INTERNATIONAL JOURNAL OF CLIMATOLOGY
Int. J. Climatol. 33: 1140–1152 (2013)
Published online 27 April 2012 in Wiley Online Library
(wileyonlinelibrary.com) DOI: 10.1002/joc.3499
Copula-based spatio-temporal patterns of precipitation
extremes in China
Qiang Zhang,a,b,c * Jianfeng Li,a,b Vijay P. Singhd,e and Chong-Yu Xuf
a
b
Department of Water Resources and Environment, Sun Yat-sen University, Guangzhou, China
Key Laboratory of Water Cycle and Water Security in Southern China of Guangdong High Education Institute, Sun Yat-sen University,
Guangzhou, China
c School of Geography and Planning, and Guangdong Key Laboratory for Urbanization and Geo-simulation, Sun Yat-sen University,
Guangzhou, China
d Department of Biological and Agricultural Engineering, Texas A&M University, College Station, TX, USA
e Department of Civil and Environmental Engineering, Texas A&M University, College Station, TX, USA
f Department of Geosciences and Hydrology, University of Oslo, Blindern, Oslo, Norway
ABSTRACT: Daily precipitation data from 590 stations in China covering a period of 1960–2005 are analysed using
copulas, the modified Mann–Kendall (MK) trend test and linear regression. Changing characteristics of eight precipitation
indices are investigated in both time and space. Results indicate that (1) the regions west of 100 ° E, particularly northwest
China, exhibit a wetting tendency as reflected by increasing/decreasing number of consecutive rain/non-rain days; (2) the
drying tendency is observed mainly in the regions covered by the Yellow River basin, the Huaihe River basin, and the Haihe
River basin, and relatively moderate changes in precipitation indices are found in northeast China; (3) precipitation extremes
are intensifying in the regions east of 100 ° E, particularly in case of south China, specifically the lower Yangtze River
basin, the southeast rivers and the Pearl River basin. The intensification of precipitation extremes in south China is mirrored
mainly by the decreasing number of rain days and increasing number of consecutive non-rain days. Besides an increasing
percentage of P90 to the annual total precipitation, (4) the intensification of precipitation extremes has the potential to
increase the probability of occurrence of natural hazards, particularly floods and droughts. The spatial distribution of floodand drought-affected crop areas is in agreement with that of precipitation extremes, showing considerable impacts of
precipitation extremes on meteor-hydrological hazards. An increasing number of consecutive non-rain days in south China
will cause a higher risk of droughts. The regions east of 100 ° E are heavily populated and are economically developed.
Food security, water security, and sustainable socioeconomy in China urgently call for effective water resource management
policy. Copyright  2012 Royal Meteorological Society
KEY WORDS
precipitation extremes; copula functions; climate changes; spatio-temporal distribution; natural hazards;
agricultural responses
Received 2 September 2011; Revised 15 March 2012; Accepted 26 March 2012
1.
Introduction
Climate change, characterized by global warming, is now
believed to be intensifying the hydrological cycle (Allen
and Ingram, 2002; World Meteorological Organization,
2003; Ziegler et al., 2003), altering the spatio-temporal
patterns of precipitation and increasing occurrences of
precipitation extremes, such as floods and droughts
(Easterling et al., 2000; Vörösmarty et al., 2010). Arnell
(1999) indicated that the hydrological cycle would intensify with more evaporation and more precipitation and the
extra precipitation would be unequally distributed around
the globe and hence would cause more frequent floods
and droughts.
Changing properties of precipitation and hydrological
extremes have been investigated in China and other
∗ Correspondence to: Q. Zhang, PhD, Department of Water Resources
and Environment, Sun Yat-sen University, Guangzhou 510275, China.
E-mail: zhangq68@mail.sysu.edu.cn
Copyright  2012 Royal Meteorological Society
places of the world. Groisman et al. (1999) indicated that
the probability of daily precipitation exceeding 50.8 mm
in mid-latitude countries increased by ∼20% in the later
twentieth century. Suppiah and Hennessy (1998) showed
that heavy precipitation events in most parts of Australia
have increased. Zhai et al. (1999) indicated that extreme
precipitation events have increased in western China
since 1950. Increasing extreme precipitation events can
also be found in south-eastern China (e.g. Zhang et al.,
2009a).
Zolina et al. (2010) found the lengthening of wet periods in Europe, indicating that heavy precipitation events
during the past two decades have become much more
frequently associated with longer wet spells and intensified in comparison with the 1950s and the 1960s.
Analysis of precipitation extremes in the Pearl River
basin, south China, also indicated increased precipitation variability and high-intensity rainfall (Zhang et al.,
2009a). Besides, Zhang et al. (2009a) also found that the
COPULA-BASED SPATIO-TEMPORAL PATTERNS OF PRECIPITATION EXTREMES
amount of rainfall has changed little, but its variability
has increased.
The probabilistic behaviour of hydro-meteorological
variables has been receiving increasing attention in recent
years, perhaps due to increasing risk of natural hazards
under the influence of climate change and human activities. Leonard et al. (2008) considered maximum values
that occur within a given season and the relationship
between seasonal maxima and annual maxima. Hashino
(1985) generalized the Freund bivariate exponential distribution (Freund, 1961) to represent the joint probability distribution of rainfall intensity and maximum storm
surge in Osaka Bay, Japan. Using copulas, De Michele
et al. (2005) and Zhang and Singh (2006, 2007a) derived
bivariate distributions for modelling flood peak and volume; Singh and Zhang (2007) and Zhang and Singh
(2007b) determined joint rainfall frequencies; and Kao
and Govindaraju (2010) and Song and Singh (2010a,
2010b) characterized droughts.
The flexibility of copulas for constructing joint distributions is evident from related studies on rainfall frequency analysis (Zhang and Singh, 2006, 2007a, 2007b;
Kao and Govindaraju, 2008). Therefore, copulas are
becoming important tools in the bivariate analysis of precipitation or streamflow extremes (e.g. Leonard et al.,
2008). Copulas are a flexible representation of multivariate distributions, as each marginal distribution can have a
different distributional form and there is a wide range of
copulas to select from to be able to yield the correlated
joint distribution (Leonard et al., 2008).
China, the most populous country, is heavily dependent on agriculture for food production to support the
growing population. However, agricultural development
is prone to be affected by precipitation extremes and
hence droughts and floods. Understanding of the probabilistic behaviour of precipitation extremes, particularly
the joint probability of precipitation extremes, is the first
step towards the scientific management of agricultural
activities and the mitigation of the influence of floods and
droughts on agriculture. Precipitation extremes have been
analysed in both time and space (e.g. Zhang et al., 2011)
However, no such reports are available so far concerning changing probabilistic characteristics of precipitation
extremes in China. This constituted the motivation for
this study.
The objectives of this study therefore are (1) to analyse
the joint probabilistic behaviour of precipitation extremes
using copulas and (2) to discuss the implications of the
probabilistic behaviour for occurrences of floods and
droughts and related impacts on agriculture in China.
1141
two days were filled in by average precipitation values
of neighbouring days. If consecutive days had missing
data, the missing values were replaced with long-term
averages of the same days. It was assumed that this
gap filling method would have no influence on the longterm temporal trend. Furthermore, the data consistency
was checked by the double-mass method and the result
showed that all the data series used in the study were
consistent (Zhang et al., 2009b, 2011). Eight extreme
precipitation indices were defined and are displayed in
Table I, which are similar to the precipitation indices used
in other studies (e.g. Tebaldi et al., 2006; Fatichi and
Caporali, 2009; Zhang et al., 2010). The NW and CDD
are the number of rainy days, and the maximum number
of consecutive dry days; the D90, P90, and I90 are
the number of days, total precipitation, and precipitation
intensity of the extreme heavy precipitation events; and
the D10, P10, and I10 are the number of days, total
precipitation, and precipitation intensity of the extreme
weak precipitation events.
3.
3.1.
Methodology
Marginal probability distributions
Extreme precipitation indices can be categorized into two
types: discrete and continuous. NW, D90, CDD, and
D90 are discrete indices, whereas P90, I90, P10, and
I10 are continuous indices. There are several discrete
probability distributions, e.g. uniform distribution, Poisson distribution, geometric distribution, binomial distribution, and negative binomial distribution (Spiegel et al.,
2000). Wilks (1999) employed geometric, negative binomial, and mixed geometric distributions to represent the
number of wet days in America. On the basis of the virtual attributes of precipitation indices, binomial, Poisson,
geometric, and negative binomial distributions were used
2. Data
Daily precipitation data from 590 rain gauge stations
covering a period of 1960–2005 were obtained from
the National Climate Center of China Meteorological
Administration. The spatial distribution of rain stations
is shown in Figure 1. Missing data of one day or
Copyright  2012 Royal Meteorological Society
Figure 1. Locations of the meteorological stations and river basins. The
black triangles denote meteorological stations. Numbers denote river
basins, i.e. 1, the Songhuajiang River; 2, the Liaohe River; 3, the Haihe
River; 4, the Yellow River; 5, the Huaihe River; 6, the Yangtze River;
7, the southeast rivers; 8, the Pearl River; 9, the southwest rivers; and
10, the northwest rivers.
Int. J. Climatol. 33: 1140–1152 (2013)
1142
Q. ZHANG et al.
Table I. Definitions of precipitation extreme indices.
Indices
NW
D90
P90
I90
CDD
D10
P10
I10
Definitions
Unit
Number of wet days in a year. The wet day is defined as the day with precipitation ≥1 mm
Annual number of days with daily precipitation exceeding the 90th percentile threshold. The 90th
percentile threshold is calculated based on the precipitation series of all wet days at each station
Total precipitation of D90 in a year
Precipitation intensity of D90 in a year
Maximum number of consecutive dry days of a year. The dry day is defined as the day with
precipitation <1 mm
Annual number of days with precipitation less than the 10th percentile threshold. The 10th percentile
threshold is calculated based on the precipitation of all wet days at each station
Total precipitation of D10 of a year
Precipitation intensity of D10 of a year
d
d
to analyse the marginal probability properties of NW,
D90, CDD, and D10. Moreover, generalized extreme
value (GEV), generalized Pareto (GP), Pearson III type,
lognormal, Wakeby, and exponential distributions were
analysed and the right distribution was selected for based
on the goodness-of-fit test.
The maximum likelihood estimate method was used
to estimate parameters of the discrete probability distribution, while the L-moments method (Hosking, 1990)
was applied to calculate parameters of the continuous probability distribution. The goodness-of-fit of the
probability distributions was evaluated using the Kolmogorov–Smirnov (K-S) test (Frank and Masse, 1951)
at >95% confidence level. After selecting the probability
distribution with high goodness-of-fit, the specific precipitation indices corresponding to different return periods,
denoted as z values, were computed. Let t denote return
period, the z value related to t can be obtained as follows:
z = F −1 (1 − 1/t) for NW, D90, P90, I90,
CDD, and D10
and
z = F −1 (1/t) for P10 and I10
(1)
(2)
where F −1 is the inverse cumulative distribution function. For NW, D90, P90, I90, CDD, and D10, values
≥z were considered; for P10 and I10, values ≤z were
considered.
3.2.
Copulas are a flexible representation of multivariate
distributions. Assume X and Y are two random variables,
with the marginal distributions as F (x) = P [X ≤ x]
and G(y) = P [Y ≤ y]. The joint distribution, H (x, y) =
P [X ≤ x, Y ≤ y], can be formulated using the copula
function C as follows:
H (x, y) = C[F (x), G(y)]
(3)
The Copula function, C, is the bivariate joint distribution
of X and Y . Copulas can be used for multivariate joint
distributions (Nelsen, 2006).
Copyright  2012 Royal Meteorological Society
d
mm
mm d−1
{(xk , yk )}nk=1 denotes the observed X and Y series the
size of which is n. Then, the empirical Copula, Ce , can
be expressed as follows:
Ce
i j
,
n n
=
ni,j
n
(4)
where 1 ≤ i, j ≤ n, x(i) denotes the rank i of the x series
arranged in ascending order; y(j ) denotes the rank j of the
y series arranged in the ascending order, and ni,j denotes
the number of observed values that xk ≤ x(i) , yk ≤ y(j ) .
The Gumbel–Hougaard copula, Clayton copula, Frank
copula, Gauss copula, and t copula are employed in
this study. The Gauss copula and t copula are families
of the elliptical copula family, and the coefficient of
linear correlation ρ is the parameter. The other three
copulas belong to the Archimedean copula family. Each
Archimedean copula was constructed using a different
generating unit ø with parameter θ.
3.3. Identification of joint probability distribution
The identification of a joint probability distribution follows the procedure proposed by Genest and Rivest
(1993):
(1) The Kendall correlation coefficient τ is given by
τ=
Copula functions
mm
mm d−1
d
sign[(xi − xj )(yi − yj )]
i<j
n(n − 1)
2
(5)
where n denotes size of the sample, i, j = 1, 2, . . . , n; if
xi ≤ xj and yi ≤ yj , then sign() = 1, else sign() = −1.
(2) For the Gumbel–Hougaard, Clayton, and Frank copulas, the generating unit parameter θ was computed
by the relation of θ and τ . For the Gauss and t copulas, parameter ρ was also calculated by τ .
(3) Construct the copula function with θ or ρ.
(4) Employ a statistical method, such as the Akaike
information criterion (AIC; Akaike, 1974), to select
the most appropriate copula family.
Int. J. Climatol. 33: 1140–1152 (2013)
COPULA-BASED SPATIO-TEMPORAL PATTERNS OF PRECIPITATION EXTREMES
3.4. Akaike information criterion
The AIC (Akaike, 1974) was used to evaluate the
goodness-of-fit of the copulas. Two segments were considered in AIC: bias of fit and the unreliability from the
number of the model parameters. AIC is expressed as
follows:
AIC = n log(RSS/n) + 2m
(6)
where n is the sample size, m is the number of parameters, and RSS is the residual sum of squares. The probability distribution function with the minimum AIC value
is the right choice.
3.5. Bivariate joint return period
For precipitation variables X and Y , let Fx (x) be the
marginal distribution of X, Fy (y) be the marginal distribution of Y , and F (x, y) be the joint distribution function
of these two variables. Two types of the bivariate joint
return periods (Salvadori and Michele, 2004) were used
in this study:
T{X>x,Y >y} =
1
P (X > x, Y > y)
1
(7)
=
1 − Fx (x) − Fy (y) + F (x, y)
T{X>x,Y ≤y} =
1
P (X > x, Y ≤ y)
1
=
Fy (y) − F (x, y)
(8)
where T{X>x,Y >y} denotes the joint return period with
both X and Y exceeding the specific threshold; T{X>x,Y ≤y}
denotes the joint return period with X exceeding
the specific thresholds and Y less than and equal
to the specific threshold; T{NW, CDD:X>x,Y >y} denotes
the joint return period of the event that NW and
CDD exceed their specific thresholds simultaneously;
T{P90, P10:X>x,Y ≤y} denotes the joint return period of the
event that P90 exceeds its specific threshold, and P10 is
less than and equal to its specific threshold. The bivariate
joint return periods of extreme precipitation indices and
related definitions are listed in Table II.
Table II. Joint return periods of extreme precipitation and their
meaning.
Return periods
T{NW,
CDD:X>x,Y >y}
T{D90,
D10:X>x,Y >y}
T{P90,
I90:X>x,Y >y}
T{P90,
P10:X>x,Y ≤y}
T{I90,
I10:X>x,Y ≤y}
T{D10,
The trend was detected by the MK test (Mann, 1945;
Kendall, 1955) and linear regression. The MK trend test is
a rank-based nonparametric method that does not require
any assumption about a distribution. It should be noted
that the persistence within a hydro-meteorological series
can heavily influence the MK test results (von Storch,
1995; Hamed and Rao, 1998).
Hamed and Rao (1998) proposed a modified MK test
based on the equivalent sample size to eliminate the
effect of persistence. In their modification, the modified
variance of the MK statistic was proposed to replace
the original one if the lag-i autocorrelation coefficients
were significantly different from zero. von Storch (1995)
Copyright  2012 Royal Meteorological Society
P10:X>x,Y ≤y}
Definition
Joint return period of the event that
numbers of wet days and dry days in a
year exceed their specific thresholds
Joint return period that D90 and D10
events occur simultaneously
Joint return period that P90 and I90
events occur simultaneously
Joint return period that P90 and P10
events occur simultaneously
Joint return period that I90 and I10
events occur simultaneously
Joint return period that D10 and P10
events occur simultaneously
suggested pre-whitening to eliminate the lag-1 autocorrelation before the use of the MK test. In pre-whitening,
if the lag-1 autocorrelation coefficient, c, was larger than
0.1, then the analysed time series (x1 , x2 , . . . , xn ) should
be replaced by (x2 − cx1 , x3 − cx2 , . . . , xn+1 − cxn ).
However, pre-whitening has the potential to underestimate the trend in a time series (Yue et al., 2002). Moreover, significant lag-1 autocorrelation is still detected
even after pre-whitening, because only lag-1 autocorrelation is considered in pre-whitening. The modified
MK considers lag-i autocorrelation and its robustness
has been demonstrated by Hamed and Rao (1998) and
was used successfully in a meteor-hydrological study by
Daufresne et al. (2009).
The modified MK test was used in this study to
analyse trends within the time series. Besides, a linear
regression was also employed to estimate the linear trend
in the series. The student t-test was then employed to
check the significance of the estimated linear trend. The
significance of trend was tested at the >95% confidence
level.
4.
4.1.
3.6. Trend detection
1143
Results
Case study
To show the computation procedure, we used data from
the Huiyang station in southeast China as a case study.
Parameters of probability functions were estimated for
eight extreme precipitation indices. Then, the K-S test
was used to evaluate the reliability of the probability
distribution function and the probability function with the
highest goodness-of-fit was accepted as the best choice.
The probability function with the largest p value by the
K-S test was the most appropriate choice. The p values
by the K-S test for the discrete precipitation indices are
provided in Table III, and the p values for the consecutive
precipitation indices are provided in Table IV.
It should be noted that due to the statistical characteristics, it is possible that parameters of a certain probability
Int. J. Climatol. 33: 1140–1152 (2013)
1144
Q. ZHANG et al.
Table III. p values of the K-S test for discrete precipitation
indices.
Distributions
Negative
binomial
Poisson
Geometric
Binomial
NW
D90
CDD
D10
0.7753a
N/A
0.8719a
N/A
0.2461
0.0471
N/A
0.4949
N/A
N/A
N/A
N/A
N/A
0.0544a
N/A
0.5315a
N/A = the distribution parameters cannot be estimated for the index,
or that distribution fails to pass the K-S test.
a The distribution passes the K-S test.
Table IV. p values of the K-S test for consecutive precipitation
indices.
GEV
P90
I90
P10
I10
0.9820
0.9591
0.6950
0.7044
GP
N/A
N/A
N/A
N/A
Pearson Lognormal Wakeby
ExpIII
onential
0.9819
0.9793
0.7174
0.7184
0.9842
0.9813
0.6889
0.7007
0.9995a
0.9871a
0.8818a
0.7398
N/A
N/A
N/A
N/A
N/A = the distribution parameters cannot be estimated for the index or
the distribution fails to pass the K-S test.
a The distribution passes the K-S test.
distribution cannot be estimated. For example, parameters of the negative binomial distribution can be estimated
for a time series, it is unnecessary that parameters of the
binomial distribution are obtained for the same series.
Besides, even though the parameters of a distribution are
available, the distribution failing to pass the K-S test will
still be ignored.
The goodness-of-fit of the probability density functions
of GEV, Pearson III, Wakeby, and exponential distributions for P90 were evaluated (Figure 2). It can be seen
from Table IV that the exponential distribution failed to
pass the K-S test. The p values of GEV and Pearson III
were similar. However, it can be observed from Figure 2
that these two functions fitted very similarly. The p value
for the Wakeby distribution was the largest, showing a
good goodness-of-fit. The 10 year return period for P90
was estimated with parameters obtained as above based
on Equations (1) and (2) (Table V). Different return periods for the extreme precipitation indices for the rainfall
stations considered in this study were estimated following
this computation procedure.
To illustrate the computation of joint return periods of
two extreme precipitation indices, an example computing
the joint return period for P90 and I90 was considered.
Figure 2. Probability density functions for P90 at the Huiyang station
as a case study.
Selection of the copula function was done following the
procedure proposed by Genest and Rivest (1993). Parameters of copulas were calculated by τ . AIC was used to
evaluate the goodness-of-fit of the copulas. Parameters
and AIC values of the copulas are shown in Table VI.
The t copula with the minimum AIC value was the
most appropriate copula for P90 and I90 at the Huiyuan
station. For the marginal distribution of P90 and I90,
the joint cumulative distribution function is shown in
Figure 3. The joint return period that P90 exceeding the
P90 with 10 year return period and I90 exceeding the P90
with 10 year return period occurred simultaneously, i.e.
T{P90, I90:X>x,Y >y} = 31.25 from Equation (7). The joint
return periods of other precipitation extremes were estimated by the same computation procedure as introduced
above.
4.2. Spatial distribution of precipitation indices
with 10 year return period
Increasing NW was identified in the direction from northwest to southeast China (Figure 4(a)). The maximum NW
was observed in the Pearl River basin and southern parts
of the Yangtze River basin. Thus, southeast China is characterized by abundant rainy days and northwest China by
Table VI. Parameters and AIC values for the copulas of P90
and I90 at the Huiyang station.a .
Gumbel
Clayton
Frank
Gauss
t
Parameter 1.4744 0.9487 3.1681 0.4841
0.4841
AIC
−15 954 −16 046 −16 036 −16 190 −16 199b
a Parameters,
θ, for the Gumbel, Clayton, and Frank copulas; parameters, ρ, for the Gauss and t copula functions.
b The copula functions with best fits.
Table V. Precipitation values corresponding to 10 year return periods at the Huiyang station.
Precipitation values (mm)
NW
D90
P90
I90
CDD
D10
P10
I10
123
15
1084.32
90.53
54
289
21.14
0.08
Copyright  2012 Royal Meteorological Society
Int. J. Climatol. 33: 1140–1152 (2013)
COPULA-BASED SPATIO-TEMPORAL PATTERNS OF PRECIPITATION EXTREMES
Figure 3. Joint CDF of the P90 and I90 at the Huiyang station.
scarce rainy days. Smaller changes can be observed for
CDD in space (Figure 4(b)) when compared with that of
NW (Figure 4(a)). CDD reaches its peak values in northwest China and the trough values in southeast China. The
northwest rivers, the southwest rivers, the upper Yellow
River, and the upper Yangtze River are dominated by
CDD being longer than 100 d and other regions by CDD
being below 50 d.
It can be observed from Figure 4(c) that D90 is
increasing from northwest to southeast China, indicating
higher occurrence probability of heavy rains in southeast
1145
China in comparison to northwest China. The opposite
spatial patterns of D10 (Figure 4(d)) can be found in
comparison with D90 (Figure 4(c)). Therefore, larger
occurrence probability of low precipitation is detected in
northwest China when compared with that in southeast
China (Figure 4(c) and (d)). In general, Figure 4(a)–(d)
imply that southeast China suffers the most extreme
strong precipitation and northwest China endures the
longest extreme weak precipitation and consecutive dry
days. This result illustrates the occurrence probabilities
or natural risks of floods and droughts in both space and
time across the entire country.
Figure 4(e) shows the largest P90 in the Pearl River
basin and the lower Yangtze River basin. Northwest
China is still characterized by smaller P90. Relatively
complicated spatial patterns of P10 can be found in
Figure 4(f). Generally, two areas are dominated by larger
P10 values, i.e. northeast China and the areas covered by
the upper Yangtze River basin, the Pearl River basin,
and the east parts of the southwest rivers. The lower P10
is found in the Yellow River basin, the northwest rivers,
the Haihe River, the Huaihe River, and the lower Yangtze
River.
I90 represents the extreme strong precipitation intensity. Figure 4(g) indicates that I90 increases from
northwest to southeast China. The maximum I90 value is
observed in the Pearl River basin. Besides, I90 larger than
Figure 4. Spatial distribution of precipitation indices corresponding to ten year return periods across China: (a) NW, (b) CDD, (c) D90, (d) D10,
(e) P90, (f) P10, (g) I90, and (h) I10.
Copyright  2012 Royal Meteorological Society
Int. J. Climatol. 33: 1140–1152 (2013)
1146
Q. ZHANG et al.
Figure 5. Spatial distribution of the modified Mann–Kendall trends for precipitation indices across China: (a) NW, (b) CDD, (c) D90, (d) D10,
(e) P90/ATW, (f) P10/ATW, (g) I90, and (h) I10. ATW, annual total precipitation.
60 mm d−1 was observed mainly in the lower Yangtze
River basin and the Pearl River basin, showing increasing precipitation extremes in these regions, which is in
agreement with the result by Zhang et al. (2011). I10, the
precipitation index showing extreme weak precipitation
intensity, is in a relative complex spatial pattern. Higher
I10 was found in the southern parts of the southwest
rivers, the lower Pearl River, and northeast China and
lower I10 was observed in other regions (Figure 4(h)).
Figure 4(e)–(h) indicates higher probability of heavy precipitation events in southeast China and weak precipitation in northwest China.
4.3.
Trends in precipitation indices
Figure 5 displays the spatial patterns of trends of precipitation indices. It can be seen that northwest China
and the southwest China are characterized by increasing NW, showing wetting tendency in these regions, and
the increasing rate is 0.1–0.2 d year−1 (Figure 6(a)). Significant decreasing NW can be observed in the upper
Pearl River basin, the upper Yangtze River basin, the
Yellow River basin, the Huaihe River basin, and parts
of northeast China, implying drying tendency in these
areas. The changing rate of NW is −0.1 to −0.2 d year−1
Copyright  2012 Royal Meteorological Society
(Figure 6(a)). NW changes in other regions are not statistically significant except some regions are distributed
sporadically with significant NW changes. The changing
magnitudes of NW in these regions are nearly 0 d year−1 .
Significant decreasing CDD can be found in parts of
the Tibet Plateau and the northwest China and the changing rate can reach −0.2 to −0.6 d year−1 (Figure 6(b)).
Increasing CDD with the changing rate of 0–0.2 d year−1
(Figure 6(b)) is detected in the Haihe River, the Yellow River, the Huaihe River, and north parts of the
Yangtze River (Figure 6(b)). Therefore, heavy drying tendency can be expected in these regions due to significant
decreasing NW and increasing CDD.
Northwest China and the Tibet Plateau tend to be
subjected to a wetting tendency (Zhang et al., 2011).
Figure 6(c) and (d) show the spatial distribution of D90
and D10. Similar but opposite spatial distribution properties can be found from Figure 6(c) and (d) for D90
and D10. Significant increasing (decreasing) D90 (D10)
is detected in the regions west of 100 ° E; the upper
Pearl River basin, the upper Yangtze River basin, the
Yellow River basin, and the Huaihe River basin and
parts of northeast China are characterized by significant decreasing (increasing) D90 (D10). The increasing
rate of D90 in northwest China and Tibet Plateau is
Int. J. Climatol. 33: 1140–1152 (2013)
COPULA-BASED SPATIO-TEMPORAL PATTERNS OF PRECIPITATION EXTREMES
1147
Figure 6. Spatial distribution of linear coefficients of precipitation indices across China: (a) NW; (b) CDD; (c) D90; (d) D10, d year−1 ;
(e) P90/ATW; (f) P10/ATW; (g) I90; and (h) I10. Unit for (a)–(d) is d year−1 ; unit for (e)–(f) is 10−2 % year−1 ; unit for (g) is mm year−1 ; and
unit for (h) is 10−2 mm year−1 .
0.04–0.08 d year−1 and the decreasing rate of D90 is
0 to −0.04 d year−1 (Figure 6(c)). The increasing and
decreasing rate of D10 is 0.1–0.2 and about −0.2 d
year−1 , respectively. It can be seen from Figure 6(c) and
(d) that the changing magnitude of D90 is smaller than
that of D10. Most regions of China are dominated by
nearly 0 d year−1 of D10 in the changing magnitude.
A similar phenomenon was found in the spatial distribution properties of P90/ATW and P10/ATW. P90/ATW
denotes the percentage of P90 to the annual total precipitation. Specifically, P90/ATW represents the percentage
of the precipitation of extreme heavy precipitation events
to the annual total precipitation. Similarly, P10/ATW
denotes the percentage of P10 (the precipitation of
extreme weak precipitation events) to the annual total
precipitation. It can be seen from Figure 6(e) that the
majority of regions in China are dominated by increasing
P90/ATW. Significant P90/ATW can be detected in the
lower Pearl River basin, the middle and the lower Yangtze
River basin, and the southern parts of the Huaihe River
basin. Other regions with significant increasing P90/ATW
are distributed sporadically across China without obvious
spatial patterns. Figure 6(f) shows that the regions characterized by significant increasing P90/ATW are roughly
Copyright  2012 Royal Meteorological Society
featured by significant decreasing P10/ATW, showing the
precipitation changes in these regions shifting to heavy
precipitation and to the extreme side. Figure 6(e) and
(f) shows distinctly different changing properties of the
changing magnitude of P90/ATW and P10/ATW when
compared with those of MK trends (Figure 6(e) and (f)).
Larger changing magnitude of P90/ATW and P10/ATW
can be found in northwest China but not in the regions
covered by significant MK trends. It should be due to the
higher nonlinear precipitation changes and larger changing variability in the east and southeast China when
compared with northwest China. The changing magnitude
of P90/ATW and P10/ATW in east and southeast China
is nearly zero. However, a large increase (decrease) in
P90/ATW (P10/ATW) can be found in northwest China
and parts of the Tibet Plateau regions. The absolute
changing rate is about 0.2–0.8 × 10−2 % year−1 .
Figure 5(g) shows that a majority of regions in east
China, southeast China, southwest China, and northwest
China are characterized by increasing I90. Significant
I90 is observed mainly in the lower Yangtze River
basin, the Pearl River basin, the southwest rivers, and
the north parts of northwest China. As for changes in
I10 (Figure 5(h)), significant I10 was detected mainly in
Int. J. Climatol. 33: 1140–1152 (2013)
1148
Q. ZHANG et al.
Figure 7. Spatial distribution of joint return period of different precipitation indices across China: (a) T{NW, CDD:X>x,Y >y} ; (b) T{D90,
(c) T{P90, I90:X>x,Y >y} ; (d) T{P90, P10:X>x,Y >y} ; (e) T{I90, I10:X>x,Y ≤y} ; and (f) T{D10, P10:X>x,Y ≤y} .
the regions east of 100 ° E. Parts of the region west of
100 ° E are characterized by significant increasing I10.
Figure 6(g) also indicates that most of the regions in
China are dominated by increasing trends of I90. The
changing magnitude is about 0–0.02 mm year−1 . The
largest increase is detected in the lower Pearl River basin,
the lower Yangtze River, and the Huaihe River basin,
which can reach 0.04 mm year−1 . The spatial distribution
of linear trends of I10 (Figure 6(h)) is similar to that of
the MK trends (Figure 5(h)). Decreasing trends in I10 can
be found mainly in southeast, southern, and southwest
China. The decrease is −0.02 to −0.08 × 10−2 mm
year−1 . The largest decrease is detected in southeastern
rivers, being −0.08 × 10−2 mm year−1 .
4.4.
Copula-based joint return periods
The spatial patterns of joint return periods of NW versus CDD (or NW-CDD thereafter) are the same for
other couples of precipitation indices, D90 versus D10,
P90 versus I90, P90 versus P10, I90 versus I10, and
D10 versus P10, as illustrated in Figure 7. Figure 7(a)
shows the distribution of joint return periods of NWCDD, T{NW, CDD:X>x,Y >y} . Larger joint return periods
imply smaller probability that NW and CDD occur simultaneously and vice versa. Figure 7(a) shows relatively
smaller probability that NW and CDD occurs simultaneously in one year in the Pearl River basin, the southeast rivers, the north parts of northeast China, the upper
Yangtze River basin and the upper and the lower Yellow
River basin, and also in the Huaihe River basin, implying larger risk of natural hazards, floods, or droughts
in these regions. In other words, precipitation changes
in these regions tend to shift to the extreme sides, i.e.
extreme heavy or low precipitation. The spatial distribution of T{D90, D10:X>x,Y >y} is illustrated in Figure 7(b).
Copyright  2012 Royal Meteorological Society
D10:X>x,Y >y} ;
Comparison between Figure 7(a) and (b) shows similar
spatial distribution properties of T{NW, CDD:X>x,Y >y} and
T{D90, D10:X>x,Y >y} .
Relatively higher probability of D90 and D10 can
be detected in the middle and the lower Pearl River
basin, the upper and the lower Yangtze River basin, the
southwest rivers, and parts of northeast China. Our previous investigations also found increasing precipitation
extremes or precipitation maxima in the lower Yangtze
River basin and the Pearl River basin (Zhang et al., 2008,
2009a, 2009b). Other regions are dominated by relatively longer joint return periods. The joint return periods
of >1000 years imply that it is almost impossible that
D90 and D10 occur simultaneously in one year. Thus,
in this sense, the increasing precipitation extremes occur
mainly in eastern, southeastern, southwestern, and northeast China.
The spatial distribution of T{P90, I90:X>x,Y >y} is shown
in Figure 7(c), showing joint probability that the frequency of extreme precipitation indices with both heavy
precipitation and high precipitation intensity. It can be
observed from Figure 7(c) that the joint probability of
P90 and I90 is relatively even in space across China.
The highest joint probability can be observed in the south
parts of northwest China. Besides, relatively higher probability can be found in northeast China, the lower Yangtze
River basin, and the upper Pearl River basin. Figure 7(d)
shows the spatial distribution of T{P90, P10:X>x,Y ≤y} aiming to investigate the joint probability that extreme
heavy and weak precipitation events occur simultaneously in the same year. Relatively higher joint probability (longer joint return periods) can be found in the
Pearl River basin, the lower Yangtze River basin, the
Huaihe River basin, and parts of northeast China and
southwest river. On the basis of the meaning of the
Int. J. Climatol. 33: 1140–1152 (2013)
COPULA-BASED SPATIO-TEMPORAL PATTERNS OF PRECIPITATION EXTREMES
T{P90, P10:X>x,Y ≤y} , the above-mentioned regions may be
subjected to a higher risk of heavy precipitation events.
Relatively lower joint probability is found in northwest
China. Roughly similar spatial distribution properties can
be found for T{I90, I10:X>x,Y ≤y} (Figure 7(e)) when compared with those for T{P90, P10:X>x,Y ≤y} (Figure 7(d)).
Higher joint probability is found along the coastal
regions of east China and also in the upper Yangtze River,
the Yellow River basin, the Huaihe River basin, and the
Haihe River basin, implying higher risk of heavy precipitation larger than the 10 year return period precipitation
value. The spatial distribution of T{D10, P10:X>x,Y ≤y} is
demonstrated in Figure 7(f), showing longer dry duration
and at the same time the low precipitation volume. It can
be seen from Figure 7(f) that relatively higher joint probability of D10 and P10 can be found in the regions west of
100 ° E, the Yellow River basin, the Huaihe, and the Haihe
River basins, implying drying tendency of these regions
reflected by longer no-rain days and correspondingly less
total precipitation.
5. Discussion
The spatial distribution of precipitation extremes exerts
a tremendous influence on the occurrence of floods
and droughts in both time and space. China is an
1149
agricultural country and food requirements are heavily dependent on agricultural development and production. In this sense, analysis of precipitation extremes in
both time and space is of great scientific and practical value in the socioeconomic development of China.
Many studies have addressed the changing characteristics of precipitation extremes (e.g. Zhai et al., 1999;
Zhang et al., 2008, 2011). However, no such reports are
available in China concerning probabilistic characteristics of precipitation extremes based on copula functions.
Besides, we link the spatial distribution of precipitation extremes to the influence of floods and droughts on
agriculture. Discussions on the implications of precipitation extremes for agriculture are also presented in this
study.
Figure 8 illustrates the province-based statistics of population, crop areas, and flood- and drought-affected crop
area. The bars inside provinces are the MK trend results
reflected by the province-based statistics. The significance of trend was detected at the >95% confidence
level. Related time intervals of the data can be referred
to the complimentary materials in Table VII. The first
glance at Figure 8 shows that the population of China
is increasing, particularly in Beijing, Guangdong, and
Jiangsu. Increasing trends can also be observed in the
crop area in most provinces of China, except Jiangsu,
Shannxi, Guangdong, Shanxi, Tijin City, Beijing City,
Figure 8. Province-based changes in population growth, crop area, and flood- and drought-affected crop areas over China.
Copyright  2012 Royal Meteorological Society
Int. J. Climatol. 33: 1140–1152 (2013)
1150
Q. ZHANG et al.
Table VII. Length of time series of population growth, crop fields, flood-affected crop fields, and drought-affected fields in the
provinces of China.
Provinces
Population
Crop area
Flood-affected crop area
Drought-affected crop area
Beijing
Tianjin
Hebei
Shanxi
Inner Mongolia
Liaoning
Jilin
Heilongjiang
Jiangsu
Zhejiang
Anhui
Fujian
Jiangxi
Shandong
Henan
Hubei
Hunan
Guangdong
Guangxi
Hainan
Chongqin
Sichuan
Guizhou
Yunnan
Tibet
Shannxi
Gansu
Qinghai
Nixia
Xinjiang
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1960–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
1978–2000
/
1960–2000
1960–1998
/
/
/
1960–1985
1960–1998
1960–1987
1960–2000
/
/
1960–2000
1960–2000
/
/
1960–2000
1960–1994
1960–2000
/
/
/
1960–2000
/
/
1960–2000
1960–2000
1960–1987
/
/
1972–2000
1960–2000
/
/
1960–1994
/
/
1960–1985
1960–1987
1960–2000
/
1960–1990
/
1960–2000
/
1960–1999
1960–2000
1960–1997
1960–1993
/
/
1960–2000
1960–2000
/
/
1963–1990
1960–2000
1960–1987
/
1960–1985
/ = no records are available.
and Liaoning. However, the focus of this study is on the
flood- and drought-affected crop areas. It can be shown
in Figure 8 that crops are easily affected by droughts in
the provinces of north China, such as Shandong, Tianjin
City, Heilongjiang, Shannxi, and Hubei. However, floodaffected crop areas are observed mainly in the provinces
of the south China, such as Guangdong, Guangxi, Hunan,
Guizhou, and Zhejiang. The drought-affected crop areas
in northwest China are increasing but not statistically
significant.
The spatial distribution of flood- and drought-affected
crop areas is in agreement with that of precipitation
extremes. Precipitation is relatively abundant in the south
China, which is reflected by the spatial patterns of
precipitation indices of the 10 year return periods in
Figure 4 such as NW, P90, and P10. In general, the
Yangtze River and Pearl River basins are characterized
by relatively more precipitation than other river basins,
particularly the basins in northwest China. Northwest
China is having a wetting tendency, which is mirrored
by increasing wet days and decreasing consecutive dry
days.
Copyright  2012 Royal Meteorological Society
In southeast China, the number of consecutive dry days
is increasing and precipitation intensity defined by the
mean daily precipitation of rainy days with daily precipitation exceeding the 90th percentile is also increasing,
showing a higher risk of heavy rains. Increasing CDD in
southeast China shows a higher risk of the occurrence of
droughts. In this sense, southeast China will be subjected
to increasing hazard risks of both droughts and floods.
The lower Pearl River basin is economically developed
with many mega-cities. The East River, a tributary of
the Pearl River, is the source of water supply for Shenzhen and Hong Kong, where about 80% of Hong Kong’s
annual water demands are met by the East River. Therefore, the precipitation changes shifting to the extreme
sides in the Pearl River basin mean much for the water
resource management and sustainable development of the
regional social-economy.
The regions covered by the Yellow River basin, the
Huaihe River basin, and the Haihe River basin are
characterized by a drying tendency as reflected by the
increasing number of consecutive dry days, i.e. CDD
and decreasing wet days, i.e. NW. D10 is increasing
but P10/ATW is decreasing. The increasing rate of D10
Int. J. Climatol. 33: 1140–1152 (2013)
COPULA-BASED SPATIO-TEMPORAL PATTERNS OF PRECIPITATION EXTREMES
in north China is 0.2–0.4 d year−1 , implying weak
precipitation.
Different climate systems control precipitation changes
over China. Precipitation changes in the regions east of
100 ° E are controlled mainly by the east Asian summer
monsoon (Wang et al., 2004). Our previous studies
indicated the weakening of east Asian summer monsoon
after about the mid-1970s and increasing geopotential
height in north China, South China Sea, and west Pacific
regions, all of which combine to negatively affect the
northward propagation of vapour flux. Besides, weaker
east Asian summer monsoon in recent decades does
not benefit the northward propagation of water vapour
flux and has potential to cause increasing (decreasing)
moisture content and moisture budget in the regions south
(north) to the Yangtze River basin (Zhang et al., 2008,
2011).
Precipitation changes are heavily affected by the transport of moisture in the latitudinal direction (Jin et al.,
2006). Increasing precipitation in northwest China should
be attributed to the increasing geopotential height in
Siberia and the decreasing geopotential height in the
Iran Plateau. Besides, the increasing water vapour convergence after 1987 also contributes to the increasing
precipitation in the western part of northwest China.
However, the precipitation changes in the eastern part
of the northwest China are still partly influenced by the
strength variations in the east Asian summer monsoon
(Chen and Dai, 2009).
6. Conclusions
The probabilistic behaviours of precipitation extremes
based on copulas are investigated in both space and
time. Trends and changing magnitudes of precipitation
extremes are also studied using the modified MK trend
test and linear regression. The following conclusions are
drawn from this study:
(1) Precipitation is increasing from northwest to southeast China. Regions west of 100 ° E are dominated by
increasing NW; the decreasing NW is found mainly
in the regions west of 100 ° E. Significant decreasing NW is observed in the Yellow River basin, the
Huaihe River basin, the upper Yangtze River, and the
upper Pearl River basin, and these regions are also
characterized by significant increasing CDD. These
results imply a wetting tendency in the northwest
China and a drying tendency in northern China.
(2) In south China, NW is decreasing but is not significant and is increasing in southeast China with parts
of the regions dominated by significant increasing
CDD. The percentage of P90 to the annual total precipitation and I90 are both increasing in south China,
especially in the lower Yangtze River basin and the
Pearl River basin. Besides, larger occurrence probability of heavy precipitation events is also found in
these regions, implying a higher risk of flood hazards in the lower Yangtze River basin and the Pearl
Copyright  2012 Royal Meteorological Society
1151
River basin. Moreover, joint return periods of the
events that P90 and I90 are both exceeding their
10 year return period values shows larger probability
of heavy precipitation in the regions east of 100 ° E,
implying that precipitation changes in east China are
shifting to the extreme side. Extreme tendency of
precipitation in northwest China is not evident.
(3) The spatial distribution of flood- and drought-affected
crop areas is in agreement with that of precipitation
extremes, showing a considerable influence of precipitation changes, particularly the variations in precipitation extremes, on the occurrence of floods and
droughts. Generally, agriculture in the south China
is mostly affected by floods; however, agriculture
in north China is mostly affected by droughts. The
drought-affected crop area in the northwest China is
increasing but is not significant at >95% confidence
level, which should be due to increasing precipitation
in recent decades. A drying tendency reflected by
the increasing number of consecutive non-rain days
should be paid enough attention. Generally, the precipitation extremes in the regions east of 100 ° E tend
to be intensifying and enhancing. It should be noted
here that the regions east of 100 ° E are usually heavily populated and bears the heavy responsibility for
agricultural production and socioeconomy of China.
Therefore, effective water resource management and
scientific management of agricultural activities and
related water-saving irrigation facilities are urgently
required for the sustainable development of socioeconomy and enhancing social resilience and human
mitigation of natural hazards.
Acknowledgements
This work was financially supported by Xinjiang Technology Innovative Program (Grant Nos. 201001066 and
200931105), the National Natural Science Foundation of
China (Grant Nos. 41071020 and 50839005), the Project
of the Guangdong Science and Technology Department
(Grant Nos. 2010B050800001 and 2010B050300010),
and by a grant from the Research Grants Council of
the Hong Kong Special Administrative Region, China
(Project No. CUHK405308). Thanks should be owed to
the National Climate Centre of China for providing meteorological data. The last but not the least, our cordial
gratitude should also be extended to the editor, Prof. Dr.
Glenn McGregor, and reviewers for their constructive
and pertinent comments and suggestions, which greatly
helped improve the quality of this article.
References
Akaike H. 1974. A new look at the statistical model identification.
IEEE Transactions on Automatic Control 19(6): 716–723.
Allen M, Ingram WJ. 2002. Constraints on future changes in climate
and the hydrologic cycle. Nature 419: 224–232.
Arnell NW. 1999. Climate change and global water resources. Global
and Environmental Change 9: S31–S49.
Chen DD, Dai YJ. 2009. Characteristics and analysis of typical
anomalous summer rainfall patterns in Northwest China over the
Int. J. Climatol. 33: 1140–1152 (2013)
1152
Q. ZHANG et al.
last 50 years. Chinese Journal of Atmospheric Sciences 33(6):
1247–1258 (in Chinese).
Daufresne M, K Lengfellner, U Sommer. 2009. Global warming
benefits the small in aquatic ecosystems. Proceedings of the National
Academy of Sciences of the United States of America 106(31):
12788–12793.
De Michele C, Salvadori G, Canossi M, Petaccia A, Rosso R. 2005.
Bivariate statistical approach to check adequacy of dam spillway.
Journal of Hydrologic Engineering 10(1): 50–57.
Easterling RD, Meehl AG, Parmesan C, Changnon AS, Karl RT,
Mearns OL. 2000. Climate extremes: observations, modeling, and
impacts. Science 289: 2068–2074.
Fatichi S, Caporali E. 2009. A comprehensive analysis of changes
in precipitation regime in Tuscany. International Journal of
Climatology 29(13): 1883–1893.
Frank J, Masse J. 1951. The Kolmogorov–Smirnov test for goodness of
fit. Journal of the American Statistical Association 46(253): 68–78.
Freund JE. 1961. A bivariate extension of the exponential distribution.
Journal of the American Statistical Association 56: 71–977.
Genest C, Rivest LP. 1993. Statistical inference procedures for
bivariate Archimedean copulas. Journal of the American Statistical
Association 88(423): 1034–1043.
Groisman PY, Karl TR, Easterling DR, Knight RW, Jameson PF,
Hennessy KJ, Suppiah R, Page CM, Wibig J, Fortuniak K, Razuvaev
V, Douglas A, Rorland E, Zhai PM. 1999. Changes in probability of
heavy precipitation: important indicators of climatic change. Climatic
Change 42: 243–283.
Hamed KH, AR Rao. 1998. A modified Mann–Kendall trend test for
autocorrelated data. Journal of Hydrology 204(1–4): 182–196.
Hashino M. 1985. Formulation of the joint return period of two
hydrologic variates associated with a Poisson process. Journal of
Hydroscience and Hydrolic Engineering 3(2): 73–84.
Hosking JRM. 1990. L-moments: analysis and estimation of
distributions using linear combinations of order statistics. Journal
of the Royal Statistical Society 52(1): 105–124.
Jin LY, Fu JL, Chen FH. 2006. Spatial and temporal distribution of
water vapor and its relationship with precipitation over the Northwest
China. Journal of Lanzhou University 42(1): 1–5 (in Chinese).
Kao SC, Govindaraju RS. 2008. Trivariate statistical analysis of
extreme rainfall events via the Plackett family of copulas. Water
Resources Research 44: W02415, DOI: 10.1029/2007WR006261.
Kao SC, Govindaraju RS. 2010. A copula-based joint deficit index for
droughts. Journal of Hydrology 380: 121–134.
Kendall MG. 1955. Rank Correlation Methods. Griffin: London.
Leonard M, Metcalfe A, Lambert M. 2008. Frequency analysis
of rainfall and streamflow extremes accounting for seasonal and
climatic partitions. Journal of Hydrology 348: 135–147.
Mann HB. 1945. Nonparametric tests against trend. Econometrica 13:
245–259.
Nelsen RB. 2006. An Introduction to Copulas. Springer Science:
Portland, 7–269.
Salvadori G, Michele C. 2004. Frequency analysis via copulas:
theoretical aspects and applications to hydrological events. Water
Resource Research. DOI: 10.1029/2004WR003133.
Singh VP, Zhang L. 2007. IDF curves using the Frank Archimedean
copula. Journal of Hydrologic Engineering 12(6): 651–662.
Song S, Singh VP. 2010a. Meta-elliptic copulas for drought frequency
analysis of periodic hydrologic data. Stochastic Environmental
Research and Risk Assessment 24(3): 425–444.
Song S, Singh VP. 2010b. Frequency analysis of droughts using
the Plackett copula and parameter estimation by genetic algorithm.
Stochastic Environmental Research and Risk Assessment 24(5):
783–805.
Copyright  2012 Royal Meteorological Society
Spiegel MR, Schiller J, Srinivasan RA. 2000. Outlines of Theory and
Problems of Probability and Statistics, 2nd edn. McGraw-Hill: USA,
2–7.
von Storch H. 1995. Misuses of statistical analysis in climate research.
In Analysis of Climate Variability: Applications of Statistical
Techniques. Springer-Verlag: Berlin, 11–26.
Suppiah R, Hennessy K. 1998. Tends in seasonal rainfall, heavy raindays, and number of dry days in Australia 1910–1990. International.
Journal of Climatology 18: 1141–1155.
Tebaldi C, Hayhoe K, Arblaser JM, Meechl GA. 2006. Going to
the extremes, an inter-comparison of model-simulated historical and
future changes in extreme events. Climatic Change 79: 185–211.
Vörösmarty CJ, Mclntyre PB, Gessner MO, Dudgeon D, Green P,
Glidden S, Sullivan CA, Liermann CR, Davies PM. 2010. Global
threats to human water security and river biodiversity. Nature 467:
555–561.
Wang BJ, Huang YX, He JH. 2004. Relationship between moisture
transportation during the East Asian Monsoon period and the
droughts in the northwest China. Plateau Meteorology 23(6):
912–918.
Wilks DS. 1999. Interannual variability and extreme-value characteristics of several stochastic daily precipitation models. Agricultural
and Forest Meteorology 93: 153–169.
World Meteorological Organization (WMO). 2003. Statement on the
Status of Global Climate in 2003. WMO Publication No. 966. WMO:
Geneva, Switzerland.
Yue S, Pilon P, Phinney B, Cavadias G. 2002. The influence of
autocorrelation on the ability to detect trend in hydrological series.
Hydrological Processes 16(9): 1807–1829.
Zhai PM, Ren FM, Zhang Q. 1999. Detection of trends in China’s
precipitation extremes. Acta Meteorologica Sinica 57(2): 208–216.
Zhang L, Singh VP. 2006. Bivariate flood frequency analysis using
the copula method. Journal of Hydrologic Engineering 11(2):
150–164.
Zhang L, Singh VP. 2007a. Bivariate rainfall frequency distributions
using Archimedean copulas. Journal of Hydrology 332: 93–109.
Zhang L, Singh VP. 2007b. Gumbel–Hougard copula for trivariate
rainfall frequency analysis. Journal of Hydrologic Engineering 12(4):
431–439.
Zhang Q, Xu C-Y, Becker S, Zhang ZX, Chen YD, Coulibaly M.
2009a. Trends and abrupt changes of precipitation extremes in the
Pearl River basin, China. Atmospheric Science Letter 10: 132–144.
Zhang Q, Xu C-Y, Gemmer M, Chen YD, Liu C-L. 2009b. Changing
properties of precipitation concentration in the Pearl River basin,
China. Stochastic Environmental Research and Risk Assessment 23:
377–385.
Zhang Q, Xu C-Y, Chen XH, Zhang ZX. 2011. Statistical behaviors
of precipitation regimes in China and their links with atmospheric
circulation 1960–2005. International Journal of Climatology. DOI:
10.1002/joc.2193.
Zhang Q, Xu C-Y, Zhang ZX, Chen YD, Liu C-L. 2008. Spatial and
temporal variability of precipitation maxima during 1960–2005 in
the Yangtze River basin and possible association with large-scale
circulation. Journal of Hydrology 353: 215–227.
Ziegler AD, Sheffield J, Maurer EP, Nijssen B, Wood EF, Lettenmaier
DP. 2003. Detection of intensification in global- and continentalscale hydrological cycles: temporal scale of evaluation. Journal of
Climate 16: 535–547.
Zolina O, Simmer C, Gulev KS, Kollet S. 2010. Changing structure
of European precipitation: longer wet periods leading to more
abundant rainfalls. Geophysical Research Letters 37: L06704, DOI:
10.1029/2010GL042468.
Int. J. Climatol. 33: 1140–1152 (2013)