Design Flow and Stage Computations in the Teesta River, Bangladesh, Using Frequency Analysis and...

CASE STUDIES

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Design Flow and Stage Computations in the Teesta River,Bangladesh, Using Frequency Analysis and MIKE 11

ModelingMd. Mizanur Rahman1; D. S. Arya2; N. K. Goel3; and Anand Prakash Dhamy4

Abstract: A case study was conducted in the Teesta subcatchment in Bangladesh for determining design flood flows and correspondingflood stages for different return periods using frequency analysis and MIKE 11 model. Different distribution functions of frequencyanalysis were tested for their goodness of fit. The observed discharge data at Kaunia on the river Teesta were used for estimation of designflood. The Pearson type-III distribution was found best fitted by the Kolmogorov-Smirnov, D-index, and L-moment diagram ratio tests,and accordingly 25-, 50-, and 100-year return period design floods were computed. The river network of Teesta River was extracted fromSRTM 90-m digital elevation model. The river network of Teesta subcatchment was then simulated by MIKE 11 rainfall-runoff Nedbor-Afstromnings-Model �NAM� and HD model. The resultant time series of river stage was then compared with corresponding observedvalues. From the model, a stage-discharge relationship �Q-h� curve and respective equation were developed for Kaunia station on the riverTeesta. The developed equation determines the corresponding flood stage of estimated flood flow of 25-, 50-, and 100-year return periods.The resulting flows and stages will be useful to design hydraulic structures, prepare flood extent maps, assess vulnerability of flooddamage for different return periods, and provide flood forecasting for early warnings of floods. The approach presented would beapplicable to similar river basin systems where data are limited and scarce.

DOI: 10.1061/�ASCE�HE.1943-5584.0000299

CE Database subject headings: Frequency analysis; Design flood frequency; Computations; Rivers; Bangladesh.

Author keywords: Frequency analysis; Design flood; MIKE 11; Discharge-stage equation; Flood stage.

Introduction

Floods are one of the major causes of loss of life and physicalproperty every year across the globe affecting adversely the over-all economy of a country. Flood is a natural disaster but its be-havior changes due to human intervention in the floodplains andcatchments such as construction of houses, roads, and bridges,consequently increasing the risk and losses to the properties andlife �Hassan et al. 2006�. There are two common approaches tomanage a flood problem, viz., �1� structural measures and �2�nonstructural measures, and in both cases of flood management,design flow and stage have vital role.

1Executive Engineer, Bangladesh Water Development Board,Ministry of Water Resources, Dhaka, Bangladesh �corresponding author�.E-mail: [email protected]

2Associate Professor, Dept. of Hydrology, Indian Institute of Technol-ogy, Roorkee, India. E-mail: [email protected]

3Professor, Dept. of Hydrology, Indian Institute of Technology, Roor-kee, India. E-mail: [email protected]

4Senior Divisional Engineer, Dept. of Irrigation, Ministry of WaterResources, Katmandu, Government of Nepal. E-mail:[email protected]

Note. This manuscript was submitted on July 6, 2009; approved onJuly 21, 2010; published online on July 22, 2010. Discussion period openuntil July 1, 2011; separate discussions must be submitted for individualpapers. This paper is part of the Journal of Hydrologic Engineering, Vol.16, No. 2, February 1, 2011. ©ASCE, ISSN 1084-0699/2011/2-176–186/
$25.00.
176 / JOURNAL OF HYDROLOGIC ENGINEERING © ASCE / FEBRUARY 2

J. Hydrol. Eng. 2011

The design flow and stage are important events to design dif-ferent hydraulic structures of a flood management project. Thedesign flood stage is also useful to prepare flood extent maps toassess vulnerability of flood damage for different return periods.The objective of this case study is to determine design flood flowsand corresponding flood stages for different return periods usingfrequency analysis and MIKE 11 modeling, respectively, at thelocation where observed data are scarce or expensive to collect.MIKE 11 is physically based deterministic hydrodynamic �HD�model to generate the discharge, stage, and their relation in a rivernetwork. Rating curve is a conventional practice to compute thecorresponding river stage or discharge. Generally, rating curvesare developed from observed discharge and stage data. In case ofdata scarcity, the discharges and stages can also be routed bymathematical modeling at any point of interest within the modeldomain.

A comprehensive study was conducted in Teesta River sub-catchment under Brahmaputra basin in Bangladesh to determinethe flood flow and stage for different return periods. Rainfall-runoff �RR� �NAM� module integrated with HD module of MIKE11 mathematical model was applied in this study for routing riverstage and discharge. Finally, a rating curve �Q-h relation� equa-tion was developed using the model output.

Flood frequency analysis was carried out by checking the suit-ability of different distributions using discharge data to determinethe flood magnitude for different return periods. The designeddischarges were then used to find the river stage from the devel-
oped equation of Q-h relationship.
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Description of Study Area and Data Used

The study area is located in Teesta subcatchment of Bangladesh.The Teesta River originates from the Himalayas in Sikkim state ofIndia. It flows approximately 180 km through a mountainous areabefore entering into the alluvial plains of northwestern part ofBangladesh. It keeps flowing in a braided course for a length of96 km before crossing the India-Bangladesh border. After travel-ing 121 km, it joins the Jamuna River near Chilmari in Bang-ladesh �Fig. 1�. The Dharla River is also flashy in nature, entersinto Bangladesh at Talukshimulbari from India, and confluenceswith Jamuna at Gujimari.

The Brahmaputra �total length of 2,700 km� originated fromChemayung-Dung glacier near Manassarowar and Mount Kailas.In Bangladesh, the river is named as Brahmaputra up to Bahdu-

Fig. 1. Location map o

rabad �71 km� and from Bahdurabad to Aricha it is named as

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Jamuna �205 km�. The Brahmaputra-Jamuna is one of the largestrivers in the world which flows through Tibet, China, India, andBangladesh. The earthquake and catastrophic flood in 1787changed the main course of Brahmaputra near Bahdurabad andnow passes southwards through Serajganj District to the conflu-ence with the Ganges at Aricha. The original Brahmaputra,flowed toward southeast, passes through Jamalpur, Mymensingh,and Kishorgonj Districts to confluence with the Upper-Meghnanear Bhairabbazar and now known as “Old-Brahmaputra.” Themain course of the Brahmaputra is now known as river Jamuna; itcarries an average of 4,000 m3 /s water in the monsoon and itexperiences maximum discharge of 98,600 m3 /s in August1998. Ghagot is a short length river, originated inside Bangladeshand confluences with Jamuna. The adjoining river systems bypass

ta River subcatchment
f Tees
excess flow into Jamuna through this river.

OF HYDROLOGIC ENGINEERING © ASCE / FEBRUARY 2011 / 177

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The area of Teesta subcatchment in Bangladesh is about2 ,000 km2. The riverbed is comprised of fine to medium sandcommon to an alluvial floodplain. This area is classified as shal-low depressions and valleys of moribund river channels formedby long morphological history of changes in the river courses.The general slope of the river varies from 0.47 to 0.55 m/km. TheTeesta subcatchment is vulnerable to flooding in each year. Thereare two main tributaries of the river Teesta, namely, Naotara andBuri-Teesta. Flash floods are caused by the Teesta River and if thepeaks are observed in rivers Jamuna and Teesta simultaneously,the worst flood situation occurs in the area. In this study, onlyBangladesh portion of the Teesta subcatchment has been consid-ered for analysis.

The region has an average annual rainfall around 1,900 mm.Maximum temperature ranges from 25°C in January to 35°C inApril/May. Evapotranspiration reaches to a maximum in Aprilwhen temperature, sunshine, and wind are all close to theirmaxima �ODA and JICA 1993�.

The hydrometeorological data were obtained from Flood Fore-casting and Warning Centre �FFWC�, which is part of the Bang-ladesh Water Development Board �BWDB�. The collectedRainfall data �1991–2004� of 10 stations, i.e., Dewangonj, Ja-malpur, Mymensingh, Chilmari, Gaibandha, Dalia, Panchagar,Rangpur, Kaunia, and Kurigram, were used for Mike 11 NAMmodel setup. Due to unavailability of evaporation data, yearlyaverage value of 1,460 mm was taken for MIKE 11 NAM modelsetup. Discharge data �1991–2004� at Dalia over River Teestaand river stage data �1991–2004� at Kurigram on river Dharla atGaibandha on river Ghagot and at Noonkhaowa and Bahdurabadon river Jamuna were used for boundary of MIKE 11 HD modelsetup. River cross sections of seven rivers, e.g., Teesta �chainagefrom 13.50 to 121.00 km�, Buri-Teesta �chainage from 0 to 35.00km�, Naotara �chainage from 0 to 10.00 km�, and Ghagot �chain-age from 132.00 to 136.00 km�. Dharla �chainage from 21.50 to48.00 km�, Jamuna �chainage from 8.00 to 84.500 km�, and Old-Brahmaputra �chainage from 0 to 31.00 km�, measured in 1999,were used for Mike 11 HD model setup. The stream network wasdelineated using ArcGIS. Shuttle Radar Topography Mission90-m digital elevation model �Version 4� available in public do-main �http://srtm.csi.cgiar.org/� was used for delineation of rivernetwork. River stage data at Chilmari on River Jamuna availablefor the period from May 1, 1996 to December 31, 2003 were usedfor comparing the simulated result.

Flood Frequency Analysis

The procedure for estimating the frequency of occurrence �return

Table 1. Summary of Randomness and Stationary Test Result

Test Zcal 1

TP 0.35 2.5

AC 1.43 2.5

Rank difference 1.43 2.5

Kendall’s rank correlation 1.27 2.5

Mann-Kendall test 1.18 2.5

period� of a hydrological event such as flood is known as fre-



quency analysis �Kwaku and Duke 2007�. The frequency analysisbegins with the calculation of the statistical parameters requiredfor a proposed probability distribution from the given data �Chowet al. 1988�. In this study, annual flood series of maximum dis-charges at Kaunia station of 22 years, obtained from FFWC, wereused for designing 25-, 50-, and 100-year flood flows. Severaltests for checking the consistency and quality of data were carriedout. The data were also checked for outliers, which are data pointsthat depart significantly from the trend of the remaining data�Chow et al. 1988�. According to procedure given by Chow et al.�1988�, the computed threshold values for high outliers and lowoutliers are 12,566 and 1,419, respectively, which are within cor-responding observed upper and lower threshold values of 8,577and 1,684, respectively. This result shows that the given timeseries can be used for flood frequency analysis.

Statistical parameters, i.e., mean, standard deviation, coeffi-cient of skewness, and coefficient of kurtosis in original, are4,627, 1,948, 0.33, and �1.04, respectively, and log-transformedseries are 8.34, 0.45, �0.26, and 14.83, respectively.

The hydrologic data must be free from short-term dependenceas well as long-term dependence and must be stationary. Turningpoint �TP� test �i.e., Kendall’s test� for randomness is a nonpara-metric test carried out for testing short-term dependence in a timeseries �Lye and Lin 1993�. Anderson’s correlogram �AC� testchecks the randomness of the annual flood series. Rank differencetest �Meacham 1968�, as referred by Lye and Lin �1993�, alsotests the randomness. Kendall’s rank correlation test checks thestationarity of a series �Shrestha 2000�. Since there is no rising orfalling trend in this series, linear regression test �Kottegoda 1980�was not applied. The Mann-Kendall test was also used in thisstudy. According to Yue et al. �2002� the lag-one �k=1� autocor-relation coefficient, r1=−0.371, was computed and since �−1−1.645�n−2� / �n−2��r1� �−1+1.645�n−2� / �n−2�, i.e., −0.41�−0.37�+0.311, which indicates that the data are independentat 10% significant level for which no prewhitening is required.Here, n is the length of the data series.

Zcal’s of TP, AC, rank difference, Kendall’s rank correlation,and Mann-Kendall test are given in Table 1 which confirm thatthe annual flood series is free from short-term dependence. Zcal iscalculated standard normal deviate, � is the level of significancein percent, and Zcritical is the standard normal deviate �standardnormal distribution, with mean �=0 and standard deviation �=1� for � percent significant level.

The Hurst coefficient is at present the only measurement avail-able for testing long-term dependence �Lye and Lin 1993�. Haanet al. �1982� suggested that the range of the cumulative departuresdepends on the length of the period. Hurst’s coefficient was alsocomputed for checking the long-term dependence in the data re-

Zcritical

Remarks

��%�

5 10

1.96 1.65 Random

1.96 1.65 Random

1.96 1.65 Random

1.96 1.65 Random

1.96 1.65 Random

8

8

8

8

8

corded at the Kaunia station. The computed value of Hurst’s co-

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efficient, K, is 0.47 which is less than all the critical values. Itimplies that the annual flood series is also free from long-termdependence. The analysis of short- and long-term dependencesshows that the obtained time series is random in nature and hencecan be used for flood frequency analysis.

Log-normal �LN�, Pearson type-III �PT-III�, log-Pearson type-III �LPT-III�, and Gumbel or extreme value type-I �EV1� distri-butions were used to estimate floods for 25-, 50-, and 100-yearreturn periods. There are number of plotting-position formulasdeveloped by different investigators but Weibull’s plotting-position formula is the most acceptable and widely used in hy-drology. Chow et al. �1988�, Haan et al. �1982�, Singh �1994�,McCuen and Snyder �1985�, Subramanya �1996�, Gray �1973�,Gupta �1989�, and Bedient and Huber �2002� recommended theuse Weibull’s plotting-position formula. Thus, in the presentstudy, Weilbull’s plotting-position formula has been used. Estima-tion of different return period floods, by different probability dis-tributions, has been presented in Table 2.

A number of analytical tests, such as the chi-square test, theKolmogorov-Smirnov �KS� test, D-index test, and L-moment dia-gram ratio, have been conducted for testing the goodness of fit ofthe proposed distribution. The results of chi-square, KS, andD-index goodness of fit tests show that EV1 �Gumbel� distribu-tion fits well based on chi-square test. All distributions are wellfitted by KS test. On the other hand, Pearson type-III distributionfits well based on D-index statistics. In order to find the best fitdistribution as described by Rao and Hamed �2000�, L-momentdiagram and ratio tests were conducted. L-moment is less biasedthan traditional product moment estimates �Hosking 1990; Wallis1988�. The goodness of fit is judged by the difference betweenregional L-kurtosis values and the theoretical L-kurtosis values.Ratios of L-kurtosis �0.1454� and L-skewness �0.2301� havefallen on the curve of Pearson type III.

The Pearson type-III distributions are found to be the best-fitdistribution. Hence, the flood flow computed from PT-III distri-bution was considered as the design flood. The design flows forthe four probability distributions examined here are given inTable 2.

Modeling Using MIKE 11 Software

MIKE 11 is a dynamic modeling tool for rivers and channels witha graphical user interface, MIKE Zero. MIKE Zero is Windowsbased software integrated with the computational core of MIKE11, which includes graphical editing facilities and improved com-putational speed. Geometric inputs such as river network, rivercross sections, etc., are imported from GIS environment to MIKE11 environment.

MIKE 11 contains the modules HD, advection-dispersion,sediment transport, ECO Laboratory �including water qualitymodeling, etc.�, RR, flood forecasting �FF�, data assimilation, andice modeling �Danish Hydraulic Institute �DHI� 2004�. In thisstudy, RR and HD modules were used to compute the design

Table 2. Summary of Design Floods for 25-, 50-, and 100-Year Return

Return period, T year LN distribution PT-III dist

25 9,258 8,24

50 10,607 8,96

100 11,988 9,62

flood flow and stage at different locations on the Teesta River.

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MIKE 11 was used because of its availability for this case study.From the early 1990s MIKE 11 NAM and HD model is beingused in Bangladesh for FF in the complex nature of the riversystem �Paudyal 2002�. The operation process of MIKE 11 NAMand HD model simulation is shown in Fig. 2. In the subsequentsections, brief description of MIKE 11 NAM and HD, applicationof MIKE 11, the procedures for model setup, comparison ofmodel result with observed value, and development of ratingcurve are presented.

Among the different types of RR model specified in MIKE 11,the NAM method was selected for this study. This NAM modelwas originally developed by Nielsen and Hansen �1973�. NAMsimulates four different and mutually interrelated storages thatrepresent different physical elements of the catchment. Thesestorages are snow storage, surface storage, lower or root zonestorage, and groundwater storage. In this study, snow storage hasnot been considered. NAM produces runoff based on evapotrans-piration, soil moisture content, groundwater recharge, andgroundwater level data. The detailed description of the model isdescribed by Nielsen and Hansen �1973� and also documented byDanish Hydraulic Institute �DHI� �2004�.

s Based on Different Distributions

n LPT-III distribution EV1�Gumbel� distribution

8,890 8,611

9,964 9,679

11,011 10,740

MIKE 11-NAM

(Rainfall –Runoff Model)

Evapotranspiration

(Average)

JAM_C

Dharala_C

Teesta_UC

Ghagot_C

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O_BRAM-UC

Teesta_LC

Naotara_C

Dalia

KauniaRangpur

Kurigram

Jamalpur

Chilmari

Gaibandha

Dewanganj

Panchagarh

Mymensingh

30 40

Miles

Catchment

Information

Shape file of

Delineated River

Network from

SRTM 90 m DEM

• US and DS Boundary (Q and

WL)

• River X-Sections

• Hydrodynamic Parameter

MIKE 11-NAM

Simulation

Result file of Runoff

Run-off QLateral

MIKE 11- HD

(Hydrodynamic Model)

MIKE 11-HD

Simulation and

Calibration,

Result file of HD

Q and h

Equation of

Rating Curve

(Q-h Relation)

Q (25, 50 and 100-year )

Estimated by

Frequency

Analysis

Flood Stage (25, 50 and 100-year )

Daily Rainfall

Time Series

Fig. 2. Flow diagram of MIKE 11 NAM and HD model simulationfor preparing rating curve

Period

ributio

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MIKE 11 HD module solves Saint-Venant’s equation with animplicit finite difference method developed by Abbott and Io-nescu �1967� for the computation of flows in rivers. It can modelsubcritical as well as supercritical flow conditions. MIKE 11 HDapplied with the dynamic wave description solves the verticallyintegrated equations of conservation of continuity and momentumbased on the following assumptions �Danish Hydraulic Institute�DHI� 2004�:• The flow is one dimension; depth and velocity vary only in the

longitudinal direction of the channel. This implies that the ve-locity is constant and the water surface is horizontal across anysection perpendicular to the longitudinal axis.

• Water is incompressible and homogeneous; i.e., there is negli-gible variation in density.

• The bottom slope �of the channel� is small; thus, the cosine ofthe angle with the horizontal may be taken as 1.

• The wavelengths are large compared to the water depth. Thisensures that the flow everywhere can be regarded as having adirection parallel to the bottom. That is, vertical accelerationscan be neglected and a hydrostatic pressure variation along thevertical can be assumed.

• The flow is subcritical �supercritical flow may also be modeledin MIKE 11 with more restrictive conditions�.The formulation can be applied to branched and looped net-

works and quasi-two-dimensional flow simulation on floodplains�Paudyal 2002�. Based on NAM-calculated lateral inflow and ad-ditional inflow from external boundaries, the HD module predictswater levels and reservoir inflows. The conservation of mass andmomentum equations was modified for varying width and waterlevels. These equations can simulate flow through cross sectionsof any shape when divided up into a series of rectangular crosssections �Danish Hydraulic Institute �DHI� 2004�. The hydraulicresistance is based on the friction slope from the empirical equa-tion, Manning or Chezy, with several ways of modifying theroughness to account for variations throughout the cross-sectionalarea. Chowdhury �2000� described the basic concept of MIKE 11NAM and HD model briefly.

Markar et al. �2004� evaluated Info-Works, Hydrologic Engi-neering Centers River Analysis System �HEC-RAS�, and MIKE11 HD model to assess the suitability for integration into the FFsystem �FFS� with criteria of accuracy, technical capability, andability to interface with customized �FFS�. They mentioned thatthe model run times for MIKE 11 were much smaller and thestability of MIKE 11 runs was less sensitive to specified initialconditions. Markar et al. �2004� then found that MIKE 11 is moresuited for using in FFS of Yangtze River in China.

Mike 11 has also been used to simulate flow in large riversystems. Paudyal �2002� described MIKE 11 NAM and HDmodel for simulation of complex river system in Bangladesh todevelop FF and warning system. He mentioned that the use ofMIKE 11 NAM and HD has been found to be very promising inbuilding the flood-preparedness system. Patro et al. �2009� cali-brated the one-dimensional model MIKE 11 using river waterlevel and discharge data of various gauging sites for the monsoonperiod in the delta region of Mahanadi River basin in India. Theyfound that the calibration and validation results of MIKE 11 showthat the model performs quite satisfactorily in simulating the riverflow for the delta region of Mahanadi river basin.

Ruch et al. �2008� developed continuous FF combined withautomatic forecast correction in the Mur River using the flexiblesoftware solution by the RR model NAM and the HD model
MIKE 11, and the FF shell MIKE FLOOD WATCH easily allows


to extent the entire system to other tasks by adding specific MIKE11 modules.

NAM Model Setup

The catchment is divided into eight subcatchments having differ-ent areas. Due to nonavailability of evapotranspiration data ineach subcatchment, yearly average data have been considered forthe Teesta River subcatchment. The time series of “daily” rainfallfor 10 stations from 1990 to 2004 have been given as rainfallinput to NAM model. The basic parameters specific to NAMmodel along with their short description are given by DanishHydraulic Institute �DHI� �2004�.

The calibration process starts with the water balance. Thewater balance should be formulated by total evapotranspirationequal to net precipitation minus runoff. The evapotranspirationwill increase when increasing the maximum surface storage�Umax� and root zone storage �Lmax�. The peak volume is adjusted

Kaunia at 79

km

Fig. 3. River network used in HD model

Reduced

Levelin

m

Reference Distance in m

Right Bank LineLeft Bank Line

Bottom Line

Fig. 4. Representative cross section of the River Teesta at Kauniachainage of 79.79 km

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by changing the overland flow �CQOF� runoff coefficient, and theshape of the peak depends on the time constant used in the runoffrouting �CK12�. The parameters Umax, Lmax, CQOF, and CK12were adjusted by different values for eight subcatchments.

Decrease in overland flow or interflow results in higher baseflow. The shape of the base flow recession is a function of thebase flow time constant. The root zone threshold value of over-land flow, threshold value of interflow, and threshold value ofgroundwater recharge are considered to be zero in the beginningof the calibration. These threshold values are adjusted by heuristicapproach. Accordingly, the parameters used in the model were

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Fig. 5. Longitudinal profile of River Teesta �chainage of 13,610–1�chainage of 0–31,000 m�

adjusted for eight subcatchments.

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HD Model Setup

River Network

To setup the HD model, the river networks of the rivers Buri-Teesta �00–35.00 km�, Naotara �00–10.00 km�, Teesta �13.50–121.00 km�, Dharla �21.5–48.00 km�, Ghagot �132.27–138.00km�, Jamuna �8.00–84.50 km�, and Brahmaputra �00–31.00 km�have been considered. Fig. 3 shows the river network of themodel and their connectivity. The model network lies within theBangladesh territory. Stage in river Teesta is also influenced dur-ing flood period by other rivers that have also been considered in

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Left Bank Level

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m�, Jamuna �chainage of 8,000–84,500 m�, and Old-Brahmaputra

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f the R

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ight Ban

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of the

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the river network. For modeling purposes, flow direction is taken


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erve

d.

positive, maximum distance between two adjacent points �dx� istaken 1000 m, and the river type is taken as regular.

River Cross SectionsThe cross sections as taken in the year of 1998 by BWDB havebeen used in this study. A sample cross section at Kaunia ofTeesta river is shown in Fig. 4. The longitudinal profiles of the

Fig. 6. Model generated inflow �Jamuna at 37,750 m, Teesta at 45,8m and Jamuna at 81,100 m� from May 1996 to November 2003

Fig. 7. Model generated inflow �Jamuna at 37,750 m, Teesta at 45,8m and Jamuna at 81,100 m� for 2001



rivers Teesta, Jamuna, and Brahmaputra are also given in Fig. 5.

Boundary ConditionsThe selection of boundary conditions depends on the availabilityof data and the physical situation of the model area. Boundaryconditions could be constant discharge from a reservoir, a dis-charge hydrograph of a specific event, constant water level, e.g.,

and Ghagot at 134,135 m� and outflow �Old-Brahmaputra at 26,000

and Ghagot at 134,135 m� and outflow �Old-Brahmaputra at 26,000

45 m,

45 m,

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in a large receiving water body, time series of water level, e.g.,tidal cycle, and a reliable rating curve, e.g., from a gauging sta-tion.

The upstream boundary conditions of rivers Jamuna, Dharla,and Ghagot are defined as the water levels measured by BWDBon three-hourly basis at Noonkhaowa, Kurigram, and Gaibandhastations. The upstream boundary condition of the Teesta River isthe inflow time series observed by BWDB. Since Naotara andBuri-Teesta Rivers originate within the study area, inflows in theupstream of these rivers are not significant. Hence, the boundaryconditions of rivers Naotara and Buri-Teesta are arbitrarily takenas constant inflow, i.e., 1 m3 /s.

The downstream boundary condition of the Jamuna River hasbeen taken the water level collected at Bahdurabad. On the otherhand, the length of the river Old-Brahmaputra has been consid-ered 31 km down the confluence. Due to nonavailability of agauging station, Q-h relationship �i.e., rating curve� developed byBWDB for FF in Bangladesh was given as downstream boundarycondition.

HD ParameterThe Teesta River is the tributary of the Jamuna River and Jamunacarries the total discharge of Brahmaputra basin to pass towardBay of Bengal. During peak discharge in the Jamuna, Teesta getssome backwater effect when flash flood occurs in Teesta catch-ment. The tributaries of Teesta, Naotara, and Buri-Teesta are alsoflashy in nature. Dharla is also a flashy river and gets some back-water effect from Jamuna; i.e., the whole water body of the rivernetwork system of the study area changes over time and space.On the other hand, the average bed slope of the river Teesta is1:3,500, Naotara is 1:18,000, Buri-Teesta is 1:20,000, Dharla is

Table 3. Statistical Parameter for Comparison of Model Results for thro

SN Statistical parameters Expected values

Obt

1996 1997

1 RB 0.00 0.02 0.04

2 MAE 0.00 0.47 0.73

3 RMAE 0.00 0.02 0.04

4 EI 1.00 0.89 0.79

5 Correlation coefficient 1.00 0.97 0.97

15

16

17

18

19

20

21

22

23

24

25

1996/0

5/0

1

1996/1

1/0

1

1997/0

5/0

1

1997/1

1/0

1

1998/0

5/0

1

1998/1

1/0

1

1999/0

5/0

1

Riv

er

Sta

ge

inm

ete

r

Fig. 8. Graphical comparison of model results with the observed riveto November 2003

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1:5,500, Jamuna is 1:14,500, and Old-Brahmaputra is 1:40,000.The slope data indicate that the study area is very flat. Hence,high order fully dynamic wave approximation has been consid-ered to simulate the above river system. The global initial condi-tion has been taken as 2-m water depth.

Integration of RR „NAM… Model with HD Model

NAM model has then been integrated with HD model to input thelateral inflow from eight subcatchments to the river channels. Thereach lengths of seven rivers were connected with eight subcatch-ments allocating the area to be drain with those reach lengths.

Simulation

Simulation period has been selected from 31 May 1996 to 30November 2003 according to data length and their consistency.For HD model, fixed time step of 30 min and the result of NAMmodel have been selected as hot start of initial condition of HDsimulation. The computation of NAM and HD model gives thetime series of water level and discharge at each 1,000-m pointwith 30-min interval. The discharge and water level time seriesare generated at every alternate point. At the point of dischargegeneration a rating curve or discharge-stage �Q-h� relation can beobtained. The model generated inflow �Jamuna at 36,100 m,Teesta at 81,100 m, and Ghagot at 134,135 m� and outflow �Old-Brahmaputra at 26,000 m and Jamuna at 25,800 m� are shown inFig. 6 �full simulation period� and Fig. 7 �representative 1 year�.

Comparison of River Stages and Discharge

The calibration process uses graphical and numerical performancemeasures. The graphical evaluation includes comparison of the

t the Full Year

rom observed and result values for each year

Averaged998 1999 2000 2001 2002 2003

.03 0.05 0.02 0.02 0.03 0.02 0.03

.69 0.93 0.60 0.64 0.87 0.72 0.71

.03 0.05 0.03 0.03 0.04 0.04 0.04

.88 0.76 0.92 0.84 0.71 0.74 0.82

.97 0.97 0.98 0.96 0.90 0.88 0.95

2000/0

5/0

1

2000/1

1/0

1

2001/0

5/0

1

2001/1

1/0

1

2002/0

5/0

1

2002/1

1/0

1

2003/0

5/0

1

2003/1

1/0

1

e

ved Data Model Result

at Chilmari �chainage of 36,100 m on river Jamuna� from May 1996

ughou

ained f

1

0

0

0

0

0

1999/1

1/0

1

Dat

Obser

r stage


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simulated and observed hydrograph and discharge. Though therewere several studies available for performance evaluation ofmodel such as by Aitken �1973� and Fleming �1975�, the methodgiven by Nash and Sutcliffe �1970� is widely used in the area ofhydrology and water resources for the detection of systematicerrors with respect to long-term simulation.

The reliability of the MIKE 11 NAM and HD was evaluatedbased on Nash-Sutcliffe efficiency index �EI�. The EI is given inEq. �1�

EI =

�i=1

n

�qi − q̄�2 − �i=1

n

�qi − qs�2

�i=1

n

�qi − q̄�2

�1�

where qi=observed flow at time i number of data points; q̄=mean value of observed flow; =�1 /n��i=1

n qi; qs=simulated flowat time i; and n=number of data points. A perfect match, corre-sponding to EI=1, is not expected because of different errorsources, including• Errors in meteorological input data;• Errors in recorded observations;• Errors and simplifications �assumptions� inherent in the model

structure; and• Errors due to the use of nonoptimal parameter values.

The resultant time series of river stages at Chilmari �chainageof 36,100 m of the river Jamuna� has been validated visuallycompared with the observed stage data from 31 May 1996 to 30November 2003.

The model efficiency can be high for cases where there is aconstant bias in the model result; that is, the model result is equal

Table 4. Statistical Parameter for Comparison of Model Result for Mon

SN Statistical parameters Expected values

Obt

1996 1997

1 RB 0.00 0.01 0.01

2 MAE 0.00 0.29 0.37

3 RMAE 0.00 0.01 0.02

4 EI 1.00 0.97 0.74

5 Correlation coefficient 1.00 0.95 0.91

450 slope lin

e, y = x; R2 =1

Model vs Observed

slope line, y = 1.0386x - 0.8017; R

2 = 0.8832

19

20

21

22

23

24

25

19 20 21 22 23 24 25

Observed Values (meter)

Mo

de

lR

es

ult

Va

lue

s(m

ete

r)Model Vs Observed Value

45 Degree Slope Line

Model vs Observed slope line

Fig. 9. XY plot of model river stage versus observed river stageconsidering monsoon period at Chilmari



to the observation plus or minus a constant value. The betterstatistical parameters are the bias and mean absolute error �MAE�or relative MAE �RMAE� �Lettenmaier and Wood 1993�. MAE orrelative mean square error is preferred to mean squared errorbecause mean squared error or root mean squared error is influ-enced by the square of small numbers of large errors �Lettenmaierand Wood 1993�.

Statistical analysis was also carried out for obtaining param-eters such as relative bias �RB�, MAE, RMAE, EI, and coefficientof correlation for the comparison of the results, and the equationsof RB, MAE, and RMAE are given below where qs=simulatedvalue and qi=observed values

relative bias =

1

n�i=1

N

�qs − qi�

1

N�i=1

N

qi

�2�

MAE =1

N�i=1

N

�qs − qi� �3�

RMAE =MAE

1

N�i=1

N

qi

�4�

The yearwise values of the statistical parameters are given inTable 3. The RB is the measure of the degree to which the modelresults are consistently above or below the observed value�Lettenmaier and Wood 1993�. Analyses of these parameters�Table 3� show the existence of systematic errors that spread over

eriod Only

rom observed and result values for each year

Averaged98 1999 2000 2001 2002 2003

.01 0.01 0.00 �0.01 0.00 �0.01 0.00

.38 0.31 0.39 0.21 0.40 0.33 0.34

.02 0.01 0.02 0.01 0.02 0.01 0.02

.87 0.81 0.81 0.92 0.85 0.83 0.85

.96 0.95 0.94 0.98 0.94 0.94 0.95

0

1000

2000

3000

4000

5000

6000

31/5/1996

06:00:00

13/8/1996

09:00:00

30/6/1997

15:00:00

11/09/1997

15:00:00

18/7/1998

12:00:00

18/7/1999

18:00:00

29/9/1999

18:00:00

26-7-2000

12:00:00

07/10/2000

12:00:00

24-7-2001

18:00:00

06/10/2001

6:00:00

24-7-2002

06:00:00

17-6-2003

18:00:00

Date and Time

Dis

ca

hrg

eQ

,c

um

ec

Observed Dischrage Model Discharge,

Fig. 10. Graphical comparison of model results. Solid line representssimulated discharges �30-min time step� and the squares representobserved �low frequency and irregular time steps� discharge data atKaunia for monsoon period only

soon P

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many years. It is also evident from the graph as shown in Fig. 8.It is clear that the model results are consistently above the ob-served value in the lean period only. It implies that either thequality of observed data in the lean period is not good or themodel setup parameters require further adjustment for the dryperiod simulation.

Most of the floods in Bangladesh occur during the monsoonseason. Hence, if we consider only monsoon period for the cali-bration and validation then a XY plot of the model result andobserved value with a 45° line is shown in Fig. 9. After consid-ering the model result for monsoon period only, the error indiceshave been recalculated as given in Table 4. The average values ofstatistical parameters for either case were then compared with theexpected value of these parameters. The statistical parameters formonsoon period are showing better results than the statistical pa-rameters for full year.

The RB of the monsoon period indicates that the variability ofmodel results and the observed data are minimized significantly.EI and coefficient of correlation show the same in both cases.Table 4 shows that RB, MAE, root MAE, EI, and coefficient ofcorrelation are good fit with the expected value.

The resultant time series of discharge was also compared withthe observed discharge at Kaunia �chainage of 79,790 m of theriver Jamuna� for the monsoon period only and is shown in Fig.10. The average values of statistical parameters such as RB, rela-tive mean error, EI, and coefficient of correlation were then com-pared with the expected value of these parameters and found alsosatisfactory. So, it may be concluded that the model results arecalibrated and validated very well for the monsoon period.

Development of Rating Curve Equation

Mosley and McKercher �1993� described the general form of therating curve as given in Eq. �5�

Q = C�h + a�N �5�

where Q=discharge; C and N=constants; h=stage; and a=stageat which discharge is zero. Values of N for different cross sectionshapes are rectangular N=1.67 �assuming width of �20 depth�;parabolic N=2.17 �assuming width of �20 depth�; and triangularN=2.67.

Natural channels are generally parabolic in cross section,which is why about 2 for the N may be considered. From themodel result file, rating curve for discharge verses stage timeseries at chainage of 78,645 m of the Teesta river has been ex-tracted.

The equation of the rating curve was developed by fitting withthe time series of discharge versus river stage computed from themodel results for monsoon period. This computed time seriesfrom developed equation has been compared with the correspond-ing time series of rating curve. The statistical error parameterssuch as multiplicative bias, RMAE, and coefficient of correlationwere calculated as 1.06, 0.06, and 0.95, respectively, which aresignificantly close to the expected values of 1.00, 0.00, and 1.00.Therefore, the calibrated rating curve of Eq. �6� is

Q = 116�h − 26.2�2.33 �6�

3
where Q=discharge �in m /s� and h=river stage �in m�.
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Flood Stage Computation

Using rating curve equation, the flood stages for 25-, 50-, and100-year return periods were calculated as 32.43, 32.66, and32.86 m, respectively. The above results are useful for calculatingthe extent of the flooding for 25-, 50-, and 100-year return periodsfor flood risk analysis, flood zoning, and vulnerability assessment.The water resources engineers and hydrologists may find the re-sults of flood stages useful for the flood control projects too.

Conclusion

Teesta River subcatchment in Bangladesh is vulnerable to flood-ing almost every year with different magnitudes and extents.Short term FF and warning system can protect life and can reduceinfrastructural loss to some extent but cannot give the sustainablesecurity of agricultural production and infrastructural develop-ment. A long-term prediction of river flood in terms of its flowand stage can provide the confidence to the planner for an inte-grated sustainable flood management project. Under this studyflood frequency analysis of stochastic approach was used for es-timation of long-term design flood flow prediction and the corre-sponding flood stage computed from equation of stage-dischargerelation curve in the same location. MIKE 11 NAM and HDmodel was applied in this study for computing discharge, riverstage, and stage-discharge relation curve. During the study thefollowing aspects have been observed:1. The simulated river stage was verified by observed data at

Chilmari on Jamuna River and model result was found wellmatching with observed data during monsoon period andsome systematic errors were occurred in dry season.

2. To avoid the effect of those errors, the stage-discharge rela-tion rating curve at Kaunia was developed excluding themodel result values during dry season which may lead somelimitation of the rating curve to use in low stage computa-tion.

3. The discharge used in the rating curve was compared withthe observed discharge at Kaunia and RMAE was found 0.2.This uncertainty may be occurred due to the following rea-son. Kaunia is located at chainage of 79.790 km of TeestaRiver. MIKE 11 generated discharge �Q� at chainage of78.645 km and developed the rating curve relating with thestage �h� at chainage of 79.790 km of Teesta River. It ismentioned here that MIKE 11 calculates Q and h in the al-ternate reach of the river and because of this limitation de-veloped rating curve shows some uncertainty.

4. The another limitation of the rating curve is that it may bevaried with time in response to a change in channel shape atthe control section which can be minimized by updating themodel input.

Acknowledgments

The writers would like to acknowledge the help extended by theBWDB in providing data. Mr. Md. Saiful Hossain �ExecutiveEngineer, FFWC, BWDB, Bangladesh� is also acknowledged forhis cooperation and for allowing us to use the relevant software inthe center. The writers acknowledge the constructive suggestionsreceived from Mr. A. K. M. Zeaul Hoque, DHI, Mr. S.M Mah-bubur Rahman, Institute of Water Modeling, Dhaka, Bangladesh,
and the anonymous reviewers.

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Design Flow and Stage Computations in the Teesta River, Bangladesh, Using Frequency Analysis and...

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