Annual Journal of Hydraulic Engineering, JSCE, Vol.52, 2008, February
Annual Journal of Hydraulic Engineering, JSCE, Vol.52, 2008, February

REGIONALIZATION OF NEPALESE RIVER BASINSFOR FLOOD FREQUENCY ANALYSIS
Binaya Kumar MISHRA1, Kaoru TAKARA2 and Yasuto TACHIKAWA3
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, Dept. of Urban and Environmental Eng., Kyoto University(Kyoto 615-8540, Japan)

Regional flood frequency analysis which is applicable for estimating design flood at both gauged
and ungaged sites needs grouping of river basins into hydrological homogeneous regions. Specific flood,timing of flood events and spatial location are significant in reflecting physiogrpahy and climate of any
river basins. These three physiographic/climatic characteristics of 46 independent Nepalese river basins
have been used successfully to delineate the homogeneous regions. This study uses a clustering algorithm
as a starting point for partitioning the independent catchments. The regions thus formed are subsequently
revised to improve the regional homogeneity after performing the L-moment based homogeneity test.
Spatial proximity consideration has been used to delineate region for mountainous dependent river basins
whereas subjective considerations have been made to delineate region for river basins of alluvial plain
region.
Key Words: Regionalization, specific flood, clustering, L-moment, homogeneity test

1. INTRODUCTION
Reliable estimation of design flood is required indesign of hydraulic structures like reservoirs, levees,
culverts, bridges, drainage works, irrigation
diversion works etc. Regional flood frequency
analysis is an effective method for estimating
design flood. It can be used at both gauged andungauged sites. Among the various methods ofregional flood frequency analysis1), index flood
method2) is the most popular. The index floodprocedure
includes
three
major
steps:
regionalization of river basins, estimation ofregional distribution function and estimation ofindex flood. Regionalization refers to grouping ofbasins in hydrological homogeneous regions.
Homogeneity implies that regions have similar
flood generating mechanisms. A more specificdefinition of a homogeneous region is the region
that consists of sites having identical frequency
distribution apart from a site-specific scale factor.
Regionalization is required to affect the spatialtransfer of hydrologic information. For sites where
flood data are not available, the analysis is based onregional data. For sites with available data, the joint

use of measured data at a site, called at-site data,
and regional data from a number of stations in aregion provides sufficient information to enable a
probability distribution to be used with greater
reliability.
There are no specific guidelines for identifying
homogeneous regions. This is due to the complexity
in understanding precisely the factors that haveeffect on the generation of floods. Several attempts
have been made by different authors to identifyhydrologically homogeneous regions in different
parts of the world based on physiographic
characteristics or on flood data characteristics or a
combination of both. Burn and Goel3) used threephysiographic characteristics: catchment area,
length of the main stream, and slope of the mainstream of central Indian River basins.
Regionalization using basin characteristics such as
catchment area, rainfall and soil type was suggested
as an attractive alternative to geographicalregionalization by Wiltshire4). Mosley5) usedclustering of flood statistics in terms of specificflood (peak discharge generated by unit drainagearea) and coefficient of variance (Cv) for
delimitation of New Zealand river basins. Burn6)- 91 -

used seasonality statistics (average date of flood
events) to avoid the dual use (region forming andhomogeneity test) of statistics derived from flood
magnitudes. Mkhandi & Kachroo7) used mapping
technique by superimposing the digitized
information on catchment boundaries, topography
map, mean annual rainfall map, flood statistics andlocation of gauging stations. Research onregionalization of Nepalese rivers is extremely
limited. Water and Energy Commission Secretariat(WECS), Nepal developed relationships as WECS
method8) for estimating low, mean and peak flow
duration statistics in ungauged river basins,
considering Nepal as one homogeneous region.
Medium Irrigation Project (MIP) design manuals8)
have classified the Nepalese basins into 7 regions
for estimating mean and 80% reliable flow.
David et al.9) has studied flow regimes across the
Nepalese Himalaya by classifying long-term
average monthly runoff data for 28 independent
river basins.
Flood generation is governed by many
physiographic and climatic factors. Data for a
sufficient number of physiographic characteristics
are not always available, particularly of remoteareas or developing countries. As a result, thegroupings formed using the available physiographic
variables may not be hydrologically homogeneous.
The resulting regions are often hydrologicallyhomogeneous when flood statistics are used as thevariables in the similarity measure. However withthis approach, the integrity of homogeneity test iscompromised10) as flood statistics are used both toform the regions and to subsequently evaluate thehomogeneity. Also, regionalization is not possible
for ungauged river basins by the mere use of flood
statistics as similarity measure variables. Hence,delineation of homogeneous regions based onlimited factors discussed above may be inadequate.
Specific flood indirectly reflects all thephysiographic and climatic factors governing thegeneration of flood. In addition to specific flood,
the factors like date of flood events as seasonality
measure and basins’ centroid lat-long as spatial
proximity will be helpful in better grouping of theriver basins. Spatial proximity also acts as
significant similarity measure variable for groupingof ungauged river basins. Unlike the WECS methodof flood frequency analysis which considered thewhole Nepal as one homogeneous region, it will bewise to divide whole Nepal into sub-regions forbetter prediction of flood because there is a vastphysiographic and climatic difference among theriver basins of Nepal.
The present work addresses the regionalizationof the Nepalese river basins for flood frequency
analysis that can be used for estimating design
flood. The approach uses, as a starting point, aclustering technique that employs specific flood,

average date of flood events and spatial location of
the river basins. An overview has been provided on
study area and data screening process, followed bypresentation of proposed region forming processes.
The L-moment-based regional homogeneity test has
been described in the successive section to test thevalidity of initially formed regions. Results
obtained after application of the proposed method
herein and discussions on those obtained results
have been presented simultaneously in the
successive section. The final section summarizes
the important research conclusions.

2. STUDY AREA AND DATA SCREENING
Nepal, roughly a rectangle in shape with an areaof 147,181 square kilometer, is situated between
China in north and India in remaining three sides. It
has a length of 885 km east–west and width of
145–248 km north–south. Within this relatively
small latitudinal extent, altitude rises from 60 m insouth to the 8848 m (Mount Everest, the world’s
highest peak) in North. The country can be divided
into five physiographic regions (Fig. 1) namely the
Terai (Plain), Siwalik Hills, Middle Mountains,
High Mountains and High Himalayas. The averageannual precipitation is around 1600 mm of whichalmost 80% occurs during the period ofJune-September.
Nepal’s hydrometric network comprises 170
gauging stations, of which 54 have been establishedsince 19999). Annual instantaneous maximum flow
values of 46 independent watersheds have beenused to carry out the present study. These basins
were selected on the basis of availability of highquality data and to provide reasonable spatial
coverage. These all river basins have a record
length of at least 8 years to a maximum of 34 years.
These flood data were collected from thehydrological data books published in 1998, 2003
and 2004 by Department of Hydrology andMeteorology, Nepal.
Data screening was started by visual inspectionof the annual instantaneous maximum discharge ofeach gauge station. These maximum discharge data
series being independent and homogeneous are thebasic assumptions. Test for independence andhomogeneity (assumption that the whole dataset
come from same distribution) of the data was
performed as discussed by Mann and Whitney11).
Presence of outliers in the data causes difficulties
when fitting a distribution to the data (Rao and
Hamed12)). Test for outlier was performed
according to Grubbs13) and Grubbs and Beck14) andchecked at 5% significance level. Out of total 46
gauge stations, there were 5 outliers at one station(station index 610), 2 outliers at seven stations and1 outlier at 15 stations.

- 92 -

Fig.1 Physiographic map of Nepal

3. PROPOSED APPROACH
This work employs a clustering technique as thestarting point for the formation of regions that arehomogeneous, identifiable, and sufficiently large.
Clusters (groups) of catchments are initially formed
using hierarchical, agglomerative cluster analysis
according to their values of;z
Specific flood,z
Average date of flood occurrence, andz
Spatial location
The initially delineated groups are then modified, if
necessary, to improve the homogeneity.
(1) Specific flood
Specific flood, defined as peak discharges perunit drainage area, indirectly reflects thephysiographic characteristics like soil type, averageslope, drainage density, shape of the basins. In
addition, it represents the intensities and amount ofstorm occurred to generate those series of floods.
The magnitudes of specific flood are affected withthe size of the basins. To reduce the effect ofcatchment area on the specific flood values, allthese values were standardized to catchment area of
500 km2 obtained after analyzing the plot of specificflood against the respective drainage area. The
standardized specific flood was calculated as:

Qsp = Qasp A 0.245 500 −0.245(1)where Qsp is the standardized specific flood andQasp is the actual specific flood of a catchment ofarea A (km2). Qasp is obtained by dividing theobserved average annual flood with thecorresponding drainage area. The exponent 0.245
was found by authors using regression analysis
between actual specific floods (Qasp) and catchment
area (A) for the 89 Nepalese catchments (Fig. 2).
(2) Average date of flood occurrence
Timing of flood events was used in view ofclimatic similarity among the 46 independent river
basins. It has been expressed in terms of averageoccurrence date (Fig. 4) of the annual instantaneous
flood series by considering a flood cycle startingfrom mid-June to mid-September. The total numberof days in one cycle (2π radian) consists of 92 daysby considering mid-June as 1st day andmid-September as 92nd day. Average date of flood(θf) in angular unit radian was obtained afterconverting flood cycle dates (df) similar to Burn6)
and expressed as:θ f = d f 2π / 92

(2)(3) Spatial location
Merz and Bloschl15) examined the predictive
performance of various regionalization methods andconcluded that the methods that only use catchment
attributes perform significantly poorer than themethods based on spatial proximity. In addition,
they concluded that the method that combines
spatial proximity and catchment attributes yields
the best predictive performance. Hence, in addition
to specific flood and average date of flood, thelatitudinal and longitudinal coordinates of river
basins’ centroid were used for spatial proximity
consideration.
Clustering is a standard method of statistical- 93 -

multivariate analysis for dividing a data set into
groups. A data vector is associated with each site,and sites are partitioned or aggregated into groups
according to the similarity of their data vectors. The
present study employs Ward’s hierarchicalagglomerative clustering method16) to form theregions according to basins’ specific flood, average
flood date and centroid lat-long values. In thismethod, initially there are N clusters, eachcontaining one basin’s attributes, labeled 1 throughN. At each stage of clustering, two clusters are
merged. In the Ward’s procedure, the clusters thatare merged are chosen to minimize thewithin-cluster sum of squared deviations of each
attribute about the cluster mean.

4. REGIONAL HOMOGENEITY TESTRegional homogeneity can be evaluated using
L-moments based homogeneity test10). Basically,
there are two ways to check regional homogeneity.
The first one is discordancy measure, intended to
identify those sites that are unusual with the groupas a whole. The discordancy measure estimates how
far a given site is from the centre of the group. If
ui=[t(i) t3(i) t4(i)]T is a L-moment ratios (LCv,
LCs & LCk) vector for the site i and superscript T astranspose of the vector, then discordancy (Di) canbe expressed as Eq. (3a).

Di =

−
−
1
( ui − u ) T A −1 ( ui − u )3( 3a )

where ū and A for N gauge locations in a region are
defined as;

1 N
∑ ui
N i =1−u=N−( 3b )−A = ∑ ( u i − u )( u i − u ) T( 3c )i

A site (i) is declared to be discordant if Di islarge10).
The second way of homogeneity test isheterogeneity measure, intended to estimate thedegree of heterogeneity in a group of sites and toassess whether they might be reasonably treated ashomogeneous. This test compares the variability ofL-moment ratios for the catchments in a region withthe expected variability, obtained from simulation,with the same record lengths as those in the region.
The heterogeneity measure is defined as Eq. (4).

H =(V − μ v )

σv

(4)

where V is the weighted variance of the LCv or LCs
or LCk for the region, µv is mean and σv standard
deviation of V obtained after simulation.
Heterogeneity measure is symbolized as H1, H2 andH3 when considered LCv, LCs and LCk respectively
for calculating V. Heterogeneity measure based on
LCv is suggested as the most reliable parameter for
testing regional homogeneity. A region ishomogeneous if H<1, possibly heterogeneous if 1 <H < 2, and definitely heterogeneous if H > 2.

5. RESULTS AND DISCUSSION
Specific flood was calculated for average ofannual instantaneous flood data of the available
time series. Fig. 2 shows a plot of average specificfloods against corresponding drainage area. The
plot suggests that the points are highly scattered as
the specific flood is governed by many
physiographic/climatic factors other than basin areaand hence, there is poor correlation between
specific flood and drainage area. Roughly it can beseen that specific flood is of high value in the rangeof drainage area 100-1000 km2 and then starts
decreasing with further increase in drainage area.
The authors carried out 15 point moving
average in order to offset the influence ofphysiographic and climatic factors other thandrainage area and to see the effect of drainage area
more clearly. Fig. 3 shows that the specific floodincreases with drainage area up to a value of about
500 km2 (break point) and then starts decreasing
with the increase in drainage area. Hence, to avoid
the effect of drainage area on specific flood, all theactual average specific flood values werestandardized to a drainage area of 500 km2 forcarrying out regionalization. The values ofstandardized specific flood varied from a minimum
0.198 m3/s/km2 to a maximum 2.15 m3/s/km2.
Almost all the flood occurs in monsoon period
which starts in June and ends in September. The
mean date of occurrence of annual instantaneous
flood was calculated for all the 46 independent river
basins. All the mean dates were converted in radianunit by considering flood cycle of 92 days(equivalent to 2π radian) where June 16 is start offlood cycle and September 15 is end of flood cycle.
On the inspection of mean flood date expressed inangular unit radian, it is found varying from 2.684
to 4.175. In other words, it can be said that averageannual flood occurs between the fourth week ofJuly and the second week of August. Considering
the spatial location of river basins against average
flood date values, timing of flood is found relatively
earlier in the eastern part of Nepal (Fig. 4).
The difficult aspect of clustering is deciding
suitable weight to the attributes and number ofcluster. In this study, unit weight was applied to
specific flood, average flood date and latitude
values. Longitude was given double weight to thatof latitude to make the very small basins not
spreading over two regions. Starting from thenumber of clusters as two, while performing the- 94 -

clustering, all the 46 independent catchments were
finally divided into five clusters (Fig. 5) until
reasonable value of homogeneity was achieved.
Ungauged and dependent river basins are shown as
blank area.
Average specific flood (m3/s/km2)

10.0-0.245y = 2.6448x
2

R = 0.4137

1.0

Fig. 4 Mean flood date of 46 independent river basins locatedfrom west to east.
0.1
1

10

100

1000

10000

100000Catchment area (km2)

Fig. 2 Average specific flood vs. drainage area plot for 89
Nepalese river basins.
Using 15-point moving average method

Average specific flood (m3/s/km2).
10.00.3141y = 0.1623x
2

R = 0.9024-0.3187

y = 6.863x2

R = 0.8942

1.0

0.1
100

1000

10000

100000Catchment area (km2)

Fig. 3 Moving average specific flood vs. drainage area plot for
all Nepalese river basins.

Values of the discordancy measure Di and theheterogeneity measure H were computed using
FORTRAN programme developed by Hosking16).
Table 1 shows heterogeneity measures H1, H2 andH3 based on LCv, LCs and LCk respectively fortesting the homogeneity of those regions. The
whole Nepal can not be considered as ahydrological homogeneous region since the valueof heterogeneity measure is large. Heterogeneity
measures got highly reduced after removing thediscordant sites. However, the heterogeneity
measure, H1, for Regions 3 and 5 is larger than thatsuggested by Hosking and Wallis10). Therefore,
estimates of frequency distribution parameters may
be obtained by using at site mean and LCv in these
two regions
Since spatial proximity is significant inregionalization as discussed in Section 3, thedependent river basins of mountainous regions werecategorized in earlier defined regions based on
spatial proximity as shown in Fig. 6. Concerned toriver basins of south part of Nepal which consists ofplain terrain and alluvial soil unlike the steep andnon-alluvial mountainous river basins, these river
basins were classified as a separate region (Fig. 7).

Table 1 Heterogeneity measures for Nepalese river basins
All stations
RegionHeterogeneity measure

Number ofsites

Discordant stations removed
Heterogeneity measure

Number of

H1

H2

H3

sites

H1

H2

H3

All

46

12.39

2.39

-1.68

44

12.19

2.13

1.70

1

11

2.93

-0.36

-1.23

10

1.00

-0.83

-1.39

2

10

3.46

0.84

-0.23

9

-0.14

0.15

-0.31

3

7

5.98

0.49

-1.28

5

2.90

-0.54

-1.47

4

12

8.72

2.56

-0.03

7

1.07

0.48

-0.20

5

6

6.00

2.16

0.33

5

2.57

1.92

1.06

- 95 -

on generation of floods. Since the heterogeneity
measure values of the delineated regions arereasonable, this paper concludes effective attributes
for delineation of regions as specific flood, average
flood date and centroid lat-long of river basins. The
authors found large heterogeneity measure value
when considered all the 46 independent Nepaleseriver basins as one region. Hence, the present
regionalization work will be able to predict design
flood better as compared to the previous method
developed in Nepal which considered whole Nepal
as one homogeneous region. In the next stage, theauthors will estimate regional distribution function
and index flood value for each delineated region toaccomplish the regional flood frequency analysis.

Fig. 5 Regionalization of 46 independent river basins.

REFERENCES

Fig. 6 Regionalization of mountainous river basins.

Fig. 7 Regionalization of all Nepalese river basins.

The present work can be compared with theprevious works to observe similarity or
dissimilarity in the regions. David et al.9) classifies
Himalanyan Nepalese basins into three clusters
namely A, B &C while Medium Irrigation Project(MIP) method classifies the Nepalese basins into 7
regions. On comparing the results of David et al.
with present study, we find the river basins ofCluster A are spread either over region 3 or region
5. Similarly, Cluster B covers a part of region 1
while the cluster C is partially spread over regions 1
and 4. On comparing the MIP classification withpresent classification, region 7 of MIP is very muchsimilar to region 6 of the present study. Other
regions are partially similar or quite different, maybe, because of their different purposes.

6. CONCLUSIONS
The main objective to delineate hydrologicalhomogeneous regions for flood frequency analysis
was achieved despite the complexity inunderstanding precisely the factors that have effect

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- 96 -(Received September 30, 2007)