1. 168
Proceeding Paper for the World Environmental and Water Resources
Congress, Hilton Omaha, Omaha, Nebraska. USA.
EWRI & ASCE、、、、May 21－－－－25, 2006
A hydrologic analysis on inundation in the flooding area of the Mekong
Delta, Cambodia
-The combined deterministic and stochastic models for flood forecasting-
K. Sothea1
, A. Goto2
and M. Mizutani2
,
1
United Graduate School of Agriculture Sciences, Tokyo University of Agriculture
and Technology. Utsunomiya University, Department of Agriculture Environmental
Engineering, Mine-machi 350, Utsunomiya-shi, Tochigi Pref.321-8505; TEL. (81) 28-
6495504; FAX (81) 28-6495508; email: sothea@env.mine.utsunomiya-u.ac.jp
2
Utsunomiya University, Faculty of Agriculture, Mine-machi 350, Utsunomiya shi,
Tochigi Pref. 321-8505, Japan, TEL. (81) 28-6495497; FAX (81) 28-6495508; email:
goto@cc.utsunomiya-u.ac.jp; mizutani@cc.utsunomiya-u.ac.jp .
Abstract
Since the watershed of the Mekong River is situated under the typical
monsoon climate, the Mekong River presents a distinct variation in its water levels
between the dry and rainy seasons, and causes heavy inundation in the Delta area
along the river every year. In order to analyze the flow phenomena and inundation
process for agricultural practice in the Mekong Delta, this study tried to establish
three models: the combine of “3*4+1-type” model and the ARMA time series model,
Tonle Sap Lake Storage Model and Delta Water Balance Model. The “3*4+1- type”
Model was employed to calculate the runoff of the Lower Mekong River Basin from
Chiang Saen to Kompong Cham and its sub catchments. The ARMA time series
model was applied to the residuals of the Tank Model application in order to obtain 1
day to 5 days ahead flow forecasting after the present day based on the available data
of the present day. The inflow to the Tonle Sap Lake was also estimated by the
“3*4+1- type” Model, whereas outflow of the lake was formulated based on the
relationship between storage volumes and water level of the Lake surface. The
application of the ARMA to the “3*4+1-type” model was found effective to improve
flood forecasting at the outlets point of each sub-catchment. The established storage
model for the Tonle Sap Lake could calculate well for simulating the outflow and the
seasonal water balance of the Tonle Sap area. Deltaic area was divided into four
zones, and water balance of each zone was formulated by considering the zone’s
inflow/outflow between rivers and flooding areas. The establishment of these three
models could provide a basic framework for modeling the Mekong Delta, Cambodia.

2. 169
Introduction
Flooding of Mekong River has remained a major problem for human
settlements and rural infrastructures, and cause serious damage to agricultural
production in the low-lying area of Mekong Delta every year. For example, at Phnom
Penh, the difference between the minimum and maximum water level reaches as
much as 8-10 meters. Identifying the inundation processes has been attempted for
many years, and still has not been completely attained. To accomplish this goal and
based on data availability, this study tried to establish three basic models that could
represent the inundation process and flow phenomena of the Mekong Delta in
Cambodia. These three models are: the combination model between the “3*4+1-
type” model and the ARMA time series model for flood forecasting, the Storage
Model for estimation of inflow and outflow of the Tonle Sap Lake and the Water
Balance Model for calculation of water level in each divided zone of the low-lying
area in Cambodia. These models are to be used for evaluating the impact of inflow
into the low-lying area of the Mekong Delta, Cambodia.
Several advanced models have been developed since the early 1960s for the Mekong
River to simulate hydrological processes, such as flood control, water balance and
related water resources development, by various organizations and consultants.
Carbonnel et al.(1962~63) conducted a project research on sedimentology and
hydrology of Tonle Sap Lake. Though it still provides useful data and information, the
up-to-date topographic, hydraulic and hydrologic data are necessary for accurate
calculation of water balance in the present condition. In addition to this, Kite G.
(2000) applied SLURP model (Semi-Distributed Land-Use Runoff Process) with
Muskingum-Cunge method to estimate runoff of the Mekong River from Yunnan
(China) to the South China Sea in Vietnam, based on data obtained from internet and
some public institutions (MRC’s). Tawatachi T. (2001) applied a simple tank model
(4 tanks in one column) combined with autoregressive (AR) model for flood
forecasting in the Pasak River of the Chao Phraya River watershed.
The combination of the “3*4+1-type” and ARMA time series models was applied for
the Lower Mekong Basin from Chiang Saen to Kg. Cham. The “3*4+1-type” model
was used also to estimate the inflow from the Tonle Sap Lake catchments. Daily water
balance of the lake and deltaic areas were formulated based on the relationship
between the storage volumes and water levels of the Lake Surface and deltaic areas.
Catchment Characteristic
The Mekong River is one of the world’s 12 largest rivers, and rated as the 14th
by volume and discharges measured at Pakse in Laos PDR. It covers the drainage area
of 795,000 km2
with length 4,500 km. The river starts in Tibet at elevation of 5,000 m
of China and flows through Myanmar, Thailand, Lao, Cambodia and Viet Nam before
reach the South China Sea. The Lower Mekong Basin covered about 609,000 km2
in

3. 170
0 100 200 300 400㎞
ⅠⅠⅠⅠ
ⅡⅡⅡⅡ
ⅢⅢⅢⅢ
ⅣⅣⅣⅣ
ⅤⅤⅤⅤ
●
●
●
●
● ●
ⅦⅦⅦⅦ
ⅥⅥⅥⅥ
N
S
W ECHIANG
SAEN
LUANG
PRABANG
VIENTIANE
MUKDAHAN
UBON
PAKSE
① ③
④
⑤ ⑥
KG.CHAM
⑦
②
0 100 200 300 400㎞
ⅠⅠⅠⅠ
ⅡⅡⅡⅡ
ⅢⅢⅢⅢ
ⅣⅣⅣⅣ
ⅤⅤⅤⅤ
●
●
●
●
● ●
ⅦⅦⅦⅦ
ⅥⅥⅥⅥ
N
S
W ECHIANG
SAEN
LUANG
PRABANG
VIENTIANE
MUKDAHAN
UBON
PAKSE
① ③
④
⑤ ⑥
KG.CHAM
⑦
②
B
A1
A2
A3
A4
z1
z2
z3
Q upper zones
Q root zones
Rainfall
ETa
B
A1
A2
A3
A4
z1
z2
z3
Q upper zones
Q root zones
Rainfall
ETa
B
A1
A2
A3
A4
z1
z2
z3
Q upper zones
Q root zones
B
A1
A2
A3
A4
z1
z2
z3
B
A1
A2
A3
A4
z1
z2
z3
Q upper zones
Q root zones
Rainfall
ETa
four riparian countries, Cambodia, Laos, Thailand and Vietnam (about 77% of the
Mekong total catchment) from Chiang Saen (the borders of Myanmar, Thailand and
Lao at altitude of 500 m) to the Sea in Vietnam. The Tonle Sap Lake is the largest
freshwater lake in Southeast Asia and is important source for agricultural production
and fishery in Cambodia. From May to the end of October, when the water level of
the Mekong River is high, water flows through the Tonle Sap River and fills the Lake
up to five times its normal size, from about 2,500 km2
to 15,000 km2
depending on
the flood intensity. During the year, the lake’s water level varies from 1 meter above
the mean sea level (MSL) in the dry season to 9 meters in the rainy seasons. The
Mekong Delta in Cambodia comprises about 963,000 hectares. The Delta has a rather
flat topographical feature and lies at a low elevation varying from 0.6 to 10 meters on
average. Data were available for 39 rainfall and 12 stream gauging stations spread
across the modeling catchments for the Tank Model and 14 rainfall and 2 stream
gauging stations for the Tonle Sap Lake Model. The outline of study area in the
Lower Mekong Basin is shown Figure 1. In 1996, Cambodia experienced serious
floods due to the rapid flow of the Mekong River caused by storm rainfall in the
upstream countries and in the mountainous regions. Consequently, the years of 1995,
1996 and 1997 were chosen for this analysis.
Figure 1. The outline of the study area with application of “3*4+1- type” model
Description of model and its application
1. The “3*4+1- type” Tank Model. In a non-humid basin, some parts are wet and
the remaining parts are dry. Sugawara M. (1974) proposed the 4*4 type Tank Model

4. 171
0
5000
10000
15000
20000
1 51 101 151 201 251 301 351
Day
Discharge,(m3
/sec)
0
100
200
300
400
Rainfall,(mm)
Qobs
Qcal
Mukdahan
0
20000
40000
60000
1 51 101 151 201 251 301 351
Day
Discharge,(m3
/sec)
0
100
200
300
400
Rainfall,(mm)
Qobs
Qcal
Kg. Cham
to be applied for the watershed having dry season. Tatano M. et al. (1999) applied the
4*4 type model for the Lower Mekong River Basin. It showed that the “4*4-type”
Tank Model had a tendency to show too much increase in stored water in the lowest
tank of the nearest column to the river. Therefore, the modification of the model
structure from the “4*4” to “3*4+1- type” model was examined. The “3*4+1- type”
model consists of 13 storage tanks with four columns, in which each column has three
storage tanks. Each of the four columns is connected with a ground water tank as
illustrated in figure 1. The coefficient for the hole sizes and hole heights are the model
parameters. For simplicity in model calibration, the same set of parameter values can
be adapted in every column.
To separate the channel flow from the slope water moment, an open book scheme was
employed, in which catchment is presented as a quadrangle with a straight channel.
The “3*4+1” Model, coupled with the Kinematic wave for channel routing sub-model,
was employed to calculate the runoff from the drainage area of 471,995 km2
from
Chiang Sean to Kg. Cham. The whole drainage area was divided into six sub-
catchments (II~VII), and one Tank Model was applied to each sub-catchment, as
shown in figure1. Model calibration was done for the year 1995 through the trial-and-
error approach, and the data for 1996~97 were used for model validation. Figure 2
shows the obtained hydrograph of the catchment outlet at Mukdahan and Kg. Cham.
Figure. 2 The simulated runoff hydrographs at Mukdahan and Kg. Cham
2. The Autoregressive and Moving-Average model (ARMA). The ARMA time
series model was applied to the residuals (different between calculated and observed
discharges) of the Tank model application, in order to forecast 1day to 5 days ahead
flow forecasting after the present day based on the available data. By using the Box-
Jenkins (1970) approach, the basic equations of the ARMA model with autoregressive
parameters (p) and moving average parameter (q) for flow forecasting in time step t
are written as follows:
For 1 day ahead:
112111231211 .......... +−−++−−−+ −−−−+++++= qtqtttptptttt eeeeZZZZZ θθθφφφφ (1)

5. 172
Modified Tank ModelModified Tank Model
Residual
PresentdayDayafter
Obs. rainfall
Qcal. Qobs. Residual (different between
Qcal. and Qobs.)
Flow forecasting
+
Forecast rainfall
ARMA Model
Modified Tank ModelModified Tank Model
Qcf.
For 2 days ahead:
221122132112 .......... +−+++−−++ −−−−+++++= qtqtttptptttt eeeeZZZZZ θθθφφφφ (2)
Where, Zt+1 is dependent variable at time t+1(which corresponds to residuals from
Tank Model); Z t-p+1 is independent variable from the previous time t-p+1; et is the
white noise factor value; et-q+1 is error estimated from the previous time t-q+1; and
φ and θ are model parameters.
Though rainfall forecast is also necessary in real flood forecasting, this analysis
assumed future rainfall can be perfectly forecast, and used the rainfall records as input
to the Tank Model. Then, the combination of ARMA time series model to Tank Model
was finally obtained the final flow forecasting in each sub-catchment reach. The
procedure of this analysis is summarized in Figure 3.
Figure 3. The procedure of the flood forecasting
The evaluation criteria for evaluating model performance of the goodness-to-fit
between the calculated and observed flow was obtained by mean relative error (MRE)
as follows:
%100
1
×
−
=
obs
calobs
Q
QQ
N
MRE (3)
Where, N is the number of data; Qobs is the observed discharge (m3
/s); and Qcal is the
calculated discharge (m3
/s). The best performance can be obtained when MRE is
equal to zero.
The parameter values and model performances of Tank Model and the combined Tank
and ARMA models are summarized in Table 1. It shows that, for 1 day to 5 days

6. 173
0
500
1000
1500
200 210 220 230 240 250
Day
Discharge(m3
/sec)
Observed flow
0
10000
20000
30000
40000
50000
193 213 233 253 273 293Day
Discharge(m3
/sec)
Observed flow
3 days after
5 days after
Ubon Kg. Cham
ahead forecasting, the combined Tank and ARMA models were found better
performances than Tank Model application alone. Figure 4 is showed the forecast
hydrographs at Ubon and Kg.Cham. Based on this performance, the better results
produced from ARMA time series model depends on the good estimation of the
residuals from the Tank Model.
.
Table 1 Summary of parameter values and ARMA model performance
Sub-
catchment
Flow
forecasting
point
Mean Relative Error (Tank+ARMA), %
MRE(%)
(Tank Model)
Forecasting Day
1day 2days 3days 4days 5days
Sub II II 8.83 2.74 4.44 5.30 5.79 6.04
Sub III III 7.38 2.01 2.94 3.61 4.08 4.43
Sub IV IV 8.50 3.17 5.57 7.30 8.37 9.02
Sub V V 30.80 1.80 3.80 5.86 7.89 9.81
Sub VI VI 7.15 2.98 4.39 5.14 5.50 5.66
Sub VII VII 28.00 2.56 3.90 8.20 8.90 10.60
Figure 4. Hydrographs of flow forecasting of 1 to 5 days ahead at Ubon and
Kg.Cham sub-catchments
3. The Tonle Sap Lake Storage Model. The Tonle Sap Lake area was divided into
the catchment area and the lake surface. Due to insufficient runoff data from other
sub-catchments of the Tonle Sap area, the result of regression analysis between
discharge data derived from Carbonnel’s studies in 1962-63 and the calculated
discharge of the two sub-catchments (Pursat and Sen) by the Tank Model was used to
estimate the total inflow from the whole catchment to the lake (see figure 5). The
daily change of storage volume was maintained the mass balance equation between
the inflow and out flow of the lake:
( ) ( ) ( )a
t
t
out
t
out
t
in
t
in
tttt
ETRW
QQQQWW
t
HH
−+
+−+
=
+
∆
− ++++
22
1111
(4)
Where, t, t+1 are the time step; H is water level of the Lake (mm); Qin is inflow into
the lake (mm); Qout is outflow/reverse flow of the lake (mm); W is storage area of the

7. 174
Sen-Catchment
Pursat-Catchment
Prekdam
Tonle Sap Lake
Phnom Penh
Tonle Sap River
N
EW
S
Lake
Flooded area
Modeling catchment
Catchment area
Discharge St.
Rainfall St.
Flow Direction
Water level St.
0 8000000 km8000000
Sen-Catchment
Pursat-Catchment
Prekdam
Tonle Sap Lake
Phnom Penh
Tonle Sap River
N
EW
S
Lake
Flooded area
Modeling catchment
Catchment area
Lake
Flooded area
Modeling catchment
Catchment area
Discharge St.
Rainfall St.
Flow Direction
Water level St.
0 8000000 km8000000
Lake *106
(mm); R is net rainfall (mm); ETa is evapotranspiration (mm), which was
calculated using Penman-Moneith method of FAO version for pan evaporation. The H
and W were estimated based on the relationship between storage volume and water
level of the lake.
When the water level of the Mekong River becomes high in the flood season, water is
pushed into the lake (reverse flow), and when the water level of the Mekong River
recedes in the dry season, water flows from the lake to the Mekong River (outflow).
The Manning equation was used in this calculation, as expressed as follows:
L
HH
AR
n
Q 013/21 −
= (5)
Where, Q is outflow/reverse flow (m3
/s); A is cross-sectional area (m2
); R is hydraulic
radius (m); H1 is water level in side the reach (m); H0 is water level outside the reach
(m); L is distant between two key stations (m); n is Manning coefficient. Cross-
section of the river assumed to be trapezoidal for open channel flow.
From the digital elevation data, the relationship curve between storage volumes and
water levels was established. Water balance of the lake was computed based on the
equation of storage-water level relation combined with evapotranspiration, rainfall,
inflow and outflow of the lake. Equation (5) was solved by Newton-Raphson iteration
method. The summarized results of the monthly changes in the water balance
components of the Tonle Sap Lake are depicted in Figure 6.
Figure 5. The Tonle Sap Lake’s catchment model

8. 175
8000000
6000000
4000000
2000000
0
2000000
4000000
6000000
8000000
May-95 Oct-95 Mar-96 Aug-96
Month
Inflow,Outflow,Storage
change(mm,monthly)
0
20
40
60
80
100
120
Rainfall,(mm,monthly)
Inflow Outflow/reverse flow
Rainfall Storage change
Figure 6. The results of the Tonle Sap Lake Storage Model
4. The Delta Water Balance Model. The Mekong Delta covers the main Mekong
River, Tonle Sap River and Basac River. This river system divides the whole deltaic
area in Cambodia into four zones. The extents of the flooding areas in each zone were
determined by choosing an area below 10-meter contour lines in the 1996 topographic
map (scale, 1:100,000). Water level data at Kg. Cham, Prekdam, Chau Doc, and Tan
Chau were derived from the MRC’s hydrological yearbooks from 1995 to 1997.
Figure 7 presented the zoning areas of the Mekong Delta and a schematic modeling
of the delta water balance model. Considering each divided zone as a storage
reservoir, the zone inflow and outflow water balance was formulated, based on mass
balance equation as following:
( ) tETRQQQQSS aoutinreturnover
n
SD
n
SD ∆−+−+−+=+1
(6)
Where, n and n+1 are the time steps; Sn is the storage volume in each Zone at time
step n (mm); Q over is the overflow from the river (mm); Q return is the return flow from
the floodplain into the river (mm); Qin is the inflow from tributaries (mm); Qout is the
outflow from the zone to the connected low-lying areas (mm); R is the daily rainfall
(mm); and ETa is evapotranspiration (mm). The infiltration was assumed to be
negligible. Daily rainfall (R) was formulated based on Thiessen polygons method.
The inflow into the inundated area was considered as overflow from the main rivers
(or inflow from upper catchment) during the rainy season, and return flow from the
inundated area to the main river occurs when the dry season starts. The equations
used in this calculation are given by:
if 1111
2
2
2
3
2
ghhBQ
h
h
××=⇒





< µ (7) for complete overflow
if )(2
3
2
21222
2
2
hhghBQ
h
h
−××=⇒





> µ (8) for submerge flow

9. 176
N
Z on in g.s h p
Zo ne 1
Zo ne 2
Zo ne 3
Zo ne 4
SD 1
SD 2
SD 4SD 3
Prekdam
TanChau
ChauDoc
Kg.Cham
WL1
WL2
WL3
WL5WL4
Qin3
Qout3
Qover23
Qover21
Qreturn21
Qreturn4
Qreturn3
4
Qout2Qout4
Qreturn12
Qover12
Qover32
Qreturn24
Mekong R
Mekong R
Tonle
SapR
BasacR
P.Penh
SD
Calculated flows
Sub-zone
Water Level St.
Qover4PrekThnot
Tonle Touch
1 0 0 1 0 2 0 K m
SD 1
SD 2
SD 4SD 3
Prekdam
TanChau
ChauDoc
Kg.Cham
WL1
WL2
WL3
WL5WL4
Qin3
Qout3
Qover23
Qover21
Qreturn21
Qreturn4
Qreturn3
4
Qout2Qout4
Qreturn12
Qover12
Qover32
Qreturn24
Mekong R
Mekong R
Tonle
SapR
BasacR
P.Penh
SD
Calculated flows
Sub-zone
Water Level St.
Qover4PrekThnot
Tonle Touch
1 0 0 1 0 2 0 K m1 0 0 1 0 2 0 K m
0
2
4
6
8
10
12
14
16
Jun-96
Jul-96
Aug-96
Sep-96
Oct-96
Nov-96
Dec-96
Date
Waterlevel,(m,MSL)
0
20
40
60
80
100
120
Rainfall,(mm/day)
Rainfall
Obs WL2
Obs WL5
Obs WL1
Cal WLd1
Cal WLd2
Cal WLd3
Cal WLd4
WL1
WLd1
WL3
WLd3WL5
WLd4
WLd2
Where, Q1, Q2 are the flow rates of overflow and submerged flow, respectively (m3
/s);
µ1 and µ2 are the discharge coefficients of complete overflow and submerged flow; g
is the acceleration due to gravity (g =9.81 m/s2
); h1, h2 are water head above crest
elevation in river and inundated area, respectively(m); B is length of weir (m).
Figure 7. Zoning and schematic modeling of the Mekong Delta
Figure 8. Calculated water level in comparison with between upstream and
downstream observed water level in each zone of 1996
Figure 8 shows a result of the calculated water level in each zone in comparison with
observed water levels upstream at Kg. Cham (WL1), Prekdam (WL3), and
downstream at Tan Chau (WL5), of the Mekong Delta. The simulated results show
that the inundation depth of each zone ranged in between the upstream and
downstream water levels, and reached as high as about 8 meters in 1996. Due to the

10. 177
lack of available data, the inundation depth could not be compared with actual values.
However, according to the results of interview that was conducted to the farmers in
the study area, the calculated water level of each zone were similar, compared to the
actual flood situation in the year 1995 to 1997. Therefore, this analysis on water
balance was considered in reasonable outcomes to provide the basic framework for
modeling in the Mekong Delta.
Conclusion
The combination of Tank Model and ARMA time series model was found
effective to improve flood forecasting at the outlets point of each sub-catchment. The
accuracy of time series model for flood forecasting is fundamental to many decisions-
making, related to flood warning system in the region. The results of the Tonle Sap
Lake model were proved to be a better way for local drainage analysis. It is also
suitable to evaluate the change in water level of the Lake and rivers for various
activities, related to navigation, fisheries and floodplain management. The Delta
Water Balance Model was also established and considered to provide the basic
framework for modeling the Delta inundation. To obtain more accurate modeling of
the Delta water balance, it is necessary to collect detailed data on topography, rainfall,
discharge and water level records.
For the next inundation study of the Mekong Delta, it is necessary to consider the
distribution of water on the floodplain, using a hydraulic model and Geographic
Information System (GIS) technique. The modeling application will particularly focus
on analyzing the inundation in a specific area for examining the possibility and
effectiveness of the semi-control of flooding for the improvement of the agricultural
land conditions of the area.
References
Carbonnel J.P., Guiscafre J. (1963). Grand Lac du Cambodge. Sedimentologie et
Hydrologie. Repport de mission. Mekong Secretariat, p.64-176, (in French).
Geoff K. (2000). Developing a Hydrological Model for the Mekong Basin: Impact for
Basin Development on Fisheries Productivity. ISBN: 92-9090-424-0.
MRC. (1995~97). Lower Mekong Hydrologic Yearbook Mekong River Commission.
Sugawara M., Ozaki E., Watanabe I., Katsuyama Y. (1974). Tank Model and its
application to Bird Creek, Wollombi Brook , Bikin River, Kitsu River, Sanaga
River, and Nam Mune. Research Notes of the National Research Center for
Disaster Prevention, No. 12, p. 1-64.
Tatano M., Goto A. (1998). Real-Time Flow Forecasting in the Midstream Basin of
the Mekong River by Combination of a Deterministic Model and a Stochastic
Model. Proceeding Annual Meeting JSIDRE, 1998, p. 126-127, (in Japanese).
Tawatachai T., Mashesh R.G. (2000). Application of Tank, NAM, ARMA and neural
network models to flood forecasting. HYDROLOGICAL PROCESSES,
Hydrol. Process. 14, 2473-2487 (2000), p. 2474-2487.