Advances in Hydro-Science and Engineering, vol. VIII
Proc. of the 8th International Conference on Hydro-Science and Engineering, Nagoya, Japan, Sept. 9-12, 2008

NRCS CURVE NUMBER EMPLOYED HYDROLOGICHOMOGENEOUS REGIONALIZATION IN REGIONAL FLOODFREQUENCY ANALYSIS
Binaya Kumar Mishra1, Kaoru Takara2 and Yasuto Tachikawa3
1

Graduate Student, Department of Urban and Environmental Engineering, Kyoto University
Uji Campus, Kyoto, 611-0011, Japan, e-mail: mishra@flood.dpri.kyoto-u.ac.jp
2
Professor, Disaster Prevention Research Institute, Kyoto University
Uji Campus, Kyoto, 611-0011, Japan, e-mail: takara@flood.dpri.kyoto-u.ac.jp
3
Associate Professor, Department of Urban and Environmental Engineering, Kyoto University
Katsura Campus, Kyoto, 615-8540, Japan, e-mail: tachikawa@mbox.kudpc.kyoto-u.ac.jp

ABSTRACT
Estimation of extreme flood for different return period is required in design of various
hydraulic structures. Regional flood frequency analysis is an effective method for estimatingsuch extreme flood. Delineation of hydrologic homogeneous regions is key step in success ofregional flood frequency analysis. This study deals hydrologic regionalization of Nepaleseterritory. Cluster analysis, a multivariate technique, is generally used to identify objectivelyhydrological regions. This work addresses the difficulty of allocating suitable weight todifferent clustering attributes by employing NRCS runoff curve number. On superimposing
monsoon rainfall pattern map over runoff curve number map, five hydrologic regions were
proposed. L-moment based regional hydrologic homogeneity test led finalization ofhydrological homogeneous regions.
Keywords: curve number, flood frequency, homogeneity test, L-moment
1.

INTRODUCTION

Estimation of extreme flood for different return periods is required in design andplanning of various water related structures. This extreme flood is popularly known as design
flood. Design flood estimation methods can be broadly classified into two groups:
streamflow-based methods and rainfall-based methods. This work is related to streamflowbased methods which base their analysis purely on stream-gauging data. The most common
streamflow-based methods are the flood frequency analysis and regional flood frequency
analysis. Flood frequency analysis is applicable to locations which possess long records ofobserved flood data. However, the gauged locations rarely coincide with the locations at
which water-related structures are going to be constructed. In such situation, regionalhydrological characteristics need to be used in estimation of design flood. Regional flood
frequency analysis is such method which makes the use of regional hydrologicalcharacteristics for estimating design flood. Regional flood frequency analysis is popularmethod for estimating flood peaks within specified probabilities of exceedance at ungauged
sites or enhancing estimation at gauged sites where historical records are short.
Among various methods (Cunnane, 1998) of regional flood frequency analysis, index
flood method is the most popular. The index flood procedure includes three major steps:
hydrologic homogeneous regionalization, selection of regional distribution function andestimation of index flood (scale factor). This study deals with the first step i.e. hydrologic
homogeneous regionalization. Regionalization refers grouping of territory/basins having

similar flood generating mechanisms. In other word, all the sites in a hydrologic
homogeneous region possess identical frequency distribution apart from a site-specific scale
factor. Regionalization is required to affect the spatial transfer of hydrologic information.
There are no specific guidelines for identifying homogeneous regions. This is due tothe complexity in understanding precisely the factors that have effect on the generation offloods. Several attempts have been made by different authors to identify hydrologicalhomogeneous regions in different parts of the world. Earlier research work used subjective
consideration on the attributes like location, topography of the basin in forming hydrologic
homogeneous regions. More recent works used multivariate technique such as cluster analysis
to identify objectively hydrologic homogeneous regions. The cluster analysis is based either
on physiographic characteristics or on flood data characteristics. Burn and Goel (2000) used
three physiographic characteristics: catchment area, length of the main stream and slope of themain stream in central Indian River basins. Regionalization using basin characteristics such as
catchment area, rainfall and soil type was suggested as an attractive approach ofregionalization by Wiltshire (1985). Mosley (1981) used clustering of flood statistics: specificflood (peak discharge generated by unit drainage area) and coefficient of variance (Cv) for
delimitation of New Zealand river basins. Burn (1997) used seasonality statistic (average dateof flood events) to avoid the dual use (region forming and homogeneity test) of statistics
derived from flood magnitudes.
Research on regionalization of Nepalese rivers is extremely limited. McDonald andPartners (1990) divided Nepalese territory into 7 regions using information for low flow
estimation. Sharma and Adhikari (2004) has developed relationships for estimating extreme(minimum and maximum) and long-term (average) flows using regression technique by
considering the whole Nepalese territory as one homogeneous region. Except similar previous
work of Mishra et al. (2008), no other study is found on hydrologic regionalization of
Nepalese rivers for design flood estimation. In the previous regionalization work, the authors
used specific flood, date of flood events and lat-long of river basins as clustering attributes.
A number of difficulties were experienced by the authors in the earlier attempt. One of
the major difficulties is different measuring units of clustering attributes. For example, one
attribute like soil type is expressed in term of infiltration rate (mm/h) whereas anotherattribute like catchment area is expressed in km2. Another problem is measuring scale (e.g.,
mm/hr or cm/hr) of clustering attributes. Because of different units/scale, a suitable weightneeds to be allocated to each clustering attribute. Allocation of suitable weight to different
clustering attributes is difficult and subjective work. A new approach of regionalization ispresented here which addresses problems associated with different measuring units/scale ofclustering attribute. Soil type, land cover, land slope and rainfall pattern are considered major
physio-climatic attributes which govern flood generation. Effect of soil type, land slope andland cover can be taken into account by using NRCS runoff curve number (CN).
The present work identifies hydrologic homogeneous regions inside Nepaleseterritory. The work started with the estimation of runoff curve number fordifferent
combinations of soil type, land cover and land slope ranges. In next step, area-weighted CN
was computed for spatially well-representing sample basins. These sample basins withdrainage area smaller than 250 km2 were generated from GTOPO30 digital elevation model(DEM). Hydrological regions were proposed by superimposing digitized monsoon rainfall
map over CN associated basins map. Validation of proposed regions was made using the Lmoment based regional homogeneity test. Theoretical background on NRCS runoff curve
number and regional homogeneity test has been discussed in section 2 and 3 respectively. The
following section deals study area, data analysis and region forming process. Results of thework and discussion on the obtained results have been discussed in section 7. The final
section summarizes and concludes the present work.

2.

NRCS RUNOFF CURVE NUMBER

The runoff curve number (CN), an index developed by USDA Natural Resource
Conservation Service (NRCS), represents potential for storm water runoff within a drainage
area. USDA developed runoff curve number from field experiments in small catchments fordifferent combinations of hydrological soil group, land cover and soil moisture. Further
research in different part of the world suggested adjustments in CN for different range of land
slope and others. The curve number varies from 0 to 100; lower numbers indicate low runoff
potential while larger numbers indicate increasing runoff potential. The CN is widely used for
estimating direct runoff from a rainfall event. The runoff equation (Ritzema, 1994) is;Q=(P − I a ) 2
P − Ia + S(1)

where Q is direct runoff (mm), P is rainfall (mm), S is potential maximum retention (mm),and Ia is initial abstraction (mm). Ia is usually taken 20% of S. The runoff curve number, CN,
is then related to S as:
CN =

25400
254 + S

(2)For NRCS runoff curve number estimation, the available soil data needs to be
expressed into hydrological soil group. There are four hydrologic soil groups: A, B, C and D.
These soil groups are roughly indicate high, moderate, slow and very slow infiltration rates
respectively. The land cover is defined like woodland, forest, cropland, urban area etc. inestimating runoff curve number.
Soil moisture condition in the drainage basin before runoff occurs is another importantfactor influencing the CN value. Antecedent moisture condition (AMC) is based on the 5-day
antecedent rainfall i.e. the accumulated total rainfall preceding the runoff under consideration.
AMC I, II and III roughly indicate dry, average and saturated condition of drainage basins.
A curve number value based on different combination of hydrological soil group, land
cover, land treatment, impervious percentage and land slope is available in tabular form. This
table is popularly known as look-up table. Initially the look-up table is available for averagemoisture condition (AMC II). Then, if necessary, these CN values are modified based on 5day antecedent rainfall data.

3.

REGIONAL HOMOGENEITY TESTRegional hydrologic homogeneity test is required for each proposed hydrologic
regions. The L-moment based regional homogeneity test (Hosking and Wallis, 1997) needs
computation of L-moment ratios: L-coefficient of variance (LCv), L-skewness (LCs) and Lkurtosis (LCk) at each station for the available data series. Visually, regional homogeneity canbe identified from the plot of LCv versus LCs or LCs versus LCk on L-moment ratio diagram(Rao and Hamed, 1997). If the plotted points are closer, the region can be expected ashydrological homogeneous. Numerically, there are two ways to check regional homogeneity.
The first one is discordancy measure, intended to identify those sites that are unusual with thegroup as a whole. The discordancy measure estimates how far a given site is from the centreof the group. If ui=[t(i) t3(i) t4(i)]T is L-moment ratios vector for the site i and superscript
T as transpose of the vector, then discordancy (Di) can be expressed as Eq. (3).

Di =

−
−
1
( u i − u ) T A −1 ( u i − u )3( 3)

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

u=

1 N
∑ ui
N i =1
−

N

( 4)
−

A = ∑ ( u i − u )( u i − u ) T

(5 )

i

A site i is declared to be discordant if Di is large. Critical value of Di is 3 for the region
having 15 or more nos. of gauged sites. For the region with smaller nos. of gauge sites,
critical value of Di varies with nos. of gauge sites in the region.
The second regional homogeneity test is heterogeneity measure, intended to estimate
the degree of heterogeneity in a group of sites and to assess whether they might be reasonably
treated as homogeneous. This test compares the variability of L-moment ratios for thecatchments in a region with the expected variability obtained from simulation. The
heterogeneity measure is expressed as:

H =(V − μ v )

σv

(6)

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 from simulation. Heterogeneity measure H1, H2 and H3
indicates variability in LCv, LCs and LCk respectively. Heterogeneity measure H1 is suggested
as the most reliable parameter for testing regional homogeneity. A region is consideredhomogeneous if H<1, possibly heterogeneous if 1 ≤ H < 2, and definitely heterogeneous if H
≥ 2.

4.

STUDY AREA

This study is intended to form hydrologic regions inside the Nepalese territory forcarrying regional flood frequency analysis. Nepal, roughly a rectangle in shape with an areaof 147,181 square kilometer, is situated between China in north and India in remaining threesides. It has a length of 885 km east–west and width of 145–248 km north–south. Within thisrelatively small latitudinal extent, altitude rises from 60 m in south to the 8848 m (Mount
Everest, the world’s highest peak) in North. Physiographically, the country is divided into five
regions (Figure 1): Terai (Plain), Siwalik Hills, Middle Mountains, High Mountains and High
Himalayas.

Figure 1 Physiographic regions of Nepal.
The average annual precipitation is around 1600 mm of which almost 80% or more
occurs during the period of June-September. All the river systems of Nepal are tributaries to
the Ganges river draining ultimately to the Bay of Bengal. The major tributaries generally
flow towards south direction.

5.

DATA AND PRELIMINARY ANALYSISThe physiographic/climatic attributes: soil type, land cover, land slope and monsoon
rainfall pattern have been considered in proposing hydrologic regions. Effect of soil type, land
cover and land slope has been dealt using runoff curve number (CN). GTOPO30 digital
elevation model (DEM) was used in generating sample basins for the study purpose. Areaweighted runoff curve number value was calculated for each spatially representing sample
basins. Annual instantaneous flood data of 49 river basins have been used for regional
homogeneity test. Discussion on these data used is dealt in the following subsections.
5.1

Soil type

Global soil data at resolution of 5 arc-min (approx. 10 km) has been prepared by FAO
and can be freely downloaded through internet. This digital soil map is available in shape fileformat with geographic coordinate system. Digital soil data of the study area was extracted
from the downloaded large data set. Textural classification associated with soil data wasconsidered important here since it can be easily converted into hydrological soil group whichis required in CN estimation. Textural classes reflect the relative proportions of clay (fraction
less than 0.002mm), silt (0.002 - 0.05mm) and sand (0.05 - 2mm) in the soil. Based on their
proportion, hydrological soil group map of Nepal (Fig.2) was prepared.
5.2

Land cover
The University of Maryland, Department of Geography generated global land coverclassification collection in 1998. The university made fourteen land cover categories from theanalysis of AVHRR satellites imagery acquired between 1981 and 1994. This land cover data
can be freely downloaded at various resolutions through internet. Land cover data of the study
area at resolution of 1km was made available from the internet site maintained by Global
Land Cover Facility (GLCF). Digital land cover map (Figure 3) required for CN estimation
purpose was prepared after simple modification in original classification.

Figure 2 Hydrological soil groups of Nepal.
5.3

Figure 3 Land cover map of Nepal.

Rainfall distribution

Rainfall pattern i.e. distribution of rainfall over time and space is important inhydrologic regionalization. In general, annual rainfall amount decreases slightly from east to
west and increases with elevation from south to north on windward slopes. Monsoon rainfall
which occurs during the months of June to September has more importance in regionalization
for design flood estimation. About 80 or more percent of the annual rainfall occurs during thisseason and the rainfall regime covers the whole country except the northern Himalayan
region. Such concentration of rainfall during a few months results large floods and landslides.
The study made three classes of monsoon rainfall pattern from mean monsoon precipitation
map available at http://www.fao.org/ag/agL/swlwpnr/reports/y_sa/z_np/npmp134.htm . These
classes (Figure 4) were defined for rainfall value less than 1000 mm, 1000 to 1500 mm andmore than 1500 mm.

Figure 4 Monsoon rainfall map of Nepal.
5.4

Figure 5 GTOPO30 DEM of Nepal.

Digital elevation model

Digital elevation model (DEM) of the study area (Figure 5) was clipped from large
GTOPO30 DEM of Asia. This can be freely downloaded from the internet site maintained byglobal data centre of NASA. This 30 arc-sec (approx. 1 km) resolution DEM was used togenerate spatially representing sample basins and stream network using Arc GIS. The stream
network derived from this DEM was compared with the stream network available in various
reports available at internet and found acceptably okay. Also, the areas of river basins for thegauged outlets generated from DEM were compared with the areas made available bydepartment of hydrology and meteorology (DHM), Nepal for further validation of
downloaded DEM.
5.5

Flood data

Regional hydrologic homogeneity test need to be performed on each of the proposedhydrologic region. It needs adequate number of gauge station with long record length of flood
data. Department of Hydrology and Meteorology (DHM), Nepal is one and only governmentorganization responsible for collecting and distributing flood data in Nepal. Regularly
observed instantaneous annual maximum stream flow data were collected for 49 stream
gauging stations in Nepal. Selection of these stream gauging stations were based on basins’boundary position and record length of observed data. Boundaries of all these stations are
restricted inside a proposed hydrologic region. Most of these stations are situated in middle
mountain region. Out of these 49 considered river basins, 46 have observed length of morethan 10 years. Because of inadequate gauging stations in lower region, 3 stations wereselected though their record length is smaller.
Analysis of flood data was started by visual inspection. These flood data have beenobtained from the 1998, 2003 and 2004’s DHM publications. In addition, some recent flood
data were collected in digital format from the authority of DHM, Nepal. In case ofoverlapping mismatched data, the latest publication was considered as correct flood data. The
flood data series being homogeneous and stationary are the basic assumptions in flood
frequency analysis. Test of homogeneity and stationary for the flood data series was
performed as discussed by Mann and Whitney (1947). All the data series were foundhomogeneous and stationary at 5% significance level. Presence of outliers in the data causes
difficulties when fitting a distribution to the data. The G-B test (Grubbs and Beck, 1972, Raoand Hamed, 2000) was used to detect outlier. Approximate relationship proposed at 10%
significance level by Pilon and Harvey (1993) was used in calculating G-B statistic. The study
found 1 no. of outliers at 14 stations (station indices: 267, 404.6, 438, 439.8, 445.3, 465, 530,
570, 589, 602, 620, 627.5, 650 & 660), 2 nos. at station index 447.9 and 3 nos. at stationindex 241.

6

REGION FORMING PROCESS

The region forming started with development of NRCS runoff curve number map forhydrological soil group, land cover and land slope. Since information on rainfall amount prior
to the instantaneous flood data series could not be obtained, average soil moisture wasconsidered while estimating the runoff curve number. Arc CN-runoff tool (Zhan and Huang,
2004), a rainfall-runoff model on Arc GIS platform, can generate efficiently runoff curve
number map. The tool Arc CN-runoff requires with a look-up table (Table 1) consisting
specific number between 0 and 100 for different soil type, land cover and land slope
combination. Area-weighted average runoff curve number was calculated for each of 650
sample basins. The present study did not consider sample basins from Himalayan region
considering its insignificance in monsoon flood. Hydrologic regions were proposed bysuperimposing monsoon rainfall map over sample basins associated with CN values.

Table 1 CN association with HSG and land cover.
Land cover
Meadow
Woods - Grass (Fair)
Woods (Fair)
Deciduous Forest
Evergreen Forest
Mixed Forest
Urban
CroplandCropland (terraced)
Shrub / Brush Tundra
Glaciers/Stream/Lake

Soil Type
A
30
43
36
36
40
38
68
49
65
48
0

B
58
65
60
60
66
63
80
69
74
67
0

C
71
76
73
73
77
75
88
79
82
77
0

D
78
82
79
79
85
82
94
84
86
83
0

The L-moment based regional hydrologic homogeneity test was applied on each
proposed regions. To apply the homogeneity test, L-moments/ratios were computed forcollected flood data at each station. Heterogeneity measure, particularly H1, was checked foreach region. The region for which heterogeneity measure was found smaller/nearer to 2 wasaccepted as homogeneous region. For the region having heterogeneity measure far beyond 2,
discordancy measure (Di) was taken into consideration to make adjustment in proposed
regions. When heterogeneity measure and discordancy measure reduced to limiting value, theregion was declared hydrological homogeneous.

7

RESULTS AND DISCUSSION

Out of total 650 sample basins, 450 nos. were found with CN varying from 73 to 80.
The remaining basins were found with smaller curve number ranging from 50 to 65. Thisobservation led 2 divisions of Nepalese territory. The basins with higher CN were foundmostly in mid-mountain and higher mountain whereas sample basins with smaller CN values
were found in low-mountain and plain region.
Monsoon rainfall map was superimposed over the proposed CN based regional map
for further regionalization. Superimposition of monsoon rainfall map over CN-regional map
led additional 3 hydrologic homogeneous regions. In this way, the study proposed total of 5hydrologic regions and proceeded for validation of the regions.
For validation, hydrologic homogeneity test was performed in each region using
historical flood data series. Heterogeneity measures H1, H2, H3 before and after removing thediscordant stations are given in Table 2. A value of H1= 8.9 was found when considered all
stations of Nepalese territory. The situation improved not much even after removing
discordant sites. This value is far beyond the acceptable limit indicating hydrological nonhomogeneity of Nepal. The regions 2, 3 and 5 were found with acceptable value ofheterogeneity measure and with no discordant sites in first attempt. The value of H1 wasfound as 5.72 and 4.77 for regions 1 and 4 respectively before removing the discordant sites.
When discordant sites were removed and some adjustments were made in the proposed
region, the heterogeneity measure reduced near acceptable limit for region 1 and region 4.
Figure 6 shows the finally identified 5 nos. of hydrologic homogeneous regions.

Table 2 Regional heterogeneity measures for Nepalese river basins.
Region% area

All
1
2
3
4
5

100
16.24
14.67
33.20
24.63
11.26

All
Nos. of sites ( NS)
49
9
2
10
26
2

H1
8.9
5.72
-0.41
1.96
4.77
-1.08

H2
2.53
1.41
-0.7
1.1
1.22
0.69

H3
-0.45
-0.44
-0.62
0.09
-0.14
0.01

Discordant sites removed
NS
H1
H2
H3
44
6.36
1
-1.67
7
1.13 -0.07 0.11
2
-0.41 -0.7 -0.62
10
1.96
1.1
0.09
24
2.09 0.08 -0.96
2-1.08 0.69 0.01

Figure 6 Hydrological homogeneous regions of Nepal.

8

SUMMARY AND CONCLUSIONS

Difficulties associated with mostly used regionalization technique i.e. clustering
technique were discussed. Use of runoff curve number (CN) was proposed to addressdifficulties like attributes’ measuring units/scale and suitable weight in cluster analysis. To
estimate the runoff curve number, land cover map prepared from AVHRR satellite imagery
and soil data prepared by FAO were brought in use. Hydrologic regions were proposed bysuperimposing monsoon rainfall map over runoff curve number map. The L-moment based
regional hydrologic homogeneity test led some adjustment in proposed regions and finally 5hydrologic regions were identified inside the Nepalese territory.
The main objective to delineate hydrological homogeneous regions for flood
frequency analysis was achieved despite the complexity in understanding precisely the factorsthat have effect on generation of floods. Heterogeneity measures for each region were foundwithin or near critical values. This led to conclude the runoff curve number employedregionalization approach as effective approach of hydrologic regionalization. The present
regionalization work will be able to predict design flood better as compared to the previous
work. In the next stage, the authors will estimate regional distribution function and index
flood for each delineated region to accomplish the regional flood frequency analysis. To
justify this new approach of hydrologic regionalization, the approach will be applied incountry/territory other than Nepal.

ACKNOWLEDGMENTS
We would like thank to MEXT, Japan for providing financial support in carrying
research work. We would also like to thank Innovative Disaster Prevention Technology and
Policy Research Lab, Kyoto University, Japan for funding/technical support.

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