Rainfall is the primary trigger of landslides in Hong Kong; hence,
rainstorm spatial distribution is an important piece of information
in landslide hazard analysis. The primary objective of this paper is
to quantify spatial correlation characteristics of three
landslide-triggering large storms in Hong Kong. The spatial maximum
rolling rainfall is represented by a rotated ellipsoid trend surface
and a random field of residuals. The maximum rolling 4, 12,
24, and 36 h rainfall amounts of these storms are assessed via
surface trend fitting, and the spatial correlation of the detrended
residuals is determined through studying the scales of fluctuation
along eight directions. The principal directions of the surface
trend are between 19 and 43
Severe rainstorms are one of the most dangerous meteorological phenomena which pose risks to human lives and properties. A large rainstorm may cause serious damage to infrastructure and threaten public safety. For instance, a large storm hit Lantau Island, Hong Kong, on 5–7 June 2008 and caused about 2400 natural terrain landslides and 622 flooding spots (CEDD, 2009). Historical records show that the spatial rainstorm variation and the potential for triggering landslides are closely correlated. The Geotechnical Engineering Office (GEO) maintains a Natural Terrain Landslide Inventory (NTLI; King, 1999; Maunsell-Fugro Joint Venture, 2007), which has records of 19 763 natural terrain landslides and debris flows up to 2013 as well as 89 571 relict natural terrain landslides. The data of natural terrain landslides that occurred on 5–7 June 2008 are extracted and the distributions of the landslide volume and the maximum 24 h rolling rainfall are plotted in Fig. 1. There is a close correspondence between the observed landslide volume and the maximum 24 h rolling rainfall in space. Characterizing the spatial characteristics of storms is therefore essential for assessing rain-induced landslide hazards.
Spatial distributions of the maximum 24 h rolling rainfall and the landslides triggered in Hong Kong on 5–7 June 2008.
Geotechnical and environmental factors that affect the triggering of natural terrain landslides.
Numerical analyses have also been conducted to establish the relation between rainfall characteristics and landslides (e.g., Gao et al., 2016, 2017). Geotechnical and environmental factors, such as slope gradient, rock and soil formations, groundwater conditions, vegetation, and the presence of civil infrastructure, are believed to ultimately affect the triggering of landslides in addition to rainfall intensity. The main factors that affect triggering of natural terrain landslides are summarized in Fig. 2.
In hazards mitigation and engineering design, certain “design storms” must be considered, and the engineering system should be sufficiently safe under such design storms (Gao et al., 2017). A design storm is often defined by a hyetograph (time distribution) and an isohyet (spatial distribution). For a particular region where the spatial rainfall variation is significant, a uniform representation of the spatial distribution is not reasonable since a storm has a centre and influences a limited area (AECOM and Lin, 2015). Instead, relevant spatial variation factors of rainfall must be characterized, such as the geometry of spatial form (agglomerate and local gradient) and the spatial correlation.
A storm is difficult to model due to its intermittence (i.e., no rainfall at a particular position during a particular short period) and strong spatial and temporal heterogeneity (e.g., Barancourt et al., 1992; Bacchi and Kottegoda, 1995; Mascaro, 2013). However, the rainfall amount, which is in the form of regionalized variables, is spatially correlated over a certain distance (Panthou et al., 2014; de Luca, 2014). A regionalized variable is any variable distributed in space. Random field theory is recognized as a suitable theory for describing regionalized variables (Vanmarcke, 1977) and has been proven effective for the regionalized variables (e.g., Dasaka and Zhang, 2012; Li et al., 2015). The random field theory has also been used in spatial storm analysis (e.g., Rodríguez-Iturbe et al., 1986; Bouvier, 2003) and adopted to describe storm spatial structures (e.g., Zawadzki, 1973; Lebel et al., 1987; Gyasi-Agyei and Pegram, 2014).
Research on spatial rainfall distribution using statistical models has been performed in Hong Kong for different engineering purposes (Leung and Law, 2002; Jiang and Tung, 2014; AECOM and Lin, 2015). Leung and Law (2002) conducted kriging analysis on Hong Kong hourly rainfall data in 1997 and 1998. Rainfall contours were interpolated to qualitatively estimate possible flooding locations. Jiang and Tung (2014) derived rainfall depth–duration–frequency relations at ungauged sites in Hong Kong using an ordinary kriging approach based on annual maximum daily rainfall data. The extreme rainfall estimates are sensitive to assumed statistical parameters and uncertainties of the interpolation method.
The storm characteristics such as distribution form and spatial correlation are not sufficiently analyzed when studying the hydrological response of a target system such as a slope safety system. In particular, limited attention has been paid to event-based spatial characteristics of large rainstorms in Hong Kong, whose patterns and structures are as useful as the statistical trend based on historic rainfall records, especially when one needs to select large rainstorms for landslide risk assessment. Sufficient information should be provided, including both spatial variation and correlation. However, several key questions have not been answered. Can the spatial precipitation distribution of a large storm be represented using a particular spatial form? How does the spatial correlation of rainfall change with the rainstorm magnitude? What are the key factors that influence the spatial structure of rainfall distribution? Such questions motivate the present study on the spatial characteristics of large rainstorms over hilly terrains in Hong Kong.
The objective of this paper is to identify the spatial variations
and correlation of large rainstorms in Hong Kong. Three large
storms that caused the most severe landslide hazards in Hong Kong
in the past 20
Hong Kong is located at the southeast coast of China. The
subtropical climate in Hong Kong is characterized by notable dry
and wet seasons. About 85 % of the annual rainfall is recorded
during the wet season from April to September. Storms with high
intensity and short duration in Hong Kong are typically associated
with southwest monsoon or tropical cyclones. The ground surface
elevation on the GIS platform is shown in Fig. 3. The two highest
mountain peaks in Hong Kong are Tai Mo Shan (near rain gauge N14)
and Lantau Peak (near rain gauge N21), with peak elevations of 957
and 934
AECOM and Lin (2015) studied the orographic factors of rainfall
spatial distribution based on historical records. A spatial
distribution of orographic intensification factors has been
developed based on historical hourly data. The 24 h orographic
intensification factors at a resolution of
The GEO rain-gauge network in Hong Kong.
The 24 h orographic intensification factors in Hong Kong (modified from AECOM and Lin, 2015).
Trend surfaces of 24 h PMP with
The magnitude of storms can be assessed corresponding to
a depth–area relation, and characterized by the probable maximum
precipitation (PMP). PMP is frequently used to quantify extreme
storm events (WMO, 2009). The scenarios of 4 and 24 h PMP for
Hong Kong have been assessed by the Hong Kong Observatory and AECOM
(Chang and Hui, 2001; AECOM and Lin, 2015). AECOM and Lin (2015)
updated the 24 h PMP for Hong Kong considering the local
orographic intensification. The trend surface is an expected-value
surface. The trend surfaces of 24 h PMP with different storm
centers have been updated by AECOM and Lin (2015), and the typical
trends are shown in Fig. 5. The trend surfaces are derived based
on the historical hourly rainfall. According to the 24 h PMP
updating study, an elliptical isohyet is recommended as
a generalized convergence pattern. For storms cantered at Tai Mo
Shan, the orientation of 22.5
The most traditional way to describe the rainstorm severity is by
return period, which is recognized as a combination of intensity
and duration. Another measure of the severity of a storm is the
consequence of the storm, such as rain-induced landslides or
flooding. An index measuring the potential to trigger landslides,
named “Landslide Potential Index (LPI)”, is used in Hong Kong
(CEDD, 2009). The LPI is based on the historic records of landslide
events since 1984. For instance, a storm in late July 1994 caused five
fatalities and its LPI was 10. The value of LPI can be greater than
10 if a storm is more damaging than the July 1994 storm. According
to the LPI, the top three largest storms in the past
20
Hyetographs of three storms:
Spatial distribution of the total rainfall amount:
The rainfall data in this study are provided by Geotechnical Engineering Office (GEO) and the Hong Kong Observatory in Hong Kong. The GEO and Hong Kong Observatory rain gauge networks comprise 88 and 46 stations, respectively (Fig. 3). The rain gauges are more concentrated in the northern Hong Kong Island and Kowloon, where the population density is high. The raw digital data at 5 min interval from the high-quality network ensure the reliability of this study. The data cover the period from 00:00 LT on 5 June to 24:00 LT on 7 June 2008, from 00:00 LT on 17 August to 24:00 LT on 21 August 2005, and from 00:00 LT on 22 July to 24:00 LT on 24 July 1994. Some of the rain gauges had not been installed in July 1994. The numbers of effective rain gauges for the three events are 105, 112, and 56, respectively. The three storm hyetographs corresponding to the maximum local precipitation depth are shown in Fig. 6. The 17–21 August 2005 storm is more moderate in short durations compared with the 5–7 August 2008 storm and the 22–24 July 1994 storm.
Magnitudes of the three storms characterized by
According to Hong Kong Observatory, the weather was
influenced by an active low pressure trough over the south China
coastal area during the first 10 days of June 2008, and was
heavily rainy and thundery. Figure 7a shows contours of the total
rainfall amount of the 5–7 June 2008 storm. The maximum total
rainfall amount was 670
The maximum rolling rainfall values at different locations may not be in the same period, though most of them tend to be in the same period. Hazard consequences are more related to the maximum rolling rainfall values than instantaneous consequences are (Dai and Lee, 2001). In formulations for a hydrological model, the effect of the timescale of aggregation of the rainfall data and the hydrological response of catchments of different sizes should be investigated in order to identify the critical scale on which the resulting discharge will be the largest and could potentially generate flash floods.
The most concentrating periods of precipitation are selected. Figure 9 shows the instantaneous rainfall process from 06:55 to 07:35 LT on 7 June 2008. During this period, the vapour was concentrated on the southwest of Lantau Island and transported northeast across the mountains on Lantau Island. A large amount of precipitation was retained on the island.
Instantaneous rainfall process from 06:55 to 07:35 LT on 7 June 2008.
Instantaneous rainfall process from 10:35 to 11:15 LT on 20 August 2005.
Instantaneous rainfall process from 15:00 to 15:40 LT on 23 July 1994.
August 2005 was much wetter than normal. A very active southwest
monsoon during 17–22 August brought in plenty of
moisture. Figure 7b shows contours of the total amount of
rainfall. The maximum total rainfall amount was 890
Figure 10 shows the instantaneous rainfall process from 10:35 to 11:15 LT on 20 August 2005, which is recognized as the heaviest rainfall period in this storm event. The prevailing moisture inflow mainly came southerly during this period. The rainfall center concentrated on the south of Tai Mo Shan.
The total precipitation amount in the storm event from 21 to
24 July 1994 was recorded as the highest for any consecutive days
in July. The weather was related to a trough of low pressure (Tam
et al., 1995). Figure 7c shows contours of the total amount of
rainfall of this storm concentrating in the middle of the New Territories,
at Tai Mo Shan. The maximum total rainfall amount was
1450
Figure 11 shows the instantaneous rainfall process from 15:00 to 15:40 LT on 23 July 1994, which records the heaviest rainfall process in this storm event. During this period, the moisture air came from on the northwest of Tai Mo Shan. Most of precipitation concentrated on Tai Mo Shan, and the spatial distribution of rainfall was quite uneven. As the moisture flux rose across Tai Mo Shan, a large amount of moisture began to fall as rain. The orographic intensification effect was very significant in this rainstorm event.
All the aforementioned three storms are related to monsoons other than typhoons. The meteorological factors for these storms are beyond the scope of this paper. This research focuses on the areal distribution of precipitation, which is believed to be more relevant to the evaluation of the performance of the slope safety system. Thus the maximum rolling rainfall values are estimated in different durations. According to the records from the automatic rain gauges, the maximum rolling rainfall among all the rain-gauge stations in each of the three events can be calculated. The corresponding peak values and stations are summarized in Table 1. The 22–24 July 1994 storm is the largest among the three storms with regard to the amounts of the maximum rolling 1 h and 24 h rainfall. However, in terms of the maximum rolling 4 h rainfall, the 5–7 June 2008 storm is the most critical.
The contours of the total rainfall for the three storms, interpolated using a triangular method, are shown in Fig. 7. The total precipitation amount of the 5–7 June 2008 storm is the smallest among the three events, while that of the 21–24 July 1994 storm is the largest due to its longer duration. However, the LPI value for the 5–7 June 2008 storm is 12, larger than those of the other two storms; that is, the 5–7 June 2008 storm is the largest one in terms of damage. One of the reasons is that the variability of spatial and temporal distributions of the storm affects both the infiltration dynamics of the surface soil and the water levels above and below the ground surface. The entire hydrological system is governed by the spatial and temporal distribution of rainfall.
The varying space–time distribution of rainfall in Hong Kong is a result of the interaction between governing meteorological covariates and local hilly terrain. Instead of attempting to use a physical model to capture the spatial characteristics, our analysis presents a two-step approach in which a surface trend is firstly established to assess the spatial distribution of the rainfall amount in a fixed duration, followed by a further analysis of the spatial correlation of the detrended residuals.
A storm is a phenomenon with gradual geographical changes in space; the rainfall amount can be simulated as a spatially correlated random field superimposed on a trend surface (Grimes and Pardo-Igúzquiza, 2010). Such an artificial rainfall trend surface can be used to represent design storms. One could comprehend that the rainfall is correlated with the local terrain and the design storm centers are likely to be around the mountain peaks. Hong Kong has a relatively small area, and an individual storm is usually designed to have one or two centers for engineering design purposes (AECOM and Lin, 2015). Distinguishing two peaks is not necessary, as the distance between any two peaks will be small with regard to the scale of a typical rainstorm.
Trend surfaces and residuals of the total rainfall
amounts:
Values of maximum rolling rainfall of three landslide-triggering storms in Hong Kong.
Locations of maximum rainfall on the trend surfaces (km)
Directions and lengths of the axes of trend surfaces.
Directions and semilengths of the axes of scale of fluctuation (SoF).
Scale of fluctuation values and ellipse-fitting curves
for the 5–7 June 2008 storm:
Based on random field theory (Vanmarcke, 1977), the trend surface
is the expected value of the precipitation distributed over the
rainfall domain, while the residuals are stationary and not
affected by any shift in the coordinate system. Thus, the first
step is to divide the spatial distribution into a trend surface
and residuals by finding a trend surface fitting function. Though
most natural processes such as storms exhibit spatial variability
with complex trends, this paper uses a polynomial function for
simplicity, with observations of a storm denoted as
The computed trend surfaces for the total rainfall amounts of the
three storms and the detrended residuals are shown in Fig. 12. The
residuals of the rainfall amounts in different durations are often
assumed to be stationary. Taking the maximum 4 h rolling rainfall
as an example, the trend surface is
Scale of fluctuation values and ellipse-fitting curves
for the 17–21 August 2005 storm:
Scale of fluctuation values and ellipse-fitting curves
for the 22–24 July 1994 storm:
Range values for
Normalized semivariances of the maximum rolling 24 h rainfall of the three storms and the mean annual maximum daily rainfall in Hong Kong.
A classical way to characterize the spatial correlation is
through an autocorrelation function (ACF),
In order to assess the autocorrelation structure of the detrended
storm amounts, it is necessary to perform regression analysis to
fit the ACF. Among many correlation structures, the single
exponential structure is the most common:
The scale of fluctuation is evaluated in the directions of N 0, N 45,
N 90, and N 135
The direction and major and minor scales of fluctuation are
summarized in Table 4. The SoF values of the rainfall residuals are
between 6 and 37
Though rainfall varies over space, the rainfall amount of
a particular storm in terms of maximum rolling rainfall can be
fitted by a polynomial function. The spatial form of the rainfall
amount can be represented by a rotated ellipsoid with only one
center. Such an artificial spatial form may exhibit geometrical
regularity. For each storm, the trend surfaces in different
durations show good consistency in the shape parameters in terms of
the peak point, long-axis direction and axis length. The peak
points on the trend surfaces of the three storms are located in
a relatively small range. The long-axis directions of the spatial
forms of each event in different durations almost remain unchanged
between 19 and 43
With respect to the instantaneous rainfall processes shown in Figs. 9–11, the rainfall distributions in terms of maximum rolling rainfall are quite consistent to the heaviest rainfall process in each storm event. The rainfall distributions are strongly affected by the storm humidity transportation and are so uneven that the entire area should not be described as a single site. The locations of the storm centers determine the general trend of the areal rainfall distribution. The polynomial trend surfaces are effective for representing large rainstorm distributions in terms of maximum rolling rainfall.
The spatial connectivity can be assessed by the SoF
values. A smaller scale of fluctuation indicates more rapid
fluctuations of the mean. According to Figs. 13–15, all of the SoF
values are within 30
Besides the three large rainstorm events in this paper, ordinary
rainstorm events in Hong Kong have also been studied (Liu, 2013;
AECOM and Lin, 2015). Liu (2013) proposed a framework for
analyzing dynamic time–space evolution of rain fields in her
thesis. Four rain events were chosen to illustrate the spatial
structure of rainfall in Hong Kong: the 18 and 19 May 2007,
19 April 2008, and 15 September 2009 rain events in Hong Kong. The 19 April 2008
rainstorm event was under a combined effect of Typhoon
Neoguri and a northeast monsoon, while the other three rainstorms
were results of tropical depressions. The total rainfall amounts
during the four rainfall events on 18 and 19 May 2007, 19
April 2008, and 15 September 2009 were 67.0 and 99.6, 157.9, and
130.3
The spatial structure of annual maximum daily rainfall using the
variogram model provides additional information for generating
design storms from another point of view. According to the study
conducted by Jiang and Tung (2014), the spatial variability
represented by a variogram is used to establish the rainfall
depth–duration–frequency relationships. By normalizing the
indicator semivariogram by the variance of the indicator data, the
normalized semivariances of the mean annual maximum daily rainfall
and the maximum rolling 24 h rainfall of the three storms are
shown in Fig. 17. Based on the samples and the fitted exponential
variogram model, the range of the mean of annual maximum daily
rainfall is 7.1
With aspect to the local terrain impacts, the major directions of both the three large rainstorms and the ordinary rainfall events are all consistent with the mountain range alignment in Hong Kong (Fig. 3). However, the severe storms are highly uncertain and it is difficult to ascertain and predict the future precipitation and extreme rainfall. Lu et al. (2013), Lu and Lall (2016), and Najibi et al. (2017) suggest a potential direction to further study the associated atmospheric circulation with moisture transport that has improved the predictability of extreme rainfall and flooding in various regions, including western Europe and the Midwest and northeast of the United States. The spatial structure found in this study also indicates that there might be a link between the distribution and the convergence of the moist air into the Hong Kong region.
A random rain-field model has been proposed to study the spatial characteristics of three large landslide-triggering rainstorms in Hong Kong. The cumulative rainfall depths in terms of maximum rolling rainfall in different durations are of particular importance for landslide studies and are taken as random variables in this study. Based on the study, the following conclusions can be drawn:
The amounts of maximum rolling rainfall in different durations share
a dominating spatial structure that can be represented by a rotated
ellipsoid surface established using the ordinary least-squares
method. The shapes change slightly in different durations for
a particular storm. The major principal directions of the surface trends of the three
rain storms are between 19 The spatial connectivity of large storms in Hong Kong is estimated
to be between 5 and 30 To verify the rationality and reliability of the spatial structures
of large rainstorms, the spatial characteristics of four ordinary
rainfall events are also studied. The spatial structures of the
three large rainstorms are similar with those of the ordinary
rainfall events and consistent with the mountain range alignment in
Hong Kong.
The key rainfall data for this research are available
at
The authors declare that they have no conflict of interest.
The authors would like to thank the Geotechnical Engineering Office (GEO) of the Civil Engineering and Development Department (CEDD) for providing the rainfall data described in this paper. This research is supported by the Research Grants Council of the Hong Kong SAR (nos. C6012–15G and 16202716). Edited by: Thomas Kjeldsen Reviewed by: two anonymous referees