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The high precipitation variability over North Africa presents a major challenge for the population and the infrastructure in the region. The last decades have seen many flood events caused by extreme precipitation in this area. There is a strong need to identify the most relevant atmospheric predictors to model these extreme events. In the present work, the effect of 14 different predictors calculated from NCEP-NCAR reanalysis, with daily to seasonal time steps, on the maximum annual precipitation (MAP) is evaluated at six coastal stations located in North Africa (Larache, Tangier, Melilla, Algiers, Tunis, and Gabes). The generalized extreme value (GEV) B-spline model was used to detect this influence. This model considers all continuous dependence forms (linear, quadratic, etc.) between the covariates and the variable of interest, thus providing a very flexible framework to evaluate the covariate effects on the GEV model parameters. Results show that no single set of covariates is valid for all stations. Overall, a strong dependence between the NCEP-NCAR predictors and MAP is detected, particularly with predictors describing large-scale circulation (geopotential height) or moisture (humidity). This study can therefore provide insights for developing extreme precipitation downscaling models that are tailored for North African conditions.
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Atmospheric Predictors for Annual Maximum Precipitation in North Africa
BOUCHRA NASRI
Canada Research Chair on the Estimation of Hydrometeorological Variables, Eau Terre Environnement Research Centre,
Institut National de la Recherche Scientifique, Québec, Québec, Canada
YVES TRAMBLAY
UnitéMixte de Recherche Hydrosciences, Institut de Recherche pour le Développement, Montpellier, France
SALAHEDDINE ELADLOUNI
Département de Mathématique et de Statistique, Universitéde Moncton, Moncton, New Brunswick, Canada
ELKE HERTIG
Institute of Geography, University of Augsburg, Augsburg, Germany
TAHA B. M. J. OUARDA
Canada Research Chair on the Estimation of Hydrometeorological Variables, Eau Terre Environnement Research Centre,
Institut National de la Recherche Scientifique, Québec, Québec, Canada, and Masdar Institute of Science
and Technology, Abu Dhabi, United Arab Emirates
(Manuscript received 5 May 2014, in final form 21 July 2015)
ABSTRACT
The high precipitation variability over North Africa presents a major challenge for the population and the
infrastructure in the region. The last decades have seen many flood events caused by extreme precipitation in
this area. There is a strong need to identify the most relevant atmospheric predictors to model these extreme
events. In the present work, the effect of 14 different predictors calculated from NCEP–NCAR reanalysis,
with daily to seasonal time steps, on the maximum annual precipitation (MAP) is evaluated at six coastal
stations located in North Africa (Larache, Tangier, Melilla, Algiers, Tunis, and Gabès). The generalized
extreme value (GEV) B-spline model was used to detect this influence. This model considers all continuous
dependence forms (linear, quadratic, etc.) between the covariates and the variable of interest, thus providing a
very flexible framework to evaluate the covariate effects on the GEV model parameters. Results show that no
single set of covariates is valid for all stations. Overall, a strong dependence between the NCEP–NCAR
predictors and MAP is detected, particularly with predictors describing large-scale circulation (geopotential
height) or moisture (humidity). This study can therefore provide insights for developing extreme precipitation
downscaling models that are tailored for North African conditions.
1. Introduction
Heavy precipitation events are causing extensive
damage to the populations and infrastructure of the
countries located in the southern part of the Mediter-
ranean basin. The last decades saw several deadly flood
events caused by extreme precipitation, including the
2001 flood near Algiers, Algeria, causing more than 700
fatalities (Argence et al. 2008), the 1969 floods in the
region of Kairouan, Tunisia, with 150–400 fatalities
(Poncet 1970), or the 1995 flood in the Ourika valley,
Morocco, with more than 200 fatalities (Saidi et al.
2003). To better mitigate the impacts of these extreme
events, there is a need to evaluate their predictability on
different time scales. In particular, it is necessary to es-
timate their return periods in a climate change context
Corresponding author address: Bouchra Nasri, INRS-ETE, 490
Rue de la Couronne, Québec, QC G1K 9A9, Canada.
E-mail: bouchra.nasri@ete.inrs.ca
APRIL 2016 N A S R I E T A L . 1063
DOI: 10.1175/JAMC-D-14-0122.1
Ó2016 American Meteorological Society
since several countries experienced an increased vul-
nerability to these events during the last decade (Di
Baldassarre et al. 2010). Several recent studies have
focused on seasonal precipitation and its extremes in the
Mediterranean region, with the objective of identifying
the associated large-scale patterns and the relevant
predictors (Knippertz et al. 2003;Xoplaki et al. 2004;
Martín-Vide and Lopez-Bustins 2006;Toreti et al. 2010;
Tramblay et al. 2011;Kallache et al. 2011;Hertig et al.
2012;Tramblay et al. 2012a,b;Hertig et al. 2013;
Ouachani et al. 2013;Donat et al. 2014). Indeed, to re-
solve the mismatch of scales between general circulation
models and the locations of interest for impact studies,
there is a need to develop downscaling techniques tai-
lored for extreme precipitation (Fowler et al. 2007;
Maraun et al. 2010a). To overcome the limitations of
climate models in reproducing extremes (Sillmann et al.
2013), several studies have used covariates in non-
stationary extreme precipitation frequency analysis
(e.g., Vrac and Naveau 2007;Aissaoui-Fqayeh et al.
2009;Beguería et al. 2010;Friederichs 2010;Kallache
et al. 2011;Tramblay et al. 2011;Maraun et al. 2010b;
Ouachani et al. 2013;El Adlouni and Ouarda 2009;
Cannon 2010;Ouarda and El Adlouni 2011). However,
even if several authors have shown the efficiency of at-
mospheric humidity and moisture flux as predictors for
daily rainfall modeling and downscaling (Cavazos and
Hewitson 2005;Bliefernicht and Bárdossy 2007;
Tramblay et al. 2011,2013), the best predictors may
differ from one site to another (Kallache et al. 2011;
Hertig et al. 2013;Chandran et al. 2016). In addition, it
should be noted that the above studies have mostly ap-
plied polynomial dependence (linear or quadratic) be-
tween the covariate and the variable of interest. In the
present work, the nonstationary generalized extreme
value (GEV) model with B-spline dependent function
(Nasri et al. 2013;Chavez-Demoulin and Davison 2005)
is applied. B-spline functions are piecewise polynomial
functions that have certain advantages. A smoothing
B-spline basis is independent of the response variable
and depends only on the following information: (i) the
extent of the explanatory variable, (ii) the number and
position of the knots, and (iii) the degree of the B-spline.
These advantages make it a suitable option for use in the
GEV model with covariates to explain the effect of co-
variates on the response variable. Therefore, the goal of
this study is to identify relevant large-scale predictors
influencing the annual maximum precipitation at coastal
stations in the southern part of the Mediterranean re-
gion using the GEV B-spline model. This model will
help describe the predictors’ influence on the pre-
cipitation records within the study period. A number of
studies on the impact of climate variability on extreme
precipitation in the Mediterranean region have em-
ployed atmospheric–oceanic teleconnection indices
such as the North Atlantic Oscillation (NAO; Wanner
et al. 2001), the Mediterranean oscillation (Conte et al.
1989), or the western Mediterranean oscillation (WEMO)
(Knippertz et al. 2003;Vicente-Serrano et al. 2009).
However, in Morocco Tramblay et al. (2012a) observed a
possible dependence of precipitation extremes with these
indices only at 2 stations (Larache and Tangier) out of 10.
In the present study, we tested the effect of different
predictors measured with NCEP–NCAR reanalysis
data to evaluate their influence on the maximum annual
precipitation (MAP) time series. To our knowledge, no
studies have previously examined these extreme precip-
itation events and their relationship to large-scale atmo-
spheric influences in this area at the daily time step with
rain gauge data, mainly because of the limited access to
the data. Since reanalysis data are available at a spatial
scale similar to that of global circulation models (GCMs),
this study provides the first step toward the development
of extreme precipitation downscaling methods that are
tailored for North African conditions.
2. Datasets
In the present study, we collected long daily pre-
cipitation time series maintained by the governmental
hydrological services of Algeria [Agence Nationale des
Ressources Hydrauliques (ANRH)], Morocco [Di-
rection de la Recherche et de la Planification de l’Eau
(DRPE)], and Tunisia [Direction Générale des Re-
ssources en Eau (DGRE)]. The daily data of the Melilla
station located in northern Morocco were obtained
from the European Climate Assessment and Dataset
(ECAD; http://eca.knmi.nl). The data from each station
were carefully scrutinized, in particular to look for shifts,
absurd values, and missing data (Tramblay et al. 2013).
The stations that were subsequently selected had less
than 5% missing days between September and May. The
years with more than 5% missing days during this period
were discarded. Figure 1 illustrates the geographic lo-
cation of all stations, and Table 1 presents a description
of the selected stations with long precipitation records.
Reanalysis data from the National Centers for Envi-
ronmental Prediction (NCEP; Kalnay et al. 1996;Kistler
et al. 2001) are used to compute several large-scale
predictors. Various variables were extracted to be tested
in the model; the selection of covariates is based on the
previous studies of Cavazos and Hewitson (2005),
Kallache et al. (2011),Tramblay et al. (2011), and Hertig
et al. (2013). The NCEP–NCAR reanalysis data have
been selected over more recent products such as
ERA-Interim because the time span of the NCEP–
1064 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 55
NCAR reanalysis is larger and encompasses the whole
period of observations, up to the present. The advan-
tages of recent reanalysis products are manifold, in-
cluding new atmospheric and assimilation systems and
finer grid spacing. However, they cover only the recent
period (from 1979 to present for MERRA, CFS re-
analysis, or ERA-Interim; Hofer et al. 2012). Thus the
advantage of the choice of the NCEP–NCAR reanalysis
is to cover the whole period where observations are
available using a single reanalysis product in order to
identify possible associations with large-scale climate
dynamics. It must be noted that our goal is not to check
the adequacy of the particular NCEP–NCAR reanalysis
product but to evaluate if the distribution of extreme
precipitation can be related to large-scale predictors, if
the same predictors are valid for different stations, and
at which time scales the large-scale forcings are relevant.
For these objectives, the bias of a given reanalysis
product compared to other products is of little rele-
vance, and because of the strong interannual variability
of precipitation in North Africa, it is important to
evaluate the relationships with large-scale dynamics
over long time periods to obtain robust results. The
gridded NCEP–NCAR data (six grid cells covering the
study area) were interpolated by the inverse distance
method to the station locations in order to provide in-
dividual descriptor sets for each station. The selected
variables include the following:
dgeopotential height at 500 and 850 hPa (geopot_500
and geopot_850),
dvertical velocity at 500 and 850 hPa and at surface
(omega_500, omega _850, and omega _surf),
dpotential temperature at surface (ptemp_surf),
dprecipitable water content (pwater_surf),
drelative humidity at surface (rhum_surf),
dspecific humidity at 500 and 850 hPa (shum_500 and
shum_850),
dmean sea level pressure (slp_surf),
dsurface temperature (temp_surf),
dzonal wind at surface (uwind_surf), and
dmeridional wind at surface (vwind_surf).
The homogeneity of these covariates has been
assessed by following Pettitt (1979) and by using the
modified version of the standard normal homogeneity
test (SNHT) by Khaliq and Ouarda (2007). Indeed, the
gradual introduction of satellite data into reanalysis
products can introduce an artificial changepoint leading
FIG. 1. Geographic location of all stations (three selected stations in Morocco, one in Algeria,
and two in Tunisia).
TABLE 1. Description of the selected stations with long records of precipitation.
Station Country Lat Lon Alt (m) Record length (yr) Starting year Ending year
Algiers Algeria 36.7483.068140 47 1951 2005
Larache Morocco 35.18826.1585 51 1942 2011
Tangier Morocco 35.77825.8085 33 1972 2006
Melilla Morocco 35.29822.94847 46 1907 2009
Gabès Tunisia 33.88810.1084 57 1950 2009
Tunis Tunisia 36.83810.23866 58 1950 2009
APRIL 2016 N A S R I E T A L . 1065
to the false detection of trends or homogeneity breaks
(Sterl 2004). The Pettitt and SNHT tests agree only on a
significant changepoint at the 5% level in relative hu-
midity, in 1957 for SNHT and in 1963 for the Pettitt test.
Therefore, no changepoints are detected in the beginning
of the 1980s following the introduction of satellite data.
These covariates are considered at different time
steps. In the first case, we considered the maximum
observed daily precipitation during the extended winter
season (October–March) and the simultaneous daily
covariate in the reanalysis data associated with this ex-
treme rainfall event. This gives one observation of
maximum daily winter rainfall and its associated co-
variate for each year (hereafter case 1). In case 2, we
considered the maximum winter precipitation and the
average value of each covariate 5 days before the date of
the annual maximum rainfall during the winter. These
two cases can be considered as dealing with the short-
term effect of covariates on MAP. In case 3, we calcu-
lated the 30-day average of the covariate before the date
of maximum winter precipitation. Finally, in case 4, we
considered the maximum daily winter precipitation and
the value of each covariate for the entire season
(October–March average). These last two cases can be
considered as dealing with the long-term effect of co-
variates on MAP.
3. Methods
For modeling extreme rainfall events, we used the
GEV distribution (Coles 2001).TheroleoftheGEV
distribution is to describe a sample that follows a
maximum of distributions introduced by Fisher and
Tippett (1928). The GEV distribution is flexible and
has been the subject of several theoretical studies
and applications for modeling extreme flood, pre-
cipitation, and wind events (El Adlouni et al. 2007;
Hundecha et al. 2008). The development of stationary
GEV distribution models for univariate extreme value
analysis can be found in the literature (Coles 2001;
Olsen et al. 1999). The use of this distribution in the
frequency analysis of extreme events is based on a
number of specific hypotheses concerning the variable
of interest. Indeed, the observations must be in-
dependent and identically distributed. However, the
stationarity assumption is often not met for observed
hydroclimatic datasets (Khaliq et al. 2006). In this case,
the distribution parameters and the distribution itself
could be changing in time. Therefore, it is essential to
develop the GEV model in the multivariate space,
where extreme events can be associated with other
variables. To model the relationship between the co-
variates and the extreme variable of interest, we can
use the GEV B-spline approach (Nasri et al. 2013). This
approach has been developed to describe the associa-
tion of an external covariate with the variable of
interest. The estimation of the parameters of the GEV
B-Spline model is done in a Bayesian framework to
obtain the posterior distribution by applying Markov
chain Monte Carlo (MCMC) algorithms.
a. The GEV distribution
The GEV distribution is characterized by three
parameters: the location m,scales,andshapejparameters.
Depending on the value of the shape parameter we have
three types of extreme value distributions—namely, the
Gumbel (j50), Fréchet (j.0), and Weibull (j,0).
Considering a sample Y5(y1,,yn), the GEV distri-
bution function is as follows:
F(y,m,s,j)5expn2h11jy2m
si2(1/j)oj0
F(y,m,s,j)5exph2exp2y2m
si j50.
(1)
This classical GEV distribution is based on the statio-
narity assumption and does not consider the de-
pendence of extreme events on other variables. In the
following section, the nonstationary GEV approach is
presented to consider the effect of a covariate on
extreme values.
b. The nonstationary GEV B-spline model
In the nonstationary case of a GEV distribution, the
parameters of the GEV distribution are assumed to
change in time or depend on a covariate. In the present
form of the GEV, parameters sand jare assumed to be
constant. Having a random variable Ythat follows the
GEV(mx,s,j) and a vector of pcovariates given by
X5(X1,X2,,Xp), the location parameter of the
GEV is written as follows:
mx5
p
i51
fi(Xi)5f1(X1)1f2(X2)11fp(Xp), (2)
where fiis a function that represents the relationship
between the parameter and the covariates X
i
. This
function can be described by the following B-spline
function:
fi(xi)5b0,i1
m
j51
bj,iBj,i,d(xi), (3)
where Bj,d(x) is a polynomial function of degree dand m
is the number of control points (Nasri et al. 2013).
Therefore, Eq. (2) can be rewritten as follows:
1066 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 55
mx5
p
i51
fi(xi)5
p
i51"b0,i1
m
j51
bi,jBj,i,d(xi)#. (4)
The predictors’ interaction can be expressed in our
model by using multivariate B-spline functions (de
Boor 2001). These functions allow considering the
correlation between the predictors. In this study 14
predictors are used. Consequently, in order to simplify
the model we did not consider the interaction between
predictors.
c. Parameter estimation
In this study, the estimation of the parameters of
the GEV B-spline model is carried out in a Bayesian
framework. In the Bayesian approach, the unknown
parameters are not constant and are considered as
random variables with a prior distribution p(u).
Bayes’s theorem therefore gives the following
definition of the posterior distribution of these
parameters:
f(ujy)5f(yju)3p(u)
f(y), (5)
where
u5(mx,s,j)5(b,s,j) and b5b0
b. (6)
According to Nasri et al. (2013), we choose a multivar-
iate normal distribution as a prior for a location pa-
rameter b;N(0, Sb3I), a noninformative prior for
scale parameter 1/s, and a beta distribution as prior for a
shape parameter [b(6, 9)].
The posterior distribution is written as follows:
f(ujy)}1
s8
>
>
>
<
>
>
>
:
11j2
6
6
6
4
y2
j
(1 B)b0
b
s3
7
7
7
5
9
>
>
>
=
>
>
>
;
2(1/j)21
exp0
B
B
@
28
>
>
<
>
>
:
11j2
6
6
4
y2
i
(1 B)b0
b
s3
7
7
59
>
>
=
>
>
;
2(1/j)1
C
C
A
[2pdet(Sb)]2(k/2)exp 2jjbjj2
2s2!1
sjffiffiffiffiffiffi
2p
pexp"2(j20:1)2
2s2
j#1
s. (7)
The GEV B-spline model, which takes into account
nonstationarity and nonlinearity, offers a great flexibil-
ity and takes into account the heavy-tailed character of
the extreme distribution.
The posterior distribution is estimated by the
Metropolis–Hasting algorithm (see appendix).
To select the number of knots (kt; 1 kt 50.51 m s
21
)
and the degree of B-spline functions used in this
study, we compared several combinations of degrees
and knots using the maximum likelihood method.
The following algorithm explains how these parameters
are chosen:
(i) set d2[1, 10] and m2[1, 10],
(ii) calculate Eq. (7) for all combinations of (d,m), and
(iii) choose values of (d,m) that maximize Eq. (7).
In this case, we apply the B-spline functions with 38
and 3 kt. This choice was found to be optimal for the
majority of the stations’ data.
d. Validity of the model with covariates
To validate the influence of covariates on the vari-
able of interest, the log likelihood of the GEV B-spline
(M1) model and the stationary GEV (M0) model
(without covariates) are compared using the test of
deviance:
D52[l(M1) 2l(M0)], (8)
where lis the maximum log likelihood function for
model M. Large values of Dindicate that model M1 is
more adequate at representing the data than model M0.
The Dstatistic is distributed according to a chi-square
distribution x2, with ydegrees of freedom, where yis
the difference between the number of parameters of
the M1 and M0 models. For a given aconfidence level,
we reject H0 hypothesis (H0: M1 and M0 are similar)
when D $x2
12a. This statistic is often used to compare
two models when one model is a special case of the other
(M0 M1; Coles 2001;El Adlouni and Ouarda 2009).
This test accounts for differences in model complexity to
avoid overfitting.
e. Quantile estimation
The MCMC algorithm also produces the conditional
quantile distribution for an observed value x0of the
covariate Xt. Indeed, for each iteration iof the MCMC
algorithm i51, ...,N, the quantiles corresponding to
APRIL 2016 N A S R I E T A L . 1067
the nonexceedance probability 1 2p,x(i)
p,x0, and the pa-
rameter vector [m(i)
x0,s(i)
x0,j(i)
x0] are estimated using the
inverse of the cumulative distribution function of the
GEV distribution:
y(i)
p,x0
5m(i)
x0
2s
j(i)f12[log(1 2p)]2j(i)g, (9)
where m(i)
x0is the position parameter conditional on the
particular value x0of X.
4. Results
a. Tests for independent and identically distributed
random variables
In the first step of using the nonstationary GEV model
(in this case GEV B-spline) we checked stationarity,
homogeneity, and independence using the Mann–
Kendall (Mann 1945), Mann–Whitney (Wilcoxon 1945),
and Wald–Wolfowitz tests (Wald and Wolfowitz 1940),
respectively, for MAP series for each station. The results
of these tests showed that all MAP series are non-
stationary, except for the Algiers station where a nega-
tive trend is observed and is significant at the 5% level,
as previously observed by Reiser and Kutiel (2011).
However, all the time series of MAP respect the hy-
potheses of homogeneity and randomness. Figure 2
shows the variation of all MAP series versus time, and
Fig. 3 shows the monthly frequency of occurrence of
annual maximum daily precipitation.
b. Predictors from reanalysis data
We selected the 14 NCEP–NCAR covariates
extracted from reanalysis (see section 2) and tested our
models with these covariates considering the four time
scales (cases 1–4). The negative log likelihood and de-
viance between the GEV B-spline model and the sta-
tionary GEV model are analyzed to detect the influence
of NCEP–NCAR predictors on extreme rainfall for each
of the four cases. To avoid overfitting, each covariate is
considered separately in the GEV B-spline model. This
allows evaluating whether each covariate leads to a
better fit than the stationary GEV model. As there are
14 covariates for each case, the results are presented in
Table 2 only for the significant covariates on MAP at
each station at the 5% and 10% significance levels, ac-
cording to the test of deviance. We note that all 14 co-
variates, depending on the station, are selected into
nonstationary GEV models that better reproduce ex-
treme precipitation than a standard stationary model,
with both short-term and long-term associations.
Overall, a similar number of significant covariates is
selected for the four cases tested (i.e., from daily to
seasonal averages of covariates), with 11 covariates
identified for case 1, 13 for case 2, 16 for case 3, and 13
for case 4. This shows that all considered covariates may
have an impact on extreme daily precipitation at dif-
ferent time steps, from daily values to seasonal averages.
It is observed that the geopotential height (geopot_
500 and geopot_850) generally affects rainfall at all
FIG. 2. Variation of all MAP series vs time for selected stations.
1068 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 55
stations excluding Melilla (station in northern Mo-
rocco). For the stations of Tangier and Larache, the
geopotential heights have a short-term association with
MAP (case 1 and case 2). On the other hand, for the
Algiers station, these variables have an influence
generally at the seasonal time scale (case 4), and for the
stations of Tunisia (Gabès and Tunis) these variables
influence MAP in both the short and long term (cases 1,
2, and 4). Humidity predictors (rhum_surf, shum_500,
and shum_850) generally influence precipitation at all
FIG. 3. Monthly frequencies of occurrence for daily MAP in each selected station.
TABLE 2. The significant covariates at 5% and 10% significance levels for each station.
Station
Predictors significant
at 5% (case)
Predictors significant
at 10% (case) Station
Predictors
significant at 5% (case)
Predictors significant
at 10% (case)
Algiers Slp_surf (case 4) pwater_surf (case 1) Melilla omega_surf (case 1) rhum_surf (case 4)
geopot_500 (case 4) omega_500 (case 2)
omega_850 (case 2)
rhum_surf (case 2)
ptemp_surf (case 3)
slp_surf (case 3)
Gabès geopot_500 (case 1) geopot_850 (case 2) Tangier pwater_surf (cases 1 and 2) geopot_850 (case 1)
geopot_850 (cases 1, 2, and 4) rhum_surf (case 4) shum_850 (case 1) temp_surf (case 4)
pwater_surf (case 3) omega _850 (case 2) uwind_surf (case 4)
slp_surf (cases 1 and 4) uwind_surf (case 2)
shum_500 (case 3) ptemp_surf (case 3)
shum_850 (case 1) shum_850 (case 3)
vwind_surf (case 3)
geopot_500 (case 4)
Larache temp_surf (case 2) pwater_surf (case 4) Tunis pwater_surf (case 2) rhum_surf (case 1)
omega_500 (case 2) rhum-surf (cases 2 and 3) shum_850 (case 1)
shum_850 (case 2) shum_500 (case 2) geopot_850 (case 2)
geopot_500 (case 3) shum_850 (case 2)
ptemp_surf (case 3) omega_500 (case 3)
pwater_surf (case 3) slp_surf (case 3)
rhum_surf (case 3) omega_850 (case 4)
omega_surf (case 4)
ptemp_surf (case 4)
APRIL 2016 N A S R I E T A L . 1069
stations, excluding Algiers. For stations in Morocco,
these predictors appear in almost all cases (cases 1 and
3 for the Tangier station, case 4 for the Melilla station,
and cases 1, 2, and 3 for the Larache station). For sta-
tions in Tunisia, these predictors have both short- and
long-term effects on MAP time series at the stations of
Gabès (cases 1, 3, and 4) and Tunis (cases 1, 2, and 3).
Velocity predictors (omega_500, omega_850, and
omega_surf) have more effects on precipitation in
Morocco. We see a stronger influence of these pre-
dictors on rainfall in Morocco. Wind predictors
(uwind_surf and vwind_surf) influence the MAP only
at the Tangier station. Overall, we note the small in-
fluence of wind covariates on precipitation extremes at
all stations. The potential temperature at the surface
(ptemp_surf) influences MAP at stations located in
Morocco for the long term (cases 3 and 4). The surface
temperature influences the MAP in Morocco at dif-
ferent time scales (case 3 for Melilla, case 1 for Larache,
and case 4 for Tangier stations). The precipitable water
content has an influence on MAP at all stations, usually
only for the short-term cases (1 and 2) at all stations.
The mean sea level pressure influences MAP in only
the Tunis, Gabès, and Algiers stations, generally in the
long-term cases 3 and 4.
c. Principal analysis of components for NCEP–
NCAR predictors
After the analysis of the dependence of MAP with
individual covariates, the possible relationships are also
investigated in a multivariate context. Principal com-
ponent analysis (PCA; Preisendorfer 1988) is used to
that end. The reason for using PCA is to take into con-
sideration the common signals in multivariate datasets.
PCA represents a method for dimensionality reduction.
PCA has been used for this purpose in many other
studies (e.g., Wetterhall et al. 2005;Maraun et al. 2010a).
The objective of this analysis is to summarize as much
information as possible by transforming interrelated
variables into new components (principal components)
that are uncorrelated with each other. In this study, we
first applied PCA on the 14 covariates for each station.
Figures 4 and 5show the results of the projections of the
14 covariates on the first and second components (F1
and F2, respectively) for the first and last case in each
station. A number of criteria, such as the Kaiser crite-
rion (Kaiser 1960), can be used for the selection of the
factorial axis. The Kaiser criterion lies on the factorial
axis choices, where their eigenvalues are greater than 1.
In the present study, we noticed that for all factors that
FIG. 4. Contributions of the 14 NCEP–NCAR reanalysis covariates on the two principal components (F1 and F2) in selected station
(results for case 1). The numbers in the parentheses represent the percentage of explained variance for the represented axes (F1 and F2).
1070 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 55
have an eigenvalue greater than 1, those are generally
factors 1 and 2. This justifies the choice of two factorial
axes. It can be seen that at all stations, there are signif-
icant correlations between the covariates, depending on
the case (1–4) considered for temporal aggregation. To
avoid overfitting, each component is considered sepa-
rately in the GEV B-spline model to evaluate if it
provides a better fit than a stationary GEV model. The
results show, first, that most variables contribute to the
formation of the components F1 and F2, with some co-
variates having a larger contribution, such as the geo-
potential height (geopot_500 and geopot_850), velocity
(omega_500, omega_850, and omega_surf), and hu-
midity (rhum_surf, shum_500, and shum_850). Pre-
dictors such as uwind_surf and vwind_surf contribute
more in stations close to the Mediterranean coast such
as Tangier, Tunis, and Gabès. We then applied the GEV
B-spline model of the MAP series for each station and each
case using F1 and F2 as covariates. Next, we calculated
the deviance between the results of the GEV B-spline
and GEV0 models to investigate the influence of these
components on MAP data. Table 3 shows the results of
deviance with a threshold of 5% and 10%. According to
these results one can see that, at all stations, there is at
least one component (F1 or F2) that influences the MAP
series. For stations in Morocco (Larache, Melilla, and
Tangier), we note that the component that contains
more information about the geopotential height, hu-
midity, velocity, and wind has the largest influence on
MAP. For the station in Algeria (Algiers), the MAP is
more influenced by the geopotential height predictors
rather than by others. For stations in Tunisia (Tunis and
Gabès), we can see that the influence of geopotential
FIG.5.AsinFig. 4, but for case 4.
TABLE 3. The results of the deviance for PCA.
Station Significant component Case
Algiers F1 at 5% 4
Larache F1 at 5% 1
Tangier F1 at 5% 1
F2 at 5% 1
Melilla F2 at 5% 2
F1 at 10% 3
F2 at 5% 4
Tunis F1 at 10% 3
F2 at 5% 3
Gabès F1 at 10% 1
F2 at 5% 1
F1 at 5% 2
F2 at 5% 2
F2 at 5% 4
APRIL 2016 N A S R I E T A L . 1071
height, velocity, temperature, and sea surface pressure
on MAP is important.
d. Quantile estimation
We can also see the impact of the covariates on the
estimated quantile level for each of the models. In the
case of the GEV B-spline model, quantile values depend
not only on the nonexceedance probability 1 2pbut
also on the covariate values. This allows computing
quantiles on a seasonal or annual basis, depending on
the values of the covariates. To demonstrate the co-
variates’ impact on quantile values, we show some
quantile estimation examples for each station. Figure 6
displays a nonstationary quantile estimation example
for each station for the 2-yr return period (non-
exceedance probability 50.5), which represents the
median value of MAP.
For each station, we observed different values of the
2-yr quantiles estimated with the GEV B-spline model
since quantile values are dependent on covariates. In
contrast, the GEV0 model provides just one estimate for
the 2-yr quantile (e.g., for the Algiers station, the me-
dian precipitation value corresponding to the 2-yr
quantile is 100 mm for the GEV B-spline and 64 mm
for the GEV0 model, and for the Tunis station, the
stationary quantile is equal to 50 mm and the median of
the nonstationary quantiles is equal to 70 mm). Ac-
cording to this figure, we notice that the covariate-
dependent quantile values are more flexible and allow
reaching more extreme data values, unlike the station-
ary quantiles that do not take into consideration the
interannual climatic variability. The estimated quantiles
show the advantage of incorporating additional in-
formation into nonstationary models.
5. Conclusions
In this work, the influences of climatic variables such
as geopotential height, pressure, or temperature on
maximum annual daily precipitation have been studied
at six stations located in North Africa with long pre-
cipitation time series. A total of 14 variables were
computed from NCEP–NCAR reanalysis data. To
study the influence of these covariates at the different
stations, the GEV B-spline model (Nasri et al. 2013)
was used. The originality of this model, as opposed to
other nonstationary models, is that it takes into con-
sideration the nonstationary and the nonlinear tem-
poral fluctuations of covariates. Nonstationary models,
such as the GEV1 (linear dependence) and the GEV2
(quadratic dependence), define in advance the form of
dependence between the variable of interest and the
covariates. On the other hand, the GEV B-spline
model takes into consideration all continuous de-
pendence forms between the covariates and the vari-
able of interest.
The results of this study are divided into two parts. In
the first part, the possible dependencies between the
FIG. 6. Example of nonstationary and stationary median for each station using the first or the second principal component analysis as
covariates.
1072 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 55
maximum annual precipitation and each of the individ-
ual climatic covariates were considered. The GEV
B-spline model was used to detect these dependencies, and
the deviance likelihood ratio test was used to identify
the nonstationary models with covariates that provide
an improvement in comparison to stationary models in
each station. In the second part, the combined de-
pendencies were analyzed using principal component
analysis of the different atmospheric predictors. From
the results of the principal component analysis, we an-
alyzed the influence of the combined variables using the
two principal components (F1 and F2) for each station in
the GEV B-spline model. Our results indicate that no
single combination of atmospheric predictors is optimal
for stations. The relevant covariates may vary from one
station to another and also depend on the considered
time scale, from daily to annual averages. These results
are consistent with the fact that extreme precipitation
is a process exhibiting a high spatiotemporal variability
between different locations. Given this variability, it
must be noted that the covariates describing the mois-
ture flux in the atmosphere (relative or specific humid-
ity) or in atmospheric circulation (pressure and
geopotential heights) are often selected in the different
stations as valid predictors. During winter, when most of
the annual maximum precipitation occurs, geopotential
height might be more important because of the south-
erly position of the extratropical westerlies. In other
seasons thermodynamic predictors like humidity may
gain significance because of the convective nature of
precipitation in these seasons.
The present work provides a first step prior to the
development of statistical downscaling methods tai-
lored for extreme precipitation in North Africa. The
next step would be to use GCM outputs to first validate
the method in the present climate, with the covariates
that are correctly reproduced in historical climate
simulations, and then to make future projections.
However, in this case the use of the nonstationary GEV
model with B-spline functions would probably be less
appropriate because of some limitations: (i) the in-
troduction of several covariates within these types of
models increases the number of hyperparameters,
which increases the number of parameters to estimate
as well as the estimation errors; (ii) the interactions
between the predictors make the model much more
complex since we need to take into consideration
multivariate spline functions (de Boor 2001)oruse
some decisional model, such as an artificial neural
network as in Cannon (2010); and (iii) this type of
model allows the description of the impact of co-
variates on the variable of interest and is not able to use
them for prediction outside this period of study.
Consequently, an alternative to this type of model is
quantile regression methods (Buchinsky 1998). Unlike
linear regression, which results in the estimation of the
conditional mean for the response variable given cer-
tain values of predictor variables, quantile regression
aims at estimating either the conditional median or
other quantiles of the response variable. Quantile re-
gression was considered by Jagger and James (2006) for
wind speed and by Friederichs and Andreas (2008) for
precipitation, based on several climatic covariates.
Future work can focus on the comparison of extreme
value models and the quantile regression approach to
distinguish the relative benefits of the use of these two
types of models for downscaling purposes.
Acknowledgments. The datasets were provided by
the Agence Nationale des Ressources Hydrauliques
(Algeria), Direction de la Recherche et de la Planifica-
tion de l’Eau (Morocco), Direction Générale des
Ressources en Eau (Tunisia), and European Climate
Assessment and Dataset. Special thanks are given to
H. Ben-Mansour, R. Bouaicha, L. Behlouli, K. Benhattab,
R. Taibi, and K. Yaalaoui for their helpful contribution
to database collection. The authors are indebted to ed-
itor Thomas Mote and to two anonymous reviewers
whose comments helped considerably improve the
quality of the manuscript.
APPENDIX
MCMC Algorithm for GEV B-Spline Model
The basic idea of the MCMC method is, for each
parameter, to construct a Markov chain with the pos-
terior distribution being a stationary and ergodic dis-
tribution. After running the Markov chain of size N
for a given burn-in period N0, one obtains a sample
from the posterior distribution f(ujy). One popular
method for constructing a Markov chain is via the
Metropolis–Hastings (MH) algorithm (Metropolis
et al. 1953;Hastings 1970). We simulated the re-
alizations from the posterior distribution by way of a
single-component MH algorithm (Gilks et al. 1996).
Each parameter was updated using a random-walk MH
algorithm with a Gaussian proposal density centered at
the current state of the chain. Some techniques to as-
sess the convergence of the MCMC methods, such as
the Raftery and Lewis diagnostic (Raftery and Lewis
1992,1995) and subsampling methods (El Adlouni
et al. 2006), make it possible to determine the length of
the chain and the burn-in time. In all cases, the con-
vergence methods indicated that the Markov chains
converged within a few iterations. In this study, we
APRIL 2016 N A S R I E T A L . 1073
considered chains of size N515 000 and a burn-in
period of N058000 runs. In every case, a sample of
N2N057000 values is collected from the posterior of
each of the elements of u.
The principal steps of the MH algorithm can be
summarized as follows:
(i) Initialization: assign initial value u(0)and choose
an arbitrary proposal probability density Q(u*ju).
In this case we propose a multivariate normal
distribution.
(ii) For each iteration t, generate u*, a candidate for the
next sample, by picking from the distribution
Q(u*jut).
(iii) Calculate the acceptance ratio, given by
a(u*, ut)5[p(u*jy)/p(utjy)].
(iv) If a$1, then the candidate is more likely than ut;
automatically accept the candidate by setting
ut115u*. Otherwise, accept the candidate with
probability a; if the candidate is rejected, set
ut115utinstead.
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1076 JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY VOLUME 55
... Indeed, the time intervals used to compute extreme quantiles (typically 30 years) are usually too short to identify climate changes against the background of high-frequency components of climate variability (Paeth et al. 2017). This is particularly true in the case of semiarid areas where the inter-annual variability of extreme precipitation can be very strong (Nasri et al. 2016). An alternative to this approach is to use nonstationary extreme value models with parameters dependent on time (Min et al. 2009;Fowler et al. 2010;Tramblay et al. 2012b;Aalbers et al. 2017) or a covariate (Tramblay et al. 2012a;Nasri et al. 2016). ...
... This is particularly true in the case of semiarid areas where the inter-annual variability of extreme precipitation can be very strong (Nasri et al. 2016). An alternative to this approach is to use nonstationary extreme value models with parameters dependent on time (Min et al. 2009;Fowler et al. 2010;Tramblay et al. 2012b;Aalbers et al. 2017) or a covariate (Tramblay et al. 2012a;Nasri et al. 2016). By doing so, the models are fitted on much longer time periods, reducing the uncertainties on extreme quantiles (Aalbers et al. 2017). ...
... Besides the decline in the amount of rainfall during the wet season, since the 1970s, an accompanying drying during winter has also been detected in large areas of western North Africa [8], leading to food safety problems. If, on the one hand, it is possible to affirm that there have been no notable trends of heavy rainfall events over most parts of North Africa in recent decades [9,10], on the other hand there has been a general increase in drought frequency all over [5]. ...
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The problem of food insecurity is growing across the world, in particular in developing countries. Due to their economic structure, climate change represents one of the major threats for food security levels in African countries. The object of this work was to assess the impact of climate change on the level of food security in the North and East African countries, using a panel data analysis for the period 2000–2012. Average protein supply and average dietary energy supply adequacy were the two different indicators of food security we identified as most appropriate. Indeed, both indicators can provide information concerning the amount and the nutritional value of food supply. The determinants of food security are expressed as a function of rainfall, temperature, land area under cereal production, size of population and GDP. Findings showed that food security in the Northern and Eastern African countries is adversely affected by climate change. Policy makers need to promote those actions capable of mitigating global warming and reducing its economic impact.
... Despite being preferable to traditional trend detection techniques (Zhang et al., 2004), quantifying changes between two periods is subject to large uncertainties because the temporal slices are usually short (Paeth et al., 2017). Possible alternatives to this approach include nonstationary models in which changes of the distribution parameters are modeled using covariates, which are expected to be related to extreme precipitation, such as temperature (Tramblay et al., 2012;Nasri et al., 2016;Tramblay and Somot, 2018;Chagnaud et al., 2021). For the case of central and eastern Africa, Afuecheta and Omar (2021) tested a number of nonstationary models for annual and monthly maxima of daily precipitation using time as covariate, and combined them with an analysis of trends in temperature extremes with the objective of improving crop resilience and flood risk management. ...
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Extreme precipitation heavily affects society and economy in Africa because it triggers natural hazards and contributes large amounts of freshwater. Understanding past changes in extreme precipitation could help us improve our projections of extremes, thus reducing the vulnerability of the region to climate change. Here, we combine high-resolution satellite data (1981-2019) with a novel non-asymptotic statistical approach, which explicitly separates intensity and occurrence of the process. We investigate past changes in extreme daily precipitation amounts relevant to engineering and risk management. Significant (α=0.05) positive and negative trends in annual maximum daily precipitation are reported in ∼20% of Africa both at the local scales (0.05°) and mesoscales (1°). Our statistical model is able to explain ∼90% of their variance, and performs well (72% explained variance) even when annual maxima are explicitly censored from the parameter estimation. This suggests possible applications in situations in which the observed extremes are not quantitatively trusted. We present results at the continental scale, as well as for six areas characterized by different climatic characteristics and forcing mechanisms underlying the ongoing changes. In general, we can attribute most of the observed trends to changes in the tail heaviness of the intensity distribution (25% of explained variance, 38% at the mesoscale), while changes in the average number of wet days only explain 4% (12%) of the variance. Low-probability extremes always exhibit faster trend rates than annual maxima (∼44% faster, in median, for the case of 100-year events), implying that changes in infrastructure design values are likely underestimated by approaches based on trend analyses of annual maxima: flexible change-permitting models are needed. No systematic difference between local and mesoscales is reported, with locally-varying impacts on the areal reduction factors used to transform return levels across scales.
... With high spatial resolution and spatial and serial completeness, ERA5 is ideal for investigating synoptic scale circulation variability and links with the surface extreme precipitation record. Previous studies (Junker et al., 1999;Johnson, 2005, 2006;Tryhorn and Degaetano, 2011;Kunkel et al., 2013;Nasri et al., 2016) have established that synoptic scale drivers of extreme precipitation include measures of circulation and atmospheric humidity. We therefore use 500-hPa geo-potential height to reflect circulation and 850-hPa specific humidity to characterize moisture availability. ...
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Extreme precipitation contributes to widespread impacts in the U.S. Great Lakes region, ranging from agricultural losses to urban floods and associated infrastructure costs. Previous studies have reported historical increases in the frequency of extreme precipitation in the region and downscaled model projections indicate further changes as the climate system continues to warm. Here, we conduct trend analysis on the 5 km NOAA NClimDiv data for the U.S. Great Lakes region using both parametric (Ordinary Least Squares) and non-parametric methods (Theil-Sen/Mann-Kendall) and accounting for temporal autocorrelation and field significance to produce robust estimates of extreme precipitation frequency trends in the region. The approaches provide similar overall results and reflect an increase in extreme precipitation frequency in parts of the U.S. Great Lakes region. To relate the identified trends to large scale drivers, a bivariate self-organizing map (SOM) is constructed using standardized values of 500 hPa geo-potential height and 850 hPa specific humidity obtained from the ECMWF ERA-5 reanalysis. Using a Monte Carlo approach, we identify six SOM nodes that account for only 25.4% of all days, but 50.5% of extreme precipitation days. Composites of days with and without extreme precipitation for each node indicate that extreme events are associated with stronger features (height gradient and background humidity) than their non-extreme counterparts. The analysis also identifies a significant increase in the frequency of one SOM node often associated with extreme precipitation (accounting for 8.5% of all extreme precipitation days) and a significant increase in the frequency of extreme precipitation days relative to all days across the six extreme precipitation nodes collectively. Our results suggest that changes in atmospheric circulation and related moisture transport and convergence are major contributors to changes in extreme precipitation in the U.S. Great Lakes region.
... For the model that shows stationarity, GEV1, the percentages were 14.5% for the historical period, reduced to 7.3% for RCP 4.5, and reduced to 2.2% for RCP 8.5. According toNasri et al. (2016), emphasized that for complex predictors, the GEV-CDN configuration as a decision model is proper. However,Um et al. (2017) emphasize that non-stationary models for GEV configuration must be developed and tested because the future is undetermined and cannot be fully predicted.Um et al. (2017) found a non-stationarity signal for gauged and projections for eight cities in the United States. ...
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Climate change alters the spatial and temporal distribution of extreme global and regional scales, affecting several human activities. There is a need to shed more light on the understanding of local impacts of different greenhouse gas emission rates over such extreme events. This study's main goal is to evaluate the impact of distinct Representative Concentration Pathways on the probability of extreme rainfall events in the State of São Paulo using climate downscaled models provided by the Intergovernmental Panel on Climate Change - Fifth Assessment Report. In an unprecedented way, this study applied statistical models based on a probabilistic extension of the multilayer perceptron neural network, capable of incorporating non-linear and non-stationary relationships to assess the probability of extreme rainfall events. It was being used 19 regional climate projections from the database NASA Earth Exchange (NEX) Global Daily Downscaled Projections (GDDP) to make a mean multi-model ensemble for calculation of block maxima (bmax) values. As a quality control assessment, Quantile Delta Mapping (Chapter 2) evaluated these global models' ability to describe the probability of such events concerning those events that have already been recorded by weather stations (control run: 1950-2005). This study should supply a detailed description of the influence of different greenhouse gas emissions scenarios on such events' probability. Provided that the selection of an appropriate statistical model is frequently based on selection criteria methods, it was evaluated in Chapter 1 the performance of four often used selection criteria (Akaike information criterion, second-order Akaike information criterion, Bayesian information criterion, and likelihood ratio test) for selecting appropriate models based on the non-stationary Generalized Extreme Value distribution (GEV Conditional density network or simply GEV-CDN)) – Chapter 2. The results show improvement of QDM calibration for the retrospective run (1950-2005) of extreme values from maximum daily precipitation. In the conclusion of those statements, the mean multi-model ensemble could describe, with cautions, extreme rainfall values for climate change pathways (RCP 4.5 W m-2 and RCP 8.5 W m-2) in São Paulo for the prospective run (2020-2095). GEV-CDN demonstrated it appropriated to assess extreme values of rainfall in climate transition.
... However, some wet years observed since the 2000s can be attributed to increased climate variability (Donat et al. 2013;Nouaceur and Murărescu 2016). With respect to heavy rainfall events, most parts of North Africa show no significant trends over the last decades (Nashwan et al. 2019;Nasri et al. 2016;Tramblay et al. 2012), while a general increase in drought frequency can be observed in all countries (see Hertig and Tramblay 2017 and Table 1). ...
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North Africa is considered a climate change hot spot. Existing studies either focus on the physical aspects of climate change or discuss the social ones. The present article aims to address this divide by assessing and comparing the climate change vulnerability of Algeria, Egypt, Libya, Morocco, and Tunisia and linking it to its social implications. The vulnerability assessment focuses on climate change exposure, water resources, sensitivity, and adaptive capacity. The results suggest that all countries are exposed to strong temperature increases and a high drought risk under climate change. Algeria is most vulnerable to climate change, mainly due to the country's high sensitivity. Across North Africa, the combination of climate change and strong population growth is very likely to further aggravate the already scarce water situation. The so-called Arab Spring has shown that social unrest is partly caused by unmet basic needs of the population for food and water. Thus, climate change may become an indirect driver of social instability in North Africa. To mitigate the impact of climate change, it is important to reduce economic and livelihood dependence on rain-fed agriculture, strengthen sustainable land use practices, and increase the adaptive capacity. Further, increased regional cooperation and sub-national vulnerability assessments are needed.
... In the vast majority of non-stationary hydro-climate models, the location and/or scale parameters of the probability function are made dependent on covariates. However, shape parameters are usually assumed to be constant 9,[11][12][13][14][15] . ...
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Hydro-climatic extremes are influenced by climate change and climate variability associated to large-scale oscillations. Non-stationary frequency models integrate trends and climate variability by introducing covariates in the distribution parameters. These models often assume that the distribution function and shape of the distribution do not change. However, these assumptions are rarely verified in practice. We propose here an approach based on L-moment ratio diagrams to analyze changes in the distribution function and shape parameter of hydro-climate extremes. We found that important changes occur in the distribution of annual maximum streamflow and extreme temperatures. Eventual relations between the shapes of the distributions of extremes and climate indices are also identified. We provide an example of a non-stationary frequency model applied to flood flows. Results show that a model with a shape parameter dependent on climate indices in combination with a scale parameter dependent on time improves significantly the goodness-of-fit.
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Non-stationarity of extreme climate events has been reported worldwide in recent decades, and traditional stationary analysis methods are no longer sufficient to properly reveal the occurrence probability of climate extremes. Based on the 0.25°C × 0.25°C gridded precipitation data (i.e., CN05.1), stationary and non-stationary models of generalized extreme value (GEV) and generalized Pareto (GP) distributions are adopted to estimate the occurrence probability of extreme precipitation over China during 1961–2018. Low-frequency oscillation (LFO) indices, such as El Niño-Southern Oscillation (ENSO), Indian Ocean Dipole (IOD), North Atlantic Oscillation (NAO), Southern Annular Mode (SAM), and Pacific Decadal Oscillation (PDO), are included as time-varying covariates in the non-stationary GEV and GP models. Results illustrate that the occurrence probability of extreme precipitation estimated from the stationary GEV and GP distributions shows a significant increasing trend in northwestern and southeastern China, and the opposite trend in southwestern, central, and northeastern China. In comparison with stationary model, the fitness of extreme precipitation series is improved for both the GEV and GP distributions if these LFO indices are used as time-varying covariates. Positive ENSO, IOD and PDO tend to cause negative anomalies in the occurrence probability of extreme precipitation in northeastern China and Tibet Plateau, and positive anomalies in southern China. Positive NAO and SAM phases mainly tend to cause positive anomalies in southern China. The circulation patterns of extreme precipitation anomalies associated with these LFO indices are discussed from aspects of precipitable water, vertical integrated moisture transport, 500-hPa geopotential height and 850-hPa wind field.
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Predicting the impacts of climate change on water resources remains a challenging task and requires a good understanding of the dynamics of the forcing terms in the past. In this study, the variability of precipitation and drought patterns is studied over the Mediterranean catchment of the Medjerda in Tunisia based on an observed rainfall dataset collected at 41 raingauges during the period 1973–2012. The standardized precipitation index and the aridity index were used to characterize drought variability. Multivariate and geostatistical techniques were further employed to identify the spatial variability of annual rainfall. The results show that the Medjerda is marked by a significant spatio-temporal variability of drought, with varying extreme wet and dry events. Four regions with distinct rainfall regimes are identified by utilizing the K-means cluster analysis. A principal component analysis identifies the variables that are responsible for the relationships between precipitation and drought variability.
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Rainfall Intensity‐Duration‐Frequency (IDF) curves are commonly used for the design of water resources infrastructure. Numerous studies reported non‐stationarity in meteorological time series. Neglecting to incorporate non‐stationarities in hydrological models may lead to inaccurate results. The present work focuses on the development of a general methodology that copes with non‐stationarities that may exist in rainfall, by making the parameters of the IDF relationship dependent on the covariates of time and climate oscillations. In the recent literature, non‐stationary models are generally fit on data series of specific durations. In the approach proposed here, a single model with a separate functional relation with the return period and the rainfall duration is instead defined. This model has the advantage of being simpler and extending the effective sample size. Its parameters are estimated with the maximum composite likelihood method. Two sites in Ontario, Canada and one site in California, USA, exhibiting non‐stationary behaviors are used as case studies to illustrate the proposed method. For these case studies, the time and the climate indices Atlantic Multi‐decadal Oscillation (AMO) and Western Hemisphere Warm Pool (WHWP) for the stations in Canada, and the time and the climate indices Southern Oscillation Index (SOI) and Pacific Decadal Oscillation (PDO) for the stations in USA are used as covariates. The Gumbel and the Generalized Extreme Value distributions are used as the time dependent functions in the numerator of the general IDF relationship. Results shows that the non‐stationary framework for IDF modeling provides a better fit to the data than its stationary counterpart according to the Akaike Information Criterion. Results indicate also that the proposed generalized approach is more robust than the the common approach especially for stations with short rainfall records (e.g. R2 of 0.98 compared to 0.69 for duration of 30 min and a sample size of 27 years).
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This paper provides a first overview of the performance of state-of-the-art global climate models participating in the Coupled Model Intercomparison Project Phase 5 (CMIP5) in simulating climate extremes indices defined by the Expert Team on Climate Change Detection and Indices (ETCCDI), and compares it to that in the previous model generation (CMIP3). For the first time, the indices based on daily temperature and precipitation are calculated with a consistent methodology across multimodel simulations and four reanalysis data sets (ERA40, ERA-Interim, NCEP/NCAR, and NCEP-DOE) and are made available at the ETCCDI indices archive website. Our analyses show that the CMIP5 models are generally able to simulate climate extremes and their trend patterns as represented by the indices in comparison to a gridded observational indices data set (HadEX2). The spread amongst CMIP5 models for several temperature indices is reduced compared to CMIP3 models, despite the larger number of models participating in CMIP5. Some improvements in the CMIP5 ensemble relative to CMIP3 are also found in the representation of the magnitude of precipitation indices. We find substantial discrepancies between the reanalyses, indicating considerable uncertainties regarding their simulation of extremes. The overall performance of individual models is summarized by a "portrait" diagram based on root-mean-square errors of model climatologies for each index and model relative to four reanalyses. This metric analysis shows that the median model climatology outperforms individual models for all indices, but the uncertainties related to the underlying reference data sets are reflected in the individual model performance metrics. Key PointsWe calculate indices in a consistent manner across models and reanalysesMulti-model ensembles compare reasonably well with observation-based indicesThere are large uncertainties in the representation of extremes in reanalyses
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In this study, we investigate the influence of global climate oscillations on the local temperature and precipitation over the United Arab Emirates (UAE), which is one of the driest regions in the world with very high temperatures and low precipitation. The identification and assessment of remote interactions (teleconnections) are carried out by using ground station and gridded data sets. Monthly rainfall data from six ground stations over the UAE for the period of 1982–2010 is used in this study along with the long-term gridded precipitation and temperature data from the Global Precipitation Climatology Center and Global Historic Climatic Network. Linear correlations, wavelet analysis, and cross-wavelet analysis have been applied to identify the relation between climate indices and precipitation (temperature). The analysis reveals that the strong variability in precipitation is closely associated with the Southern Oscillation Index (SOI) and the Indian Ocean Dipole Index (IOD) during the months of August–March, September–January, respectively. In case of temperature, the strong variability is associated with the North Atlantic Oscillation Index (NAO) and the East Atlantic Oscillation Index (EAO) during the months of April–October, July–December. Spatial analysis of cross-wavelet reveals that the winter precipitation is significantly influenced by SOI and temperature during summer by the NAO. This research concludes that the negative phases of SOI (NAO) play a significant role in the increase of precipitation (decrease in summer temperatures) over the UAE region.
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Non-parametric techniques are introduced for the change-point problem. Exact and approximate results are obtained for testing the null hypothesis of no change. The methods are illustrated by the analysis of three sets of data illustrating the techniques for zero-one observations, Binomial observations and continuous observations. Some comparisons are made with methods based on CUSUMS.
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Seasonal precipitation variability in the east of the Iberian Peninsula is weakly linked to the North Atlantic Oscillation (NAO) during autumn and winter. For the purpose of improving the study of its performance, low-frequency variability patterns specific to the Mediterranean basin have been searched for. In this way, the Western Mediterranean Oscillation (WeMO) has been defined by means of the dipole composed, in its positive phase, by the anticyclone over the Azores and the depression over Liguria, and its index (WeMOi), as a result of the difference of the standardised values in surface atmospheric pressure in San Fernando (Spain) and Padua (Italy). This new index allows the detection of the variability relevant to the cyclogenesis next to the western Mediterranean basin, which determines in a predominant way the types of rainfall in the Gulf of Valencia. In this area, the WeMO is significantly better than the NAO to explain the monthly pluviometric anomalies during these seasons. Also, a daily resolution of the WeMOi can provide a useful tool to forecast torrential rainfall events in the north-western zones of the Mediterranean (eastern part of the Iberian Peninsula and the south of France), and such significantly daily rainfall frequencies for different thresholds. Copyright © 2006 Royal Meteorological Society.