regional analysis for the estimation of low-frequency daily rainfalls in cheliff

Regional analysis for the estimation of low-frequency daily rainfalls in Cheliff catchment -Algeria-

BENHATTAB Karima 1 ; BOUVIER Christophe 2; MEDDI Mohamed 3

1USTO Mohamed Boudiaf-Algérie2 Hydrosciences Montpellier-France

3 ENSH BLIDA-Algérie

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

L-CV = lL-CV = l22/ l/ l11 (coefficient of (coefficient of LL-variation)-variation)t3 = lt3 = l33/ l/ l22 ((LL-skewness)-skewness)t4 = lt4 = l44/ l/ l22 ((LL-kurtosis)-kurtosis)

Regional Frequency Analysis

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 !



H<1




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?


LCs–LCk moment ratio diagram for group 1.

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


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)


Local

Regional0

20

40

60

80

100

120

140

160

1 10 100 1000


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).

regional analysis for the estimation of low-frequency daily rainfalls in cheliff

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