In this study, a regional rainfall event (RRE) is defined by observed rainfall at multiple, well-distributed stations in a given area. Meanwhile, a regional rainfall coefficient (RRC), which could be used to classify local rain (LR) and regional rain (RR) in the given area, is defined to quantify the spatiotemporal variation of rainfall events. As a key parameter describing the spread of rainfall, RRC, together with duration and intensity, presents an effort to explore more complete spatiotemporal organization and evolution of RREs. Preliminary analyses of RREs over the Beijing plain reveal new, interesting characteristics of rainfall. The RRC of RRE increases with longer duration and stronger intensity. Most of the RREs with maximum peak rainfall intensity below 2 mm h−1 or duration shorter than 3 h have RRC less than 0.4, indicating that these events are not uniformly spread over the region. Thus, they are reasonably classified into LR. RREs with RRC above 0.5 could be classified into RR, which usually lasts longer than 4 h and has primary peak rainfall occurring from 1700 to 0600 LST. For most of the intense long-duration RR, evolutions of RRC and rainfall intensity are not consistent. The RRC reaches a maximum a few hours after the peak intensity was reached. The results of this study enrich the understanding of rainfall processes and provide new insight into understanding and quantifying the space–time characteristics of rainfall. These findings have great potential to further evaluate cloud and precipitation physics as well as their parameterizations in numerical models.
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 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 is defined, where is the measurable rainfall (≥0.1 mm h−1) at the station i. The time series of are then used to represent the rainfall intensity at hour t over the selected region. The hourly mean rainfall intensity at each hour t is also calculated. The results using the time series of show no significant differences with those using , as presented below. Using the time series of , the RREs are then classified according to their durations without any intermittence or at most 1-h intermittence during a single rainfall event following Yu et al. (2007a).
A regional rainfall coefficient (RRC) is defined to quantify the rainfall temporal variability in space. Both the for each hour rainfall occurred and for each RRE is defined. For each hour of the RRE with measurable rainfall (from the beginning hour t1 to end hour t2), the rainfall amount (i = 1, N) at each hour t is reordered from largest to smallest , that is, , then the is defined by , where , N is the number of stations, and is the number of stations that observed rainfall at the hour t. The first item of the RRC equation includes the distribution of rainfall intensity at stations that observed rainfall. As is a monotonically decreasing permutation, the first item of the equation implies that if more than half of the stations observe rainfall intensity that is larger than the mean intensity in the region, then the could be large and could indicate a regional feature of the event. The second item of the equation involves the number of stations that can be regarded as rainfall area. The is calculated based on the accumulated rainfall amount of the event e instead of in defining , and .
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 at N = 8 stations at each hour. The and are presented by red and purple dashed lines, respectively. The time series of and are highly correlated and show similar trends of evolution despite the magnitude. As shown in the figure, when the time series of is used to define RRE, the threshold of more than 1-h intermittence between two events is reasonable, because the RRE is very likely to cease when no rainfall occurs at all stations in the selected region. Consistent with Yu et al. (2013), the temporal evolution of rainfall is asymmetric at individual stations, especially at the stations that observe intense rainfall. For example, the rain at the station marked by orange rhombuses starts at 0200 LST and quickly reaches the peak intensity 2 h after it begins. The rainfall intensity then relatively slowly decreases and the rain ceases at 0800 LST, 4 h after its peak. Similar situations are also obvious at stations marked by blue squares, red triangles, and red pentagrams. The evolution of also shows some asymmetric trends. From 0300 to 0400 LST, the intensity of RRE defined by increases and reaches the peak 26.6 mm h−1 within 1 h, while it decreases and reaches 2.8 mm h−1 after 3 h.
The of the event is 0.63, indicating that it is a regional rainfall event. The value of also corresponds to the figure that more than half of the stations observe rainfall during most hours during the selected period. To demonstrate the temporal evolution of the spatial feature, the is also shown in Fig. 2 by the blue dotted line. Generally, well represents the spatial spread of a rainfall event. From the beginning of the RRE, the rainfall occurs at only one station (2100–2300 LST) so the is 0. The RRC increases when the rainfall spreads to more stations and reaches the maximum at 0600 LST, 2 h later than the peak of , implying the organization of convection systems or development of widespread stratiform rainfall after the decay of strong local convection. Coherent with the equation, the defined here not only indicates the spatial spread of rainfall system, but also reflects the uniformity of rainfall system. For example, when the intensity of RRE reaches the peak at 0400 LST, the rainfall occurs at seven stations simultaneously with the intensity unevenly spreading. The largest intensity reaches 33.1 mm h−1 only at one station, while the intensity is less than 3 mm h−1 at four stations. Five out of seven stations observe rainfall smaller than the mean intensity mm h−1, resulting in an of only 0.4 in this situation.
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 is smaller than 0.4, indicating that the rainfall covers no more than half of the stations in the given region, or the rainfall intensity at more than half of the stations is smaller than the mean intensity , which is more likely to be caused by a local convection. The RREs with intensity larger than 2 mm h−1 occur less frequently, but the mean intensity is much larger and the of these events are generally larger than 0.4, indicating that the rain covers most of the stations and spreads uniformly over the region, which can be regarded as RR.
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 increases dramatically for the RREs lasting less than 5 h. For the RREs lasting longer than 4 h, the is larger than 0.5, indicating that the most of the RR is characterized by long duration.
To further investigate the climatic characteristics of RREs with different , Fig. 5 shows the variation of frequency, intensity, and duration time of RREs with . For LR events with smaller than 0.4, the frequencies are larger than 10%, while for RR events with larger than 0.5, the frequencies of different events show smaller variances with the increase of . The mean intensity of most of the LR is less than 2 mm h−1, and it increases quickly with the . Similarly, LR shows a mean duration not longer than 4 h, while the duration time becomes longer for the events that occur at more than half of the stations or that are uniformly spread over the region.
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 smaller than 0.4, and less than 20% of these events have larger than 0.5. The RREs with larger than 0.4 tend to last longer, and most of the rainfall amounts of these events are contributed by RREs with larger than 0.6, which is consistent with the above results that most of the RR is characterized by long-duration events with large intensity. It is noted that few RREs lasting longer than 8 h have less than 0.4.
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 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.
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 . Consistent with the results from a rainfall case shown in Fig. 2, the composite of RREs show some asymmetric trend before and after the peak time (time zero). The frequency before the peak is slightly smaller than that after the peak. The frequency of RRE reaches maximum and persists for several hours after it begins to decrease. The composite increases before the peak intensity is reached. It is interesting to note that the peak hour of is 1 h later than that of frequency, indicating that most RREs uniformly spread to more stations after reaching the peak. The lag of the may imply the extension of the convection system to stratiform rainfall after its peak. Similar to the results from individual stations, both the maximum intensity of the intense long-duration RR and the mean intensity are quite prominent at the peak time and increase (decreases) rapidly before (after) the peak.
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 . For the RREs with intensity less than 2 mm h−1 or duration shorter than 3 h, the RRC is generally less than 0.4, indicating that these events usually occur locally and can be regarded as LR. Most of the intense and long-duration RREs have a greater than 0.5, implying that these events are usually controlled by regional rainfall systems.
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 . The reaches the maximum at one or more hours after the time when peak intensity occurs.
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.
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.