Using salt intrusion measurements to determine the freshwater discharge distribution over the branches of a multi-channel estuary: The Mekong Delta case

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Estuarine, Coastal and Shelf Science 77 (2008) 433e445www.elsevier.com/locate/ecss

Using salt intrusion measurements to determine the freshwaterdischarge distribution over the branches of a multi-channel estuary:

The Mekong Delta case

Anh Duc Nguyen a,b,*, Hubert H.G. Savenije a,b, Duc Nghia Pham c, Duc Thang Tang c

a Department of Management and Institutions, UNESCO-IHE Institute for Water Education, 7 Westvest, PO Box 3015, 2601 DA Delft, The Netherlandsb Department of Water Management, Faculty of Civil Engineering and Applied Geosciences, Delft University of Technology,

Stevinweg 1, PO Box 5048, 2600 GA Delft, The Netherlandsc Southern Institute for Water Resources Research, 2A Nguyen Bieu Street, District 5, Ho Chi Minh City, Vietnam

Received 22 May 2007; accepted 5 October 2007

Available online 30 October 2007

Abstract

The fresh water discharge is an important parameter for modelling salt intrusion in an estuary. In alluvial converging estuaries during periodsof low flow, when salinity is highest, the river discharge is generally small compared to the tidal flow. This makes the determination of the freshwater discharge a challenging task. Even if discharge observations are available during a full tidal cycle, the fresh water discharge is seldommuch larger than the measurement error in the tidal discharge. Observations further upstream, outside the tidal region, do not always reflectthe actual flow in the saline area due to withdrawals or additional drainage. Discharge computation is even more difficult in a complex systemsuch as the Mekong Delta, which is a multi-channel estuary consisting of many branches, over which the freshwater discharge distributioncannot be measured directly. This paper presents a new approach to determine the freshwater discharge distribution over the branches of theMekong Delta by means of an analytical salt intrusion model, based on measurements made during the dry season of 2005 and 2006. It appearsthat the analytical model agrees well with observations and with a hydraulic model. This paper demonstrates that with relatively simple andappropriate salinity measurements and making use of the analytical salt intrusion model, it is possible to obtain an accurate discharge distributionover the branches of a complex estuary system. This makes the analytical model a powerful tool to analyze the water resources in tidal regions.� 2007 Elsevier Ltd. All rights reserved.

Keywords: salt intrusion; Mekong Delta; estuaries; discharge distribution

1. Introduction

The river discharge, together with relevant parametersdefining estuary shape and tidal forcing, is the key parameterdetermining salt intrusion in alluvial estuaries. This was dem-onstrated in a large number of estuaries by Savenije (1986,1989, 1993b, 2005, 2006) and Nguyen and Savenije (2006),by the use of an analytical model. The model depends ontwo major drivers, the tidal variation at the estuary mouthand the fresh water discharge entering the saline area.

* Corresponding author.

E-mail address: [email protected] (A.D. Nguyen).

0272-7714/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ecss.2007.10.010

The determination of the fresh water discharge in estuariesis complicated, as it requires detailed measurements duringa full tidal cycle. Moreover, in the dry season when the salt in-trusion matters most, the magnitude of the fresh discharge issmall compared to the tidal flow (often within the measure-ment error of the tidal flow). It is even more difficult to deter-mine the discharge in a complex system such as the MekongDelta, which consists of eight branches over which the freshwater discharge is distributed (see Fig. 1).

The Mekong river delta has been subject to a number ofstudies including: Wolanski et al. (1996, 1998), Nguyen et al.(2000), Wolanski and Nguyen (2005), Le (2006), Le et al.(2007). These publications focus on the sediment dynamics

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Tran De branch

Cung Hau branch Co Chien branch

Ham Luong branch Ba Lai branch

Dai branch

Mekong river Bassac river

Tieu branch

Chau Doc

Tan Chau

South China Sea

Gulf of Thailand

Vam Nao river

Long Xuyen

Cao Lanh

My Thuan

My Tho

Tra Vinh Can Tho

Soc Trang

Ca Mau

Dinh An branch

Fig. 1. The Mekong Delta.

434 A.D. Nguyen et al. / Estuarine, Coastal and Shelf Science 77 (2008) 433e445

of the delta (Wolanski et al., 1996, 1998), and the flow andtransport regime during the flood season (Nguyen et al.,2000; Le et al., 2007). In the past, several hydraulic modelshave been developed over time to simulate the hydrodynamicregime of the Mekong river system. Although these modelswere not developed for the purpose of determining the dis-charge distribution over the branches of the Mekong Delta,they can indeed provide this information. However, it appearsthat the results from these models do not always agree dueto the different topographical dataset (due to the changes inthe Mekong over years) and different modelling objectives(Le, 2006).

Nguyen and Savenije (2006) developed a predictive ana-lytical model for salt intrusion in the Mekong Delta in Viet-nam, which can be used to predict the salinity distribution inthe Mekong branches if topography, tide and river dischargeare known. The reverse also applies: if the salinity distribu-tion in the Mekong is known, we can estimate the riverdischarge.

This paper presents a new approach to determine thedischarge distribution over the branches of the Mekong bymeans of the salt intrusion model developed by Nguyenand Savenije (2006), based on dry season data of 2005 and2006. These results will be compared with the results ob-tained by a hydraulic model, both for accuracy andefficiency.

2. The Mekong Delta, Vietnam

2.1. The Mekong Delta’s estuary system

The Mekong river when it enters Vietnam splits into twobranches, the Bassac (known as the Hau river in Vietnam)and the Mekong (known as the Tien river in Vietnam). Thesetwo branches form the Mekong Delta. The Hau river is themost southern branch of the Mekong. When the Hau ap-proaches the sea, it splits into two sub-branches: Tran De andDinh An. The Tien river is the northern branch of the Mekongriver system, which separates into two sub-branches at MyThuan: Co Chien and My Tho. At a distance of 30 km fromthe South China Sea, the Co Chien river again splits into twosmaller branches, Co Chien and Cung Hau. In the downstreampart, the My Tho river separates into four branches: Tieu, Dai,Ba Lai and Ham Luong (see Fig. 1).

As a typical delta, the Mekong Delta is affected by bothriver floods and tides. Tides in the South China Sea havea mixed diurnal and semi-diurnal character. The amplitudecan be up to 3 m. There are generally two troughs and twopeaks during a day, but their relative height varies over a fort-night. When the first trough decreases from day to day, theother trough increases, and vice versa.

In the dry season, there are two main sources for the freshwater: (1) from the main Mekong river; and (2) from the Great

435A.D. Nguyen et al. / Estuarine, Coastal and Shelf Science 77 (2008) 433e445

Lake (TonleSap) in Cambodia via the Bassac river. The totalfresh discharge in the dry season is in the order of 2000 m3/s,which distributes unequally over the eight branches. Observa-tions further upstream, outside the tidal region, are available.There are several discharge measurement stations located inthe main Mekong river (e.g. Kratie and Kompong Cham,about 330 km from the Dai mouth), the Bassac river (e.g.Bassac Chaktomouk, 240 km from the Dinh An mouth) andin several tributaries (e.g. Prek Kdam in the Tonle Sap riveror Vam Nao in the Vam Nao river). Inside the tidal regionin Vietnam, there are four discharge stations: Tan Chau andMy Thuan in the Tien (Upper) river, which are located200 km and 95 km from the Dai mouth, respectively; andChau Doc and Can Tho, which are located 190 km and80 km from the Dinh An mouth, respectively (see Fig. 1).However, the distribution of the discharge over the branchesdownstream of the river system depends on a complex inter-action of topography, tide, network layout (hydraulic struc-tures, canals, etc.) and additional withdrawals or drainage.Therefore it is difficult to obtain a reasonable estimate ofthe discharge distribution over the branches of the system.There are two discharge stations located in the tidal region(i.e. My Thuan and Can Tho on the Tien and Hau mainbranches). However, based on observations from these twostations, it is not possible to obtain a reliable estimate of thedistribution of the freshwater discharge. The reason is thatthe fresh water discharge, which is in the order of 1000 m3/s,is probably smaller than the measurement error in the tidaldischarge, which is in the order of 12,000 m3/s. It would becostly to carry out detailed measurements during a full tidalcycle in the downstream end of the Mekong’s eight branchesand we would face a similar problem related to the measure-ment error.

During our measurements by the moving boat in April 2005and June 2006, we measured the vertical salinity distributionat several points in the Dinh An, Tran De, Co Chien andCung Hau branches. It appeared that these branches werepartially-mixed to well-mixed estuaries according to the clas-sification of Dyer (1997).

2.2. Shape of the Mekong Delta branches

The estuary branches Dinh An and Tran De, Co Chien andCung Hau have the characteristics of paired estuary branches(Nguyen and Savenije, 2006). The Tieu and Dai may also beconsidered as paired, although we should realize that thelength of the Tieu branch is slightly larger than that of theDai (34.5 km vs. 32.5 km). The Ham Luong branch is a singlebranch estuary. The Ba Lai branch, which is closed by a tidalbarrier at its mouth, is not taken into account in this paperbecause it is relatively small and it no longer is a naturalbranch.

The estuarine characteristics of the Tran De-Dinh An, theCo ChieneCung Hau, the My Tho (combination of the Tieuand Dai) and the Ham Luong branches correspond very wellwith exponential functions that follow the concept of idealestuaries:

A¼ A0exp�� x

a

�ð1Þ

B¼ B0exp�� x

b

�ð2Þ

and

h¼ h0exp�x

d

�ð3Þ

where A (L2), B (L) and h (L) are the cross-sectional area,width and depth at location x (km) from the mouth, respec-tively. A0 (L2), B0 (L) and h0 (L) are the area, width and depthat the mouth. Finally, a (L), b (L) and d (L) are the area, widthand depth convergence length, respectively. It follows thatd ¼ ab/(a � b). The cross-sectional area and width are ob-tained from observations, defined at the tidal averaged waterlevel (this level is close to mean sea level). The convergencelength, which is the length scale of the exponential function,is obtained by calibration of Eqs. (1), (2) and (3) againstmeasured data. It can be seen very clearly in Fig. 2 and inTable 1 that the combined estuary branches indeed behaveas a single estuaries with a regular topography according toEqs. (1)e(3).

The combined My Tho and the combined Hau estuary havean inflection point located 45 km from the Dai mouth and57 km from the Dinh An mouth, respectively. Upstreamfrom the inflection point, the shape of the estuaries also corre-sponds with exponential functions, and the depth is constant:

A1 ¼ A00exp

�� x

a1

�ð4Þ

B1 ¼ B00exp

�� x

b1

�ð5Þ

where A1 (L2) and B1 (L) are the area and width of the up-stream reach at location x (km) from the mouth, respectively.A00 (L2) and B00 (L) are the area and width at the mouth for theupstream reach if extended to the mouth. Finally, a1 (L) and b1

(L) are the convergence lengths of the upstream reach.

2.3. Description of the Mekong Delta’s data set

In the Tien river, there are two discharge stations locatedat Tan Chau and My Thuan. In the Hau river, there arealso two discharge stations located at Chau Doc and CanTho (see Fig. 1). Normally, the discharge at Tan Chau is3e5 times larger than the discharge at Chau Doc (Le,2006). One special thing is that just 30 km downstream ofTan Chau and Chau Doc, there is a connecting river calledVam Nao, which conveys water from the Tien to the Hauriver. As a result, the discharge ratio between the Hau andthe Tien rivers after the Vam Nao changes substantially.Downstream from My Thuan and Can Tho, there are nomore discharge stations.

The river discharge and tidal data during the 2005 and 2006field measurement periods were provided by the Vietnamese

1

10

100

1,000

10,000

100,000

0 20 40 60 80 100 120

0 20 40 60 80 100 120

Distance from the mouth (km)

0 10 20 30 40 50 60 70 80 90Distance from the mouth (km)

1

10

100

1000

10,000

100,000

0 10 20 30 40 50 60 70 80Distance from the mouth (km)

Area (m2) Width (m) Depth (m)


ba

dc

1

10

100

1,000

10,000

100,000

1

10

100

1,000

10,000

100,000

Area (m2) Width (m) Depth (m) Area (m2) Width (m) Depth (m)

Area (m2) Width (m) Depth (m)

Fig. 2. Shape of the combined branches in the Mekong: (a) Hau (combination of Dinh An and Tran De); (b) Co ChieneCung Hau (combination of Co Chien and

Cung Hau); (c) Ham Luong; and (d) My Tho (combination of Tieu and Dai) estuary, showing A (triangles), B (squares) and h (circles).


National Hydrometeorology Services (VNHS). Salinity data ofthe Mekong Delta used in this paper consist of three sets: (1)the first set is from field measurements carried out by the au-thors during the dry season of 2005 (Nguyen and Savenije,2006); (2) the second data set is from field measurements car-ried out by the authors during the end of the dry season of2006; and (3) the third data set is obtained from the networkof fixed stations near intakes and quays, which measure salin-ity values during the dry season at hourly intervals. The firstset has been presented in Nguyen and Savenije (2006). Theother data sets are presented here.

Table 1

Estuarine characteristics of seven branches in the Mekong Delta

River Estuary A0

(m2)

B0

(m)

Hau river Dinh An branch 18,400 3400

Tran De branch 8200 1500

Combined estuary 26,600 4900

Co Chien river Co Chien branch 11,100 1600

Cung Hau branch 13,200 2500

Combined estuary 24,300 4100

My Tho river Tieu branch 7100 1100

Dai branch 14,500 2,300

Combined estuary 21,600 3,400

Ham Luong river Ham Luong branch 17,000 2,800

The values for the width, depth and cross-sectional area were measured at mean s

3. Estimation of the discharge distribution over theMekong branches

3.1. Previous studies determining the dischargedistribution over the Mekong branches

The recent book of Le (2006) on the salinity intrusion ofthe Mekong Delta provides an overview of the discharge dis-tribution over the river system. Because it is difficult to obtaina reasonable estimate of the discharge distribution, Le (2006)discussed several hydraulic models of the Mekong Delta,

h(m)

a(km)

b(km)

d(km)

a1

(km)

b1

(km)

7.6 100 47 89 e e

5.5 800 800 N e e

7.5 105 51 99 140 140

7.6 93 71 300 e e

5.7 45 40 360 e e

6.6 69 54 250 e e

6.5 180 180 N e e

9.3 70 38 84 e e

7.7 71 50 170 420 420

6.1 55 55 N e e

ea level (MSL).


which were developed over the last four decades. Although,they were not developed for the purpose of determining thedischarge distribution over the branches of the Mekong Delta,they can be used to assess the discharge distribution over theriver system. These models include:

(1) The NEDECO model, developed in 1974;(2) The Vietnamese National Hydrometeorology Services

(VNHS) model, developed in 1984;(3) The SALO89 model, used by NEDECO in 1991;(4) The model developed by Nguyen Van So in the combination

with the observed data in 1992;(5) The VRSAP model, developed in 1993.

Estimates of the discharge distribution over the branches ofthe Mekong Delta, based on the data of these five models, arepresented in Table 2. One can see that the discharge distribu-tion ratio over the branches of the Mekong is not the same forthe different models. The main reason is that these modelswere developed at different times, therefore the topographicaldata are different due to the changes that have taken place overyears. Moreover, these models were developed to satisfy dif-ferent purposes (i.e. water balance, the first and second model;irrigation, the fourth model; and salinity intrusion, the thirdand fifth model), therefore the choices of boundary conditionsand hydraulic parameters were not the same.

Note that the results from the first two models (i.e. NE-DECO 1974 and VNHS 1984) are almost identical. The firsttwo models are relatively simple models and they did not suf-ficiently take into account the flows through the inland channelsystem. The results of the next three models show more or lessthe same pattern. Note that in the SALO89 and VRSAPmodel, the total discharge ratio of the Tien and Hau riverbelow the Vam Nao connection is not 100%. This can beexplained by the fact that before approaching the Vam Nao,a certain amount of water flows into the inland channelsystem.

As we know, the Mekong Delta is morphologically activeand the topography is continuously changing due to the highsediment transport capacity of the river. It is expected thatthere have been some changes over the branches of theMekong for the last four decades and they may have led tothe adjustment of the discharge distribution over the branches.Unfortunately, we do not have enough data to further analyse

Table 2

Discharge distribution in the Mekong river system (after Le, 2006, p. 43)

Model name Discharge

Computed

(m3/s)a

Tien river

below Vam

Nao (%)

Hau river

below Vam

Nao (%)

Co

Chien

(%)

Cung

Hau (%

NEDECO 1974 2385 51.0 49.0 13.0 15.0

VNHS 1984 1926 55.0 45.0 13.0 18.0

SALO89 1991 2274 43.6 54.4 11.8 7.8

Nguyen Van So

1992

e e e 11.0 12.0

VRSAP 1993 2280 49.7 44.3 10.9 4.5

a Total discharge of both the Tien and the Hau rivers, upstream of the Vam Naob Internal (inland) canal system.

this issue, but we expect that the main reason for the changingflow regime in the Mekong delta. Some changes in the waterdischarge distribution may also have occurred due to the de-velopment of the inland channel system. Considering thequick development of the inland channel system for irrigationand navigation, especially during the period from 1990 to2000, it is expected that a substantial amount of water flowsin and out of the main branches, which may be conveyedfrom one branch to another. The fourth and the fifth modelsshow an increasing trend. Since 1990, a large number of intakestructures and sluice gates have been constructed to control theflow of the inland channel system, especially in the down-stream part of the branches in order to prevent salt-waterintrusion.

3.2. The analytical salt intrusion model

Savenije (1989, 2005) demonstrated that the steady statesalt balance equations for high water slack (HWS), low waterslack (LWS) and tidal average (TA) can be written as:

Si� Sf ¼ ci

vSi

vxð6Þ

where i ¼ 1,2,3 indicating the three different states, HWS, LWSand TA, respectively. Si (e) is the steady state salinity and Sf (e)is the fresh water salinity. The coefficient ci is an x-dependentcoefficient defined by:

ci ¼A

Qf

Di ð7Þ

where Di (L2 T�1) is the dispersion coefficient for each state i,Qf (L3 T�1) is the river discharge, which is negative since thepositive x-axis points upstream, and A (L2) is the tidal aver-aged cross-sectional area (see Eq. (1)).

The relationship between the salinity and the dispersioncoefficient, developed by Van der Burgh (1972) is defined by:

dDi

dx¼ K

Qf

Að8Þ

where K(e) is the Van der Burgh’s coefficient, which has a valuebetween 0 and 1. This equation can be integrated for an estuary

)

Dinh

An (%)

Tran

De (%)

Ba Lai

(%)

Ham

Luong (%)

Tieu

(%)

Dai

(%)

Others

(%)b

28.0 21.0 0.0 15.0 2.0 6.0 0.0

27.0 18.0 0.0 17.0 1.0 6.0 0.0

25.6 24.3 1.6 13.6 5.2 2.0 8.1

19.0 16.0 1.0 14.0 1.5 6.0 19.5

18.2 18.0 0.1 8.7 2.3 8.4 28.9

connection.


with an exponentially varying cross-section (see Eq. (1)) toyield the expression for the dispersion along the estuary:

Di

Di0

¼ 1� bi

�exp�x

a

�� 1�

ð9Þ

with

bi ¼�KaQf

Di0A0

¼ Ka

ai0A0

and ai0 ¼�Di0

Qf

ð10Þ

where Di0 (L2 T�1) is the boundary condition at the rivermouth (x ¼ 0) for HWS, LWS or TA conditions, A0 (L2) isthe tidal average cross-sectional area at the estuary mouthand a (L) is the convergence length of the cross-sectionalarea. The values of K and ai0 can be obtained throughcalibration.

The longitudinal variation of the salinity can be computedthrough combination of Eqs. (6), (7), (8), (9) and (10):

Si� Sf

Si0� Sf

¼�

Di

Di0

�1=K

ð11Þ

where Si0 (e) is the boundary salinity at the estuary mouth (forHWS, LWS and TA conditions). The salt intrusion curve de-rived for the TA situation, which represents the TA longitudi-nal variation of the salinity, can be used for LWS and HWS aswell, by shifting the curve upstream or downstream over halfthe tidal excursion E.

The salt intrusion length Li can be obtained at the point thatSi ¼ Sf, then according to Eq. (11), Di equals zero. WithDi ¼ 0, Eq. (9) can be elaborated to yield an expression forthe intrusion length:

Li ¼ a ln

�1

bi

þ 1

�ð12Þ

where Li (L) is the salt intrusion length at HWS, LWS or TA.Because the method has been applied in 17 different estu-

aries all over the world, particularly for the HWS situations,it was possible to derive two predictive equations for K andDHWS

0 (Savenije, 1993b). These relations were generalisedand improved by Savenije (2005) and Nguyen and Savenije(2006) into:

DHWS0 ¼ 1400

h

b

ffiffiffiffiffiffiNR

pðyEÞ ð13Þ

and

K ¼ 0:2� 10�3

�E

H

�0:65�E

C2

�0:39

ð1� dbÞ�2:0

�b

a

�0:58�Ea

A0

�0:14

ð14Þ

where A0 (L2) is the cross-sectional area at the estuary mouth,b (L) is the width convergence length of Eq. (2); E (L) is thetidal excursion. H (L) is the tidal range, h (L) is the tidalaverage depth along the saline part of the estuary, NR(e) isthe Estuarine Richardson number given by:

NR ¼�Dr

r

ghQfT

A0E0y20

ð15Þ

where T (T) is the tidal period, y (LT�1) is the tidal velocityamplitude and E0 (L) is the tidal excursion at the mouth. Inideal estuaries, the tidal range, the tidal velocity amplitude,the tidal excursion and the depth are constant along the estu-ary, while the convergent lengths of the width and the cross-sectional area are equal: b ¼ a. In estuaries where there isa certain degree of damping or amplification, the ratio ofH/E is still constant, but values of E and y can vary alongthe estuary. Finally if a s b there is a bottom slope and thedepth is not constant. In the Mekong estuary branches thesesituations apply, and subsequently procedures had to be deve-loped to deal with this situation.

In the reverse mode, using the same model, if the salinitydistribution is known, we can use the model to predict the riverdischarge.

From Eq. (10), we have:

Qf ¼�DHWS

0

aHWS0

ð16Þ

Substitution Eqs. (13) and (15) into Eq. (16), we obtain:

Qf ¼�DHWS

0

aHWS0

¼�1400

h

b

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�Dr

r

ghQfT

A0E0y20

sðy0E0Þ

aHWS0

¼�1400

h

b

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�Dr

rgT

h

A0

E0Qf

s

aHWS0

or

Qf ¼�0@1400

h3=2

b

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDr

rgT

E0

A0

raHWS

0

1A

2

ð17Þ

4. Using the analytical salt intrusion model to compute thedischarge distribution

4.1. Salinity distribution in the Mekong branches in thedry season of 2005

There are two important parameters that have to be known inorder to determine Qf with Eq. (17): (1) aHWS

0 and (2) E0. Thelongitudinal salinity curves, calibrated against measurementsduring HWS and LWS, provide us with accurate estimates ofboth parameters. aHWS

0 can be obtained through calibration,and E0 is the distance between the HWS and LWS curves.

In order to obtain the theoretical longitudinal salinitycurves, we have to calibrate the salt intrusion model against ob-servations. There are two calibration parameters, i.e. K andaHWS

0 . A first estimate of K can be obtained by the predictiveequation (i.e. Eq. (14)). However, due to the large uncertainty


of this predictive equation, the K estimate should be refined onthe basis of salinity measurements. K, the Van der Burgh’s co-efficient, is a ‘shape factor’ influencing the shape of the salt in-trusion curve (Savenije, 1993a). K particularly determines theshape of the toe of the salt intrusion curve. Most importantly,K is not dependent on time but purely dependent on topographyand tidal characteristics. aHWS

0 plays a small role in the shape ofthe salt intrusion curve but the main role in the intrusion length.The calibration process has been carried out on the basis ofa quantitative procedure employing a weighted chi-squaremethod with special weight to the toe of the salinity intrusioncurves. It is particularly important to give emphasis to the toeof the intrusion curve because it incorporates all errors incurredin the integration of the differential equation (i.e. Eq. (12)),which uses the downstream boundary salinity (i.e. at themouth) as the input. The toe represents the total intrusionlength, which is the key outcome of the salt intrusion model.The weighted chi-square method reads:

c2W ¼

Xn

i¼1

"½ðxi� yiÞ�2

yi

� jy0� yi

y0

j#

ð18Þ

where xi and yi are the observed and simulated value (spaceseries), y0 is the simulated value at the mouth of the estuary(boundary condition), n is the sample size, and c2

T is minimized.The quantitative procedure for salt intrusion model calibra-

tion can be expressed as the two following steps:

(1) Basing on the observed salinity curves and applyinga quantitative analysis of the chi-square statistical method,as well as a weighted chi-square method with specialattentions on the toe of the curves, we established a fixedvalue of K for each estuary branch.

(2) Using the chi-square method and the weighted chi-squaremethod, we quantitatively determined the alpha values.

The calibrated results on 8 and 9 April 2005 for the Haubranch and on 21 and 22 April 2005 for the Co ChieneCung Hau branch were presented in Nguyen and Savenije(2006), therefore we do not repeat them here. However, withsome small changes in the topographical data, we obtainedsome minor changes of aHWS

0 and E0. The salt intrusion lengthin the Hau estuary during the dry season of 2005 was in theorder of 50 km. This agrees with the value observed by Wolan-ski et al. (1998) during the dry season of 1996.

On the same dates, we used routine measurements to obtaina full set of salinity distribution in the different branches of thedelta (see Fig. 3). These measurements are part of standardmeasurements taken at fixed locations along the estuary, oftenat intakes and well beside the main current. As a result, theseobservations sometimes underestimate the HWS salinity, orthey are affected by land drainage. This is clearly visible inthe Hau, at 4 km from the mouth, where the gauge is locatedin an inlet. This makes the calibration results less reliable,but we feel that they are still useful for our purpose.

4.2. The freshwater discharge distribution in the MekongDelta during the dry season of 2005

On the basis of the observed salinity distribution in theMekong Delta branches, the freshwater discharge distributionhas been calculated using Eq. (17). There are two approachesto determine the discharge distribution over the estuarybranches:

Approach 1. Using the parameters obtained with the salin-ity distribution in individual branches, combined with theestuary shape of each individual branch, we are able tocompute the discharge in each individual branch. This ap-proach is only applicable for the Dinh An, Tran De, CungHau and Co Chien branch, where we have sufficient salinitymeasurements.Approach 2. Using the estuary shape of the combined estu-ary branches, together with the parameters from the salinitydistribution, we can compute the fresh water discharge ofthe combined branches (i.e. Hau, Co ChieneCung Hauand My Tho).

Table 3 presents the computation of the fresh water dis-charge over the Mekong branches, using both approaches. Forreasons of simplicity, here and in the following, we use the ab-solute value of the river discharge, which has a negative valuesince the positive x-axis points upstream. One can see that inthe case of the Tran De branch, of which the downstream shapeis almost constant (i.e. very large convergence length), we arenot able to use Eq. (17) to compute the discharge value. Thisis a disadvantage of the first approach when applied to brancheswith near constant cross-sections. Note that in Table 3, the dis-charges of the Hau, Co ChieneCung Hau and My Tho (i.e.three combined branches) are computed by the second ap-proach, while the discharges of the Co Chien, Cung Hau andDinh An branch are computed by the first approach. One cansee that the values computed by the second approach and thefirst approach for the Co ChieneCung Hau are identical.This, once again, implies that the paired estuaries function asan entity.

The value of the Tran De branch has been obtained by sub-tracting the values of the combined Hau estuary and the DinhAn branch. On 8 and 9 April 2005 the salinity data were notsufficient in the Cung Hau, Co Chien, Dai and Tieu branchin order to get accurate parameters for the discharge computa-tion in each individual branch. Similarly, on 21 and 22 April2005, data were not sufficient to obtain the right parametersfor the Dinh An, Dai and Tieu branch.

Table 3 shows the discharge distribution over the systemand Fig. 4 presents an overview of the discharge distributionover the estuary branches on 8 and 9 April 2005. The follow-ing conclusions can be drawn:

(1) The discharge ratio between the Dinh An and the Tran Deis in the order of 70%/30%.

(2) The discharge ratio between the Co Chien and the CungHau is in the order of 50%/50%.

My Tho estuary

α = 2.40, K = 0.50

0

5

10

15

20

25

30


Salin

ity

CoChien - Cung Hau estuary

α = 1.79, K = 0.50

0

5

10

15

20

25

30

0 10 20 30 40 50 60 70 80

0 10 20 30 40 50 60 70 80

0 10 20 30 40 50 60 70 80


Salin

ity

Hau estuary

α = 1.53, K = 0.50

0

5

10

15

20

25

30


Salin

ity

My Tho estuary

α = 2.29, K = 0.50

0

5

10

15

20

25

30


Salin

ity

Ham Luong estuary Ham Luong estuary

α = 2.79, K = 0.50

0

5

10

15

20

25

30


Salin

ity

α = 2.82, K = 0.50

0

5

10

15

20

25

30


Salin

ity

a

b

c

d

e

f

0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80

0 10 20 30 40 50 60 70 80

Fig. 3. Salinity distribution of individual branches and combined branches of the Mekong on 8 and 9 April 2005: (a) Co ChieneCung Hau; (b) My Tho; (c) Ham

Luong. On 21 and 22 April 2005: (d) Hau; (e) My Tho; (f) Ham Luong, showing values of measured salinity at HWS (diamonds), and LWS (triangles), and

calibrated salinity curves at HWS (red curve) and LWS (blue curve).


(3) The discharge ratio between the combined Hau and thecombined Co ChieneCung Hau is in the order of 70%/30%.

(4) If we assume that the value of the ‘‘others’’ component,that is, the amount of river flow that feeds the inland canalnetwork (see Fig. 4), can be split equally between the Hauand the Tien river, then we see that the discharge ratiobetween the Hau and the Tien river after the Vam Nao con-nection is in the order of 42%/58%.

4.3. The freshwater discharge distribution in the MekongDelta at the end of the dry season of 2006

On 10 and 11 June 2006, field measurements were carriedout, using the moving boat method described by Nguyen andSavenije (2006). The advantage of this measurement approachis that observations can be carried out on the same day in thepaired estuary branches (i.e. Dinh An and Tran De, Co Chien

and Cung Hau). Unfortunately, due to a limited number ofmeasurement devices and boats, we could not manage to domeasurements in the Tieu, Dai and Ham Luong branches aswell. Therefore, routine measurements at fixed locationshave been used to obtain the salinity profile of the combinedMy Tho and Ham Luong branch.

We measured the vertical salinity distribution at severalpoints in the Dinh An, Tran De, Co Chien and Cung Haubranches. It appeared that these branches were partially mixed.This is understandable since the discharge is relatively largecompared to the dry period. The total discharge of the Tienand Hau river on 10 and 11 June was in the order of6000 m3/s compared to a discharge of 2000 m3/s in the dryseason of 2005. The actual total discharge of the Tien andHau river on 10 and 11 June 2006 provided by the VietnameseNational Hydrometeorology Services was 6276 m3/s.

The calibrated results, based on measurement data of 10and 11 June 2006, are presented in Fig. 5. Table 3 shows the

Table 3

Discharge values in the Mekong branches computed by means of the salt intrusion model

Date River Estuary aHWS0

(m�1)

E0

(km)

Qf

(m3/s)

Percentage of

observations (%)a

8 and 9 April 2005 Hau Dinh An branch 2.39 16 649 27.4

Tran De branch 4.48 16.5 273 11.5

Combined Hau estuary 1.53 16.5 922 38.9

Co Chien Combined estuary 1.79 16 435 18.3

My Tho Combined My Tho estuary 2.29 19 657 27.7

Ham Luong Ham Luong branch 2.79 18 219 9.2

21 and 22 April 2005 Hau Combined Hau estuary 1.53 16 894 42.1

Co Chien Co Chien branch 3.83 16.5 189 8.9

Cung Hau branch 4.12 16.5 183 8.6

Combined estuary 1.91 16.5 394 17.5

My Tho Combined My Tho estuary 2.40 18 567 26.7

Ham Luong Ham Luong branch 2.82 17.5 208 9.8

10 and 11 June 2006 Hau Dinh An branch 1.46 10.5 2,283 36.4

Tran De branch 2.73 11.0 840 13.4

Combined Hau estuary 0.96 11.0 3123 49.8

Co Chien Co Chien branch 2.96 11.0 423 6.7

Cung Hau branch 2.99 11.0 463 7.4

Combined estuary 1.45 11.0 911 14.5

My Tho Combined My Tho estuary 1.37 14.0 1353 21.6

Ham Luong Ham Luong branch 1.68 13.5 453 7.2

a Observations: total discharge of both the Tien (Tan Chau station) and the Hau river (Chau Doc station), about 30 km upstream of the Vam Nao connection.


computation of the fresh water discharge over the Mekongbranches on 10 and 11 June 2006.

From the computed results on 8e9 April 2005 and 10e11June 2006 in the Hau river, and 21e22 April 2005 and 10e11June 2006 in the Tien river, one can conclude that the dis-charge values computed by the two approaches (i.e. the singlebranch and the combined branch approach) agree fairly wellfor the computed days. This implies that the paired estuariesfunction as an entity.

One can see in Table 3 that: (1) the discharge ratio betweenDinh An and Tran De is 73%/27%; (2) the discharge ratio bet-ween Co Chien and Cung Hau is 48%/52%. This agrees wellwith what we have seen in Section 4.2. However, we can alsosee that the discharge ratio between the Hau and Co ChieneCung Hau is 78%/22% and the discharge ratio between theHau and Tien river is 53%/47%. Apparently the discharge ratioin the Hau is larger at the start of the wet season. This may also bebecause of errors in the salinity measurements, which werecarried out under difficult (rainy and windy) weather conditions.

Hence, we can conclude that the salinity intrusion regimeand the discharge distribution pattern in the Mekong duringcan be well described by the analytical salt intrusion approachover a wide range of river discharge.

5. Using a hydraulic model to compute the dischargedistribution

5.1. Schematization

The new approach to use the salinity measurements to esti-mate the discharge distribution is tested against the results of

a hydraulic model that uses the observed upstream dischargeas upstream input and the observed tidal variation at the down-stream boundary. For this purpose, we have used the MIKE11model. For detailed information on the MIKE11 package,readers are referred to: http://www.dhigroup.com/Software/WaterResources/MIKE11.aspx.

The data for the schematization of the hydraulic model, in-cluding topographical and infrastructure data, have been ob-tained from the 1998 and 2000 version of the Mekong riversystem schematization developed by the Mekong River Com-mission in the ISIS software. Some parts of the estuarine to-pography of the Dinh An, Tran De, Cung Hau, Co Chien,Dai and Tieu branches have been obtained from the data ofthe Southern Institute for Water Resources Planning of Viet-nam. The model has been calibrated based on data of thedry seasons of 2000 and 2005.

5.2. Freshwater discharge distribution

Based on the model results, we are able to derive the freshwater discharges in the branches of the Mekong Delta. Thecomputed results are presented in Table 4, also as a percentageof the observed upstream river discharge. Fig. 4 also showsthese results compared to the discharge distribution computedwith the salt intrusion model.

Note that the sum of the discharge values of all branches is notnecessary equal to the total discharge. This is understandablesince a certain amount of water can enter or leave the inlandchannel system and a certain amount of water can go into theBa Lai branch.

http://www.dhigroup.com/Software/WaterResources/MIKE11.aspx

http://www.dhigroup.com/Software/WaterResources/MIKE11.aspx

2015 m3/s

(85.0 %)

Tien river

355 m3/s

(15.0 %)

Hau river

Vam Nao river

69 m3/s

(2.9 %)

Others

46 m3/s

(1.9 %)

69 m3/s

(2.9 %)

Others

46 m3/s

(1.9 %)

Observations

1380 m3/s

(58.2 %)

Tien river

1312 m3/s

(55.5 %)

991 m3/s

(41.8 %)

Hau river

966 m3/s

(40.8 %)

657 m3/s

(27.7 %)

My Tho

745 m3/s

(31.5 %)

435 m3/s

(18.3 %)

Co Chien

326 m3/s

(13.8 %)

219 m3/s

(9.2 %)

Ham Luong

241 m3/s

(10.2 %)

273 m3/s

(11.5 %)

Tran De

316 m3/s

(13.3 %)

649 m3/s

(27.4 %)

Dinh An

650 m3/s

(27.5 %)

Co Chien

247 m3/s

(10.5 %)

Cung Hau

79 m3/s

(3.3 %)

Tieu

252 m3/s

(10.7 %)

Dai

493 m3/s

(20.8 %)

991 m3/s

(41.8 %)

Hau river

966 m3/s

(40.8 %)

Branch's name

Salinity model

Hydraulic model

Legends

Fig. 4. Discharge distribution over the branches of the Mekong Delta computed on the basis of the salinity observations carried out on 8 and 9 April 2005.


6. Discussion

6.1. Comparison between the salt intrusion and thehydraulic model

Fig. 6 compares the discharge distribution obtained by thesalt intrusion model and the hydraulic model for the twodifferent survey dates (see also Tables 3 and 4). It appearsthat: (1) the results of the two models agree reasonablywell, especially in the determination of the discharge of thepaired branches; (2) the discharge ratio between the Tienand Hau river after the Vam Nao connection is in the orderof 58%/42%; and (3) there are no substantial changes inthe discharge distribution over the branches between 8e9April and 21e22 April 2005, although some differencesoccur in the Ham Luong, My Tho and the inland canalsystem.

The good agreement between the hydraulic model and theanalytical model confirms the validity of the new approachfor determining the discharge distribution of the Mekong. Inaddition, the joint consideration of the two models reducesthe uncertainty of the predictions. The comparison with thehydraulic model is no proof of the correctness of the newmethod, but it certainly is a strong indication of the applicabil-ity of the analytical model.

The application of MIKE11 is in fact a solution methodfor the 1-D mass and momentum balance equation. Theflow distribution determined by MIKE11 depends on theboundary conditions and the topography. These have beentaken from the official database of the Mekong river commis-sion (project on Water Utilization Programme (WUP)), whichis the most reliable source so far. A 2-D hydraulic modelcould be useful and could possibly provide a better solutionbecause the topography at the separation points would be

Tran De estuary

α(branch) = 2.73;K = 0.55;

0

5

10

15

20

25

0 10 20 30 40 50 60 70 80Distance from the mouth (km)

Salin

ity

Co Chien estuary

α(branch) = 2.96;K = 0.50;

0

5

10

15

20

25


Salin

ity

Dinh An estuary

α(branch) = 1.46;K = 0.55

0

5

10

15

20

25


Salin

ity

Cung Hau estuary

α(branch) = 2.99; K=0.50 ;

0

5

10

15

20

25


Salin

ity

α = 0.96, K= 0.55

0

5

10

15

20

25


Salin

ity

Co Chien - Cung Hau estuaryHau estuary

α = 1.45, K = 0.50

0

5

10

15

20

25


Salin

ity

My Tho estuary

α = 1.45, K = 0.50

0

5

10

15

20

25


Salin

ity

Ham Luong estuary

α = 1.68, K = 0.50

0

5

10

15

20

25


Salin

ity

a d

b e

c f

gh

0 10 20 30 40 50 60 70 80

0 10 20 30 40 50 60 70 80

0 10 20 30 40 50 60 70 80

0 10 20 30 40 50 60 70 80

0 10 20 30 40 50 60 70 80

0 10 20 30 40 50 60 70 80

0 10 20 30 40 50 60 70 80

Fig. 5. Salinity distribution of individual branches and combined branches on 11 and 12 June 2006 in the Mekong: (a) Tran De; (b) Dinh An; (c) Combined Hau

estuary; (d) Co Chien; (e) Cung Hau; (f) combined Co ChieneCung Hau estuary; (g) Ham Luong; and (h) combined My Tho estuary, showing values of measured

salinity at HWS (diamonds), and LWS (triangles), and calibrated salinity curves at HWS (red curve) and LWS (blue curve).


Tab

le4

Dis

char

ged

istr

ibu

tio

nab

ove

and

bel

owth

eV

amN

aori

ver

(com

pu

ted

by

the

hy

dra

uli

cm

odel

)

Dat

eO

bse

rvat

ion

s

(m3/s

(%))

aT

ota

ld

isch

arge

up

stre

amV

N

(m3/s

(%))

a

Tie

nri

ver

up

str.

VN

(m3/s

(%))

Hau

rive

r

up

str.

VN

(m3/s

(%))

Tie

nri

ver

dow

nst

r.V

N

(m3/s

(%))

Hau

rive

r

dow

nst

r.V

N

(m3/s

(%))

Co

Chi

en

bra

nch

(m3/s

(%))

Cu

ng

Hau

bra

nch

(m3/s

(%))

Din

hA

n

bra

nch

(m3/s

(%))

Tra

nD

e

bra

nch

(m3/s

(%))

Tie

u

bra

nch

(m3/s

(%))

Dai

bra

nch

(m3/s

(%))

Ham

Lu

on

g

(m3/s

(%))

To

tal

(m3/s

(%))

8an

d9

Ap

ril

20

05

23

70

(10

0)

21

97

(92

.7)

16

84

(71

.1)

51

3

(21

.6)

12

20

(51

.5)

98

9

(41

.7)

24

7

(10

.4)

79

(3.3

)

65

0

(27

.5)

31

6

(13

.3)

25

2

(10

.6)

49

3

(20

.8)

24

1

(10

.2)

22

77

(96

.2)

21

and

22

Ap

ril

20

05

21

22

(10

0)

21

91

(10

3.3

)

16

82

(79

.3)

50

9

(24

.0)

11

99

(56

.5)

10

12

(47

.7)

21

8

(10

.3)

95

(4.5

)

61

6

(29

.1)

31

8

(15

.0)

21

2

(10

.0)

40

9

(19

.4)

16

6

(7.9

)

20

34

(96

.1)

aO

bse

rvat

ion

s:to

tal

dis

char

ge

of

bo

thth

eT

ien

(Tan

Cha

ust

atio

n)

and

the

Hau

rive

r(C

hau

Do

cst

atio

n),

abo

ut

30

km

up

stre

amo

fth

eV

amN

aoco

nn

ecti

on

.


more realistic. However, considering the data set of the Me-kong Delta, it is not yet possible to develop such a model forthe entire delta.

6.2. Limitation of the salt intrusion model

We have seen that the salt intrusion model performs identi-cally to the hydraulic model, which is a complex model requir-ing a heavy set of data and built on the basis of detailedtopographical information and the latest knowledge aboutthe infrastructure. This implies that a simple model can pro-vide a good insight into a complicated system like the MekongDelta. However, the salt intrusion model, when used to com-pute the discharge distribution, also has its limitations.

First, the predictive discharge values obtained by Eq. (17)are sensitive to errors in aHWS

0 , h and b. aHWS0 is obtained

from the salt intrusion model. Due to K being constant inthe model, only aHWS

0 is sensitive to the prediction of the freshwater discharge. We can see from Eq. (17) that a relative errorof 5% in aHWS

0 results in a 10% error in the discharge predic-tion. This may seem a large error, but a direct observation ofthe freshwater discharge is subject to much larger errors (seeSection 2.1). The values of h and b can be obtained accuratelydue to the sufficient topographical data of the Mekong Deltabranches. In addition, the uncertainty in the average depthmay even be reduced by using analytical relations for tidaldamping and tidal wave propagation presented by Savenije(2001, 2005) or Savenije and Veling (2005), but this will re-quire additional observations of tidal damping and tidalwave propagation.

Second, it is required to carry out salinity measurementsover every branch within the same period (preferably withinthe same day). Although these measurements provide a goodoverview of how salinity and discharge distribute over thebranches of the Mekong, the organization of these measure-ments requires substantial equipment, transportation and hu-man resources. The authors could not manage to carry outall these measurements at the same time. Therefore, the solu-tions given in Sections 4.2 and 4.3 are not complete for theTieu, Dai and Ham Luong branch; and instead we used salinityobservations at fixed stations. The calibrated results in thesebranches are hence less reliable.

Third, the salt intrusion model and the discharge distribu-tion over the branches of the Mekong Delta are obtained underthe assumption that the discharge values and ratios are con-stant during the considered period. In the view of the fast re-action time for a change in freshwater discharge of theMekong Delta during the dry season, in the order of oneweek (Nguyen and Savenije, 2006), it is a justified assumption.However, this assumption might not be correct for estuarieswith a long reaction time.

Finally, Eq. (17) is limited to partially to well-mixed estu-aries where stratification effects are not significant and hence,where riverine flows are relatively small comparing to tidalflows. This, however, is the case in most alluvial coastal plainestuaries during the dry season (Savenije, 2005).

0

10

20

30

40

50

CC-CH

Co Chie

n

Cung H

au

My Tho

Ham Lu

ong

Hau

Dinh An

Tran D

e

Others

Percen

tag

e o

f

ob

servatio

ns (%

)

0

10

20

30

40

50

CC-CH

Co Chie

n

Cung H

au

My Tho

Ham Lu

ong

Hau

Dinh An

Tran D

e

Others

Percen

tag

e o

f

ob

servatio

ns (%

)

a b

Hydraulic modelSalt intrusion model

Hydraulic modelSalt intrusion model

Fig. 6. Comparison between the salt intrusion model and the hydraulic model: (a) on 8 and 9 April 2005; (b) on 21 and 22 April 2005. CCeCH, Co ChieneCung

Hau.


7. Conclusion

This paper presents a new approach to determine the dis-charge distribution over the branches of the Mekong Deltaby means of a predictive analytical salt intrusion model. It ap-pears that the analytical model agrees well with observationsand with the results of a more complex hydraulic model.This paper shows that with relatively simple salinity measure-ments, it is possible to obtain a good picture of the dischargedistribution over a multi-channel estuary. This makes the ana-lytical model a powerful tool to analyze the water resources intidal regions.

Acknowledgments

The authors would like to acknowledge the Southern Insti-tute for Water Resources Research (SIWRR), Ho Chi MinhCity, Vietnam, for their enthusiastic support during the datacollection period and the field measurement campaign. Weare particularly grateful to Le Sam and Nguyen Van Sang(SIWRR), who kindly provided the database of the MekongDelta salinity, topography and hydrology. We also wouldlike to convey our thanks to Adri Verwey (WLj Delft Hydrau-lic, The Netherlands), who provided us valuable advices onmodelling of the Mekong river system.

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Documents

Using salt intrusion measurements to determine the freshwater discharge distribution over the branches of a multi-channel estuary: The Mekong Delta case