Application of Index Procedures to Flood Frequency Analusis in Turkey

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APPLICATION OF INDEX PROCEDURES TO FLOOD FREQUENCY ANALUSIS IN TURKEY

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NDICE

APPLICATION OF INDEX PROCEDURES TO FLOOD FREQUENCY ANALUSIS INTURKEY....................................................................................................................................... 2

I. ABSTRACT: .................................................................................................................... 2

II. INTRODUCTION ............................................................................................................ 2

THE REGIONAL FREQUENCY ANALYSIS .................................................................. 3

III. APPLICATION OF THE IFM..................................................................................... 5

STATISTICAL PROPERTIES........................................................................................... 5

TESTING FOR REGIONAL HOMOGENEITY ............................................................... 7

HOMOGENEITY TEST...................................................................................................... 7

IV. RESULTS .................................................................................................................. 14

V. CONCLUSIONS AND RECOMMENDATIONS ....................................................... 18


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APPLICATION OF INDEX PROCEDURES TO FLOOD

FREQUENCY ANALUSIS IN TURKEY

I. ABSTRACT:

This study investigates the regional analysis of annual maximum flood series of 48

stream gauging stations in the basins of the west Mediterranean region in Turkey.

The region is divided into three homogeneous subregions according to both Student-t

test and Dalrymple homogeneity test. The regional relationships of mean annual flood

per unit area-drainage area and coefficient of skew-coefficient of variation are

obtained. Two statistically meaningful relationships of thee mean flood per unit area-

drainage area and a unique relationship between skewness and variation coefficients

exist. Results show that the index-flood method may be applicable to each

homogenous subregion to estimate flood quantiles in the study area.

(KEY TERMS: flood regionalization; Gumbel distribution; flood-index method; regional

homogenity; flood frequency.)

Saf: betl, 2008. Application of index procedures to Flood Frequency Analysis in

Turkey. Journal of the American Water Resources Association (JAWRA) 44(1):37-47.

DOI: 10.1111/j.1752-1688.2007.00136.x

II. INTRODUCTION

Floods cause damage to properties and agricultural lands that result in an economic

loss for the affected areas. Besides these direct costs, floods can cause loss of life,

injury, inconvenience, and other indirect losses. One method of decreasing flooddamages and economic losses is to use flood frequency analysis for determining

efficient designs of hydraulic structures, such as dams, spillways, highway bridges,

culverts, water-supply systems, and flood control structures. Underdesign of hydraulic

structure, such as a spillway , may cause failure, while overdesign may be safe but

can be costly an optimum design can be achieved whit proper flood frequency and

risk analyses.

At-site estimation of floods considers only the data available from the specific site

under consideration, and the reliability of the estimate is directly related to length of

record information available. Regional flood frequency analysis may be preferable to

an at-site frequency analysis for two main reasons. First, because of short record

length, individual stations in any watershed may have large sampling errors, and

these errors can be reduced by combining data from many sites. Second is the

amount of hydrologic data needed at one site. Thus, transformation from gauged sites

to ungauged sites is required. The regional flood analysis incorporates two main

steps; first, the identification of homogenous regions, and second, the establishment

of a flood frequency distribution model for each region.

Several approaches have been proposed for the delineation of homogeneous regions

(Wiltshire, 1986; Cavadias, 1990; Burn 1190a,b; 1997;Zrinji and Burn, 1993, 1994;

ouarda et al., 2201)and for regional estimation (dalrymple, 1960; hosking et al., 1985;Fill and Stedinger, 1998; Pandey and Nguyen 1999). Cunnane (1998) provided a


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general review of flood frequency analysis. More recently, theoretical and numerical

comprasion of the various regional estimation methodologies was presented in detail

by GREHYS (1996a,b). The index-flood method (IFM) is commonly used to develop

flood frequency models for gauged in stations, where hydrologic information is not

sufficiently available. As Maidment (1993) pointed out, the IFM is an accurate method

when its assumptions are satisfied. The basic assumptions of the IFM are that theregion under consideration is homogeneous in terms of the coefficient of variation

(i.e., the Cv of flood data series is constant within the region), and that the data at all

sites in the homogeneous region follow the same distribution.

Cunnane (1998) found that the IFM with a regional Wakeby distribution is the best

regional procedure. Moreover, Potter and Lettenmaier (11990) found that better

results could be achieved whit a regional Generalized Extreme Value (GEV)

distribution. Pitlick (1994) obtained regional flood frequency curves via the IFM for five

regions in the western United States based on probability-weighted moments of the

GEV distribution. The IFM was applied to the Portugal mainland, based on the

records of annual maximum flood series at 120 Portuguese stream gauging stations

(SGS) (Portela and Dias, 2005). As a result six homogeneous regions were identified,

and the models applicable to each region to estimate flood quantiles were

established. In Canada, there are 21 studies for the various regions of the country

that use the IFM method (Watt et al., 1989).

In this paper, regional flood frequency curves are developed based on the flood index

method and relationship(s) of mean annual flood (MAF) whit drainage area for

ungauged sites, which take as inputs flood data for basins of the West Mediterranean

region of Turkey.

THE REGIONAL FREQUENCY ANALYSIS

Gumbel Distribution

The Gumbel distribution is commonly used for maximum storm and flood

events. The cumulative probability function of the distribution is

(1)

Correspondingly, the T-year flood is given by

(2) (3)

Where is the location parameter, is the scale parameter, and is theGumble reduced variate for a T-year return period.

The mean and the variance of Gumble distribution are calculated as follows:

,

(4)

Where is Eulers constant. Hence the T-year event can be writtenas


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, (5)

Where is the frequency factor that depends on the return period. For N , the asymptotic values of the frequency factor ( ) can be written as

(6)Gumbel Distribution of Index Flood

Consider homogeneous region with M sites, each site j having sample size

and an observed annual flood series in year . The floodseries from a homogeneous region are identically distributed except for a site

specific scaling factor viz., the FIM. At each site, the flood series is normalized

by

, (7)

Where is the MAF at Site j, which is often used as the index-flood and isthe dimensionless flood coefficients. Each set of has thecharacteristics of and according to the expectations laws andthe variance theorems, and its skewness has the same skewness as

() (). This variable transformation produces observations ateach SGS in the series whit the same mean , but differentvariation coefficients. In this way, the comparison of flood observations at

different SGSs and also the comparison of various probability distribution

characteristics can be easily performed.

According to the above transformation, the T-year dimensionless flood

coefficient of any SGS can be written as

(8)When the Gumble distribution like the two-parameter lognormal distribution, is

selected to be representative for all SGSs in the region. Its distribution

characteristics will depend on the variation coefficients. Therefore, the regional

frequency distribution of dimensionless floods will only depend on the regional

coefficient of variation (, given as (NREC, 1975)

(9)

This value may be regarded as the expected value of variation coefficients in

the homogeneous region.

Then, the parameters of the regional Gumble distribution are given as

(10)


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III. APPLICATION OF THE IFM

The study area covers the three major hydrologic basins in the West Mediterranean

region of Turkey (see Figure 1). The General Directorate of State Hydraulic Works

(GDSHW) and General Directorate of Electrical Power Resources Survey and

Development Administration (GDEPSD) are responsible for the measurement of

stream data. The basins are named the West Mediterranean Basin (8th), AntalyaBasin (9th), and Burdur-Lakes Basin (10th).

River flows in the basins of the West Mediterranean Region are fed by rainfall

snowmelt, and karstic springs. Meanwhile, annual peak floods, especially at the

Upper-West Mediterranean subregion, are due to snowmelt. In the remaining parts

of the region, floods are caused by either heavy rainfall or snowmelt. Taking this fact

into account, the study area is divided into three subregions, namely the Upper-

West Mediterranean, the Lower-West Mediterranean, and the Antalya subregion.

Principal tributaries of the 8th basin are the Dalman, Esencay, and Basgoz Rivers,

and of the 9th basin are Aksu, Koprucay, Manavgat, and Alara Rivers, all originating

in the Taurus Mountains and flowing into the Mediterranean. The largest tributary in

the Burdur-Lakes basin is the Bozcay. The total drainage area of the three basins is

almost 48,000 km2 (GDSHW, 2000), with 48 streams gauging stations 19 of them

operated by GDEPSD (1956/2000) and 29 by GDSHW.

The GDSHW stations are identified by two numbers with the first number indicating

the basin number (for example, 08-019, 09-002, 10-002). The stations operated by

GDEPSD have a three or fout digit numbers in which the first or first two digits

designates the basin number (for example, 802, 901, 1003).

STATISTICAL PROPERTIES

The mean (Q0), standard deviation (s), coefficients of variation and skewness

, and mean annual flood per unit area (q0) of the historical data at 48gauging sites were obtained. A total of 48 historic time series of annual peak

flow discharges of West Mediterranean rivers were available for a common

period of years, from 1940 to 2000. The drainage areas ranged from 36to 6472 km2, and the coefficients of variation ranged from 0.167 to 1.823, witha mean of equal to 0.756. All coefficients of variation ranged from 0.3 to 1,

except at eight stations (906, 08-018, 09-007, 09-022, 09-039, 1003, 10-010,

and 10-011). Furthermore annual peak floods at all gauging sites are positively

skewed except at four stations (807, 906, 09-021, and 10-023). In addition the

peak floods at 09-011 and 09-042 are highly skewed. Because natively skewed

flood series are likely to occur in basins with substantial surface and

underground storage from year to year, the stream gauging stations that have

negative skewness coefficients are omitted from the analysis.

Mean Annual Flood per Unit Area-Drainage Area Relationships

The IFM is based on the identification of homogeneous groups of sites for which

the T-years flood can be expressed as the product of two terms. These two

terms are scale factor, which is called the index flood, and a growth factor,

which describes the relationship between the dimensionless flood and the


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recurrence interval, T.A fundamental assumption of the IFM is that flood data at

different sites in a region will follow the same distribution except for a scale or

an index factor, which is a function of the physiographical basin characteristics.

The catchment area is usually the most important factor is designated as the

flood magnitudes. The scaling factor is designated as the flood-index and is

usually taken as the mean annual flood.

For ungauged catchments, at-site means cannot be computed in absence of

observed flow data. In such a situation, a relationship between the mean annual

peak flood of gauged catchments in the region and their pertinent physiographic

and climatic characteristics is needed. As drainage areas (A) of the various

gauging sites were the only physiographic characteristics readily available , a

regional relationship has been developed in terms of drainage area for

estimation of mean annual peak flood (Qmean) for ungauged catchments. In this

study, two distinct zones were determined for the regional relationships

between mean annual flood per unit area ( and catchment area 8a).The regional relationships between and A were deloped in the log domainusing a least squares approach.

The relationship between mean annual flood per unit area and drainage area in

the Lower Zone was calculated as

(11)for and Similarly, the Upper Zone relationship is

(12)for and , where A designates the catchment area, in km2,and is the mean annual flood per unit area in (m3/s/km2), N is the number ofgauging stations, and is the correlation coefficient between the mean annualfloods per unit area and drainage areas of the SGSs.

Skewness Variation Coefficient Relationship

In the regional flood frequency analyses, the skewness coefficient is an

important parameter that can describe whether the assumed probabilitydistribution model for the peak flow values in a region is consistent or not.

Lettenmaier an Potter (1985) showed that the performance of the IFM gets

worse as either the regional mean increases. Homogeneity would beexpected to increase as regions are defined to include a smaller number of

sites. However, the performance of regional estimators also declines as smaller

and smaller regions are defined, because of the increasing variance of

parameter estimates. This suggests that a compromise is required. This can be

achieved by recognizing that different key characteristics of flood behavior are

approximately constant over different spatial scales. By measuring different

flood characteristics at different scales, we can maximize the benefits of poolingdata while minimizing the consequences of defining too large a region.


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In this study the linear relationship between the coefficient of skewness and

variation and is obtained as (13)

where

stations and

TESTING FOR REGIONAL HOMOGENEITY

Estimation of Missing Records

The Dalrympie (1960) method is a regional averaging IFM using records of

equal length, N. Whit this method, the missing records of the SGSs must be

filled. Dalrymple (1960) used regression analysis to fill records, but other record

filling methods have been reviewed, analyzed, and improved by Vogel and

Stedinger (1985).

In this study, the stations with longer records in the study area 901, 902, 802,

and 809. Station 701 was also used, although it is not within the study area, as

a base station representative of the 8th and 9thmajor basins to fill in missing

data in these basins. The common period of observation is selected as 1940-

2000, as nonce of the stations have records prior to 1940 (except 701). Missing

records at the stations in the study area were estimated by linear and nonlinear

regression analysis. For example, the missing records of Station 802 in 1959-

1963 and 1971-2000 were estimated by 809.

The power law regression between 802 and 809 is 0.3831;

(14)

HOMOGENEITY TEST

General. As a first approximation, regional homogeneity test were performed on

grouped stations based on their geographic proximity, whit the first group being

901 and 906, and the second group being 8-009, 8-061, 8-070, 9-047, 9-065,

10-013, and 10-023. This did not satisfy the regional homogeneity conditions

required. To preserve the base station Homa (901), another approach for the

partition of the study area, which consists of the three subregions, was tried.

After carious trials partitioning of the study area into subregions, it was decided

that Stations 08-018, 8-054, and 08-055 from the 8th basin, and 09-002, 09-

007, 09-011, 09-018,09-021,09-022, 09-039, 09-042, 09-047, and 09-065 fromthe 9th basin should be included with the 10th basin for homogeneity testing.

These three subregions are now called the Lower-West Mediterranean

subregion, Upper-West Mediterranean subregion, and Antalya subregion. In

tables 4-6, is the critical value at a selected level of confidence.Student Test on Coefficients of Variation.

To test whether or not the sample variation coefficient at any station issignificantly different from the regional variation coefficient (, the student-statistic (

) and the standard error of the variation coefficient (

) of a random

variable that follows a Gumble distribution are calculated as follow (Yevjevich,

1972):


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(15)

{[ ]} (16)The statistic follows a student- distribution with degrees offreedom. A comparison of with the critical value at a selected level ofconfidence is performed. The regional variation coefficients of each subregion,

along with sample estimates of variation coefficients at each site and theirstandard errors (), were calculated. Regional parameters of the homogenoussubregions are given in Table 1, and the Student- statics () and 95%confidence limits () for each gauging site are given null hypothesis is strictlyrejected for one station (812) in the Lower-West Mediterranean subregion, one

station (906) in the Antalya subregion, and seven stations (08-55,09-002, 09-

021, 09-047, 10-002, 10-013, and 10-023) in the Upper-West Mediterraneansubregion.

Dalrymples Homogeneity Test for Index Flood.

The homogeneity test recommended by Dalrymple (1960) has been very

popular among practicing hydrologists and has been recommended in various

studies (Chow, 1988; Kite, 1988; Singh, 1992). The homogeneity test is based

on an assumed underlying Gumble population. In this method, the mean

annual flood () of each at-site , the 10-year dimensionless flood coefficients(

), and the mean of the 10-year dimensionless flood coefficients (

are

calculated at each station in the region.

In this method, missing records in the common period are filled in by interstation

correlations. Data points are filled in this way are not used directly but only as

aids in assigning representative return periods to the recorded events. Both the

mean annual floods and return periods ( of the gauging stations in thecommon period are calculated analytically assuming a Gumbel distribution.


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For this purpose, the mean, the standard deviation, and variation coefficient, ofthe completed datasets are calculated. As the sample sizes at each site are

equal, the mean regional variation coefficient of the completed series is equal to

the arithmetic mean of the variation coefficients of the gauging stations in the

region.

The return period Tej corresponding to b10 in the parent distribution of each

gauging station are calculated as follows:

Tej = (1-exp (-exp (- ((10-1) / Cvoj + 0,45) / 0,7797)))^-118

Darlymple 1960 has derived the confidence limits (CL) for the standardderivation of the reduced variable Yt as.

(yT) exp (yT)/( )j 19

Assuming the yT values are normally distributed around the expected value

E(yT) as

yTj (CL) = E (yT)zc

.20

for 95% confidence, the standard normal deviate is approximately Zc=2.

Substituting Zc=2, T=10, and y10=2.25(for gumbel distribution, expected value


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of the reduced variate Yt corresponding to T=10 years is 2.25) in equation (20)

the confidence limits of the reduced variate are

U10j (CL) =E (yT).21

Moreover, dalrymple (1960) has recommended using the average efficient

sample size by the following equation, instead of the actual record lengths, Nj

Nej =

..22

The 95% confidence limits of the reduced variable corresponding to a return

period of 10 years can then be written as

U10f(CL) =2.25

..23

The 95% confidence limits of the return periods corresponding to b10 and

estimated from Naj samples are then calculated by

LCL(Tej)=(1-exp(-exp LCL(U10j)))^-1 ..24a

LCL(Tej)=( 1-exp(-exp UCL(U10j)))^-1..24b

The regional homogeneity hypothesis is rejected if Tej of the jth station lies

outside the confidence limits.

In this study, both the mean annual flood (x) and recurrence intervals (Tej) of

the SGSs in the common period are calculated analytically with respect to the

gumbel distribution. For this purpose, the mean, standard deviation and

variation coefficients of the completed datasets are calculated (xoj, Soj, Cvoj).

As the sample size at each site is equal to the arithmetic mean of the variation

coefficients of variation is computed as

Cvo =. . .25

Substituting this statistic in equation (8), the regional dimensionless flood

frequency factor relationship can be written as

T = 1+KTCvo26It should be noted that the b10 value defined by equation (17) can be replaced

by the value that is calculated from equation (27) for T=10 years.

10 = 1+K10Cvo.27

Furthermore, the Tej value at any site can be estimated analytically by using the

individual variation coefficient (Cvoj) of that SGS in the asymptotic relations.

Tej = (1-exp (-exp (- ((

10-1) / Cvoj + 0,45) / 0,7797)^

-128


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To check if some gauging stations do not satisfy regional homogeneity

Dalrymples 10 year event test was applied to each station. For this purpose,

the return periods (Tej) corresponding to the regional dimensionless flood (b10)

were calculated using the extended data at each site (Tables 5-7). According to

Dalrymples test, two gauges (818 and 08-058) in the Lower-West

Mediterranean subregion, five gauges (o8-055, 09-018, 09-021, 09-047, and10-013) in the Upper-West Mediterranean subregion, and one gauge (906) in

the Antalya subregion were omitted. These stations are showed with ($) in

tables 5-7.

TABLE 5. Dalrymple Test for Regional Homogeneity of SGSs in the Lower-West

Mediterranean.

Station N b10 Ne Te LCL(Te)

UCL

(Te)

802 1.6645 44 18 4 25

807 1.968 36 8 4 28

808 2.0204 50 8 4 24

809 1.8778 53 9 4 23

811 1.7253 50 13 4 24

812 1.5784 49 21 4 24

815 1.8487 45 10 4 25

818 1.406 42 58 4 26

08-001 2.6698 44 5 4 25

08-009 1.6481 46 16 4 25

08-013 1.9032 43 9 4 26

08-019 1.8668 47 10 4 24

08-028 1.7655 49 12 4 24

08-049 1.8241 46 10 4 25

08-058 1.4911 37 32 4 2808-060 1.98 42 8 4 26

08-061 2.1842 45 6 4 25

08-070 1.9053 45 9 4 25


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TABLE 6. Dalrymple Test for Regional Homogeneity of SGSs in the Lower-West Mediterranean.

Station

Nb10 Ne Te LCL(Te)

UCL

(Te)

08-018 2.5244 49 8 4 24

08-054 3.111 47 5 4 24

08-055 1.6098 43 58 4 26

09-002 1.9352 51 18 4 24

09-007 2.39 41 9 4 26

09-011 2.6216 49 7 4 24

09-018 1.5589 36 80 4 28

09-021 1.5763 36 71 4 28

09-022 2.2343 37 10 4 2709-039 2.0455 45 14 4 25

09-042 2.1811 42 11 4 26

09-047 1.5557 40 82 4 26

09-065 2.3074 43 10 4 25

1001 2.3376 36 9 4 28

1003 2.5423 42 8 4 26

10-002 2.3408 45 9 4 25

10-010 3.1908 41 8 4 26

10-011 3.1908 42 5 4 26

10-013 1.6387 44 50 4 25

10-023 3.17 42 5 4 25

TABLE 7. Dalrymple Test for Regional Homogeneity of SGSs in the Lower-West Mediterranean.

Station N b10 Ne Te LCL(Te)UCL

(Te)

901 1.3783 53 15 4 23902 1.6828 61 6 5 22

906 1.1684 39 187 4 27

911 1.4983 36 9 4 28

912 1.4157 49 12 4 24

916 1.4657 42 10 4 26

917 1.5721 42 8 4 26

918 1.5387 44 8 4 25

09-034 1.4951 37 9 4 27


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IV. RESULTS

This study attempted to use all unregulated gauging stations in the study area.

Gauging stations having long-term observation records were preferred. But stations

having shorter periods of observations were also considered with regression relations

between stream gauging stations used were poor, records of stations having shortobservations were extended to the common period, 1940-2000. Initially, a total of 48

stream gauging stations were used, and general statistical properties like variation

and skewness coefficient of the stream gauging stations, whether or not variation

coefficients were different from regional variation coefficient were evaluated. A total of

mine eight nonhomogeneous stations were determined by STUDENT-t test and

Dalrymple test, respectively, and omitted from the study.

The main objective of this study was to develop regional flood frequency estimates for

hydrologically homogeneous subregions, from which design event magnitudes at

desired location can be estimated.

Statistical and distributional characteristics of at-site flood data, mean annual flood

per unit vs drainage area and coefficient of skew vs.coefficient of variation

relationships were investigated. Three homogeneous subregion were identified and

the models applicable to each region to estimate flood quantiles were established.

The adopted index-flood was the mean annual flood. The regional frequency

distributions of the dimensionless floods at given return periods were determined for

the three subregions, namely the Upper-West Mediterranean, the Lower-West

Mediterranean, and Antalya regions of Turkey.

Regional parameters of the homogeneous subregio ns

The mean and the regional values of variation and skewness coefficients

(C,Cs,RC,RCs) of each homogeneous subregion were estimated through the

simple linear regression (equation 13) using RC, as the independent

variable(see Table 1)

The dimensionless peak floods, estimated individually at each site for

T=5,10,20,and 100 year return periods, along with their averages, are

computed under the assumption function at all sites is the Gumbel distribution.

The parameter estimates given in Tables 8-10 are also the asymptotic moment

estimators of and .

Hidrological ly Homogeneous Subregions

Regional homogeneity can be considered as a special case regional smoothing

where the component is constant. The two most commonly considered

measures by which regional homogeneity is assessed are dimensionless scale

and shape parameters, usually expressed as Cv and Cs. Alternatively, a

particular flood quantile, normalized by division by a particular index flood

(Dalrymple, 1960), may be the measure by which homogeneity is assessed.

Under the hypothesis that the Gumbel distribution is valid for all the gaugingsites in these three subregions, the Student-t test for equality of station and


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subregion variation coefficients and Dalrymples 10 year event recurrence

interval test were both applied at a 5% significance level. Results showed that

stations 812 in the Lower-West Mediterranean subregion; 08-055, 09-002, 09-

021, 09-047, 10-002, 10-013,and 10-023 in the Upper-West Mediterranean

subregion; and 906 in the Antalya subregion did not satisfy the regional

homogeneity conditions. Therefore, the remaining steps of regional analysiswere carried out by omitting these stations (remaining were 17 stations in the

Upper-West Mediterranean, 8 in the Antalya subregion and 19 in the Lower-

West Mediterranean).

Table 8. Dimensionless Floods for Various Return Periods in the Lower-West

Mediterranean.

Estacin N Cv T=5 T=10 T=20 T=50 T=100

802 1.198 1.07053 0.4609 1.862 2.563 3.236 4.106 4.758

807 1.148 1.11716 0.4834 1.826 2.498 3.142 3.977 4.602

808 0.678 1.89159 0.6949 1.488 1.885 2.265 2.758 3.127

809 0.619 2.07189 0.7215 1.445 1.807 2.154 2.604 2.94

811 1.061 1.20877 0.5226 1.763 2.384 2.979 3.75 4.327

815 0.806 1.59119 0.6373 1.58 2.051 2.503 3.088 3.527

08-001 1.14 1.125 0.487 1.821 2.488 3.128 3.956 4.577

08-009 0.517 2.48066 0.7674 1.372 1.675 1.965 2.341 2.623

08-013 0.666 1.92568 0.7003 1.479 1.868 2.242 2.726 3.088

08-019 0.623 2.05859 0.7197 1.448 1.812 2.162 2.614 2.953

08-028 0.578 2.21886 0.7399 1.416 1.754 2.078 2.498 2.813

08-049 0.638 2.01019 0.7129 1.459 1.832 2.19 2.654 3.001

08-060 0.715 1.79371 0.6783 1.515 1.933 2.335 2.885 3.244

08-061 0.529 2.42439 0.762 1.381 1.69 1.987 2.371 2.659

08-070 0.873 1.46907 0.6072 1.628 2.139 2.629 3.263 3.738

Mean 0.7322 1.75157 0.6705 1.5268 1.9553 2.3662 2.8982 3.2968


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Table 9. Dimensionless Floods in the UpperWest Mediterranean.


08-018 1.168 1.09803 0.4744 1.841 2.524 3.18 4.03 4.665

08-054 0.836 1.53409 0.6238 1.602 2.091 2.56 3.167 3.623

09-007 1.514 0.84709 0.3187 2.09 2.976 3.82 4.93 5.75

09-011 1.273 1.00746 0.4272 1.916 2.66 3.37 4.23 4.992

09-022 0.964 1.33039 0.5662 1.694 2.258 2.8 3.5 4.024

09-039 0.822 1.56022 0.6301 1.592 2.073 2.53 3.13 3.579

09-042 0.927 1.3835 0.5829 1.667 2.209 2.73 3.4 3.907

1001 1.025 1.25122 0.5388 1.738 2.338 2.91 3.66 4.216

1003 1.182 1.08503 0.4681 1.851 2.542 3.2 4.07 4.708

10-010 1.152 1.11328 0.4816 1.829 2.503 3.15 3.99 4.615

10-011 1.679 0.76385 0.2445 2.208 3.191 4.23 5.35 5.267

mean 1.0578 1.21242 0.524 1.7614 2.38 2.97 3.74 4.32

Tabla 10. Inundaciones adimensional en la subregin de Antalya


901 0.29 4.42241 0.8695 1.209 1.373 1.541 1.752 1.909

902 0.523 2.4522 0.7647 1.377 1.683 1.977 2.357 2.642

911 0.393 3.26336 0.8232 1.283 1.513 1.733 2.019 2.233

912 0.346 3.70665 0.8443 1.249 1.452 1.646 1.898 2.086

916 0.411 3.12044 0.8151 1.296 1.536 1.766 2.065 2.289

917 0.439 2.92141 0.8025 1.316 1.572 1.818 2.137 2.376

918 1.898 0.67571 0.1459 2.366 3.476 4.541 5.92 6.953

09-034 1.802 0.71171 0.1891 2.296 3.351 4.362 5.671 6.652

mean 0.7627 1.68153 0.6568 1.549 1.995 2.223 2.9773 3.392

Regional Relat ionsh ips

The correspondence of mean annual floods per unit area to the drainage area

indicated that these exist two distinct relations for the study area, with the

relationship of the Lower Zone differing from, but having the same form as, that

of the Upper Zone (Equations 11 and 12).

In the study, the relationship between skewness and variation coefficients is

statiscally meaningful. Although the regression coefficient (the slope) of

Equation (13) is very close to 3 (as for the lognormal), and the derived


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relationship is close to that for the Gamma, none of the probability distribution

functions has evaluated similar behavior for the whole region. When the

regional values of skew in the three subregions are considered, the choice of

Gumbel distribution has been approved for the Lower West Mediterranean,

Upper West Mediterranean, and Antalya subregions, but not for the entire West

Mediterranean has the regional skewness in that region is almost three timesthe theoretical skew of the Gumbel distribution(y1=1.14).

Using the regional values of coefficient of variation of the three subregions the

following dimensionless flood frequency factor relationships were obtained as

follows:

For the Upper-West Mediterranean

bt=1+0.9529KT

For the Lower-West Mediterranean

bt=1+ 0.5933Kt

for the Antalya subregion

bt=1-0.4848kT

WhereKt is the frequency factor.


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V. CONCLUSIONS AND RECOMMENDATIONS

In hydrology, sufficient information is rarely available at a site to adequately determine

the frequency of rare events. This is certainly the case for the extremely rare events,

which are of interest in hydraulic structures safety and risk assessment. Coping withfloods in an efficient manner and reducing damages necessitate efficient methods of

forecasting to provide sufficient lead-times to alert people living in the flood zones.

In this study, the regional analysis of annual peak floods in the basins of the West

Mediterranean Region of Turkey has been investigated. First, regional relationships of

mean annual flood per unit area-drainage area and coefficient of skew-coefficient of

variation were examined. Second two statistically meaningful relationships of mean

flood-per unit area and drainage area were obtained, one for the Upper Zone and one

for the Lower Zone. After removal of gauging stations that did not satisfy regional

homogeneity conditions, regional values of variation and skewness coefficients were

estimated, and a unique relationship between skewness and variation coefficients

relatively close to that of Gamma distribution was determinated.

IFM in available data at 48 gauging stations has shown that the study area that is

almost 48.132 km2 should be divided into three subregions as the Lower- West

Mediterranean the Upper- West Mediterranean, and the Antalya subregion.

This study serves as a preliminary aid in estimating design events that will be used to

design hydraulic structures in the basins of the West Mediterranean Region. The

purpose of the study was to derive regional flood frequency curves that could be of

initial usefulness in practical applications. This study should be improved by the other

regional frequency methods, and the results of these methods should be compared

with the results of this study.

Application of Index Procedures to Flood Frequency Analusis in Turkey

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