with open circles) of intense long-duration RRE, and the normalized occurrence frequency of these events with peak hour (green line with open squares), the beginning hour (orange dashed line with solid squares), and ending hour (red dotted line with solid triangles) at each LST. The x axis denotes LST.
Citation: Journal of Hydrometeorology 16, 1; 10.1175/JHM-D-14-0086.1
Yu et al. (2013) revealed the asymmetric rainfall process. To investigate the evolution of RREs, Fig. 9a shows the ratio of the rainfall frequency before and after the peak to that at the peak time as well as the evolution of 
(a) The ratio (%) of composed frequency (line with solid circles, left y axis) before and after the rainfall peak to that at the peak time (time zero) and corresponding evolution of RRC (dashed line with open squares, right y axis) for intense long-duration RR. (b) As in (a), but for the hourly maxima intensity among all stations (line with solid circles, left y axis; mm) and mean intensity of RREs averaged over all stations (dashed line with open squares, right y axis; mm).
Citation: Journal of Hydrometeorology 16, 1; 10.1175/JHM-D-14-0086.1
4. Conclusions and discussion
Using the hourly rain gauge data from eight well-distributed stations over the Beijing plain, a new method is introduced to define the RRE and to measure the spatiotemporal organization of rainfall systems in a given region. A new parameter RRC, which determines the spread of the rainfall events, is also defined to examine the regional spread of the events. The intensity, duration, and regional characteristics of RREs are analyzed to investigate the spatiotemporal organization of rainfall systems in the given region. The diurnal variation and evolution of intense RREs with long duration are further examined to demonstrate the evolution of events that largely contribute to the total rainfall in the region. The major conclusions are summarized as follows.
The intensity and duration of RRE generally increases with an increase in
The RREs with duration shorter than 4 h occur more frequently, but the longer-duration RREs contribute more to the warm season rainfall amount. The short-duration RREs usually reach the diurnal peak in the late afternoon, while the long-duration RREs tend to peak overnight.
Similar to the evolution of rainfall events observed at a single station, the evolution of intense long-duration RREs show some asymmetric tendency in both intensity and
This work provides a new method for studying spatiotemporal evolution of the rainfall events. It is worth noting that the conclusions above only present the spatiotemporal features of RRE over the Beijing plain, but the method introduced here should be independent of geophysical regions. We have also tested the method using different numbers of stations over the Beijing plain and in a larger region including the hillside stations surrounding the Beijing plain. The results show no evident differences. It is expected that the method will be further applied to inquire into the detailed features of regional rainfall systems in various climate regimes.
With an increasing amount of observations from climatic reference network and weather surface network, especially the observations from regional automatic stations, the observational networks are now available to sample phenomena in meso-β scale, which relates to the most significant weather affecting human activities. The method introduced here provides a new application to use these data to explore the rainfall characteristics. Physically, RRC represents the spatial spread of a rainfall evolution. For randomly occurring local convections, the RRC is small because of the limited spatial scale. When the convection develops and organizes to a mesoscale system that spreads a larger area, the RRC increases as the numerator increases in the equation. Meanwhile, after the convection begins to decay and large-scale stratiform rainfall appears, the RRC also increases as the rain uniformly covers a larger region.
By using rain gauge data in a limited region, this study quantifies the spatial and temporal variation of RREs over a given region. The evolution of different RREs corresponds to different cloud features. The LR is related with randomly triggered local convections, while the RR is more often associated with organized mesoscale systems or stratiform rainfall related with frontal systems. Since the individual station is in a fixed location, it cannot always observe the lifetime of rainfall systems that usually have large spatial and temporal variation. Further investigations into the characteristics of rainfall and cloud systems should take full advantage of the high-resolution satellite and radar data to gain more physical understandings. Previous studies using satellite data showed that precipitation associated with MCCs lingered past midnight, and the size grew in nocturnal hours (e.g., Chen et al. 2012; Ichikawa and Yasunari 2006). By applying the method to the satellite brightness temperature (BT) data, it is also found that the convection systems defined by the lowest BT in the region show similar evolution to the intense rainfall (figures omitted). The defined rainfall parameters in this study, along with satellite and radar data, will favor tracking organization and evolutions of rainfall systems (Feng et al. 2012) and understanding the different stages of the life cycle of rainfall systems.
The observational results will not only enrich our knowledge about the rainfall processes over a meso-β-scale range but will also provide new metrics for the evaluation of climate models. The simulation of precipitation is always a challenge issue in numerical models. Since precipitation by nature has large variability and low predictability at cloud-resolving scales, the skills of the model are largely affected by the representation of nonlinear cloud/precipitation physics. A commonly recognized deficiency is that the model tends to produce peak continental precipitation near noon, much earlier than observed (e.g., Dai 2006; Yuan et al. 2013). This is partly due to the premature triggering of deep convection and the absence of mesoscale organization, which extends the lifetime of convective systems beyond the decay time of individual convective events and prevents significant precipitation later in the day (Guichard et al. 2004; Rio et al. 2009; Del Genio et al. 2012). Therefore, the rainfall processes in the model need to be further examined. The evaluation of rainfall diurnal variation in the model can partly reflect the model ability, but it is more worthwhile to understand the details in the simulated organization and evolution of rainfall systems. The rainfall parameters introduced by this study should shed light on the evaluation of the local and regional features of rainfall systems and the discrimination of convection cells, MCCs, and stratiform rainfall in model simulations, which will further benefit the understanding of parameterizations of rainfall and cloud processes.
Acknowledgments
The authors gratefully acknowledge the anonymous referees whose valuable comments contributed a great deal to improving this paper. This research was jointly supported by the Outstanding Tutors for doctoral dissertations of S&T project in Beijing under Grant 20138005801 and National Natural Science Foundation of China under Grant 41221064.
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