Annual Journal of Hydraulic Engineering, JSCE, Vol.53, 2009, February

ESTIMATION OF INDEX FLOOD IN
HYDROLOGIC REGIONS WITH LIMITED FLOODDATA AVAILABILITY
Binaya Kumar MISHRA1, Kaoru TAKARA2, Yosuke YAMASHIKI3and Yasuto TACHIKAWA4
1Student Member of JSCE, Graduate student, Dept. of Urban and Environmental Eng., Kyoto University(Kyoto 615-8540, Japan) E-mail:mishra@flood.dpri.kyoto-u.ac.jp
2Fellow of JSCE, Dr. Eng., Professor, DPRI, Kyoto University (Uji 611-0011, Japan)
3Member of JSCE, Dr. Eng., Associate Professor, DPRI, Kyoto University (Uji 611-0011, Japan)
4Member of JSCE, Dr. Eng., Associate Professor, Dept. of Urban and Environmental Engineering,
Kyoto University (Kyoto 615-8540, Japan)

Delineation of hydrologic homogeneous regions, selection of regional frequency distribution andestimation of index flood are three major steps of regional flood frequency analysis. This study deals withthe estimation of index flood relationship in each of the previously identified five hydrologic regions of
Nepal. In three regions which have enough hydrologic stations, regression technique was employed on
observed annual maximum discharges. The remaining regions possess only two streamflow gauge
stations each. Hence, the index flood relationship derived using regression technique with such limited
stations may not be reliable. To address this problem, the authors, at first, used a conceptual daily rainfallrunoff model, SimHyd, to generate synthetic annual maximum discharge series and then, derived
relationship for index flood estimation using regression technique. Nash-Sutcliffe efficiency coefficient
was used to assess the predictive power of the derived relationships.
Key Words : Index flood, rainfall-runoff model, regression, SimHyd, synthetic

1. INTRODUCTION
Information on maximum discharge of different
return periods is required in design and planning ofvarious hydraulic structures. Such maximum
discharge is popularly known as design flood.
Regional flood frequency analysis1) is one of thewidely used design flood estimation techniques atungauged sites or the sites with short length ofobservation data.
This work is related with index flood based
regional flood frequency analysis approach. It
assumes that the coefficient of variation (Cv) of
floods is constant and does not vary with drainage
area2). The previous work3) which identified fivehydrologic homogeneous regions inside the
Nepalese territory was tested for similarity of Cv
among the basins in a region. The basic relationshipfor estimating design flood (QTi) of return period T

at site i in index flood4) based regional flood
frequency analysis method is expressed as Eq.(1):QTi = qT μi(1)
The first right-side term qT in Eq.(1) represents
regional frequency distribution parameter which
remains the same throughout a hydrologic region fora specific return period. The second term µi is called
index flood. It is defined as the average likely flood.
For the gauged site, it is usually taken as mean ormedian of the annual maximum discharge series5).
The mean of the maximum discharge seriescorresponds to 2.33-years flood in Gumbel
distribution.
Index flood is related tophysiographic/climatic factors like catchment area,
land cover, soil type, rainfall, etc for ungauged
basins. Index flood is popularly known as scale
factor because it is mostly governed by thecorresponding catchment area. For each hydrologic
region, a particular relationship needs to be- 55 -

established for estimation of index flood. The
present study intends to establish relationship for
estimating index flood in each of the identifiedhydrologic homogeneous region.
Index flood estimation may be constrained by thedata availability for the application of a particular
procedure. For gauged sites, the estimation of index
flood is generally made by taking mean6) of theobserved annual maximum discharge series. In thecase of ungauged sites, most of the previous works7)
used simple regression for deriving index flood
relationship. A very limited studies8) have used
multi-regression technique by employing theattributes: main stream slope, basin’s elevation, etc.
in addition to drainage area. No specific study isavailable on estimating index flood for Nepalesecontext.
The regression technique can be considered
reliable only when the number of observation
stations is large enough. According to Reddy9),
number of observation stations should be at least 3
to 4 times the number of regression parameters forreliable regression relationship. In addition,according to 5T guideline10), a minimum of 5 times
T observed annual maximum discharge values
should be available in the concerned hydrologic
region for reliable estimation of T-year return period
design flood. If the 50 year event is selected, then5T guideline implies that at least 250 station-years
flood values are required for an effective quantile
estimate.
The hydrologic regions 2 and 5 (Fig.1) have only
two streamflow gauging stations, hence inadequate
for performing regression technique. To address thisproblem, the study generated synthetic annual
maximum discharge series for various ungauged
basins using climatic (rainfall, evaporation etc.) data
available in the regions. Then, regression technique
was applied on synthetic-observed values. But, theremaining regions 1, 3 and 4 were found with large
number of streamflow gauging stations. Therefore,
for these regions, index flood relationships were
derived using observed annual maximum discharge
series.
The present work addresses the problem
associated with estimation of index flood,
particularly in the region having limited observed
streamflow data. An overview on study area anddata availability has been provided in the next
section. The methodology section deals the generalapproaches used in deriving index flood
relationship. Description on the rainfall-runoff
model, SimHyd11), which is intended for generating
synthetic annual maximum discharge series, hasbeen discussed in Section 4 and 5. The adopted

Fig.1 Hydrologic homogeneous regions of Nepal with regions
1, 2 and 5 are spread over different area.

procedure in establishing index flood relationship is
discussed in Section 6. The results and discussion
have been dealt in second last section. The final
section concludes the achievement of the study.

2. STUDY AREA AND DATAAVAILABILITY
Estimation of index flood relationships isintended for previously identified five hydrologic
homogeneous regions (Fig.1) of Nepal. In general,
Nepal gets more than 1500 mm of rainfall annually.
About 80% of total annual rainfall is concentrated in
the months of July, August and September.
Consequently, it brings many large floods andlandslides. The regions 1, 2, 3, 4 and 5 covers
16.24%, 14.67%, 33.20%, 24.63% and 11.26% landarea of the total Nepalese territory area respectively.
The total area of Nepal is 147,181 km2.
About two-third of total hydrological stations inregions 1, 3 and 4 were used for deriving index
flood relationship. Because the statistical parameters(mean, coefficient of variance, skewness etc.)
largely fluctuate for smaller sample size, the stations
which consisted at-least 10 years of annual
maximum discharge series were only considered.
The remaining one-third stations are intended forvalidation of derived relationship. These three
regions cover mostly steep terrain. The regions 1
and 4 get more rainfall with increasing elevation
whereas region 3 gets less rainfall with increasing
elevation.
The hydrologic regions 2 and 5 have only tworiver discharge gauging stations. The daily
discharge data of one hydrological station was used
for calibration of the rainfall-runoff model. These
daily discharges are the mean of streamflows
corresponding to stage readings at 08:00, 12:00 and
16:00 hours. The discharge data of another station
was used for validation of the model. Enoughclimatological stations are available in these tworegions for generating synthetic discharge data using- 56 -

the calibrated model in ungauged basins. Region 2
gets relatively more rainfall than region 5.
Hydrological (discharge) and climatological(rainfall, evapotranspiration) data were collectedfrom Department of Hydrology and Meteorology,
Kathmandu, Nepal. The information like basin’s
elevation and river slope were derived from SRTM
90 m DEM whereas land cover and hydrologicalsoil group were derived from AVHRR satellite
imagery and FAO global soil data respectively.
These physiographic data can be freely downloaded
from the concerned websites.

3. METHODOLOGY
The index flood estimation methods (Fig. 2)
depend on whether the site of interest is gauged or
ungauged. If the site of interest is gauged,
estimation methods use information on annual
maximum discharge series at the site of interest.
This method may be called as direct method. The
observed sample mean is mostly used as estimatorof index flood.
For the ungauged site in a hydrologic
homogeneous region, the index flood estimation
methods use information on regional basins’ floodvalues and the corresponding physiographic/climatic
properties. This method may be called as indirect
method. This work is related with indirect methodof index flood estimation. Different index flood
estimation techniques are discussed hereunder.
Index flood estimation

Direct methods

Indirect methods

Regression techniqueHydrologic simulation(1) Using simple regression technique
Index flood at any location is mainly governedby its drainage area, A. Another advantage of using
only drainage area is its easy availability. To
establish relationship for index flood estimation interm of drainage area, there should be enoughnumbers of gauged stations in the concernedhydrologic region. At first, index flood at eachgauged station is computed as mean of the annual
maximum discharge series. These mean values arecalled observed index flood values. Then, a plot ofthese observed index flood values is made against
the corresponding drainage area. As illustration,
Fig.3 shows the plot of index flood against drainage
area for region 4. Equation of the line which fits
most closely to these plot points is defined as index
flood relationship. The present study intends toperform simple regression for all the hydrologic
regions.
(2) Using multiple regression technique
For better estimation of index flood, therelationship may be expressed in term of more than
one independent variable. In addition to drainage
area, the information like slope, land cover, soil
type, rainfall, etc. can be integrated in estimation ofindex flood. Such integration may be performed byapplying multiple regression technique. The multiregression model expresses the estimate of index
flood, µi as:(2)
μi = C0 A1c1 A2c2 ......Ancn
In Eq.(2), A1, A2,….,An represents an appropriate setof physiographic/climatic attributes of the basin.
The constant C0 and exponent c1, c2, …,cn are
estimated from observed index flood of each basin
andcorresponding
physiographic/climatic
information. In the present study, the authors intend
to perform multiple regressions for different
possible combinations of physiographic/climatic
attributes to establish better index flood relationship.

Fig.2 Index flood estimation methods.
10000

0.7228y = 5.147x

R = 0.7342

3

index flood, m /s

2

1000

100

10
10

100

1000

10000

2

area, kmFig.3 Index flood versus catchment area for different gauged
basins in Region 4.

(3) Using hydrological simulation
As already mentioned in Section 2, there are only
two river gauging stations in each of the region 2
and 5. Index flood relationship derived using
regression technique with the data of such limited
gauged stations can not be considered reliable for
estimation of index flood. A rainfall-runoff model,
after calibration and validation with the help ofavailable streamflow data in the region, enables
generation of annual maximum discharge series atsite of interest. Then, index flood is computed bytaking average of these synthetic annual maximum
discharge series.

- 57 -

Rainfall

Pervious fraction
Pervious incident

Impervious incident

Impervious ET

Interception ET
Impervious threshold

Interception store

Impervious runoff

Rainfall interception store capacity
Throughfall

Infiltration excess
runoffInfiltration

Infiltration coefficient,
Infiltration shape

Recharge

Interflow coefficient,
Recharge coefficient
Soil ET

Saturation excess
runoff
Interflow

Soil input
RunoffSoil moisture store
Soil moisture store capacity
Baseflow

Groundwater store
Baseflow coefficientFig.4 Structure of SimHyd model.

4. SIMHYD: A RAINFALL-RUNOFF
MODEL
In order to generate the synthetic annual
maximum discharge series at different sites in theregion 2 and 5, the study uses hydrologicalsimulation with SimHyd11), a lumped conceptual
daily rainfall-runoff model. SimHyd simulates daily
runoff using daily precipitation and potential
evapotranspiration (PET) as input data. SimHyd is
one of the commonly used rainfall-runoff models
and has been extensively tested using data fromvarious countries. SimHyd is one of the rainfallrunoff models in RRL (Rainfall-Runoff Library), a
software product in the Catchment Modelling
Toolkit.
The structure of SimHyd and the algorithms
describing water movement into and out of thestorages are shown in Fig.4. In SimHyd, daily
rainfall first fills the interception store, which is
emptied each day by evaporation. The excess
rainfall is then subjected to an infiltration functionthat determines the infiltration capacity. The excess

rainfall that exceeds the infiltration capacity
becomes infiltration excess runoff. Moisture that
infiltrates is subjected to a soil moisture function
which diverts the water to the stream (interflow),
groundwater store (recharge) and soil moisture store.
5. CALIBRATION AND VALIDATION

Calibration of the model was performed using
daily stream flow of the Kiran River basin (stationindex 296) located in region 5 over the period
2000/01/01 to 2005/12/31. The model possesses
both manual as well as well-established automatic
optimization facilities for parameter calibration.
This study used both: manual method for matchingannual maximum discharge values and automatic
optimization for other periods. The SCE-UA(shuffled complex evolution - university of Arizona)
option was selected for carrying automatic
optimization. The Nash-Sutcliffe efficiency was
selected as objective function while calibrating themodel. The derived calibration parameters withNash coefficient 0.61 is shown in Table 1.

- 58 -

relationship got started with computation of meanannual maximum discharge values at all the stations.
The average value, called as observed index flood,
was plotted against the corresponding drainage area(A) to carry out simple regression.
For better estimation of index flood, multiple
regression technique needs to be applied. The
additional attributes which were proposed incarrying multiple regressions are: average annual
daily maximum rainfall (P), soil type, river slope (S)and land cover information; since these attributes
may strongly govern index flood values. But, theannual daily maximum rainfall in different basins ofregions 1, 3 and 4 could not be collected. Therefore,basin elevation (H) was considered instead of
average annual daily maximum rainfall (P) because
rainfall is largely governed by elevation in Nepalesecontext as mentioned in Section 2. Impact of land
cover and soil type was considered in term of NRCS
runoff curve number.
ArcHydro delineate basins and streams fromdigital elevation models, extract limited set ofhydrologic modeling parameters from the DEMs in
ArcGIS environment. HEC-geoHMS finds use inpreparing additional parameters from the DEMs andother supported data layers, and write parameter
files. For computing basin’s average elevation (H),runoff curve number (CN) and river slope (S), thesoftware ArcHydro and HEC-GeoHMS were used.

Table 1 Calibrated model parameter values at the Kiran River.

Parameter

Value

Base flow coefficient

0.45

Impervious threshold (mm)0.51

Infiltration coefficient (mm)252.00Infiltration shape

2.50

Interflow coefficient

0.14

Pervious fraction

0.40

Rainfall interception store capacity (mm)3.50

Recharge coefficient

0.80

Soil moisture store capacity (mm)370.002

R = 0.74

3

Modelled flood (m /s)

90
70
50
30
10
10

30

50

70

90

3

Observed flood (m /s)

Fig.5 Model performance in the Jhanjhari River basin.

The model performance was checked bycomparing the observed annual maximum discharge
values and simulated values of the Jhanjhari Riverbasin (station index 363) located in the samehydrologic region. The performance correlation
between modeled and measured flow is shown in
Fig.5. The plotted point corresponds to six years ofannual maximum discharge values at the JhanjhariRiver.
The physiographic characteristics of region 2 and5 are very similar. Different regions were made only
because of different rainfall pattern. At the time ofcarrying out the present study, streamflow data
could not be made available for the stations inregion 2. Therefore, for the time being, the samemodel parameter derived for region 5 is was used forsynthetic annual maximum discharge generation
purpose in region 2.
6. RELATIONSHIP ESTABLISHMENTWith the generation of synthetic annual
maximum discharge data, there are finally six andfive data basins in region 2 and 5 respectively. There
are 7, 10 and 24 observed data basins in region 1, 3
and 4 respectively. Establishment of index flood

7. RESULTS AND DISCUSSION
Table 2 shows the index flood (µi in m3/s)
relationships for different hydrologic regions. It was
obtained after analyzing the results of simple andmultiple regressions. Except for Region 3, no otherparameters than the drainage area (A in km2) was
found effective in governing index flood although
the study performed multiple regressions for all thepossible combinations of drainage area (A), riverslope (S), average annual daily maximum rainfall(P), runoff curve number (CN) and average basin
elevation (H) . The index flood relationships were
found weakly correlated (smaller R2) when
considered the parameters: CN, S and P. This isbecause of similar values of CN, S and P throughout
a particular hydrologic region as the previous work3)
has delineated hydrological homogeneous regions
based on similarity in CN, S and average monsoon
rainfall pattern among the river basins,.
To assess predictive power of the derived
relationship, the estimated index flood values werecompared with observed index flood values. Nashefficiency coefficient (Eq.3) has been used toevaluate predictive power of the derived
relationship.

- 59 -

Table 2 Index flood relationship for five hydrologic regions of Nepal.

RegionRegression relationship of index flood

R2-value

Nash coefficient1μi = 0.71A

0.75

0.56

2

μi = 0.99 A

0.97

0.99

3

μ i = 0.18 A − 5.94

0.83

0.29

μ i = 0.18 A − 0.22 H + 732

0.89

0.49

4

μ i = 5.15 A

0.73

0.64

5

μ i = 1.68 A − 110.37

0.90

0.91

0.99

1.06

0.72

The index flood (µi) relationship involving
drainage area (A) has been presented for all the fivehydrologic regions. In case of Region 3, anadditional relationship involving elevation (H) anddrainage area (A) is shown because the inclusion of
H found improving the predictability considerably.
The Nash coefficient (E) for N observation basins
with average index flood ( Qo ) is (Eq. 3):
N∑ (Qoi − Qmi ) 2

E = 1 − Ni

∑ (Q − Q )
i
o

(3)

2

o

i

Here, Qio and Qim are observed index flood andmodelled index flood in basin i respectively.

8. CONCLUSIONSThis study analyzed several indirect estimation
methods of index flood. The first method was simple
regression which is suitable for the basins having noother information than the drainage area. For thebasins with additional information available,
multiple regression techniques were applied forestablishing better index flood relationships.
For the hydrologic regions with inadequate
discharge data, hydrologic simulation was proposed
for generating synthetic annual maximum discharge
series. For this purpose, a conceptual rainfall-runoff
model: SimHyd was successfully calibrated andvalidated. This model was used for estimating index
flood by taking mean of the synthetic annual
maximum discharge series. Nash efficiency
coefficient was used to check their predictive
accuracy.
In this way, the authors successfully developed
index flood estimation tools for the regions withdifferent conditions of data availability. The authors
intend to use these index flood relationships inaccomplishing the regional flood frequency analysis
of Nepalese river basins in next step.

to thank MEXT, Japan for providing financial
support in carrying research work. The authors also
wish to thank Visiting Prof. Ismail Abustan(Universiti Sains Malaysia) and all lab members fortheir helpful suggestions and comments at different
instances.
REFERENCES
1) Rao A.R. and Hamed, K.H.: Flood Frequency Analysis, CRC
press LLC, Florida, USA, 2000.
2) Kalma, J.D. and Sivapalan, M.: Scale issues in hydrologicalmodeling, Advances in Hydrological Processes, John Wiley& Sons, 1995.
3) Mishra, B.K., Takara, K. and Tachikawa, Y.: NRCS curve
number employed hydrologic homogeneous regionalizationin regional flood frequency analysis, Proceedings on
International
Conferenceon
Hydro-scienceandEngineering, Nagoya, Japan, 2008.
4) Dalrymple, T.: Flood frequency analysis, US Geol. Survey
Water Supply Paper 1543A, pp. 11-51, 1960.
5) Bocchiola, D., De Michele, C. and Rosso, R.: Review ofrecent advances in index flood estimation, Hydrology and
Earth System Sciences, Vol.7 (3), pp. 283-296, 2003.
6) Hosking, J.R.M. and Wallis, J.R.: Regional Frequency
Analysis: An approach based on L-moments, Cambridge
University Press, Cambridge, UK, 1997.
7) Kumar, R., Singh, R.D. and Seth, S.M.: Regional flood
formulas for seven subzones of zone 3 of India, Journal of
Hydrologic engineering, ASCE, Vol. 4 (3), pp. 240-244,
1999.
8) Brath, A., Castellarin, A., Franchini, M. and Galeati, G.:
Estimating the index flood using indirect methods,
Hydrological sciences-Journal, Vol. 46(3), pp. 399-418,
2001.
9) Reddy, P.J.: Stochastic hydrology, Laxmi Publications (P)LTD, New Delhi, 1997.
10) Burn, D.H. and Goel, N.K.: The formation of groups forregional flood frequency analysis, Hydrological Sciences
Journal, Vol. 45, No. 1, pp. 97-112, 2000.
11) Podger, G.: Rainfall runoff library, CRC for Catchment
Hydrology,(http://www.toolkit.net.au/cgibin/WebObjects/toolkit), Australia, 2004.

ACKNOWLEDGMENT: The authors would like- 60 -(Received September 30, 2008)