nitish thesis

CHAPTER I

INTRODUCTION

Estimation of design flood is one of the important components of planning, design and operation

of water resources projects. Information on flood magnitudes and their frequencies is needed for

design of hydraulic structures such as dams, spillways, road and railway bridges, culverts, urban

drainage systems, flood plain zoning, economic evaluation of flood protection projects etc.

Methods of flood estimation may be broadly divided into five categories viz. (i) flood formulae

and envelope curves, (ii) rational formula, (iii) flood frequency analysis, (iv) unit hydrograph

techniques and (v) watershed models. The generally adopted methods of flood estimation are

based on two types of approaches viz. (i) deterministic approach, and (ii) statistical approach.

The deterministic approach is based on the hydro meteorological technique, which requires

design storm and the unit hydrograph for a catchment. The statistical approach is based on the

flood frequency analysis using the observed annual maximum peak flood data. The choice of

method depends on the design criteria applicable to the structure and availability of data.

Hydrologic processes may be thought of as stochastic processes. Annual maximum daily rainfall

serves as example of stochastic hydrologic process. Hydrologic processes are continuous

process. Determination of the probability distribution of yearly maximum and minimum

discharges is of fundamental importance in many water resource design problems. In flood

frequency analysis, the objective is to establish a flow magnitude (Q) corresponding to any

required return period (T) of occurrence. That is, a past record is fit with a statistical distribution

function, which is then used to make inferences about future events. Identification of the true

statistical distributions for the various hydrologic and meteorological data sets (annual flood

peaks and annual maximum daily rainfall) continues to be a major question facing engineers and

scientists. An even greater problem facing hydrologists and meteorologists is the identification of

the distribution form for regional data.

1

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

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

rare events, which are of interest in dam safety risk assessment. One substitutes space for time by

using hydrologic information at different locations in a region to compensate for short records at

a single site.

Three approaches (Cudworth, 1989) have been considered for regional flood frequency analysis:

(1) average parameter approach; (2) index flood approach; and (3) specific frequency approach.

With the average parameter approach, some parameters are assigned average values based upon

regional analyses, such as the log-space skew or standard deviation. Other parameters are

estimated using at-site data, or regression on physiographic basin characteristics, perhaps the real

or log-space means. The index flood method is a special case of the average parameter approach.

It is a simple regionalization technique. The specific frequency approach employs regression

relationships between drainage basin characteristics and particular quantiles of a flood frequency

distribution. Regional analysis can be used to derive equations to predict the values of various

hydrologic statistics (including means, standard deviations, quantiles, and normalized regional

flood quantiles) as a function of physiographic characteristics and other parameters.

Flood frequency analysis, as commonly practiced, focuses on the estimation of return periods

associated with annual maximum flood peaks of various magnitudes. Based on an assumed

distribution, it is possible to make probability statements of future flows of various magnitudes.

The expected value of the random variable is also estimated for a given probability. For the

design purpose, T year design flood (T = 100, 50, 25, 10 or any desired year) is often required to

calculate from the best-fit distribution. So probability distribution plays a vital role in designing

structures and proper management of resources.

2

Popularly used continuous distributions are: Normal, Lognormal, Gamma, Pearson, LogPearson,

Generalized Extreme Value, Weibull, and Gumbel distribution. Commonly used parameter

estimation procedures are the method of moments (MOM) and the method of maximum

likelihood (MLE). Probability weighted moments (PWM) and method of maximum entropy

(MME) are of recent interest. But of late, a new method called L-moments was introduces which

has gained immense popularity.

L-moments of a random variable were first introduced by Hosking (1990). They are analogous to

conventional moments, but are estimated as linear combinations of order statistics. Hosking

(1990) defined L-moments as linear combinations of the Probability Weighted Moments. In a

wide range of hydrologic applications, L-moments provide simple and reasonably efficient

estimators of characteristics of hydrologic data and of a distribution's parameters (Stedinger et

al., 1992).

Frequency based design flood estimation primarily needs proper selection of the distribution to

be used to the previous years data to calculate T year return period flood. Selection of the

distribution can be done by goodness of fit test: Chi- Square Test or Kolmogorov-Smirnov Test.

Apart from the aforementioned tests the recently introduced L-moment ratio diagram based on

the approximations given by Hosking (1990) and the goodness of fit or behavior analysis

measure for a frequency distribution given by statistic distiZ described below, are also used to

identify the suitable frequency distribution. They have been proved to be very efficient in

selection of the distribution to be used.

In India, a number of studies have been carried out for estimation of design floods for various

structures by different organizations. Prominent among these include the studies carried out

jointly by Central Water Commission (CWC), Research Designs and Standards Organization

(RDSO) and India Meteorological Department (IMD) using the method based on synthetic unit

hydrograph and design rainfall considering physiographic and meteorological characteristics for

estimation of design floods3 and regional flood frequency studies carried out by RDSO using the

USGS and pooled curve methods4 for some of the hydro meteorological sub-zones of India.

3

Besides these, regional flood frequency studies have also been carried out at some of the

academic and research institutions. But, most of the regional flood frequency analysis studies

carried out in India are based on the conventional approaches.

The objectives of this study are:

(a) To test the independency of the data in space and time

(b) To screen the data using discordancy measure (Di), outliers test and regional

homogeneity test.

(c) To estimate the parameters of the various distributions considered.

(d) To carryout comparative regional flood frequency analysis employing some of the

commonly adopted frequency distributions using L-moment ratio diagram

(e) To develop a regional flood frequency relationship for the selected distribution of the

Mahanadi river basin.

4

CHAPTER II

REVIEW OF LITERATURE

For hydraulic structure design, to estimate the design flood, selection of return period and

probability distribution are required. Generally last 35 years data are necessary to analyze and

compute design flood. For a distribution, there may be more than one method of parameter

estimation. So it is necessary to know (a) which distribution function is to be used and (b) which

method should be followed. . The main modelling problem is the selection of the probability

distribution for the flood magnitudes coupled with the choice of estimation procedure .As such

there are essentially two types of models adopted in flood frequency analysis literature: (i)

annual flood series (AFS) models and (ii) partial duration series models (PDS). Maximum

amount of efforts have been made for modelling of the annual flood series as compared to the

partial duration series. In the majority of research projects attention has been confined to the

AFS models.

2.1 Data Screening

In flood frequency analysis, the data collected at various sites should be true representative of the

annual maximum peak flood measured and must be drawn from the same frequency distribution.

The first step in flood frequency analysis is to verify that the data are appropriate for the analysis.

They should be checked for randomness in time and space domain and presence of outliers etc.

Tests for outliers and trends are well established in the statistical literature (e.g., Barnett and

Lewis, 1994; W.R.C., 1981; Kendall, 1975).

Hosking and Wallis (1997) mention that in the context of regional frequency analysis using L-

moments, useful information can be obtained by comparing the sample L-moment ratios for

different sites, incorrect data values, outliers, trends and shifts in the mean of a sample can all be

5

related to L-moments of the sample. A convenient amalgamation of the L-moment ratios into a

single statistic, a measure of discordancy between L-moment ratios of a site and the average L-

moment ratios of a group of similar sites, has been termed as “discordancy measure”, Di.

2.2 Identification of Homogeneous Region

Hosking and Wallis (1997) mention that of all the stages in regional frequency analysis involving

many sites, the identification of homogeneous regions is usually most difficult and requires the

greatest amount of subjective judgement. The aim is to form groups of sites that approximately

satisfy the homogeneity condition, that the sites’ frequency distributions are identical apart from

a site-specific scaling factor. Several authors have proposed methods for forming groups of

similar sites for use in regional frequency analysis. A summary of these procedures and some of

the examples of their applications in regional frequency analysis, described by the authors is

given below.

The methods for forming homogenous group of sites can be categorized as geographical

convenience, subjective partitioning, objective partitioning, cluster analysis and other

multivariate analysis method

Under the procedure of geographical convenience the regions are often chosen to be sets of

contiguous sites based on administrative areas or major physical groupings of sites. To define

regions subjectively by inspection of the site characteristics such as annual maximum peak flood

data. Schaefer (1990) analyzing annual maximum peak flood data for sites in Washington State

formed regions by grouping together sites with similar values of mean annual precipitation. In

objective partitioning methods, regions are formed by assigning sites to one of the two groups

depending on whether a chosen site characteristic does or does not exceed some threshold value.

The threshold is chosen to minimize a within-group heterogeneity criterion.

6

Cluster analysis is a standard method of statistical multivariate analysis for dividing a data set

into groups and has been successfully used to form regions for regional frequency analysis. A

data vector is associated with each site, and sites are partitioned or aggregated into groups

according to the similarity of their data vectors. Hosking and Wallis (1997) regard cluster

analysis of site characteristics as the most practical method of forming regions from large data

sets.

For testing homogeneity, the Discordancy measure test and Heterogeneity measure test are

proposed and are used regularly since they give better results. Hosking and Wallis2

recommended a homogeneity test based on L-moment ratio. The importance of regional

homogeneity has been demonstrated by Hosking (1985), Wiltshire (1986) and Lettenmaier

(1987). There are several tests available to examine regional homogeneity in terms of the

hydrologic response of stations in a region, (Zrinji Z, 1996). In order to ensure that the resulting

regions are unique internally to a given level of tolerance, homogeneity and heterogeneity test

need to be performed.

2.3 Methods of parameter estimation

Method of moments (MOM) is the most commonly used for parameter estimation. The other

methods are method of maximum likelihood (MML), method of probability-weighted moments

(PWM) and method of maximum entropy (MME). For a distribution with m parameters, the

technique in method of moments is to equate the first m moments of the distribution to the first

m sample moments. This result in m equations that can be solved for the m unknown parameters.

Moments about the origin, the mean, or the any other points can be used. L-moments is a

recently found method which was proved to be very effective.

Method of moments can be applied in two ways to estimate parameters of the LogPearson type

III distribution. Method of W.R.C is the method of moments applied to the logarithms of flood

flows (referred to as the indirect method). Bobee (1975) proposed that the method of moments be

applied directly to the observed data (direct method). This method is named as Method of Bobee

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(MOB). First three moments about zero are used to estimate parameters in MOB. Phien and Hira

(1983) provided four additional methods for estimating parameters of the LogPearson type III

distribution, denoted by MM1, MM2, MM3 and MM4 (MM : mixed moments, as moments of x

and y (=logex) both are used ) and investigated the reliability of methods among that four

method, WRC and MOB. They showed that WRC, MM3 and MM4 produce unreliable estimates

for the parameters, and MOB did not performed well. Among the remaining three methods,

MM2, which is based on the first two moments of x and the variance of y, is the best, but it is

only slightly better than the MML, which in turn slightly better than the MM1, which is based on

the first two moments of x and the mean of y.

Singh et al (1986) employed the principle of maximum entropy to develop a procedure for

derivation of a number of frequency distributions used in hydrology. And they found that

principle of maximum entropy led to a unique technique for parameter estimation. The technique

is named as method of maximum entropy.

2.4 Selection of Distribution Function

There are several methods for regional selection of distribution such as moment ratio diagram,

product moment ratio diagram and L-moment ratio diagrams. An L-moment diagram compares

sample estimates of the L-moment ratios L-cv, L-skew, and L-kurtosis with their population

counterparts for a range of assumed distributions.

Haktanir (1992) made a comparison of various flood frequency distributions using annual flood

peaks data of rivers in Anatolia. He applied the 2-parameter lognormal, 3-parameter lognormal,

SMEMAX, two-step power, log-Boughton, Gumbel, general extreme value, Pearson type 3, log-

Pearson type 3, log-logistic and Wakeby distribution to the annual flood peaks series of 45

unregulated streams in Anatolia. He found that lognormal (3-parameter and 2-parameter) and the

Gumbel distribution predicted better than other distribution functions for the return period of

100, 1000 and 10000 years.

8

Vogel and Wilson (1996) studied extensively with the data of 1455 sites for the selection of

probability distribution of annual maximum, mean, and minimum stream flows in the US with

the help of L-moment diagrams. They concluded that the Log- Normal (3-parameter), Log

Pearson type 3, and Generalized Extreme Value models are all acceptable models in the

continental US, whereas other three-parameter alternatives such as the Pearson type 3 and

Extreme Value type 3 and two-parameter alternatives such as Normal, Gamma, Extreme Value

type 1 (maximum), and Log- Normal (2-parameter) are not acceptable for the entire continent.

Their study revealed that annual minimum stream flows in the US are best approximated by the

Pearson type 3 distribution, yet the Log Pearson type 3 or Extreme Value type 3 distribution

would suffice, whereas Pearson type 3, Log- Normal (3-parameter) and Log Pearson type 3

distributions provide better fit for annual average stream flows.

Parmesraran et al. (1999) developed a flood-estimating model for individual catchment and for

the region as a whole using the data of fifteen gauging sites of Upper Godavari Basins of

Maharashtra. Seven probability distributions have been used in the study. Based on the goodness

of fit tests log normal distribution is reported to be the best-fit distribution. A regional

relationship between mean annual peak flood and catchment area has been developed for

estimation of mean annual peak flood for ungauged catchments and regional relationship for

maximum discharge of a known recurrence interval for the ungauged catchments.

Kumar et al (2003) carried on flood frequency analyses by the method of L-moment diagrams

for Middle Ganga Plains Subzone (which covers parts of Uttar Pradesh, Bihar, Jharkhand and

West Bengal) and identified GEV distribution as the robust distribution for their study area.

9

CHAPTER III

THEORY

The following aspects of methodology used for development of L-moment based regional flood

frequency relationship for gauged catchments as well as development of regional flood formula

for estimation of floods of various return periods for ungauged catchments of are discussed as

follows.

(i) Probability weighted moments (PWMs) and L-moments,

(ii) Data screening

(iii) Test of regional homogeneity,

(iv) Frequency distributions used

3.1 Probability Weighted Moments (PWMs) and L-moments

L-moments of a random variable were first introduced by Hosking (1990). Hosking and Wallis

(1997) state that L-moments are an alternative system of describing the shapes of probability

distributions. Historically they arose as modifications of the probability weighted moments’

(PWMs) of Greenwood et al. (1979).

3.1.1 Probability weighted moments (PWMs)

The conventional moments or “product moments” involve higher powers of the quantile function

x(F); whereas, PWMs involve successively higher powers of non-exceedance probability (F) or

exceedance probability (1-F) and may be regarded as integrals of x(F) weighted by the

polynomials Fr or (1-F)r. As the quantile function x(F) is weighted by the probability F or (1-F),

10

hence these are named as probability weighted moments. The PWMs have been used for

estimation of parameters of probability distributions.

The first PWM estimator b0 is the sample mean µx. The higher PWMs can be calculated from the

order statistics Xn≤……≤X1. A simple estimator of br for r≥1 is:

(3.1)

When unbiasedness is important, the following relationships can be employed:

b0 = µx (3.2)

(3.3)

(3.4)

However, PWMs are difficult to interpret as measures of scale and shape of a probability

distribution. This information is carried in certain linear combinations of the PWMs. These linear

combinations arise naturally from integrals of x(F) weighted not by polynomials F r or (1-f)r but

by a set of orthogonal polynomials (Hosking and Wallis, 1997).

3.1.2 L-moments

Hosking (1990) defined L-moments as linear combination of probability weighted moments. L-

moments are summary statistics for probability distributions and data samples. They are

analogous to ordinary moments -- they provide measures of location, dispersion, skewness,

kurtosis, and other aspects of the shape of probability distributions or data samples -- but are

computed from linear combinations of the ordered data values (hence the prefix L).

L-moments have the following theoretical advantages over ordinary moments:

For L-moments of a probability distribution to be meaningful, we require only that the

distribution have finite mean; no higher-order moments need be finite

11

For standard errors of L-moments to be finite, we require only that the distribution have

finite variance; no higher-order moments need be finite

Although moment ratios can be arbitrarily large, sample L-moment ratios have algebraic

bounds

L-moments provide better identification of the parent distribution that generated a

particular data sample.

L-moments are less sensitive to outlying data values

L-moments are easily computed in terms of probability-weighted moments (PWMs) as given

below.

1 = 0 = 0 (3.5)

2 = 0 - 21 = 21 - 0 (3.6)

3 = 0 - 61 + 62 = 62 - 61 + 0 (3.7)

4 = 0 - 121 + 302 – 20 3 = 203 – 302 + 121 + 0 (3.8)

The procedure based on PWMs and L-moments are equivalent. However, L-moments are more

convenient, as these are directly interpretable as measures of the scale and shape of probability

distributions. Clearly 1, the mean, is a measure of location, 2 is a measure of scale or dispersion

of random variable. It is often convenient to standardise the higher moments so that they are

independent of units of measurement.

(3.9)

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Analogous to conventional moment ratios, such as coefficient of skewness 3 is the L-skewness

and reflects the degree of symmetry of a sample. Similarly 4 is a measure of peakedness and is

referred to as L-kurtosis. These are defined as:

L-coefficient of variation (L-CV), () = 2 / 1

L-coefficient of skewness, L-skewness (3) = 3 / 2

L-coefficient of kurtosis, L-kurtosis (4) = 4 / 2

Symmetric distributions have 3 = 0 and its values lie between -1 and +1. Although the theory

and application of L-moments is parallel to that of conventional moments, L-moment have

several important advantages. Since sample estimators of L-moments are always linear

combination of ranked observations, they are subject to less bias than ordinary product moments.

This is because ordinary product moments require squaring, cubing and so on of observations.

This causes them to give greater weight to the observations far from the mean, resulting in

substantial bias and variance.

3.2 Data Screening

In flood frequency analysis, the data collected at various sites should be true representative of the

annual maximum peak flood measured and must be drawn from the same frequency distribution.

The first step in flood frequency analysis is to verify that the data are appropriate for the analysis.

The preliminary screening of the data must be carried out to ensure that the above requirements

are satisfied. Statistical analysis of hydrologic data often assumes certain conditions of the data,

which have to be tested before proceeding with the analysis. One must verify that the flood data

is random based on statistical tests of independence in space and time.

3.2.1 Tests of independence

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When a sequence of observations is uncorrelated the auto correlation function for all lags other

than zero is theoretically equal to zero. However, when sampling from an uncorrelated series, the

estimated autocorrelation function rk is not equal to zero, but it has a sampling distribution,

which depends on the sample size N. This sampling distribution may be used to test hypothesis

that rk is not significantly different from zero. If the hypothesis is accepted, then the series is

uncorrelated, otherwise it is correlated. Thus the test of independence of time is based on the test

of correlogram rk. In addition to correlogram test, three other tests of independence are presented.

3.2.1.1 Anderson’s correlogram test

It has been shown that when the sample size N is large the distribution of rk is normal with mean

zero and variance 1/N.Therefore, the hypothesis is tested based on the 2 sided tolerance limits

given as

Where N =sample size

K=Lag=1

is the (1-α/2) quantile of the standard normal distribution.

The 95% confidence limits for the correlogram are mostly used for hydrologic data and that

implies that any given rk has a 5% chance of being outside the confidence limits.

The lag one serial correlation coefficient is calculated as

(3.10)

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, Where is the overall mean.

If the rk falls between the limits the data can be considered as independent in time.

3.2.1.2 Runs test

The basic principle behind the test is to look for a run of 0 or 1 in a sequence. The runs test looks

at a sequence to see if the oscillations between the zeros and ones are too fast or too slow.

Consider a series of observations yi, i=1, 2, 3……………….N, with N=sample size and as the

sample mean. The sequence of ones and zeroes can be found as

Wi =1 if

Wi =0 if

The run test is based on the assumption that if a series is independent, the number of total runs U

(runs of zeros and ones) is approximately normal with mean E(u) and variance

(3.11)

(3.12)

Where N1 is the no of ones in the series Wi, and N2 is the number of zeros. The test statistic T is

computed by

(3.13)

The hypothesis of independence is accepted at the γ= (1-α/2) probability level if:

15

(3.14)

Where is the (1-α/2) quantile of the standard normal distribution.

3.2.1.3 Spearman’s rank correlation coefficient test

Spearman’s Rank Correlation Test is used to test the strength of a correlation. When applied to

any two sets of results, the Spearman Test produces a Spearman Correlation Coefficient, r. This r

can take values between -1 and + 1. When r = -1, we have two sets of numbers that have a

perfect negative correlation. That is, without exception, as the value of one quantity in our

sample becomes larger, the value of the second quantity gets smaller. Similarly an r = +1

indicates a perfect positive correlation. Consider a sample series y i , i=1, 2, 3…………….N,

where N=sample size and let wi be the rank of yi when the series of observations is arranged in

ascending order. The spearman’s test is based on the rank correlation coefficient R between the

pairs (i,wi) for i=1, 2,………..N. This coefficient is computed by:

(3.15)

If the sample series is independent, the spearmans rank correlation coefficient R is normally

distributed, and 1-R2 has a chi square distribution with (N-2) degrees of freedom. Then the ratio

(3.16)

Follow the student t-distribution with N-2 degrees of freedom. The hypothesis is accepted when

(3.17)

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Where, t(1-α/2) ,(N-2) is the (1-α/2) quantile of the student’s t-distribution with N-2 degrees of

freedom.

3.2.1.4 Turning point test

This test counts the number of turning points (peaks and troughs) in a sequence. Let M be the

total no of peaks and troughs. To calculate the test statistic the number of samples tested needs to

be large. This allows for the assumption of a normal distribution with a mean of

E(M) = 2/3 (n − 2) (3.18)

and a variance of

(3.19)

The test characteristic T can then be calculated with the following equation

(3.20)

The hypothesis of independence is accepted at the (1-α) probability level if

(3.21)

Where is the (1-α/2) quantile of the standard normal distribution.

3.2.2 Discorancy and Homogenity

17

Once a set of physically plausible regions has been identified, it is desirable to assess whether the

region is meaningful and may be accepted as homogeneous. These tests include 2 types which

test the discordancy and heterogenity test. A convenient amalgamation of the L-moment ratios

into a single statistic, a measure of discordancy between L-moment ratios of a site and the

average L-moment ratios of a group of similar sites, has been termed as “discordancy measure”,

Di.

3.2.2.1 Discordancy measure

The aim of the discordancy measure is to identify those sites from a group of given sites that are

grossly discordant with the group as a whole. Discordancy is measured in terms of the L-

moments of the data of the various sites as defined below (Hosking and Wallis, 1997). Suppose

that there are N sites in the group. Let ui = [t(i) t3(i) t4

(i)]T be a vector containing the t, t3 and t4

values for site i: T denotes transposition of a vector or matrix. Let

(3.22)

be (unweighted) group average. The matrix of sums of squares and cross products is defined as:

(3.23)

The discordancy measure for site i is defined as:

(3.24)

The site i is declared to be discordant, if the discordancy measure is larger than the critical value

of the discordancy statistic Di given in Table 3.1.

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Table 3.1: Critical values of discordancy statistic, Di

No. of sites

in region

Critical value No. of sites in

region

Critical value

5 1.333 10 2.491

6 1.648 11 2.632

7 1.917 12 2.757

8 2.140 13 2.869

9 2.329 14 2.971

15 3

For a discordancy test with significance level an approximate critical value of maxi Di is (N-

1)Z/(N-4+3Z), where Z is the upper 100/N percentage point of an F distribution with 3 and N-4

degrees of freedom. This critical value is a function of and N, where = 0.10. Di is likely to be

useful only for regions with N 7.

3.2.2.2 Outliers test

Outliers are the data points which depart significantly from the trend of the remaining data. The

retention, modification, deletion of these outliers can significantly affect the statistical

parameters computed from the data. All the procedures for treating outliers require judgment

involving hydrological and mathematical considerations. The basic decision needed to be taken

are that the skewness values of the logarithm values should be less than 0.4 , if we get the

skewness more than 0.4 , we need to recompute the test statistics by adjusting the values of mean

and coefficient of variation.

The following equation is used to detect the high outliers

(3.25)

Where

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XH =high outliers threshold in log units

=Mean logarithm of systematic peaks excluding zero flood events and outliers

previously detected

S =standard deviation of peaks

Kn =K value from table given

If the logarithms peaks are in the sample are greater than XH then they are considered as high

outliers.

The equation used to detect the low outliers is

(3.26)

Where

XL=low outlier threshold in log units

And other terms are same as in above equation.

All the data, which are above the high outlier threshold and lower than the low outlier threshold,

are removed. Now for the sites identified as discordant, this outlier test is carried out to identify

the outliers and they are removed, now again all the L-moments are calculated and the L-moment

ratios are calculated.

3.2.2.3 Test of Regional Homogeneity

The test based on the heterogeneity measure H takes into consideration that in a homogeneous

region, all sites have same population L-moment ratios. But their sample L-moment ratios may

differ at each site due to sampling variability. The inter-site variation of L-moment ratio is

measured as the standard deviation of the at-site L-Coefficient of variation weighted

proportionally to the record length at each site. To establish what would be the expected inter-

site variation of L-moment ratios for a homogeneous region, 500 simulations were carried out

using the Kappa distribution for computing the heterogeneity measure, H.

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Heterogeneity measure H as given below.

v

VH v

(3.27)

Where V is the weighted standard deviation of the L-CV’s

v , v are the mean and standard deviation of the 500 sites generated.

If the value of

H 2 then region is heterogeneous

1 H < 2 region is possibly homogenous

H<1 region is acceptably homogenous

3.3 Probability distribution function and parameter estimation

The various distributions (Rao and Hameed, 2000) that are considered in the analysis are

3.3.1 Normal distribution

- < x < +; , >0 (3.28)

by integrating, we get the P(X)

Parameter estimation:

μ = l1 = b0 = sample average (3.29)

(3.30)

where l1 , l2 are the L moments.

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3.3.2 Exponential distribution

x>0, >0 (3.31)

else, (3.32)

Where λ, k are the parameters

Parameter estimation

Scale parameter λ is estimated as λ =2 l2 (3.33)

Location parameter k is estimated as k= l1 – λ (3.34)

where l1 , l2 are the L moments

3.3.3 Extreme Value Type I distribution

a, b>0 (3.35)

(3.36)

Where a, b are the scale and location parameters.


a = l2 / log (2)

b = l1 – 0.5772157a

Where l1, l2 are the L moments.

3.3.4 Pearson Type III distribution

(3.37)

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a>0 when >0, else a<0, b>0, 0<c<x


If t3 ≥ 1/3 , then

tm = 1 – t3 (3.38)

(3.39)

If t3 < 1/3 , then

tm = 3πt32 (3.40)

(3.41)

(3.42)

c = l1 –ab (3.43)

where l1 , l2 are the L moments,

t3 is the L-skewness ratio

3.3.5 Generalized Extreme Value Distribution

; k ≠ 0 (3.44)

; k = 0 (3.45)


(3.46)

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where, (3.47)

the scale parameter α is calculated by:

(3.48)

the location parameter ε is calculated from:

(3.49)

Where b0 , b1, b2 are the probability weighted moments.

3.3.6 Generalized Pareto distribution

(3.50)


(3.51)

(3.52)

(3.53)

where l1 , l2 are the L moments,

t3 is the L-skewness ratio.

24

3.3.7 Generalized Logistic distribution (GLO)

Inverse form of the Generalized Logistic distribution (GLO) is expressed as:

x (F) = u + [ [ 1 - {(1-F) / F}k ] / k; k 0 (3.54)

x (F) = u - ln {(1-F) / F}; k = 0 (3.55)

Where, u, and k are location, scale and shape parameters respectively. Logistic distribution is

the special case of the Generalized Logistic distribution, when k = 0.

3.3.8 Lognormal distribution (3 - parameter)

(3.56)


This is same as estimation of parameters for Pearson distribution. The difference is that

t3 is calculated from yi ( = log(Xi)).

If t3 ≥ 1/3 then

tm = 1 – t3 (3.57)

(3.58)

If t3 < 1/3 then

tm = 3πt32 (3.59)

25

(3.60)

c = l1 –ab (3.61)

3.4 Identification of Regional Frequency Distribution

The choice of an appropriate frequency distribution for a homogeneous region is made by

comparing the moments of the distributions to the average moments statistics from regional data.

This can be done by plotting the L-moment ratio diagram. The goodness-of-fit is judged by how

well the L-Skewness and L-kurtosis of the fitted distribution match the regional average L-

Skewness and L-kurtosis of the observed data. A sample L-moment ratio diagram can be shown

in fig 3.1

Fig 3.1 Theoretical L-moment ratio diagram

26

The data point of the regional average is highlighted and the distribution lying close to the point

is taken as the regional average distribution. This distribution is subjectively selected as the

regional distribution and the further analysis is carried on using this.

The L-moment ratio diagram for our region is drawn by the theoretical relationships and

approximations provided by Hosking, which can be used to identify the suitable regional flood

frequency distribution. Hosking has provided some relationships between L-skewness and L-

kurtosis, for all the distributions.

Generalized Pareto

t4= t3*(1+5* t3)/ (5+ t3) (3.62)

Generalized Logistic

t4= (1+5* t3* t3)/6 (3.63)

Generalized Extreme Value

t4=0.10701+0.1109* t3+0.84838* (t32)-0.3669(t3

3) +0.00567(t34)-0.04208(t3

5) +0.03763(t36)

(3.64)

Pearson Type 3

t4=0.1224 0.30115(t3) +0.95812(t34)-0.57488(t3

6) + 0.19383(t38) (3.65)

Lognormal

t4=0.12282+0.77518(t32) +0.12279(t3

3)-0.13638(t36)0.11368(t3

8) (3.66)

Where t4, t3 are the L-Skewness and L-Kurtosis for the site.

27

3.5 Estimation of the regional Parameters and Quantiles

The regional distribution is identified and the parameters for the whole region are to be

calculated. This is done using the regional mean method in which we consider the data of the

whole region as a single site and divide the site data by the site mean. Then the L-moments are

calculated for the whole region and the regional parameters are estimated for the selected

distribution. Substituting values of these regional parameters in the regional flood frequency

relationship, estimation of floods of various return periods for the catchments of Mahanadi river

system is done.

28

CHAPTER IV

DESCRIPTION OF THE STUDY AREA

The present study has been carried out for the region comprising of the catchment area of the

Mahanadi river basin. A brief description of the Mahanadi river basin and some of the tributaries

of the river Mahanadi whose data have been used in carrying out the study is given below.

4.1 Mahanadi river basin

Mahanadi basin extends over an area of 1,41,589 sq. km which is nearly 4.3% of the total

geographical area of India. It is bounded on the north by the Central India hills of Bundelkhand,

on the south and east by the Eastern Ghats and in the west by the Maikala range. The basin lies

in the state of Chhatisgarh, Orissa, Bihar and Maharasthra. Mahanadi rises from Raipur district

of Chhatisgarh and flows for about 851 km before it outfalls into the Bay of Bengal. Its main

tributaries are the Seonath, the Jonk, the Mand, the Ib, the Ong and the Tel.

The 15 sites are Baroda, Basanatapur, Ghatora, Jondhra, Kantamal, Kesinga, Kotni, Kurubhata,

Rajim, Ramnidh, Rampur, Salebhata, Sigma, Sundargarh, and Tikarapada.

The river system is as shown in the fig 1.the state wide distribution of the Mahanadi river basin

is given in table 4.1

Table 4.1 State-wise drainage area of Mahanadi basin

State Drainage area (sq. km)

Chhatisgarh 75136

Orissa 65580

29

Bihar 635

Maharastra 238

Fig. 4.1: Index map of river system of Mahanadi river basin

4.2 Data Availability for the Study

30

Annual maximum discharge data has been collected from the Office of the Central Water

Commission, Burla, Orissa and Office of the Central Water Commission, Bhubaneswar, Orissa.

The sites, which have minimum 20 years data, are analyzed. There are 15 sites in the Mahanadi

basin for which observed yearly maximum discharge data are available for at least 20 years.

Only measured discharge data are used for the analysis, no estimated values are considered. The

yearly maximum discharge for the 15 sites is given in Appendix A.

CHAPTER V

RESULTS AND DISCUSSION

The annual maximum peak flood data of the 12 gauging sites are available for carrying out the

study. The following aspects of analysis and discussion of results are described in this chapter

1) Calculation of L moments and L moment ratios for the data available for each

sample

2) Testing the data for independence in time and space using the following tests

- Anderson’s correlogram test

- Runs test

- Spearman’s rank correlation coefficient test

- Turning point test

3) Screening the data of the sites with Discordancy test and removing the outliers in

the discordant sites and testing the Homogeneity of the region.

4) Estimation of parameters for the sites for each distribution used.

5) Identifying the regional frequency distribution and estimation of the quantiles for

several return periods.

5.1 Calculation of L moments and L moment ratios

The sample statistics of all the sites are given in Table 5.1.1.

31

Table 5.1.1 statistics of the various sites in Mahanadi river basin

S.

No.

Name Sample

Size

(Years)

Mean Annual

Peak Flood

(m3/s)

Standard

Deviation

(m3/s)

Variance

(m3/s)2

1Baronda

26 2119.107 235.686 5563509

2Basantpur

33 13161.12 6718.263 45135052

3Ghatora

24 715.52 464.5778 215832.5

4Jhondhra

25 5024 2224.912 4760766

5Kantamal

29 8152.24 5185.042 26884659

6Kesinga

25 6540.83 5246.126 27521839

7Kotni

25 1888.74 1216.11 1478923

8Kurubhata

26 1463.99 455.2309 207235.2

9Rajim

30 3466.157 2983.992 8904207

10Ramnidhi

33 3831.076 2408.109 5798989

11Rampur

33 1658.969 1021.466 1043392

12Salebata

32 2372.672 2696.87 7273108

13Sigma

33 4066.924 2183.834 4769133

14Sundargarh

26 2709.873 2113.604 4467321

15Tikarpada

31 18466.14 7156.092 51209648

The probability weighted moments are calculated and then the L-moments are calculated from

them.The L-moments and the L- moment ratios L-coefficient of variation, L-skewness and L-

kurtosis and L- for the different sites are given in table 5.1.2.

32

Table 5.1.2 L-moments and L-moment ratios for the sites

Name L1 L2 L3 L4 L-cv L-s L-k

1Baronda

2119.1 1210.911 501.708 174.986 0.571425 0.414323 0.144508

2Basantpur

13161.1 3755.337 342.2685 525.6396 0.28533 0.09114 0.13997

3Ghatora

715.52 237.273 77.01019 62.3448 0.3316 0.3245 0.26275

4Jhondhra

5024 1204.117 184.4243 271.7705 0.23967 0.15316 0.2257

5Kantamal

8152.24 2996.834 104.8853 -291.51 0.367609 0.034999 -0.09727

6Kesinga

6540.83 2927.29 726.8339 163.139 0.447541 0.248296 0.05573

7Kotni

1918.532 656.7888 153.2407 124.4524 0.342339 0.233318 0.189486

8Kurubhata

1457.8 263.1805 -17.4602 -11.2457 0.180533 -0.06634 -0.04273

9Rajim

3466.157 1673.526 347.8738 -124.524 0.482819 0.207869 -0.07441

10Ramnidhi

3831.076 1360.212 137.5156 64.5708 0.355047 0.101099 0.047471

11Rampur

1658.969 593.4039 31.22839 19.68567 0.357694 0.052626 0.033174

12Salebata

2372.672 1156.504 522.5823 415.6877 0.487427 0.451864 0.359435

13Sigma

4066.924 1225.851 60.02222 153.032 0.30142 0.048964 0.124837

14Sundargarh

2709.873 993.614 449.1975 318.5188 0.366664 0.452085 0.320566

15Tikarpada

18466.14 4174.721 -53.4453 192.4355 0.226074 -0.0128 0.046095

5.2 Testing the Data for Independence in time and space

The selected data is tested for independence in time and space. For this 4 test have been

performed.

33

5.2.1 Anderson’s correlogram test

In this test if the lag one serial coefficient is with in the tolerance limits, then the data is accepted

as independent in space. The results of the test are given in Table 5.2.1.

Table 5.2.1 Anderson’s correlogram test results

S.no Name Lag one serial

coefficient

Upper

tolerance limit

Lower

tolerance limit

1Baronda

-0.27838 -0.42408 0.34408

2Basantpur

0.063 -0.37228 0.309776

3Ghatora

0.06 -0.44318 0.356227

4Jhondhra

0.0934 -0.43333 0.349993

5Kantamal

0.116 -0.39944 0.328016

6Kesinga

-0.029 -0.43333 0.349993

7Kotni

-0.105 -0.43333 0.349993

8Kurubhata

-0.258 -0.42408 0.34408

9Rajim

0.074 -0.39212 0.32315

10Ramnidhi

0.029 -0.37228 0.309776

11Rampur

-0.184 -0.37228 0.309776

12Salebata

0.0003 -0.37856 0.314044

13Sigma

0.0718 -0.37228 0.309776

14Sundargarh

-0.225 -0.42408 0.34408

15Tikarpada

0.219 -0.38516 0.318497

The table shows that for all the sites lag one serial coefficient is with in the tolerance limits.

Hence, the data is independent in time and can be considered as random.

5.2.2 Runs test

34

Run test is based on the assumption that, the hypothesis of independence is accepted if the mod

of test statistic T is less than the quantile of standard normal distribution. It is calculated as 1.96

from the statistics table for normal distribution. The results of the run test are given in Table

5.2.2.

Table 5.2.2 Run test results

S.no Name N1 N2 U E V T

1Baronda

9 17 14 12.76923 5.069822 0.546613

2Basantpur

16 17 16 17.48485 7.977043 -0.52573

3Ghatora

8 16 14 11.66667 4.483092 1.102016

4Jhondhra

8 17 10 11.88 4.478933 -0.88832

5Kantamal

15 14 13 15.48276 6.973841 -0.94015

6Kesinga

11 14 12 13.32 5.810933 -0.54758

7Kotni

11 14 16 13.32 5.810933 1.111762

8Kurubhata

15 11 18 13.69231 5.936095 1.768049

9Rajim

12 18 14 15.4 6.653793 -0.54274

10Ramnidhi

16 17 12 17.48485 7.977043 -1.94198

11Rampur

14 19 13 17.12121 7.617883 -1.49317

12Salebata

11 21 16 15.4375 6.258191 0.224853

13Sigma

14 19 16 17.12121 7.617883 -0.40623

14Sundargarh

8 16 12 11.66667 4.483092 0.157431

15Tikarpada

15 16 13 16.48387 7.475546 -1.27421

Note: N1 is the no of ones in the series; N2 is the number of zeros; E is mean; V is Variance

T is test statistic

As the test statistic is observed to be with in the limits (-1.96, +1.96), the run test shows all the

data to be independent.

5.2.3 Spearman’s rank correlation coefficient test

35

The Spearman’s test is based on the rank correlation coefficient R .If the sample series is

independent, the Spearman’s rank correlation coefficient R is normally distributed.The

hypothesis is accepted when the ratio T is within the desired limits. The results of test are given

in Table 5.2.3.

Table 5.2.3 Results for Spearman’s rank correlation coefficient test

S.no Name R T Quantile of students-tdistribution

1Baronda

0.153504 0.761034 2.06

2Basantpur

-0.37433 -1.2476 2.04

3Ghatora

0.046087 0.216397 2.07

4Jhondhra

-0.44769 -1.40113 2.07

5Kantamal

-0.06502 -0.33859 2.05

6Kesinga

0.093846 0.452065 2.07

7Kotni

-0.14885 -0.72188 2.07

8Kurubhata

0.123419 0.609284 2.07

9Rajim

0.23782 1.295596 2.05

10Ramnidhi

0.233623 1.337778 2.04

11Rampur

0.462901 2.007598 2.04

12Salebata

0.171371 0.952732 2.04

13Sigma

-0.31952 -1.87742 2.04

14Sundargarh

-0.21778 -1.09313 2.07

15Tikarpada

-0.13871 -0.75427 2.04

Note- R is Spearman’s rank correlation coefficient; T is test statistic

As the test statistic T is within the specified limits of the quantile of students-t distribution, the

hypothesis of independence can be accepted.

5.2.4 Turning point test

36

The turning point test is used to test the independence, and the test statistic T is calculated to

check if it is in the required limits of quantile of standard normal distribution. It is calculated as

1.96 from the statistics table for normal distribution. The results of the turning point test are

given in Table 5.2.4.

Table 5.2.4 Results of turning point test

S.no Name M E(M) Var(M) T

1Baronda

18 16 4.3 0.964486

2Basantpur

25 20.66667 5.544444 1.840319

3Ghatora

15 14.66667 3.944444 0.167836

4Jhondhra

16 15.33333 4.122222 0.328355

5Kantamal

18 18 4.333 0

6Kesinga

14 15.33 4.12222 -0.65507

7Kotni

17 16.6666 4.477 0.157569

8Kurubhata

21 16.667 4.477 1.047836

9Rajim

18 18.667 5.011 -0.29796

10Ramnidhi

23 20.667 5.5444 0.990803

11Rampur

25 20.6667 5.5444 1.415

12Salebata

22 20 5.3666 0.8633

13Sigma

22 20.6666 5.5444 0.566

14Sundargarh

16 16 4.33 0

15Tikarpada

19 19.33 5.188 -0.14

Note - E is mean; V is Variance; T is test statistic.

As all the calculated T values are with in the specified limit (-1.96, +1.96), the data can be

considered random.

5.3 Screening of Data

5.3.1 Discordancy test

37

The objective of the Discordancy measure (Di) test is to identify those sites from a group of

given sites that are grossly discordant with the group as a whole. Values of discordancy measure

have been computed in terms of the L-moments for all the 12 gauging sites of Mahanadi river

basin and are given in Table 5.3.1

Table 5.3.1 Discordancy measure for the 15 sites in Mahanadi river basin

S.no Name Sample

size

Di

1Baronda

26 1.368668

2Basantpur

33 0.383616

3Ghatora

24 0.762493

4Jhondhra

25 0.692982

5Kantamal

29 0.830140

6Kesinga

25 0.411843

7Kotni

25 0.113334

8Kurubhata

26 1.558653

9Rajim

30 1.585622

10Ramnidhi

33 0.173700

11Rampur

33 0.704656

12Salebata

32 1.764878

13Sigma

33 1.087157

14Sundargarh

26 2.005929

15Tikarpada

31 0.556330

As the numbers of sites are 15, the critical value of D i will be 3.0.The sites with value of Di

greater than 3.0 can be safely assumed to be discordant. It is observed in the table 5.3.1 that the

Di values for all the sites are less than the critical D i value of 3. Hence, as per the discordance

measure test, all the data of each site can be used for analysis.

5.3.2 Outliers test

38

Outliers are defined as the data which are extreme values and which deviate from the mean .So

we perform the outliers test to remove these extreme data values to get non discordant sites

which can be used in the flood frequency analysis. In the outliers test the higher outlier threshold

and lower outlier threshold is calculated and the data which are out side the threshold are

considered as outliers and are removed. Since the skewness values of the log values of the data

of all the sites are less than 0.4 the threshold values can be calculated using equation 3.25 and

3.26.The threshold values are given in Table 5.3.2

Table 5.3.2 Threshold outlier values for the sites

S.no Name Station

skewness

High outlier

threshold

Low outlier

threshold

No of

outliers

1Baronda 0.000259 4.365356 1.740561 Nil

2Basantpur -0.08464 4.717746 3.394231 Nil

3Ghatora 0.02416 3.4325 2.04521 Nil

4Jhondhra 0.2564 4.2198 3.1256 Nil

5Kantamal 0.0051 4.3105 2.9152 Nil

6Kesinga 0.00215 4.45621 2.8952 Nil

7Kotni -0.00312 3.8541 2.6874 Nil

8Kurubhata -0.3812 3.8756 2.8451 2

9Rajim 0.0023 3.9451 2.7456 Nil

10Ramnidhi 0.1456 4.1258 2.8923 Nil

11Rampur 0.2549 3.6412 2.1954 Nil

12Salebata 0.0045 4.2174 2.5621 1

13Sigma 0.0984 4.3567 2.689 Nil

14Sundargarh 0.2478 4.1247 3.0114 1

15Tikarpada 0.0098 4.5129 3.7489 Nil

The data of the sites, which are outside the higher outlier and lower outlier, are removed and the

remaining data is considered for further analysis.

39

5.3.3 Test of Regional Homogeneity

The test based on the heterogeneity measure H takes into consideration that in a homogeneous

region, all sites have same population L-moment ratios. To establish what would be the expected

inter-site variation of L-moment ratios for a homogeneous region, 500 simulations were carried

out using the Kappa distribution for computing the heterogeneity measure, H.

By performing the heterogeneity test we find that

Heterogeneity measure H = 2.48

Simulated mean of standard deviation of group L-CV = 0.06899

Simulated standard deviation of standard deviation of group L-CV = 0.013

Since the region heterogeneity measure H is more than 2, the region is declared as

heterogeneous. Based on the statistical properties (L-moment ratio) one by one, two sites of the

region were excluded till H value less than 1.0 was obtained.

The site with L-moments ratios near the theoretical limits are removed, the site Baronda is

identified with such kind of L-moment ratios and is removed. The heterogeneity measure H is

calculated after removing the site.




This shows that the region is not completely homogeneous, so the site Kurubhata is removed and

the heterogeneity measure H is calculated



40


The region is declared as homogeneous after the removal of the 2 sites Baronda and Kurubhata.

5.4 Probability distribution and parameter estimation

The parameters are estimated from the L moments calculated after removing the outliers.

For each distribution the parameters are estimated for all the sites and the values are shown in the

tables below.

5.4.1 Normal distribution

The normal distribution is a 2-parameter distribution with location and scale as the 2 parameters.

The values of these parameters for each of the site are given in Table 5.4.1.

Table 5.4.1 parameters for normal distribution

S.no Name Scale

Parameter

Location

Parameter

1 Basantpur 2119.107 377.833

2 Ghatora 13161.12 -1069.2

3 Jhondhra 5024 -563.84

4 Kantamal 8152.24 -1113.58

5 Kesinga 1888.74 -103.24

6 Kotni 1463.99 75.09

7 Rajim 3466.157 -197.426

8 Ramnidhi 3831.076 -547.844

9 Rampur 1658.969 -143.335

10 Salebata 2372.672 28.03418

11 Sigma 4066.924 -58.822

12 Sundargarh 2709.873 187.7129

41

13 Tikarpada 18466.14 -1528

5.4.2 Exponential distribution

This exponential distribution is also a 2-parameter distribution with the parameters as scale and

location; in this we usually find the lower endpoint of the distribution. The parameters are given

in Table 5.4.2.

Table 5.4.2 Parameter for Exponential distribution

S.no Name Scale

parameter

Location

parameter

1 Basantpur 2119.107 377.833

2 Ghatora 13161.12 -1069.2

3 Jhondhra 5024 -563.84

4 Kantamal 8152.24 -1113.58

5 Kesinga 1888.74 -103.24

6 Kotni 1463.99 75.09

7 Rajim 3466.157 -197.426

8 Ramnidhi 3831.076 -547.844

9 Rampur 1658.969 -143.335

10 Salebata 2372.672 28.03418

11 Sigma 4066.924 -58.822

12 Sundargarh 2709.873 187.7129

13 Tikarpada 18466.14 -1528

5.4.3 Extreme Value Type I distribution

42

The 2-parameters of Gumbell distribution are scale and location. The parameters are estimated as

given in Table 5.4.3.

Table 5.4.3 Parameters for Extreme Value Type I distribution

S.no Name Scale parameter Location parameter

1 Basantpur 2119.107 377.833

2 Ghatora 13161.12 -1069.2

3 Jhondhra 5024 -563.84

4 Kantamal 8152.24 -1113.58

5 Kesinga 1888.74 -103.24

6 Kotni 1463.99 75.09

7 Rajim 3466.157 -197.426

8 Ramnidhi 3831.076 -547.844

9 Rampur 1658.969 -143.335

10 Salebata 2372.672 28.03418

11 Sigma 4066.924 -58.822

12 Sundargarh 2709.873 187.7129

13 Tikarpada 18466.14 -1528

5.4.4 Generalized Extreme Value Distribution

Generalized Extreme Value distribution (GEV) is a generalized three-parameter extreme value

distribution; with location, scale and shape parameters .The parameters calculated are given in

Table 5.4.4.

Table 5.4.4 Parameters for Generalized Extreme Value distribution

S.no Name Location parameter Scale parameter Shape parameter

1 Basantpur 1715.964 160.9073 -0.66519

2 Ghatora 12435.99 -1402.02 2.025296

43

3 Jhondhra 5204.192 -1119.77 0.634611

4 Kantamal 8899.843 -1899.14 0.221893

5 Kesinga 2000.659 6.827214 -1.08763

6 Kotni 1415.525 135.5867 0.348667

7 Rajim 3402.287 -356.506 1.413514

8 Ramnidhi 3899.201 -1106.03 0.855534

9 Rampur 1811.089 -41.883 -0.75805

10 Salebata 2358.699 52.80088 0.430737

11 Sigma 4081.273 -5.82743 -2.15349

12 Sundargarh 2879.634 140.0148 2.72744

13 Tikarpada 19941.5 -1682.29 -0.23534

5.4.5 Generalized Pareto distribution

The 3-parameters of Generalized Pareto distribution are location, scale and shape. The estimated

parameters are given in Table 5.4.5.

Table 5.4.5 Parameters of Generalized Pareto distribution

S.no Name Location

parameter

Scale parameter Shape

parameter

1 Basantpur 1597.622 -0.6198 198.2689

2 Ghatora 26099.01 10.10053 -143617

3 Jhondhra 7212.318 1.881098 -6304.76

4 Kantamal 11340.17 0.862775 -5938.39

5 Kesinga 2006.745 -0.85698 -16.8772

6 Kotni 1220.07 1.248373 548.4241

7 Rajim 4848.422 5.001435 -8295.58

8 Ramnidhi 6332.483 2.565914 -8919.81

9 Rampur 1839.794 -0.73845 -47.2952

44

10 Salebata 2337.642 -0.75044 8.742157

11 Sigma 4136.54 -0.81651 -12.7738

12 Sundargarh -3162.82 29.28553 177857.8

13 Tikarpada 21534.17 0.007874 -3092.19

5.4.6 Generalized logistic distribution (GLO)

The 3 parameter of Generalized logistic distribution are location, scale and shape. The estimated

parameters are given in Table 5.4.6.

Table 5.4.6 Parameter of Generalized logistic distribution

s.no Name Location

parameter


parameter

1 Basantpur 1782.044 148.4513 -0.68053

2 Ghatora 12196.89 -399.379 0.694669

3 Jhondhra 4858.692 -534 0.180512

4 Kantamal 8217.497 -1111.26 -0.03553

5 Kesinga 1990.281 -15.2519 -0.86652

6 Kotni 1471.224 74.66708 0.058463

7 Rajim 3322.223 -125.446 0.50009

8 Ramnidhi 3586.455 -479.022 0.28134

9 Rampur 1794.464 -39.1811 -0.7687

10 Salebata 2346.041 7.312231 -0.77813

11 Sigma 4124.129 -11.2321 -0.83193

12 Sundargarh 2894.983 25.53706 0.876106

13 Tikarpada 19254.36 -1268.01 -0.32984

5.4.7 Pearson Type III distribution

45

The 3 parameter of Pearson Type III distribution are location, scale and shape. The estimated

parameters are in the Table 5.4.7.

Table 5.4.7 parameters for Pearson Type III distribution

S.no Name Location

parameter


parameter

1 Basantpur 2119.108 1092.799 4.694024

2 Ghatora 13161.12 -3165.31 -4.86308

3 Jhondhra 5024 -1037.57 -1.09478

4 Kantamal 8152.245 -1977.08 0.218141

5 Kesinga 1918.532 524.32 1.1562

6 Kotni 1457.8 132.1077 -0.2157

7 Rajim 3466.157 -454.186 -3.07984

8 Ramnidhi 3831.076 -1060.17 -1.69059

9 Rampur 1658.969 -489.287 5.94009

10 Salebata 2372.672 50.0616 -0.48235

11 Sigma 4066.924 2563.8 2.2489

12 Sundargarh 2709.873 880.997 -8.7679

13 Tikarpada 18466.14 -3049.44 1.97941

5.5 Identification of Regional Frequency Distribution

5.5.1 L-moment ratio diagram

The choice of an appropriate frequency distribution for a homogeneous region is made by

comparing the moments of the distributions to the average moments statistics from regional data.

46

The L-moment ratios for the different distributions and the different sites are calculated, using

the approximations provided by Hosking. The L-moment ratios are given in Table 5.5.1.

Table 5.5.1 L-moment ratios for different distributions

Name t3 t4 for

Generalized

pareto

t4 for

Generalized

logistic

t4 for

Generalized

extreme

value

t4 for

Pearson

type 3

t4 for

Lognormal

Basantpur 0.09114 0.026059 0.17359 0.124114 0.149913 0.129352

Ghatora 0.3245 0.159827 0.25442 0.230008 0.2301 0.208497

Jhondhra 0.15316 0.052482 0.18621 0.143657 0.169044 0.141444

Kantamal 0.034999 0.008167 0.16769 0.111928 0.132941 0.123775

Kesinga 0.248296 0.106044 0.21804 0.185819 0.200684 0.17246

Kotni 0.233318 0.096594 0.21203 0.178215 0.195412 0.166557

Rajim 0.207869 0.081399 0.20267 0.166119 0.186743 0.157407

Ramnidhi 0.101099 0.029837 0.17518 0.126824 0.152945 0.13087

Rampur 0.052626 0.013156 0.16897 0.115186 0.138256 0.124985

Salebata 0.451864 0.270141 0.33682 0.323956 0.293866 0.291463

Sigma 0.048964 0.012072 0.16866 0.114466 0.137151 0.124693

Sundargarh 0.452085 0.270353 0.33698 0.32414 0.293998 0.291631

Tikarpada -0.0128 -0.0024 0.1668 0.105729 0.118545 0.122947

The L-moment ratio diagram is plotted using these L-moment ratios with L-Skewness on X-axis

and L-kurtosis on Y-axis. The regional average is shown as a point in the Fig 5.1.

47

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

L-sk

L-k

u

Series2

Generalized pareto

Generalized logistic

GEV

pearson type 3

Log Normal (2 & 3 Parameters)

Regional Average

Fig 5.1 L-moment ratio diagram for the Mahanadi river basin

As shown in Fig 5.1, the GEV distribution lies closest to the point defined by the regional

average values of L-skewness, 3=0.180769 and L-kurtosis, 4 =0.147863 and the same is

identified as the regional distribution.

5.5.2 Estimation of the regional Parameters and Quantiles

The parameters for the whole region are estimated using the regional mean method in which we

consider the data of the whole region as a single site and divide the site data by the site mean.

The mean of each site is given in Table 5.5.2

48

Table 5.5.2 Mean of Annual peak flood of each region

S.no Name Mean Annual Peak

Flood

(m3/s)

1 Basantpur 13161.1

2 Ghatora 715.52

3 Jhondhra 5024

4 Kantamal 8152.24

5 Kesinga 6540.83

6 Kotni 1918.532

7 Rajim 3466.157

8 Ramnidhi 3831.076

9 Rampur 1658.969

10 Salebata 2372.672

11 Sigma 4066.924

12 Sundargarh 2709.873

13 Tikarpada 18466.14

The new data is obtained after dividing the site data by the site mean, it is shown in Appendix B.

Data samples = 33+24+25+29+25+25+30+33+33+32+33+26+31=379 samples

Then the L-moments are calculated for the whole region and the regional parameters are

estimated for the selected distribution.

The total number of data Sample for the whole region =379

Mean Annual Peak Flood =1.000003 (m3/s)

The Probability weighted moments and the first 4 L-moments are

L1 =1.000003, L2=0.355577, L3=0.066369, L4=0.048527

49

The L-moment ratios are

L-coefficient of variation (L-CV), () = 0.355576

L-coefficient of skewness, L-skewness (3) = 0.186653

L-coefficient of kurtosis, L-kurtosis (4) = 0.136473

The regional parameters for the GEV distribution are calculated from the regional average L-

moments, as

Location parameter, ξ = 0.697923

Scale parameter, α = 0.500565

Shape parameter, k = -0.025920

The GEV distribution has been identified as the robust distribution for the study area.

The form of the regional frequency relationship for GEV distribution is expressed as:

Qt/Qm = ξ + α (yt) (5.1)

Where, Qt is T-year return period flood estimate;

Qm is the mean of the

ξ and α are the parameters of the GEV distribution

Qt/Qm is called the growth factor.

and yt is GEV reduced variate corresponding to a T year return period

(5.2)

Where, K=regional shape parameter

Substituting values of the regional parameters in the above equations the regional flood

50

frequency relationship for estimation of floods of various return periods for the catchments of

Mahanadi river system is calculated and shown in Table 5.5.3

Table 5.5.3 Values of the Peak Flood for various return periods

Return

period, T

Growth factor for

various return periods

Flood estimate of

T year return periods

2 0.881387 5030.604

5 1.448740 8268.828

10 1.824377 10412.81

25 2.184698 12469.38

50 2.298996 13121.75

100 2.651096 15131.4

200 3.000596 17126.2

500 3.348820 19113.73

1000 3.808242 21735.92

5.6 Summary of the Results

The results shown above can be summarized as following

1) Regional flood frequency analysis has been carried out based on L-moments approach,

considering the annual maximum peak flood data of 15 locations of the Mahanadi river

basin. The data collected were tested for independence in space and time. Four tests were

performed to test the hypothesis of independence and the data was found to be

independent and random.

2) Discordancy measure (Di) test was carried out and it was found that the data of the sites is

not discordant. Outlier test was performed to remove the outliers existing in the data. By

carrying this test the outliers were removed and this data was used for further analysis.

The L-moment based homogeneity test, namely, heterogeneity measure, shows that the

51

region is heterogeneous. Hence 2 of the sites Baronda and Kurubhata are removed based

on the statistical properties (L-moment ratio), and the remaining sites are found to be

homogeneous.

3) Various distributions, namely 2 parameter distributions as Normal, Exponential, and

Extreme Value Type 1, 3 parameter distributions as Generalized Extreme

Value,Generalized Logistic, Generalized Pareto and Pearson Type 3 have been

employed. Regional parameters of the distributions have been estimated using the L-

moments based approach. Based on the L-moment ratio diagram GEV distribution has

been identified as the robust distribution for the study area.

4) For estimation of floods of various return periods for the catchments of the study area the

developed regional flood frequency relationship is used and the flood estimates for

various return periods are calculated.

52

CHAPTER VI

Conclusions

On the basis of this study following conclusions are drawn:

The annual maximum discharge data collected from the Office of the Central Water

Commission has been tested for independence and made free from extreme values.

The flood frequency analysis is carried out using L-moments and L-moment ratio

diagram is helpful in easy identification of frequency distribution.

GEV distribution has been identified as the robust distribution for the study area and this

is used to calculate the flood frequency formulae. The peak floods for various return

periods are calculated.

The superiority of using this method has been thoroughly proved in this study. This

method can be easily employed for both the at-site and regional flood frequency analysis.

53

REFERENCES

1. Bobee, B., (1975). “The log Pearson type 3 distribution and its applications in hydrology”. Water Resour. Res., 11(5): 681-689.

2. Haktanir, T., (1992). “Comparison of various flood frequency distributions using annual flood peaks data of rivers in Anatolia”. J. Hydrol., 136: 1-31.

3. Hosking J.R.M., (1990). L–moments: analysis and estimation of distribution using linear

combination of order statistic. J. Royal Stat. Soc. B, 52, 105-124.

4. Hosking, J.R.M. (1985). The theory of probability weighted moments. Res. Rep. RC12210,

IBM Res., Yorktown Heights, N.Y.

5. Hosking, J. R.M., and Willis, J. R., (1997). “Some statistics useful in regional frequency

analysis”. Water Resour. Res., 29(2): 271-281.

6. Kumar, R., Chatterjee, C., Kumar, S., Chani, A. K. L., and Singh, R. D., (2003).

“Development of regional flood frequency relationships using L-moments for middle

Ganga Plains subzone 1(f) of India”. Water Resources Management.,17:243-257.

7. National Institute of Hydrology, (1992). Hydrologic design criteria. Course Material of

Regional Course on Project Hydrology, Roorkee.

8. Rao, A. R., and Hamed, K. H., (2000). Flood Frequency Analysis. CRC Press, Boca Raton,

Florida.

9. Singh, V. P., Rajagopal, A. K. and Singh, K., (1986). “Derivation of some frequency

distributions using the principle of maximum entropy (POME)”. Adv. Water Resources.,

9: 91-106.

54

10. J R Stedinger, R M Vogel and E Foufoula-Georgiou (1992). Frequency Analysis of Extreme

Events.in. Handbook of Hydrology. (ed) D R Maidment, Mc Graw- Hill, New York.

11. Subramanya, K., (1999). Engineering Hydrology. Tata McGraw-Hill Publishing Company

Limited, New Delhi, India.

12. Wiltshire, S.E., (1986a). Regional flood frequency analysis I: Homogeneity Statistics.

Hydrological Sciences Journal, 31, 321-333

13. Vogel, R. M., and Wilson, I., (1996). “Probability distribution of annual maximum, mean,

and minimum stream flows in the United States”. J. Hydrologic Engg., 1(2) :69-76.

55

APPENDICES

Appendix A: Yearly maximum discharge data of 15 sites of Mahanadi river basin.

Table A1 Yearly maximum discharge data of Baronda

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1978 118.7 1987 384 1996 784.3

1979 546.2 1988 205.5 1997 4754

1980 6034 1989 219.5 1998 244.7

1981 597 1990 3104 1999 466.4

1982 1069 1991 2466 2000 452.8

1983 1607 1992 3456 2001 6256

1984 1709 1993 848 2002 406.7

1985 1087 1994 3795 2003 9323

1986 3968 1995 1195

Table A2 Yearly maximum discharge data of Basantpur

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1971 17875 1982 9624 1993 10506

1972 9552 1983 9340 1994 17661

1973 15431 1984 15655 1995 12987

1974 15381 1985 11200 1996 5983

1975 19823 1986 18512 1997 4355

1976 26142 1987 5650 1998 8789

1977 15632 1988 6002 1999 7234

1978 18819 1989 2742 2000 5134

1979 12516 1990 14916 2001 15685

1980 21920 1991 14059 2002 3402

1981 12310 1992 16392 2003 33088

56

Table A3 Yearly maximum discharge data of Ghatora

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1980 1300 1988 628 1996 1019

1981 545 1989 137.2 1997 450.4

1982 275 1990 453.6 1998 1259

1983 529.5 1991 1033 1999 658.2

1984 588 1992 579.8 2000 220.8

1985 729 1993 1315 2001 749.5

1986 478 1994 2276 2002 383.2

1987 680 1995 436.5 2003 449

Table A4 Yearly maximum discharge data of Jondhra

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1979 7390 1988 3737 1997 5980

1980 11033 1989 1720 1998 4341

1981 4444 1990 7132 1999 3681

1982 4372 1991 5076 2000 2811

1983 4704 1992 5001 2001 4669

1984 6752 1993 4428 2002 1600

1985 5953 1994 8533 2003 4402

1986 7679 1995 4309

1987 2068 1996 3785

Table A5 Yearly maximum discharge data of Kantamal

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1975 4700 1985 14781 1995 8648

57

1976 11973 1986 5098 1996 1891

1977 15374 1987 3231 1997 11982

1978 10998 1988 1541 1998 924.1

1979 14317 1989 2336 1999 2274

1980 12960 1990 13623 2000 3661

1981 8851 1991 11428 2001 12770

1982 16300 1992 15223 2002 2852

1983 2059 1993 5950 2003 3815

1984 5196 1994 11659

Table A6 Yearly maximum discharge data of Kesinga

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1979 5891 1988 1160 1997 8143

1980 11157 1989 1463 1998 576.0

1981 9220 1990 19396 1999 1368

1982 4829 1991 9584 2000 2452

1983 1655 1992 17569 2001 13200

1984 4142 1993 2753 2002 1988

1985 8655 1994 11734 2003 10814

1986 3707 1995 6638

1987 2484 1996 2943

Table A7 Yearly maximum discharge data of Kotni

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1979 1883 1988 439.0 1997 2094

1980 2017 1989 463.3 1998 938.9

1981 1429 1990 3305 1999 754.4

1982 1917 1991 2399 2000 1513

1983 1499 1992 2286 2001 2000

1984 2934 1993 895.4 2002 613.3

1985 1536 1994 4972 2003 2269

58

1986 5098 1995 2754

1987 1004 1996 950

Table A8 Yearly maximum discharge data of Kurubhata

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1978 756 1987 1925 1996 1625

1979 1149 1988 973.1 1997 1033

1980 1721 1989 1809 1998 1828

1981 789.2 1990 1167 1999 2160

1982 1780 1991 1788 2000 820

1983 871 1992 881.5 2001 1978

1984 1548 1993 1008 2002 1671

1985 2120 1994 1638 2003 1919

1986 1660 1995 1285

Table A9 Yearly maximum discharge data of Rajim

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1974 690.8 1984 1678 1994 7916

1975 2765 1985 1652 1995 3019

1976 8154 1986 4498 1996 3468

1977 7100 1987 414.4 1997 6094

1978 7669 1988 272.4 1998 475

1979 818.7 1989 254.5 1999 863.6

1980 8376 1990 7449 2000 1161

1981 1681 1991 6122 2001 713.3

1982 1210 1992 5926 2002 838

1983 2680 1993 1577 2003 8449

59

Table A10 Yearly maximum discharge data of Ramnidhi

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1971 5760 1982 4594 1993 1259

1972 4688 1983 1195 1994 6401

1973 4575 1984 7202 1995 3046

1974 3150 1985 4940 1996 4507

1975 10889 1986 3473 1997 814.3

1976 5446 1987 6658 1998 4187

1977 5802 1988 1546 1999 1719

1978 2707 1989 916.0 2000 930.8

1979 2349 1990 1318 2001 3037

1980 6137 1991 5304 2002 722.4

1981 3663 1992 759 2003 6731

Table A11 Yearly maximum discharge data of Rampur

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1971 1090.4 1982 3578.0 1993 2250.0

1972 1396.0 1983 1079.0 1994 2815.0

1973 3278.0 1984 1433.0 1995 2764.0

1974 1435.0 1985 1511.0 1996 231.2

1975 1340.0 1986 2063.0 1997 2520.0

1976 2132.0 1987 2582.0 1998 291.6

1977 1366.8 1988 79.24 1999 1044.0

1978 2472.0 1989 371.9 2000 84.55

1979 1880.0 1990 2803.0 2001 1365

1980 3163.0 1991 889.7 2002 619.6

1981 482.0 1992 3240.0 2003 1096

60

Table A12 Yearly maximum discharge data of Salebhata

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1972 764.8 1983 3864 1994 2577

1973 787.0 1984 1701 1995 4764

1974 3423 1985 2645 1996 398.3

1975 800.0 1986 3771 1997 2428

1976 2696 1987 939.0 1998 581.7

1977 1356 1988 310.0 1999 1935

1978 2352 1989 533.7 2000 114.0

1979 1547 1990 1514 2001 3225

1980 2317 1991 1560 2002 1545.0

1981 1087 1992 924 2003 7616.0

1982 14509 1993 1341

Table A13 Yearly maximum discharge data of Sigma

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1971 665 1982 2727 1993 2353

1972 1703 1983 3572 1994 10726

1973 6319.5 1984 5338 1995 4557

1974 3484 1985 4064 1996 4028

1975 5761 1986 5615 1997 4917

1976 3423 1987 499 1998 2189

1977 5563 1988 843 1999 2216

1978 6965 1989 1157 2000 2825

1979 4392 1990 5909 2001 3441

1980 6522 1991 5050 2002 1950

1981 4110 1992 6460 2003 4865

61

Table A14 Yearly maximum discharge data of Sundargarh

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1978 1528 1987 6343 1996 6341

1979 1180 1988 2842 1997 1306

1980 1808 1989 914.4 1998 10404

1981 2400 1990 1350 1999 2030

1982 2152 1991 3556 2000 2000

1983 2070 1992 1896 2001 3200

1984 3409 1993 1208 2002 2069

1985 3965 1994 2587 2003 1338

1986 1710 1995 850.3

Table A15 Yearly maximum discharge data of Tikarapada

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1972 9928.4 1983 30042 1994 22068

1973 20625 1984 24727 1995 15831

1974 16871 1985 23921 1996 11930

1975 22715 1986 26391 1997 18536

1976 26324 1987 9757 1998 15226

1977 28693 1988 9575 1999 9524

1978 30863 1989 6539 2000 4632

1979 14227 1990 19918 2001 26700

1980 26324 1991 15883 2002 12306

1981 14961 1992 20085

1982 19528 1993 17800

62

Appendix B: Yearly maximum discharge data of 13 sites of Mahanadi river basin after dividing

each one of them by the regional mean.

Table B1 Yearly maximum discharge data of Basantpur

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1971 1.358169 1982 0.731246 1993 0.798262

1972 0.725775 1983 0.709667 1994 1.341909

1973 1.17247 1984 1.18949 1995 0.986772

1974 1.168671 1985 0.850993 1996 0.454597

1975 1.506181 1986 1.406569 1997 0.330899

1976 1.986308 1987 0.429295 1998 0.667801

1977 1.187743 1988 0.456041 1999 0.54965

1978 1.429896 1989 0.208341 2000 0.390089

1979 0.950984 1990 1.13334 2001 1.19177

1980 1.665514 1991 1.068224 2002 0.258489

1981 0.935332 1992 1.245489 2003 2.514076

Table B2 Yearly maximum discharge data of Ghatora

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1980 1.81686 1988 0.877683 1996 1.424139

1981 0.761684 1989 0.191749 1997 0.629472

1982 0.384336 1990 0.633945 1998 1.759559

1983 0.740021 1991 1.443705 1999 0.91989

1984 0.82178 1992 0.81032 2000 0.308587

1985 1.018839 1993 1.837824 2001 1.04749

1986 0.668046 1994 3.180903 2002 0.535555

1987 0.950358 1995 0.610046 2003 0.627516

63

Table B3 Yearly maximum discharge data of Jondhra

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1979 1.470939 1988 0.74383 1997 1.190287

1980 2.196059 1989 0.342357 1998 0.864053

1981 0.884554 1990 1.419586 1999 0.732683

1982 0.870223 1991 1.01035 2000 0.559514

1983 0.936306 1992 0.995422 2001 0.929339

1984 1.343949 1993 0.881369 2002 0.318471

1985 1.184912 1994 1.698447 2003 0.876194

1986 1.528463 1995 0.857683

1987 0.411624 1996 0.753384

Table B4 Yearly maximum discharge data of Kantamal

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1975 0.576529 1985 1.813121 1995 1.060813

1976 1.468676 1986 0.62535 1996 0.231961

1977 1.885862 1987 0.396333 1997 1.46978

1978 1.349077 1988 0.189028 1998 0.113355

1979 1.756204 1989 0.286547 1999 0.278942

1980 1.589747 1990 1.671074 2000 0.449079

1981 1.085714 1991 1.401823 2001 1.566441

1982 1.99945 1992 1.86734 2002 0.349842

1983 0.252569 1993 0.729861 2003 0.46797

1984 0.637371 1994 1.430159

Table B5 Yearly maximum discharge data of Kesinga

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

64

1979 0.90065 1988 0.177348 1997 1.244949

1980 1.705747 1989 0.223672 1998 0.088062

1981 1.409607 1990 2.965373 1999 0.209148

1982 0.738286 1991 1.465257 2000 0.374876

1983 0.253026 1992 2.686051 2001 2.018093

1984 0.633253 1993 0.420895 2002 0.303937

1985 1.323227 1994 1.793962 2003 1.653307

1986 0.566748 1995 1.014856

1987 0.379768 1996 0.449943

Table B6 Yearly maximum discharge data of Kotni

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1979 0.981496 1988 0.228825 1997 1.091478

1980 1.051342 1989 0.241491 1998 0.489393

1981 0.744853 1990 1.7227 1999 0.393224

1982 0.999218 1991 1.250456 2000 0.788637

1983 0.78134 1992 1.191556 2001 1.042481

1984 1.52932 1993 0.466719 2002 0.319677

1985 0.800625 1994 2.591608 2003 1.182695

1986 2.657284 1995 1.435496

1987 0.523326 1996 0.495179

Table B7 Yearly maximum discharge data of Rajim

year

maximum

discharge

(m3/sec)year

maximum

discharge

(m3/sec)year

maximum

discharge

(m3/sec)1974 0.199299 1984 0.484111 1994 2.283802

1975 0.797715 1985 0.476609 1995 0.870995

1976 2.352466 1986 1.297693 1996 1.000534

1977 2.048382 1987 0.119556 1997 1.758147

1978 2.212541 1988 0.078589 1998 0.13704

1979 0.236199 1989 0.073424 1999 0.249153

1980 2.416514 1990 2.14907 2000 0.334954

1981 0.484976 1991 1.766225 2001 0.20579

1982 0.34909 1992 1.709678 2002 0.241767

65

1983 0.773192 1993 0.454972 2003 2.437575

Table B8 Yearly maximum discharge data of Ramnidhi

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1971 1.503496 1982 1.199143 1993 0.328629

1972 1.223679 1983 0.311923 1994 1.670813

1973 1.194183 1984 1.879893 1995 0.795078

1974 0.822225 1985 1.289457 1996 1.176434

1975 2.842287 1986 0.906535 1997 0.212552

1976 1.421535 1987 1.737896 1998 1.092906

1977 1.514459 1988 0.403543 1999 0.4487

1978 0.706591 1989 0.239098 2000 0.242961

1979 0.613145 1990 0.344029 2001 0.792729

1980 1.601902 1991 1.38447 2002 0.188564

1981 0.95613 1992 0.198117 2003 1.75695

Table B9 Yearly maximum discharge data of Rampur

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1971 0.657279 1982 2.156773 1993 1.356271

1972 0.841491 1983 0.650407 1994 1.696846

1973 1.975937 1984 0.863794 1995 1.666104

1974 0.865 1985 0.910812 1996 0.139364

1975 0.807735 1986 1.24355 1997 1.519024

1976 1.285142 1987 1.556397 1998 0.175773

1977 0.82389 1988 0.047765 1999 0.62931

1978 1.49009 1989 0.224177 2000 0.050966

1979 1.13324 1990 1.689613 2001 0.822805

1980 1.906616 1991 0.5363 2002 0.373487

1981 0.290543 1992 1.953031 2003 0.660655

66

Table B10 Yearly maximum discharge data of Salebhata

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1972 0.322337 1983 1.628545 1994 1.086118

1973 0.331694 1984 0.716914 1995 2.007865

1974 1.442679 1985 1.114778 1996 0.16787

1975 0.337173 1986 1.589349 1997 1.02332

1976 1.136273 1987 0.395757 1998 0.245167

1977 0.571508 1988 0.130654 1999 0.815537

1978 0.991288 1989 0.224936 2000 0.048047

1979 0.652008 1990 0.6381 2001 1.359228

1980 0.976537 1991 0.657487 2002 0.651165

1981 0.458134 1992 0.389435 2003 3.209886

1982 6.115052 1993 0.565186

Table B11 Yearly maximum discharge data of Sigma

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1971 0.163514 1982 0.670532 1993 0.578571

1972 0.418744 1983 0.878306 1994 2.637377

1973 1.553879 1984 1.312541 1995 1.120504

1974 0.856668 1985 0.999282 1996 0.99043

1975 1.416551 1986 1.380652 1997 1.209023

1976 0.841669 1987 0.122697 1998 0.538245

1977 1.367866 1988 0.207282 1999 0.544884

1978 1.712598 1989 0.28449 2000 0.694629

1979 1.079933 1990 1.452942 2001 0.846095

1980 1.603671 1991 1.241726 2002 0.479478

1981 1.010593 1992 1.588426 2003 1.196237

67

Table B12 Yearly maximum discharge data of Sundargarh

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1978 0.563865 1987 2.340703 1996 2.339965

1979 0.435445 1988 1.048759 1997 0.481942

1980 0.667191 1989 0.337433 1998 3.839299

1981 0.885651 1990 0.498179 1999 0.749113

1982 0.794134 1991 1.31224 2000 0.738043

1983 0.763874 1992 0.699665 2001 1.180868

1984 1.257994 1993 0.445778 2002 0.763505

1985 1.46317 1994 0.954658 2003 0.493751

1986 0.631027 1995 0.313779

Table B13 Yearly maximum discharge data of Tikarapada

year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec) year

maximum

discharge

(m3/sec)

1972 0.537655 1983 1.626873 1994 1.195055

1973 1.116912 1984 1.339048 1995 0.857301

1974 0.91362 1985 1.295401 1996 0.646049

1975 1.230092 1986 1.429159 1997 1.003785

1976 1.425531 1987 0.528374 1998 0.824538

1977 1.55382 1988 0.518518 1999 0.515756

1978 1.671333 1989 0.354108 2000 0.250838

1979 0.770439 1990 1.078625 2001 1.445893

1980 1.425531 1991 0.860117 2002 0.66641

1981 0.810187 1992 1.087669

68

1982 1.057505 1993 0.963928

69

nitish thesis

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