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Regional analysis for the estimation of low-frequency daily rainfalls in Cheliff catchment -Algeria-
FRIEND project - MED group;UNESCO IHP-VII (2008-13)4th International Workshop on Hydrological Extremes
15 september 2011
LGEE
Introduction Sizing of minor hydraulic structures is based on design
Rainfall quantiles (QT) of medium to high return periods (T).
If the length of the available data series is shorter than the T of interest, or when the site of interest is ungauged (no flow data available) obtaining a satisfactory estimate of QT is difficult.
Regional flood Frequency analysis is one of the approaches that can be used in such situations.
1800 m asl
0 m asl
46 rainfall stations located in the northern part of the basin: daily rainfalls records from 1968 to 2004
The Cheliff watershed, Algeria
Oued Chlef
0 60 km
Algeria
Oued Chlef
0 60 km
1800 m asl
0 m asl
Mean annual rainfall 1968-2004(mm)
The Cheliff watershed, Algeria
2 main topographic regions : valley and hillslopes ; influence on mean annual rainfall
Why L-moment approach?
Able to characterize a wider range of distributions
Represent an alternative set of scale and shape statistics
of a data sample or a probability distribution.
Less subject to bias in estimation
More robust to the presence of outliers in the data
Brief Intro to L-Moments
Hosking [1986, 1990] defined L-moments to be linear combinations of probability-weighted moments:
k
r
kkrr p
0,1
Let x1 Let x1 x2 x2 x3 be ordered sample . Define x3 be ordered sample . Define
k
r
kkrr bpl
0,1
Estimating L-moments wherewhere
then the then the LL-moments can be estimated as follows: -moments can be estimated as follows: llb0b0ll222b1 - b02b1 - b0ll336b2 - 6b1+ b06b2 - 6b1+ b04420b3 - 30b2 + 12 b1 - b020b3 - 30b2 + 12 b1 - b0
Delineation of homogeneous groups and testing for homogeneity within each group
Estimation of the regional frequency distribution and its parameters
Estimation of precipitation quantiles corresponding to various return periods
Steps for success of Regionalisation
Heterogeneity test (H)
Fit a distribution to RtRt3
Rt4
Regional L-Moment ratios
Sim
ulati
on 5
00
H?
H : is the discrepancy between L-Moments of observed samples and L-Moments of simulated samles Assessed in a series of Monte Carlo simulation :
Calculate v1, v2, v3…….v500
Weighted Standard deviation of at site LCV´s
Heterogeneity test (H)
H2 : Region is definitely
heterogeneous.
1 ≤H<2 : Region is possibly heterogeneous .
H<1: Region is acceptably
homogeneous.
The performance of H was Assessed in a series of Monte Carlo simulation experiments:
v
vVH
H<1
Delineation of homogeneous groups
Dendrogram presenting clusters of rainfall originated in Cheliff basin
H>1 !
Delineation of homogeneous groups
Dendrogram presenting clusters of rainfall originated in Cheliff basin
H<1
Delineation of homogeneous groups
Dendrogram presenting clusters of rainfall originated in Cheliff basin
Delineation of homogeneous groups
Dendrogram presenting clusters of rainfall originated in Cheliff basinGroup1 Group2 Group3
Clusters pooling
0 60 km
Group1
Group2
Group3
The stations located in the valleys correspond to the group 1 (downstream valley) or 3 (upstream valleys) whereas stations located on the hillslopes correspond to the group 2.
t4(L
-Kur
tosi
s)
t3 (L-Skewness)
The L-moment ratio diagram
Estimation of the regional frequency distribution
Hypothesis What is the appropriate Distribution?
Estimation of the regional frequency distribution
LCs–LCk moment ratio diagram for group 1.
LCs–LCk moment ratio diagram for group 2.
Estimation of the regional frequency distribution
LCs–LCk moment ratio diagram for group 3.
Estimation of the regional frequency distribution
444
DIST4
DIST )/σβτ(τZ “Dist” refers to the candidate distribution, τ4 DIST is the average L-Kurtosis value computed from simulation for a fitted distribution. τ4 is the average L-Kurtosis value computed from the data of a given region, β4 is the bias of the regional average sample L-Kurtosis,
σv is standard deviation.
A given distribution is declared a good fit if |ZDist|≤1.64
The goodness-of-fit measure ZDist
Distribution selection using the goodness-of-fit measure
Groups Number of stations Regional frequency distribution
Zdist
1 17 Generalized Extreme Value 0,51
2 16 Generalized Extreme Value 0,97
3 9 Generalized Extreme Value -0,84
Generalized Extreme Value (GEV) distribution
Estimation of precipitation quantiles
k= shape; = scale, ξ = location
Quantile is the inverse :
Regional Estimation
N
ii
N
i
irir nln
11
)( /
N
ii
N
i
irir ntnt
11
)( /
Estimation of precipitation quantiles
321 ,,,
t
Local Estimation
At-site and regional cumulative distribution functions (CDFs) for one representative station at each group
Bougara Station Ain Lelloul
The regional and at-site annual rainfall group 1
0
20
40
60
80
100
120
140
160
1 10 100 1000
Return Period (year)
Rainf
all (m
m)
Local
Régional
0
50
100
150
200
250
1 10 100 1000
Return Period (year)
Rainf
all (m
m)
Local
Regional
Teniet El Had station Tissemsilt station
0
20
40
60
80
100
120
140
160
180
200
1 10 100 1000
Rainf
all (m
m)
Return Period (year)
Local
Regional0
20
40
60
80
100
120
140
160
1 10 100 1000
Return Period (year)
Rainf
all (m
m)Local
Regional
The regional and at-site annual rainfall group 2
we observe a reasonable underestimation or overestimation of quantiles estimated for the high return periods .
Reliability of the regional approach group1
0
10
20
30
40
50
60
70
80
0 20 40 60 80 100
% Gaps
Rel
ativ
e ro
ot
mea
n s
qu
are
erro
r
RMSE 3-10
RMSE 10-100
RMSE 100-1000
The values of RMSE is greater and the discrepancy is growing when T> 100 years.
Conclusions and Recommendations
the regional approach proposed in this study is quite robust and well indicated for the estimation of extreme storm events ;
L-moments analysis is a promising technique for quantifying precipitation distributions;
L-Moments should be compared with other methods (data aggregation for example).