Hydraulic Engineering Software VIII, C.A. Brebbia & W.R ...

Overland inundating flow analysis for

Mekong Delta in Vietnam

K. Lionel T. Toda* & 0. Maeda^* Disaster Prevention Research Institute, Kyoto University, Japan.^Department of Civil Engineering, Kyoto University, Japan.

Abstract

A mathematical model is developed to analyze the flood in 1-D rivers andinundating flow over a 2-D floodplain. The model ia applied to MekongDelta in Vietnam where the rivers and canals form a network and blocks inthe floodplain are surrounded by these rivers. The informations necessaryfor the application are summarized. Using the results of simulation, thecharacteristics of inundating flow in Mekong Delta is discussed from thepoint of view of flood diversion capacity. The result is compared with theactual inundation record in 1994.

1 Introduction

A mathematical model expressing overland inundating flow is constituted.The rivers considered here are main Mekong river (Tien Giang), Basak riverand several major channels and canals which run in the objective floodplain.The floodplain is the region located in the Mekong Delta in Vietnam.

A 1-D model is applied to rivers including channels and canals (they aresimply called 'river' hereafter), and a finite difference scheme using char-acteristics form is developed for the flood in the rivers. A finite leap-frogdifference scheme using horizontally 2-D model is applied to analyze theoverland flow and inundation processes on the floodplain.

Two schemes of 1-D and 2-D models are combined at several connectionpoints which are comprised of a 1-D river cross section and a grid in a 2-Dfloodplain, where an overflow discharge formula is applied.

2 The studied region

Figure 1 shows the studied region which is the northern half Mekong Delta

Hydraulic Engineering Software VIII, C.A. Brebbia & W.R. Blain (Editors) © 2000 WIT Press, www.witpress.com, ISBN 1-85312-814-7

124 Hydraulic Engineering Software VIII

in Vietnam. The bold lines with arrow denote the rivers considered here,to which the 1-D flow model is applied. The region divided by grids showsthe floodplain considered here, to which 2-D flow model is applied.

Rivers are comprised of 88 branches(segments), and they can be ex-pressed as a network. The floodplain is comprised of 28 blocks. The flood-plain is divided by the square whose one side length is 2km, and the totalarea, is about 18,900km̂ . This region includes the cities such as Long Xuyen,Can Tho and My Tho.

CAMBODIAN Basak river

3.503.002.502.001.50

11.00#0.500.00

Gulf of Thailand

Figure 1: Northern half Mekong Delta in Vietnam

3 Basic equations and model

For rivers, the following 1-D continuity equation and St. Yen ant equationare applied;

dA dQ

1 dv 1 dv dh--%- + -%- 4- T- = so -g ot g ox ox

(2)

In the computation, the above two equations are transformed into the char-acteristics form.

ra+=«±". (3)

1 .dA dQ ldv dHt(4)


Hydraulic Engineering Software VIII 125

dAin which B is the top width of cross section, B — (-— ) , c is the^ ' V QYi ' x -.const. '

celerity of disturbance, given by c = \l — , HI is the total head measured\ B

%2from a reference datum, Ht — -- h h + z&, in which z\, is the bottom eleva,-

2#tion, sj = n*v\v\/R*/^ is the friction slope.

For floodplain, the following 2-D continuity equation and linear momen-tum equation in two directions are applied.

__ . , _,+ — uM H- —vM = -gh- --- ̂ , (6)

ot ox oy ox p

07v a „ 9 ,a^ r.(&)— 4- j-uN + ̂~vN = -gh- --- 2^2 702 <9% <9i/ 0% p

in which h: water depth, M — u/i, TV = vh : discharge flux in x- and y-direction, H : water stage from reference datum, T(b)/p : friction slope.

The discretized forms of these 1-D and 2-D basic equations are omitted^.For simplicity, the convective terms are not included in the 2-D computa-tion.

For the overflow discharge formula, combining rivers and a floodplain, thefollowing equations are used.

, for the complete overflow, (8)

Qi — ///%2 V 2#(/%i — ^2) , for the submerged overflow, (9)

where /?-i,^2 are water stage from the crest of overflow levee, /i, // denotedischarge coefficients, and // = 0.35, //—0.91 is respectively adopted.

4 Computation conditions

Computation conditions in this analysis are summarized as follows.

• Cross-sections of rivers: Cross-section shapes are assumed rectangularfor all of the rivers, and sections for computation are located at about4km intervals.

The river width is set 900m~ 1,700m for the main Mekong river,400 m ~ 1,200m for Basak river^, 250m for channels and canals in thefloodplain, and 500m for the small bay (inlet shaped sections).The bed elevation is set 7 m ~ 10 m^ below the reference datum. Man-

ning coefficient n is assumed 0.030 (m-s) for all the rivers.

• Floodplain: The ground elevation of floodplain is acquired from the Fig-

ure in Reference^), and shown in Figure 1. The maximum and minimum



elevation in the floodplain result in 3.49m, and 0.12m higher than thereference datum, respectively. Manning coefficient n of the floodplain is0.050(rn-s).

Upstream boundary condition: The discharge is imposed at the up-stream boundaries of the main Mekong river, Basak river. The inflowthrough Cambodian border is also considered.

The shape of discharge hydrograph at the upstream boundary of themain Mekong river is similar to that reported in Reference*), as 50year period flood at Kratie. The peak discharge is, however, reducedto 46,800 m̂ /s. The discharge hydrographs of Basak river and inflowthrough Cambodian border are also similar to that of the main Mekongriver, and their peak discharges are 12,300rn̂ /s and ll,600m^/s, re-spectively. Figure 2 shows the discharge hydrographs.

The total water volumes of the main Mekong river, Basak river andinflow through Cambodian border are 244.3x10̂ m^, 64.1x10^ m^ and60.9x10^ m^, respectively, in Figure 2. These values of water volume arenearly equal to those in the Figure of Reference"*) reporting the flood in1994.

Downstream boundary condition: The tidal stage hydrograph is givenat the river downstream boundaries. Some tidal stage differences areexpected among the downstream boundaries of the main Mekong river,Basak river ( South China Sea), and channels and canals ( Gulf of Thai-land). However, for simplicity, the tidal stage at all downstream bound-aries is assumed to be same and given as shown in Figure 2, which is thecyclic extension of tidal stage measured at Long Phu during April 1988̂ .Inflow through Cambodian border: The discharge is distributed to sev-eral grids in the floodplain along the border.

0.0-2.0

rQ(M3/S)

40000

30000

20000

10000

0,

tidal stage

main Mekong river Q

river Q

t ~~^through Cambodian border Q

20 40 60

Figure 2: Boundary condition

80 DAY



• Flood protection levee: An overflow levee is assumed between the rivercross-section and floodplain grid. Its crest elevation is supposed suchthat there occurs no inundation under the condition of annual meandischarge in the main Mekong river and Basak river.

• Rainfall to floodplain: This is not taken into account.

• Initial condition: Keeping the discharges of the main Mekong river andBasak river, and the tidal stage as their initial values, that is, ̂ Mekong =8,600nf/s, Qsasak = 2,300nf/s, #tide = 0.08m, the unsteady flowcomputation in the rivers (without the inundation into the 2-D flood-plain, and no inflow through Cambodian border) is repeated until thesolution is reduced to a steady state.

• Computation case: Two simulation cases are executed. First is the casein which the inundation into the 2-D floodplain is not considered at alland the floods in the main Mekong river and Basak river are confined inthe river including the channel and canals in the floodplain. In this case,only 1-D analysis is applied. The inflow through Cambodian border isnot taken into account. This case is referred as 'without inundation'.

In the second case, not only the flood flow in the 1-D rivers but theinundation into the 2-D floodplain are considered. The inflow throughCambodian border is taken into account by the means mentioned above.This case is referred as 'with inundation'.

• Discretization size: Distance between the consecutive two sections of 1-D river is about 4km. Az and At/ are equal to 2km in the floodplain.The time increment At is 60 seconds.

5 Results and discussion

Figure 3 compares the discharge and the water stage hydrographs at themiddle points of the branches by the cases with and without overland inun-dation flow (the branch number in Figure 3 is shown in Figure 1). The flowdirection is defined such that the arrow direction in Figure 1 is positive andthe opposite direction is negative.

Figure 3 shows that both of the discharge and the water stage hydro-graphs with inundation become much more flattened than those without in-undation. In the case without inundation, the water stage reaches 4 m ~ 7 min each river, while with inundation it declines to 2.0 m^ 3.0 m. The flat hy-drographs and the water stage decline is caused by the reason that the floodwater confined in the rivers without inundation expands over the floodplaindue to inundation. If the flood control by confining flood water in rivers istaken, it would result in the water stage rise of about 4 m in rivers in thestudied area, which would be an important factor to consider the feasibilityof the flood control. Some inundation into the floodplain might be accept-able in flood prevention planning. It is also a significant factor that the inun-



QCM3/5)30000

r- 20000 -

10000-

BRANCH NO.=33 DIRECTION=POSITI7EDISCHARGECQ)

WATER STAGE(H)

.withoutinundation

20 40 60(a) Branch 33

DAY

QCM3/S)H(M) 30000

8

BRANCH NO.=39DISCHARGECQ)

WATER STAGE(H)

DIRECTION=NEGATIVE

withoutinundation

6h 20000

4

2- 10000

0

_Ol_ p i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 j 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 /* % h,HhM,.,M,hM,h,U,M,,h,,,,,M,.M,MM,

(b) Branch 39

Figure 3: Discharge and water stage hydrograph

dation contributes to the fertilization and flushing of the deteriorated soil.The oscillation with short period in the discharge and the water stage

hydrographs is conspicuous especially in the case without inundation. Thisis caused by the tidal stage imposed as the downstream boundary condi-tion (Figure 2). The variation of hydrographs appears remarkably whenthe river discharge is low, and the variation is somewhat small in the casewith inundation. This is due to the reason that large capacity of floodplaindiminishes the variation of flood water. The damping of oscillation, the flat-tening of hydrographs and the water stage decline imply that the floodplainplays a kind of buffer role for flooding process.

Figure 4 shows the distributions of river discharge and inundation depthin floodplain in the case with inundation. According to the result at 30 days



WATER DEPTHCM)<0.0i<0.50

(a) at 30 days after \

WATER DEPTHCM)<0.01<0.50<1.00<1.50<2.00<2.5052.50 (b) at 50 days after

Figure 4: Distribution of discharge and inundation depth

after, inundation is seen in the northern part of the studied region, while itis not yet seen in the central and southern parts. In the northern region,the water stage is high in the main Mekong river and Basak river, fromwhich inundation occurs into the floodplain, while the central and southernregions seem still protected by the assumed overflow levees. In the right



WATER DEPTHCM)<0.01<0.50

0050

Figure 4: (continued)

side of the main Mekong river, the discharges through the river network toGulf of Thailand are fairly large, that is, the channels and canals in thefloodplain have a considerable effect on flood diversion.

At 50 days after, the inundation depth of about 2m is seen in almostall the studied region. Especially in the blocks of both sides of the mainMekong river and Basak river near the upstream boundaries and the blocksalong the border, the inundation depth reaches over 2m, which implies avery serious inundation disaster. As typically shown in the branch 39 ofFigureS, the discharge at the branches connecting the main Mekong riverwith Basak river in this case decreases more than in the case without inun-dation. In the branch 33 of Figure 3, it is also seen that the discharge at thedownstream of Basak river decreases compared with that in the case with-out inundation ( the similar decrease is seen in the downstream of the mainMekong river). These changes show the discharge from the main Mekongriver and Basak river to Gulf of Thailand through the floodplain is largerthan that flowing out through the channels and canals in the floodplainwithout inundation, in other words, the floodplain itself makes the greatereffect on flood diversion.

At 85 days after, the inundation decreases all over the studied region,which proves that the decreasing process of inundation is well expressed.In this computation, the drainage from the floodplain to the channels andcanals is underestimated and delayed due to the existence of assumed over-flow levees. Anyway, the computed result shows that the inundation depthis more than 0.5m in the relatively lower place, which implies the inunda-



tion is expected to last over a long period.Figure 5 shows the distribution of maximum inundation depth in this

computation. According to the comparison of the observed maximum in-undation depth in 1994 ( Figure 6 )^\ in the northern half part of the studiedregion, the computed inundation depth and its distribution make a fairly

WATER DEPTH(M)<0.50<1.00

HI < 1.50<2.00<2.50>2.50

Figure 5: Maximum inundation depth

WATER DEPTH(M)<0.50

iil<i-ooii|<1.50

<2.50

Figure 6: Maximum inundation depth observed in 1994



good agreement with the record. In Figure 6, however, the inundation areaexpands fanwise from the upstream boundaries of the studied region, whilethe distribution of computed inundation depth is much affected by the localground elevation shown in Figure 1.

The computed inundation is somewhat deeper than the record in 1994flooding. The long duration of inundation in the whole region, and the over-estimation of inundation depth are caused by the reason that the dischargeimposed in this computation would be higher than that in 1994.

As the boundary conditions of discharge and tidal stage, and other con-ditions differ from the actual ones, more detailed comparison does not seemsignificant here. However, judging from the total tendency of the computedresults, the mathematical model proposed here can be applicable enough toflood inundation analysis in Mekong Delta.

6 Concluding remarks

Except for horizontal geography of the studied region, the topographical in-formations (e.g. exact floodplain elevation, cross-section and bed elevationof rivers), the hydraulic and hydrological informations (e.g. the discharge atthe upstream boundaries, the tidal stage at the downstream boundary, rain-fall data on the studied region, Manning's coefficient) have been scarcelyobtained so far. Therefore, the data required for the present analysis weresubstituted by those gathered from the various materials. However, themodel has been successfully made here which can be applied well to floodand inundation analysis in Mekong delta. If the detailed informations areobtained, the present model would give more realistic results.

Acknowledgements

This research is supported by the Grant-in -Aid for International ScienceResearch ( No. 09041121, Principal researcher: Professor Nobuyuki Tamai,University of Tokyo ) by the Ministry of Education, Science and Culture,Japan.

References[1] Inoue, K., Nakagawa H. & Tod a, K. Numerical analysis of overland flood flows

by means of one- and two- dimensional models, Proc. 5th JSPS- VCC Seminaron Integrated Engineering, Johore Bahru, Malaysia, pp.388-397, 1994.

[2] Data given by Prof. Vu Thanh Ca, Saitama University, JAPAN, 1998.[3] Short-Term Flood Control Planning in the Mekong Delta, Ministry of Agri-

culture and Rural Development, Sub-Institute for Water Resources Planningand Management, Ho Chi Minh, June 1997.

[4] Report on Indicative Basin Plan, A Proposal Framework for the Develop-ment of Water and Related Resources of the Lower Mekong Basin, Com-mittee for the Coordination of Investigations of the Lower Mekong Basin,E/CN.11/WRD/MKG/L.340, Annex V-3, 1970.


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