Journal of Hydrology 380 (2010) 386–405
Contents lists available at ScienceDirect
Journal of Hydrology
journal homepage: www.elsevier.com/locate/jhydrol
Regional frequency analysis and spatio-temporal pattern characterization
of rainfall extremes in the Pearl River Basin, China
Tao Yang a,e,*, Quanxi Shao b, Zhen-Chun Hao a, Xi Chen a, Zengxin Zhang c, Chong-Yu Xu d, Limin Sun a
a
State Key Laboratory of Hydrology-Water Resources and Hydraulics Engineering, Hohai University, Nanjing 210098, China
CSIRO Mathematical and Information Sciences, Private Bag 5, Wembley, WA 6913, Australia
c
Jiangsu Key Laboratory of Forestry Ecological Engineering, Nanjing Forestry University, Nanjing 210037, China
d
Department of Geosciences, University of Oslo, P.O. Box 1047, Blindern, 0316 Oslo, Norway
e
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
b
a r t i c l e
i n f o
Article history:
Received 7 July 2009
Received in revised form 2 November 2009
Accepted 7 November 2009
This manuscript was handled by G. Syme,
Editor-in-Chief
Keywords:
Regional frequency analysis
Rainfall extremes
L-moments
Cluster analysis
Spatial patterns
Large-scale circulation
s u m m a r y
This paper presents a method for regional frequency analysis and spatio-temporal pattern characterization of rainfall-extreme regimes (i.e. extremes, durations and timings) in the Pearl River Basin (PRB) using
the well-known L-moments approach together with advanced statistical tests including stationarity test
and serial correlation check, which are crucial to the valid use of L-moments for frequency analysis.
Results indicate that: (1) the entire Pearl River Basin (40 sites) can be categorized into six regions by cluster analysis together with consideration of the topography and spatial patterns of mean precipitation in
the basin. The results of goodness-of-fit measures indicate that the GNO, GLO, GEV, and PE3 distributions
fit well for most of the basin for different HOM regions, but their performances are slightly different in
term of curve fitting; (2) the estimated quantiles and their biases approximated by Monte Carlo simulation demonstrate that the results are reliable enough for the return periods of less than 100 years; (3)
excessive precipitation magnitude records are observed at Guilin region of Guangxi Province and Fogang
region of Guangdong Province, which have sufficient climate conditions (e.g. precipitation and humidity)
responsible for the frequently occurred flood disasters in the regions. In addition, the spatial variations of
precipitation in different return periods (Return period = 1, 10, 50 years to 100 years) increase from the
upstream to downstream at the regional scale; (4) the seasonal patterns of precipitation extremes for different topographical regions are different. The major precipitation events of AM1R, AM3R, AM5R and
AM7R in regions of low-elevation in lower (south-eastern) part of the basin occur mainly in May, June,
July and August, while the main precipitation periods for the mountainous region upstream are June, July
and August. Further analysis of the NCAR/NCEP reanalysis data indicates that the eastern Asian summer
monsoon and typhoons (or hurricanes) are major metrological driving forces on the precipitation
regimes. Additionally, topographical features (i.e. elevation, distance to the sea, and mountain’s influences) also exert different impacts on the spatial patterns of such regimes. To the best of our knowledge,
this study is the first attempt to conduct a systematic regional frequency analysis on various annual precipitation extremes (based on consecutive 1-, 3-, 5-, 7-day averages) and to establish the possible links to
climate pattern and topographical features in the Pearl River Basin and even in China. These findings are
expected to contribute to exploring the complex spatio-temporal patterns of extreme rainfall in this basin
in order to reveal the underlying linkages between precipitation and floods from a broad geographical
perspective.
Ó 2009 Published by Elsevier B.V.
Introduction
Due to the influence of global warming, the magnitude and pattern of precipitation extremes are expected to change. In particu-
* Corresponding author. Address: State Key Laboratory of Hydrology-Water
Resources and Hydraulics Engineering, Hohai University, Nanjing 210098, The
People’s Republic of China. Tel.: +86 25 8378 6973; fax: +86 25 8378 6606.
E-mail addresses: enigama2000@hhu.edu.cn, tfrank.yang@gmail.com (T. Yang).
0022-1694/$ - see front matter Ó 2009 Published by Elsevier B.V.
doi:10.1016/j.jhydrol.2009.11.013
lar, extreme weather events such as floods, droughts, and
rainstorms are likely to increase in frequency (Dore, 2005; Zhang
et al., 2008). Since the beginning of the 20th century, there has
been a statistically significant increase of about 2% in global land
precipitation (Hulme et al., 1998). But this has been neither spatially nor temporally uniform (Karl and Knight, 1998; Doherty
et al., 1999). Dai et al. (1997) found that the long-term increase
in global precipitation is not related to the ENSO phenomenon
and other patterns of climate variability.
387
T. Yang et al. / Journal of Hydrology 380 (2010) 386–405
0
0
102 E
0
27 N
0
104 E
108 E
odology. He showed that the coefficient of variation (Cv) and
skewness (L-CV) vary systematically with the spatial mapping for
above parameters (MAP). The study area was found to be climatically heterogeneous, and homogeneous sub-regions were delineated within the heterogeneous region based on MAP values.
However, the study for flood data by Gabriele and Arnell (1991)
indicated that different parameters (i.e. Cv, Cs) can be assumed to
be approximately constant over different spatial scales. Particularly, in comparison with the coefficient of variation, the skewness
was found to be constant over a larger area, meaning that the mean
value varies less over space. Furthermore, Pilion et al. (1991) found
that the probability distribution of extreme rainfall events depends
on the duration of rainfall. The utility of regional analysis depends
on the satisfactory solution of the following issues: the selection
and verification of homogenous regions, the identification of regional rainfall probability distributions, and the estimation of the regional distribution parameters. All of these issues require the
knowledge of statistical parameters such as skewness and kurtosis.
Unfortunately, the estimates of these parameters are statistically
challenging due to possible outliers in the data (Royston, 1992).
To address this problem, developed the so-called L-moments techniques which have several advantages over conventional moment
parameters. 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 then 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 (Yang et al., 2009). L-moment diagrams and related goodness-of-fit procedures are useful for distribution selection (Hosking and Wallis, 1997).
Regarding regional extreme precipitation analysis, Fowler and
Kilsby (2003) reported that multi-day rainfall events are an important cause of recent severe flooding in the UK and any change in
0
11 0 E
0
0
114 0 E
112 E
116 E
270N
Elevation
0-310
310-621
621-931
931-1242
1242-1552
1552-1863
1863-2173
2173-2484
2484-2795
260N
250N
0
26 N
0
25 N
0
24 N
0
24 N
230N
230N
0
80 E
0
0
100 E
120 E
0
220N
50 N
0
22 N
Catchments boundary
Beijing
Meteorological gauges
N
0
21 N
30 0 N
Pearl River Basin
W
N
Provincial boundary
E
Provincial capital
S
100
200
400 Km
Streams
0
20 N
0
102 E
0
104 E
0
108 E
0
11 0 E
0
112 E
210N
0
114 E
Longtitudeo(E)
Fig. 1. Sketch map of the Pearl River Basin (PRB), South China and meteorological gauging sites.
200N
0
116 E
Latitu de ( oN)
Extreme precipitation in conjunction with extended precipitation events has the potential to trigger floods and droughts, which
is expected to put considerable pressure on water resources (Yang
et al., 2008a, 2009; Zhang et al., 2008a). The situation, particularly
for highly developed regions, is worsened by sharp increases in
population, unprecedented rise in standards of living, and enormous economic development (Xu and Singh, 2004). Furthermore,
precipitation extremes may influence the soil vulnerability to erosion, which changes plant growth conditions and agricultural practices, causing altered land-use management strategies (Scholz
et al., 2008).
The Pearl River Basin, the second largest drainage basin in China
with a thriving regional socio-economy in south China, is presently
confronted with insufficient water resources to sustain its rapid regional socio-economy development. The spatial and temporal variations of water resource in the basin are closely related to
precipitation changes (Zhang et al., 2008; Yang et al., 2008b). Uneven spatio-temporal distribution of water resource has a negative
influence on the effective use of water resources. Quality-induced
water shortage further deteriorates its regional water security
(Zhang et al., 2008a,b). The East River, one of the major tributaries
of the Pearl River Basin, is responsible for the primary annual water
demand of major cities such as Hong Kong, Guangzhou, Shenzhen,
Dongguan and Huizhou, with over forty million dwellers in total.
Considering the significance of water security in the Pearl River Basin, an improved understanding of the statistical structure with respect to precipitation extremes and its spatial patterns is of
paramount importance to formulating a regional water resources
management strategy for the basin.
A number of studies on precipitation extremes have been
undertaken using various statistical procedures, including regionalization techniques which can potentially reduce the uncertainties in quantile estimates that are inherent in the at-site
approach. Schaefer (1990) conducted a regional analysis for precipitation data from Washington State using an ‘‘index-flood” meth-
388
T. Yang et al. / Journal of Hydrology 380 (2010) 386–405
the magnitude of such events may result in severe damages. Regional 1-, 2-, 5- and 10-day annual maxima rainfall for 1961–2000
from 204 sites across the UK were used in a standard regional frequency analysis to produce generalized extreme value growth
curves for long return period rainfall events in each of nine defined
climatological regions. Wallis et al. (2007) improved the spatial
mapping method and reliability of frequency estimates of precipitation in the broad areas of Washington State using PRISM mapping and L-moments method. The results identify the GEV
distribution as statistically acceptable distribution of up to 1 in
500 recurrence intervals for all regions. Norbiato et al. (2007) utilized index variable method and L-moments to analyze the annual
maximum precipitation for the Friuli-Venezia Giulia region of
north-eastern Italy. Radar rainfall estimates, adjusted by a physically-based method and data from a raingauge network, are used
to characterize the return period of the storm rainfall amounts in
the study. Endreny and Pashiardis (2007) assessed the rainfall frequency analysis in the regional and global approaches by relative
bias and root mean square error (RMSE) values. Results indicated
that relative RMSE values were approximately equal at 10% for
the regional and global method when regions were compared.
However, when time intervals were compared with, RMSE of the
global method had a parabolic-shaped time interval trend. Relative
bias values were also approximately equal for both methods when
Table 1
List of 42 precipitation gauges and associated characteristics in the Pearl River Basin
(Source of data: The National Center of Climate, China).
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
Site name
Xianning
Zhanyi
Yuxi
Luxi
Mengzi
Anshun
Xingyi
Wangmo
Luodian
Dushan
Rongjiang
Rongan
Guilin
Nanxiong
Guangnan
Fengshan
Hechi
Du’an
Liuzhou
Mengshan
Hexian
Shaoguan
Fogang
Lianping
Xunwu
Napo
Baise
Jingxi
Laibin
Guiping
Wuzhou
Guangning
Gaoyao
Guangzhou
Heyuan
Zengcheng
Huiyang
Longzhou
Nanning
Luoding
Taishan
Shenzhou
Longitude
104°170 E
103°500 E
102°330 E
103°460 E
103°230 E
105°550 E
105°110 E
106°050 E
106°460 E
107°330 E
108°320 E
109°240 E
110°180 E
114°190 E
105°040 E
107°020 E
108°030 E
108°060 E
109°240 E
110°310 E
111°310 E
113°350 E
113°320 E
114°290 E
115°390 E
105°500 E
106°360 E
106°250 E
109°140 E
110°050 E
111°180 E
112°260 E
112°280 E
113°190 E
114°410 E
113°490 E
114°250 E
106°510 E
108°210 E
111°340 E
112°470 E
114°060 E
Latitude
26°520 N
25°350 N
24°210 N
24°320 N
23°230 N
26°150 N
25°260 N
25°110 N
25°260 N
25°500 N
25°580 N
25°130 N
25°190 N
25°080 N
24°040 N
24°330 N
24°420 N
23°560 N
24°020 N
24°120 N
24°250 N
24°480 N
23°520 N
24°220 N
24°570 N
23°250 N
23°540 N
23°080 N
23°450 N
23°240 N
23°290 N
23°380 N
23°030 N
23°080 N
23°440 N
23°180 N
23°050 N
22°200 N
22°490 N
22°460 N
22°150 N
22°330 N
Altitude
(m)
Annual precipitation
total (mm)
2237.5
1898.7
1636.7
1704.3
1300.7
1392.9
1378.5
566.8
440.3
1013.3
285.7
121.3
164.4
133.8
1249.6
484.6
211.0
170.8
96.8
145.7
108.8
69.3
67.8
214.5
303.9
793.6
173.5
739.4
84.9
42.5
114.8
56.8
71.0
41.0
40.6
38.9
22.4
128.8
73.1
53.3
32.7
18.2
915.6
992.4
905.0
938.4
842.6
1345.2
1321.3
1235.3
1148.5
1319.1
1203.4
1922.3
1906.0
1524.7
1001.8
1535.1
1497.1
1723.8
1465.0
1743.0
1555.7
1565.5
2173.7
1768.2
1617.4
1403.9
1093.5
1639.5
1367.2
1727.5
1478.9
1705.6
1644.2
1732.4
1939.3
1882.3
1720.6
1329.4
1306.0
1358.9
1947.3
1943.7
regions were compared, but again a parabolic-shaped time interval
trend was found for the global method. This may be caused by fitting a single scale value for all time intervals.
A variety of L-moments based methods have been extensively
employed in the regional frequency analysis of extreme precipitation (e.g. Adamowski et al., 1996; Sveinsson et al., 2002; Burgueno
et al., 2005; Endreny and Pashiardis, 2007; Gaál and Kyselý, 2009).
However, most the studies mentioned above conduct regional
flood frequency analysis without testing stationarity and serial
correlation in the samples to guarantee reliable estimates. Both
stationarity and independence are 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 tests prior to the regional frequency analysis. Furthermore, characterization of the
spatial variations for rainfall extremes is essential to reveal the potential influences of climate change and topographical factors,
hence will be carried out in the current study to support flood/
drought risk assessment and water resources management for
gauged/ungauged regions.
Table 2
Results (P-values) of trend test for the precipitation extremes (AM1R, AM3R, AM5R,
and AM7R) over the period (1960–2005) in the Pearl River Basin using MK test.
No.
Site name
P-value
AM1R
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
Xianning
Zhanyi
Yuxi
Luxi
Mengzi
Anshun
Xingyi
Wangmo
Luodian
Dushan
Rongjiang
Rongan
Guilin
Nanxiong
Guangnan
Fengshan
Hechi
Du’an
Liuzhou
Mengshan
Hexian
Shaoguan
Fogang
Lianping
Xunwu
Napo
Baise
Jingxi
Laibin
Guiping
Wuzhou
Guangning
Gaoyao
Guangzhou
Heyuan
Zengcheng
Huiyang
Longzhou
Nanning
Luoding
Taishan
Shenzhen
0.1203()
0.4459(+)
0.0003(+)
0.1241()
0.0663(+)
0.6422(+)
0.2199(+)
0.1633(+)
0.9710(+)
0.9363()
0.5703(+)
0.3935(+)
0.1169(+)
0.0629(+)
0.9497(+)
0.5695()
0.1937(+)
0.5651(+)
0.1816()
0.8746()
0.0730(+)
0.3527(+)
*
0.0437()
0.4466(+)
0.6819()
0.8729(+)
0.9306()
*
0.0325(+)
0.9733(+)
0.1949(+)
0.4459()
0.3091()
0.3861()
0.8503()
0.7036(+)
0.2939()
0.5912(+)
0.7013()
0.3199(+)
0.9245()
0.5651()
0.6015()
*
AM3R
0.1348()
0.7112(+)
0.0004(+)
*
0.0281()
*
0.0392(+)
0.5042(+)
0.1569(+)
0.7138()
0.3528()
0.2424()
0.6181()
0.4079(+)
0.1746(+)
0.0617(+)
0.7583()
0.6000()
0.6202(+)
0.7415()
0.4679()
0.2693(+)
0.3654(+)
0.5911(+)
0.0524()
0.1842(+)
0.4566()
0.5456(+)
0.3453()
0.3343(+)
0.6880()
0.4803()
0.2396()
0.3609()
0.4250()
0.7112(+)
0.8932()
0.7173(+)
0.8814(+)
0.4615()
0.0729(+)
0.1428()
0.5807(+)
0.7203()
*
AM5R
0.0994()
0.4813(+)
0.0353(+)
0.2515()
*
0.0299(+)
0.5277(+)
0.2145(+)
0.4576()
0.1723()
0.3129()
0.7765()
0.4129(+)
0.7220(+)
0.0959(+)
0.5646()
0.2590()
0.3937()
0.3945()
0.3235()
0.2303(+)
0.2209(+)
0.7715()
0.1452()
0.2074(+)
0.3843()
0.7693(+)
0.8731()
0.5180(+)
0.4124()
0.3736()
0.5420()
0.9176()
0.6383()
0.7275(+)
0.3827()
0.6540(+)
0.3787()
0.4996()
0.3307(+)
*
0.0494()
0.3613(+)
0.5115()
*
AM7R
0.2484()
0.3997(+)
0.0316(+)
0.3507()
*
0.0392(+)
0.4373(+)
0.0921(+)
0.3836()
0.6370()
0.2605()
0.7415()
0.4228(+)
0.7329(+)
0.2262(+)
0.5807()
0.3282()
0.3716()
0.5966()
0.3416()
0.7648(+)
0.2969(+)
0.7660()
0.1815()
0.4034(+)
0.5250()
0.5165(+)
0.8846()
0.7238(+)
0.3707()
0.4206()
0.6579()
0.3430(+)
0.8902(+)
0.8276(+)
0.9524()
0.7959 ()
0.9168()
0.2627()
0.4768(+)
0.5180()
0.2226(+)
0.7427()
*
Note: The ‘(+)’ sign means an upward trend, the ‘()’ sign means a downward trend,
‘()’ means no trend, and ‘*’ denotes trend are statistically significant at 5% confidence level.
389
T. Yang et al. / Journal of Hydrology 380 (2010) 386–405
Meanwhile, 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 hydrological frequency analysis across China (MWR, 1999), and the L-moments
method has not acquired popularity. Only a few reports concerning
regional frequency analysis using L-moments method can be
found. Zhang and Hall (2004) used the Ward’s cluster, fuzzy
c-means and artificial neural networks method together with
L-moments method to conduct a regional flood frequency analysis
for the Gan-Ming River basin in China. The results demonstrated
that the artificial neural network (ANN) has lower standard errors.
Chen et al. (2006) applied L-moments method to analyze 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. Yang et al. (2009) used
the well-known index-flood L-moments approach for a regional
flood frequency analysis and the spatial pattern of flood frequency
in the Pearl River Delta, which drains a contributing area of 3% the
total area of Pearl River Basin. The study was beneficial to understanding the flood behaviors in the PRD region, but the investigated domain is quite limited.
Furthermore, it is well-evidenced that the regional patterns of
the surface hydro-climatological changes due to the currently
well-evidenced global warming are more complicated as compared
to temperature changes. However, both decreasing and increasing
precipitation or runoff can be expected (e.g., Milly et al., 2005). Precipitation efficiency is the fraction of the average horizontal water
vapor flux over an area that falls as rain. Summer rainfall, whether
forced by synoptic-scale disturbances or by meso-scale mechanisms, is overwhelmingly subject to moisture transportation and
deep convection. The NCEP/NCAR reanalysis dataset, a joint product from the National Centers for Environmental Prediction and
the National Center for Atmospheric Research, is continually updated at gridded scale to reproduce the state of the Earth’s atmosphere by incorporating observations and global climate model
output since 1948. Nowadays, it is widely used into the investigation including estimation of atmospheric moisture budget, recognition of moisture transport, and associated impacts on
hydrological processes (e.g. Zhang et al., 2008, 2008c). In order to
better understand the spatio-temporal variations of rainfall extremes, potential influences of meteorological forces (e.g. moisture
transport regimes) should be studied. With this regard, a further
analysis based on the NCAR/NCEP reanalysis data in the same period would be very beneficial.
To our best knowledge, the regional frequency analysis of precipitation extremes with the state-of-art L-moments techniques
has not been conducted in the whole Pear River Basin, south China,
which is a highly complicated river system that encompasses a
large area with various random and systematic variations (PRWRC,
1991, 2006). Furthermore, past studies addressing the inter-annual
pattern or seasonality of extreme precipitation for this region are
Table 3
Serial independence test for precipitation extremes in the Pearl River Basin.
No.
Site name
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Xianning
Zhanyi
Luxi
Anshun
Xingyi
Wangmo
Luodian
Dushan
Rongjiang
Rongan
Guilin
Nanxiong
Guangnan
Fengshan
Hechi
Du’an
Liuzhou
Mengshan
Hexian
Shaoguan
Fogang
Lianping
Xunwu
Napo
Baise
Jingxi
Laibin
Guiping
Wuzhou
Guangning
Gaoyao
Guangzhou
Heyuan
Zengcheng
Huiyang
Longzhou
Nanning
Luoding
Taishan
Shenzhen
AM1R
AM3R
AM5R
pffiffiffi
Di 1:96= n
AM7R
r1
r5
r10
r1
r5
r10
r1
r5
r10
r1
r5
r10
0.053
0.035
0.127
0.041
0.292
0.266
0.051
0.030
0.018
0.193
0.099
0.044
0.221
0.132
0.056
0.217
0.020
0.178
0.091
0.201
0.078
0.069
0.021
0.112
0.039
0.179
0.219
0.119
0.048
0.010
0.023
0.175
0.141
0.055
0.018
0.130
0.111
0.024
0.095
0.026
0.056
0.055
0.004
0.175
0.021
0.059
0.018
0.146
0.095
0.211
0.175
0.321
0.138
0.151
0.140
0.054
0.063
0.185
0.176
0.050
0.155
0.030
0.047
0.183
0.140
0.080
0.169
0.005
0.080
0.194
0.195
0.088
0.026
0.133
0.164
0.116
0.101
0.076
0.002
0.152
0.018
0.011
0.136
0.122
0.403
0.008
0.018
0.304
0.118
0.233
0.211
0.064
0.032
0.221
0.224
0.110
0.034
0.165
0.036
0.055
0.107
0.050
0.055
0.272
0.168
0.008
0.127
0.121
0.138
0.006
0.090
0.075
0.142
0.108
0.082
0.281
0.145
0.066
0.076
0.137
0.191
0.042
0.074
0.174
0.241
0.187
0.067
0.045
0.056
0.204
0.165
0.081
0.006
0.059
0.096
0.029
0.014
0.034
0.263
0.210
0.145
0.264
0.220
0.006
0.063
0.258
0.216
0.174
0.015
0.055
0.125
0.136
0.098
0.068
0.116
0.035
0.030
0.072
0.077
0.078
0.072
0.081
0.016
0.160
0.059
0.108
0.112
0.026
0.009
0.116
0.241
0.042
0.080
0.200
0.051
0.039
0.164
0.116
0.060
0.146
0.221
0.028
0.075
0.231
0.125
0.155
0.156
0.004
0.182
0.159
0.038
0.080
0.096
0.072
0.226
0.037
0.040
0.173
0.113
0.111
0.005
0.029
0.152
0.104
0.389
0.148
0.190
0.144
0.046
0.361
0.204
0.057
0.067
0.005
0.193
0.029
0.132
0.041
0.095
0.122
0.137
0.052
0.109
0.040
0.098
0.132
0.149
0.239
0.165
0.127
0.142
0.137
0.112
0.134
0.020
0.237
0.128
0.155
0.316
0.091
0.240
0.015
0.105
0.208
0.207
0.105
0.051
0.187
0.166
0.191
0.222
0.009
0.078
0.047
0.106
0.092
0.115
0.134
0.242
0.135
0.009
0.153
0.180
0.017
0.078
0.236
0.195
0.227
0.0003
0.142
0.184
0.110
0.093
0.145
0.026
0.119
0.093
0.162
0.076
0.082
0.140
0.067
0.025
0.015
0.034
0.289
0.107
0.167
0.180
0.091
0.261
0.034
0.133
0.105
0.122
0.063
0.157
0.086
0.089
0.176
0.222
0.077
0.067
0.055
0.146
0.130
0.091
0.014
0.136
0.100
0.103
0.056
0.095
0.003
0.078
0.029
0.0004
0.142
0.114
0.073
0.009
0.029
0.195
0.191
0.333
0.144
0.181
0.127
0.007
0.246
0.170
0.110
0.001
0.088
0.224
0.014
0.238
0.047
0.013
0.063
0.180
0.016
0.170
0.051
0.048
0.094
0.122
0.061
0.129
0.010
0.095
0.099
0.138
0.214
0.139
0.137
0.041
0.100
0.239
0.089
0.158
0.032
0.025
0.181
0.222
0.034
0.004
0.257
0.155
0.155
0.130
0.084
0.010
0.022
0.153
0.013
0.091
0.157
0.159
0.233
0.056
0.183
0.164
0.043
0.067
0.180
0.229
0.223
0.018
0.051
0.159
0.136
0.203
0.179
0.052
0.113
0.059
0.239
0.051
0.063
0.109
0.125
0.078
0.010
0.098
0.117
0.0002
0.168
0.131
0.126
0.189
0.021
0.146
0.048
0.111
0.125
0.092
0.080
0.050
0.165
0.119
0.013
0.036
0.042
0.003
0.140
0.031
0.004
0.057
0.186
0.136
0.003
0.095
0.092
0.104
0.028
0.023
0.222
0.080
0.170
0.096
0.147
0.150
0.142
0.186
0.141
0.070
0.040
0.089
0.121
0.140
0.143
0.042
0.043
0.241
0.144
0.297
0.039
0.052
0.059
0.116
0.166
0.237
0.007
0.099
0.148
0.043
0.045
0.168
0.041
0.156
0.130
0.224
0.219
0.200
0.051
0.055
0.013
0.208
0.066
0.264
0.264
0.283
0.264
0.264
0.286
0.264
0.264
0.269
0.280
0.264
0.274
0.272
0.283
0.274
0.269
0.264
0.272
0.280
0.264
0.280
0.267
0.277
0.283
0.264
0.280
0.277
0.269
0.264
0.280
0.269
0.264
0.267
0.280
0.267
0.269
0.264
0.280
0.269
0.267
390
T. Yang et al. / Journal of Hydrology 380 (2010) 386–405
limited (Chen et al., 2006; Zhang et al., 2009). From the meteorological point of view, it is essential to identify the spatio-temporal
patterns of extreme precipitation to reveal the underlying linkages
between precipitation and floods in a broad geographical perspective. However, no study with reference to comprehensive regional
precipitation-frequency and spatio-temporal patterns analysis on
the rainfall extremes has been conducted across the entire Pearl
River Basin. Therefore, extensive efforts should be enforced to carry
out the regional frequency analysis of extreme precipitation in the
basin, which is the fastest growing economic region in south China.
The objectives of this article are to: (1) examine the stationarity
and serial correlation of annual maximum observations for multi-day precipitation, namely (i.e. 1-, 3-, 5-, 7- consecutive days)
and identify the hydrological homogeneous sub-regions; (2) identify and delineate the hydrological homogeneous regions for above
annual precipitation extremes in the Pearl River basin by clusteranalysis; (3) determine the best probability distribution for rainfall
extremes, conduct regional frequency analysis with uncertainty
assessment including the corresponding error bounds and root
mean squared error (RMSE) using the L-moments; (4) characterize
the spatio-temporal patterns of extreme precipitation events in order to reveal the underlying impacts of climate variations dominated in the PRB. This investigation is expected to contribute to
exploring the unique and complex features of extreme rainfall in
PRB, which is beneficial for policymakers and stakeholders in water
resource management formulating regional strategies against the
menaces of frequently emerging floods.
Study region
The Pearl River (102°140 E–116°530 E; 20°310 N–26°490 N) shown
in Fig. 1, is the second largest river (in terms of streamflow magnitude) in China with drainage area of 4.42 105 km2 (PRWRC, 1991,
2006; Zhang et al., 2008a,b). The Pearl River basin has three major
tributaries: West River, North River and East River. Of these, the
largest is the West River, involving Nanpan River, Hongshui River,
Qian River and West River. Its main tributaries are: Beipan River,
Liu River, Yu River and Gui River (Fig. 1). It is about 2075 km long
with a drainage area of 353,120 km2, accounting for 77.8% of the
total drainage area of the Pearl River Basin. The North River is
the second largest tributary, having length of 468 km and drainage
area of 46,710 km2. The East River is about 520 km long with a
drainage area of 27,000 km2, accounting for 6.6% of the total area
of the Pearl River (PRWRC, 1991, 2006; Chen et al., 2008). Pearl River Basin is located in the tropical and sub-tropical climate zones.
The annual mean temperature ranges from 14 to 22 °C. The multi-annual average humidity is between 71% and 80% (PRWRC,
1991). Precipitation during April–September accounts for 72–88%
of the annual total. The Pearl River Basin, especially the Pearl River
Delta region, is economically developed and is of great importance
in the socio-economic development of China.
Data availability
Daily precipitation observations (1960–2005) were collected
from 42 national standard rain gauges located in the Pearl River
Basin (Fig. 1 and Table 1). These observations were obtained from
the National Climate Center, which is officially in charge of monitoring, collecting, compiling and releasing high-quality hydrological data in China. Hence the quality of hydrological data can be
guaranteed in this study. The following variables are derived for
analysis:
Annual maximum 1-day rainfall (AM1R, mm).
Annual maximum 3-day rainfall (AM3R, mm).
Table 4
Transformation of site characteristics.
Site characteristics, X
Latitude (deg)
Longitude (deg)
Elevation (m)
Mean annual precipitation (mm)
Cluster analysis, Y
Y = X/90
Y = X/150
Y = X/3000
Y = X/2000
Table 5
Result of hydrological homogenous regions of 40 rainfall gauges in the Pearl River
Basin (PRB) using cluster-analysis approach.
No.
Site name
Annual
precipitation(mm)
Altitude
(m)
1st result of
homogeneity
testa
2nd result of
homogeneity
testb
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Xianning
Zhanyi
Luxi
Anshun
Xingyi
Wangmo
Luodian
Dushan
Rongjiang
Rongan
Guilin
Nanxiong
Guangnan
Fengshan
Hechi
Du’an
Liuzhou
Mengshan
Hexian
Shaoguan
Fogang
Lianping
Xunwu
Napo
Baise
Jingxi
Laibin
Guiping
Wuzhou
Guangning
Gaoyao
Guangzhou
Heyuan
Zengcheng
Huiyang
Longzhou
Nanning
Luoding
Taishan
Shenzhen
915.6
992.4
938.4
1345.2
1321.3
1235.3
1148.5
1319.1
1203.4
1922.3
1906
1524.7
1001.8
1535.1
1497.1
1723.8
1465
1743
1555.7
1565.5
2173.7
1768.2
1617.4
1403.9
1093.5
1639.5
1367.2
1727.5
1478.9
1705.6
1644.2
1732.4
1939.3
1882.3
1720.6
1329.4
1306
1358.9
1947.3
1943.7
2237.5
1898.7
1704.3
1392.9
1378.5
566.8
440.3
1013.3
285.7
121.3
164.4
133.8
1249.6
484.6
211.0
170.8
96.8
145.7
108.8
69.3
67.8
214.5
303.9
793.6
173.5
739.4
84.9
42.5
114.8
56.8
71.0
41.0
40.6
38.9
22.4
128.8
73.1
53.3
32.7
18.2
I
I
I
III
III
III
III
III
III
IV
IV
V
II
V
V
VI
V
VI
V
V
IV
VI
V
II
II
VI
VII
VI
V
VI
VI
VI
IV
IV
VI
VII
VII
VII
IV
IV
I
I
I
II
II
II
II
II
II
VI
VI
III
II
III
III
IV
III
IV
III
III
VI
IV
III
II
II
IV
V
IV
III
IV
IV
IV
VI
VI
IV
V
V
V
VI
VI
a
The 1st result of homogeneity test is the initial detection result of homogenous
regions for annual precipitation totals in the Pearl River Basin (PSB), South China
using cluster-analysis approach, the geographical location and containing sites of
each homogenous region can be referred to Fig. 2.
b
The 2rd result of homogeneity test is adjusted manually, taking into account the
topography and spatial patterns of the annual precipitation in the areas covered by
the clusters, suggested several natural and physically reasonable modifications to
clusters, which lead to more nearly homogeneous clusters; As a result, the number
(6) of region refinement is less than that (7) of the initial detection result by clusteranalysis approach.
Annual maximum 5-day rainfall (AM5R, mm).
Annual maximum 7-day rainfall (AM7R, mm).
Those variables are widely used in rainfall-extremes analysis
and recognition the associated spatio-temporal patterns across
the world nowadays (e.g. Fowler and Kilsby, 2003).
Besides, the NCAR/NCEP reanalysis data from 1960 to 2005
(Trenberth and Guillemot, 1998) are used to explore the whole
391
T. Yang et al. / Journal of Hydrology 380 (2010) 386–405
104 0 E
1020 E
270N
108 0 E
110 0 E
112 0 E
116 0 E0
27 N
0
114 E
I
0
26 N
III
I
III
III
III
III
0
25 N
I
V
240N
II
V
VI
0
100 E
0
VI
VI
VII
0
VI
23 N
IV
VII
50 N
240N
IV
IV
0
120 E
0
22 N
IV
VI
V
VII
0
VI
V
VI
VII
VI
80 E
V
V
VII
230N
250N
V
V
VI
II
IV
V
III
Latitude ( oN)
0
26 N
IV
220N
Beijing
N
0
21 N
0
30 N
Pearl River B asin
W
N
Catchments boundary
Meteorological gauges
E
200N
1020 E
104 0 E
108 0 E
110 0 E
200
Homogeneous regions
I
S
100
400 Km
112 0 E
0
21 N
Streams
0
20 N
116 0 E
0
114 E
Longtitude (oE)
Fig. 2. Initial detection result of homogenous regions for annual precipitation totals in the Pearl River Basin (PRB), South China using cluster-analysis approach.
layer of the atmospheric moisture and related transport features.
In the actual atmosphere, the moisture content is very low above
300 hPa, so that a top of the atmosphere pressure of 300 hPa will
be used in the study (Zhang et al., 2008c).
Methodology
The methods are presented in this section, including the stationarity test, serial correlation check, L-moments approach, spatial analysis, and atmospheric moisture transport calculation.
Stationarity test and Serial correlation check
Stationarity has a strict statistical definition and a stationary
series has constant mean, variance and autocorrelation, etc., but
for our purpose here we mean a flat looking series. The trend test
is one of the most popular methods in examining the stationarity
in 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 (Mitchell et al., 1966), as
it has the advantage of not requiring any distribution assumptions
in the data while having the same power as its parametric competitors. The effect of the serial correlation on the Mann–Kendall (MK)
test was eliminated using a pre-whitening technique (e.g. Yang
et al., 2008a, 2009) in this study.
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
pffiffiffi
not larger than the typical critical value, i.e. 1:96= n corresponding to the 5% significance level (Douglas et al., 2000; Xiong and
Guo, 2004), 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.
Table 6
L-moment ratios of AM1R for 40 precipitation gauges in the Pearl River Basin (PRB).
No.
Site name
ni
l1
i
tðiÞ ¼ u
t3
t4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Xianning
Zhanyi
Luxi
Anshun
Xingyi
Wangmo
Luodian
Dushan
Rongjiang
Rongan
Guilin
Nanxiong
Guangnan
Fengshan
Hechi
Du’an
Liuzhou
Mengshan
Hexian
Shaoguan
Fogang
Lianping
Xunwu
Napo
Baise
Jingxi
Laibin
Guiping
Wuzhou
Guangning
Gaoyao
Guangzhou
Heyuan
Zengcheng
Huiyang
Longzhou
Nanning
Luoding
Taishan
Shenzhen
55
55
48
55
55
47
55
55
53
49
55
50
51
48
51
53
55
52
49
55
49
54
50
48
55
49
49
53
55
49
53
55
54
48
54
53
55
49
53
54
101.7
90.8
105.9
94.5
88.7
80.3
161.1
133.1
92.1
67.2
109.8
104.0
136.5
111.1
117.3
102.1
93.7
96.9
145.0
104.8
104.7
90.8
95.9
105.0
103.6
121.0
106.2
102.6
109.3
124.7
136.5
141.1
99.9
102.0
102.13
130.34
133.40
120.82
146.28
151.19
0.1649
0.2405
0.2102
0.2904
0.2042
0.1843
0.2004
0.1551
0.1673
0.1355
0.2360
0.3499
0.2213
0.0576
0.2020
0.2718
0.1329
0.2309
0.1958
0.2429
0.2378
0.1897
0.1766
0.1272
0.2921
0.2792
0.1983
0.2999
0.2270
0.2572
0.2966
0.2480
0.1754
0.2814
0.0272
0.0680
0.1149
0.1499
0.0086
0.0045
0.1220
0.1921
0.2649
0.3090
0.1551
0.1708
0.1231
0.1054
0.1252
0.1464
0.2097
0.1995
0.1709
0.0704
0.1435
0.2311
0.1555
0.1907
0.1969
0.1454
0.1492
0.1805
0.1625
0.1871
0.2246
0.2259
0.2507
0.2364
0.1622
0.1966
0.2595
0.2169
0.1899
0.2404
0.1803
0.1280
0.2039
0.1587
0.1340
0.1285
0.0283
0.0946
0.0784
0.2079
0.0150
0.1470
0.0843
0.0493
0.0104
0.0479
0.1247
0.0787
0.0729
0.0458
0.0500
0.0944
0.0602
0.0538
0.0535
0.0324
0.0479
0.0581
0.0673
0.0625
0.0885
0.1249
0.1669
0.1083
0.0519
0.0746
0.1358
0.1257
0.0985
0.0898
0.0330
0.0560
0.0230
0.0240
0.0220
0.0140
ðiÞ
ðiÞ
392
Table 7
Results of discordance, heterogeneity and goodness-of-fit tests for 40 rainfall gauges in Pearl River Basin (PRB).
HOM
region
Containing sites (Di)
Discordancy
measure
Dcritical
H1
H2
H3
1.AM1R
I (3 sites)
II (9 sites)
Xianning (1.01), Zhanyi (0.97), Luxi (0.98)
Anshun (2.15), Xingyi (0.77), Wangmo (1.52), Luodian (1.67), Dushan (0.81), Rongjiang (0.64),
Guangnan (1.15), Napo (0.28), Baise (0.21)
Nanxiong (1.96), Fengshan (0.13), Hechi (1.38), Liuzhou (1.13), Hexian (0.39), Shaoguan (0.18), Xunwu
(0.40), Wuzhou (1.43)
Du’an (0.43), Mengshan (0.70), Lianping (1.10), Jingxi (1.59), Guiping (0.57), Guangning (1.90), Gaoyao
(0.31), Guangzhou (0.43), Huiyang (0.92)
Laibin (1.00), Longzhou (0.91), Nanning (0.89), Luoding (1.00)
Rong’an (0.84), Guilin (1.43), Fogang (0.32), Heyuan (1.40), Taishan (0.98), Shenzhen (1.03), Zengcheng
(0.79)
1.333
2.329
0.24
0.19
0.24
0.19
2.140
0.28
2.329
III (8 sites)
IV (9 sites)
V (4 sites)
VI (7 sites)
2.AM3R
I (3 sites)
II (9 sites)
III (8 sites)
IV (9 sites)
V (4 sites)
VI (7 sites)
3.AM5R
I (3 sites)
II (9 sites)
III (8 sites)
IV (9 sites)
V (4 sites)
VI (7 sites)
4.AM7R
I (3 sites)
II (9 sites)
III (8 sites)
IV (9 sites)
V (4 sites)
VI (7 sites)
*
|Z| 6 1.64
Best fit
0.53
1.31
0.10
0.23
GNO
GLO
0.30
0.05
0.51
GEV
0.08
0.08
1.83
0.84
GLO
1.333
1.648
0.13
0.09
0.13
0.09
0.91
0.22
0.23
0.32
GLO
GEV
Xianning (1.17), Zhanyi (0.93), Luxi (0.89)
Anshun (1.86), Xingyi (0.65), Wangmo (0.68), Luodian (0.73), Dushan (0.17), Rongjiang (0.36),
Guangnan (1.87), Napo (1.45), Baise (0.98)
Nanxiong (1.67), Fengshan (1.10), Hechi (1.45), Liuzhou (1.84), Hexian (0.88), Shaoguan (0.65), Xunwu
(0.09), Wuzhou (0.33)
Du’an (0.92), Mengshan (0.52), Lianping (0.53), Jingxi (0.76), Guiping (0.83), Guangning (0.81), Gaoyao
(0.48), Guangzhou (0.45), Huiyang (1.08)
Laibin (1.00), Longzhou (0.99), Nanning (0.81), Luoding (0.93)
Rong’an (1.30), Guilin (1.42), Fogang (0.66), Heyuan (1.17), Taishan (0.29), Shenzhen (1.16), Zengcheng
(0.81)
1.333
2.329
0.20
0.16
0.20
0.17
0.27
0.55
0.12
0.55
GNO
GLO
2.140
0.28
0.29
0.68
0.39
GLO
2.329
0.17
0.17
0.82
0.65
GEV
1.333
1.648
0.23
0.11
0.23
0.11
1.04
1.90*
0.15
0.30
GLO
GNO
Xianning (1.01), Zhanyi (0.98), Luxi (1.00)
Anshun (1.19), Xingyi (1.41), Wangmo (1.02), Luodian (0.82), Dushan (0.19), Rongjiang (0.65),
Guangnan (1.77), Napo (0.89), Baise (1.07)
Nanxiong (1.37), Fengshan (0.48), Hechi (1.83), Liuzhou (2.00), Hexian (1.08), Shaoguan (0.43), Xunwu
(0.18), Wuzhou (0.64)
Du’an (0.93), Mengshan (0.51), Lianping (1.27), Jingxi (0.80), Guiping (0.37), Guangning (1.43), Gaoyao
(1.89), Guangzhou (1.26), Huiyang (0.55)
Laibin (1.02), Longzhou (0.93), Nanning (0.99), Luoding (1.00)
Rong’an (0.28), Guilin (1.46), Fogang (1.30), Heyuan (1.07), Taishan (0.35), Shenzhen (1.54), Zengcheng
(1.01)
1.333
2.329
0.13
0.09
0.13
0.10
0.03
0.30
0.11
0.28
GLO
GLO
2.140
0.09
0.09
0.58
0.54
GEV
2.329
0.07
0.07
1.38
0.79
GEV
1.333
1.648
0.16
0.12
0.16
0.12
1.10
0.89
0.70
0.30
GLO
PE3
Xianning (0.97), Zhanyi (0.91), Luxi (0.88)
Anshun (1.46), Xingyi (0.48), Wangmo (1.44), Luodian (0.47), Dushan (0.94), Rongjiang (0.98),
Guangnan (1.69), Napo (0.42), Baise (1.14)
Nanxiong (1.43), Fengshan (0.83), Hechi 1.81), Liuzhou (1.30), Hexian (0.26), Shaoguan (0.71), Xunwu
(0.10), Wuzhou (1.54)
Du’an (1.76), Mengshan (0.40), Lianping (1.03), Jingxi (0.40), Guiping (0.23), Guangning (0.83), Gaoyao
(1.17), Guangzhou (1.89), Huiyang (0.24)
Laibin (1.10), Longzhou (0.88), Nanning (1.01), Luoding (1.00)
Rong’an (0.66), Guilin (0.84), Fogang (1.45), Heyuan (1.11), Taishan (0.90), Shenzhen (1.05), Zengcheng
(0.75)
1.333
2.329
0.15
0.08
0.15
0.09
0.44
1.15
1.31
0.26
GLO
GLO
2.140
0.08
0.08
1.44
0.84
GLO
2.329
0.04
0.04
1.62
0.29
GLO
1.333
1.648
0.10
0.11
0.10
0.11
1.25
1.35*
0.40
0.11
GLO
GNO
Denotes failure in the heterogeneity test.
Heterogeneity measure
T. Yang et al. / Journal of Hydrology 380 (2010) 386–405
Item
393
T. Yang et al. / Journal of Hydrology 380 (2010) 386–405
L-moments theory
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. Details about the L-moments
approach can be found in Hosking and Wallis (1997). In brief, it is a
modification of the probability weighted moments (PWM) method
with the advantage of offering a description of the shape of a probability distribution by L-skewness and L-kurtosis (e.g. Wallis et al.,
2007). The L-moment is a linear combination of the probability
weighted moments. The sample L-moment ratios, defined as
t ¼ l2 =l1
and
t r ¼ lr =l2 ;
r ¼ 3; 4; . . .
Table 8
Accuracy measures for estimated growth curve of the PRB precipitation extreme
(AM1R).
No.
Region
F
RMSE
1
I (3 sites)
.010
.100
.500
.900
.990
.999
.168
.061
.043
.048
.121
.241
2
II (9 sites)
.010
.100
.500
.900
.990
.999
.419
.071
.022
.046
.132
.243
3
III (8 sites)
.010
.100
.500
.900
.990
.999
.734
.093
.041
.059
.189
.370
4
IV (9 sites)
.010
.100
.500
.900
.990
.999
.322
.065
.029
.054
.155
.286
5
V (4 sites)
.010
.100
.500
.900
.990
.999
.226
.073
.048
.059
.158
.310
6
VI (7 sites)
.010
.100
.500
.900
.990
.999
.474
.110
.031
.038
.110
.223
ð1Þ
with lr being the unbiased rth L-moments, are analogue to the traditional ratios, that is, t is the coefficient of variation (L-CV); t3 the
L-skewness and t4 the L-kurtosis. The L-moment ratios will be used
for homogeneity analysis in the regional frequency analysis.
Experience shows that, compared with conventional moments,
L-moments have less bias in estimation and their asymptotics are
closer to the normal distribution in finite samples. The L-moments
approach covers the characterization of probability distributions,
the summary of observed data samples, the fitting of probability
distributions to data, and the testing of the distributional form.
The ‘‘L” in L-moments emphasizes the linearity. The mean, variance, and skewness are defined in terms of moments as, respectively, the L-mean, L-scale and L-skewness (e.g. Wallis et al., 2007).
The regional frequency analysis based on L-moments method
Suppose that there are N sites in the region with sample size
n1, n2, . . . , nN, respectively. The sample L-moment ratios (L-CV,
ðiÞ
L-Skewness and L-kurtosis) at-site i are denoted by t(i), t3 and
ðiÞ
t 4 . The regional weighted average L-moment ratios are given by:
t¼
N
X
i¼1
,
ni t
ðiÞ
N
X
i¼1
ni
and
tr ¼
N
X
i¼1
,
ni t ðiÞ
r
N
X
ni
r ¼ 3; 4; . . .
i¼1
ð2Þ
The regional frequency analysis using L-moments consists of
five steps (Hosking and Wallis, 1993, 1997): (i) identification of
homogenous regions by cluster analysis; (ii) screening of the data
using the discordancy measure Di; (iii) homogeneity testing using
the heterogeneity measure H; (iv) distribution selection using the
goodness-of-fit measure Z; and (v) regional estimation of precipitation quantiles using the L-moment approach. These five steps were
followed to conduct a regional frequency analysis for the Pearl River basin and the statistical methods employed are discussed below.
Identification of homogenous regions by cluster analysis
Guttman et al. (1993) analyzed annual precipitation totals for
1119 sites in the USA and formed 104 regions by cluster analysis,
101 of which were accepted as homogenous. Other examples of
the use of cluster analysis in forming hydrological or climatological
regions, albeit not for use in frequency analysis, have given by
Mosley (1981), Richman and Lamb (1985) and Fovell and Fovell
(1993). Farhan (1984) used cluster analysis to classify stream gauging sites in Jordan into regions on the basis of four principal components formed from a matrix of characteristics. The cluster
analysis by site characteristics is regarded as the most practical
method of forming regions from large data sets (Hosking and Wallis, 1997). It has several major variants and involves subjective
decisions at several stages. The site characteristics used are judged
to be of importance in defining site’s precipitation climate, including indicators of precipitation amounts and the sites’ geographic
location. In this study, four variables are chosen to describe the
precipitation climate: latitude, longitude, elevation and the mean
annual precipitation. The observed scales of the variables are very
different, and the standard methods of cluster analysis are sensitive to such scale difference. Therefore these variables were rescaled so that their ranges are comparable. The location,
precipitation amount are rescaled to lie between 0 and 1.
Cluster analysis was performed using SAS average linkage and
Wards’ minimum variance hierarchical clustering software. In the
average-linkage method the distance between two clusters is the
average Euclidean distance between two observations, one in each
cluster. Clusters with small variance tend to be joined, and the procedure is biased in favor of producing clusters with equal dispersion in the space of clustering variables. In Ward’s method, the
distance between two clusters is sum of squares between the
two clusters summed over all the variables. This method tends to
join clusters that contain a small number of sites and is strongly
biased in favor of producing clusters containing approximately
equal numbers of sites. Both clustering methods are based on
Euclidean distances and are sensitive to redundant information
that may be contained in the variables as well as to the sale of variables being clustered (Fovell and Fovell, 1993). Theoretical details
on cluster analysis can be referred to in the literatures mentioned
above.
The output from the cluster analysis is not the final results. Subjective adjustments can often be found to improve the physical
coherence of regions and to reduce the heterogeneity of regions
as measured by the heterogeneity measure. Several adjustments
of regions may be recommended (Hosking and Wallis, 1997):
T. Yang et al. / Journal of Hydrology 380 (2010) 386–405
1020E
0
27 N
1040E
1080E
1100E
1120E
1160E
270N
1140E
Elevation
0-310
310-621
621-931
931-1242
1242-1552
1552-1863
1863-2173
2173-2484
2484-2795
260N
250N
0
26 N
0
25 N
0
24 N
0
24 N
230N
230N
0
80 E
0
100 E
Latitu de (oN)
394
0
120 E
0
220N
50 N
0
22 N
Beijing
N
0
21 N
0
30 N
Pearl River Basin
N
W
Catchments boundary
Meteorological gauges
E
Homogeneous regions
S
100
200
400 Km
Streams
200N
0
116 E
0
20 N 0
102 E
0
104 E
0
108 E
0
0
110 E
210N
112 E
1140E
Longtitude(oE)
Fig. 3. Homogenous regions refinement for annual precipitation totals in the Pearl River Basin (PRB), South China, in which region III and IV is marked as a joint region:
‘‘III + IV” because their containing sites are totally mixed together geographically and can not bordered as separated homogenous regions.
move a site or a few sites from one region to another;
delete a site or a few sites from the dataset;
subdivide the region;
break up the region by reassigning its sites to other regions;
merge the region with another or others;
merge two or more regions and redefine groups; and
obtain more data and redefine groups.
9
>
>
ni >
>
>
>
i¼1
i¼1
>
>
=
N
N
P
P
ðiÞ
R
t3 ¼ ni t 3
ni
>
i¼1
i¼1
>
>
N >
>
N
>
P
P
>
ðiÞ
R
t4 ¼ ni t 4
ni >
;
tR ¼
N
P
ni t ðiÞ
i¼1
N
P
ð5Þ
i¼1
.P
N
Screening the data using the discordancy measure
h
iT
ðiÞ ðiÞ
be the vector containing the t, t3 and t4 valLet ui ¼ tðiÞ ; t 3 ; t 4
ues for site i where the superscript T denotes transposition of a vector or matrix. Let
u¼
N
X
,
ui
N
ð3Þ
i¼1
be the (unweighted) regional average. The discordancy measure for
site i is then defined as:
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.
R
The regional average mean l1 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 (V1); (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-skewnessand L-kurtosis (V3).
N
N 12
2 P
P ðiÞ
V1 ¼
ni t tR
ni
i¼1
Di ¼
1
Nðui uÞT A1 ðui uÞ
3
ð4Þ
PN
where A ¼ i¼1 ðui uÞðui uÞT .
Obviously, a large value of Di indicates the discordancy of
site i with other sites. Hosking and Wallis (1997) found that
there was no single fixed number which can 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.
Homogeneity testing using the heterogeneity measure
V2 ¼
i¼1
ni t ðiÞ t R
2
ðiÞ
þ t 3 t R3
2
12 N
P
ni >
>
>
>
>
>
n
o12 P
N
N
>
P
>
ðiÞ
ðiÞ
R 2
R 2
V 3 ¼ ni ðt 3 t 3 Þ þ ðt4 t 4 Þ
ni >
;
i¼1
i¼1
ð6Þ
i¼1
i¼1
Let lv, lv 2 and lv 3 denote the mean and rv, rv2 and rv3 the
standard deviation of the Nsim values of V1, V2 and V3, respectively.
These statistics are used to estimate the following three heterogeneity measures
H1 ¼
H2 ¼
The regional average L-CV, L-skewness and L-kurtosis, represented by tR, tR3 and tR4 , respectively, are computed as:
N
P
9
>
>
>
>
>
>
>
>
>
=
H3 ¼
9
ðV 1 lv Þ
>
>
rv
>
=
ðV 2 lv 2 Þ
rv 2 >
>
ðV 3 lv 3 Þ >
;
rv 3
ð7Þ
395
T. Yang et al. / Journal of Hydrology 380 (2010) 386–405
0.4
0.4
(A) Region I
GLO
0.3
GNO
0.2
GEV
GNO
L-KURTOSIS
L-KURTOSIS
(B) Region II
GLO
0.3
PE3
0.1
GPT
0.0
0.2
GEV
GPT
0.0
-0.1
-0.1
0.0
0.1
0.2
0.3
0.4
-0.1
-0.1
0.5
0.0
0.1
L-SKEWESS
0.3
0.4
0.5
0.4
(C) Region III
(D) Region IV
GLO
GNO
0.2
GEV
PE3
0.1
GPT
0.0
-0.1
-0.1
0.0
0.1
0.2
0.3
GLO
0.3
0.4
L-KURTOSIS
0.3
L-KURTOSIS
0.2
L-SKEWESS
0.4
GNO
0.2
GEV
GPT
0.0
-0.1
-0.1
0.5
PE3
0.1
0.0
0.1
L-SKEWESS
0.2
0.3
0.4
0.5
L-SKEWESS
0.4
0.4
(E) Region V
(F) Region VI
GLO
GNO
0.2
GEV
PE3
0.1
GPT
0.0
-0.1
-0.1
GLO
0.3
L-KURTOSIS
0.3
L-KURTOSIS
PE3
0.1
GNO
0.2
GEV
PE3
0.1
GPT
0.0
0.0
0.1
0.2
0.3
0.4
0.5
-0.1
-0.1
0.0
L-SKEWESS
0.1
0.2
0.3
0.4
0.5
L-SKEWESS
Fig. 4. L-moment ratio plot for AM3R at six HOM regions.
In order to obtain reliable values of lv and rv, the number Nsim
of simulations needs to be large and Nsim = 1000 was used in this
study. The region is regarded to be ‘‘acceptably homogeneous” if
H1 < 1 and H2 < 1, ‘‘possibly heterogeneous” if 1 6 H1 < 2 or
1 6 H2 < 2, and ‘‘definitely heterogeneous” if H1 P 2 and H2 P 2.
Furthermore, Hosking and Wallis (1993) 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 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 recommended
by Norbiato 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.
The fit is considered to be adequate if |ZDIST| is sufficiently close
to zero, and a reasonable criterion being |ZDIST| 6 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 Lkurtosis combination in the L-moment ratio diagram.
Distribution selection using the goodness-of-fit measure
Assessment of regional frequency analysis
For each candidate distribution, the goodness-of-fit measure:
Z
DIST
¼
sDIST
t 4 þ b4 r4
4
ð8Þ
was used, as suggested by Hosking and Wallis (1993, 1997) using
is the L-kurtosis of the fitted distribution
the L-kurtosis, where sDIST
4
to the data using the candidate distribution, and:
b4 ¼
N sim
X
ðt4 ðmÞ t 4 Þ Nsim
ð9Þ
m¼1
is the bias of t4 estimated using the simulation technique as before
with t 4 ðmÞ being the sample L-kurtosis of the mth simulation, and:
(
r4 ¼ ðNsim 1Þ1
"N
sim X
t 4 ðmÞ t 4
2
#)12
Nsim b24
ð10Þ
m¼1
The relative bias and relative RMSE can be expressed as percentages of the site-i quantile estimator (Hosking and Wallis,
1997) by:
396
T. Yang et al. / Journal of Hydrology 380 (2010) 386–405
3.0
3.0
(B: Region II)
2.5
2.5
2.0
2.0
Gowth curve
Gowth curve
(A: Region I)
1.5
1.0
Return period
0.5
2
5
10
50
100
1.5
1.0
Return period
0.5
500 1000
2
0.0
0
2
4
6
-2
Gumbel reduced variate, -log(-log(-F))
50
500 1000
100
0
2
4
6
Gumbel reduced variate, -log(-log(-F))
3.0
3.0
(C: Region III)
(D: Region IV)
2.5
2.5
2.0
2.0
Gowth curve
Gowth curve
10
0.0
-2
1.5
1.0
Return period
0.5
2
5
10
50
100
1.5
1.0
Return period
0.5
500 1000
2
0.0
5
10
50
500 1000
100
0.0
-2
0
2
4
6
-2
Gumbel reduced variate, -log(-log(-F))
0
2
4
6
Gumbel reduced variate, -log(-log(-F))
3.0
3.0
(E: Region V)
(F: Region VI)
2.5
2.5
2.0
2.0
Gowth curve
Gowth curve
5
1.5
1.0
Return period
0.5
2
5
10
50
100
1.5
1.0
Return period
0.5
2
500 1000
5
10
50
500 1000
100
0.0
0.0
-2
0
2
4
6
Gumbel reduced variate, -log(-log(-F))
-2
0
2
4
6
Gumbel reduced variate, -log(-log(-F))
Fig. 5. Estimated regional growth curves, with their 90% error bounds for six HOM regions (AM1R).
Bi ðFÞ ¼ M 1
Ri ðFÞ ¼ M
1
M ^m
X
Q i ðFÞ Q i ðFÞ
Q i ðFÞ
m¼1
!
M
^ m ðFÞ Q ðFÞ 1=2
X
Q
i
i
Q i ðFÞ
m¼1
ð11Þ
ð12Þ
Then, 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) through:
BR ðFÞ ¼ N1
N
X
Bi ðFÞ
ð13Þ
i¼1
and the regional average absolute relative bias of the estimated
quantile through:
AR ðFÞ ¼ N 1
N
X
Bi ðFÞ
ð14Þ
i¼1
Furthermore, the regional average relative RMSE of the estimated quantile is obtained through:
RR ðFÞ ¼ N 1
N
X
i¼1
Ri ðFÞ
ð15Þ
The relative bias from the regional average measures the tendency of quantile estimates across the whole region, which is
either to be too high or too low. 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, the relative bias from the regional average shows
the tendency that the quantile estimates are to be consistently
high at some sites. 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) are equal (Stedinger
et al., 1993; Hosking and Wallis, 1997).
Spatial Interpolation
To understand the spatial patterns of statistical characteristics
of rainfall-extreme regime across the PRB, the geostatistical or stochastic methods were used because they capitalize on the spatial
correlation between neighboring observations to predict attributed
values at unsampled locations (e.g. Goovaerts, 1999; Hartkamp
et al., 1999). Goovaerts (1999) indicated that the major advantage
of the Kriging method over other simpler interpolation methods is
that sparsely sampled observations of the primary attribute can be
397
T. Yang et al. / Journal of Hydrology 380 (2010) 386–405
102°E
27°N
104°E
108°E
110°E
112°E
114°E
116°E
27°N
(A)L-CV (AM1R)
26°N
26°N
102°E
104°E
108°E
110°E
112°E
114°E
116°E
27°N
27°N
(B)L-CV (AM3R)
26°N
26°N
25°N
25°N
25°N
25°N
24°N
24°N
24°N
24°N
23°N
23°N
23°N
23°N
Legend
Legend
11-15 -2/-1 STD. DEV
15-20 -1/ 0 STD. DEV
20
MEAN
22°N
22°N
20-25 0 / 1 STD. DEV
25-29 1 /2 STD. DEV
21°N
3- 11 -3/-2 STD. DEV
11-20 -2/-1 STD. DEV
20-28 -1/ 0 STD. DEV
28
MEAN
28-37 0 / 1 STD. DEV
22°N
N
W
E
N
20°N
102°E
104°E
108°E
110°E
112°E
114°E
102°E
104°E
108°E
110°E
112°E
114°E
27°N
W
21°N
20°N
116°E
20°N
102°E
104°E
108°E
110°E
112°E
114°E
116°E
27°N
102°E
27°N
104°E
108°E
110°E
112°E
114°E
(C)L-CV (AM5R)
E
N
21°N
S
29-34 2/ 3 STD. DEV
34-39 >3 STD. DEV
22°N
N
21°N
S
37-45 1 /2 STD. DEV
45-53 2/ 3 STD. DEV
53-55 >3 STD. DEV
20°N
116°E
116°E
27°N
(D)L-CV (AM7R)
26°N
26°N
26°N
25°N
25°N
25°N
25°N
24°N
24°N
24°N
24°N
23°N
23°N
26°N
23°N
2- 12
12-22
22-32
32
32-42
42-52
52-62
62-63
22°N
21°N
-3/-2 STD. DEV
-2/-1 STD. DEV
-1/ 0 STD. DEV
MEAN
0 / 1 STD. DEV
1 /2 STD. DEV
2/ 3 STD. DEV
>3 STD. DEV
22°N
104°E
22°N
N
W
E
N
21°N
S
20°N
116°E
20°N
102°E
23°N
Legend
Legend
108°E
110°E
112°E
114°E
21°N
20°N
102°E
2- 13
13-24
24-35
35
35-46
46-57
57-68
68-70
-3/-2 STD. DEV
-2/-1 STD. DEV
-1/ 0 STD. DEV
MEAN
0 / 1 STD. DEV
1 /2 STD. DEV
2/ 3 STD. DEV
>3 STD. DEV
104°E
22°N
N
N
W
E
21°N
S
108°E
110°E
112°E
20°N
116°E
114°E
Fig. 6. Spatial variations of L-CV for four type of annual rainfall extremes, (A) AM1R; (B) AM3R; (C) AM5R; (D) AM7R. Each name of region and associated sites can be referred
to Fig. 3.
102°E
104°E
108°E
110°E
112°E
114°E
116°E
27°N
27°N
(A)L-SKEW (AM1R)
27°N
102°E
104°E
108°E
110°E
112°E
114°E
116°E
27°N
(B)L-SKEW (AM3R)
26°N
26°N
26°N
25°N
25°N
25°N
25°N
24°N
24°N
24°N
24°N
23°N
23°N
26°N
23°N
23°N
Legend
Legend
0.06-0.07
0.07-0.12
0.12-0.18
0.18-0.23
0.23
0.23-0.28
0.28-0.33
0.33-0.38
22°N
21°N
<-3 STD. DEV
-3/-2 STD. DEV
-2/-1 STD. DEV
-1/0 STD. DEV
MEAN
0/ 1 STD. DEV
1/ 2 STD. DEV
2/ 3 STD. DEV
22°N
N
W
E
21°N
S
100
200
27°N
102°E
104°E
104°E
108°E
108°E
110°E
110°E
112°E
112°E
20°N
116°E
114°E
114°E
116°E
27°N
(C)L-SKEW (AM5R)
26°N
21°N
400 Km
20°N
102°E
0.05-0.06
0.06-0.11
0.11-0.16
0.16-0.21
0.21
0.21-0.26
0.26-0.30
0.30-0.35
22°N
N
20°N
<-3 STD. DEV
-3/-2 STD. DEV
-2/-1 STD. DEV
-1/0 STD. DEV
MEAN
0/ 1 STD. DEV
1/ 2 STD. DEV
2/ 3 STD. DEV
22°N
N
N
W
E
21°N
S
100
200
102°E
104°E
108°E
110°E
112°E
114°E
102°E
27°N
104°E
108°E
110°E
112°E
114°E
400 Km
20°N
116°E
116°E
27°N
(D)L-SKEW (AM7R)
26°N
26°N
25°N
25°N
25°N
25°N
24°N
24°N
24°N
24°N
23°N
23°N
23°N
Legend
22°N
21°N
20°N
102°E
0.01-0.07
0.07-0.13
0.13-0.18
0.18
0.18-0.24
0.24-0.29
0.29-0.35
104°E
26°N
23°N
Legend
-3/-2 STD. DEV
-2/-1 STD. DEV
-1/0 STD. DEV
MEAN
0/ 1 STD. DEV
1/ 2 STD. DEV
2/ 3 STD. DEV
108°E
22°N
22°N
N
W
N
E
21°N
S
100
110°E
112°E
114°E
200
21°N
400 Km
20°N
116°E
20°N
102°E
0.01-0.04
0.04-0.08
0.08-0.13
0.13-0.17
0.17
0.17-0.22
0.22-0.26
0.26-0.31
<-3 STD. DEV
-3/-2 STD. DEV
-2/-1 STD. DEV
-1/0 STD. DEV
MEAN
0/ 1 STD. DEV
1/ 2 STD. DEV
2/ 3 STD. DEV
104°E
108°E
22°N
N
W
N
E
21°N
S
100
110°E
112°E
114°E
Fig. 7. Spatial variations of L-SKEW for four type of annual rainfall extremes, (A) AM1R; (B) AM3R; (C) AM5R; (D) AM7R.
200
400 Km
20°N
116°E
398
T. Yang et al. / Journal of Hydrology 380 (2010) 386–405
Table 9
Estimated precipitation extremes (AM1R) corresponding to different non-exceedance probability (recurrence periods) in the PRB using L-moment regional frequency analysis.
No.
Site name
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Non-exceedance probability (Return period)
Xianning
Zhanyi
Luxi
Anshun
Xingyi
Wangmo
Luodian
Dushan
Rongjiang
Rongan
Guilin
Nanxiong
Guangnan
Fengshan
Hechi
Du’an
Liuzhou
Mengshan
Hexian
Shaoguan
Fogang
Lianping
Xunwu
Napo
Baise
Jingxi
Laibin
Guiping
Wuzhou
Guangning
Gaoyao
Guangzhou
Heyuan
Zengcheng
Huiyang
Longzhou
Nanning
Luoding
Taishan
Shenzhen
0.10
1 year
0.50
2 year
0.80
5 year
0.90
10 year
0.95
20 year
0.98
50 year
0.99
100 year
0.999
1000 year
39.5
45.8
43.6
63.5
56.7
66.1
58.9
55.4
50.1
100.6
83.1
57.5
41.9
68.5
64.9
85.2
69.3
73.2
63.7
58.5
60.5
90.5
65.4
65.3
56.7
59.8
65.5
64.6
75.5
66.3
64.0
68.2
77.8
85.2
88.1
62.3
63.6
55.1
93.8
111.8
58.7
68.0
64.7
94.3
84.2
98.2
87.6
82.3
74.4
149.4
123.4
85.4
62.3
101.8
96.4
126.6
103.0
108.8
94.7
86.8
89.9
134.4
97.2
97.1
84.2
88.9
97.3
96.0
112.2
98.5
95.1
101.3
115.6
126.6
130.8
92.6
94.5
81.9
139.4
166.0
78.4
90.8
86.5
126.0
112.5
131.2
117.0
109.9
99.4
199.6
164.9
114.1
83.2
136.0
128.9
169.2
137.6
145.4
126.6
116.1
120.1
179.6
129.8
129.7
112.5
118.8
130.0
128.3
149.9
131.6
127.1
135.4
154.5
169.1
174.8
123.8
126.3
109.4
186.3
221.9
92.4
107.0
101.9
148.5
132.6
154.6
137.9
129.6
117.2
235.3
194.3
134.5
98.1
160.3
151.9
199.4
162.2
171.3
149.1
136.8
141.5
211.7
153.0
152.9
132.6
140.0
153.3
151.2
176.7
155.1
149.8
159.6
182.1
199.3
206.0
145.9
148.9
129.0
219.5
261.5
106.5
123.5
117.6
171.3
153.0
178.3
159.1
149.4
135.1
271.4
224.1
155.1
113.1
184.9
175.2
229.9
187.0
197.6
172.0
157.7
163.2
244.2
176.5
176.3
153.0
161.4
176.8
174.4
203.7
178.9
172.8
184.0
210.0
229.9
237.6
168.2
171.7
148.8
253.2
301.6
126.0
146.0
139.1
202.7
181.0
210.9
188.2
176.8
159.9
321.0
265.1
183.5
133.8
218.7
207.2
272.0
221.2
233.7
203.5
186.6
193.1
288.8
208.8
208.6
181.0
191.0
209.1
206.3
241.0
211.6
204.4
217.7
248.4
271.9
281.1
199.0
203.1
176.0
299.5
356.8
141.5
164.0
156.2
227.6
203.2
236.9
211.3
198.5
179.5
360.5
297.8
206.1
150.2
245.6
232.7
305.4
248.5
262.5
228.5
209.6
216.8
324.3
234.5
234.2
203.2
214.4
234.8
231.7
270.7
237.6
229.5
244.5
279.0
305.4
315.7
223.5
228.1
197.6
336.3
400.7
198.8
230.4
219.4
319.7
285.5
332.7
296.8
278.8
252.2
506.4
418.2
289.5
211.0
345.0
326.9
429.0
349.0
368.7
321.0
294.3
304.6
455.6
329.3
329.0
285.4
301.2
329.8
325.4
380.2
333.7
322.4
343.4
391.8
428.9
443.4
313.9
320.4
277.6
472.4
562.8
complemented by secondary attributes that are more densely sampled. Therefore, the Kriging interpolation method was used to
demonstrate the spatial patterns of the rainfall-extreme changes
for the study region.
respectively; and /1, /2, k1, k2 are the latitude and longitude according to the regional boundaries (Zhang et al., 2008c).
Atmospheric moisture transport calculation
Stationarity test and serial correlation check
The zonal moisture transport flux (QU), the meridional moisture
transport flux (QV), and the whole layer moisture budget (QT) at regional boundaries are calculated based on the following equations:
The Mann–Kendall test was conducted on the observations of
precipitation extremes (AM1R, AM3R, AM5R, and AM7R) over the
period (1960–2005) in this basin. The results are given in Table 2.
It can be seen that for precipitation extremes, 2 out of 42 sites
(Yuxi and Mengzi) show increasing trends with 5% confidence level
and the remaining 40 sites have no significant trends (at the 5%
confidence level). The results suggest most observations of precipitation extremes in this study have no trends and therefore can be
treated as stationary series with the exception of the two sites Yuxi
and Mengzi.
The results of autocorrelation test are shown in Table 3,
from which it can be seen that all of the autocorrelation coefficients of lag-1, lag-5 and lag-10 for precipitation extremes serpffiffiffi
ies of each site are smaller than 1:96= n. Hence, these
observations of precipitation extremes can be identified as independent series at the 5% significance level. Therefore, most of
the series (40 sites) can be accepted as stationary and without
serial correlation, allowing the precipitation-frequency analysis
to be applied.
Q u ðx; y; tÞ ¼
Q v ðx; y; tÞ ¼
Qw ¼
QS ¼
u2
X
u1
u2
X
1
g
1
g
Z
Ps
qðx; y; p; tÞuðx; y; p; tÞdp
ð16Þ
qðx; y; p; tÞv ðx; y; p; tÞdp
ð17Þ
P
Z
Ps
P
Q u ðk1 ; y; tÞ
Q v ðx; u1 ; tÞ
QE ¼
QN ¼
u1
QT ¼ QW QE þ QS QN
u2
X
Q u ðk2 ; y; tÞ
u1
u2
X
Q v ðx; u2 ; tÞ
ð18Þ
ð19Þ
u1
ð20Þ
where u and v are the zonal and meridional components of the wind
field, respectively; q is the specific humidity; ps is surface pressure;
p is atmospheric top pressure; g is acceleration of the gravity; QW,
QE, QS, QN are the west, east, south and north regional boundaries,
Results and discussion
399
T. Yang et al. / Journal of Hydrology 380 (2010) 386–405
102°E
27°N
104°E
108°E
110°E
112°E
114°E
116°E
27°N
(A)AM1R
102°E
104°E
108°E
110°E
112°E
114°E
116°E
27°N
27°N
(B)AM3R
26°N
26°N
25°N
25°N
25°N
25°N
24°N
24°N
24°N
24°N
23°N
23°N
26°N
23°N
Legend
22°N
21°N
20°N
102°E
102°E
27°N
140 - 186
186 - 232
232
232 - 278
278 - 324
324 - 370
370 - 418
26°N
23°N
Legend
-2/-1 STD. DEV
-1/ 0 STD. DEV
MEAN
0 / 1 STD. DEV
1 /2 STD. DEV
2/ 3 STD. DEV
>3 STD. DEV
22°N
22°N
N
N
W
E
21°N
S
1 00
200
104°E
108°E
110°E
112°E
114°E
104°E
108°E
110°E
112°E
114°E
21°N
4 0 0 Km
20°N
116°E
179 - 253
253 - 326
326
326 - 400
400 - 474
474 - 548
548 - 616
-2/-1 STD. DEV
-1/ 0 STD. DEV
MEAN
0/ 1 STD. DEV
1 /2 STD. DEV
2/ 3 STD. DEV
>3 STD. DEV
22°N
N
W
N
E
21°N
S
100
200
400 Km
20°N
102°E
104°E
108°E
110°E
112°E
114°E
20°N
116°E
102°E
104°E
108°E
110°E
112°E
114°E
116°E
116°E
27°N
27°N
26°N
26°N
25°N
25°N
25°N
25°N
24°N
24°N
24°N
24°N
23°N
23°N
(C)AM5R
26°N
23°N
Legend
22°N
21°N
20°N
102°E
202 - 284
284 - 366
366
366 - 448
448 - 530
530 - 612
612 - 665
(D)AM7R
26°N
23°N
Legend
-2/-1 STD. DEV
-1/ 0 STD. DEV
MEAN
0 / 1 STD. DEV
1 /2 STD. DEV
2/ 3 STD. DEV
>3 STD. DEV
104°E
27°N
22°N
22°N
N
W
N
E
21°N
S
100
108°E
110°E
112°E
114°E
200
21°N
400 Km
20°N
116°E
20°N
102°E
229 - 316
316 - 402
402
402 - 488
488 - 575
575 - 661
661 - 705
104°E
-2/-1 STD. DEV
-1/ 0 STD. DEV
MEAN
0/ 1 STD. DEV
1 /2 STD. DEV
2/ 3 STD. DEV
>3 STD. DEV
108°E
22°N
N
W
N
E
21°N
S
100
110°E
112°E
114°E
200
400 Km
20°N
116°E
Fig. 8. Spatial mapping of estimated annual precipitation extremes in PRB when return periods = 100 years using L-moments based regional frequency analysis approach,
(A): AM1R; (B): AM3R; (C): AM5R; (A): AM7R. Each name of region and associated sites can be referred to Fig. 3.
Identification of homogenous regions
Identification of the homogeneous region(s) in PRB was performed in two steps as suggested by Hosking and Wallis (1997):
(1) Initial homogenous regions were formed by identifying clusters in the space of site characteristics as described in the
methodology section. The clusters were viewed to assess
whether they are spatially continuous and physically reasonable. The discordancy and heterogeneity measures Di
and H defined in Eqs. (4) and (7) were computed for each
region identified by the clustering procedure. When the
computed heterogeneity measure H (both H1 and H2)
exceeded two, indicating that the region was ‘‘definitely heterogeneous”, the sites in the region were separated by the
clustering algorithms into smaller groups. The discordancy
measure occasionally indicated that several neighboring
sites in a region are discordant with the rest of region. In
these cases, a new region containing only the discordant
sites was formed. This continued until no further subdivision
of heterogeneous regions could be made. Table 4 shows the
transformations from four sites characteristics into variables
used in cluster analysis. Smaller weights for coordinates are
assigned, as we will use them again in the next step to determine the final regions. The results (Table 5 and Fig. 2) indicate that 40 sites of the PRB can initially be divided into
seven clusters.
(2) The homogenous regions were refined manually. Inspection
of the initial clusters, taking into account the topography
and spatial patterns of mean precipitation suggested several
natural and physically reasonable modifications to the clus-
ters, resulting in more homogenous clusters. The final set of
regions (result of 2nd homogeneity test) is shown in the 2nd
and 3rd column of Table 8, whose spatial distribution is
illustrated in Fig. 3. The 40 sites are grouped into six regions.
These regions can be categorized as definite homogenous
(named HOM) with heterogeneity measures H1, H2 < 1 following the recommendation by Daniele et al. (2007), that
heterogeneity is tested by H1 and H2 collectively. Fig. 3 demonstrates the final result of heterogeneity refinement, in
which region III and IV is marked as a joint region (‘‘III + IV”)
because the sites contained are totally mixed together geographically and cannot bordered as separated homogenous
regions.
Test of discordancy measure and goodness-of-fit
The discordancy measure test is considered as a means of
screen analysis aiming to identify those sites that are grossly discordant with the group as a whole. Table 6 presents the statistics
of the 40 sites, record lengths, L-moment ratios, and D-statistic values. The results of discordancy measure and heterogeneity test for
the 40 sites in the Pearl River Basin are given in Table 8. Results
show that all Di values are less than the critical discordancy thresholds which depend on the number of sites in each region (Hosking
and Wallis, 1993, 1997). Therefore, the entire 40 sites in the PRB
are regarded to pass the discordancy test. The results for goodness-of-fit measures are listed in Table 7, which indicate that they
are satisfactory with |Zcrit| 6 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:
T. Yang et al. / Journal of Hydrology 380 (2010) 386–405
Generalized Extreme-value, GNO: Generalized Normal, GPA: Generalized Pareto, PE3: Pearson type III and WAK: Wakeby) are investigated. Among these six candidate distributions, the GNO, GLO,
GEV, and PE3 distribution fits best for most of the entire basin with
Z value less than |Zcrit| 6 1.64 for different HOM regions (Table 7
and Fig. 4). The L-moment ratio plot (Fig. 4) demonstrates the performances of GNO, GLO, GEV, and PE3 distribution for the AM3R as
a paradigm. It implies these performances in curving fitting for the
AM3R are slightly different. The best distribution identified for
each HOM region in this step is used to estimate the regional
growth curve and associated frequency.
Accuracy of estimation in regional frequency analysis for rainfall
extremes
A quantile procedure using Monte Carlo simulation described in
the methodology section was used. For each region, simulated data
was generated from the distribution that is best fitted to the actual
regional data with the same number of sites in the region and the
same record lengths in each site. Quantile estimates were then calculated for each site. After a large number of simulations (1000 in
this study), the differences between the simulated and estimated
quantiles was used to approximate the error bounds and root mean
square errors (RMSE) of the quantile estimates and to assess the
accuracy of the estimated quantiles. The simulation results for
the estimated quantiles and bias for six HOM regions of AM1R
are presented in Table 8 and Fig. 5. The results demonstrate that
the RMSE values of the estimated quantiles for six precipitation regions of PRB range from 0.022 to 0.189 when return periods of
AM1R are less than 100 years; however, the RMSE value of 0.370
is observed when return period equals to 1000 years. This implies
that the RMSEs are reliable enough to enable the quantile estimates to be used with confidence when return periods are less
than 100 years. Estimates of higher return periods (e.g. 1000 years)
require sufficient historical records in order to enhance the reliability in the quantile estimation.
Spatial mapping of L-moment statistical parameters
To compute precipitation estimates for the recurrence intervals
selected, the appropriate value of L-Cv and L-skewness need to be
obtained for each grid-cell. This was accomplished by populating
the grid-cells in the study area domain using the functional relationships for the L-Cv and L-skewness developed in the regional
precipitation-frequency analysis. Values of grid-cells in transition
zones were accomplished as a weighted average of the L-moment
ratio in adjoining climatic regions. The weights were based on the
distance between a given grid-cell to the boundaries of the transition zone. This provided continuity at the boundaries of the regions
and a smooth transition between regional boundaries within the
transition zones. Color-shaded maps of L-Cv and L-Skewness values are depicted in Figs. 6 and 7 for the AM1R, AM3R, AM5R, and
AM7R. In order to reveal their distinct patterns, the standard deviation is used in classifying the spatial variations of L-CV and
L-Skewness values. The results are summarized as below:
Fig. 6 demonstrates that the spatial patterns of L-CV for the four
types of annual rainfall extremes (AM1R, AM3R, AM5R, and AM7R)
are very similar. These spatial variations are in strong agreement
with the spatial pattern of the five homogenous regions. High
L-Cv values are observed in the two HOM regions (region VI).
One region is situated in the west Guangxi Province and centered
at the Rong’an & Guilin site. The other region is located in the costal
area of the Pearl River delta (PRD). Although similarly high L-Cv
values are identified in both HOM regions, their dominant influencing factors are apparently different. For the PRD region, the precipitation regime is dominated by the strong impacts of tropical
Table 10
Variation of AM1R (DP: mm) corresponding to different increments of return periods
(DR: year) in the PRB.
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Site name
Xianning
Zhanyi
Luxi
Anshun
Xingyi
Wangmo
Luodian
Dushan
Rongjiang
Rongan
Guilin
Nanxiong
Guangnan
Fengshan
Hechi
Du’an
Liuzhou
Mengshan
Hexian
Shaoguan
Fogang
Lianping
Xunwu
Napo
Baise
Jingxi
Laibin
Guiping
Wuzhou
Guangning
Gaoyao
Guangzhou
Heyuan
Zengcheng
Huiyang
Longzhou
Nanning
Luoding
Taishan
Shenzhen
DP (mm)
Increment of annual precipitation (mm)
400
DP (mm)
DR = (1–
10 year)
DR = (10–
50 year)
DR = (50–
100 year)
52.9
61.3
58.4
85.1
76.0
88.5
79.0
74.2
67.1
134.7
111.3
77.0
56.1
91.8
87.0
114.2
92.9
98.1
85.4
78.3
81.0
121.2
87.6
87.5
76.0
80.1
87.8
86.6
101.2
88.8
85.8
91.4
104.3
114.1
118.0
83.5
85.3
73.9
125.7
149.7
33.7
39.0
37.1
54.1
48.3
56.3
50.3
47.2
42.7
85.7
70.8
49.0
35.7
58.4
55.3
72.6
59.1
62.4
54.3
49.8
51.6
77.1
55.8
55.7
48.3
51.0
55.8
55.1
64.4
56.5
54.6
58.1
66.3
72.6
75.1
53.1
54.2
47.0
80.0
95.3
15.5
18.0
17.1
24.9
22.3
25.9
23.2
21.8
19.7
39.5
32.6
22.6
16.5
26.9
25.5
33.5
27.2
28.8
25.0
23.0
23.8
35.5
25.7
25.7
22.3
23.5
25.7
25.4
29.6
26.0
25.1
26.8
30.6
33.5
34.6
24.5
25.0
21.6
36.8
43.9
90.0
57.2
26.4
140
Region I
Region II
120
Region III
Region IV
100
Region V
Region VI
80
60
40
20
1y-10y
10y-50y
50y-100y
Increment of return period
Fig. 9. Increment of AM1R (mm) vs. increment of return period.
cyclonic weather systems and frequently emerged typhoons, while
the precipitation regime in the inland region of the west Guangxi
Province is found to be controlled by a regional convective weather
401
T. Yang et al. / Journal of Hydrology 380 (2010) 386–405
0.8
0.5
AM7R
AM5R
AM3R
AM1R
0.4
0.3
0.2
(B) Region I I
0.7
FREQUENCY
FREQUENCY
(A) Region I
AM7R
AM5R
AM3R
AM1R
0.6
0.5
0.4
0.3
0.2
0.1
0.1
0.0
0.0
APR
MAY
JUN
JUL
AUG
APR
SEP
MAY
0.5
JUL
AUG
SEP
0.5
(C) Region V
AM7R
AM5R
AM3R
AM1R
0.4
0.3
0.2
0.1
(D) Region VI
FREQUENCY
FREQUENCY
JUN
MONTH
MONTH
AM7R
AM5R
AM3R
AM1R
0.4
0.3
0.2
0.1
0.0
0.0
APR
MAY
JUN
JUL
AUG
SEP
MONTH
APR
MAY
JUN
JUL
AUG
SEP
MONTH
Fig. 10. Seasonality of precipitation extremes in the four typical HOM regions (relative monthly frequency).
system (Chi et al., 2005). High L-Cv values of various rainfall extremes means considerable floods in these two regions. Low L-Cv
values of rainfall extremes are observed in mountainous area such
as region I and II. The remaining parts (regions III–V) are identified
with moderate L-Cv values. Meanwhile, Fig. 7 implies there are no
regular spatial variation patterns of L-Skewness for 4 types of
annual rainfall extremes (i.e. AM1R, AM3R, AM5R, and AM7R).
Spatial mapping of annual rainfall extremes with different return
periods
Spatial patterns of annual precipitation extremes, which serves
as one of the most important environment indicator for regional
integrated water resources management, is a spatially continuous
variable, thus we can quantify the spatial associations of precipitation extremes between sites and map precipitation with different
return periods for the PRB by kriging interpolation. Table 9 and
Fig. 8 provides the estimated map of annual precipitation extremes
(RP = 10, 50, and 100 years) in the PRB. Generally, the spatial map
of precipitation extremes (Fig. 8A–D) indicate that precipitation
amount increases gradually from the upstream (regions I and II)
to downstream areas (regions V and VI). However, a plenty of precipitation observation was also found in the Rong’an and Guilin region of Guangxi province, the underlying reasons will be analyzed
in the section ‘‘Seasonality of extreme rainfall events”. Excessive
precipitation magnitude records are observed in Guilin of Guangxi
province and Shenzhen of Guangdong province, which provide sufficient climate conditions (e.g. precipitation and humidity) responsible for the frequently occurring floods in these regions from the
meteorological point of view.
Characterization of spatial patterns for rainfall-extreme variations in
the PRB
Variations of annual precipitation totals corresponding to different increments of return periods in the PRB are offered in Table 10 and Fig. 9. Table 10 suggests that the precipitation
increments in 40 sites show obvious downward trends when
occurrence frequencies increase from 1, 10, 50 years to 100 years.
From a regional perspective, regional curve of precipitation increments (Table 10 and Fig. 9) for six hydrological regions indicates
that region VI (centered at the Guilin in Guangxi province and
the Pearl River Delta in Guangdong province) has the highest precipitation increases among 40 sites in PRB. The precipitation increase in upstream region I (Yun’nan province), is the lowest
among 40 sites of the study basin. The remaining regions (II, III,
and IV) lie between those of region I (the lowest) and VI (the highest). In summary, the spatial precipitation variations in different
return periods (Return period = 1, 10, 50 years to 100 years) are
identified to be increasing from west to east (upstream to downstream) in the PRB.
Seasonality of extreme rainfall events
The seasonality of extreme rainfall is valuable for application of
precipitation-frequency information in rainfall–runoff modelling.
In particular, information on the seasonality of extreme rainfall is
helpful in decision-making for setting catchment conditions antecedent to the storm (Wallis et al., 2007). Here, the seasonality of
extreme storms is investigated by constructing frequency histograms of the storm date for annual maximum 1-, 3-, 5-, and 7-days
rainfall for each of the HOM regions. Precipitation amounts/gauges
with duplicate storm dates (generally dates within about three calendar days) were removed before constructing the frequency histograms. The results of seasonality analysis are presented as below.
Seasonality of precipitation extremes in 4 typical HOM regions
is shown in Fig. 10, of which, Fig. 10A and B reveals the seasonal
patterns of precipitation extremes for the mountainous region (regions I and II) in upstream basin. Fig. 10C and D represents the seasonal patterns of precipitation extremes for the low-elevation
region (region V and VI) in lower Pearl River basin. The precipitation pattern for these regions is strongly affected by the Asian
monsoon system. Most of the rainfall (80%) occurs during the summer monsoon months (May–October), with much less precipitation (20%) occurring during the winter monsoon months
(November–April). These events are mainly the result of
402
T. Yang et al. / Journal of Hydrology 380 (2010) 386–405
(A)
(C)
(B)
(D)
Fig. 11. The monthly mean moisture transports for the period 1961–2005. The scale of the vectors is given below and contours indicate magnitudes in kg(ms)1. (A) May, (B)
June, (C) July, (D) August.
synoptic-scale cyclonic weather systems and associated fronts,
which remain organized and penetrate a considerable distance inland from the coast. In particular, various strong typhoons with a
variety of water vapor and energy originating from the South China
Sea exert remarkable influences on the extreme precipitation
events in the PRB (Zhang et al., 2008a,b). Additionally, the Rong’an
and Guilin in region VI (Fig. 8) is climatically dominated by a strong
convection, which takes the place of the fronts and become the
main weather systems that affect the extreme precipitation over
this region in summer monsoon months (Chi et al., 2005), therefore, the observed extreme precipitation records in this region
are also very high. Fig. 10C and D indicates the precipitation events
of AM1R, AM3R, AM5R and AM7R mainly concentrate in May, June,
July and August. These events will trigger floods with different
magnitudes, and June and July are well recognized as the primary
flood-season for such regions. Meanwhile, moderate floods occur
in May in these two regions due to their proximity to the sea; this
is known as the early flood-season for these regions in South China.
There is a gradual transition in the seasonality of precipitation extremes when they are transported from the coast to inland area.
Therefore, the impacts of cyclonic weather systems on region I
and II are comparatively small. Furthermore, few floods occur in
May in region I and II due to the long distance and weak effects
of the water vapor (Fig. 10A and B). Finally, it is well identified that
AM1R events in July happen more frequently than AM3R, AM5R
and AM7R (Fig. 10). However, the phenomenon is different in
May, June and August. This may be attributed to the frequently
emerging thunderstorms with short durations (less than 1 day)
triggered by typhoons which mainly happen in July.
Underlying links with large-scale circulation and topographical
characteristics
In order to reveal the possible underlying link between patterns
of extreme precipitation and large-scale circulation, the moisture
and related transport properties of the whole Ps layer (surface
pressure) 300 hPa in China are analyzed based on the NCAR/NCEP
reanalysis.
Fig. 11 clearly demonstrates the routes and the magnitudes of
the moisture propagation across the South China, including the
Pearl River Basin (102°140 E–116°530 E; 20°310 N–26°490 N) in floodseason which consists of four different months (i.e. May, June, July,
and August). It can be seen from Fig. 11 that enormous northeastward moisture entered the Pearl River basin from the India Ocean
and Southwest Pacific Ocean. Different moisture transporting patterns are identified in May–August (Fig. 11A–D), showing monthly
variations of moisture propagation from different directions of the
Pearl River basin in the flood-season. Among these four months,
strong northeast-ward moisture are found in May (Fig. 11A) and
June (Fig. 11B), leading to a variety of precipitation and increasing
T. Yang et al. / Journal of Hydrology 380 (2010) 386–405
extreme precipitation events in the costal region (e.g. Fig. 10C and
D). This period has been widely recognized as the early flood-season for the PRB (e.g. Zhang et al., 2008a,b). The eastern Asian summer monsoons are the main driving meteorological forces or
conditions for precipitation events in these months for this region
(from May to June).
However, resulted from different impacts of topographical features (i.e. elevation, distance to the coast, and mountain’s influences), extreme precipitation events in May occurred less
frequently in inland regions, which are partly due to influences
of high-elevation and long distance to the sea of these regions
(e.g. region I and II, Figs. 3 and 10A and B) than coastal regions,
which are low-elevation areas and near to the sea (e.g. region V
and VI, Figs. 3 and 10C and D). For the later flood-season in the
PRB (July and August), the influences of the eastern Asian summer
monsoon will decrease, and typhoons or hurricanes originated
from the Pacific Ocean will happen and visit such regions more frequently. The precipitation regimes in this period will be dominated
collectively by two meteorological forces: namely, the eastern
Asian summer monsoon and typhoons. Therefore, more extreme
precipitation events can also be found in August and even in September. In general, a number of observations (e.g. Li et al., 2002)
indicated the magnitudes and frequencies in early flood-season
(May and June) is higher than later flood-season (July and August).
It means more extreme floods will occur in early flood-season (May
and June) than later flood-season (July and August). The hydrological regimes regarding extreme precipitation of PRB are quite distinctive from the other large basins in China, such as the Yangtze
River and Yellow River basin where the major flood-seasons are
in July and August (e.g. Zhang et al., 2008; Yang et al., 2008b).
(3)
(4)
(5)
Conclusions
Regional frequency analysis based on multi-day consecutive
rainfall extremes has scientific and practical value in the context
of basin-scale water resource and flood risk management. L-moments based regional frequency analysis technique, which has definite advantages over conventional moment parameters, provides
promising insights into regional frequency analysis and is widely
used by hydrologists nowadays. This article presents a regional frequency analysis of rainfall extremes and characterization of the
spatio-temporal pattern of rainfall extremes variations in the Pearl
River Basin using the well-known index-flood L-moments approach together with some advanced statistical tests and spatial
analysis methods. Further analysis of, the whole layer of the atmospheric moisture and related transport features based on the
NCAR/NCEP reanalysis data (1960–2005) reveals the possible
underlying links between patterns of extreme precipitation and
large-scale circulation. The extreme precipitations are also related
to the basin’s topographical characteristics, especially the elevation
and distance to the coast. Some interesting findings are obtained
from this investigation as follows:
(1) The Pearl River Basin (40 sites) can be categorized into six
regions after inspection of initial result of heterogeneity
detection by cluster analysis taking into account the topography and spatial patterns of mean precipitation in the
areas. Five of these six regions can be categorized as definite
homogenous with heterogeneity measures H1, H2 < 1 followed by the recommendation by Daniele et al. (2007). Only
one region (six sites, region VI) is identified as ‘‘possibly heterogeneous‘‘ with H3 > 1 for AM3R and AM7R.
(2) The goodness-of-fit results indicate that among the six candidate distributions (i.e. GLO: Generalized Logistic, GEV:
Generalized Extreme-value, GNO: Generalized Normal,
(6)
403
GPA: Generalized Pareto, PE3: Pearson type III and WAK:
Wakeby), the GNO, GLO, GEV, and PE3 distributions fit better
for most of the basin with Z value less than |Zcrit| 6 1.64 in
the HOM regions. The L-moment ratio plot shows that the
performances of GNO, GLO, GEV, and PE3 distributions in
curving fitting are slightly different.
The estimated quantiles and their bias produced by Monte
Carlo simulation (m = 1000 times) demonstrate that they
are reliable to enable the quantile estimates to be used with
confidence when return periods are less than 100 years. The
RMSE values of the estimated quantiles for six precipitation
regions of PRB range from 0.022 to 0.189 when return periods of rainfall extremes are less than 100 years. However,
estimates for higher return periods (e.g. 1000 years) require
sufficient historical records to extend record length to
enhance the reliability of quantile estimation eventually.
The spatial map of precipitation extremes indicate that precipitation amount increases gradually from the upstream to
downstream regions. Excessive precipitation magnitude
records are observed in Guilin of Guangxi province and
Fogang of Guangdong province, which provide sufficient climate conditions (e.g. precipitation and humidity) responsible for the frequently occurred flood disasters in these
regions. Besides, the spatial precipitation variations in different return periods (with return period of 1, 10, 50 years to
100 years) are identified to be increased from the upstream
to downstream in the PRB.
The seasonal patterns of precipitation extremes for different
topographical regions are different. The major precipitation
events of AM1R, AM3R, AM5R and AM7R in low-elevation
region in lower Pearl River basin mainly concentrate in
May, June, July and August. These events will trigger floods
with different magnitudes, and June and July are well recognized as the primary flood-season for such regions. Meanwhile, in these regions moderate floods occur in May
because it’s close to the sea, which is known as the early
flood-season for the regions in South China. There is a gradual transition in the seasonality of precipitation extremes
when they are transported from the coast to inland area.
Therefore, the impacts of cyclonic weather systems on the
mountainous region in upstream basin are comparatively
small. Furthermore, a few floods occur in May in these
regions due to long distance and weak effects from the water
vapor.
Two major flood-seasons and associated meteorological, and
topographical driving forces are identified. The precipitation
regimes in early flood-season (May and June) are mainly
impacted by the strong influences of the eastern Asian summer monsoon, and the later flood-season (July and August)
are dominated collectively by two meteorological forces:
namely, the eastern Asian summer monsoon and typhoons.
In general, the magnitudes and frequencies of precipitation
in early flood-season (May and June) is higher than later
flood-season (July and August). The extreme precipitation
events in May occurred less frequently in inland regions
than coastal regions. This constitutes one of a unique regime
of extreme precipitation events for PRB.
To the best of our knowledge, this study is the first attempt to
conduct a systematic regional frequency analysis on various annual multi-day consecutive precipitation extremes (1-, 3-, 5-, 7days) in the light of power of L-moments approach, over the Pearl
River Basin and even in China. Besides, stationarity and serial correlation test are carried out prior to the regional frequency analysis
to ensure validation of the regional frequency analysis. Furthermore, characterization of the spatio-temporal patterns of
404
T. Yang et al. / Journal of Hydrology 380 (2010) 386–405
frequency variations for rainfall extremes is beneficial to compare
and reveal the potential influences of climate change and topographical factors in individual regions. The approach together with
the statistical tests utilized in this study and the findings in characterization of the spatio-temporal patterns of frequency variations for rainfall extremes in the entire Pearl River Basin
constitute the major contributions distinct from the past literature.
This study is of great scientific and practical merit towards the better understanding of the spatio-temporal patterns of extreme precipitation to reveal the underlying linkages between precipitation
and floods in a broad geographical perspective.
Acknowledgements
The work was financially supported by the grant from the National Natural Science Foundation of China (40901016,
40830639), the National Basic Research Program (‘‘973 Program”,
2006CB403200), the grant from State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering (2009586612),
the grant from State Key Laboratory of Water Resources and
Hydropower Engineering Science (2008B041), and the Programme
of Introducing Talents of Discipline to Universities – the 111 Project of Hohai University (B08048). We would like also express
our thanks to the editor, Professor Geoff Syme and two anonymous
referees for their valuable comments which greatly improved the
quality of this paper.
References
Adamowski, K., Alila, Y., Pilion, P.J., 1996. Regional rainfall distribution for Canada.
Atmospheric Research 42, 75–88.
Burgueno, A., Martinez, M.D., Lana, X., Serra, C., 2005. Statistical distributions of the
daily rainfall regime in the catalonla (Northeastern Spain) for the years 1950–
2000. International Journal of Climatology 25, 1381–1403.
Chen, Y.D., Huang, G., Shao, Q.X., Xu, C.Y., 2006. Regional analysis of low flow using
L-moments for Dongjiang basin, South China. Hydrological Sciences Journal 51
(6), 1051–1064.
Chen, Y.D., Yang, T., Zhang, Q., Xu, C.Y., Chen, X., 2008. Hydrologic alteration along
the Middle and Upper East River (Dongjiang) Basin, South China: A visually
enhanced mining on the results of RVA method. Stochastic Environment
Research and Risk Assessment. doi:10.1007/s00477-008-0294-7.
Chi, Y.Z., He, J.H., Wu, Z.W., 2005. Features analysis of the different precipitation
periods in the pre-flood season in South China. Journal of Nanjing Institute of
Meteorology 28, 163–171 (in Chinese).
Dai, A., Fung, I.Y., Del, Genio, A.D., 1997. Surface observed global land precipitation
variations during 1900–88. Journal of Climate 10, 2943–2962.
Daniele, N., Marco, B., Marco, S., Francesco, Z., 2007. Regional frequency analysis of
extreme precipitation in the eastern Italian Alps and the August 29, 2003 flash
flood. Journal of Hydrology 345, 149–166.
Doherty, R.M., Hulme, M., Jones, C.G., 1999. A gridded reconstruction of land and
ocean precipitation for the extended tropics from 1974–1994. International
Journal of Climatology 19, 119–142.
Dore, M.H.I., 2005. Climate change and changes in global precipitation patterns:
what do we know? Environment International 31, 1167–1181.
Douglas, E.M., Vogel, R.M., Kroll, C.N., 2000. Trends in floods and low flows in the
United States: impact of spatial correlation. Journal of Hydrology 240, 90–105.
Endreny, T.A., Pashiardis, S., 2007. The error and bias of supplementing a short, arid
climate, rainfall record with regional vs. global frequency analysis. Journal of
Hydrology 334, 174–182.
Farhan, Y.I., 1984. Regionalization of surface water catchments in the east bank of
Jordan. In: Proceeding of the Symposium ‘‘Problems in Regional Hydrology”.
University of Freiburg.
Fovell, R.G., Fovell, M.Y.C., 1993. Climate zones of conterminous United States
defined using cluster analysis. Journal of Climate 6, 2103–2135.
Fowler, H.J., Kilsby, C.G., 2003. A regional frequency analysis of United Kingdom
extreme rainfall from 1961 to 2000. International Journal of Climatology 23,
1313–1334.
Gaál, L., Kyselý, J., 2009. Regional frequency analysis of heavy precipitation in the
Czech Republic by improved region-of-influence method. Hydrology and Earth
System Sciences Discussions 6, 273–317.
Gabriele, S., Arnell, N., 1991. A hierarchical approach to regional flood frequency
analysis. Water Resources Research 27 (6), 1281–1289.
Goovaerts, P., 1999. Performance comparison of geostatistical algorithms for
incorporating elevation into the mapping of precipitation. In: The IV
International Conference on GeoComputation was hosted by Mary
Washington College in Fredericksburg, VA, USA, 25–28 July 1999.
Guttman, N.B., Hosking, J.R.M., Wallis, J.R., 1993. Regional precipitation quantile
values for the continental US computed from L-moments. Journal of Climate 6,
2326–2340.
Hartkamp, A.D., Beurs, K.D., Stein, A., White, J.W., 1999. Interpolation Techniques for
Climate Variables. NRG-GIS Series 99-01. CIMMYT, Mexico, DF.
Hosking, J.R., Wallis, J.R., 1993. Some statistics useful in regional frequency analysis.
Water Resources Research 29 (2), 271–281.
Hosking, J.R., Wallis, J.R., 1997. Regional Frequency Analysis: An Approach based on
L-moments. Cambridge University Press, Cambridge, UK.
Hulme, M., Osborn, T.J., Johns, T.C., 1998. Precipitation sensitivity to global
warming: comparison of observations with HadCM2 simulations. Geophysical
Research Letters 25, 3379–3382.
Karl, T.R., Knight, R.W., 1998. Secular trends of precipitation amount, frequency, and
intensity in the USA. Bulletin of the American Meteorological Society 79, 231–
241.
Kendall, M.G., 1975. Rank Correlation Methods. Griffin, London, UK.
Li, J.N., Wang, A.Y., Meng, W.G., Fan, Q., Fong, S.K., Hao, P., 2002. The meteorological
characteristics of precipitation of the prior flood-season and posterior floodseason in Guangdong Province. Acta Scientiarum Naturalium Universitatis
Sunyatseni 41 (3), 91–98.
Mann, H.B., 1945. Nonparametric tests against trend. Econometrica 13, 245–
259.
Milly, P.C.D., Dunne, K.A., Vecchia, A.V., 2005. Global pattern of trends in streamflow
and water availability in a changing climate. Nature 438, 347–350.
Mitchell, J.M., Dzerdzeevskii, B., Flohn, H., Hofmeyr, W.L., Lamb, H.H., Rao, K.N.,
Wallen, C.C., 1966. Climate Change. WMO Technical Note No. 79. World
Meteorological Organization.
Mosley, M.P., 1981. Delimitation of New Zealand hydrological regions. Journal of
Hydrology 49, 173–192.
Norbiato, D., Borga, M., Sangati, M., Zanon, F., 2007. Regional frequency analysis of
extreme precipitation in the eastern Italian Alps and the August 29, 2003 flash
flood. Journal of Hydrology 345, 149–166.
Pilion, P.J., Admowski, K., Alila, Y., 1991. Regional analysis of annual maxima
precipitation using L-moments. Atmosphere Research 27, 81–92.
Pearl River Water Resources Committee (PRWRC), 1991. Pearl River Water
Resources Committee (PRWRC), The Zhujiang Archive, vol. 1. Guangdong
Science and Technology Press, Guangzhou (in Chinese).
Pearl River Water Resources Commission (PRWRC). Pearl River Bulletins of 2000,
2001, 2002, 2003, 2004 and 2005. <http://www.pearlwater.gov.cn/>, 2006
(November, 2006) (in Chinese).
Richman, M.B., Lamb, P.J., 1985. Climatic patterns analysis of three- and seven- day
summer rainfall in the central United States: some methodological
considerations and a regionalization. Journal of Climate and Applied
Meteorology 24, 1325–1342.
Royston, P., 1992. Which measures of skewness and kurtosis are best? Statistics in
Medicine 11, 333–343.
Schaefer, M.G., 1990. Regional analysis of precipitation annual maximum in
Washington State. Water Resources Research 26, 119–131.
Scholz, G., Quinton, J.N., Strauss, P., 2008. Soil erosion from sugar beet in Central
Europe in response to climate change induced seasonal precipitation variations.
Catena 72, 91–105.
Stedinger, J.R., Vogel, R.M., Foufoula-Georgiou, E., 1993. Frequency analysis of
extreme events. In: Maidment, D.A. (Ed.), Handbook of Applied Hydrology.
McGraw-Hill, New York (Chapter 18).
Sveinsson, O.G.B., Salas, J.D., Duane, C.B., 2002. Regional frequency analysis of
extreme precipitation in Northeastern Colorado and Fort Collins flood of 1997.
Journal of Hydrologic Engineering 7 (1), 49–63.
Trenberth, K.E., Guillemot, C.J., 1998. Evaluation of the atmospheric moisture and
hydrological cycle in the NCEP/NCAR reanalyses. Climate Dynamics 14, 213–
231.
Wallis, J.R., Schaefer, M.G., Barker, B.L., Taylor, G.H., 2007. Regional
precipitation-frequency analysis and spatial mapping for 24-hour and 2hour durations for Washington State. Hydrology and Earth System Sciences
11 (1), 415–442.
Xiong, L.H., Guo, S.L., 2004. Trend test and change-point detection for the annual
discharge series of the Yangtze River at the Yichang hydrological station.
Hydrological Science Journal 49 (1), 99–112.
Xu, C.Y., Singh, V.P., 2004. Review on regional water resources assessment under
stationary and changing climate. Water Resource Management 18 (6), 591–
612.
Yang, T., Chen, X., Xu, C.Y., Zhang, Z.C., 2008a. Spatio-temporal changes of
hydrological processes and underlying driving forces in Guizhou Karst area,
China (1956–2000). Stochastic Environment Research and Risk Assessment.
doi:10.1007/s00477-008-0278-7.
Yang, T., Zhang, Q., Chen, Y.D., Tao, X., Xu, C.Y., Chen, X., 2008b. A spatial assessment
of hydrologic alteration caused by dam construction in the middle and lower
Yellow River, China. Hydrological Processes 22, 3829–3843.
Yang, T., Xu, C.Y., Shao, Q.X., Chen, X., 2009. Regional flood analysis in Pearl River
Delta region, China using L-moments approach. Stochastic Environment
Research and Risk Assessment. doi:10.1007/s00477-009-0308-0.
Zhang, J.Y., Hall, M.J., 2004. Regional flood frequency analysis for the Gan-Ming
River basin in China. Journal of Hydrology 296, 98–117.
Zhang, Q., Xu, C.Y., Zhang, Z.X., Chen, Y.Q., Liu, C.L., 2008. Spatial and temporal
variability of extreme precipitation during 1960–2005 in the Yangtze River
basin and possible association with large scale circulation. Journal of Hydrology
353 (3–4), 215–227.
T. Yang et al. / Journal of Hydrology 380 (2010) 386–405
Zhang, Q., Xu, C.Y., Gemmer, M., Chen, Y.D., Liu, C.L., 2008a. Changing properties of
precipitation concentration in the Pearl River basin, China. Stochastic
Environmental Research and Risk Assessment. doi:10.1007/s00477-008-0225-7.
Zhang, Q., Xu, C.Y., Zhang, Z.X., 2008b. Observed changes of drought/wetness
episodes in the Pearl River basin, China, using the standardized precipitation
index and aridity index. Theoretical and Applied Climatology. doi:10.1007/
s00704-008-0095-4.
405
Zhang, Z.X., Zhang, Q., Xu, C.Y., Liu, C.L., Jiang, T., 2008c. Atmospheric moisture
budget and floods in the Yangtze River basin, China. Theoretical and Applied
Climatology. doi:10.1007/s00704-008-0010-.
Zhang, Q., Xu, C.Y., Zhang, Z.X., Chen, Y.Q., Liu, C.L., 2009. Observed changes of
drought/wetness episodes in the Pearl River basin, China, using the
standardized precipitation index and aridity index. Theoretical and Applied
Climatology. doi:10.1007/s00704-008-0095-4.