Characterization and indexing of heavy rainstorms in Hong Kong

ABSTRACT

Heavy rain events or rainstorms of various scales often occur in Hong Kong from April to September. In extremes cases, they lead to serious landslides and flash floods resulting in loss of life, and damage to property and infrastructure. With climate change, extreme rain events are projected to be more frequent and more intense in this region. A system to gauge and label the severity of rainstorms would be useful for identifying and communicating extreme conditions in warning and disaster prevention operations. In parallel, a better understanding of the characteristics of rainstorms would also be important for impact assessments and engineering design purposes. This paper formulates a practical framework to index the magnitude and severity of rainstorms in Hong Kong. An index termed as the Severity Index combining the magnitude of different rainstorm attributes is devised for quantifying the overall severity of rainstorms. This index is flexible to allow tuning for specific applications.

1. Introduction

Hong Kong is a small city (land area of near 1100 km², see Figure 1), situated on the southeast coast of China and has a sub-tropical climate with well distinguished dry and wet seasons (Heywood, 1953). On average, about 85% of the annual rainfall is recorded from April to September in Hong Kong (Lee et al., 2006) when heavy rain events of various scales often occur. In general, high intensity short duration heavy rain events are referred to as rainstorms. Rainstorms in Hong Kong are mostly attributed to tropical cyclones and troughs of low pressure (Chin, 1968).

Figure 1

Map of Hong Kong.

Recent study suggests that both the frequency of occurrence and intensity of heavy rain events in Hong Kong exhibit a long term rising trend in the past century (Wong et al., 2011). Possibly due to an increase in moisture associated with global warming (Kharin et al., 2007; O'Gorman and Schneider, 2009; Lenderink and Meijgaard, 2010), extreme rain events are also projected to be more frequent and more intense in this region in the 21^st Century (IPCC, 2007; Lee et al., 2011).

Severe rainstorms can lead to serious landslides and flash floods resulting in traffic disruptions, loss of life and damage to infrastructure. While Hong Kong has varied and rugged topography, it is highly populated with over 700 million people. The threat posed to people by the occurrence of inclement weather can be tragic. Both of two recent rainstorms on 7 June 2008 and 22 July 2010 caused two fatalities in landslip or flash flood. As a developed city, the economic losses due to rainstorms in Hong Kong are also high. For example, it is estimated that the rainstorm on 7 June 2008 caused loses of some HK$ 578 million (Greenpeace China, 2009). As such, the prevention of casualty and damage brought by adverse weather events like heavy rain cannot be emphasized enough.

To warn the public and raise awareness of heavy rain situations (Ho, 2003), various warnings (e.g. thunderstorm warning, flood warning, heavy rain warning) have been introduced in Hong Kong since 1967. The flood and heavy rain warnings have evolved into a three-level Rainstorm Warning System (RWS) since 1998 to alert the public of the occurrence of territory-wide heavy rainstorms which are likely to bring about major flooding and disruptions to their daily economic and social activities. The Amber/Red/Black Rainstorm Warnings are issued when the prescribed rainfall threshold of 30/50/70 mm in an hour affecting Hong Kong generally is reached or is expected to be reached (HKO, 2011a).

While the Rainstorm Warnings are effective in mobilizing the response of the public and emergency personnel to heavy rain events in general, they are not very effective in highlighting extreme and high impact rainstorms. A system to gauge and label the severity of rainstorms would be useful for identifying and communicating extreme conditions in warning and disaster prevention operations as well as for impact assessments and engineering design purposes. Furthermore, categorizing the severity of rainstorms could enable benchmarking of future rainstorms for raising awareness of extreme rain events both on the weather and climate scales. In these regards, an index to quantify the relative severities of rainstorms is essential.

With reference to WMO guidance on the criteria for different categories of precipitation intensity (WMO, 2008), precipitation can be referred to as violent (the most intense category according to the guidance) if the hourly rainfall is ≥ 50 mm. In a similar vein, Molini et al. (2011) designated the heavy rain event in the Mediterranean areas as severe if it contained at least one hourly rain-gauge reading exceeding 50 mm. However, this criterion may not be suitable for categorizing the severity of rainstorms in Hong Kong since hourly rainfall of more than 50 mm is not uncommon in Hong Kong (Brand et al., 1984).

According to the China Meteorological Association (see http://www.cma.gov.cn), the classification of rainstorm severity in mainland China is based on the 24 h accumulated rainfall (R₂₄ for short hereafter). A heavy rain event is classified as a rainstorm if the R₂₄ is in the range between 50 and 99.9 mm; a heavy rainstorm if it is between 100 and 250 mm; and a severe rainstorm if it exceeds 250 mm. A minor modification to this classification was adopted in some studies (e.g., in Svensson and Berndtsson, 1996) such that daily rainfall was considered and the threshold of 250 mm for severe rainstorm was lowered to 200 mm.

Both the WMO's and China's R₂₄ classification of rainstorm severity consider point rainfall only (in practice, generally the maximum value of R₂₄ at the centre of rainstorm is referred) without taking into account other fundamental descriptions of rainstorms as listed in Boyer (1957) such as the areal extent. Besides, both classify the severity of rainstorms according to fixed universal criteria which may not be adequate for local applications.

The ranking of rainstorm severity in terms of spatial extent can be made by comparing the areal rain depth for different durations by means of depth-area-duration analysis (e.g., Dhar et al., 1984; Angel and Huff, 1999) in which the isohyetal method (see WMO, 1969; Linsley et al., 1982) is commonly used for estimating the areal rain depth. However, the isohyetal method is basically subjective depending on the skill of the analyst in producing the isohyetal map (e.g. Gupta, 2011). As rainstorms are often volatile and erratic in nature, real-time analysis using the isohyetal method is not practical. Thus, it is desirable to have a simpler alternative representation to compare the spatial extent of rainstorms (without converting point values to areal values).

The severity of a rainstorm can also be described in terms of specific impacts the rainstorm leads to. An example is the Landslide Potential Index (LPI) which expresses the relative severity of the rainstorm in comparison with the most severe rainstorm on record with respect to the number of landslides caused in Hong Kong (CEDD, 2009). For this and indices of a similar kind, a comprehensive database of specific impacts is required which may not always be readily available. Besides, the relationship between rainfall and landslide occurrence or other hazards could be changed for a number of reasons related to urban development (e.g. Chan et al., 2003). Actually, the severity of a rainstorm defined by these indices depends on a number of factors other than meteorological characteristics. These include the method of impact assessment, precautionary measures taken as well as policy actions to reduce the vulnerability (such as improving stability of slopes for landslip hazard). As such, a change if any (accompanied with climate change) in the severity of rainstorm may not be discriminated, for those indices solely tied with the consequent impacts.

Instead of relying only on one or two measures of rainstorm independently, it is the objective of the present study to formulate a practical framework to index the magnitude and severity of rainstorms in Hong Kong, putting together various measures of the rainstorm characteristics by means of various defined attributes using hourly rainfall data from a network of rain gauges. Rainstorm events during the period from 1998 to 2010 are employed to illustrate how the index is formulated.

The layout of the present study is arranged as follows. The rainstorm cases studied and data used are described in Section 2. The methods of characterizing and indexing the rainstorms are given in Section 3. Results of the study are discussed in Section 4. Section 5 contains a summary of the study and results.

2. Rainfall data and rainstorm cases

Rainstorms in the period from 1998 to 2010 will be considered in the present study. The start year of 1998 was chosen to align with the introduction of current RWS for identification of rainstorm events. Rainfall data used is the hourly rainfall data from a network of 125 automatic rain gauges (tipping bucket type) which consists of 40 Hong Kong Observatory (HKO) and 85 Geotechnical Engineering Office (GEO) stations. (At HKO's Headquarters, an ordinary rain gauge co-exists with the automatic rain gauge. As the official rainfall record for Hong Kong refers to that measured by the ordinary rain gauge, hourly rainfall at the Headquarters is substituted by observations made at this ordinary gauge for consistency.) The severity of rainstorm will be evaluated from available observations recorded at these stations and missing data will be ignored. Rainfall data from HKO's stations and GEO's stations have gone through automatic and manual quality control procedures including range checks, spatial consistency checks as well as checks against radar respectively by HKO and GEO. The hourly rainfall data are computed from raw data at 1 min intervals for HKO gauges and 5 min intervals for GEO gauges. Figure 2 presents the spatial distribution of the rain gauges. The density of the rain gauges is relatively higher in the northern part of Hong Kong Island and the Kowloon Peninsulas where higher population and more urban development are concentrated.

Figure 2

(a) Locations of the 125 raingauges (red triangle: HKO gauge, blue circle: GEO gauge) and clusters of the 39 principal zones. The insert is a summary of the gauges separation within zones. (b) Labelling of the zones. Basically, zones are labelled from west to east by uppercase letter B through K (the letter I is omitted), and from north to south by number from 1 to 8. In (b), red, black and green coloured labels represent zones classified as urban, sub-urban and rural type respectively according to population density whereas diagonal-lines filled denote flood prone zones in the northern part of the New Territories for illustration of regional vulnerability.

Ground-based gauge data are considered to be the most accurate in general (e.g. Guirguis and Avissar, 2008) providing the footprint of rainstorms (Legates, 2000). The present study uses raw gauge data alone, considering that: (1) although radar data have been employed to estimate the rainfall for nowcasting purposes (e.g. Porcú et al., 1999) and for analysing characteristics of severe rainstorm (e.g. Min et al., 2007), Lam and Li (1989) noted that radar data could underestimate gauge rainfall by about 50% on average in studying the major rainstorms in 1987–1988 in Hong Kong; (2) for satellite derived rainfall products, Wong and Chiu (2008) indicated the likelihood of underestimation of the rainfall rate for heavy rainfall conditions in Hong Kong; and (3) for gridded precipitation datasets, Ensor and Robeson (2008) pointed out that the statistical characteristics could be very different from the original point datasets.

All rainstorm cases which warranted the issue of Red or Black Rainstorm Warning (hereafter referred to as ‘rainstorm cases’ unless otherwise stated) during 1998–2010 were chosen for this study (a full list of records of the RWS is available online at http://www.weather.gov.hk/wxinfo/climat/ warndb/warndb3_e.shtml). Two rainstorm cases separated by no more than 3 h (with both warning issuance and cancellation time rounded to nearest hour) are pooled together and counted as one single case. Altogether, 51 major rainstorm cases are identified for this study as listed chronologically in Table 1.

Table 1. List of the 51 rainstorm cases and the associated types of synoptic background

No.	Date	Type	No.	Date	Type	No.	Date	Type
1	26.04.1998	T	21	2001.09.03	T	41	25.06.2008	TC
2	02.05.1998	T	22	07.09.2001	T	42	26.06.2008	TC
3	24.05.1998	O	23	14.09.2002	O	43	12.07.2008	T
4	09.06.1998	T	24	18.10.2002	O	44	03.06.2009	T
5	22.08.1999	TC	25	05.05.2003	T	45	19.07.2009	TC
6	24.08.1999	TC	26	08.05.2004	O	46	22.07.2010	TC
7	25.08.1999	TC	27	24.06.2005	T	47	28.07.2010	T
8	16.09.1999	TC	28	24.04.2006	T	48	05.08.2010	O
9	02.04.2000	T	29	02.05.2006	T	49	08.09.2010	O
10	14.04.2000	O	30	02.06.2006	T	50	10.09.2010	T
11	22.04.2000	T	31	09.06.2006	T	51	20.09.2010	TC
12	12.06.2000	T	32	13.06.2006	T
13	23.08.2000	TC	33	16.07.2006	O
14	08.06.2001	T	34	09.09.2006	O
15	09.06.2001	T	35	13.09.2006	TC
16	11.06.2001	T	36	24.04.2007	T
17	12.06.2001	T	37	10.06.2007	T
18	27.06.2001	T	38	19.04.2008	TC
19	02.08.2001	T	39	07.06.2008	T
20	01.09.2001	T	40	13.06.2008	T

• Cases are listed in chronological sequence and the date refers to the case start day. T refers to Trough, TC refers to Tropical Cyclone and O refers to situations other than T and TC.

According to Chin (1968), Trough (T) and Tropical Cyclone (TC) situations are the two major synoptic scenarios conducive to heavy rainstorms in Hong Kong. As observed from Table 1, T and TC situations accounted for about 60 and 20% of cases, respectively. Other mechanisms, including upper-level disturbance, southwest monsoon, cold front and local unstable conditions, altogether contributed less than 20% of cases. Due to their relatively low frequency of occurrence, they are grouped together and labelled as type ‘Other’ (O) in the present study. It is noted that rainstorms occur every year but the variability is large. A total of nine cases is noted in 2001 but only one case is found in 2003, 2004 and 2005. June has the highest probability of having rainstorms with about one-third of the sample rainstorms occurring in this month. Visual inspection indicates no discernible trend in the annual number of rainstorms in the study period (figure not shown).

3. Methodology and definitions

3.1. Principal zones

Despite a relatively high average rain gauge density (about 1 for less than 10 km² compared to an average of 1 for over 600 km² in the US (see USACE, 1994)), the spatial distribution of rain gauges is rather irregular so that it may not be meaningful to treat each station individually in evaluating the spatial extent of a rainstorm. In order to minimize possible bias resulting from the irregularity of rain gauge distribution (in particular, multiple gauges within a small area) while preserving the spatial locality of rainfall at regional scale in describing the bulk features of a rainstorm, rain gauges are clustered into principal zones of similar domain size in the present study. It should be noted that it is not the intention to partition the territory into regular spatial cells but, rather, to cluster rain gauges into zones to facilitate a comparison of the spatial extents of rainstorms. The zones are presented visually to be circular or elliptical in shape (see Figure 2) to align with the fact that heavy rain clusters are mostly described in circular or elliptical cell shapes in space (Huff, 1979).

Correlation between the maximum hourly rainfall recorded during rainstorms between any two rain gauges are computed and are presented as a function of horizontal distance between rain gauges in Figure 3 (neglecting the difference in gauge altitudes). For this part of correlation analysis, rainstorm duration was taken to be the period from an hour before the issuing time (round down to nearest hour) to an hour after the cancelling time of the rainstorm warning (round up to nearest hour). It can be seen that there is a very high correlation for a distance up to around 5–6 km. By making reference to such rain gauge separation and geographical continuity and preserving the spatial locality of rainstorms, a total of 39 zones are defined subjectively as shown in Figure 2(a). For ease of reference, the zones are labelled as shown in Figure 2(b). Figure 4 shows the principal zone allocation of the 125 stations.

Figure 3

Correlation between the maximum hourly rainfall recorded during rainstorms between any two gauges as a function of horizontal distance between gauges. The horizontal lines indicate the significant levels of the correlation coefficient.

Figure 4

Summary of the allocation of stations (in station code) for the 39 principal zones. Each zone in Figure 2 is identified in the grid by the letter at the top followed by the number to the left of the grid reference. GEO's gauges are coded in format of Hmn, Kmn or Nmn where mn is numeric suffix, while the remaining ones are HKO's gauges. Station information for HKO's gauges can be found in HKO (2011b) whereas that for GEO's can be found at http://hkss.cedd.gov.hk/hkss/eng/download.aspx.

A summary of the separation between the rain gauges within the 39 zones are given in Figure 2(a). Most of the rain gauge separations are within 5 km. The diameter of the vast majority of zones in circular shape is around 4 km (corresponding to an area of ∼20 km²) whereas the diameter of the major axis of the largest elliptical zone is around 7 km (corresponding to an area of ∼22 km² if a minor axis of ∼4 km is assumed). Effectively, the zone density is comparable to the minimum density of station of 25 km² per station for mountainous islands with irregular precipitation as recommended by WMO (1974) for hydrometeorology applications. With reference to Henry (1974), a typical tropical rainstorm is about 30 km in diameter. It is thus realistic to assume that the size of principal zones defined here is also comparable to the spatial scale of the rain cells/clusters in a typical rainstorm, if not finer, such that the spatial details of a rainstorm could be resolved properly. Although the delineation of principal zones adopted is not unique, it is reasonable and practical considering that some form of zoning is necessary for the study if data from all the available unevenly distributed gauges are used. In fact, correlation between maximum hourly rainfall during rainstorms between any two stations within all individual zones is significant at the 5% level. (Actually, all correlations are significant at 0.1% level for the vast majority of zones.) A similar result with even higher correlations is obtained if the total rainfall recorded during rainstorms is considered.

In light of the considerable spatial-temporal variability of rainstorms, minimal effect can be assumed for a gauge located at the edge of a zone if it were otherwise located in an adjacent zone. In fact, re-allocating gauges at the edge of a zone to the closest adjacent zone will have little influences to the overall severity of rainstorms evaluated as shown in Figures S1 and S2. If the total number of zones is kept more or less the same, inferences made regarding the overall severity of a rainstorm should be relatively stable even if the zone partitioning is altered.

3.2. Zone and total hyetographs

In line with the principle proposed by Rao and Clapp (1986) in evaluating rainfall intensities, the hourly rainfall at an individual zone is taken to be the maximum rainfall recorded from available rain gauges within the zone. This simple approach in evaluating the spatial distribution is adopted but not other alternatives (such as the mean areal rainfall), to probe the most probable adverse condition for the purpose of indexing rainstorms relevant to potential risk evaluation. In brief, the hourly rainfall at each principal zone is constructed analytically to reflect the maximum hourly rainfall experienced in the zone in the corresponding hour, which is referred to as the zone hyetograph in the present study. If a zone comprizes a single rain gauge, the zone hyetograph is simply the hyetograph recorded at that rain gauge.

The total hyetograph, which is hypothetical, is synthesized by tracking the maximum hourly rainfall among all zones (or all rain gauges equivalently) during a rainstorm. Theoretically, different rainstorm cases which have different spatial rainfall distributions over time could have similar total hyetographs, yet in reality the temporal characteristics of individual rainstorm cases should readily be differentiated because of the highly variable nature of rainstorms both in space and time. The rationale to formulate the total hyetograph is to facilitate the definition of the lifespan of a rainstorm, as if Hong Kong were a unified catchment area. In other words, the total hyetograph represents the upper envelope of all zone hyetographs.

3.3. Rainstorm lifespan

The lifespan or duration of a rainstorm is defined by the onset and the end time. A rainstorm is considered to start when the hourly rainfall as shown in the total hyetograph exceeded a predefined threshold in the growing stage. Taking into account possible intermittent fluctuations, a rainstorm is considered to have ceased when the hourly rainfall shown in the total hyetograph began to fall below a predefined threshold for at least two successive hours in the dissipating stage. This identification of the duration of extreme rainfall events based on the hourly condition of any one rain gauge is similar to Molini et al. (2009, 2011) in classifying heavy rainfall events in Italy. The time elapsed between the onset and the cessation is taken to be the duration of a rainstorm, which can be divided into two segments: time-to-peak (i.e. the time period between the onset and the peak of an event) and peak-to-end (i.e. the time period between the peak and the end of an event). Figure 5 shows a schematic diagram of the lifespan of a rainstorm.

Figure 5

Schematic depiction of rainstorm lifespan according to the total hyetograph. The duration of rainstorm is the time elapse between T_Onset and T_End (ie t1 + t2). R_Threshold equals 10 mm in this study.

In this study, an hourly rainfall of 10 mm is adopted as the threshold for identifying the onset and end time of the rainstorms. This in general aligns with the specification of heavy precipitation given in UK Met Office (2007), WMO (2008) and Wong and Chiu (2008) in describing the intensity of precipitation. Moreover, the hourly rainfall of 10 mm was also adopted by Wu et al. (2006) in extracting rainstorm events from the hourly rainfall data recorded at the Hong Kong Observatory Headquarter and by Henry (1974) in defining a tropical rainstorm over Southeast Asia.

3.4. Rainstorm attributes

In this study, four attributes are used to characterize the magnitude and the severity of the rainstorm cases: (1) the Peak Intensity (PI), (2) the Peak Rainfall Amount (PA), (3) the Outer Area (A₃₀), and (4) the Inner Area (A₇₀). Definitions of these 4 attributes are detailed as follows.

1. Peak Intensity (PI) is the maximum hourly rainfall of the total hyetograph (see Figure 4). Equivalently, it is the maximum hourly rainfall recorded by any rain gauge according to the definition of total hyetograph.
2. Peak Rainfall Amount (PA) is the maximum local rainfall amount (or rainfall depth in the hydrology community) among all zones. The local rainfall amount at an individual zone is the sum of the hourly maximum rainfall experienced in a zone over the lifespan of rainstorm and is evaluated from the zone hyetograph.
3. Outer Area (A₃₀) is the total number of zones with maximum hourly rainfall exceeding 30 mm, and,
4. Inner Area (A₇₀) is the total number of zones with maximum hourly rainfall exceeding 70 mm.

The duration of a rainstorm is not used (i.e, not considered as an individual attribute) to characterize a rainstorm because its influence has been reflected in PA, as a relatively long-lasting rainstorm will likely yield a larger PA than that of a short-lived one.

The PA compares the maximum rainfall accumulated over zones rather than the maximum at-gauge total rainfall (or point rainfall). Assuming the simplest circumstance of a single centre rainstorm, then if the storm centre is over a zone with only one gauge, the PA would be the same as the at-gauge maximum rainfall amount. If the storm centre is over a zone with multiple gauges available, the rainfall amount over the zone (as computed from the zone hyetograph according to the principle given in Section 3.2) will most likely be greater than the rainfall amount recorded at any individual gauges within the zone. Since the maximum at-gauge rainfall amount recorded may underestimate significantly the true peak amount of a rainstorm (e.g. Foufoula-Georgiou, 1989), it is anticipated that the PA would be a more suitable quantity to compare the maximum rainfall amount of a rainstorm. In fact, correlation between PA and maximum at-gauge rainfall is high (r = 0.98). The PA is greater than the maximum at-gauge rainfall for 45 rainstorms (out of the 51 cases) with an average difference of about 30 mm and the maximum difference of nearly 90 mm.

For A₃₀, the 30 mm h⁻¹ threshold is chosen as it is the threshold for issuing an Amber warning in the RWS. For A₇₀, the limit of 70 mm h⁻¹ is the criterion for issuing a Black rainstorm warning in the RWS and this rainfall rate was also once regarded as a potential indicator of the occurrence of landslides anywhere locally (Brand et al., 1984). It should be noted that both A₃₀ and A₇₀ portray how many zones experience a severe downpour of considerable hazardous risk during rainstorm cases, but these zones (if any) could be located contiguously or scattered (e.g., in situation when a rainstorm has multiple cells located apart). Both A₃₀ and A₇₀ quantify the spatial extent of rainstorms and two intensity levels (i.e. 30 and 70 mm) are considered to cater for cases with different intensity. It should be noted that if areal extent of rainstorm is compared in terms of areal rain amount (depth), the areal extent for a rainstorm of higher intensity shorter duration could be similar to or even smaller than one of lower intensity but longer duration. For the purpose of quantifying the severity of a rainstorm, it is more appropriate to consider the areal extent of the rainstorm from the perspective of potential risk it could cause. While flash flooding is mostly a result of intense rainfall in a period of time, and short period intensities could be critical for assessing landsliding risk in Hong Kong as stated in Evans et al. (1999), it seems more relevant to compare the spatial extent of rainstorms by referring to the areal coverage ‘affected’ by high rainfall rate as by A₃₀ and A₇₀ during a rainstorm. On the other hand, if the spatial extent of ‘affected’ areas was determined by counting the number of gauges, the result would be biased to areas of high gauge density. For example, the rainstorms on 9 June 1998 and 16 July 2006 have, respectively, 11 and 12 zones with hourly rainfall exceeding 70 mm (i.e. their A₇₀ are similar, see Table 2). For the rainstorm on 16 July 2006, heavy rainfall is concentrated in Hong Kong Island and Kowloon (see http://www.weather.gov.hk/wxinfo/news/2006/pre0716e.htm) where the gauge density is high such that there are 38 gauges with hourly rainfall exceeding 70 mm. However, there are only 12 gauges with hourly rainfall exceeding 70 mm for the rainstorm on 9 June 1998 because heavy rain condition mainly affect various parts of the New Territories (see http://www.weather.gov.hk/wxinfo/pastwx/mws199806.htm) where gauge density is relatively lower.

Table 2. Summary of the attributes and the values of the SI of the 51 rainstorms from 1998 to 2010

Rainstorm No.	Date	Duration (h)	Attributes				SI
			PI	PA	A30	A70
1	26.04.1998	7	79.5	195.5	26	2	3.8
2	02.05.1998	3	53.5	74.0	16	0	1.7
3	24.05.1998	13	74.0	338.0	28	2	4.4
4	09.06.1998	18	98.0	575.0	31	11	7.4
5	22.08.1999	30	91.0	616.5	30	7	6.8
6	24.08.1999	9	69.5	245.0	26	0	3.5
7	25.08.1999	14	71.0	261.0	15	1	2.9
8	16.09.1999	17	90.0	327.5	26	2	4.6
9	02.04.2000	9	77.0	219.5	26	1	3.7
10	14.04.2000	16	106.0	585.5	22	7	6.4
11	22.04.2000	7	103.5	244.4	30	10	5.9
12	12.06.2000	6	102.0	205.0	23	5	4.6
13	23.08.2000	9	121.5	405.5	28	10	6.9
14	08.06.2001	9	62.0	235.0	13	0	2.3
15	09.06.2001	13	95.0	400.5	27	3	5.2
16	11.06.2001	11	77.5	249.0	24	1	3.7
17	12.06.2001	15	94.0	264.0	21	2	4.1
18	27.06.2001	15	65.5	263.0	30	0	3.7
19	02.08.2001	8	90.5	180.0	16	3	3.6
20	01.09.2001	11	99.5	255.5	32	7	5.6
21	03.09.2001	13	69.0	159.0	12	0	2.1
22	07.09.2001	11	65.0	241.5	16	0	2.6
23	14.09.2002	23	93.5	381.0	23	5	5.1
24	18.10.2002	9	127.5	278.0	11	4	4.5
25	05.05.2003	24	118.5	452.0	36	8	7.3
26	08.05.2004	9	94.5	199.5	25	4	4.4
27	24.06.2005	14	75.0	283.5	34	2	4.6
28	24.04.2006	8	143.5	287.0	15	4	5.2
29	02.05.2006	10	91.0	262.0	35	2	5.0
30	02.06.2006	8	106.5	311.0	24	7	5.4
31	09.06.2006	6	94.0	221.5	29	6	5.0
32	13.06.2006	5	84.0	132.5	11	3	2.7
33	16.07.2006	6	126.0	224.0	28	12	6.5
34	09.09.2006	6	76.0	156.0	14	1	2.5
35	13.09.2006	20	80.5	465.5	36	2	5.7
36	24.04.2007	4	66.0	86.0	36	0	3.5
37	10.06.2007	12	86.5	210.5	27	2	4.1
38	19.04.2008	7	104.5	292.5	38	17	7.7
39	07.06.2008	24	145.5	565.5	37	17	9.7
40	13.06.2008	12	73.0	277.5	33	1	4.3
41	25.06.2008	16	81.5	390.0	27	1	4.6
42	26.06.2008	8	63.0	108.5	14	0	1.9
43	12.07.2008	7	99.5	245.0	21	9	5.0
44	03.06.2009	5	69.5	87.0	19	0	2.3
45	19.07.2009	7	71.5	198.5	35	1	4.1
46	22.07.2010	8	125.0	275.5	28	10	6.4
47	28.07.2010	16	92.5	204.5	27	3	4.3
48	05.08.2010	3	61.0	79.5	7	0	1.2
49	08.09.2010	6	79.5	128.5	28	2	3.7
50	10.09.2010	3	80.0	164.0	16	1	2.8
51	20.09.2010	16	70.5	267.0	26	1	3.7
Minimum		3	53.5	74.0	7	0	1.2
First quartile		7	72.3	199.0	18	1	3.6
Median		9	86.5	249.0	26	2	4.4
Third Quartile		15	99.5	301.8	30	6.5	5.3
Maximum		30	145.5	616.5	38	17	9.7

• Values in the top quartile are italic and highest value in each column is shown in bold.

3.5. Standardization and indexing

The relative severity of rainstorms in terms of individual attributes can be determined according to the corresponding ranking. An overall rainstorm severity index is devised by combining the relative severity of the four individual attributes. Since each attribute has its own unit, variability and scale, it is preferable to standardize the four attributes into the same range and unit while preserving the relative ranking between values. To translate the values of different attributes into the same scale, the continuous scoring technique of percentile rescaling with a common and fixed range from 1 to 10 for increasing degree of severity is used. The two steps below illustrate how the percentile rescaling for each attribute is accomplished:

Step 1:

Step 2:

The lowest and highest values are determined from the statistics of the 51 selected rainstorms.

The overall rainstorm severity index, termed as severity index (SI) hereafter, is constructed using the weighted average of the four attributes in rescaled value:

where μ,α,β,γ are weightings of the respective attributes. These weightings are set according to the importance of different attributes in different hazards such as landslip or flooding. In this study, all these parameters were set equal to 1 (i.e. equal weighting) for illustration purpose. Values of SI range from 1 to 10, as for all attributes. The SI is tailored to local circumstances in the sense that it ranks according to historical rainstorm data (c.f. fixed universal criteria in the R₂₄ scheme). A comparison of the severity of rainstorms can be made in terms of the SI and the composition of the severity can be interpreted with respect to each of the components (i.e. the attributes).

To align with the newly implemented three-tier typhoon classification in Hong Kong (see http://www.hko. gov.hk/aviat/outreach/product/20th/TCclass.htm for details) and to facilitate a comparison with the rainstorm severity based on the R₂₄ classification scheme, the severity of rainstorms will further be categorized into three classes. The rainstorm cases are classified in an ascending order as either Category 1 (C1), Category 2 (C2) or Category 3 (C3) according to the corresponding SI value. For simplicity, the partitioning of these three categories is set to be evenly spaced. Since the value of SI ranges from 1 to 10, a rainstorm is assigned as C3 (the strongest class) if SI was ≥ 7; or C1 (the weakest class) if it was < 4; or C2 rainstorm if otherwise. On top of the categorical classification, the scales or the levels of classes can be adjusted, if desired, for specific usages through a calibration against impact figures such as damage statistics, number of landslips or whether flooding occurred. However, as damage figures depend not only the physical attributes of rainstorms, but also on the effort of disaster preparedness and reduction, a homogeneous set of damage figures for the SI is difficult to obtain and such calibration has not been performed.

Given the complex topography of Hong Kong and the large land-use diversity, vulnerability to various hazards varies regionally over all the territory. For example, low-lying areas in the northern part of the New Territories are prone to flooding whereas areas with more man-made slopes and natural hillside are more susceptible to landslips during rainstorms. As such, the severity in terms of impact brought by rainstorms of similar SI (as well as the values of other attribute) as computed above could be different if intense rainfall is concentrated in areas of different regional vulnerability. To include a measure of the regional vulnerability, the value of A₇₀ is modified by assigning weighting factors to different zones according to specific regional vulnerability. Such modification could also be applied to other attributes.

4. Results and discussion

Table 2 summarizes the values of the four attributes (PI, PA, A₃₀ and A₇₀) and the values of SI for all the 51 rainstorms. It is noted that an event can be in the highest SI quartile without all of its attributes being in the highest quartile. In fact, it is evident that the severity of rainstorms would change considerably if it is determined by individual attributes. For example, the most severe rainstorm would be the one on 22 August 1999 according to PA but 7 June 2008 according to PI. Similarly, the rainstorm on 2 May 1998 is the least severe in terms of both the PI and PA but the one on 5 August 2010 is the most ‘localized' as inferred from A₃₀ and A₇₀. Also depicted in Table 2 is the duration of rainstorms. With the exception of one case, all rainstorms last shorter than 24 h.

Table 3 lists in descending order the severity of rainstorms in terms of SI and the corresponding category. Among the 51 rainstorms, there are 4 C3, 27 C2 and 20 C1 rainstorms. It can be observed that all rainstorms which warranted the issue of the Black Rainstorm Warnings are of either C2 or C3 category, except for the rainstorm on 24 August 1999 which is classified as a C1 case. This rainstorm is considered not quite severe as the maximum hourly rainfall registered in all zones is less than 70 mm during the rainstorm (and thus the A₇₀ is equal to zero).

Table 3. Classification of rainstorms with the ranking in descending order in the severity index

C3				C2				C1
Rank	Rainstorm	RWS	R24 Class	Rank	Rainstorm	RWS	R24 Class	Rank	Rainstorm	RWS	R24 Class
1	07.06.2008 (T)	Blk	SR	5	23.08.2000 (TC)	Blk	SR	32	26.04.1998 (T)	Red	SR
2	19.04.2008 (TC)	Blk	SR	6	22.08.1999 (TC)	Blk	SR	33	27.06.2001 (T)	Red	SR
3	09.06.1998 (T)	Blk	SR	7	22.07.2010 (TC)	Blk	SR	34	20.09.2010 (TC)	Red	SR
4	05.05.2003 (T)	Red	SR	8	14.04.2000 (O)	Red	SR	35	02.04.2000 (T)	Red	SR
				9	16.07.2006 (O)	Blk	HR	36	11.06.2001 (T)	Red	SR
				10	22.04.2000 (T)	Blk	SR	37	08.09.2010 (O)	Red	HR
				11	13.09.2006 (TC)	Red	SR	38	02.08.2001 (T)	Red	HR
				12	01.09.2001 (T)	Blk	SR	39	24.08.1999 (TC)	Blk	HR
				13	02.06.2006 (T)	Red	SR	40	24.04.2007 (T)	Red	HR
				14	09.06.2001 (T)	Red	SR	41	25.08.1999 (TC)	Red	SR
				15	24.04.2006 (T)	Blk	SR	42	10.09.2010 (T)	Red	HR
				16	14.09.2002 (O)	Red	SR	43	13.06.2006 (T)	Red	HR
				17	12.07.2008 (T)	Red	SR	44	07.09.2001 (T)	Red	SR
				18	02.05.2006 (T)	Red	SR	45	09.09.2006 (O)	Red	HR
				19	09.06.2006 (T)	Blk	SR	46	03.06.2009 (T)	Red	R
				20	24.06.2005 (T)	Red	SR	47	08.06.2001 (T)	Red	HR
				21	16.09.1999 (TC)	Red	SR	48	03.09.2001 (T)	Red	HR
				22	25.06.2008 (TC)	Red	SR	49	26.06.2008 (TC)	Red	HR
				23	12.06.2000 (T)	Blk	HR	50	02.05.1998 (T)	Red	HR
				24	18.10.2002 (O)	Red	SR	51	05.08.2010 (O)	Red	R
				25	24.05.1998 (O)	Red	SR
				26	08.05.2004 (O)	Blk	HR
				27	28.07.2010 (T)	Blk	HR
				28	13.06.2008 (T)	Red	SR
				29	19.07.2009 (TC)	Red	HR
				30	10.06.2007 (T)	Red	HR
				31	12.06.2001 (T)	Red	SR

• ‘Blk’ and ‘Red’ indicates that the rainstorm warranted the issue of Black or Red rainstorm warnings respectively. For comparison purpose, the classification based on the R₂₄ scheme is also given: SR, HR and R stands for severe rainstorm, heavy rainstorm and rainstorm respectively (see Section 4 for details on the definition). Besides, the rainstorm type is given in the brackets.

Among the 51 rainstorms, the most severe rainstorm (the highest SI value) occurred on 7 June 2008 whereas the weakest (the lowest SI value) one occurred on 5 August 2010. During the rainstorm on 7 June 2008, the Observatory recorded 145.5 mm during the hour from 0800 to 0900, the highest hourly rainfall since records began in 1884. About 200 mm of rainfall was recorded generally over Hong Kong on that day, exceeding 300 mm at Lantau Island and urban areas (see http://www.hko.gov.hk/wxinfo/news/2008/pre0607e.htm). This rainstorm caused several hundred landslides, including many debris flows that affected developed areas (CEDD, 2008) and caused two fatalities in a landslip.

All of the 51 rainstorm cases studied are of the violent category when applying WMO's criteria to the PI of rainstorm (see Table 2 for the values of PI). Thus the WMO's criteria is not suitable for further categorizing the severity among the 51 rainstorms because violent is the highest category.

To compare with China's R₂₄ classification scheme, the severity of a rainstorm based on R₂₄ is determined according to the maximum R₂₄ among the 39 zones, using 24 h rainfall after onset under the zone hyetograph. Table 4 shows the comparison of the number of rainstorms in each category of the R₂₄ classification (i.e. Rainstorm (R), Heavy Rainstorm (HR) and Severe Rainstorm (SR)) and the C1, C2 and C3 proposed in this study. It is noted that, 49 of the 51 rainstorms studied are classified as either HR or SR, and 21 out of the 27 C2 cases and all the 4 C3 cases are of SR class in China's R₂₄ scheme. It is noteworthy that the majority of the 51 rainstorms (i.e., 31 of the cases) belong to the highest class in China's R₂₄ scheme. It appears that the R₂₄ scheme, which employs a single parameter with fixed universal thresholds, may not be sufficient to track the severity of rainstorms in Hong Kong. On the other hand, by integrating a suite of attributes, the classification based on the SI could better differentiate the overall severity of rainstorms in Hong Kong where the nature of rainstorm-induced hazards is diverse (as a result of high population density and complex topography) such that the magnitude of a single attribute might not be adequate in describing the overall severity of a rainstorm.

Table 4. Comparison matrix of the R₂₄ classification scheme and the classification proposed in this study

Rainstorm severity	Rainstorm classification based on R24			Total
	Rainstorm (R)	Heavy rainstorm (HR)	Severe rainstorm (SR)
C1	2	11	7	20
C2	0	6	21	27
C3	0	0	4	4
Total	2	17	32	51

To illustrate how the severity of rainstorm may vary if a measure of the regional impact is introduced, the A₇₀ is modified by assigning weighting factors to different zones according to regional vulnerability in terms of (1) population density and (2) flooding risk. Two conditions are considered for the purpose of comparison.

For (1), three types of population density (Urban (U), Sub-urban (S) and Rural (R)) are applied with the classification of zones depicted in Figure 2(b). Accordingly, heavy downpour (i.e. with hourly rainfall > 70 mm) occurring in urban areas with high population density will have a much higher A₇₀ than that in rural areas with the same rainfall intensity. For (2), flooding threat due to heavy downpour occurring in low-lying and natural flood-plains in the northern part of the New Territories is highly emphasized. This is done by attaching very high weight to zones in vicinity of the flood-prone area (C3,D2,D3,E1,E3,F2,F3,G1,G3 and H1, see also Figure 2(b)).

To enhance the influence of regional impact, large contrast in the weighting is applied: [R:S: U = 1:10:100 for scenario (a) and 1:100 for scenario (b)]. Figure 6 compares the SI computed with regional impacts and without regional impact. Correlation between the SI with and without regional impact is high (r = 0.99 for scenario (a) and 0.95 for scenario (b)). While including a measure of regional impact does not have substantial influence on the overall SI ranking such that there is one category change (increase or decrease) for a couple of rainstorm cases, it is worth noting that for scenario (b), the most severe rainstorm becomes the one that occurred on 14 April 2000 rather than the one on 7 June 2008. In fact, the SI for rainstorm on 14 April 2000 (7 June 2008) increased (decreased) significantly by 1.3 (2.2) by introducing the influence of specified regional flooding risk. For the rainstorm on 14 April 2000, over 500 mm rainfall was recorded in the western part of the New Territories. Villages were half-submerged in flash floods and water was about a metre deep and there were 128 reports of flooding and 28 landslides (see http://www.weather.gov.hk/wxinfo/pastwx/mws200004.htm). The regional difference in heavy rainfall condition between the rainstorms on 14 April 2000 and 7 June 2008 can be seen from Figure 7 which compares the location of zones with hourly rainfall exceeding 70 mm. It can be seen that although the rainstorm on 7 June 2008 is more wide-spread with more zones affected by heavy rainfall, its overall severity would be lower than the one on 14 April 2000 which has centre located at low-lying area in the New Territories where flooding risk is specifically emphasized. (In fact, the Special Announcement on Flooding in the northern New Territories (to alert the public of potential flooding due to heavy rain, see http://www.hko.gov.hk/wservice/warning/flood.htm) is issued during the rainstorm on 14 April 2000 but not for the one on 7 June 2008.) Therefore, the severity of rainstorms could vary with regional vulnerability depending on how the regional vulnerability is measured with respect to the nature of hazard emphasized.

Figure 6

Comparison of SI computed with and without regional impact. Circle symbol shows a change in the severity class if an emphasis on regional impact is applied. Left panel shows regional impact is based on (a) population density and right panel that based on (b) flood risk in the northern part of the New Territories. Rainstorms on 14 April 2000 and 7 June 2008 mentioned in text are also indicated.

Figure 7

Comparison of the locality of heavy rainfall condition for the rainstorms on (a) 14 April 2000 and (b) 7 June 2008. Zones with hourly rainfall exceeding 70 mm are shown. The shaded zone(s) denotes where the maximum hourly rainfall (i.e. PI) occurred which can be referred to as the centre(s) of rainstorm. It can be seen that the rainstorm on 14 April 2000 centred in the western New Territories whereas the one on 7 June 2008 has two peaks (over Lantau Island and Kowloon Peninsulas).

Given that trough situations accounted for the majority of rainstorms (refer to Table 1), there is no conclusive evidence to support that the severity of a rainstorm bears any relationship to its prevailing synoptic background as indicated in Table 3, though three of the four C3 rainstorms are associated with trough pattern and the only C3 TC case was an early TC occurring in spring interacting with the northeast monsoon. Actually, no statistically significant relationship is found in the SI between various rainstorm types. The lack of relationship between the SI and the type of rainstorms is not unexpected because heavy rainfall in T and TC (being the major rainstorm types) is related to the intense convective cells embedded in the disturbances which are highly variable (Chin, 1968).

5. Conclusion

The present study attempts to formulate a practical framework to index the severity of rainstorms in Hong Kong. Making use of the hourly rainfall data of over 120 rain gauges, the characteristics of 51 rainstorms occurring in Hong Kong between 1998 and 2010 are examined. The characteristics of the rainstorms, viz their rainfall amount, maximum hourly rainfall intensity and spatial coverage, are standardized and used to derive a severity index (SI) for describing the severity of the rainstorm cases. A three-tier classification is also proposed to classify the severity of the rainstorms according to their SI value.

The SI quantifies the relative severities of rainstorms by incorporating various physical characteristics of the rainstorms rather than relying only on one or two measures of rainstorm independently as commonly considered. It can be computed easily from the hourly rainfall data and with suitable adjustment, may be determined in real-time for identifying extremely severe rainstorm conditions. Besides, the categorization of rainstorm severity is quantified with respect to historical rainstorms rather than labelled with reference to fixed universal criteria and is therefore applicable to places of different climate regimes. In the present framework, a measure of regional impact is also allowed in assessing the severity of rainstorms. Depending on how the regional vulnerability is measured, the relative severity of rainstorms can be evaluated with respect to the nature of hazard emphasized and the relative severity of rainstorms may change accordingly.

In this study, a comprehensive scheme to describe the severity of rainstorms based on their physical attributes has been derived. The exercise is useful to enable benchmarking of future rainstorms for raising awareness of extreme rain events both on the weather and climate scales. How the severity is related to the impact of the rainstorm, which is of interest to disaster reduction personnel, may be further studied when comprehensive figures of casualty and damage are available. It is conceivable that different users may put different weights on the various attributes, e.g. flash flood control staff may be more interested in maximum intensity while landslip emergency response staff may pay more attention to the peak total rainfall amount in specific zones. The approach of setting up the severity index proposed in this paper is flexible enough to allow tuning of the index for specific applications.

Acknowledgement

The authors would like to thank Mr. K C Chu of the Chinese University of Hong Kong for his help in data extraction and computation. Acknowledgments also go to Mr. C M Shun, Mr. H Y Mok and Dr. T C Lee of the Hong Kong Observatory for their useful and constructive comments. Last but not least, the authors would like to thank the anonymous reviewers for their insightful suggestions to enrich the content of the paper.