Identification and Classification of Heavy Rainfall Areas and their Characteristic Features in Japan

We propose a new procedure for the objective identification and classification of heavy rainfall areas (HRAs) to advance the understanding of mesoscale convective systems (MCSs) in Japan. The distributions of accumulated precipitation amounts are evaluated from the radar/raingauge-analyzed precipitation amounts and characteristic features of HRAs are examined. The HRAs extracted during the warm seasons (April–November) in 2009 – 2018 are classified into four types (e.g., linear-stationary, linear, stationary, and others) based on their morphological features and temporal variations. HRAs are frequently observed on the Pacific sides of eastern and western Japan; 80 % of HRAs appeared from June to September and 60 % of the HRAs were observed in association with stationary fronts and tropical cyclones. Approximately 80 % of those HRAs of the linear-stationary type corresponded to typical elongated and stagnated MCSs, as suggested in previous studies.


Introduction
In various regions of Japan (Fig. 1), localized heavy rainfall events occur frequently during the warm season (e.g., Watanabe and Ogura 1987;Hirockawa and Kato 2012;Tsuguti and Kato 2014b;Kato et al. 2018;Sueki and Kajikawa 2019). Some of these events cause severe natural disasters, such as landslides, floods, and mudflows, which sometimes result in deaths and injuries. Such heavy rainfall is mostly brought by mesoscale convective systems (MCSs) that remain in nearly stationary for several hours. In this study, we discuss heavy rainfall events associated with MCSs that are classified as meso-β scale (Orlanski 1975). MCSs have various characteristic features in their configurations, movement speeds, and longevity. Many previous studies have revealed that the elongated and stagnated type of MCSs (ES-MCSs), which are usually called "senjo-kousuitai" in Japanese, are associated with localized heavy rainfall events in the Japanese Islands (e.g., Kato 1998Kato , 2006Yoshizaki et al. 2000;Hirota et al. 2016;Takasaki et al. 2019;Tsuguti et al. 2019). Kato (2020) suggested that ES-MCSs cause approximately half of localized heavy rainfall events as extracted by the method of Tsuguti and Kato (2014a, hereafter TK14a). Therefore, understanding the characteristic features of ES-MCSs is important not only for improving forecasting but also for preventing disasters; resolving these issues requires statistical classification of MCSs based on their configuration and longevity.
In the United States, many statistical studies to classify MCSs have been conducted using radar observations. Bluestein and Jain (1985) classified squall lines into four modes, namely broken line, back-building, broken areal, and embedded areal. Parker and Johnson (2000) identified three modes of linear MCS archetypes, based on the relative locations of stratiform precipitation to convection lines, namely, trailing stratiform (TS), leading stratiform (LS), and parallel stratiform (PS). They revealed differences in internal airflow structures, movement speeds, and longevity in the three modes of linear MCSs. Schumacher and Johnson (2005) added training line/adjoining stratiform and back-building/quasi-stationary categories to the classification of Parker and Johnson (2000). Gallus et al. (2008) classified MCSs into nine morphologies, consisting of three cellular types, five linear types, and a nonlinear type. The cellular types are divided into individual cells, clusters of cells, and broken squall lines. The linear types are the three modes defined in Parker and Johnson (2000) (e.g., TS, LS, and PS), squall lines with no stratiform precipitation, and bow echoes. Various other morphological classifications for MCSs have also been proposed in the United States (e.g., Jirak et al. 2003;Klimowski et al. 2004;Cohen et al. 2007;Corfidi et al. 2016;Miller and Mote 2017). Furthermore, similar classification studies have been conducted in other countries (e.g., Fragoso and Gomes 2008;Zheng et al. 2013;Mulder and Schultz 2015). These MCS classifications have contributed to understanding their structures, development mechanisms, and maintenance processes.
Meanwhile, there are fewer MCS classification studies in Japan than in overseas countries. Shimura et al. (2000) classified radar-observed MCSs into front formation, cells advection, and isolated cell types. Seko (2010) performed numerical simulations in addition to analyses of radar observations, to clarify the internal structures and maintenance mechanisms of elongated MCSs (E-MCSs) and classified them into three types, namely squall-line, back-building, and back-and side-building types. Unuma and Takemi (2016a, b; hereafter UT16a and UT16b) objectively identified quasi-stationary convective clusters (QSCCs) from radar observations to examine their horizontal scales and longevity. They clarified that the horizontal scales of QSCCs with circular shapes averaged approximately 20 km with a maximum of 72 km; 95 % of these QSCCs have lifetimes shorter than 60 minutes. Moreover, they showed that 87 % of QSCCs have aspect ratios greater than 1.4, thus suggesting that E-MCSs are dominant in Japan.
ES-MCSs produce band-shaped rainfall areas in the distributions of accumulated precipitation amounts and frequently lead to localized heavy rainfall events. Instead of the radar observations used in previous studies, TK14a utilized radar/raingauge -analyzed precipitation amounts (RAP, Nagata 2011), which are the hourly accumulated amounts produced by the Japan Meteorological Agency (JMA), to objectively extract localized heavy rainfall events in Japan. They demonstrated that approximately 60 % of the heavy rainfall events not directly related to tropical cyclones exhibit a band-shaped rainfall area that could be caused by ES-MCSs. Kato (2020) proposed the favorable occurrence conditions for band-shaped rainfall areas leading to localized heavy rainfall events, named "senjo-kousuitai". For further analysis of the relationships between MCSs and heavy rainfall areas (HRAs), effective procedures for objectively identifying and classifying HRAs must be developed.
Thus, the goal of this study is to propose procedures for objectively identifying and classifying HRAs by improving TK14a methods and statistically examining the characteristic features of the extracted HRAs in Japan. The proposed procedures for identifying and classifying HRAs use the distributions of accumulated precipitation amounts instead of snapshots from radar observations, which have been used conventionally in previous studies. In Section 2, the data and method-ology used in this study are described. The results of HRAs, identified and classified by the improved procedures, are provided in Section 3. Section 4 contains examples of HRAs, and the issues regarding the data and methodology are discussed in Section 5. Finally, the conclusions are summarized in final section.

Data
Three-hour accumulated RAP (RAP3) values, produced with one-hour intervals, are used to identify HRAs observed during the warm season (April-November) from 2009 to 2018. RAP is more accurate than radar observations because it is produced by calibrating radar observations with rain gauge observations. In this study, RAP is reconstructed with a resolution of 5 km (0.0625° × 0.05°) from finer resolution datasets using the method of Urita et al. (2011). In this study, using RAP with the coarse resolutions is based on the following two factors: (1) most meso-β scale (horizontal scale is 20 -200 km, as in Orlanski 1975) convective systems can be sufficiently resolved by 5 km grids and (2) since the operational resolution of RAP produced by the JMA has changed twice (e.g., 5 km: until February 2001, 2.5 km (0.03125° × 0.025°): March 2001 to February 2006, and 1 km (0.0125° × 0.00833°): from March 2006 to the present), homogeneous statistical studies can be performed over longer periods using reconstructed RAP data with the same resolution. The procedure for this reconstruction is shown in Fig. 2. Each grid with 5 km resolution consists of 30 segments with 1 km resolution (Fig. 2a) and of four segments with 2.5 km resolution (Fig. 2b). For the first step, the segments with 1 km resolution are converted to segments with 2.5 km resolution. Since each segment with 2.5 km Fig. 1. Topography (shading)  resolution contains six segments and three halfsegments with 1 km resolution, its value is computed by using the weighted mean, i.e., multiplying by a factor of 1.0 on the former and by a factor of 0.5 on the latter and then averaging the results. For the second step, each value of a grid with 5 km resolution is set to the maximum of the values of the four segments with 2.5 km resolution within the grid (Fig. 2c).

Identification of HRA candidates
Eight connected-component labeling (Samet and Tamminen 1988) is used to identify the HRA candidates. This labeling algorithm is one of the most fundamental operations in pattern recognition using binary images. In RAP3 binarization processing, an independent lump of RAP3 exceeding an arbitrary criterion is classified as an HRA candidate.
This study targets heavy rainfall events that occur several times a year in each grid. The RAP3 criteria for identifying HRA candidates are set from the climatological appearance frequencies based on this targeting. Figure 3 displays the distributions of the top 25 RAP3 during the warm season (April-November) from 2009 to 2018. The value of the top 25 RAP3 indicates the 0.04 percentile and corresponds to the frequency of heavy rainfall events occurring during one year at each grid. Values exceeding 100 mm (3h) −1 in RAP3 are found mainly in western Japan, whereas those values near 50 mm (3h) −1 are distributed widely in northern Japan. The criterion for identifying an HRA candidate is assumed to be 80 mm (3h) −1 from the climatological features of RAP3. This criterion could be too high for northern Japan, especially the Hokkaido district. In this study, a uniform criterion is employed for the sake of simplicity, although different criteria should be used to consider the regional variations in mean precipitation amounts. The validity and issues of this criterion will be discussed in Subsection 5.1. The other three criteria for identifying HRA candidates are defined as follows: (1) if the size of a rainfall area surrounded by 80 mm (3h) −1 is equal to or greater than 500 km 2 , which belongs to the meso-β scale defined by Orlanski (1975); (2) if there is one grid with precipitation amounts exceeding 100 mm (3h) −1 included in the rainfall area, and (3) if the rainfall area is located over land or off the coast (i.e., those regions surrounded by solid lines in Fig. 1). This procedure identified 4965 HRA candidates. It should be noted that the morphological features of HRA candidates are not considered in these identifying processes.

Aggregation of HRA candidates
The HRA candidates identified in the previous subsection are aggregated into identical events by checking their spatial and temporal continuities. The continuities of the HRA candidates are diagnosed objectively using an overlap ratio defined as follows: where A t and A t-dt denote the areas of an HRA candidate at an arbitrary time and at the previous hour, respectively. The denominator and numerator in Eq.
(1) indicate the union and intersection areas of A t and A t-dt , respectively. An example of the aggregation of HRA candidates is demonstrated in Fig. 4. The HRA candidates, oriented in a northwest-southeast direction, are identified at almost the same location for six hours .  the major/minor axis ratio (hereafter denoted as the aspect ratio) is 3.96; the area is 2891 km 2 ; and the persistent period is five hours. It should be noted that the morphological features of individual HRA candidates are not considered in this study. The aspect ratios are computed as the ratios of the lengths of the major to minor axes of the HRAs, which axes are determined using the following method, as shown in Fig. 4f: (1) the HRA is rotated clockwise from 0° and 180° by every 1°, (2) the length in the south-north direction between the southernmost and northernmost grids is measured for each degree of rotation, (3) the longest length is defined as the major axis and its rotation angle is viewed as the orientation of the HRA, and (4) the length in the east-west direction between the westernmost and easternmost grids at the rotation angle is defined as the minor axis. The HRA orientations are divided into the following four categories: south-north (0 -22° and 158 -180°), southwest-northeast (23 -67°), west-east (68 -112°), and northwest-southeast (113 -157°). Our aggregation procedure for HRA candidates is simple because the temporal and spatial continuities of the HRA candidates are considered simply, as mentioned above. To improve this procedure, comprehensive merging and splitting procedures of HRA candidates, as Shimizu and Uyeda (2012) proposed for convective cells, need to be introduced.

Classification of HRAs into four types
The HRAs extracted by the above-mentioned procedures possess the morphological features of RAP3 but cannot directly explain the physical features of MCSs, such as structures, development mechanisms, and maintenance processes. However, HRAs can almost be coincident with MCSs because such physical features can be considered indirectly through identification criteria, such as the aspect ratios, accumulated precipitation amounts, and overlap ratios. In this study, the HRAs are classified into four types from characteristic features of their configuration and stagnation: linear type, stationary type, linear-stationary type, and the other type.
The linear type corresponds to E-MCSs, and its morphological features are identified by the aspect ratios and areas of the HRAs. The criteria of aspect ratios and areas are set to be equal to, or greater than, 2.5 and 625 -12500 km 2 , respectively (Table 1). In previous studies of E-MCSs, the criteria for the aspect ratios is set to 3.0 (TK14a) and 1.4 (UT16b). Appropriate criteria, which depend on the structural characteristics and precipitation system mechanisms, need to be determined. The criterion for aspect ratios in this study is determined to be 2.5 from the distribution of their appearance frequencies, which is approximately equivalent to the median of the distribution (Fig. 5). Upper and lower limits of rainfall areas are imposed to exclude HRAs associated with meso-a scale or macro-scale (Orlanski 1975) systems, or convective systems, which are too small.
The stationary type corresponds to stagnated MCSs (S-MCSs) and its stagnation features are judged diagnostically, according to the overlap ratios and persistent periods. The criteria of overlap ratios and persistent periods are set to 50 % and five hours, respectively (Table 1). Both criteria are determined subjectively and the suitability of the criterion for persistent periods will be discussed in Subsection 5.1. UT16a evaluated the stagnation of QSCCs from motion vectors (under 10 m s −1 ) and overlap areas (greater than 1 km 2 ) of a time series of cloud clusters that were identified using the precipitation intensities that were estimated from radar observations. The linear-stationary type corresponds to ES-MCSs, which possesses the characteristics of both linear and stationary types. The other type does not belong to the above-mentioned three types.
Using the above classification, 167 HRAs are identified as being of the linear-stationary type, 844 of the linear type, 211 of the stationary type, and 1065 of the other type ( Table 2). The sum of HRAs (1011) of the linear-stationary and linear types, which is approximately 45 % of the total number of HRAs (2287), have linear morphological features. Although the rate of HRAs with linear morphological features is lower than the rate of TK14a (64 %), it becomes comparable if HRAs exhibiting the direct effects of tropical cyclones are excluded, as denoted in Subsection 3.4.

Contribution ratios of HRAs to the total
precipitation The contribution ratio of the precipitation amounts associated with HRAs to the total precipitation (CRH) is defined as an indicator of what degree of precipitation MCSs contribute to a rainfall event. The ratio is computed as follows: ordinate values indicate the aspect ratios and areas of HRAs, respectively. The red, blue, and green closed circles, and the open circles represent the linear-stationary, linear, stationary, and the other type, respectively. The bottom and right panels show the appearance frequencies of HRAs for the four types (histogram) in bins divided by the aspect ratios and areas, and the appearance numbers of the HRAs (pink solid lines). The color pattern of the histogram is the same as that of the scatter diagram.
where P HRAs and P total are the precipitation amounts associated with HRAs and total precipitation amounts, respectively. P HRAs is computed by integrating RAP within HRAs for the persistent periods. The durations of precipitation to compute P total are determined subjectively from the temporal evolution of precipitation within several hundred kilometers around the HRAs. We will conduct a statistical analysis of CRH features in the future because no procedures for determining the durations objectively to compute P total are developed in this study. The CRH can be also used as an indicator for diagnosing the structures and intensities of HRAs.

Results
The characteristic features of the extracted HRAs are examined in this section. First, the morphological features for the four classified HRA types are discussed. Figure 5 shows the distribution of their appearance frequencies in the aspect ratios and areas. It can be ascertained that the criterion for aspect ratios (2.5) corresponds approximately to the median of their distribution. HRAs with areas of 625 -1250 km 2 are identified most frequently at rates exceeding 40 %. HRAs satisfying the area criterion of 625 -12500 km 2 are approximately 90 % of the total HRAs. HRAs with larger aspect ratios tend to exhibit smaller areas, i.e., approximately 90 % of the HRAs with aspect ratios exceeding 2.5 exhibit areas smaller than 3500 km 2 . HRAs with larger areas tend to become stationary type whereas they tend to have nonlinear features. For example, approximately 60 % have stationary features, whereas approximately 30 % have linear features among those HRAs with areas exceeding 4000 km 2 .

Geographical characteristics
The geographical appearance characteristics of the four classified HRA types are examined in this subsection. Figures 6a -d show the distributions of the geographical appearance frequencies of the HRAs. These frequencies indicate the number of appearances of HRAs in each grid with 5 km resolution during the warm season (April-November) from 2009 to 2018. Figure 6e shows the configurations of HRAs of the linear-stationary type. The linear-stationary type is frequently concentrated in Kyushu Island, the Nansei Islands, Kii Peninsula, and on the Pacific sides of Shikoku Island, whereas fewer appearances are seen in northern Japan and the Sea of Japan sides of the Japanese Islands (Figs. 6a, e). These geographical characteristics are consistent with the results discussed in TK14a. The linear-stationary type is mainly oriented in the southwest-northeast and west-east directions (Fig. 6e), which is consistent with the features of QSCCs investigated by UT16b. These characteristics of the linear-stationary type, in their appearance frequencies and orientations, are similar to those of the linear type (Fig. 6b). The stationary type is concentrated in the Nansei Islands and on the Pacific sides of eastern and western Japan. It appears less frequently in northern Japan and on the Sea of Japan sides of the Japanese Islands (Fig. 6c). The distribution of the appearance frequencies of the stationary type is roughly similar to those of the linear-stationary and linear types, but their features for Kyushu Island are considerably different. High appearance frequencies are found in eastern and western Kyushu Island for the stationary and linear-stationary types, respectively. The high frequencies for the stationary type found in eastern Kyushu Island result from the fact that stagnated HRAs often occur associated with directly tropical cyclones (Fig. S2c), which is consistent with the appearance frequencies of localized HRAs, as demonstrated in TK14a. These distributions of appearance frequencies for the above-mentioned three types are consistent with those of the QSCCs, examined in UT16a and UT16b, and with the ES-MCSs provided in Kato (2020). The other type frequently appears widely in Japan, except in the Hokkaido district and the inland areas of central and northern Japan (Fig.  6d).
The high appearance frequencies of HRAs in western Japan could be produced by the continuous inflow of low-level warm and humid air that initiates, intensifies, and maintains convective activities with the help of terrain-induced updrafts (Fig. 1). In contrast, HRAs are extracted less often in the inland areas of central and northern Japan, especially in the Hokkaido district, where only four HRAs are extracted for the linear-stationary type (Fig. 6a, e). This could be because the criteria for identifying HRA candidates are unsuitable, as mentioned in Section 2. The suitability of the criteria and procedures for identifying HRA candidates will be discussed in Subsection 5.1. Table 3 shows the numbers of HRAs classified into the four types, and the data are divided into four regions (NORTH, EAST, WEST, and NANSEI-IS.; see Fig. 1 for their areas). It should be noted that the total numbers in Table 3 are inconsistent with those in Table 2 because HRAs crossing two regions are counted twice for each region. The numbers of HRAs for all types are the greatest in western Japan and the smallest numbers are in northern Japan, whereas the appearance frequencies show no significant regional differences for the HRA types (e.g., linear-stationary and stationary types: 5 -10 %, linear type: 30 -40 %, and the other type: approximately 50 %). These characteristics do not suggest that the favorable formation factors for each HRA type may be largely influenced by geographical effects. Figure 7a shows the yearly appearance frequencies of HRAs classified into four types. HRAs of each type appear at almost the same rate, except for 2010 and 2012. The linear type rate in 2010 and 2012 was approximately 50 %, which is 10 -20 % greater than the rates in other years. The total numbers of HRAs are larger in 2011 and 2018 and are the smallest in 2009. The yearly variations in the total number of HRAs could be related to annual rainfall amounts that are greater (the smallest) in 2011 and 2018 (2009) than to the climatology.

Temporal characteristics
The monthly appearance frequencies of HRAs are presented in Fig. 7b. The HRAs are concentrated from June to September and their number is 80 % of the total number during the warm season (April-November). The monthly frequency characteristics are comparable with those of TK14a, except for the frequency in June, which is considerably higher than that in TK14a. From August to October, the linear type rates (~ 30 %) are lower than those in the other months (~ 50 %), whereas the stationary type rates (~ 10 %) are higher than those from April to June (~ 5 %).

Characteristics of the precipitation amounts
The characteristics of the precipitation amounts for the four types are examined. Figure 8 shows the relationship between the maximum RAP3 and the maximum total accumulated precipitation amounts for the HRAs classified into four types. The maximum accumulated precipitation amounts in the HRAs is determined by the maximum value among the total precipitation amounts in the aggregated HRAs. HRAs of the linear-stationary and stationary types tend to have larger maximum RAP3 and total accumulated precipitation amounts than HRAs of the linear and other types. This indicates that stagnated MCSs increase not only in total precipitation amounts but also the maximum RAP3. However, examining the correlation between the stagnation of MCSs and the maximum RAP3 intensification is beyond the scope of this study.

Characteristics for synoptic fields
The appearance characteristics of HRAs for synoptic fields are examined. According to TK14a, synoptic fields are classified subjectively into six categories using surface weather maps produced by the JMA (Table 4): low pressure (LP), cold front (CF), stationary front (SF), direct precipitation associated with tropical cyclones (DTC), indirect precipitation associated with tropical cyclones (ITC), and no disturbances (ND). The classifications of synoptic fields are determined by the distances between the location with the maximum rainfall in HRAs and the corresponding disturbances, which are within 500 km but are within 200 km for CF and more than 500 km away and within 1500 km for ITC. When several synoptic disturbances exist on a surface weather map, the synoptic field is determined by priority order as follows: (1) DTC, (2) ITC, and (3) the closest disturbance (e.g., LP, CF, and   Figure 9 shows the appearance frequencies of the HRAs for synoptic fields. The rate of the sum of SF and DTC exceeds 60 %, whereas that of CF is below 5 %. The rates for LP and ITC are around 15 %. These synoptic field characteristics are consistent with those shown in TK14a as well as with the temporal characteristics. The rates for the linear-stationary type for LP, SF, and ITC (~ 10 %) are higher than those for the other synoptic field types (~ 5 %). The rates for the linear type for SF and CF (~ 50 %) are two times or higher than those for DTC (~ 20 %), while the rates for the stationary type for SF and CF (~ 6 %) are much lower than for DTC (~ 15 %). These characteristics indicate that HRAs associated with a stationary or cold front tend to be elongated, whereas HRAs which are associated directly with tropical cyclones tend to be spread out. The rate of linear HRAs with linear shapes, e.g., the linear-stationary and linear types, for SF and CF is approximately 60 % and is comparable to the results of shown by TK14a (64 %).
The monthly appearance frequencies of HRAs are examined for synoptic fields (Fig. 10). Higher frequencies are found in different months for synoptic fields, e.g., June and September for LP (Fig. 10a), June and July for SF (Fig. 10b), and August and September for DTC and ITC (Figs. 10c, d). The high frequencies seen in June and July for SF support the fact that heavy rainfall events often occur around the Baiu front, which is usually considered a stationary front during the rainy season in Japan (e.g., Ninomiya and Akiyama 1992;Yoshizaki et al. 2000;Kato and Aranami 2005;Kato 2006). The season with high DTC and ITC frequencies (August and September) corresponds to the periods when typhoons approach frequently and make landfall on the Japanese Islands (e.g., Aoki 1985).
The geographical appearance characteristics of HRAs of the linear-stationary type are also examined for synoptic fields. The locations and orientations of the linear-stationary type strongly depend on the synoptic fields. The linear-stationary type is found mostly on the western sides of Kyushu Island and on the Pacific sides of the Japanese Islands for LP, DTC,   9. Same as Fig. 7, but for the appearance frequencies for synoptic fields. LP is low pressure, CF is a cold front, SF is a stationary front, DTC is direct precipitation associated with tropical cyclones, ITC is indirect precipitation associated with tropical cyclones, and ND is no disturbances.
and ITC (Figs. 11a,c,d) and it is also found on Sea of Japan sides of the Japanese Islands for SF (Fig.  11b). However, the linear-stationary type (Fig. 11a) and the other three types (Figs. S1a, S2a, S3a) do not appear in the Nansei Islands for LP, which suggests that HRAs are generated infrequently in association with LP in subtropical regions where the baroclinicity is relatively weak. The geographical appearance characteristics of HRAs for LP, SF, and ITC are nearly the same for all four types (Figs. 11, S1 -S3). Meanwhile, the characteristics of HRAs for the linear-stationary and linear types for DTC (Figs. 11c, S1c) are different from the HRAs of the stationary and other types for DTC (Figs. S2c, S3c), i.e., the latter are distributed more broadly on the Pacific sides of eastern and western Japan than the former. Although the major HRA orientations of the linear-stationary type for SF are in the southwest-northeast or west-east directions, approximately 40 % of those for DTC trend in a southnorth direction. These characteristics suggest that the westerly or southwesterly inflow of warm and humid air contributes to the generation and orientation of HRAs having the linear-stationary type for SF and that southerly inflow contributes to those for DTC. UT16b showed that the shear direction (1000 -700 hPa) is related to the elongated QSCCs orientation. Statistical analyses of the relevant environmental properties for determining the HRA orientations remain in our future work.

Examples of HRA identification
Our proposed procedures are verified using several examples of extracted HRAs that are typical heavy rainfall events observed in Japan; the contribution of the HRAs to total precipitation is also examined using the CRHs defined in Subsection 2.5.

The July, 2009 Chugoku heavy rainfall event
A record-breaking heavy rainfall event with precipitation amounts over 700 mm was observed in the western Chugoku district on July 20 and 21, 2009. This event caused a disaster that led to 36 deaths and approximately 60 injuries. Figure 12 provides the distributions of the accumulated precipitation amounts related to the HRA, CRHs, and total precipitation amounts. This HRA is identified as the linear-stationary type; the aspect ratio, area, and persistent period are 3.02; 7949 km 2 ; and seven hours, respectively (Fig.  12a). The CRHs exceed 70 % in nearly all portions of the HRA; more than half have values over 90 %, and the maximum value reaches 98 % (Fig. 12b). These results indicate that the HRA of the linear-stationary type contributed to the heavy rainfall event significantly.

The October, 2010 Amami-Oshima Island heavy
rainfall event On October 20, 2010, a heavy rainfall event occurred on Amami-Oshima Island, causing many landslides and flash flooding that led to three deaths and two injuries. Areas of heavy rainfall exceeding 150 mm were nearly stagnant for more than six hours over the Amami-Oshima Islands (Tsuguti and Kato 2014b). The HRA is identified as the stationary type; the aspect ratio, area, and persistent period are 1.33; 3060 km 2 ; and 10 hours, respectively (Fig. 12c). The CRHs exceed 50 % in nearly all HRA regions, particularly on the western sides of the island, which exceed 70 %, and the maximum value reaches 84 % (Fig. 12d). The region of larger CRHs is consistent with heavy rainfall areas where strong convective systems stagnated for several hours, as investigated in Tsuguti and Kato (2014b).

The July, 2011 Niigata-Fukushima heavy rainfall
event The heavy rainfall in Niigata and Fukushima Prefectures, northern Japan on July 29 and 30, 2011 caused serious damage, such as dike breaks and landslides. The heavy rainfall was caused by several linear precipitation systems that are aggregated into five HRAs; two are linear-stationary, one is linear, and two are stationary. The Japan Meteorological Agency (2013) showed that some of the systems had a back-building formation type. A typical HRA of the linear-stationary type has an aspect ratio, area, and persistent period of 2.78; 3448 km 2 ; and 13 hours, respectively (Fig. 12e). CRHs in the HRA are distributed at around 30 -50 % with a maximum of 59 % (Fig. 12f), which are smaller than those in the 2009 event (Fig. 12b). The CRHs in the other four HRAs are also distributed at around 30 -50 % (not shown) and the contribution of each HRA to the total precipitation is rather modest in this event.

The August, 2014 heavy rainfall event in
Hiroshima Prefecture Extreme precipitation exceeding 100 mm h −1 occurred in Hiroshima Prefecture, western Japan, on August 20, 2014. This heavy rainfall triggered debris flows and landslides, causing 74 deaths and 44 injuries. Kato (2020) demonstrated that the heavy rainfall was caused by a quasi-stationary, band-shaped precipitation system with the formation of a back-building type, which occurred 200 -300 km south of a stationary front. An HRA of the linear-stationary type is identified from 00 JST to 05 JST (Fig. 12g). The aspect ratio, area, and persistent period of the HRA are 3.31; 1102 km 2 ; and five hours, respectively. CRHs exceed 70 % in nearly all HRA regions, and the maximum value reaches approximately 90 % (Fig. 12h). The high contribution of HRAs to the linear-stationary type in this heavy rainfall event is the same as the 2009 event (Fig. 12b).

The September 2015, Kanto-Tohoku heavy
rainfall event Heavy rainfall with 24 -hour accumulated precipitation amounts exceeding 500 mm was observed in the Kanto and Tohoku districts on September, 2015.
Many flash floods and inundations were associated with this heavy rainfall event, which led to 20 deaths and 82 injuries. The precipitation systems causing the heavy rainfall were generated in the synoptic field, sandwiched between Typhoons Kilo and Etau, and consisted of multiple ES-MCSs (Kitabatake et al. 2017; Wada et al. 2019). Two HRAs of the linearstationary type and 10 HRAs of the linear type are extracted in the Kanto and Tohoku districts. A typical HRA with a linear-stationary type identified in the Kanto district has an aspect ratio, area, and persistent period of 4.58; 3831 km 2 ; and nine hours, respectively (Fig. 12i). CRHs of the HRA are around 50 % and the maximum value reaches 60 % (Fig. 12j). The CRHs of other HRAs of the linear-stationary type identified in the Tohoku district are approximately 60 %, and the maximum value reaches 78 % (not shown). These CRH features are similar to those of the 2011 event ( Fig. 12f), which lasted for three days, similar to this event.
4.6 The July, 2017 northern Kyushu heavy rainfall event Heavy rainfall events occurred in northern Kyushu in July, 2017, causing multiple landslides and floods, which lead to 39 deaths, four missing, and 35 injuries. Linear precipitation systems stagnated for nine hours and caused a record-breaking hourly accumulated short-term rainfall amount of 129.5 mm (Kato et al. 2018). Although the precipitation systems were regarded as typical ES-MCSs, as suggested in Kato et al. (2018), our procedures indicate the HRA was a stationary type, not a linear-stationary type. The HRA has an aspect ratio, area, and persistent period of 2.13; 1751 km 2 ; and 10 hours, respectively (Fig. 13a). Among these parameters, only the aspect ratio of 2.13 does not satisfy the linear-stationary type criterion. This unintentional classification suggests that our proposed procedures need improvement, which will be discussed in Subsection 5.2. The CRHs exceed 70 % in nearly all HRA regions, and the maximum value reaches 85 % (Fig. 13b), which suggests the HRA contributed to this heavy rainfall event significantly.

Discussion
In this study, we propose objective procedures to extract HRAs and classify them into four types. Approximately 80 % of the ES-MCSs listed in Kato (2020) are identified as HRAs of the linear-stationary type by our procedures. However, several issues that will improve the procedures remain because some HRAs were not extracted or were identified incorrectly, as mentioned in previous sections. These issues and improvements to the procedures are discussed in this section.

Validity of HRA identification criteria
In Section 3, HRA candidates and HRAs were identified and extracted using the same criteria for all regions of Japan. As a result, HRAs are extracted less frequently in northern Japan, especially in the Hokkaido district, than in the other regions (Fig. 6) because the mean precipitation amounts are, climatologically, smaller in northern Japan. Considering that disasters can be caused by smaller precipitation amounts in northern Japan than in western Japan, we should pay attention to HRAs associated with lower precipitation amounts. Therefore, the criteria are modified while considering the regional characteristics of the HRAs. The three criteria used in this study are reduced by 20 -30 % as follows: (1) the configuration criterion is changed to 60 mm (3h) −1 , (2) the maximum RAP3 criterion is changed to 80 mm (3h) −1 , and (3) the criterion for the persistent period is changed to four hours. Figure 14 provides the distributions of the appearance frequencies of HRAs that are extracted using the reduced criteria. HRAs are extracted widely, even inland, and the appearance frequencies are several times higher than those extracted using the original criteria (Fig. 6). These reduced criteria are able to extract HRAs that are missed, especially in the Hokkaido district, whereas several HRAs are not identified correctly, i.e., the reduced criteria occasionally identify HRAs as a single area that is extracted separately as multiple areas by the original criteria (not shown). These discrepancies are especially significant in the Tohoku district but not in the Hokkaido district. These results suggest that different, region-dependent criteria settings could improve the extraction and identification of HRAs.
Since most ES-MCSs last for a few hours (e.g., Kato 2020), a persistence period of five hours, which is defined as the stationary type criterion in this study, may be unsuitable. HRAs lasting longer than five hours represent approximately 15 % of all 2287 HRAs. However, some of the persistence periods of HRAs are overestimated. These discrepancies occur when accumulated RAP is used to determine persistence periods. For example, the RAP3 periods that satisfied the criteria sometimes exceed five hours, even though significant large hourly values of RAP are observed for only two hours. Such overestimated periods are confirmed in approximately 10 % of the 167 HRAs of the linear-stationary type (not shown). Further evaluations of the persistent periods of HRAs require hourly RAP, instead of RAP3, because the hourly RAP should help with setting a more appropriate stationary type criterion.

Improvement in identifying HRAs
In the 2017 heavy rainfall event (Fig. 13), the proposed HRA procedures identified the HRAs as the stationary type although typical ES-MCSs were observed. In this subsection, the improvements for identifying HRAs of the linear-stationary type are examined using the 2017 event.
According to temporal variations in the radar observations, several precipitation systems causing heavy rainfall events, consisting of multiple MCSs which formed in the neighboring area at nearly the same time (not shown). Our HRA identification procedures might represent those multiple MCSs forming in the neighboring area as a single MCS. Therefore, detecting a more detailed temporal evolution of precipitation systems by using hourly RAP instead of RAP3 may improve our HRA identification procedures. Figure  13c shows the results of identifying and classifying HRAs with hourly RAP instead of RAP3. In this examination, the criteria for identifying HRAs are modified as follows: the configuration criteria and the maximum RAP were set 30 mm h −1 and 50 mm h −1 , respectively. The HRAs identified by hourly RAP is the same stationary type (aspect ratio: 2.00; area: 1941 km 2 ; and persistent period: five hours) as identified by RAP3. Therefore, in this heavy rainfall event, substituting hourly RAP for RAP3 contributed little to the improvement in identifying and classifying HRAs.
The improvements from using a higher spatial resolution of RAP is also examined. In identifying and classifying HRAs, hourly RAP with 1 km resolution (1km-RAP) is used instead of RAP with 5 km resolution (5km-RAP), and the above-modified identification criteria are used. The HRA is identified as the linear-stationary type, whose aspect ratio, area, and persistent period are 2.77; 1484 km 2 ; and five hours, respectively (Fig. 13d). To examine the general features of HRAs identified by RAP with higher spatial resolution, statistical analyses using 1km-RAP were conducted during the same period as those using RAP3 (not shown), which revealed the following features and issues. Applying RAP with higher spatial resolution can represent the morphological features of HRAs in more detail, which leads to a great enhancement of the aspect ratio, e.g., approximately 60 % of HRAs identified using 1km-RAP have larger aspect ratios than those identified by RAP3 with 5 km resolution. However, applying 1km-RAP sometimes fails to identify HRAs because of the reduced areas. Moreover, identifying HRAs with RAP with a higher spatial resolution has the following disadvantages: (1) the extracted HRAs become more complex structures and consequently, their morphological features cannot be represented simply by an aspect ratio and (2) statistical analyses cannot be performed over long periods because 1km-RAP has limited availability after April, 2006. Since the spatial resolution of RAP should be chosen for respective examination purposes, a 5 km resolution can be suitable for our proposed procedures for identifying and classifying HRAs.
The morphological features of HRAs depend on the aggregation procedures for HRA candidates. Thus, the morphological features of HRA candidates are com- pared with those of HRAs. The characteristics of the appearance frequencies of HRA candidates (Fig. 15) are similar to those of HRAs (Fig. 5). This suggests that HRAs contain nearly the same morphological features as HRA candidates. However, the morphological features can, sometimes, be modified by the aggregation processes for HRA candidates. For example, HRA candidates satisfying the linear type criteria (Table 1) are aggregated into 83 HRAs of the stationary type, including the 2017 heavy rainfall event (Fig.  13). Among eight HRA candidates in the 2017 event, three HRA candidates satisfy the linear type criteria.
Assessing the morphological features of not only HRAs, but also of individual HRA candidates, might be effective for more correct classifications. Such a classification procedure in which the features of HRA candidates are introduced could improve the accuracy of the current procedures without a higher spatial RAP resolution.

Conclusion
In this study, the procedures for identifying and classifying HRAs in Japan were developed, and their characteristic features were examined to advance the understanding of MCSs in Japan. The development and examinations were conducted using RAP3 during the warm season (April-November) from 2009 to 2018. HRAs were extracted based on their morphological features as follows: (1) identification of HRA candidates, (2) aggregation of HRA candidates, and (3) classification of HRAs into four types. By using the classification procedure, 167 extracted HRAs were identified as the linear-stationary type, 844 the linear type, 211 the stationary type, and 1065 the other type. Most HRAs of the linear-stationary type could be produced by ES-MCSs, e.g., approximately 80 % of the ES-MCSs listed in Kato (2020) produced HRAs of the linear-stationary type.
The characteristic features of HRAs were examined for four types. HRAs of the linear-stationary and linear types are concentrated in Kyushu Island, the Nansei Islands, Kii Peninsula, and on the Pacific sides of Shikoku Island; their orientations are dominated by the southwest-northeast and west-east directions.
HRAs of the stationary type frequently appeared in the Nansei Islands and along the Pacific sides of eastern and western Japan. The numbers of extracted HRAs for all types are much smaller in northern Japan than in other regions, especially the Hokkaido district. The rates of the appearance frequencies of HRAs for the four types are nearly the same in all regions although their identified numbers show significant regional differences.
The characteristics of the yearly and monthly HRA frequencies are addressed in the following. More HRAs are extracted for 2011 and 2018, and the fewest are extracted for 2009. HRAs of each type appear at nearly the same rates, except for 2010 and 2012 when HRAs are identified more frequently as the linear type than in other years. Around 80 % of HRAs are concentrated from June to September. From August to October, the rates of HRAs of the linear type (~ 30 %) are lower than the rates in other months (~ 50 %), while the rates of HRAs of the stationary type (~ 10 %) are higher than those from April to June (~ 5 %).
There are differences in appearance frequencies that are related to the precipitation amounts associated with HRAs for the four types. HRAs of the linearstationary and stationary types tended to have larger maximum RAP3 and total accumulated precipitation amounts than HRAs of the linear and other types. According to TK14a, the synoptic fields were classified subjectively into six categories: LP, CF, SF, DTC, ITC, and ND. The appearance frequencies of HRAs are over 60 % for the sum of SF and DTC, approximately 15 % for LP and ITC, and less than 5 % for CF. The HRA rates of the linear type for SF and CF (~ 50 %) are two times higher than that for DTC (~ 20 %), while the rates of the stationary type for SF and CF (~ 6 %) are much lower than that for DTC (~ 15 %). The HRA rates, which represent the sum of the linear-stationary and linear types for SF and CF, are approximately 60 %, which are consistent with the results of TK14a. The HRA monthly frequencies for synoptic fields show seasonal differences; higher frequencies are observed in June and September for LP, in June and July for SF, and in August and September for DTC and ITC. Most HRAs of the linear-stationary type for SF are oriented between the southwestnortheast and west-east directions, but approximately 40 % of those for DTC has south-north orientations.
In this study, most HRAs were reasonably identified and classified based on their morphological features, despite the simplified procedures, in which uniform criteria were applied for all regions. The CRH proposed in this study can be used as an additional index of the HRA features. The procedures for identifying and classifying HRAs may be applicable to heavy rainfall events, not only in Japan but also in other countries. However, since some HRAs were classified incorrectly, our identification procedures need further improvement. Moreover, the structures, development mechanisms, and maintenance processes of HRAs should be introduced into the procedures. These improvements in future studies are expected to advance the understanding of the characteristic features of MCSs, causing heavy rainfall events.

Supplements
Figures S1, S2, and S3 display the distributions of the geographical appearance frequencies for HRAs of the linear, stationary, and other types classified for synoptic fields. Figure S1: Distributions of the geographical appearance frequencies for HRAs of the linear type classified for synoptic fields, (a) LP, (b) SF, (c) DTC, and (d) ITC. Figure S2: Same as Fig. S1, but for the distributions of HRAs of the stationary type. Figure S3: Same as Fig. S1, but for the distributions of HRAs of the other type.