Issue (Volume No. 34, Number 3)

INTIntecostenepowenebiom67.2souhydto discdatamapgeo

To regiAccfreqin thshowithdiscexcdiscThediveotheFDC(193

Regdifferoleparaflowvalidvarierro

Key

1.

2.

3.

TRODUCTernational oil ct has shifted rgy. Renewab

wer, biomass, rgy generationmass and smal26, 4.26 and 1

urces respectidropower projelack of gaug

charge data avaa can be estimpping the sit

ographical simi

overcome thionalization ocording to Vogquency plot thahe stream is eqwn in Fig. 1. Fhout considerincharge correseedance of timcharge is impoe low dependaerting water foer uses. ResearC estimation 34) takes the

REGIO

gionalization of fferent methods foe. The flow at geameters, other m

w estimation anddation and booious regionalizaors in the review

ywords: Regiona

Research SchInstitute of Uttarakhand, e-mail: ila.da

Senior ScienIndian InstituUttarakhand,

Professor, DTechnology R

Manuscript N

TION crisis due to limthe attention

ble energy sougeothermal ha

n. It is seen thll hydro power2.50 percent oively in Indects have problging stations ailability. Thes

mated either be data of galarity with ung

he problem of flow duratgel & Fennesseat shows the pequalled or exceFDC presents eng the sequensponding to

me is known as ortant for plannable flow studyor power generrchers in recentechniques fo

e credit of be

NAL FLO

I

flow duration cufor regionalizatioeologically similamethods like dimd this drawback tstrap resamplin

ation methods ofwed FDC method

al Flow Duration

holar; AlternateTechnology R

India; Tel.: [email protected]

tific Officer; Aute of Technolo India

Department of Roorkee, Roorkee

No. 1363

mited fossil fuetowards harneurces like solave given newhat solar energr sources of enof generation adia (MNRE lem in estimatiand inapprop

se missing, shoby mathematicauged station gauged sites.

of inapproprition curve is ey (1995) FDCercentage of timeeded during aentire range of

nce of occurrenthe particu

dependable dining of water y helps for decration or publicnt years have dor ungauged eing the initi

OW DURADE

Ila Dashor

urve (FDC) is aon of flow in thear ungauged siteensionless flow of estimation prng are highly ref FDC for hydrods.

n Curve, Hydrop

e Hydro EnergyRoorkee, Roor1 9720 429628; om

Alternate Hydroogy Roorkee, Ro

Hydrology, Inde - 247667, Utta

el and rising fuessing renewablar, wind, hydw dimensionsgy, wind pownergy share 7.3among renewab

2014). Smion of power dpriate length ort and ungaugal models or

having certa

iate flow daa useful to

C is a cumulatime that dischara specific time f streamflow dance. In FDC, tular percentascharge. The losupply schemcision making c water supply eveloped variosites but Fosator of detail

ATION CUVELOPM

a1, S. K. Si

ABa helping tool foe past. For the es can be predicand drainage arrocedure necessiecommended anopower planning

power, Uncertain

y Centre, Indiarkee - 24766

Energy Centroorkee - 24766

dian Institute oarakhand, India

uel ble dro

to wer,

31, ble

mall due

of ged by ain

ata, ool. ive rge as

ata the age ow

mes. in or

ous ster led

descrip

Cunnanreasonasamplemainly Class ilength the rankvalues discharpresent

( >QP

Where,varies bthe flowmethodconsidelose infshould

Many (1964),McMahhydroloand irrithe sele

URVE MEMENT: A R

ingal2 and

STRACT for flow estimati

estimation of rected by parametrrea methods canitates a reliabilind reliable test g. A comparativ

nty Analysis, Ung

an 7,

re, 7,

of

ption of FDC.

ne (1978) statable, as all pos size. It has btwo methods

interval methoof the availablking method isfor the high d

rge. This metted in (Eq. 1)

1)+

−=>N

iX

, N is the totalbetween 1 to Nw data are largd discharge dering suitable formation fromfall in single in

researchers lik, Gupta (1989hon (1993) andogical applicatigation planninection of a wa

J

ETHODS FREVIEW

D. K. Sriva

on at ungaugedegional FDC, phric method using be used. There ity test. It has bemethods. The p

ve analysis of va

gauged Catchme

Fig 1: T

ted that any psitions are virtubeen found in

to plot FDC iod. Selection ole data. In cases found suitabldischarge and thod is based

11

1 ++−

=+ N

iN

number of daN. The class inge like daily odata is dividinterval as larg

m data. Normalnterval.

ke Beard (1949), Warnick (d Cigizoglu (19tions such as ng. Male and Oaste water treat

Journal of India

FOR HYD

astav3

d sites. Various hysiographic pag regression tecis always an unceen found in thepresent study is alidation is also

ent.

Typical flow d

plotting positioually identicalthe literature t

i.e. (i) Rankingof method depe of monthly ole. This method

higher valuesd on Weibull

ays in observednterval method r hourly mean

ded into varige interval haslly, around 10%

43), Searcy ((1984), Maid997b) used FDhydropower,

Ogawa (1984) utment plant ca

an Water Resour Vol 34, No.3

DROPOW

researchers havarameters play ahniques. In absecertainty associa

e review that Jaca comprehensiv

o carried out to

duration curve7

on would be l for the large that there are g method, (ii) pends on the

or yearly data, d gives lower s for the low l formula as

(1)

d record and i is used when

n flow. In this ious classes, s tendency to % of the data

1959), Chow dment (1992), DC for various

water supply used FDC for

apacity. Some

rces Society, 3, July, 2014

ER

ve developed an important ence of these ated with the ckknife cross ve review of estimate the

e

reseleanWocapandusindevexte(199(199flow

REReeregiaddManKae(199Clapregigeo

MimmorLeBrankstudintenonmulgau

earchers have an flow period oods and Gulacity consider

d Fennessey (1ng stream flveloped a metending observe96), Hughes 97) explored tw and synthesis

EGIONAL Fed (1984) fouionalisation of

dressing the prny researcheremaki (1985), 96), Smakhtinps (2005) ionalization

ographical cond

mikou and Karphoclimatic Boutillier and king statistics.dy by Vogel ervals and recun-parametric fltivariate statis

uged-stations in

Dependab

applied FDC fo(Riggs 1972;

lliver (1990) ring financial b1994) developeow data. Huthod based oned time series oand Smakhtinthat annual FDse stream flow

FLOW DURund that the f FDC was giveroblem of regis such as QuLeBoutillier a

n (1997), Singand Croke

of FDC unditions through

aemaki (1985)characteristicsWaylen (19

The annual dand Fennesse

urrence intervaframework. Ystical analysis n Southern Taiw

F

With PhyParam

ble Flow

or water quality Fennessey anestimated hy

benefits based ed empirical eughes and Sn the FDC foof daily stream

n (1996) and DC can fill gapw in regional mo

RATION CUresearch worken less attentiononal flood freuimpo (1983)and Waylen (gh (2001) , Yer (2003) wnder various hout the world.

) regionalizeds of the d

993) defined data based inteey (1994) enaals associated

Yu and Yang using daily flowan.

ig. 2: Schemat

siographic meters

Param

y managementnd Vogel 199ydropower pla

on FDC. Vogequation on FDSmakhtin (199for patching am flow. Franch

Smakhtin et ps, extend streaodel.

URVE k related to tn as compared

equency analys), Mimikou a1993), Franch

Yu et al. (200worked for t

climatic a

d FDC by usidrainage basthe FDC usi

erpretation in tabled confiden

with FDCs in(2002) appli

ow data from t

tic Diagram fo

ReDu

Ungau

metric Flow

J. Indian

t in 0). ant gel DC 96) and hini

al. am

the d to sis. and hini 2), the and

ing sin. ing the nce n a ied the

Arora (estimatthat floarea anthe lonwith thand foureview carried

REGIThe pr

sites camethodliteratuapproacphysiog

Physiogstream lengthtransferof geogcan beestimatdata ndimensin the remotel

With PIn thisphysiogthe fur

or regionaliza

egional Flow ration Curve

uged catchmen

Dime

Water Resou

(2005) studiedtion of the subow for a givennd decreases wng-term FDC uhe help of statiund that these

on some of out and discus

IONALIZAroblem related

an be resolveds for regionaure. These mches: with pgraphic parame

graphic paramcharacteristicsof stream.

rred to ungauggraphical conde the basis tion without phneed to transsionless flow tabsence of inly located sites

Physiographs method, a graphic characrther computa

ation of flow d

nt

Witho

ensionless flow

ur. Soc., Vo

the effect of ab-basins of the n dependability

with altitude. Causing five yeaistical, graphice estimation te

the regionalizssed in the sub

ATION METto the assess

ed using regioalization of F

methods can bphysiographic eters as shown

meters include s such as area These parame

ged site for estditions of both

for applicabihysiographicalsform into mtechniques. Thnformation abos or in sufficien

hic Parametermodel is d

cters of the gauation of ungau

duration curve

out PhysiograpParameters

w Dr

l. 34, No. 3,

altitude on wateChenab river

y increases wiastellarine (200ars of observeal and paramechniques are azation methodsequent section

THODS ment of FDC

onalization of FDC are avaibe divided in

parameters in (Fig. 2).

rainfall-runoffand slope of ceters of gaugtimation of flogauged and un

ility. For anal parameters on

mathematical mhese methods aout geographicnt data length.

rs developed usiuged catchmenuged catchme

e

phic

rainage area ramethod

July, 2014

8

er availability and observed ith catchment 04) estimated d streamflow

etric approach accurate. The ds have been n.

at ungauged

FDC. Many ilable in the nto different and without

f relation and atchment and ged site are

ow. Similarity ngauged sites alysing flow nly discharge model using are applicable cal condition,

ing available nt to apply for ent. Different

tio

J. Indian Water Resour. Soc., Vol. 34, No. 3, July, 2014

9

methods for developing regional FDC have been evolved by various investigators in the past and out of those, two methods are outlined here under.

Dependable flows The evaluation of dependable flows can be carried out using corresponding number of probability of exceedance. In such situation, the dependable flows may be regionalized rather than regionalizing the FDC. For the accuracy of this method, adequate numbers of gauging sites having the flow series of the specific duration for a sufficiently long period are required. This method is applicable to hydro meteorological homogeneous region. In this method flow duration curve for each gauging station is plotted and the desired dependable flow for each gauging site is selected. After selecting the dependable flow, regional relation is to develop using pertinent catchment characteristics using linear regression.

The typical regional relationships for 50% and 90% dependable flows are given below

32150

aa HAaQ = (2)

32190

bb HAbQ = (3)

where, Q50 and Q90 are the 50% and 90% dependable flows, respectively. A and H represent the catchment area and relief respectively, a1, a2, a3,b1, b2 and b3 are the constants to be determined by using linear regression or stepwise regression approach.

Parametric approach Hydrological variations in different catchments are the outcome of diversification in geography and climate. Parametric approach develops a relation between these known parameters of gauged sites and then implements this relation to homogeneous ungauged site. Geographically homogeneous sites on the basis of discharge data were described by Acreman and Sinclair (1986), Wiltshire (1986), Hughes (1987) and Burn and Boorman (1993). Investigators also developed single indices to map the catchment and hydrologic responses like Reimers (1990) developed average annual flow, baseflow index were developed by Nathan & McMahon (1990) and Q95 has formulated by Laaha & Blöschl (2007), runoff ratio were generated by Berger & Entekhabi (2001), and baseflow recession curve was characterised by Zecharias & Brutsaert (1988) and McNamara et al. (1998) and Post & Jones (2001) developed relation with vegetation and topography.

Acreman and Wiltshire (1989) developed an approach by giving a fractional membership to different regions having ungauged sites and weighted by the probability of membership to obtain good prediction for each region. Burn (1990 a,b), Burn and Zrinji (1994), Robson and Reed (1999) and Burn and Goel (2000), described the method on region of influence (ROI) for an ungauged site and applied for flood estimation in further research.

GLPF GRANT Report (2007) described homogeneous region using multiple linear regression models to produce FDC and

found that the model with high flow rate show more accurate prediction in comparison to the lean flow.

Male and Ogawa (1984), Tasker (1972) and Vogel and Kroll (1990) developed multiple linear regression equations for homogeneous region of Massachusetts using physiographical, geologic, climatic and geomorphic parameters as given in (Eq. 4)

dcb XXaX 321=Θ (4)

Where, X1, X2 and X3 are the independent variables and a, b, c and d are model parameters to estimate the flow for ungauged sites.

In the initial phase of development of regionalization, Quimpo et al. (1983) proposed (Eq. 5) and (Eq. 6) for parameterizing FDC at ungauged potential small hydropower sites in Philippines.

( )cDQQ A −= exp (5) baDQ −= (6)

Where, D indicates the percentage of time that Q exceed during the period of record and QA and a, b and c are positive constants. This method only includes the discharge of the gauged site so the accuracy of the estimation is less. The drawback of this method is that, it is applicable in small catchment or part of the same river basin where other parameters are same.

Mimikou and Kaemaki (1985) performed a study analogous to the study by Quimpo et al. (1983). The authors used a third order polynomial equation to estimate Q(D) as given in (Eq. 7)

( ) 32 dDcDbDaDQ −+−= (7)

where the parameters a, b, c and d have to be positive. The parameters a, b, c and d can be calculated using (Eq. 8) by stepwise regression technique. This regression expression uses mean annual precipitation, drainage area, hypsometric fall and length of the main river course to estimate FDC at ungauged site.

HmRmAmma aaaa3210ln +++= (8)

In this method addition of more geographical features, can reduce uncertainty as inaccuracy and inconsistency in the discharge data which are the main causes of uncertainty. Geology and soil characteristics have significant impact on discharge which were not emphasised while evolving the above mentioned method. Yu et al. (2002) used cluster analysis and established relation between homogeneous catchment, using similar approach as developed by Mimikou and Kaemaki (1985). Viola (2011) added soil characteristics into account and worked on the Sicily catchment where the discharge data is divided into dry and wet period because of ephemeral behaviour of the catchment. The concluded equations are given below:

Dw =j0+j1 ln(Ar)+j2 ln(R) (9)

a =m0+m1 (Ar)+m2 ln(R)+m3 ln(CN) (10)


10

b=n0+n1 (%perm)+n2 ln(Ar)+n3 ln(R)+n4 ln(CN) (11)

It has been found that the results obtained by proposed model are optimistic with some deviation in case of high discharges.

Further the reliability of this method increases on adding more geographical parameters. As Quimpo (1983) did not added any physiographic parameters but Mimikou and Kaemaki (1985) made this method more reliable by adding rainfall, area and relief of catchment and length of the stream.

Without Physiographic Characteristic In case the catchment is remotely located and gauging stations are distantly located, then this mathematical modelling is applied for stream flow estimation and development of FDC for ungauged sites. This approach is also applicable when there is large variation in the discharge data like flood or dry period where physiographic characters do not clarify their role in streamflow. To overcome such problems, drainage area ratio method and dimensionless flow estimation technique can be used.

Drainage area ratio method The drainage area ratio method is suitable when the ungauge site is sub-basin of the main river basin. In this method, data are collected from the gauge site and extrapolated for ungauge site by applying (Eq. 12) (Gulliver, 1991)

i

n

g

ui Qg

AAQu ⎟

⎟⎠

⎞⎜⎜⎝

⎛= (12)

Here the subscript ‘u’ refers for ungauged site and ‘g’ indicates gauged site parameters. Q represents discharge and area is represented by A. The subscript ‘i’ stands for exceedance for particular time. Murdock (1993) suggested (Eq. 13) to extrapolate insufficient information where, the value of n=1 is ideal for hydropower projects where higher and lower discharges are not considered for planning. Least square optimization technique was found suitable for calculating the exponent ‘n’.

⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛

=

g

u

g

u

AA

QQ

nlog

log (13)

Sefton & Howarth (1998) used stepwise regression technique for different geographical and catchments and found statistically significant empirical relation as given in (Eq. 14)

40.013.0 −= qaqτ (14)

Here τq , is streamflow frequency, a is area and q is the discharge at various percentage exceedance. Stedinger et al. (1993) proposed

the standard drainage area ratio method given in (Eq. 15), whereas Mohamoud & Parmar (2006) introduced the nonlinear drainage area ratio method as given in (Eq. 16) and (Eq. 17). The nonlinear method does not follow linearity assumptions and these equations can be solved by stepwise regression.

Qu = Qg (Au/Ag) (15)

Qu = Qg tan (Au/Ag) (16)

Qu = Qg arctan(Au/Ag) (17)

The above studies found that drainage area ratio lies in the range of 0.5 to 1.5, whereas Ries and Friesz (2000) found that the range from 0.3 to 1.5 is appropriate for low flow statistics.

It is seen that in these methods there should not be much difference between the ungauged area and gauged area otherwise it will lead to uncertainty in the flow estimation. The uncertainty associated with this method is due to two reasons. The first reason is the fluctuation in the daily flow. The second uncertainty is because of inadvertent data acquisition method. Other finding of this method is that, the relation between drainage area and discharge should be linear for hydropower planning.

Dimensionless flow duration curve Smakhtin et al. (1997) proposed graphical approach for estimation of FDC for daily flow data. In this method the flow for each exceedance point is divided by the average annual discharge ( ), to give a dimensionless flow term. These dimensionless flow points are plotted against the exceedance interval on logarithmic probability paper as shown in Fig. 3 to

Fig. 3: Dimensionless flow duration curve, Emmett (1975)


11

give a dimensionless FDC derived by Emmett (1975).

Cigizoglu (2000) used marginal probability distributions like normal, Pearson type III, log Pearson type III, 2-parameter lognormal, and 3-parameter log normal to plot FDC and found that 2-parameter lognormal distribution does well with the daily flow. In this method several sites are selected from the basin and the discharge of each site is converted to dimensionless flow by dividing it from the corresponding area. Specific discharges selected from these dimensionless flows, follows 2-pramateter lognormal probability exceedance. The averages of these specific flows are plotted as FDC and discharge of ungauged site is determined by multiplying it with the area of ungauged site.

Singh (2001) derived a flow-duration model for ungauged sites by mapping of hydrologic data (non-dimensional) of the similar hydro-meteorological region. Data was normalized using Box-Cox transformation, thereafter transformed to dimensionless flow. The dimensionless flow derived by dividing the mean flow of the same quintile of homogeneous region by the area of the region. For ungauge site, the dimensionless flow of the region is to multiply with area of the ungauge site as shown in (Eq. 18)

00

)ln(/)1(

=≠

⎩⎨⎧

=−=

λλλλ

ifif

qWqW

(18)

Where, W is power transformed series and λ is transformation parameter, where coefficient of skewness = 0, coefficient of kurtosis = 3 and dimensionless flow is derived using following relation (Eq 19).

meanQQq = (19)

Using regression relation given in (Eq. 20) average discharge of the catchment of area A can be calculated, where C and m are the regression and exponential coefficient respectively.

Qmean = CAm (20)

Thus, dependable flow of ungauged site of area A can be estimated using (Eq. 21)

QD= Qmean .qD (21)

Ganora et al. (2009) also worked on the dimensionless FDC using the dissimilarity in FDC and its relation with distance. It was found that dimensionless FDC approach performs better in comparison to the parametric approach. A best fit curve has to be developed for a particular area having homogeneous hydrology in order to develop a single curve relating a characteristic dimensionless flow to the exceedance percentage. The reliability of this method is questionable because dimensionless curve has no limited number of values and these values are affected by unusual occurrence of flash flood.

RECENT DEVELOPMENTS IN REGIONAL FDC ANALYSIS The estimation of stream flow for ungauged basin using gauged site discharge data gives slightly uncertain and

inaccurate results. The estimation error is majorly governed due to the inappropriate model selection, avoiding changes in climatic and meteorological component in time series and imprecise input of geographical and geological basin characteristics.

To calibrate the estimation errors, cross validation and uncertainty analysis are recommended techniques. Jackknife cross validation and boot strap resampling are renowned validation techniques.

Yu et al. (2002) used area index and polynomial methods for regionalization of FDC and found that polynomial method has smaller statistical errors over area-index method. Uncertainty analysis of these synthetic and observed FDC is carried out using bootstrap resampling technique. Castellarin (2004) tested reliability of regional models of FDC for ungauged basin using Jackknife cross validation. This research work comprised statistical method, parametric procedures and graphical procedure and found that three regional models from each approach performed same degree of robustness and reliability.

Archfield and Vogel (2007) used Jackknife cross validation to compare parametric regression over nonparametric regression for FDC estimation and found that nonparametric method outperformed. Archfield et al. (2010) developed structural relation among streamflow quantiles for ungauged streamflow measurement and Jackknife cross validation is applied between rainfall-runoff modelling and the proposed technique. It is seen that both the observed and estimated flows at ungauged sites have shown good agreement.

Jackknife testing method was used to verify the accuracy of these regional curves. Uncertainty analysis was carried out using bootstrap resampling and results revealed that range of uncertainty is minute and calculated values were well contained in the range of observed flow values.

Hailegeorgis el al. (2013) worked on the reduction of uncertainties of different sources for reliable estimation of quantiles applying bootstrap resampling and found that there are huge sampling uncertainty in quantile estimation that need to be addressed. Onyutha and Willems (2013) recently worked on low and high flow duration frequency (FDF) estimation and applied uncertainty analysis using bootstrap resampling. Results show that calibration of FDF over original data and estimation of high flow for T-return periods has large uncertainties; hence uncertainty analysis should not be ignored. This uncertainty need to be quantified.

As seen in the literature, many advance applications of statistics have been employed in regional FDC for precise results. Jackknife cross validation and bootstrap resampling are current examples for estimation of inaccuracy and uncertainty. This study has also shown that Jackknife validation is prominent technique for cross validation of regionalize flow duration model whereas bootstrap resampling is useful in uncertainty analysis.


12

Jackknife Validation The Jackknife validation is a data division method for cross-validation and used for estimation of standard error. (Efron and Tibshirani, 1993).

)........,,( ,21 nxxxtT = (22)

where, a sample of size n and T is a parameter estimator. In jack knife validation, the single sample is to be removed from the sample size as shown in (Eq. 23)

),...,,....,( 111)(

niii xxxxtT +−

− = (23)

The estimate of the bias from the Jackknife sample technique is given in (Eq. 24). The bias can be defined as the difference between the expected value of estimator and the true value of the sample data.

))(1()(ˆ )( TTnTiasB Jjack −−=

(24)

Where, ∑=

−=n

i

niJ TT1

/)()(

The standard error ES using the Jackknife validation is given by (Eq. 25)

21

2)(

1

)(1)(ˆ⎥⎦

⎤⎢⎣

⎡−

−= ∑

=

− Jn

i

iJack TT

nnTES (25)

(Eq. 25) gives the standard deviation of the Jackknife validation with a factor (n-1)/n which ensures unbiasedness of the estimate.

Bootstrap resampling The bootstrap is also a non parametric method with assumptions to generate random sample from underlying population. The parameter estimator T of the sample size n is given in (Eq 26)

),...,( 1 nxxtT = (26)

Standard error θ estimation and biasness can also be computed using bootstrap resampling method. The bootstrap method is suitable where analytical method fails and )(ˆ xt=θ is complicated. In bootstrap resampling, B bootstrap samples are obtained using sampling with resampling to estimate standard error and the bias as given in (Eq.27)

);(ˆ ** bb xt=θ ;,...,1 Bb = (27)

Bootstrap resampling method is similar to Jackknife validation, except that, this method does not make any assumptions about the probability distribution of original sample and

resampling containing all the elements of original data set.

MERITS AND DEMERITS OF UNCERTAINTY ANALYSIS METHODS Based on the literature review regarding uncertainty analysis method it has been found that;

1. Both the methods are non-parametric methods so large sample size is not required and both the methods are applicable to the small flow dataset.

2. Jack-knife cross validation uses n-1 observations from the sample size of n, whereas bootstrap resampling deals with same sample size n. In case of high flow estimation the results may be fluctuating so bootstrap resampling is better than the other method.

3. Mathematically, there is not much difference between the results from both the methods.

4. Every repetition of jack-knife validation gives same result whereas bootstrap resampling gives different results.

5. Jack knife validation can only be applied to the smooth, differentiable statistics and this is the drawback of this method over bootstrap resampling.

Based on the above details it is found that jack knife validation is useful where the results are to be validated and bootstrap resampling is used where the distribution of population is important to be considered. The FDC is distribution based phenomenon and includes various types of sample populations, thus bootstrap resampling is powerful tool for uncertainty analysis.

ENERGY AND POWER GENERATION This section of the present study highlights the role of FDC for hydro power assessment. The FDC is an observation tool for interpretation of variation of stream flow for a given site data conditioned in a particular period. It provides threshold for power potential study in hydropower projects. The power generated by a hydropower plant can be given by (Eq. 28)

Fig. 4: Cumulative Probability Distribution Function for River Discharge (FDC)


13

100081.9 η×××

=HQP (28)

Where, P is power (kW), Q is discharge in cumecs, H is the net head (m) and η is overall efficiency including turbine and generator efficiencies.

For estimation of annual energy generation, the flow duration is divided into firm energy, secondary energy and dump energy as shown in Fig 4. Firm energy generation takes place on the basis of firm discharge which is 100% dependable flow, whereas secondary energy is generated at 50% dependable flow. Peak discharge (0-5% dependable flow) is not available throughout the year, so it comes under dump energy.

Total energy, SFT EEE += (29)

Firm energy, )243651(81.9 100 ××××××= ηQHE F

(30)

CONCLUSION AND RECOMMENDATIONS In the present study a detailed review has been carried out on regionalization flow duration curve methods and uncertainty estimation. The conclusions and recommendations in the study are as follows:

1. Parametric method has more accuracy in regional FDC development. The limitation of this method is the requirement of all morphological parameters of gauged as well as ungauged catchments for regionalization. This method is applicable to geographically different ungauged catchment sites. The uncertainty in the results can be reduced by adding more geological parameters.

2. Dependable flow method is found workable with long time series discharge data and availability of adequate number of gauging sites in the same catchment where ungauged site is located.

3. Dimensionless FDC can be used for heterogeneous catchments.

4. Drainage area ratio method is useful for geographically dissimilar catchments. The drainage area ratio is non linear relation, so optimization of this coefficient is required for high or low flow regionalization. In case of hydropower assessment, this is a linear relation.

5. The uncertainty associated with the flow estimation methods can be determined using Jack-knife validation and bootstrap resampling techniques.

6. Bootstrap resampling is preferred over jack-knife validation because, (i) every repetition gives different result following the parent probability distribution, so helpful for estimation of high and low flows, (ii) cross validation jack-knife technique delete one sample data that leads toward the median and quantiles related estimation errors.

7. Installation capacity of hydropower project is based on firm energy, secondary energy and the dump energy.

ACKNOWLEDGEMENTS The authors greatly acknowledge the financial support from the Ministry of Human Resource Development, Govt. of India in the form of research scholarship to carry out this work. The authors also acknowledge the use of facilities as available in AHEC, IIT Roorkee.

REFERENCES 1. Acreman, M.C. and Sinclair, C.D., 1986.

“Classification of drainage basins according to their physical characteristics; an application for flood frequency analysis in Scotland”, J. Hydrol., 84, 365– 380.

2. Acreman, M.C. and Wiltshire, S.E., 1989. “Regions are dead; long live the regions. Methods of identifying and dispensing with regions for flood frequency analysis”. Friends in Hydrology. IAHS Pub. no. 187, 175–188.

3. Archfield, S.A., Vogel R.M., and Brandt S.B., 2007. “Estimation of flow- duration curves at ungauged sites in southern New England”, Proceedings of the American Society of Civil Engineers World Water and Environmental Resources Congress, Tampa, FL, 2007.

4. Archfield, S.A. , Vogel R.M., Steeves P.A., Brandt S.B., Weiskel P .K., and Garabedian S.P., 2010. “The Massachusetts Sustainable-Yield Estimator: A decision- support tool to assess water availability at ungauged sites in Massachusetts”, U.S. Geological Survey Scientific Investigations Report 2009 – 5227, 41 p., plus CD – ROM.

5. Arora M., Goel N. K., Singh Pratap, and Singh R.D., 2005. “Regional flow duration curve for a Himalayan river Chenab”. Nordic Hydrology Vol 36 No 2 pp 193–206.

6. Beard, L. R., 1943. “Statistical analysis in hydrology”. Trans., ASCE, 108, 1110-1160.

7. Berger, K. P. and Entekhabi, D., 2001. “Basin hydrological response relations to distributed physiographic descriptors and climate”, J. Hydrol. 247, 169–182.

8. Burn, D. H. and Boorman, D. B., 1993, “Estimation of hydrological parameters at ungauged catchments”. J. Hydrol., 143, 429–454.

9. Burn, D.H., 1990a. “An appraisal of the “region of influence” approach to flood frequency analysis”, Hydrolog. Sci. J., 35, 149– 165.

10. Burn, D.H., 1990b. “Evaluation of regional flood frequency analysis with a region of influence approach”, Water Resource Research, 26, 2257–2265.


14

11. Burn, D.H. and Zrinji, Z., 1994. “Flood frequency analysis for ungauged sites using a Region of Influence approach”, J. Hydrol., 153, 1–21.

12. Burn, D.H. and Goel, N.K., 2000. “The formation of groups for regional flood frequency estimation”. Hydrolog. Sci. J., 45, 97– 112.

13. Castellarin, A., Galeati, G., Brandimarte, L., Montanari, A. and Brath, A., 2004. “Regional flow-duration curves: reliability for ungauged basins”, Adv. Water Resour. 27, 953–965.

14. Chow, W. T., 1964. “Handbook of Applied Hydrology”, Mc-Graw Hill Book Co., New York, N.Y.

15. Cigizoglu H.K., 1997b. “Flow duration curve and its applications”, Paper presented at the 3rd International Conference of FRIEND, Postajna, Slovenia, 1-4 October.

16. Cigizoglu, H.K., 2000. “A method based on taking the average of probabilities to compute the flow duration curve”, Nordic Hydrology 31: 188–207.

17. Claps P, and Fiorentino M., 2005. “Probabilistic flow duration curves for use in environmental planning and management”. In: Harmancioglu NB, et al, editors. Integrated approach to environmental data management systems. NATO-ASI series 2(31). Dordrecht, The Netherlands: Kluwer. p. 255–66.

18. Croker, K.M., Young, M.D.Z., and Rees, H.G., 2003. “Flow duration curve estimation in ephemeral catchments in Portugal”. Hydrol Sci J, 48(3):427–39.

19. Cunnane, C., 1978. "Unbiased plotting positions—a review", J. Hydrol., 37, 205-222.

20. Efron, B. and Tibshirani, R.J. (1993).An Introduction to the BootstrapChapman & Hall,New York

21. Emmett, W.W., 1975. “The Channels and Waters of the Upper Salmon River Area, Idaho”, United States Geological Survey, Professional Paper 870A.

22. Fennessey, N. M., and Vogel, R. M., 1990. “Regional flow duration curves for ungauged sites in Massachusets”, Journal of Water Resources Planning and Management, ASCE, Vol. 116 (4), pp. 530-549.

23. Foster, H. A., 1934. “Flow Duration curves”, Trans. ASCE, Vol. 99, 1213-1267.

24. Franchini M. and Suppo M., 1996. “Regional analysis of flow duration curves for a limestone region”. Water Resource Management, 10:199–218.

25. Ganora, D., Claps, P., Laio, F. and Viglione, A. (2009). An approach to estimate nonparametric flow duration curves in ungauged basins. Water Resources Research 45. doi: 10.1029/2008WR007472. issn: 0043-1397.

26. GLPF GRANT Reoprt by Apfelbaum S., Bell, J., Roland R., Mackey, S., DePhilip, M., Khoury, M., and Hinz, L., 2007. “Identifying and Valuing Restoration Opportunities and Resource Improvements at

Watershed and Sub watershed Scales”, Final Report–, November 2007.

27. Gulliver, J. S., 1991. “Preliminary studies: hydrology, hydraulics, and costs”, Hydropower engineering handbook, J. S. Gulliver and R. E. A. Arndt, eds., McGraw-Hill, New York, N.Y.

28. Gupta, R. S., 1989. “Hydrology and hydraulic systems”. Prentice-Hall, Inc., Englewood Cliffs, N.J.

29. Hailegeorgis T.T., Thorolfsson Sveinn T., Alfredsen Knut, 2013. “Regional frequency analysis of extreme precipitation with consideration of uncertainties to update IDF curves for the city of Trondheim”, Journal of Hydrology 498(8):305-318

30. Hughes, J.M.R., 1987. “Hydrological characteristics and classification of Tasmanian rivers”, Aust. Geog. Stud., 25, 61–82.

31. Hughes D.A. and Smakhtin V., 1996. “Daily flow time series patching or extension: a spatial interpolation approach based on flow duration curves”. Hydrological Science 41(6).

32. Laaha, G. and Blöschl, G., 2007. “A national low flow estimation procedure for Austria”. Hydrol. Sci. J. 52(4), 625-644.

33. LeBoutiller, D.W. and Waylen, P.R., 1993. “Stochastic model of flow duration curves”. Water Resource Research, 29 (10), 3535–3541.

34. Linsley R. K., Jr Kohler, M. A. and Paulhus, L. J. H., 1949. “Applied Hydrology”. McGraw-Hill, New York, USA.

35. Maidment, D. R., 1992. “Handbook of Hydrology”, Mc Graw Hill.

36. Male J. W., and Ogawa H., 1984. “Tradeoffs in water quality management”. Journal of Water Resource Planning and Management Division, American Society of Civil Engineers 110(4): 434-444.

37. McMahon T. A. 1993, “Hydrologic design for water use. Handbook of Hydrology”, McGraw-Hill.

38. McNamara, J. P., Kane, D. L. and Hinzman, L. D., 1998. “An analysis of streamflow hydrology in the Kuparuk River basin, Arctic Alaska: a nested catchment approach”, J. Hydrol. 206, 39–57.

39. Mimikou, M., and Kaemaki, S., 1985. “Regionalization of flow duration characteristics”. J. Hydro., Amsterdam, 82, 77–91.

40. MNRE, Ministry of New and Renewable Energy, accessed March 2014.

http://mnre.gov.in/mission-and-vision-2/achievements/

41. Mohamoud, Y. M. and Parmar, R. S., 2006. “Estimating streamflow and associated hydraulic geometry, the Mid-Atlantic Region”, USA. J. Water Resour. Assoc. 42, 755–768.


15

42. Murdock R. U. and Gulliver J. S., 1993. “Prediction of river discharges at ungauged sites with analysis of uncertainty”, Journal of Water Resources Planning and Management, ASCE, 119(4), 473-487.

43. Nathan, R. J. and McMahon, T .A., 1990. “Identification of homogeneous regions for the purposes of regionalisation”. J. Hydrol. 121, 217–238.

44. Onyutha, C. and Willems, P., 2013 “Uncertainties in flow-duration-frequency relationships of high and low flow extremes in lake Victoria basin”. Water 2013, 5, 1561-1579; doi:10.3390/w5041561

45. Post, D. A. and Jones, J. A., 2001. “Hydrologic regimes at four long-term ecological research sites in New Hampshire, North Carolina, Oregon, and Puerto Rico”, Adv. Water Resour. 24, 1195–1210.

46. Quimpo, R. G., Alejandrino, A. A., and McNally, T. A., 1983. “Regionalized flow duration for Philippines”, Journal of Water Resource Planning And Management, ASCE, 109(4), 320–330.

47. Reed, D. W., 1984. “A review of British flood forecasting Practice”, Report no. 90. Institute of Hydrology, Wallingford, UK.

48. Reimers, W., 1990. “Estimation hydrological parameters from basin characteristics for large semi-arid catchments”; In: Regionalization in Hydrology (ed. by M. A. Beran, M. Brilly, A. Becker & O. Bonacci) (Proc. Ljubljana Symp., April 1990), 187–194. IAHS Publ. 191. IAHS Press, Wallingford, UK. http://iahs.info/redbooks/a191/iahs_191_0187.pdf

49. Ries III, K.G. and Friesz, P.J., 2000. “Methods for Estimating Low-flow Statistics for Massachusetts Streams”, USGS Water Resources Investigations Report 00-4135, Northborough, MA, p. 81.

50. Riggs, H. C., 1972. “Low flow investigations”. U.S. Geological Survey techniques of water resources investigations-book 4, U.S. Geological Survey, Washington, D.C.

51. Robson, A. and Reed, D.W., 1999. Statistical Procedures for Flow Frequency Estimation. Flood Estimation Handbook, Vol. 3. Institute of Hydrology, Wallingford.

52. Searcy, J. K., 1959. “Flow duration curves, manual of hydrology. Part 2, Low flow techniques”, US Geological Survey Water Supply Paper 1542– A.

53. Sefton, C. E. M. and Howarth, S. M., 1998. “Relationships between characteristics and physical descriptors of catchments Wales”, J. Hydrol. 211, 1–16.

54. Singh R.D., Mishra S.K., and Chowdhary H., 2001. “Regional flow-duration models for large number of ungauged Himalayan catchments for planning microhydro projects”. J Hydrol Eng ;6(4):310–6.

55. Smakhtin V.Y., Hughes D.A. and Creuse-Naudine E., 1997. “Regionalization of daily flow characteristics in part of the Eastern Cape, South Africa”. Hydrol Sci J. 42(6):919–36.

56. Stedinger, J. R., Vogel, R. M. and Foufoula-Georgiou, E., 1993. “Frequency analysis of extreme events. In: Handbook of Hydrology”, 18.1–18.66. McGraw-Hill, New York, USA.

57. Tasker, G. D., 1972. "Estimating low-flow characteristics of streams in southeastern Massachusetts from maps of groundwater availability", Professional Paper 800- D, U.S. Geological Survey, Washington, D.C, D217-D220.

58. Viola F., Noto L. V., Cannarozzo M., and Loggia G. La, 2011. “Regional flow duration curves for ungauged sites in Sicily”. Hydrol. Earth Syst. Sci., 15, 323–331

59. Vogel R. M., and Kroll C. N., 1990. “Generalized low-flow frequency relationships for ungauged sites”, Journal of Water Resource Planning and Management Division, American Society of Civil Engineers 116:530-549.

60. Vogel R. M. and Fennessey N. M., 1994. “Flow-duration curves. I: new interpretation and confidence intervals”. Journal of Water Resource Planning and Management Division, American Society of Civil Engineers 120(4): 485-504.

61. Vogel, R. M. and Fennessey, N. M., 1995. “Flow duration curves. 2: A review of applications in water resources planning”. Water Resource Bulletin, 31, 1029–1039.

62. Warnick, C. C., 1984. “Hydropower Engineering, Prentice-Hall”, Inc., Englewood Cliffs, New Jersey, pp. 59-73.

63. Wiltshire, S.E., 1986. “Regional Flood Frequency analysis II: Multivariate classification of drainage basins in Britain”, Hydrolog. Sci. J., 31, 335–246.

64. Woods, J., and Gulliver, J., 1990. “Economic analysis of energy projects with uncertainty”. J. Energy Engrg., ASCE, 16(1), 1-16.

65. Yu, P. S., Yang, T. C. and Wang, Y. C., 2002. “Uncertainty analysis of regional flow duration curves”. J. Water Resource. Planning and Management. ASCE 128s, 424–430.

66. Zecharias, Y.B. and W. Brutsaert, 1988. “Recession characteristics of ground water outflow and base flow from mountainous watershed”. Water Resource Research. 24(10), 1651-1658.

Issue (Volume No. 34, Number 3)

Documents

Transcript of Issue (Volume No. 34, Number 3)