1. Introduction
Accumulative rainfall amounts of more than 250 mm in a day, i.e., severe rainstorms, may lead to devastating disasters, such as floods and landslides, which pose huge threats to human beings. For instance, a severe rainstorm hit Henan Province of China on 10–23 July 2021, causing large-scale urban waterlogging, 302 deaths, and 50 missing (Deng et al. 2022). Typhoon Bilis induced severe rainstorms in southern China in July 2006, which caused serious floods in low-lying areas and the evacuation of over 3 million people (Gao et al. 2009). It is necessary to respond promptly to these severe rainstorms to prevent derived disasters. The spatial variability and spatial correlation distance can provide valuable information for predicting likely flooding scenarios and further preventing rainstorm-induced hazards (Gao et al. 2017a; Shafiei et al. 2014).
Spatial variability is the intrinsic characteristic of regional variables such as rainfall (Western et al. 2001). Spatial correlation varying with the distance between two points can be adopted as an indicator to quantify the spatial variability of regional variables (Journel and Huijbregts 1976; Chang et al. 2005; Ochoa-Rodriguez et al. 2015; ten Veldhuis et al. 2018). The spatial correlation distance can be quantified using different methods. For example, Western et al. (2001) adopted connectivity functions to identify the spatial features of soil moisture and synthetic aquifer conductivity. Han et al. (2020) introduced relative connectivity based on an empirical copulas method to measure the joint spatial dependence of extreme rainfall events. Israelsson et al. (2020) computed the co-occurrence probability of rain–rain events and detected the spatial ranges of rainfall with different intensities. Zhuang et al. (2020) employed Moran’s I, local indicators of spatial association, and semivariance to identify the multiscale spatial variability of 3-h extreme rainfall events in four megacities in China. Other methods, such as variograms (Germann and Joss 2001), entropy (Knudby and Carrera 2005), Eulerian and Lagrangian correlation (May and Julien 1998), an index computed using conditional probabilities (Kursinski and Mullen 2008), and a bivariate framework based on copula theory and stochastic storm transposition (Zhuang et al. 2022) also can be used to portray the spatial variability of regional variables.
Spatial correlation distance of rainfall in different duration, intensities, and geographical locations was quantified using these methods. For instance, daily extreme rainfall events over the eastern United States range between 200 and 400 km spatially (Touma et al. 2018) while 2-day heavy rainfall events in the same region have a spatial extent ranging between 0.25 × 104 and 50 × 104 km2 (Konrad 2001). Israelsson et al. (2020) detected the spatial ranges of rainfall with different intensities in Ghana and found a shorter range of rainfall with low intensity. Moreover, spatial variability of rainfall amounts also depends on different weather systems such as tropical cyclone– and nontropical cyclone– (TC and NTC) associated weather systems (Panthou et al. 2014; Gao et al. 2017b). For instance, the spatial scales of heavy mei-yu precipitation [precipitation in June and July over southeast China (SEC)] events associated with mei-yu front (NTC-associated weather system) in eastern China were identified with an average length, width, and extent of approximately 1400 km, 500 km, and 40 × 104 km2, respectively (Du et al. 2020). The spatial correlation length of three severe rainstorms induced by troughs of low pressure in Hong Kong ranges from 5 to 30 km (Gao et al. 2017b). It can be concluded that the spatial correlation distance of rainfall varies significantly with its duration, intensity, geographical location, and weather systems.
The underlying reasons for varying spatial variability of rainfall under the background of climate change have been investigated by previous studies (e.g., Nam et al. 2016; Chen et al. 2021). The increasing global temperature may reduce the spatial extent of extreme rainstorms or rainstorms in the United States (Guinard et al. 2015; Chang et al. 2016) and Australia (Wasko et al. 2016). Moreover, the large-scale low-frequency climatic anomalies also potentially impact the spatial variability of rainfall. For example, Han et al. (2020) found that the spatial dependence of extreme rainfall in Australia increases during both El Niño and La Niña periods. A lot of efforts have been contributed to investigating the spatial variability of extreme rainfall in different regions in response to rising temperatures and low-frequency climatic anomalies, but it is unclear how these factors affect the spatial variability of severe rainstorms in China.
SEC has complicated weather systems associated with tropical cyclones and nontropical cyclones, which often lead to different types of severe rainstorms. However, previous studies mainly focused on the spatial structure of one type of severe rainstorm, resulting in unclear features of the spatial structure of other types of severe rainstorms. However, the statistical characteristics of the spatial structure of long-term severe rainstorms over SEC are rarely studied, leading to the incomplete and insufficient disclosure of the spatial variability of severe rainstorms in the study area. Environmental or geographical factors such as temperature, elevation, latitude, and longitude are reported to be associated with rainfall, but there are few discussions on the impact of these factors on the spatial structure of severe rainstorms over SEC.
Therefore, to fill the aforementioned research gaps, this study aims to comprehensively reveal the characteristics of the spatial structure of different types of long-term severe rainstorms over SEC. To detect the statistical features of the spatial correlation distances of severe rainstorms under different weather systems, severe rainstorms during 2000–19 over SEC are classified into TC- and NTC-induced severe rainstorms (TCSRs and NTCSRs). The spatial structure of TCSRs and NTCSRs is interpreted by co-occurrence probability and spatial correlation distance using semivariograms. The effects of location (latitude and longitude), temperature, elevation, La Niña/El Niño, and Indian Ocean dipole (IOD) on the spatial correlation distance of TCSRs and NTCSRs are discussed in this study. This study also discusses the impact of the radius of maximum wind on the spatial correlation distance of TCSRs over SEC.
2. Study area and data
a. Study area
SEC covers a region with longitudes from 105° to 125°E and latitudes from 15° to 35°N, as shown in Fig. 1. It has a long coastline enclosed by the South China Sea and the East China Sea as well as complex river networks (Fig. 1b). Elevation ranges from 0 to 4885 m, and the high altitudes are mainly distributed in the northwest of SEC. SEC is dominated by a subtropical monsoon climate, leading to warm winters and hot summers. Rainfall and temperature share a similar spatial distribution in this region with high values in the southeast while low values in the northwest. SEC has experienced rapid economic development in the past decades. Severe rainfall is very likely to cause flood and landslide hazards in this region, posing high risks to infrastructures and human lives.
(a) Location and (b) terrain of the study area.
Citation: Journal of Hydrometeorology 24, 10; 10.1175/JHM-D-22-0145.1
b. Data
The near-real-time Late Run version 6 of IMERG precipitation product during 2000–19 is used. The IMERG precipitation datasets can be freely accessed from the Goddard Earth Sciences Data and Information Services Center (GES DISC; https://disc.gsfc.nasa.gov/) since 2000. The dataset is in a raster format, and its spatial and temporal resolutions are 0.1° and 30 min, respectively. IMERG precipitation product has a near-global coverage and is developed by intercalibrating, merging, and interpolating multiple satellite estimates combined with gauge observations (Huffman et al. 2019). To keep consistency with daily gauge-based data in UTC + 8 h, daily IMERG data in UTC + 0 h are adjusted to local time.
Daily data measured at rain gauges from the period of 2000–19 are adopted in this study. They can be accessed from the China Meteorological Data Service Center (CMDSC) which controls the quality of this dataset. Other information including the location, daily mean temperature, and elevation of a gauge is also recorded in this dataset. Two-minute mean maximum sustained wind near the TC center and latitude (°) of the TC center in the TC track dataset available from China Meteorological Administration (CMA) Tropical Cyclone Center (Ying et al. 2014; Lu et al. 2021) are used. The data in UTC + 0 h are converted into those in Beijing time. The data are mainly used to compute the radius of maximum wind (RMW) according to the formula proposed by Willoughby and Rahn (2004).
The monthly ENSO index (La Niña and El Niño) is derived from the 3-month running mean of sea surface temperature anomalies in the region ranging between 120°–170°W and 5°S–5°N. It can be accessed from Climate Prediction Center (https://origin.cpc.ncep.noaa.gov/products/analysis_monitoring/ensostuff/ONI_v5.php). An El Niño episode is defined as an index above +0.5°, and a La Niña episode is determined when the index is less than −0.5°. The monthly IOD index is measured using the dipole mode index (DMI) and was defined by Saji and Yamagata (2003). According to Reddy et al. (2021), IOD can be classified into positive IOD (hereafter referred to as +IOD) events, neutral IOD events, and negative IOD (hereafter referred to as −IOD) events. Positive IOD events are defined as more than 0.5 standard deviations of the mean DMI from September to November. Accordingly, −IOD events are defined as less than −0.5 standard deviations of the mean DMI from September to November. The other IOD events are defined as neutral IOD events.
3. Methodology
a. Classification of TCSRs and NTCSRs
Figure 2 demonstrates the flowchart for characterizing the spatial correlations of severe rainstorms over SEC, in which severe rainstorms are categorized as TCSRs and NTCSRs. According to CMA, a severe rainstorm is defined as 24-h accumulative rainfall amounts of more than 250 mm at one gauge. A TCSR is recognized in the location where a TC has an influence (Li and Zhou 2015; Zhang et al. 2018). The area impacted by a TC is usually determined by the radius of this TC ranging from 200 to 1000 km. According to the report from Zhang et al. (2018), notable decreasing rainfall occurs when the radius is more than 500 km. Therefore, when the distance between the location of a severe rainstorm and a TC center is less than 500 km, this severe rainstorm is defined as a TCSR. Conversely, a severe rainstorm occurs out of the distance or when no TCs occur, this rainstorm is defined as an NTCSR. Note that if more than one rainfall amount (>250 mm day−1) was recorded at gauges during one day over SEC, the maximum rainfall amount was selected as the rainstorm center during this period. A radius of 500 km is then used to determine which other rainfall amounts will be included in the scope. Therefore, it is possible for more than one gauge to record rainfall amounts exceeding 250 mm day−1 in a single severe rainstorm.
Flowchart for characterizing the spatial correlations of severe rainstorms over SEC.
Citation: Journal of Hydrometeorology 24, 10; 10.1175/JHM-D-22-0145.1
Using sparse gauge-based rainfall data may lead to inaccurate spatial correlations of rainstorms. According to the evaluation of IMERG product, the ability of this product to capture the daily rainfall amount of more than 250 mm is relatively weak compared to gauge-based rainfall data. However, IMERG-based data have a spatial resolution of 0.1° × 0.1°, which is finer than that of gauge-based rainfall data. Moreover, Zhou et al. (2022) reported that daily IMERG-based data are highly correlated with gauge-based rainfall data with average correlation coefficients (CCs) of approximately 0.72 during 2014 and 2017 over SEC. Tang et al. (2020) evaluated the performance of IMERG-based data at daily and hourly scales between 2000 and 2018 in China and concluded that they have a better consistency with gauge-based data compared to the other nine satellite-based rainfall products. It also proves that IMERG-based data can capture the characteristics of the spatial distribution of gauge-based rainfall data. Hence, in this study, a scheme based on the gauge-satellite network is designed to avoid the possibility of inaccurate correlations due to sparse rain gauges. First, select a rainfall amount (>250 mm day−1) recorded at a gauge in one day over SEC, and then determine the location of this gauge. Second, select an area circled with a specific radius and centered at the location of this selected gauge. According to Du et al. (2020), the spatial extent of extreme mei-yu precipitation events (precipitation lasting more than 3 days with 50 mm day−1 over the specific region) over eastern China was determined as 40 × 104 km2. If the spatial extent is a circle, the radius is about 356 km. Touma et al. (2018) concluded that extreme daily precipitation events over the eastern United States had a spatial length ranging from 200 to 400 km. Hence, a longer length of 500 km is determined as the specific radius to include all the possible related rainfall data pairs with more than 250 mm day−1 over SEC. Finally, in the specific area, select the daily IMERG-based rainfall data that are defined as severe rainstorm events and then compute their spatial correlation.
b. Co-occurrence probability of rain–rain events
Co-occurrence probability of rain–rain events was proposed by Israelsson et al. (2020), which is applied to detect the spatial correlations of rainfall events with different intensities. It can intuitively quantify the cluster of one severe rainstorm with extreme rainfall amounts (>250 mm day−1). For all the gridded rainfall amounts in the space within a 500-km range centered at the location of the gauge-based severe rainstorm, if the daily rainfall amount is more than 250 mm at one gauge in the prescribed area, the corresponding grid box is assigned to 1. Use Xm×n to stand for all rainfall amounts in the prescribed area as shown in Fig. 3a. Suppose there are M rainfall amounts (>250 mm day−1) in Xm×n and then there are M grid boxes with 1. Compute all the distances between the M grid boxes and the other grid boxes, and then classify the distances into 16 groups at intervals of 50 km. That is, the distance bins are 0–50, 51–100, 101–150, 151–200, 201–250, 251–300, 301–350, 351–400, 401–450, 451–500, 501–550, 551–600, 601–650, 651–700, 701–750, and 751–800 km, respectively. Take Xm×n in Fig. 3 for an example. There are M × (m × n − 1) distance values that fall into these distance bins. In each distance category, the ratio of grid boxes assigned to 1 is calculated (Fig. 3b). The ratio is defined as the co-occurrence probability of rainfall. There are M co-occurrence probabilities in each distance bin. To identify the most accurate spatial correlation, the maximum of M co-occurrence probabilities in each distance bin is selected in this study.
The sketch map of (a)
Citation: Journal of Hydrometeorology 24, 10; 10.1175/JHM-D-22-0145.1
c. Semivariogram
In practice, the exponential model
According to previous studies (e.g., Eriksson and Siska 2000; Oliveira et al. 2022), if the semivariogram only changes with h, it is called an isotropic semivariogram; otherwise, it is defined as an anisotropic semivariogram which can be classified into geometric anisotropy, zonal anisotropy, and mixed anisotropy. Geometric anisotropy is defined when the directional semivariogram has different range values but the same sill value at different angle intervals, which is the most common feature of a semivariogram (Sari and Pasaribu 2014). Thus, geometric anisotropy is considered in this study, and the directions with an interval of 10° are used.
d. Statistical methods
Moreover, percentiles are used to portray the statistical characteristics of spatial correlation distances of rainstorms in this study. It is a term in statistics and can be defined as the value of a variable whose specific percentage of the distribution is equal to or below that value (Xia et al. 2020). The 50th percentile is the median of a random variable with an odd number of data points, and it is the average of the two middle values of a random variable with an even number of data points. In statistics, the 25th, 50th, and 75th percentiles are usually applied.
4. Spatial characteristics of severe rainstorms
a. Statistics of severe rainstorms over SEC
Table 1 summarizes the frequency of TCSRs and NTCSRs in different months during 2000–19 over SEC. There are 51 TCSRs and 91 NTCSRs, respectively. Most TCSRs are observed in July, August, and September (referred to as typhoon season), but NTCSRs are mainly recorded from May to July. There are few severe rainstorm events in the cold season for both rainfall types. Figure 4 shows the locations of gauges recording TCSRs and NTCSRs in different months. Almost all TCSRs occur along the coastlines and in Hainan Province except for three events found in Jiangxi and Henan Provinces as shown in Figs. 4d and 4e. Figures 4a–d show a majority of NTCSRs are observed in inland areas compared with TCSRs. Moreover, the downstream of the Yangtze River basin is a region where NTCSRs often occur as shown in Figs. 4b and 4c. Both TCSRs and NTCSRs are recorded at gauges in coastal provinces, especially in Guangdong Province in Figs. 4b–e. The maximum daily rainfall amounts induced by TCs and NTCs are 614.7 and 605.3 mm, which are separately recorded at the gauges in the southeast of Hainan Island (5 October 2010) and south of Guangdong (8 June 2001) as shown in Figs. 4b and 4f.
The number of TCSRs and NTCSRs occurring in different months during 2000–19 over SEC.
Locations of gauges recording TCSRs and NTCSRs in (a) May, (b) June, (c) July, (d) August, (e) September, and (f) October.
Citation: Journal of Hydrometeorology 24, 10; 10.1175/JHM-D-22-0145.1
Figure 5 shows the frequency and maximum daily rainfall amount of TCSRs and NTCSRs each year during 2000–19. In most years, the occurrences of NTCSRs are more than those of TCSRs. The maximum frequency of NTCSRs and TCSRs are 7 and 6, respectively. After 2010, the number of rainfall events in both rainfall types experiences a decreasing trend. As for the maximum daily rainfall amount in each year (Fig. 5b), relatively large rainfall amounts during NTCSR events are exhibited at the beginning of the study period. The maximum daily TC-induced rainfall is observed in 2010 located in Hainan Island. Maximum daily rainfall during NTCSR events decreases from 2001 to 2007 and then slightly increases until 2016. Because there are no severe rainstorms induced by TCs in some years, there are no data in the corresponding years. Except for the maximum daily rainfall amounts during TCSRs in 2010 and the missing data years, most of them are generally smaller than those during NTCSR events in the corresponding years.
The temporal variation of severe rainstorms in (a) frequency and (b) the maximum daily rainfall amount induced by TCs and NTCs during 2000–19 over SEC.
Citation: Journal of Hydrometeorology 24, 10; 10.1175/JHM-D-22-0145.1
b. Spatial characteristics of TCSRs and NTCSRs
1) Co-occurrence probability of severe rainstorms
There are 51 TCSRs and 91 NTCSRs in total used to compute the co-occurrence probability in this study. Around 50% of co-occurrence probabilities in the 50-km-distance bin are larger than 0.8 for TCSRs and smaller than 0.2 for NTCSRs. Hence, 0.2 and 0.8 are used as the boundary values to categorize the co-occurrence probabilities of severe rainstorms in the 50-km-distance bin to make more clear exploration. The co-occurrence probability in the 50-km-distance bin is defined as the 50-km-distance probability. It can be categorized into three ranges including [0.01, 0.20], [0.21, 0.79], and [0.80, 1.00], which are used to further classify severe rainstorms.
The co-occurrence probability of TCSRs in the duration between June and October is computed in each distance category and the results are shown in Fig. 6. Generally, the higher the 50-km-distance probability, the longer the spatial correlation distance of TCSRs over SEC to some extent. To be specific, when the 50-km-distance probability is less than 0.2, the spatial correlation distance is no more than 100 km from July to September. When the 50-km-distance probabilities fall into [0.80, 1.00], most subsequent co-occurrence probabilities are close to 0 for the first time in the 400- and 700-km-distance categories, indicating that the corresponding TCSRs have spatial correlation distances ranging between 400 and 700 km, as shown in Figs. 6c–g (from July to October). The number of TCSRs with the 50-km-distance probability falling in [0.80, 1.00] almost equals that ranging between 0.21 and 0.79. When the 50-km-distance probability ranges between 0.21 and 0.79 from June to September, the spatial correlation distance ranging from 300 to 350 km can be determined according to the co-occurrence probability approaching zero for the first time in the 300- and 350-km-distance bins. From July to October, most 50-km-distance probabilities are more than 0.2, and the spatial correlation distance of TCSRs in the typhoon season over SEC changes between 300 and 700 km. As a whole, if the 50-km-distance probability is relatively larger, the spatial correlation distance of the corresponding TCSR over SEC will be longer accordingly. When the co-occurrence probability in the current distance bin is significantly larger than that in the last three distance bins, this probability is defined as a reincreasing co-occurrence probability that can be observed in Figs. 6c–f. The reincreasing probabilities are observed between 400 and 600 km, which means these corresponding TCSRs have a longer spatial correlation distance or another severe rainstorm may occur in contrast to those having no reincreasing probabilities.
Co-occurrence probabilities of TCSRs against varying distances in (a) April, (b) June, (c) July, (d) August, (e) September, (f) October, and (g) November. Note that the solid circle line, solid square line, and solid triangle line stand for the co-occurrence probabilities of each TCSR that is categorized by the 50-km-distance probability falling into [0.01, 0.20], [0.21, 0.79], and [0.80, 1.00], respectively.
Citation: Journal of Hydrometeorology 24, 10; 10.1175/JHM-D-22-0145.1
Figure 7 shows the co-occurrence probabilities of NTCSRs in 16 distance bins. In general, 300 km is determined as the maximum spatial correlation distance for most NTCSRs. Specifically, only seven 50-km-distance probabilities of more than 0.8 in total are observed in May, June, July, and October, respectively. The subsequent co-occurrence probabilities approaching 0 for the first time can be found in the 350- and 550-km-distance bins, indicating that these NTCSRs with a 50-km-distance probability falling in [0.80, 1.00] have a spatial correlation distance ranging from 350 to 550 km. These NTCSRs with a relatively longer spatial correlation distance may be associated with large-scale frontal weather systems. Three NTCSRs with reincreasing probabilities occurring in the 350-, 500-, and 550-km-distance bins can be observed in July, August, and September. The 50-km-distance probabilities of the three NTCSRs are all between 0.80 and 1.00. Almost half of 50-km-distance probabilities of less than 0.2 are found from May to August and the corresponding co-occurrence probability approaching zero is observed in the 150-km-distance category. That is, the spatial correlation distance of most NTCSRs occurring between May and August over SEC is relatively smaller (<150 km) compared to that in other months. The formation of small spatial correlation distances of these rainstorms may be associated with the convective weather system and terrain. The number of 50-km-distance probabilities ranging between 0.21 and 0.79 is 27 and more than half of them are distributed in June and July. Corresponding to the 50-km-distance probability falling into [0.21, 0.79], the subsequent co-occurrence probability approaching zero can be found in the 250- and 300-km-distance bins. Overall, most NTCSRs over SEC especially in mei-yu season (June and July) tend to have a spatial correlation distance ranging from 150 to 300 km.
Co-occurrence probabilities of NTCSRs against varying distances in (a) May, (b) June, (c) July, (d) August, (e) September, (f) October, and (g) November. Note that the solid circle line, solid square line, and solid triangle line stand for the co-occurrence probabilities of each NTCSR that is categorized by the 50-km-distance probability falling into [0.01, 0.20], [0.21, 0.79], and [0.80, 1.00], respectively.
Citation: Journal of Hydrometeorology 24, 10; 10.1175/JHM-D-22-0145.1
2) Range values of severe rainstorms against different directions
Range values at five percentiles (including the minimum level, 25th percentile, 50th percentile, 75th percentile, and maximum level) against different directions of 51 TCSRs and 91 NTCSRs are calculated using semivariogram, and the corresponding results are shown in Fig. 8. Range values are used to indicate the correlation length which is the spatial correlation distance of one rainstorm. At the minimum level in Fig. 8a, all the range values are less than 50 km, with the maximum values in the northwest–southeast and the minimum ones in the northeast–southwest. The range values at the 25th percentile along different directions ranging between 50 and 100 km seem almost equal. As for the range values at the 50th percentile, the maximum range value (around 125 km) is observed along 50° (i.e., northeast–southwest). The relatively large range values at the 75th percentile (between 200 and 250 km) are found in different directions including 0°, 10°, 40°, 50°, 90°, 280°, 290°, and 350° (i.e., near south–north, northeast–southwest, east–west). In terms of the maximum range values, except for two range values between 600 and 700 km in 340° and 350°, the other maximum range values along different directions are roughly between 500 and 600 km. Overall, the range values of TCSRs at other percentiles (except for the minimum range values) tend to be omnidirectional. In Fig. 8b, the range values at five percentiles regularly vary with the direction. Most range values at the 25th, 50th, 75th percentiles, and the maximum level between 0° and 80° are larger than those between 270° and 350°. Moreover, the range values at the 50th and 75th percentiles in directions from 0° to 30° are larger than those in the other directions, which means that the east–northeast is the major direction along with which a larger spatial correlation distance of an NTCSR event can be observed. Generally, from a statistical perspective, NTCSRs over SEC tend to have the maximum and minimum spatial correlation distance in the northeast–southwest and southeast–northwest, respectively.
Range values at five percentiles against different directions of (a) TCSRs and (b) NTCSRs.
Citation: Journal of Hydrometeorology 24, 10; 10.1175/JHM-D-22-0145.1
To explore the seasonal variation of the range values, the average range values of TCSRs and NTCSRs in different months are calculated (Fig. 9). Severe rainstorms that occurred in April and November are not included here. For all the severe rainstorms, the average range values in different directions are no more than 300 km. As for TCSRs, the maximum average range values are exhibited in the northeast–southwest (June and August) and northwest–southeast (July, September, and October), indicating that the directions with the largest range values (hereafter referred to as major direction) vary seasonally. Moreover, the largest average range values in summer are smaller than those in autumn. That is, the average range values in the major directions in June (116.77 km) and July (179.37 km) are smaller than those from August to October (248.09, 204.29, and 212.82 km, respectively). The minimum average range value is 83.72 km along the northwest–southeast in June (Fig. 9b). As for the average range values of NTCSRs in each month, almost all the largest range values are observed in the east–west (142.07 km in May, 182.93 km in June, and 181.52 km in August) and the northeast–southwest (205.28 km in July, 297.11 km in September, and 217.39 km in October). That is, the spatial correlation distance of NTCSRs in the northeast–southwest is larger than that in east–west. September is determined as the month having the maximum average spatial correlation distance. The minimum average range keeps the value around 100 km in the former four months but decreases to 76.79 km in September and then increases to 141.23 km in October. NTCSRs in October overall tend to have relatively large spatial correlation distances in any direction. Overall, at an average level, the major direction for NTCSRs varies slightly with seasonal variation and it is mainly in the east–west and northeast–southwest.
Average range values against 38 directions of TCSRs and NTCSRs in (a) May, (b) June, (c) July, (d) August, (e) September, and (f) October.
Citation: Journal of Hydrometeorology 24, 10; 10.1175/JHM-D-22-0145.1
3) Spatial anisotropy and isotropy
To discuss whether the directional semivariogram of one severe rainstorm is anisotropic or isotropic, ratios of the shortest range to the longest range from semivariograms of TCSRs and NTCSRs are calculated in this study. If the ratio is less than 0.8 the directional semivariogram is determined to be anisotropic; otherwise, isotropy is determined (Oliveira et al. 2022). There are several values around 0.8 for TCSRs and NTCSRs indicating that the semivariogram of a few severe rainstorms shows isotropy over SEC between 2000 and 2019. In other words, anisotropy is the main spatial nature of severe rainstorms over SEC.
To explore the linkage between ratios and co-occurrence probabilities of rainstorms, the co-occurrence probabilities of rainstorms corresponding to ratios at the minimum level, the 25th percentile, the 50th percentile, the 75th percentile, and the maximum level are selected to be shown in Fig. 10, and the specific information of the corresponding rainstorms is presented in Table 2. To demonstrate whether the semivariogram method can accurately calculate the correlation distances, range values and spatial distributions of TCSRs and NTCSRs corresponding to the ratios at five percentiles are presented in Figs. 11 and 12. For both rainfall types, the maximum ratios are 0.77 and 0.76, respectively, which are close to 0.8. Hence, the semivariogram of the corresponding severe rainstorms is almost isotropic.
Co-occurrence probabilities of (a) TCSRs and (b) NTCSRs corresponding to ratios at five percentiles.
Citation: Journal of Hydrometeorology 24, 10; 10.1175/JHM-D-22-0145.1
The information of TCSRs and NTCSRs with ratios at five percentiles.
Range values of TCSRs corresponding to ratios at the (a) minimum value, (b) 25th percentile, (c) 50th percentile, (d) 75th percentile, (e) maximum value, and (f)–(j) the corresponding spatial distributions of these severe rainstorms.
Citation: Journal of Hydrometeorology 24, 10; 10.1175/JHM-D-22-0145.1
Range values of NTCSRs corresponding to ratios at the (a) minimum value, (b) 25th percentile, (c) 50th percentile, (d) 75th percentile, (e) maximum value, and (f)–(j) the corresponding spatial distributions of these severe rainstorms.
Citation: Journal of Hydrometeorology 24, 10; 10.1175/JHM-D-22-0145.1
The isotropic diagrams and spatial distributions of these two severe rainstorms are shown in Figs. 11e and 11j as well as Figs. 12e and 12j, in which average range values are around 100 km. TCSR and NTCSR with isotropic spatial structures both occurred in the south of SEC with daily rainfall amounts of 271.3 and 297.6 mm recorded at gauges, respectively. The co-occurrence probabilities of these two rainstorms are relatively small, but the 50-km-distance probability from TCSR is larger than that from NTCSR as the number of rainfall amount of more than 250 mm day−1 from this TCSR event in Fig. 11j is larger than that from the NSTCR event in Fig. 12j. The relatively small spatial distribution of daily rainfall of more than 250 mm day−1 in Fig. 12j compared to that in Fig. 11j also validates the conclusion that the higher the 50-km-distance probability, the longer the spatial correlation distance of TCSRs over SEC. Except for the major direction in the northeast–southwest in Fig. 11c, the other major directions are all along the northwest–southeast in Figs. 11a, 11b, and 11d, which is also consistent with the description of spatial distributions in Figs. 11f–i. All the TCSRs with ratios at the former four percentiles (Table 2) occurred in the southeast and the south of SEC, as well as during typhoon season. All the co-occurrence probabilities are relatively large when the distance is no more than 200 km. The probabilities corresponding to the ratios at the 25th and 50th percentiles decrease to around 0 when the distance is more than 550 km. Moreover, the spatial correlation distances indicated by co-occurrence probabilities (Fig. 10a) are consistent with those in the major directions (Figs. 11a,b,e) corresponding to ratios at the minimum level, 25th percentile, and the maximum level. It proves that co-occurrence probability and semivariogram can accurately portray the spatial correlation distance of rainstorms over SEC.
All the major directions are along the east–west or northeast–southwest for NTCSRs (Figs. 12a–e), which is consistent with descriptions of the spatial distributions in Figs. 12f–j. The corresponding NTCSRs mainly occurred in the south and the east of SEC, as well as in mei-yu season (Table 2). Due to IMERG-based rainfall data failing to capture the daily rainfall amount of more than 250 mm during gauge-based severe rainstorm events, the co-occurrence probabilities of NTCSRs with ratios at 25th, 50th, and maximum percentiles are retained as shown in Fig. 10b. The co-occurrence probability corresponding to the ratio at the 25th percentile is so small that it is close to 0 in the distance of 50 km, which is not consistent with that shown in Fig. 12b. Because of a small number of daily rainfall amounts of more than 250 mm observed from the spatial distribution in Fig. 12g, small co-occurrence probabilities are obtained in each distance category. The co-occurrence probability from NTCSR with a ratio at the 50th percentile decreases sharply when the distance is more than 250 km, indicating that this NTCSR has a spatial correlation distance of around 250 km. The range along the major direction is around 250 km (Fig. 12c), which is consistent with the spatial distribution in Fig. 12h. The spatial structure characterized by range values in Fig. 12c is unable to include the severe rainfall amounts observed in other rainstorm centers, which is able to be portrayed by co-occurrence probability corresponding to ratios at the 50th percentile. However, the semivariogram method can detect the spatial correlation distance in different directions and further identify the major direction of one rainstorm.
4) Potential factors impacting the correlation length of severe rainstorms
ENSO has been reported to affect the global climate to some extent. To detect its influence on the spatial features and correlations of severe rainstorms over SEC, the variations of spatial indicators, i.e., range values of TCSRs and NTCSRs during La Niña and El Niño events, are discussed in this study. Figures 13a and 13b show the average range values in different directions of TCSRs and NTCSRs during La Niña, El Niño, and neutral ENSO events. Note that TCSR or NTCSR events when neither La Niña nor El Niño events occur are defined as neutral ENSO events. As for TCSRs, there are 13 La Niña events, 9 El Niño events, and 29 neutral ENSO events. As for NTCSRs, there are 18 La Niña events, 16 El Niño events, and 57 neutral ENSO events. From the perspective of average range values of TCSRs (Fig. 13a), the maximum average range value in the northeast–southwest during El Niño (La Niña) events is 214 (109) km which is larger (smaller) than that during neutral ENSO events (162 km). That is, the average spatial correlation distance of TCSRs in the northeast–southwest increased by 52 km under the influence of El Niño, but it decreased by 53 km under the influence of La Niña. Furthermore, the spatial structure of TCSRs during neutral ENSO events is changed to a spatial structure with the major direction in the northwest–southeast during La Niña events. During El Niño events, the maximum average range of NTCSRs in the north–northeast is 229 km which is larger than that during neutral ENSO events (140 km) in the same direction (Fig. 13b). In other words, when El Niño events occur, the average spatial correlation distance in the north–northeast is believed to increase by 89 km. Moreover, because of El Niño–associated increasing spatial distance, the major direction is changed from the east–northeast to the north–northeast. As the average range values in each direction during La Niña events almost equal those during neutral ENSO events, no obvious influences of La Niña on the spatial structure of NTCSRs can be identified.
IOD has been reported to have a significant correlation with winter rainfall in SEC (Zhang et al. 2022). Hence, it is adopted in this study to detect its impact on the spatial variations of TCSRs and NTCSRs over SEC. There are 13 −IOD events, 19 +IOD events, and 19 neutral IOD events when TCSRs occurred between 2000 and 2019. As for NTCSRs, there are 13 −IOD events, 36 +IOD events, and 42 neutral IOD events. Figures 13c and 13d show the average ranges of TCSRs and NTCSRs during −IOD, +IOD, and neutral IOD events. Take the range values during neutral IOD events as the reference. In Fig. 13c, the relatively longer ranges during neutral IOD events can be found along the northeast–southwest, while they are changed to the northwest–southeast direction when −IOD events occur. Negative IOD events also tend to decrease the spatial correlation distances in the northeast–southwest as shown in Fig. 13c. Compared to ranges of TCSRs during neutral IOD events, it seems that ranges during +IOD events in all directions especially in the northwest–southeast are significantly increased. Overall, the occurrence of +IOD and −IOD events may increase the spatial correlation distance of TCSRs in the northwest–southeast, and −IOD events may decrease the distance in the northeast–southwest. As for the impact of IOD on the average ranges of NTCSRs in Fig. 13d, a remarkable increase can be observed in the east–northeast during −IOD events. A slight decrease can be detected in the east–southeast when +IOD events occurred. That is, the average spatial correlation distance of NTCSRs is mainly changed in the east–southeast and east–northeast during +IOD and −IOD events, respectively.
Average ranges in different directions of (a) TCSRs and (b) NTCSRs during La Niña, El Niño, and neutral ENSO events as well as (c) TCSRs and (d) NTCSRs during −IOD, +IOD, and neutral IOD events.
Citation: Journal of Hydrometeorology 24, 10; 10.1175/JHM-D-22-0145.1
The influence of latitudes, longitudes, average surface temperature, elevation, and radius of maximum wind on the range values in different directions is explored using CC values (Fig. 14). All the factors are considered for TCSRs, but the radius of maximum wind is not considered for NTCSRs as it is one of the features of TCs. As for TCSRs, the range values are remarkably positively correlated with the local geographical factors (latitudes and longitudes), especially in south–north with the maximum CC of 0.55 (latitudes, at the 95% significant level) and 0.58 (longitudes, at the 95% significant level). Most negative CCs between range values in different directions and temperatures are observed, but only one significant value of −0.29 is detected almost in south–north. That is, in the background of global warming the spatial correlation distance of TCSRs may become concentrated, which is consistent with the report from Wasko et al. (2016). There are remarkable negative CCs between range values and radiuses of maximum wind in the southeast–northwest with the maximum negative CC of −0.38. The range values in all directions are positively affected by elevation, but only that in 60° is significantly influenced with a CC of 0.31. As for NTCSRs, there are weak correlations between range values and longitudes, temperature, and elevation, but strong correlations (the maximum CC is 0.25) between range values in the directions from 40° to 80° and latitudes. In other words, in the target region, the higher the latitudes are, the larger the range values in the north–northeast are, indicating that the latitude is a potential factor that impacts the spatial correlation distance of NTCSRs over SEC.
Correlation coefficients between factors and the range values in different directions of (a) TCSRs and (b) NTCSRs. Note that the filled marks stand for the correlation at the 95% significant level.
Citation: Journal of Hydrometeorology 24, 10; 10.1175/JHM-D-22-0145.1
5. Discussion
a. The differences between TCSRs and NTCSRs in the statistical spatial model
In terms of the difference in co-occurrence probability, the 50-km-distance probability can be used to indicate the variation of spatial correlation distance of both TCSRs and NTCSRs. The proportions of the number of 50-km-distance probabilities falling into [0.80, 1.00] from TCSRs are more than those from NTCSRs in Figs. 6 and 7, indicating that TCSRs are more likely to have a larger spatial correlation distance in contrast to NTCSRs. On the other hand, the ratios of the 50-km-distance probability of <0.2 from NTCRs are larger than those from TCSRs, implying that localized NTCSRs impacting a limited region are more likely to occur especially from May to August compared with TCSRs. There are relatively longer spatial correlation distances for TCSRs in typhoon season compared with those for NTCSRs in mei-yu season.
In terms of the spatial correlations indicated by range values, the spatial correlation distances of TCSRs in different directions tend to be almost equal according to the range values at the 25th, 50th, 75th percentiles, and the maximum level. However, larger range values at five percentiles of NTCSRs tend to be in the northeast–southwest, which is the major direction as shown in Fig. 8b. As for the average range values in Fig. 9, the major directions in July, September, and October from TCSRs are northwest–southeast, while those from NTCSRs in these months are northeast–southwest. Additionally, the maximum average range values in these three months from TCSRs are smaller than those from NTCSRs. As for spatial anisotropy and isotropy, both weather systems tend to lead to severe rainstorms with anisotropic spatial structure.
The significant differences between TCSRs and NTCSRs in spatial correlations and structures are believed to be associated with different factors. From a macro perspective, the differences between TC- and NTC-associated weather systems can be used to interpret the phenomenon to some extent. The TC weather system is impacted by the northward movement of jets in the upper troposphere and the corresponding evolution of the large-scale anticyclonic (cyclonic) circulation over East Asia (Lee et al. 2010), which is the basic physical mechanism of rainfall induced by TCs leading to various spatial correlation distances. Moreover, they may vary slightly with the location and topography of TC landfall, TC tracks, etc. For instance, extreme rainfall induced by Bilis in July 2006 over China may be associated with the intercore storm circulation and the interaction between this typhoon and the monsoon (Gao et al. 2009). The spatial features of extreme rainfall induced by TCs in Hainan Island may be impacted by topography, a stronger TC intensity, a slower speed of TC movement, and a farther westward track (Jiang et al. 2018). On the other hand, NTC weather system, e.g., convective system (relatively local scale) and frontal system (relatively large scale), is associated with the extension of the western Pacific subtropical high at the 500-hPa level and movement of the East Asian and the upper jet streams (Zhou and Yu 2005). The spatial features of NTCSRs associated with the mei-yu front may also be related to the extension of the eastward South Asia high, strong westerly jet, and the larger moisture fluxes moving northeast (Sampe and Xie 2010; Du et al. 2020). Additionally, the large-scale low-frequency climatic events such as La Niña/El Niño and −IOD/+IOD events also contribute to the differences. According to the intercomparison between Figs. 13a and 13b, during El Niño events, TCSRs are more likely to have an isotropic spatial structure compared with NTCSRs. La Niña can prevent the spatial correlation distance of TCSRs from expanding to the northeast–southwest, but it rarely impacts the spatial correlation distance of NTCSRs in this direction. In terms of the influences from IOD events, the spatial correlation distances of TCSRs not only are impacted by +IOD events but also by −IOD events which are identified to influence the spatial correlation distances of NTCSRs over SEC. The spatial correlation distances in the northwest–southeast of TCSRs are impacted more by IOD events compared to those of NTCSRs. Negative IOD events tend to suppress the range values in the northeast–southwest of TCSRs but expand those of NTCSRs in this direction. External factors such as latitudes, longitudes, temperature, and elevation as well as internal factors such as the radius of maximum wind are recognized to affect the propagation of range values of TCSRs, while the spatial correlation distances of NTCSRs are only affected by latitudes (Fig. 14). That is, the difference between TCSRs and NTCSRs in spatial correlation distance to some extent is attributed to the different degrees of correlation between the range values and these factors.
b. Uncertainties
Co-occurrence probability and range values calculated using semivariograms are obtained based on 51 TCSRs and 91 NTCSRs which are relatively small sample sizes. If a greater number of rainstorms can be used, the spatial correlation distance would be characterized more accurately. In this study, co-occurrence probability and range values are both presented from the statistical perspective, which to some extent can avoid misunderstanding of just demonstrating values of one certain event. Moreover, although there is a relatively small sample size, the correlation relationship between range values and factors is still meaningful as all the CCs shown in this study are at the 95% significance level.
Gauge-based rainfall data used in this study are relatively distributed sparsely over SEC, which may lead to inaccurately estimating the spatial correlation distances. Therefore, IMERG-based data are employed. However, IMERG-based data fail to capture some daily rainfall amounts of more than 250 mm, which further leads to decreasing sample sizes. During 2000 and 2019, there are 51 TCSRs and 91 NTCSRs in total over SEC, but IMERG fails to capture 5 TCSRs and 25 NTCSRs whose co-occurrence probabilities cannot be obtained such as the NTCSRs in Figs. 12f and 12i. However, the range values indicating spatial correlation distances are still able to be obtained by the semivariogram method that is exempt from influences of failing to capture severe rainstorms. Therefore, the semivariogram method can be a supplementary method not only to calculate the range values of these rainstorms but also to detect the major direction. Although, the results using co-occurrence probability are still reasonable as they are analyzed and presented from an alternative statistical perspective.
As shown in Fig. 4, there are around 38 severe rainstorms that occurred along the coastline and at the edge of SEC which may lead to decreased rainfall data pairs for one rainstorm event to compute the co-occurrence probability and range values and further influencing measurements of spatial correlations. IMERG-based rainfall product includes rainfall data over sea areas, which can guarantee there are enough rainfall data pairs for a rainstorm on the coastline to calculate spatial correlations. Six severe rainstorms occurred respectively at the southwest edge (Fig. 4a), northwest edge (Figs. 4b,c), and south (Fig. 4d) of SEC, and the spatial correlations of these 6 severe rainstorms may be impacted by their geographical locations. The co-occurrence probability of one severe rainstorm will vary slightly if many rainfall data points of more than 250 mm day−1 are not included in the specific domain as the maximum co-occurrence probability is selected in each distance bin in this study. Under the same circumstance, the range values of these several rainstorms are more affected than the co-occurrence probability. Moreover, inaccurate range values are mainly obtained in the directions along which more than 50% of rainfall data points are not included in the specific domain (three severe rainstorms in this study). The relatively small number of inaccurate range values has a limited impact on the results at a statistical level in general. However, when the spatial correlation distance of one certain rainstorm needs to be identified, all the rainfall data points especially those of more than 250 mm day−1 in the determined domain are indispensable.
Three TCSRs with reincreasing co-occurrence probabilities of 0.267, 0.273, and 0.203 as well as three NTCSRs with values of 0.139, 0.105, and 0.067 are all observed in July, August, and September as shown in Figs. 6c–e and 7c–e, respectively. The corresponding spatial distributions of these severe rainstorms are demonstrated in Figs. 15a–c and 15g–i in which all the rainstorm events have at least two rainfall centers. Note that two rainfall centers mean that there is a certain distance between the clustered daily rainfall amounts of more than 250 mm and other clustered daily severe rainfall amounts. That is, the reincreasing probability is induced by multiple rainstorm centers which could be originated from one severe rainstorm or two independent severe rainstorms. To identify whether the reincreasing probabilities originated from one severe rainstorm or two independent severe rainstorms, range values in 38 directions of three TCSRs and NTCSRs are computed (Figs. 15d,e,j–l). The rainfall data pairs are highly correlated with each other if they are in the scope that is depicted by the range values in 38 directions. Thus, it is believed that these rainfall data pairs are from one severe rainstorm. Conversely, if the rainfall data pairs are out of the scope, they are spatially correlated with each other insignificantly. It is believed that they may be from two or more two independent severe rainstorms. In Figs. 15b and 15e, the range values in 38 directions quantify the spatial structure of TCSR located in the southwest, but the rainfall data pairs with more than 250 mm day−1 located in the east and southeast are not included in the scope. That is, the reincreasing probability is associated with two independent TCSRs in one day. A similar phenomenon can be found in Figs. 15g and 15j. Except for these two reincreasing probabilities corresponding to Figs. 15b and 15g, the other four reincreasing probabilities corresponding to Figs. 15a, 15c, 15h, and 15i are all separately associated with one severe rainstorm that has relatively long spatial correlation distance in the major direction. Therefore, the reincreasing probability generally indicates a relatively long spatial correlation distance of one severe rainstorm. Moreover, it is observed that the amplitude of reincreasing probabilities seems to be related to the maximum daily rainfall amount for each type of rainstorm. The larger the maximum daily rainfall amount is, the larger the reincreasing probability is.
Spatial distributions of (a)–(c) three TCSRs and (g)–(i) three NTCSRs with reincreasing co-occurrence probabilities and (d)–(f),(j)–(l) the corresponding range values in 38 directions.
Citation: Journal of Hydrometeorology 24, 10; 10.1175/JHM-D-22-0145.1
c. The potential relationship between El Niño/La Niña and +IOD/−IOD
The range values in the east–northeast of TCSRs are suppressed during La Niña events (Fig. 13a), and a similar phenomenon can be observed during −IOD events (Fig. 13c). Moreover, the spatial structures of TCSRs during El Niño and +IOD events are similar. That is, El Niño (La Niña) and +IOD (−IOD) events have similar effects on the spatial correlation distance of TCSRs. Through the intercomparison between Figs. 13b and 13d, not only the spatial structures indicated by the range values in all directions during El Niño (La Niña) and +IOD (−IOD) events are semblable, but also the corresponding major directions are all in the northeast–southwest. As a whole, both El Niño (La Niña) and +IOD (−IOD) events control the spatial correlation distance of TCSRs and NTCSRs, which proves that there is a potential relationship between El Niño (La Niña) and +IOD (−IOD) events. Many previous studies have proved this phenomenon and demonstrated that ENSO is one of the factors triggering IOD events and conversely IOD also regulates the amplitude and evolution of ENSO (Saji and Yamagata 2003; Behera et al. 2006; Luo et al. 2010; Guo et al. 2015; Zhang et al. 2022).
6. Conclusions
The spatial correlations and features of TCSRs and NTCSRs are characterized using the indicators, i.e., co-occurrence probability and range values from semivariograms utilizing the gauge- and IMERG-based rainfall data during 2000–19 over SEC. A statistical model that can portray the spatial structures of severe rainstorms and correlations with other factors is constructed. The major findings are summarized as follows:
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In terms of the spatial correlation distance of severe rainstorms over SEC based on co-occurrence probability, the higher the 50-km-distance probability, the longer the spatial correlation distance. There are relatively longer correlation distances for TCSRs (300–700 km) in typhoon season compared with most of those for NTCSRs (150–300 km) in mei-yu season.
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Range values of TCSRs at each percentile (except for the minimum range values) tend to be omnidirectional and NTCSRs at each percentile have the major direction of northeast–southwest. At an average level and at a seasonal scale, the major direction for TCSRs varies seasonally but for NTCSRs it varies slightly with seasonal variations, and it is mainly in the east–west and northeast–southwest.
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El Niño and La Niña events respectively increase and decrease the average spatial correlation distance of TCSRs in the northeast–southwest. The occurrence of +IOD and −IOD events may increase the spatial correlation distance of TCSRs in in the northwest–southeast, and −IOD events may decrease the distance in the northeast–southwest. IOD events especially −IOD may change the spatial correlation distance of NTCSRs in the east–northeast. The range value in the south–north of TCSRs may be positively impacted by latitudes and longitudes but negatively correlated with temperature. The radius of maximum wind may negatively affect the spatial structure of TCSR in the southeast–northwest. The spatial correlation distances of NTCSRs in the north–northeast may be positively affected by latitudes.
Acknowledgments.
The authors thank the China Meteorological Data Service Center (CMSC) and China Meteorological Administration (CMA) for providing gauge-based rainfall observations and tropical cyclone best track datasets. The authors acknowledge Goddard Earth Sciences Data and Information Services Center (GES DISC) for supplying us with the IMERG dataset. The authors also thank the Climate Prediction Center for providing the ENSO index. The financial support of the Science and Technology Development Fund, Macau Special Administrative Region, China, the UM Research Grant, and the Guangdong–Hong Kong–Macau Joint Laboratory Program are gratefully acknowledged. This research was funded by the National Natural Science Foundation of China (52209118), the Science and Technology Development Fund, Macau SAR (Files SKL-IOTSC(UM)-2021-2023, 0030/2020/A1, 0029/2022/A1), UM Research Grant (Files MYRG2020-00072-IOTSC, MYRG2022-00090-IOTSC), Shenzhen Science and Technology Innovation Committee (SGDX20210823103805043), and CORE. CORE is a joint research center for ocean research between QNLM and HKUST. The authors would like to acknowledge all these supports.
Data availability statement.
The data in this study are subject to third party restrictions. The data that support the findings of this study are available from the National Climate Centre in Beijing, China. Restrictions apply to the availability of these data, which were used under license for this study. Data are available at https://data.cma.cn/en, accessed on 11 January 2020, with the permission of the National Climate Centre in Beijing, China.
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