Stoch Environ Res Risk Assess (2010) 24:165–182
DOI 10.1007/s00477-009-0308-0
ORIGINAL PAPER
Regional flood frequency and spatial patterns analysis in the Pearl
River Delta region using L-moments approach
Tao Yang Æ Chong-Yu Xu Æ Quan-Xi Shao Æ
Xi Chen
Published online: 5 March 2009
Springer-Verlag 2009
Abstract The Pearl River Delta (PRD) has one of the
most complicated deltaic drainage systems with probably
the highest density of crisscross-river network in the world.
This article presents a regional flood frequency analysis
and recognition of spatial patterns for flood-frequency
variations in the PRD region using the well-known index
flood L-moments approach together with some advanced
statistical test and spatial analysis methods. Results indicate that: (1) the whole PRD region is definitely
heterogeneous according to the heterogeneity test and can
be divided into three homogeneous regions; (2) the spatial
maps for annual maximum flood stage corresponding to
different return periods in the PRD region suggest that the
flood stage decreases gradually from the riverine system to
the tide dominated costal areas; (3) from a regional perspective, the spatial patterns of flood-frequency variations
T. Yang (&) X. Chen
State Key Laboratory of Hydrology-Water Resources
and Hydraulics Engineering, Hohai University,
Nanjing 210098, The People’s Republic of China
e-mail: enigama2000@hhu.edu.cn
T. Yang
State Key Laboratory of Water Resources and Hydropower
Engineering Science, Wuhan University, Wuhan 430072, China
C.-Y. Xu
Department of Geosciences, University of Oslo,
P.O. Box 1047, Blindern, 0316 Oslo, Norway
Q.-X. Shao
Mathematical & Information Sciences, CSIRO,
Private Bag 5, PO Wembley, WA 6913, Australia
T. Yang
The Institute of Hydraulic Engineering of Yellow River,
Zhengzhou 450003, China
demonstrate the most serious flood-risk in the coastal
region because it is extremely prone to the emerging flood
hazards, typhoons, storm surges and well-evidenced sealevel rising. Excessive rainfall in the upstream basins will
lead to moderate floods in the upper and middle PRD
region. The flood risks of rest parts are identified as the
lowest in entire PRD. In order to obtain more reliable
estimates, the stationarity and serial-independence are
tested prior to frequency analysis. The characterization of
the spatial patterns of flood-frequency variations is conducted to reveal the potential influences of climate change
and intensified human activities. These findings will definitely contribute to formulating the regional development
strategies for policymakers and stakeholders in water
resource management against the menaces of frequently
emerged floods and well-evidenced sea level rising.
Keywords Regional flood frequency analysis Trend test Serial-independence check L-moments Flood-stage variations Spatial patterns The Pearl River Delta (PRD)
1 Introduction
Public awareness of extreme climatic and hydrological
events has increased sharply in tropical and sub-tropical
river deltas recently, especially the tremendous concerns on
the catastrophic floods, storms, typhoons and the sea-level
rising (e.g. Beniston and Stephenson 2004). After long
term human settlements, nowadays many large cities are
distributed in river deltas and a large proportion of the
global economic productivity derive from the river deltas.
Nevertheless, the global sea level has risen at the rate of
about 2 mm per year over the past century. Moreover,
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166
throughout the next century the rate of the sea level rise is
expected to increase induced by the currently well-evidenced global warming (IPCC 2007). By 2100, the global
average sea level will be expected to rise at the rate ranged
from 18–38 to 26–59 cm depending upon the greenhouse
gas emission scenarios. The rising sea level with associated
frequent floods, storm surges and typhoon events will
undoubtedly intensify the flood risk existing in the river
deltas. Therefore, it is urgent to conduct the regional flood
frequency estimation and assess the potential flood risk in
order to meet the increasing demands in ensuring the
security of human lives and large variety of properties in
low-elevation river deltas.
Regional flood frequency analysis enables estimation of
flood magnitude in different return periods at any stream
location within a region (Solana and Solana 2001; Atiem
and Harmancioglu 2006) to improve the at-site estimates by
using the available flood data within a region and attempt to
respond to the need of flood estimation in ungauged basins.
Thus, it allows flood quantile estimation for any site in a
region to be expressed in terms of flood data recorded at all
gauging sites in the same region, including those at the
specific site (Atiem and Harmancioglu 2006). The U.S.
Geological Survey index flood method proposed by Dalrymple (1960) is one of the most widely used regional flood
frequency analysis procedures. The index flood method
assumes that a region is a set of gauging sites whose flood
frequency behavior is homogeneous in some quantifiable
manner. It is expected that the more homogeneous a region
is, the greater the gain will be in using regional than at-site
estimation. Hosking et al. (1985), Lettenmaier and Potter
(1985) have demonstrated that index flood procedures
provide suitable robust and accurate quantile estimates.
Hosking and Wallis (1993) suggested an index flood procedure by assuming that the flood distributions at all sites
within a homogeneous region are identical except for the
scale or index-flood parameter and using L-moments to
undertake regional flood frequency analysis. L-moment
ratios are superior to the product moment ratios in the sense
that the former are more robust in the presence of outliers
and do not suffer from sample size related bounds (Chen
et al. 2006). L-moment diagrams and related goodness-of-fit
procedures are useful for selecting various distributional
alternatives in a region (Hosking and Wallis 1997; Hosking
1990). The method of L-moments has been used widely by
hydrologists in regional flood analysis nowadays. Parida
et al. (1998) carried out a regional flood frequency analysis
for Mahi-Sabarmati basin in India using the L-moments and
index flood procedure and found that the three-parameter
lognormal distribution (LN3) is an appropriate distribution
for modelling floods in this region. Daviau et al. (2000) used
spatially explicit kriging techniques to diagnose hierarchical spatial models for each L-moment ratio and obtain
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Stoch Environ Res Risk Assess (2010) 24:165–182
spatial estimates of parameters in central and eastern
Canada. Kumar et al. (2003) conducted a regional flood
frequency analysis for the Middle Ganga Plains sub-zone in
India using the L-moment ratios diagram and the goodnessof-fit statistical criterion of Hosking and Wallis and concluded that the generalized extreme value distribution
(GEV) is a robust distribution for the study area. Using an
index flood estimation procedure based on L-moments, Lim
and Lye (2003) found that both the generalized extreme
value and generalized logistic distributions are appropriate
for the distribution of extreme flood events in the Sarawak
region of Malaysia. Atiem and Harmancioglu (2006) used
the index flood L-moments approach to perform the regional flood frequency analysis with annual maximum stream
flood records at 14 gauged sites on the Nile River tributaries. Wallis et al. (2007) greatly improved the spatial
mapping of precipitation and increased the reliability of
frequency estimates of precipitation in the broad areas of
Washington State between precipitation measurement stations using PRISM mapping and L-Moments method. The
results identify the GEV distribution as statistically
acceptable distribution for all regions up to 1 in 500
recurrence intervals. So far, a variety of L-moments based
methods were extensively reviewed and investigated in
regional flood frequency analysis across the world to obtain
more reliable estimates (e.g. Daniele et al. 2007; Chebana
and Ouarda 2008; Rosbjerg and Madsen 2008; Kumar and
Chatterjee 2008; Meshgi and Khalili 2009a, b).
However, most of above-mentioned literatures conducted the regional flood frequency analysis without
testing stationarity and serial correlation in the samples to
guarantee reliable estimates. Both stationarity and serial
uncorrelation are two important underlying assumptions
inherent in frequency analysis. As a result, the analysis
without stationarity and serial correlation tests may lead to
incorrect results and conclusions. Therefore, it is beneficial
to draw sufficient concerns on stationarity and serial correlation test prior to the regional flood frequency analysis.
Furthermore, characterization of the spatial patterns of
flood-frequency variations is essential to reveal the potential influences of climate change and human activities,
hence will be carried out in the current study to support
flood risk assessment and water resources management for
gauged/ungauged regions.
Although the L-moments method is being increasingly
used to identify the probability distribution function for
regional frequency analysis, the Pearson-III distribution
is still widely used as the official recommendation in
flood risk analysis across China (MWR 1999), and the
L-moments method has not become a popular tool in this
country. Zhang and Hall (2004) used Ward’s cluster, fuzzy
c-means and artificial neural networks method together
with L-moments method to conduct a regional flood
Stoch Environ Res Risk Assess (2010) 24:165–182
frequency analysis for the Gan-Ming River basin in China.
Application demonstrates that estimates with lower standard errors of estimate can be produced using an artificial
neural network (ANN). Chen et al. (2006) use L-moments
method to analyse the regional frequency of low flows for
Dongjiang basin, South China. Both studies took advantages of L-moments method and launched useful initiates
of regional analysis in China.
To our best knowledge, the regional flood frequency
analysis with the state-of-art L-moments techniques has not
been conducted in the Pear River Delta region, South
China, which has one of the most complicated deltaic
drainage systems with probably the highest-density of
crisscross-river network in the world. PRD is also the most
developed region in mainland China. Therefore, extensive
efforts should be enforced to conduct the regional flood
frequency in the light of above-mentioned improvement in
this important region. The objectives of the paper are to:
(1) examine the stationarity and serial correlation of annual
maximum flood-stage series and identify the hydrological
homogeneous sub-regions; (2) determine the best probability distribution for annual maximum flood stage for each
sub-region and perform regional flood frequency analysis
with uncertainty assessment including the corresponding
error bounds and root mean squared error (RMSE) in the
L-moments based index flood method to support flood risk
management; (3) quantify and map the spatial flood frequency of maximum annual flood stage served as a
potential indicator of flood-risk management in the PRD
region, and characterize the spatial patterns of flood-frequency variations in order to reveal the underlying spatial
patterns of flood risk dominating the PRD region.
2 Methodology
The methods used in calculating the stationarity test, serial
independence check, L-moments approach, spatial mapping are presented in the following contents.
2.1 Stationarity test
Trend test is one of the most important methods in examining the stationarity of hydrological series. The rank-based
Mann–Kendall method (MK) (Mann 1945; Kendall 1975)
is highly recommended by the World Meteorological
Organization to assess the significance of monotonic trends
in hydrological series, for it has an advantage of not
assuming any distribution form for the data and has the
same power as its parametric competitors. In the test, the
null hypothesis Ho is that the deseasonalized data (x1,…,
xn) are a sample of n independent and identically distributed random variables. The alternative hypothesis H1 of a
167
two-sided test is that the distribution of xk and xj are not
identical for all k, j B n with k = j (Kahya and Kalayci
2004). The test statistic S is computed with Eqs. 1 and 2 as:
S¼
n1 X
n
X
sgnðxj xk Þ
ð1Þ
k¼1 j¼kþ1
With
8
< þ1
0
sgnðxj xk Þ ¼
:
1
if
if
if
ðxj xk Þ [ 0
ðxj xk Þ ¼ 0
ðxj xk Þ\0
ð2Þ
The statistics S is approximately normally distributed
when n C 8, with the mean and the variance as follows:
EðSÞ ¼ 0
ð3Þ
VarðSÞ ¼
nðn 1Þð2n þ 5Þ Pn
i¼1 ti iði
18
1Þð2i þ 5Þ
ð4Þ
where ti is the number of ties of extent i. The standardized
statistics (Z) is formulated as:
8 S1
pffiffiffiffiffiffiffiffiffiffi if S [ 0
>
< VarðSÞ
0
if S ¼ 0
ð5Þ
Z¼
>
: pSþ1
ffiffiffiffiffiffiffiffiffiffi if S\0
VarðSÞ
In a two-sided test for trend, the H0 of no trend should
be rejected if |z| [ Za/2 at the a level of significance. A
positive Z indicates an upward trend and vice versa (Kahya
and Kalayci 2004). The effect of the serial correlation on
the Mann–Kendall (MK) test was eliminated using a prewhitening technique (e.g. Yang et al. 2008).
2.2 Serial independence check
The serial correlation check was carried out mainly by
examining the autocorrelation coefficients of the time
series. When the absolute values of the autocorrelation
coefficients of different lag times calculated for a time
series consisting of n observations are not larger than the
pffiffiffi
typical critical value, i.e. 1:96= n corresponding to the 5%
significance level (Douglas et al. 2000), the observations in
this time series can be accepted as being independent from
each other. According to the calculated autocorrelation
coefficients of lag-1, lag-5 and lag-10 for each annual
series, the observations in that series can be accepted as
being independent at the 5% significance level.
2.3 L-moments approach
2.3.1 Basic theory
It is reported by Hosking and Wallis (1997) that conventional moment are not always satisfactory because of two
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Stoch Environ Res Risk Assess (2010) 24:165–182
major reasons: they do not always reveal easily interpreted
information about the shape of a distribution, and parameter
estimates of distributions fitted by the moments are often
less accurate than those obtained by other methods, such as
the maximum likelihood estimation. Instead, L-moments
constitute an alternative to conventional moments and can
be estimated by linear combinations of order statistics.
L-moments have the theoretical advantages over conventional moments of being able to characterize a wider range
of distributions and, when estimated from a sample, of
being more robust to the presence of outliers in the data.
Comparing with conventional moments, L-moments are
less subject to bias in estimation and can approximate their
asymptotic normal distribution more closely in finite samples (Hosking 1990). The L-moments approach covers the
characterization of probability distributions, the summary
of observed data samples, the fitting of probability distributions to data, and testing the hypothesis about the
distributional form. The mean, variance, skewness and
kurtosis are defined in terms of moments as: L-mean,
L-scale, L-skewness and L-kurtosis, respectively (Hosking
and Wallis 1997; Atiem and Harmancioglu 2006). More
details about the method of L-moments can be found in
Hosking and Wallis (1997). The ‘‘L’’ in L-moments
emphasizes the linearity in forming the moments by linear
combinations of the probability-weighted moments as
given by
krþ1 ¼
Z1
xðFÞPr ðFÞdF ¼
0
r
X
ð1Þrk ðr þ KÞ!
k¼0
ðk!Þ2 ðr KÞ!
bk
ð6Þ
rk
R1
P
ðrþkÞ! k
with Pr ðFÞ ¼ rk¼0 ð1Þ
F and br ¼ 0 xðFÞF r dF
ðk!Þ2 ðrkÞ!
where F(x) is a cumulative distribution function (cdf) and
x(F) the quantile function. L-moment ratios are the
quantities
s ¼ k2 =k1 and sr ¼ kr =k2 ;
r ¼ 3; 4; . . .
lrþ1
where bk is an unbiased estimator of bk with
n
X
ði 1Þði 2Þ ðr kÞ
xi:n :
bk ¼ n1
ðn 1Þðn 2Þ ðn kÞ
i¼Kþ1
123
t ¼ l2 =l1 and tr ¼ lr =l2 ;
ð8Þ
r ¼ 3; 4; . . .
ð9Þ
which will be used for homogeneity analysis in the regional
frequency analysis.
2.3.2 The regional frequency analysis based on L-moments
method
The following general notations are used for the regional
frequency analysis. Suppose that there are N sites in the
region with sample size n1, n2,…, nN, respectively. The
sample L-moment ratios at site i are denoted by t(i), t(i)
3 and
t(i)
4 etc. The regional weighted average L-moment ratios are
given by:
,
,
N
N
N
N
X
X
X
X
t ¼
ni tðiÞ
ni and tr ¼
ni trðiÞ
ni ;
ð10Þ
i¼1
i¼1
i¼1
i¼1
r ¼ 3; 4; . . .
The regional frequency analysis using L-moments
consists of four steps (Hosking and Wallis 1993, 1997):
(1) screening the data using the discordancy measure Di,
(2) homogeneity testing using the heterogeneity measure
H; (3) distribution selection using the goodness-of-fit
measure Z; and (4) regional estimation using the indexflood procedure. These four steps were followed to conduct
a regional frequency analysis for the Pearl River Delta
region and the statistical methods employed are discussed
below.
2.3.3 Screening the data using the discordancy measure
(i) T
Let ui = [t(i), t(i)
3 , t4 ] be the vector containing the t, t3 and
t4 values for site i where the superscript T denotes transposition of a vector or matrix. Let
ð7Þ
which are analogous to the traditional ratios, i.e. s is the
coefficient of variation (L-CV); s3 the L-skewness and s4
the L-kurtosis.
The distributional parameters are estimated by equating
the sample L-moments with the distribution L-moments. In
practice, the L-moments must be estimated from a finite
sample. Let x1:n B x2:n B _ B xn:n be the ordered sample
of size n. The unbiased sample L-moments are given by
r
X
ð1Þrk ðr þ kÞ!
¼
bk
2
k¼0 ðk!Þ ðr kÞ!
The sample L-moment ratios are defined as:
u ¼
N
X
ui =N
ð11Þ
i¼1
be the (unweighted) regional average. The discordancy
measure for site i is then defined as
1
Di ¼ Nðui uÞT A1 ðui uÞ
3
N
X
with A ¼
ðui uÞðui uÞT :
ð12Þ
i¼1
Obviously, a large value of Di indicates the discordancy
of site i with other sites. Hosking and Wallis (1997) found
that there is no fixed number which is considered to be a
‘‘large’’ Di value and suggested some critical values for
discordancy test which are dependent on the number of
sites in the study region (see Table 2).
Stoch Environ Res Risk Assess (2010) 24:165–182
2.3.4 Homogeneity testing using the heterogeneity
measure
Suppose that the region to be tested for homogeneity has N
sites, with site i having record length of peak flows ni.
(i)
Further, let t(i), t(i)
3 and t4 denote L-CV, L-skewness and
L-kurtosis, respectively, at site i. The regional average
L-CV, L-skewness and L-kurtosis, represented by tR, tR3 and
tR4 , respectively, are computed as:
,
9
N
N
X
X
>
R
ðiÞ
>
t ¼
ni t
ni >
>
>
>
>
i¼1
i¼1
>
>
,
=
N
N
X ðiÞ X >
R
ð13Þ
t3 ¼
ni t3
ni
>
>
i¼1
i¼1
>
>
,
>
>
N
N
>
X
X
>
ðiÞ
R
>
t4 ¼
ni t4
ni >
;
i¼1
i¼1
PN
where ni
i¼1 ni denotes the weight applied to sample
L-Moment Ratios at site i, which is proportional to the record
length of the site. The regional average mean lR1 is set to 1.
Heterogeneity measures used in this study are based on
three measures of dispersion: (i) weighted standard deviation of the at-site sample L-CVs (V); (ii) weighted average
distance from the site to the group weighted mean in the
two-dimensional space of L-CV and L-skewness (V2); (iii)
weighted average distance from the site to the group
weighted mean in the two-dimensional space of L-skewness and L-kurtosis (V3).
(
,
)12 9
N
N
>
h
i2 X
X
>
>
V1 ¼
ni tðiÞ tR
ni >
>
>
>
>
i¼1
i¼1
>
>
,
>
=
N
N
n
o12 X
X
ðiÞ
ðiÞ
R 2
R 2
V2 ¼
ni ðt t Þ þ ðt3 t3 Þ
ni > ð14Þ
>
>
i¼1
i¼1
>
>
,
>
>
N
N
1
n
o
X
X
>
2
>
ðiÞ
ðiÞ
R 2
R 2
V3 ¼
ni ðt3 t3 Þ þ ðt4 t4 Þ
ni >
>
;
i¼1
i¼1
In these dispersion measures, the distance of sample
L-Moment Ratios for site i from the regional average
L-Moment Ratios is weighted proportionally to the record
length of the site, thus allowing greater variability of
L-Moment Ratios for sites having small sample size in a
region.
A large number of realizations of the region are simulated from kappa distribution fitted to regional average
L-Moment Ratios: lR1 , tR, tR3 and tR4 . Each realization constitutes a homogeneous region, with N sites having same
record length as their real-world counterparts. Further, in
each realization, the data simulated at any site in the region
is serially independent and the data simulated at different
sites in the region are not cross-correlated. For each simulated realization, V, V2 and V3 are computed.
169
Let lv, lv2and lv3 denote the mean and rv, rv2 and rv3
the standard deviation of the Nsim values of V, V2 and V3,
respectively. These statistics are used to estimate the following three heterogeneity measures
9
vÞ >
H1 ¼ ðVl
>
rv
=
v2 Þ
ð15Þ
H2 ¼ ðV2rl
v2
>
ðV3 lv3 Þ >
;
H ¼
3
rv3
In order to obtain reliable values of lv and rv, the
number Nsim of simulations needs to be large and
Nsim = 1,000 was used in this study. The region is
regarded to be ‘‘acceptably homogeneous’’ if H \ 1,
‘‘possibly heterogeneous’’ if 1 B H \ 2, and ‘‘definitely
heterogeneous’’ if H C 2.
Furthermore, Hosking and Wallis (1993) and Atiem
and Harmancioglu (2006) stated that a large positive
value of H1 indicates that the observed L-moments
are more dispersed than what is consistent with
the hypothesis of homogeneity. H2 measure indicates
whether the at-site and regional estimates are close to
each other. A large value of H2 indicates that a large
deviation between regional and at-site estimates, while
H3 indicates whether the at-site and the regional estimate
will agree. Large values of H3 indicate a large deviation
between at-site estimates and observed data. Following
the method by Daniele et al. (2007), heterogeneity
hereby is tested using H1 and H2 because the L-CV and
L-skewness are required for fitting pooled growth curves
with a GEV or GLO. Note, however, that Hosking and
Wallis (1997) found that H2 is a weaker test of heterogeneity than H1.
2.3.5 Distribution selection using the goodness-of-fit
measure
After confirming the homogeneity of the study region, an
appropriate distribution needs to be selected for the
regional frequency analysis. The selection was carried
out by comparing the moments of the candidate distributions to the average moments statistics derived from
the regional data. The best fit to the observed data will
indicate the most appropriate distribution. For each
candidate distribution, the goodness-of-fit is measured
by
Z DIST ¼ ðsDIST
t4 þ b4 Þ=r4
4
ð16Þ
(Hosking and Wallis 1993, 1997), where sDIST
is the
4
L-kurtosis of the fitted distribution to the data using the
candidate distribution, and the bias is measured by
b4 ¼
Nsim
X
ðt4 ðmÞ t4 Þ=Nsim
ð17Þ
m¼1
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170
Stoch Environ Res Risk Assess (2010) 24:165–182
where t4 is estimated using the simulation technique as
before with t4 ðmÞ being the sample L-kurtosis of the mth
simulation, and
(
"
#)12
Nsim
X
1
2
ðmÞ
2
r4 ¼ ðNsim 1Þ
ðt4 t4 Þ Nsim b4
ð18Þ
AR ðFÞ ¼ N 1
The fit is considered to be adequate if |Z
| is
sufficiently close to zero, and a reasonable criterion being
|ZDIST| B 1.64. If more than one candidate distribution is
acceptable, the one with the lowest |ZDIST| is regarded
as the most appropriate distribution. Furthermore, the
L-moment ratio diagram is also used to identify the
distribution by comparing its closeness to the L-skewness
and L-kurtosis combination in the L-moment ratio diagram.
2.3.6 Assessment of regional flood frequency analysis
Hosking and Wallis (1997) recommended an effective tool
for establishing the properties of complex statistical procedures, such as the regional L-moment algorithm, through
Monte Carlo simulation. In the course of simulations,
quantile estimates for various nonexceedance probabilities
are to be calculated. In the mth simulation, let the estimated
regional growth curve and the site-i quantile estimate
for nonexceedance probability F be q^m ðFÞ and Q^m ðFÞ;,
respectively. Then, at site i, the relative error of the estimated regional growth curve as an estimator of the at-site
growth curve qi(F) is f^
qm ðFÞ qi ðFÞg=qi ðFÞ and the relative error of the quantile estimate for nonexceedance
probability F is: fQ^m
i ðFÞ Qi ðFÞg=Qi ðFÞ: To approximate
the bias and RMSE of the estimators, these quantiles can be
averaged over all M simulations. Thus, the relative bias and
relative RMSE can be expressed as percentages of the site-i
quantile estimator by
Bi ðFÞ ¼ M 1
M ^m
X
Q ðFÞ Qi ðFÞ
i
m¼1
ð19Þ
Qi ðFÞ
and
Ri ðFÞ ¼ M
1
M
X
Q^m
i ðFÞ Qi ðFÞ
Qi ðFÞ
m¼1
!1=2
:
ð20Þ
A summary of the performance of an estimation
procedure over all of the sites in the region is obtained
through computing the regional average relative bias of the
estimated quantile (Hosking and Wallis 1997) as
BR ðFÞ ¼ N 1
N
X
Bi ðFÞ
ð21Þ
i¼1
and the regional average absolute relative bias of the
estimated quantile as
123
Bi ðFÞ
ð22Þ
i¼1
Furthermore, the regional average relative RMSE of the
estimated quantile is obtained as
m¼1
DIST
N
X
RR ðFÞ ¼ N 1
N
X
Ri ðFÞ
ð23Þ
i¼1
The regional average relative bias measures the
tendency of quantile estimates to be uniformly too high
or too low across the whole region. This tendency is
apparent, for example, when a distribution with a heavy
upper tail is fitted to a region where the true frequency
distributions have relatively light upper tails, or vice
versa. The regional average absolute relative bias
measures the tendency of quantile estimates to be
consistently high at some sites and low at others. This
occurs in a heterogeneous region where the estimated
regional growth curve tends to overestimate the true
at-site growth curve at some sites and to underestimate
it at others. Thus, in a homogeneous region, the bias is
expected to be the same at each site, and, thus, AR(F) and
BR(F) should be the same (Bobée and Rasmussen 1995;
Hosking and Wallis 1997).
The regional average relative RMSE measures the
overall deviation of estimated quantiles from true quantiles
and thus is frequently used as the criterion to weight one’s
judgement on whether one estimation procedure is superior
to another. In addition, to the overall accuracy measures of
quantile estimates, the corresponding quantities for each
site’s growth curve estimate can also be defined. Comparison of the accuracy of the estimated growth curve with
the estimated quantiles facilitates judgment of the relative
importance of errors in estimating the index flood and the
regional growth curve. Accuracy measures for the growth
curve are also relevant when only the growth curve estimate is of interest. The number of simulation M needs be
large enough so that the bias and RMSE measures, Bi(F)
and Ri(F), are close to the true bias and RMSE, ensuring
reliable comparisons between the performance measures
for different regions.
2.4 Spatial interpolation
To understand the spatial patterns of statistical characteristics of flood-frequency variations across the study
region, the geostatistical or stochastic methods are used
because they capture the spatial correlation between
neighboring observations to predict attributed values at
unsampled locations (e.g., Goovaerts 1999; Desbarats
1996; Daviau et al. 2000; Wallis et al. 2007). Geostatistics incorporate classic regression techniques to deal with
Stoch Environ Res Risk Assess (2010) 24:165–182
171
113 E
Sa
ns
113 30' E
o
La
8
ui
an
yag
g
Huangpu eng1
sh
Da
7
M
ou
nd
an
12 S
uo
11
80 E
100 E
120 E
kou
Nan
ua
16
3
zui
Hengmen
ate
ng
me
an
ao
od
gsh
M
lon
ng
De
ate
in
ng
uy
me
Zh
iti
jin
J
ng
en
ua
H utiaom
a
H
Se
gate
ao
2
ga
te
en
III
18
gm
an
Hu
Ya
m
ot
ai
Huangchong
4
Xi
pa
20 N
22 N
sha
17
S hi
14
500 m
gqi
en
II
22 30'N
nh
Ron
ate
te
te
ga
ga
ng
e
en e
m at
om
qi n g
Jia
ng me
Ho eng
H
gm
an
Ji
40 N
9
en
m
Hu
Na
15
Sishengwei
140 E
7
30 N
sha
Se
a
Sa
di
ng
I
ak
23 N
Li
ng
13
5
Gauging station
Fig. 1 Location of the Pearl River Delta in South China and gauging
stations. The river channels denoted with numbers are where the
gauging stations located. The names of the river channels are listed as
following: 1: North mainstem East River; 2: Modaomen channel; 3:
Hengmen channel; 4: Yamen channel; 5: Jitimen channel; 6:
Mainstem Zhujiang River; 7: Mainstem West River; 8: Xi’nanyong
channel; 9: Ronggui channel; 10: Jiaomen channel; 11: Shunde
channel; 12: Shawan channel; 13: Mainstem North River; 14:
Tanjiang channel; 15: South mainstem East River; 16: Hongqili
channel; 17: Xiaolan channel; 18: Hutiaomen channel; 19: Dongping
channel. The Pearl River Delta is divided into three parts based on its
geomorphology as: I: the upper Pearl River Delta; II: the middle Pearl
River Delta and III: the lower Pearl River Delta. Region I, region II
and region III divided by dashed lines are the upper, middle and lower
PRD
spatially continuous or ‘regionalized’ variables—the
values of which change with spatial location and the
behavior of which is somewhere between a deterministic
and a random variable. It includes techniques to quantify
spatial autocorrelation using variograms; to model
parameter surfaces with or without dependent variables
(kriging); to assess the variance of estimates; and to
investigate the theoretical properties of data using
stochastic simulation (Desbarats 1996). Techniques such
as indicator kriging can also model spatially discontinuous hydrological variables such as proximity to water
bodies, drainage density, escarpment and lake effect, etc.
Many of these topological and directional (azimuth)
variables also can be handled using GIS methods (Daviau
et al. 2000; Wallis et al. 2007). Goovaerts (1999) indicated that the major advantage of the Kriging method
over other simple interpolation methods is that sparsely
sampled observations of the primary attribute can be
complemented by secondary attributes that are more
densely sampled. Therefore, the Kriging interpolation
method was used to characterize the spatial patterns of
flood-frequency changes within the study region.
3 The study domain and data
3.1 The study domain
The Pearl River, which consists of West, North and East
Rivers, is the third largest river system after the Yangtze
River and the Yellow River in China. Before entering to
the South China Sea, the three rivers join together and form
the Pearl River Delta (PRD; including Hong Kong and
Macao). Figure 1 shows a general layout of the PRD basin:
the basin location, the main river sources and tributaries,
topographical features of the basin, and the 19 selected
gauging stations. The area of PRD is about 9,750 km2,
wherein the West River delta and the North River delta
account for about 93.7% of the total area of PRD, and the
East River delta accounts for 6.6% (PRWRC 2006). The
PRD is dominated by a sub-tropical monsoon climate with
abundant precipitation. The long term annual mean precipitation is 1,470 mm and most precipitation occurs in
April–September. The topography of the PRD has mixed
features of crisscross river-network, channels, shoals and
river mouths (gates). The depth of the whole estuary varies
123
172
Stoch Environ Res Risk Assess (2010) 24:165–182
Table 1 The flood-stage gauges in the Pearl River Delta (PRD) region (source of data: the Guangdong provincial bureau of Hydrology)
No.
Station
Longtitude Lantitude Region
Channel or river
Gate
Length
Missing data
1.
Makou
112480
23070
Upper PRD
West River
–
1958–
2005
1959.9–12, 1966, 1968,
1969.10–12
2.
Sanshui
112500
23100
Upper PRD
North River
–
1958–
2005
1959.9–12, 1960
3.
Jiangmen
113070
22360
Middle PRD West River
–
1958–
2005
2000
4.
Laoyagang
113120
23140
Middle PRD Xinanyong
–
1958–
2005
1959.12
5.
Nanhua
113050
22480
Middle PRD Donghai channel
–
1958–
2005
6.
Rongqi
113160
22470
Middle PRD Ronggui channel
–
1958–
2005
7.
Sanduo
112590
22590
Middle PRD Shunde channel
–
1958–
2005
8.
Shizui
112540
22280
Middle PRD Tan river
–
1959–
2005
1968.11–12, 2000
9.
Dasheng
113320
23030
Lower PRD
East river
–
1958–
2005
1963.6–12
10.
Denglongshan 113240
22140
Lower PRD
Modaomen channel
Modaomen gate 1959–
2005
11.
Hengmen
113310
22350
Lower PRD
Hengmen channel
Hengmen gate
1959–
2005
12.
Huangchong
113040
22180
Lower PRD
Yamen channel
Yamen gate
1961–
2000
13.
Huangjin
113170
22080
Lower PRD
Jitimen channel
Jitimen gate
1965–
2005
14.
Huangpu
113280
23060
Lower PRD
Qianhangxian channel –
1958–
2005
15.
Nansha
113340
22450
Lower PRD
Jiaomen channel
Jiaomen gate
1963–
2005
16.
Sanshakou
113300
22540
Lower PRD
Shawan channel
Humen gate
1958–
2005
1959
17.
Sishengwei
113360
22550
Lower PRD
East river
–
1964
18.
Xipaotai
113070
22130
Lower PRD
Hutiaomen channel
Hutiaomen gate
1958–
2005
1958–
2005
19.
Zhuyin
113170
22220
Lower PRD
Modaomen channel
Modaomen gate 1959–
2005
from 0 to 30 m above sea level (m.a.s.l.). Freshwater discharges from the eight river mouths (gates) located in the
lower PRD where water depths are between 2 and 5 m.a.s.l.
These geographic and topographic features exert dynamic
influences on tidal cycles, water circulation and water
column structure, and consequently affect hydrological
regimes, water quality and estuarine eco-environmental
systems (Mao et al. 2004). The tides in the PRD mainly
come from the Pacific oceanic tidal propagation through
the Luzon Strait (Ye and Preiffer 1990) with a mean tidal
range between 1.0 and 1.7 m. The tidal influences in the
PRD can reach to Sanshui and Makou gauges in the upper
123
1958.1–9
1968–1973
PRD, above which the hydrological regimes are separately
dominated by fluvial processes of the West and North
River together. Similarly, the Boluo gauge is considered as
the last tide-affected gauge of the East River in the upper
PRD (Luo et al. 2002).
Represented as the ‘‘Golden Triangle’’ by GuangzhouHong Kong-Macau, the PRD has a highly dense agglomeration of over 100 towns and cities. It has been the fastest
developing region in China since the country adopted the
‘‘open door and reform’’ policy in the late 1970s. On less
than 0.5% of the country’s territory, the PRD region produces about 20% of the national GDP, attracts about 30%
Stoch Environ Res Risk Assess (2010) 24:165–182
173
Table 2 Trend test (P-values) of the flood-stage for gauges in the
Pearl River Delta using MK test (Indexed alphabetically on site name)
No.
Site name
ni
P-value
Table 3 Independence test for flood-stage gauges in the Pearl River
Delta (Indexed alphabetically on site name)
pffiffiffi
r1
r5
r10
Di 1:96= n
No. Site name
ni
1
Dasheng
48
0.13 (?)
1
Dasheng
2
Denglongshan
48
0.13 (?)
2
3
Hengmen
48
0.06 (?)
3
4
Huangchong
40
0.28 (?)
5
Huangjin
41
6
Huangpu
48
7
8
Jiangmen
Laoyagang
9
10
48
-0.21
0.15
0.16
0.28
Denglongshan
48
-0.27
0.01
0.16
0.28
Hengmen
48
-0.13
0.06
0.25
0.28
4
Huangchong
40
-0.18
0.07
-0.16
0.31
0.07 (?)
5
Huangjin
41
0.01
0.15
0.17
0.31
0.29 (?)
6
Huangpu
48
-0.13
0.13
0.17
0.28
46
48
0.68 (?)
0.36 (-)
7
8
Jiangmen
Laoyagang
46
48
0.01
-0.18
-0.22
0.02
0.14
-0.15
0.29
0.28
Makou
47
0.58 (?)
9
Makou
47
0.19
0.01
0.19
0.29
Nanhua
48
0.93 (-)
10
Nanhua
48
0.07
-0.18
-0.18
0.28
11
Nansha
43
0.58 (-)
11
Nansha
43
-0.28
-0.08
0.20
0.30
12
Rongqi
48
0.80 (?)
12
Rongqi
48
0.04
-0.16
-0.17
0.28
13
Sanduo
48
0.44 (-)
13
Sanduo
48
0.10
-0.21
-0.13
0.28
14
Sanshakou
47
0.25 (-)
14
Sanshakou
47
-0.23
0.23
0.17
0.29
15
Sanshui
47
0.45 (-)
15
Sanshui
47
0.08
-0.20
-0.16
0.29
16
Shizui
46
0.12 (?)
16
Shizui
46
-0.15
-0.11
-0.18
0.29
17
Sishengwei
47
0.07 (?)
17
Sishengwei
47
-0.04
0.11
0.16
0.29
18
Xipaotai
42
0.10 (?)
18
Xipaotai
42
-0.20
0.15
0.17
0.30
19
Zhuyin
48
0.38 (?)
19
Zhuyin
48
-0.14
-0.01
0.02
0.28
Note: The ‘(?)’ sign means an upward trend, and the ‘(-)’ sign
means a downward trend
of Foreign Direct Investment, and contributes about 40% of
export (therefore called ‘‘World Factory’’). Highly developed social economy puts enormous pressures on the local
environment, and makes the PRD vulnerable to flood,
storm surge and other natural hazards (Luo et al. 2000,
2002). Since 1980s, intensive channel dredging (Luo et al.
2000), sand mining, levee construction and other human
activities, together with climatic changes, including precipitation changes and sea level changes, have forced flood
stages upward and led to ‘‘man-made’’ increase in flood
stage and experienced frequent flood hazards within the
PRD river network. The floods occurred in 1994, 1997 and
1998 caused extensive losses (Liu et al. 2003). Huang et al.
(2000) examined the impacts of global warming on wellevidenced sea level rising in PRD region identified to about
1.5–2 mm per year over the past century. More seriously,
throughout the next century, the rate of the sea level rise is
expected to increase. Chen et al. (2004) and Yang et al.
(2002) studied the spatial variability and long-term trends
of water levels in river network of PRD using co-kriging
simulations and Mann–Kendall trend test methods. In the
past literatures on the flood-related analysis by a number of
hydrologists, the Pearson-III, Generalized Extreme Value
(GEV) and Gumbel distribution are usually the widely used
to detect the governing behaviors of flood magnitudes for
such region (e.g. Luo et al. 2000, 2002; Liu et al. 2003).
However, satisfactory estimates of these parameters within
these distributions is highly depending on a number of
long-term historical observations and these theories have
some theoretical and practical drawbacks compared with
L-moments theory (Hosking and Wallis 1993). Till far,
there is no systematic study on the flood frequency analysis
with the state-of-art L-moments techniques performed in
such region. Thus, it is extremely necessary to perform
regional flood analysis using L-moments techniques in
PRD region to meet the widely recognized requirements of
flood risk management.
3.2 Data
The annual extreme flood stage records of 19 tidal gauges
with sufficient length in the Pearl River delta region during
1958–2005 were collected and compiled. These hydrological data were obtained from the Guangdong Provincial
Bureau of Hydrology (GPBH), which is officially in charge
of monitoring, collecting, compiling and publishing highquality hydrological data for Guangdong province. Thus
the quality of hydrological data can be guaranteed in this
study. Detailed information of the tidal level data used in
the current research and the location of the tidal gauges are
listed in Table 1 and Fig. 1.
123
174
Stoch Environ Res Risk Assess (2010) 24:165–182
Table 4 Critical values of Di for discordancy test (Hosking and Wallis 1997)
Number of sites
5
6
7
8
9
Critical value
1.333
1.648
1.917
2.140
2.329
Table 5 Results of L-moment ratios and discordancy test, Di for
annual maximum of flood stage in the Pearl River Delta (Indexed
alphabetically on site name)
l1 (m) tðiÞ ¼ ui t(i)
3
t(i)
4
Di
No. Site name
ni
1
Dasheng
48 1.93
0.1338
0.0605 0.2147 1.13
2
Denglongshan 48 1.65
0.1611
0.2604 0.2395 0.78
3
4
Hengmen
Huangchong
48 1.86
40 1.78
0.1384
0.1277
0.2407 0.2182 0.46
0.2462 0.2451 0.62
5
Huangjin
41 1.63
0.1623
0.1952 0.2218 0.21
6
Huangpu
48 1.96
0.1352
0.0882 0.1499 0.85
7
Jiangmen
46 3.47
0.4676
0.0602 0.0891 0.87
8
Laoyagang
48 2.12
0.1776
0.0789 0.2146 0.71
9
Makou
47 7.07
0.9162
-0.0326 0.1174 1.94
10
Nanhua
48 4.23
0.5563
0.0118 0.083
11
Nansha
43 1.91
0.1382
0.2975 0.2341 1.19
12
Rongqi
48 2.71
0.3134
0.1607 0.1257 0.82
13
Sanduo
48 4.86
0.7326
0.0161 0.0703 1.20
14
Sanshakou
47 1.81
0.1295
0.1101 0.1623 0.57
15
Sanshui
47 7.26
0.9442
-0.0319 0.1356 2.50
16
Shizui
46 1.85
0.1356
0.1305 0.1685 0.39
17
Sishengwei
47 1.87
0.1465
0.0636 0.2704 2.46
18
19
Xipaotai
Zhuyin
42 1.78
48 1.90
0.1367
0.1437
0.2846 0.2456 1.05
0.1176 0.1701 0.38
0.86
4 Results and discussions
4.1 Stationarity and serial correlation tests
The Mann–Kendall test is conducted for flood-stage of
annual-maximum over the entire period (1958–2005) in the
PRD. The results are shown in Table 2. It is seen from
10
2.491
11
12
2.632
13
2.757
2.869
14
C15
2.971
3.000
Table 2 that for maximum annual flood-stage, 13 of 19
sites show slightly increasing trends and the rest 6 show
slightly decreasing trends. However, none of these trends
are significant at 5% of the confidence level. The results
suggest the flood-stage series of annual-maximum
employed in this investigation have no trends (significant at
the 5% confidence level) and they can be treated as stationary series.
The results of autocorrelation test are given in Table 3
form which it can be seen that all of the autocorrelation
coefficients of lag-1, lag-5 and lag-10 for annual maximum
pffiffiffi
series of each site are smaller than 1:96= n. Hence, the
observations in that series can be accepted as being independent at the 5% significance level. Therefore, all series
can be accepted as being stationary and without serial
correlation. It means that the flood frequency analysis can
be applied to the hydrological series for all sites.
4.2 Discordancy measure test
The discordancy measure test is considered as a mean of
screen analysis aiming to identify those sites that are
grossly discordant with the group as a whole. The results of
discordancy measure test together with the L-moment
ratios for the 19 sites in the Pearl River delta region are
given in Tables 4 and 5, together with other statistics
including record lengths, L-moment ratios and D-statistic
values. Di are compared with the critical discordancy
Dcritical = 3.00. The larger Di are 2.50 and 2.46 for sites
Sanshui and Sishengwei, and there is no site at which Di
value exceeds the critical value (3.00). Therefore, the entire
sites in the criss-cross network of PRD pass the discordancy measure test.
Table 6 Results of heterogeneity and goodness-of-fit tests for annual maximum flood stage in PRD region
No.
Region
Region
type
Containing sites
Heterogeneity measure
H1
1
Upper & middle PRD1
2
Lower PRD2
3
3
Lower PRD
4
Entire PRD
HOM
HER
1
Sanshui, Makou, Sanduo, Nanhua,
Jiangmen
H2
H3
Goodness
of fit
|Z| B 1.64
Distribution
function
0.65
0.64
-1.26
0.50
Huangpu, Dasheng, Sishengwei
-0.96
-1.54
-0.91
[1.64
WAK
Denglongshan, Hengmen, Huangchong,
Huangjin, Xipaotai
-0.68
-1.69
-2.06
-1.11
GLO
All of 19 sites in PRD
36.18*
15.35*
0.01
GLO
1.27*
2
GEV
Note: (1) Upper & middle PRD encompasses five sites in the upper and middle PRD area, Lower PRD represents the lower Dongjiang river
region which is subjected to the part of lower PRD, and Lower PRD3 is the part of lower PRD region near the outside South-sea, (2) HOM denote
a homogeneous region, and HER denote a definitely heterogeneous region, (3) * failed in the heterogeneity test, (4) GLO generalized logistic,
GEV generalized extreme-value, WAK wakeby distribution
123
Stoch Environ Res Risk Assess (2010) 24:165–182
113 E
113 30' E
g
Sa
ns
L
ui
n
aga
aoy
Huangpu eng1
sh
Da
ak
M
ou
Sa
nd
sh
San
uo
120 E
N an
140 E
nh
R on
gq i
ua
en
zui
Hengmen
Shi
u
Zh
te
ga
en
Xi
p
in
RMSE q^ðFÞ
(%)
No. Region
F
1
0.900 0.330
1.245 0.981 1.218
0.990 0.461
1.535 0.988 1.404
0.999 0.521
0.900 0.222
1.834 1.007 1.586
1.245 0.943 1.423
0.990 0.265
1.535 1.077 1.847
0.999 0.291
1.834 1.236 2.290
0.900 0.023
1.245 1.202 1.289
0.990 0.055
1.535 1.402 1.668
0.999 0.088
1.834 1.584 2.083
0.900 0.144
1.245 1.155 1.271
0.990 0.231
1.535 1.233 1.648
0.999 0.291
1.834 1.307 2.100
2
3
4
1
Upper & middle PRD
Lower PRD2
3
Lower PRD
Error
bounds
4.3 Tests for heterogeneity and goodness-of-fit
measures
Identification of the homogeneous region(s) of PRD is
performed following the steps suggested by Hosking and
Wallis (1997): (a) removing some sites from the region and
trying a completely different assignment of sites to
region(s) by re-adding site(s) to identify the homogeneous
subregion(s); and (b) adding a cluster feature to the
regional sites. In the second step different clusters are
formulated based on different attributes (geographical and
te
ga
en
im
Jit
Table 7 Simulation results for the estimated regional quantiles, their
corresponding error bounds, and RMSE values
ate
ng
me
ao
od
M
n
22 N
n
gj
Ya
m
an
e
u
H
iaom
a
Hut
Se
gate
ao
gm
an
Hu
a
gsh
lon
ng
Huangchong
De
ao
ta
i
yin
(3)
20 N
ate
te
te
ga
ga
ng
e
en e
m at
om
qi n g
Jia
ng me
Ho eng
H
gm
an
22 30'N
30 N
500 m
Entire PRD
sha
en
m
Hu
Na
40 N
(2)
Se
a
100 E
u
Sishengwei
(1)
80 E
ako
Li
ng
di
ng
23 N
Ji
Fig. 2 Three homogeneous
regions HOM detected in the
Pearl River Delta region after
heterogeneity test. In which, (1)
represents the upper and middle
PRD1 region containing five
sites in mainstem West and
North River primarily
dominated by fluvial processes;
(2) represents the lower PRD2
region containing three sites in
lower East River primarily
dominated by tidal processes;
(3) represents the lower PRD3
region containing five sites
closing to the South Huangmaosea completely dominated by
tidal processes
175
Gauging station
statistical), and different weights are assigned to attributes.
In both steps, a site or sites are assigned to selected
homogeneous region(s), and the effect of including a site or
sites in a homogeneous region or regions is investigated.
The regional analysis comprising of 19 sites and values
of 36.18, 15.35 and 1.27 are obtained for the three H
measures (Table 6), respectively. Therefore, the whole
PRD region is considered to be definitely heterogeneous.
We identify three homogenous sub-regions (HOM) (Upper
and middle PRD1 consists of five sites which are primarily
dominated by fluvial processes; Lower PRD2 consists of
three sites which are subjected to the downstream of
Dongjiang basin; Lower PRD3 consists of five sites closing
to the China outside sea). The rest sites form a heterogeneous region (HER).
The results for heterogeneity test and goodness-of-fit
measures are listed in Table 6 and Fig. 2. Most results of
goodness-of-fit test indicated that they are satisfactory with
|Z| B 1.64 (Hosking and Wallis 1993, 1997). In the goodness-of-fit test, which is the final step of the regionalization
process, six distributions (GLO: Generalized Logistic,
GEV: Generalized Extreme-value, GNO: Generalized
Normal, GPA: Generalized Pareto, PE3: Pearson type III
and WAK: Wakeby) are investigated. For each homogenous sub-region, the best distribution identified is used in
the study. It is interesting to see that the GLO distribution
fits best for the entire region with a Z value of 0.01 compared to |Zcrit| B 1.64. This might be due to the application
of the regional Kappa distribution, which becomes the
Generalized Logistic when the parameter h = -1, i.e., the
123
176
Stoch Environ Res Risk Assess (2010) 24:165–182
Table 8 Final results of water-levels (m) corresponding to different quantiles for the entire PRD region
Site number Site name
Quantiles/frequency (P)
0.1000
0.2000
0.5000
0.8000
0.9000
0.9500 0.9800 0.9900 0.9990
0.9999
P = 90% P = 80% P = 50% P = 20% P = 10% P = 5% P = 2% P = 1% P = 0.1% P = 0.01%
1
Dasheng
1.65
1.76
1.90
2.11
2.26
2.39
2.55
2.66
2.96
3.19
2
Denglongshan 1.39
1.45
1.60
1.81
1.97
2.14
2.42
2.67
3.88
6.01
3
4
Hengmen
Huangchong
1.56
1.49
1.63
1.56
1.80
1.72
2.03
1.94
2.21
2.11
2.41
2.31
2.72
2.60
3.00
2.87
4.36
4.18
6.75
6.47
5
Huangjin
1.37
1.43
1.58
1.78
1.94
2.11
2.39
2.63
3.83
5.93
6
Huangpu
1.68
1.80
1.93
2.15
2.30
2.43
2.60
2.71
3.02
3.25
7
Jiangmen
2.40
2.76
3.47
4.19
4.56
4.86
5.15
5.33
5.73
5.94
8
Laoyagang
1.70
1.83
2.08
2.38
2.57
2.78
3.06
3.29
4.21
5.41
9
Makou
4.89
5.61
7.05
8.53
9.28
9.88
10.48
10.85
11.66
12.08
10
Nanhua
2.93
3.36
4.22
5.11
5.56
5.91
6.28
6.49
6.98
7.23
11
Nansha
1.53
1.65
1.87
2.14
2.32
2.50
2.76
2.97
3.79
4.88
12
Rongqi
2.17
2.34
2.66
3.04
3.30
3.55
3.91
4.21
5.38
6.93
13
Sanduo
3.36
3.86
4.85
5.86
6.38
6.79
7.21
7.46
8.01
8.31
14
Sanshakou
1.45
1.56
1.78
2.03
2.20
2.37
2.61
2.81
3.59
4.63
15
Sanshui
5.02
5.76
7.24
8.76
9.54
10.15
10.77
11.15
11.98
12.42
16
Shizui
1.48
1.59
1.81
2.07
2.25
2.42
2.67
2.87
3.67
4.72
17
Sishengwei
1.60
1.71
1.84
2.04
2.19
2.31
2.47
2.58
2.87
3.09
18
19
Xipaotai
Zhuyin
1.49
1.53
1.56
1.64
1.72
1.87
1.95
2.13
2.12
2.31
2.31
2.49
2.61
2.75
2.88
2.96
4.18
3.78
6.48
4.86
calculated h value for the regional Kappa distribution is
h = -0.7778 & -1.
4.4 Estimation of regional flood frequency, error
bounds and root mean squared error (RMSE)
in PRD
Using the simulation program, error bounds and RMSE of
the quantile estimates for each subregion and the accuracies of the estimated quantiles are determined by relative
bias and relative RMSE. These results compare the simulated and observed estimates, and the accuracy of the
estimated quantiles are obtained. Table 7 presents the
simulation results for the estimated quantiles and RMSE
values of the four sub-regions. The results show that the
RMSE values of the estimated quantiles for one heterogeneous region (Entire PRD) are always greater than those
for three homogeneous regions (Upper and middle PRD1,
Lower PRD2, and Lower PRD3). This is because the
RMSEs of the growth curve contain the contribution from
the variability of the estimated growth curve only, while
the RMSEs of the quantiles contain a further contribution
by the variability of the estimated index flood (Atiem and
Harmancioglu 2006). Additionally, it demonstrates that
quantile estimates become less accurate at larger return
periods.
123
To reduce the bias and uncertainties of regional flood
estimation, the final results of regional flood estimation for
the PRD region are incorporated with those of the one
heterogeneous region and the three homogeneous regions.
For the sites belong to the three homogeneous regions, the
simulation results of these regions are considered to be the
final results of these sites; whilst the other sites which are
excluded from the three homogeneous regions and
belonging to the one heterogeneous region, whose regional
flood frequencies are determined through the GLO distribution recommended by the heterogeneity and goodnessof-fit tests (Table 6). Thus, the final regional flood-stage
corresponding to different quantiles or return periods of 19
sites in the PRD region can be obtained eventually
(Table 8).
4.5 Spatial mapping of annual maximum flood-stage
with different return periods for the PRD
Flood stage in the crisscross river network, serving as one
of the most important environment indicator for regional
flood risk and water resources management, is a spatially
continuous variable. Thus we can quantify spatial associations of flood stages between sites and map flood-stage
with different return periods for the PRD region by kriging
simulations. Figure 3 provides the resulted flood risk
Stoch Environ Res Risk Assess (2010) 24:165–182
113 E
113 30' E
113 E
g
gan
oya
La
Sa
ns
ui
ou
ak
M
ou
ak
nd
uo
g
en
sh
Da
Huangpu
23 N
kou
sha
San
Sa
113 30' E
g
gan
oya
La
Sa
ns
ui
Huangpu ng
e
sh
Da
M
23 N
177
kou
sha
San
Sa
nd
uo
Sishengwei
en
ng
S
di
ng
Li
gm
an
22 N
S
ao
te
ga
en
im
Jit
ate
ng
me
ao
od
Hu
M
Ya
m
ea
Xi
pa
ot
ai
in
gS
ea
Li
ng
d
Huangchong
ga
te
ot
ai
pa
Xi
an
g sh
lon
ng
ate
Hengmen
in
en
g
zui
Shi
te
te
te
ga
ga
ga
en
en e
en
om qim gat
m
n
Jia
ng me
Ho eng
H
De
j
ng
Ya
m
Hu
in
uy
en
ua
H
iaom
a
Hut
Se
gate
ao
gm
an
Hu
22 N
22 30'N
ate
ng
me
an
ao
od
gsh
M
lon
ng
De
te
in
ga
uy
en
Zh
im
jin
Jit
ng
en
ua
H utiaom
ea
H
gate
Zh
Huangchong
gqi
Ron
Nan
sha
en
m
ng
en
gm
Hengmen
J ia
an
zui
Shi
ate
te
te
g
ga
ga
n
e
en e
en
om qim gat
m
n
Jia
ng me
Ho eng
H
Ji
22 30'N
Na
nh
ua
Hu
gqi
Ron
Na
nh
ua
Sishengwei
Nan
sha
Gauging station
Gauging station
(A)
113 E
113 30' E
g
gan
oya
La
Sa
ns
ui
ou
ak
M
Sa
nd
23 N
k ou
sha
Sa n
uo
kou
sha
San
Sa
nd
uo
Sishengwei
Sishengwei
gm
en
22 30'N
zui
Hengmen
Shi
di
ng
S
Ya
m
ot
en
g
Li
ate
ng
Xi
pa
ea
i
pa
ot
a
Xi
ate
en
g
Ya
m
Huangchong
22 N
Gauging station
(C)
gm
an
Hu
gm
an
Hu
22 N
ate
ng
me
an
ao
od
gsh
M
lon
ng
De
ate
in
ng
uy
me
Zh
i
jin
Jit
ng
en
ua
H utiaom
a
H
Se
gate
ao
ate
ng
me
an
ao
od
gsh
M
lon
ng
De
ate
in
ng
uy
me
Zh
iti
jin
J
ng
en
ua
H utiaom
a
H
Se
gate
ao
Huangchong
gqi
Ron
te
te
te
ga
ga
ga
en
en e
en
m at
om
m
qi n g
Jia
ng me
Ho eng
H
an
en
Hengmen
Ji
gm
zui
Shi
te
te
te
ga
ga
ga
n
e
en e
en
m at
om
m
qi n g
Jia
ng m e
Ho eng
H
an
22 30'N
Na
nh
ua
ai
gqi
sha
Hu
Ro n
Hu
Ji
Na
nh
ua
Nan
Nan
sha
Se
a
23 N
g
en
sh
Da
Huangpu
ou
ak
M
Huangpu ng
e
sh
Da
ng
ui
di
ns
ng
Sa
113 30' E
g
gan
oya
La
Li
113 E
(B)
Gauging station
(D)
Fig. 3 Mapping (P = 2, 1, 0.1 and 0.01%) of annual maximum flood-stage in the PRD region in which (a) P = 2%; (b) P = 1%; (c) P = 0.1%;
(d) P = 0.01%. Note: the stage interval in the contour is 1 m
(P = 2, 1, 0.1 and 0.01%) map of annual maximum
flood stage in the PRD region. Generally, flood stage of
Fig. 3a–d indicate that flood frequency decreases gradually
from the riverine system to the tide controlled coastal
areas. Besides, Fig. 3a and b demonstrate similarities in the
spatial distribution of flood frequency for the PRD region
except the magnitude of Fig. 3a (P = 2%, ranging from 3
to 10 m) is slightly smaller than that of Fig. 3b (P = 1%,
123
178
Table 9 Flood-stage variations
(DH: m) corresponding to
different increments of flood
frequency in the PRD region
Stoch Environ Res Risk Assess (2010) 24:165–182
Site number
Site name
I: DP =
(5–2%)
II: DP =
(2–1%)
III: DP =
(1–0.1%)
IV: DP =
(0.1–0.01%)
1
Dasheng
0.16
0.11
0.30
0.23
2
Denglongshan
0.28
0.25
1.21
2.13
3
Hengmen
0.31
0.28
1.36
2.39
4
Huangchong
0.29
0.27
1.31
2.29
5
Huangjin
0.28
0.24
1.20
2.10
6
Huangpu
0.17
0.11
0.31
0.23
7
8
Jiangmen
Laoyagang
0.29
0.28
0.18
0.23
0.40
0.92
0.21
1.20
9
Makou
0.60
0.37
0.81
0.42
10
Nanhua
0.37
0.21
0.49
0.25
11
Nansha
0.26
0.21
0.82
1.09
12
Rongqi
0.36
0.30
1.17
1.55
13
Sanduo
0.42
0.25
0.55
0.30
14
Sanshakou
0.24
0.20
0.78
1.04
15
Sanshui
0.62
0.38
0.83
0.44
16
Shizui
0.25
0.20
0.80
1.05
17
Sishengwei
0.16
0.11
0.29
0.22
18
Xipaotai
0.30
0.27
1.30
2.30
19
Zhuyin
0.26
0.21
0.82
1.08
ranging from 3 to 11 m). The results can be observed in
Fig. 3c (P = 0.1%, ranging from 4 to 11 m) and 3D
(P = 0.01%, ranging from 4 to 12 m) similarly. The
resulting maps are extremely valuable in supporting flood
risk assessment and water resources management in ungauged regions.
4.6 Characterization of spatial patterns
for flood-frequency variations in PRD
The flood-stage increment corresponding to different
increments of flood periods (Table 9 and Fig. 4) revealing
the underlying flood risk in the PRD region can serve as
another important indicator in supporting the regional flood
risk and water resources management. The results of column I and II (DP ranges from 5% to 1%) suggest that the
flood-stage increments in all 19 sites are not obvious
compared with those of column III and IV (DP ranges from
1% to 0.01%), in which the increments of stage are mostly
larger than column 1 and II. From a regional perspective,
Regional curve of flood-stage increments (Fig. 5) for three
homogenous sub-regions indicates that the lower PRD3
near the coast comprising of five sites (Denglongshan,
Hengmen, Huangchong, Huangjin and Xipaotai) holds the
highest flood stage increment among the 19 sites in the
PRD region. This is primarily induced by the incorporated
influences of emerging extraordinary floods, typhoons,
storm surges, tsunamis and well-evidenced sea-level rising
123
DH (m)
in the PRD3 region. While, the regimes of flood-stage
variations for the upper and middle PRD region (e.g. PRD1
and PRD2) are only dominated by streamflow processes in
flood seasons and human activities in such regions. The
upper and middle PRD1 comprising of two sites (Rongqi
and Sanduo) follows the lower PRD in the flood stage
increment. The stage increment of the lower PRD2 comprising of three sites (Huangpu, Dasheng and Sishengwei),
which belongs to the downstream of Dongjiang river, is the
lowest among 19 sites of the PRD.
The spatial patterns of flood-frequency variations
addressed above demonstrate the most serious flood-risk in
the coastal region (i.e. the PRD3 region) because it is
extremely prone to the emerging extraordinary floods,
typhoons, storm surges, tsunamis and well-evidenced sealevel rising. While excessive rainfalls in the upstream
basins may lead to modest flood risks in upper and middle
PRD region (i.e. the PRD1 and PRD2 region). The flood
risks of rest parts (e.g. Shizui, Hengmen, Nansha, and
Laoyagang) are identified as the lowest in entire PRD. As
far as concerned, the underlying flood governing behaviors
of PRD region driven by a range of natural forces and
human activities are very complicated. For instance, the
changes of flood-stages across the PRD are the results of
such factors as streamflow variations, human interferences
and sea level fluctuations (Chen et al. 2008). These factors
interact on each other and give rise to alterations of floodstage components as mentioned above via dynamical
Stoch Environ Res Risk Assess (2010) 24:165–182
113 E
179
113 30'
Sa
an
yag
113 E
E
g
ns
o
ns
La
ui
e
sh
San
uo
sha
Huangpu
23 N
kou
E
ng
ng
ou
nd
ga
oya
Da
ou
ak
M
ak
M
Da
Sa
La
ui
Huangpu
23 N
113 30'
Sa
Sa
nd
San
uo
sha
sh
en
g
kou
Sishengwei
Sishengwei
Nan
gqi
sha
Shi
22 30'N
zu i
Hengmen
uy
te
ga
en
Se
a
Xi
pa
te
ga
en
im
Jit
te
ga
Gauging station
ng
di
ng
a
Se
Ya
m
ate
ng
me
ao
od
M
en
en
im
Jit
22 N
Li
i
ta
Xi
pa
o
Li
ng
di
ng
n
in
ga
te
sha
gj
en
g
lon
ng
De
ot
ai
in
Huangchong
an
en
ate
ng
me
ao
od
M
Ya
m
ua
u
H
iaom
a
Hut
Se
gate
ao
gm
an
Hu
an
gsh
lon
ng
De
in
gj
an
u
H
iaom
a
Hut
Se
gate
ao
gm
an
Hu
22 N
sha
Zh
in
uy
Zh
Huangchong
gqi
en
Hengmen
Ron
gm
zui
Sh i
nh
ate
te
te
g
ga
ga
n
e
en e
en
m at
om
m
qi n g
Jia
Hu
ng me
Ho eng
H
ua
Na
an
Ji
en
gm
an
Ji
22 30'N
nh
R on
ate
te
te
g
ga
ga
n
e
en e
en
m at
om
um
qi n g
Jia
H
ng me
Ho eng
H
Na
Na n
Gauging station
(B)
(A)
113 E
113 30'
Sa
ns
L
ui
ao
an
y ag
E
113 E
Sa
ns
ga
oya
ng
Huangpu
Da
ak
M
sh
en
g
ou
ou
ak
M
Da
La
ui
g
en
sh
Huangpu
23 N
Sa
nd
San
uo
sha
kou
Sishengwei
N an
R on
gqi
zui
Hengmen
ai
Ya
m
ot
en
ga
Li
te
Xi
pa
Se
ng
di
n
g
pa
Xi
te
ga
Ya
m
en
a
ot
ai
Shi
Huangchong
(C)
gm
m
ng
22 N
Gauging station
ua
te
te
te
ga
ga
ga
en
en e
m at
om
qi n g
Jia
ng me
Ho eng
H
22 30'N
an
Hu
a
Hu
22 N
sha
ate
ng
me
an
ao
od
gs h
M
lon
ng
De
ate
in
ng
uy
me
Zh
iti
jin
J
ng
en
ua
H utiaom
a
H
Se
gate
ao
ate
ng
me
an
ao
od
gsh
M
lon
ng
De
te
in
ga
uy
en
Zh
im
jin
Jit
ng
en
ua
H utiaom
a
H
Se
gate
ao
Huangchong
gqi
en
Hengmen
R on
m
zu i
te
te
te
ga
ga
ga
en
en e
m at
om
qi n g
Jia
ng me
Ho eng
H
en
S hi
nh
en
m
Hu
ua
m
g
an
22 30'N
Na
g
an
Ji
Ji
nh
en
m
Hu
Na
Sishengwei
Nan
sha
a
kou
Se
sh a
ng
San
uo
di
nd
ng
Sa
Li
23 N
113 30' E
g
Gauging station
(D)
Fig. 4 Mapping of flood stage variation (m) corresponding to different increments of flood frequency, in which (a) DP = (5–2%); (b) DP = (2–
1%); (c) DP = (1–0.1%); (d) DP = (0.1–0.01%)
mechanisms still remain unknown to us. Generally,
streamflow changes in flood seasons and human activities
such as intensive in-channel dredging can be regarded as
major causes for flood-stage alterations in the upper and
middle PRD region. In particular, the spatial pattern of
flood-stage variations will be influenced by different
intensities of the in-channel dredging and sand mining.
Chen et al. (2007) indicates that increasing water level is
usually identified in the channel featured by moderate and
low intensity of the dredging. River channels featured by
high intensity in-channel dredging are usually dominated
by significant decreasing water levels. The different roles
123
180
Stoch Environ Res Risk Assess (2010) 24:165–182
(3)
(4)
Fig. 5 Regional curve of flood stage increments corresponding to
different increments for flood frequency in the PRD region, of which:
DP1 = (5–2%), DP2 = (2–1%), DP3 = (1–0.1%) and DP4 = (0.1–
0.01%)
of the sand dredging in water-level alterations within the
river channels in the PRD are necessary for further research
in the future. However, the emerging flood hazards,
typhoons, storm surges, tsunamis and well-evidenced sealevel rising are collectively recognized as the major driving
forces for the coastal region.
5 Conclusions
Regional frequency analysis on annual maximum flood has
scientific and practical values in the context of regional
water resource management. L-moments based regional
frequency analysis technique, which has definite advantages over conventional moment parameters and have no
serious drawbacks, provides promising insights into
regional flood frequency analysis and is used widely by
hydrologists across the world nowadays. The following
conclusions can be drawn from the results of this study.
(1)
(2)
The whole PRD region is considered to be definitely
heterogeneous according to the heterogeneity test. In
the PRD region, three homogenous sub-regions
(HOM) are defined and evaluated: Upper & middle
PRD1, Lower PRD2 and Lower PRD3.
The RMSE values (%) of simulation results (Ranging
from 0.023% to 0.291% when F is between (0.900–
0.999)) for the sites in the three homogeneous regions
show that they are accurate enough to be applied in
supporting the flood risk management. Those for the
other sites belonging to the heterogeneous region are
below 0.521% when F = 0.999 and can be used to
estimate the regional flood frequency in these regions.
Therefore, the final regional flood-stage corresponding to different quantiles or return periods of 19 sites
123
in the PRD region can be obtained from the results of
three homogeneous regions and one heterogeneous
region.
The resulted flood maps of annual maximum flood
stage in the PRD region suggests that the frequency of
flood-stage decreases gradually from the riverine
system to the tide controlled coastal areas. Besides,
the results show that similarities in the spatial
distribution of flood stage of the PRD except for the
magnitude. The resulting maps are extremely valuable in supporting flood risk assessment and water
resources management in ungauged regions.
The results imply that the stage increments in all 19
sites when P ranges from 5% to 1% are not obvious
compared with those when P ranges from 1% to
0.01%, and in the latter case the increment of stage
are often larger than 1 m. From a regional perspective, the lower PRD3 near the coast comprising of five
sites has the highest flood stage increment among 19
sites in the PRD region. The upper and middle PRD1
comprising of five sites follows the lower PRD3 in the
flood stage increment. The stage increment of the
lower PRD2 comprising of three sites, which is
subject to the downstream of Dongjiang basin, is the
lowest among the 19 sites of the PRD. The spatial
patterns of flood-frequency variations demonstrate the
most serious flood-risk in the coastal region (i.e. the
PRD3 region) because it is extremely prone to the
emerging extraordinary floods, typhoons, storm
surges, tsunamis and well-evidenced sea-level rising.
While excessive rainfalls in the upstream basins may
lead to modest flood risks in upper and middle PRD
region (i.e. the PRD1 and PRD2 region). The flood
risks of rest parts (e.g. Shizui, Hengmen, Nansha, and
Laoyagang) are identified as the lowest in entire PRD.
Generally, streamflow changes and human activities
such as in-channel dredging can be regarded as major
causes for water level alterations in the upper and
middle PRD region. However, the emerging flood
hazards, typhoons, storm surges, tsunamis and wellevidenced sea-level rising are collectively recognized
as the major driving forces for the coastal region.
These findings will contribute to understanding the
unique features of extreme flood hazards in PRD and be
beneficial to formulating the regional development strategies for policymakers and stakeholders in water resource
management against the menaces of frequently emerged
floods and well-evidenced sea level rising.
Acknowledgments The work was financially supported by a key
grant from the National Natural Science Foundation of China
(40830639), State Key Laboratory of Water Resources and Hydropower Engineering Science (2008B041), open Research Grant from the
Stoch Environ Res Risk Assess (2010) 24:165–182
Key Sediment Lab of the Ministry for Water Resources (2008001),
key Research Grant from Chinese Ministry of Education (308012),
National Key Technology R&D Program (2007BAC03A060301), and
a grant from Ministry of Water Resources (200701039), and the Programme of Introducing Talents of Discipline to Universities—the 111
Project of Hohai University (B08048). We would like to appreciate the
editor, associate editor and three anonymous referees for their constructive comments, which greatly improve the quality of this paper.
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