Multireservoir Flood-Control Optimization with Neural-Based Linear Channel Level Routing Under Tidal Effects

Multireservoir Flood-Control Optimizationwith Neural-Based Linear Channel Level RoutingUnder Tidal Effects

Chih-Chiang Wei & Nien-Sheng Hsu

Received: 28 September 2006 /Accepted: 10 January 2008 /Published online: 22 February 2008# Springer Science + Business Media B.V. 2008

Abstract In order to determine the optimal hourly releases from reservoirs under theestuary tidal effects during typhoon periods, this paper develops a generalized multipurposemultireservoir optimization model for basin-scale flood control. The model objectivesinclude: preventing the reservoir dam and the downstream river embankment fromovertopping, and meeting reservoir target storage at the end of flood. The model constraintsinclude the reservoir operations and the neural-based linear channel level routing. Theproposed channel level routing developed from the feed-forward back-propagation neuralnetwork is employed to estimate the downstream water levels. The developed optimizationmodel has been applied to the Tanshui River Basin system in Taiwan. The results obtainedby the optimization model, in contrast to historical records, demonstrate successfully thepracticability in solving the problem of flood control operations.

Keywords Flood control . Reservoir . Optimization . Neural networks . Tidal effects

1 Introduction

Tanshui River Basin is located in the northern part of Taiwan having steep terrain andexcessive rainfall. The most severe disaster in Tanshui River Basin is flood, which is causedby intensive rainfall and rapid flows during typhoon seasons. Once typhoon strikes, the waterlevel at the estuary rises abnormally due to typhoon surge. Meanwhile, receiving voluminousrainfalls from upstream watershed, considerable streamflows usually converge downstreamwithin a short time. Therefore, it is very difficult to release such voluminous water into the

Water Resour Manage (2008) 22:1625–1647DOI 10.1007/s11269-008-9246-8

C.-C. WeiDepartment of Information Management, Toko University, No. 51, Sec. 2, University Rd., Pu-Tzu City,Chia-Yi County 61363, Republic of Chinae-mail: [email protected]

N.-S. Hsu (*)Department of Civil Engineering, National Taiwan University, No. 1 Sec. 4, Roosevelt Rd.,Taipei 106, Republic of Chinae-mail: [email protected]

ocean for the downstream reach. With all these unfavorable natural conditions, multireservoiroperations play an important role in mitigating the downstream flood disaster.

To develop a multireservoir operation model for a river basin system, Windsor (1973),Needham et al. (2000), and Braga and Barbosa (2001) described an application ofdeterministic optimization using a linear programming (LP) model to treat the flood controlproblem, using the Muskingum method for channel routing and mass balance equation forreservoir operations. Wasimi and Kitanidis (1983) applied the discrete-time linear quadraticGaussian (LQG) stochastic control for the real-time daily operation under flood conditions.The streamflow routing along a channel reach used the Muskingum linear channel routingmodel. Unver and Mays (1990) formulated a nonlinear programming (NLP) model to addressthe real-time hourly flood control problem. The constraints included the reservoir operationconstraints, which are defined by bounds on reservoir releases, surface elevations and gatefacilities, while the hydraulic constraints which are defined by the one-dimensional unsteadyflow. The above-mentioned studies have examined the multireservoir operation problem well.However, such case with tidal effects due to typhoon surge has not been studied in the past.

The purpose of this paper is to formulate a generalized multipurpose multireservoiroptimization model for basin-scale flood control to determine the optimal hourly releasesunder tidal effects. The proposed optimization model is formulated as a mixed-integerlinear programming (MILP) model. The model constraints include the reservoir operationrouting and river flow routing. The developed optimization model will be applied to theTanshui River Basin system in Taiwan.

The challenges of solving the multireservoir operation optimization problem duringflood periods include how to implement river flow routing which can be incorporated intothe proposed linear model. To solve the complicated flow routing under the interactionbetween upstream flows and tidal effects, Lai (1986, 1999, 2002) developed a graduallyvarying unsteady flow model, which deals with the compound–complex channel (networkor dendritic) system according to the multimode method of characteristics (in short,CCCMMOC; for details, see Section 5). In the last two decades, he has succeeded in usinga model to simulate the complicated behavior of water movement and interaction at eachriver section in Tanshui River (Lai 2002). The CCCMMOC model demonstrates that it isgood at analyzing accurately the variations in water surface elevation under unsteadychannel flow. The physical-based model however is mathematically a highly complicated,nonlinear numerical model in space and time. Therefore, it is not suitable for embedding itinto the proposed linear multireservoir operation model.

Artificial neural networks (ANN) are good at identifying and learning correlated patternsbetween input data sets and the corresponding target values (Chang and Chen 2001; Huang2001). After McCulloch and Pitts (1943) established the first neural network, a number ofANNs were developed to solve different problems in the field of hydrology, such as flowrouting and river stage forecasting (e.g., Karunanithi et al. 1994; Thirumalaiah and Deo 1998;Liong et al. 2000; Bazartseren et al. 2003; Chang and Chen 2003; Tissot et al. 2004;Altunkaynak 2007). Moreover, there are other techniques regarding water level predictions,such as time series modeling (ARMAX, autoregressive moving average with exogenousinputs; Iruine and Eberthardt 1992; Vaziri 1997), fuzzy logic (Altunkaynak and Sen 2007),fuzzy neural network (Deka and Chandramouli 2005), triple diagram method (Altunkaynaket al. 2003). Vaziri (1997) and Altunkaynak (2007) pointed out that the neural network modelis simpler and more reliable than the conventional methods such as autoregressive (AR),moving average (MA), and ARMAX. In view of the abovementioned reason, this articleproposes a simple neural-based linear channel level routing algorithm developed from feed-forward back-propagation neural network (BPNN) for predicting the downstream water level.

1626 C.-C. Wei, N.-S. Hsu

2 Tanshui River Basin System

2.1 System Description

Figure 1 shows the geographical location of the greater Tanshui River Basin. The TanshuiRiver consists of three major river basins: Tahan River, Hsintien River, and Keelung River.The major stream flows of Tanshui River go through the Taipei Bridge and Tudigong, andfinally reach Hekou. In this basin, the parallel Shihmen and Feitsui Reservoirs, have beenused for joint operations for flood control.

Tahan River originates from Mt. Pinten and joins the Hsintien River at Chiangchutsui,which is the starting point of Tanshui River. The length of Tahan River is 126 km with adrainage area of 1,163 km2. There are four major creeks in Tanhan River, including Yufongcreek, Shankwan creek, Shanshia creek, and Heng creek. The Shihmen Reservoir,completed in 1964, is the most important hydraulic structure in Tahan River. Themaximum elevation of 245 m is for normal operation, whereas the maximum elevation of248 m is for flood-mitigation operation. Approximately the capacity of 27×106 m3 isreserved for flood control during typhoon attack. The Shihmen Reservoir currentlymanaged by the Water Resources Agency was built primarily for flood control and thewater is used for irrigation and domestic water supply along Tanhan River (Hsu and Cheng2002).

Fig. 1 Map of Tanshui RiverBasin system

Flood control optimization under tidal effects 1627

Hsintien River originates from Mt. Chilan and joins Tanshui River at Chiangchutsui. Thelength of Hsintien River is 82 km, with a drainage area of 916 km2. There are three majorcreeks in Hsintien River, including Peishih creek, Nanshih creek, and Gingmei creek. TheFeitsui Reservoir, completed in 1985, is the most important hydraulic structure in HsintienRiver. The maximum elevation of 170 m is for normal operation and the maximumelevation of 171 m is for flood-mitigation operation. Approximately 9×106 m3 of thestorage is reserved for flood control during the typhoon season. The Feitsui Reservoircurrently managed by the Taipei City Government was built primarily to provide domesticwater supply to the Taipei Metropolitan area (Hsu and Cheng 2002).

2.2 Network Representation

For easy representation of a complex study area, the network representation (see Fig. 2) isused. In Fig. 2, nodes represent reservoirs, control points, and the estuary, while arcs denoterivers. In this study, four gauge stations (i.e., Sanying, Showlan Bridge, Taipei Bridge andTudigong locations as shown in Fig. 1) are selected as control points. Of these four controlpoints, the water levels of Sanying and Showlan Bridge (being far away from the estuary)are weakly affected by tide; whereas the water levels of Taipei Bridge and Tudigong (beingclose to the estuary) are strongly affected by tide. Then the actual configuration of thesystem (Fig. 2) can be employed in the proposed model (see next section).

Fig. 2 Network representation of Tanshui River Basin system


3 Optimization Model

The proposed linear optimization model requires all relations associated with objectivefunctions and constraints to be linear or linearized representations. The presentedoptimization model is described as follows.

3.1 Constraints

The model constraints involve two parts: (1) the multipurpose multireservoir operations forflood control, and (2) the river flow routing using neural-based linear channel level routingalgorithm. The configuration of parts 1 and 2 can be seen in Fig. 2.

For the multireservoir system operations (part 1), the constraints include reservoircontinuity and physical limitations. In addition, to implement the reservoir flood operationsin Taiwan, the flood control polices (rules) are embedded into constraints.

& Reservoir continuity: This equation developed according to the principle of continuity.In general, evaporation and leakage losses from reservoirs during flood periodsare an insignificant portion of the total flow and are therefore not included in themodel (Windsor 1973). Therefore, the constraints associated with a reservoir node(see Fig. 2) for continuity of mass in inflow Ii,t, outflow XR

i;t, and storage X Si; t, can be

expressed according to the finite difference formula

Δt

2Ii;t�1 þ Ii;t� �� Δt

2XRi;t�1 þ XR

i;t

� �¼ X S

i;t � X Si;t�1 i 2 <; t 2 t0; tT½ � ð1Þ

where i is the index of reservoir, t is the index of time period, Δt is a short time interval inhours for routing, is the set of reservoirs, tT is the flood duration, and t0 is the operatinginitial time. The whole control horizon is the time length between t0 and tT. It is noticed thatwhen t is equal to t0, both the reservoir initial release XR

i;t0�1 (can be denoted as Ri,0) andstorage X S

i;t0�1(denoted as Si,0) are known.

& Physical limitations: The reservoir storage ranges from full storage (Smaxi ) to dead

storage (Sdeadi ) over the control horizon, that is

Sdeadi � XSi;t � Smax

i i 2 <; t 2 t0; tT½ � ð2ÞIn addition, for reservoir release capacity, the amounts released by hydraulic facilities as

calculated by linearized representations are limited. A method that can address both convexand concave (or mixed convex-concave) types of relationship between the release capacity(XRC

i;t ) and the storage (X Si;t) is presented as below.

If the whole reservoir storage volume can be divided into zones (e.g., three zones inFig. 3), then the linearization method presented is accomplished by selecting carefully anumber of breakpoints (Z+1) at which the slope of the piecewise linear function changes. Zis defined as the number of linear segments; for example, in Fig. 3, Z=3. The completeformulas comprise a set of equations:

X Si;t ¼

XZþ1

p¼1

σpi;t � Spi 0 � σp

i;t � 1; i 2 <; t 2 t0; tT½ � ð3Þ

XRCi;t ¼

XZþ1

p¼1

σpi;t � Rpi 0 � σp

i;t � 1; i 2 <; t 2 t0; tT½ � ð4Þ


with

σ pi;t � g p�1

i;t þ g pi;t p ¼ 1; Z þ 1½ �; 0 � σ p

i;t � 1; g pi;t 2 0; 1f g ð5Þ

XZp¼1

g pi;t ¼ 1 gpi;t 2 0; 1f g ð6Þ

XZþ1

p¼1

σpi;t ¼ 1 0 � σp

i;t � 1 ð7Þ

Several denotations of Eqs. 3, 4, 5, 6, and 7 are defined as below:

Spi the storage volume at breakpoint index p, and S1i ¼ Sdeadi and R1i ¼ Rmin

i (i.e., the mini-mum release capacity), and when p=Z+1, let SZþ1

i ¼ Smaxi and RZþ1i ¼ Rmax

i (i.e., themaximum release capacity).

gpi;t the binary integer (0–1) variable at breakpoint p at time t. It is used for identifying thecorrect storage status. Note that g0i;t and gZþ1

i;t should physically be equal to zero. FromEq. 6, only the binary integer (0–1) variables gpi;t are equal to 1, thereby indicating thestorage status at time period t. For example, in Fig. 3, when reservoir storage X S

i;t is bet-ween breakpoints 2 and 3, then g2i;t ¼ 1 and g1i;t ¼ g3i;t ¼ 0.

spi;t the real variable between [0, 1] at breakpoint p at time t. It is used for identifying the cor-

rect release capacity status. For example, in Fig. 3, when g2i;t ¼ 1 and g1i;t ¼ g3i;t ¼ 0,from Eqs. 5 and 7, s1

i;t ¼ s4i;t ¼ 0,0 � s2

i;t � 1,0 � s3i;t � 1, and s2

i;t þ s3i;t ¼ 1 are ob-

tained. Hence, from Eqs. 3 and 4, the reservoir storage X Si;t ¼ s2

i;t � S2i þ s3i;t � S3i and the

release capacity XRCi;t ¼ s2

i;t � R2i þ s3

i;t � R3i are determined, respectively.

Fig. 3 Piecewise linear approx-imations for reservoir storageversus release capacity


Naturally, the actual releases at each period should be less than the release capacity,that is

XRi;t � XRC

i;t i 2 <; t 2 t0; tT½ � ð8Þ

& Operation rules: The reservoir flood control rules stipulate the release operationrules in Taiwan in order to mitigate flood damage (Water Resources Agency 2002;Taipei City Government 2004). Two flood stages (i.e., peak-flow-preceding stageand peak-flow-proceeding stage) during typhoon periods can be represented asshown in Fig. 4. In the figure, tpeak is the ending time of the peak-flow-precedingstage when reservoir peak inflow occurs, tb is the beginning time of regulatingtarget storage Stargeti

� �within the peak-flow-proceeding stage (note that tb is between

tpeak and tT), Ii,0, Ii,peak, Ii,b and Ii,T are the inflow rates at reservoir i related to time t0,tpeak, tb, and tT, respectively. A summary of release rules regarding the two flood stagesand the corresponding constraints are described as follows.

For the peak-flow-preceding stage, there are two rules in this stage: Rule 1, that is, thereservoir release is less than or equal to the reservoir inflow; and rule 2, that is, the releaseat the current period is greater than that at the previous period. Rules 1 and 2 can beintegrated into an equation

XRi;t�1 � XR

i;t � Ii;t i 2 <; t 2 t0; tpeak� � ð9Þ

For the peak-flow-proceeding stage, there are two rules: Rule 1, that is, the release ateach period is less than the reservoir peak inflow; rule 2, that is, the release at the currentperiod is less than that at the previous period. Rules 1 and 2 can be integrated as follows

XRi;t � XR

i;t�1 � Ii;peak i 2 <; t 2 tpeak þ 1; tT� � ð10Þ

For the downstream flood movement (part 2), a neural-based linear channel level routingalgorithm is proposed. Figure 5 is a schematic of a typical BPNN with a three layer (i.e.,an input layer, a hidden layer, and an output layer). Mathematically, a three-layer BPNN

Fig. 4 Definition of the twoflood stages during typhoonperiods


with N1 input nodes, N2 hidden nodes, and N3 output nodes, can be expressed as (Xu andLi 2002)

yr ¼ f2XN2

q¼0

w2qr � f1

XN1

p¼0

w1pq � xp

! !r 2 1;N3½ � ð11Þ

where p is the index of input nodes, q is the index of hidden nodes, r is the index of outputnodes, xp is the input node of the input layer, w1

pq is the weight set connecting the inputlayer and hidden layer, w2

qr is the weight set connecting the hidden layer and output layer, yrdenotes the outputs from the network, f1 �ð Þis the activity function of the hidden layer, andf2 �ð Þis the activity function of the output layer.

The bias weights and terms appear when p or q equals 0. The commonly used activityfunction includes linear, sigmoid and hyperbolic tangent (Imrie et al. 2000; Xu and Li2002). This study introduces the linear activity function for this algorithm. Thus, Eq. 11 canbe rewritten as

yr ¼XN2

q¼0

XN1

p¼0

w2qr � w1

pq � xp r 2 1;N3½ � ð12Þ

As in Fig. 5, the input layer can be employed to receive the hydrological time-seriesinformation including the reservoir releases, tributary and lateral runoffs, estuary levels,control-point levels, and time delay, while the output layer serves to output the control-point water level. From Eq. 12, the formula of the linear channel level routing can beexpressed as:

XLk;t ¼

Pζ1d1¼1

W1kd1 � XR

1;t�d1 þPζ2d2¼1

W2kd2 � XR

2;t�d2 þPζ3d3¼1

W3kd3 � I tribut�d3

þPζ4d4¼1

W4kd4

� I localt�d4þ Pζ5

d5¼1W5

kd5� Lmouth

t�d5þ Pζ6

d6¼1W6

kd6� XL

k;t�d6k 2 Ω

ð13Þ

Fig. 5 Architecture of the neural-based channel level routing algorithm


where k is the index of control points, Ω is the set of control points (i.e., control-points 1 to4), d1–d6 are indices of lag-time, ζ1–ζ6 are lengths of lag-time associated with the relatedhydrological information, and W 1

kd1�W 6

kd6are the weighting parameters. The seven terms

of Eq. 13 are defined as follows.

XLk;t the elevation of water level at control-point k at time t, kε{1,2,3,4},

XR1;t�d1

the release of reservoir 1 at lag-time d1,

XR2;t�d2 the release of reservoir 2 at lag-time d2,

I tribut�d3the flow of tributary at lag-time d3,

I localt�d4the flow of the total amount of lateral 1, lateral 2, and lateral 3 at lag-time d4,

Lmoutht�d5

the elevation of water level at estuary at lag-time d5,XLk;t�d6

variable associated with the elevation of water level at control-point k at lag-time d6.

3.2 Objective Function

For a multipurpose multireservoir operating system taking into consideration the purposesof controlling flood and regulating storage, the model objectives include: preventing thereservoir dam from overtopping, reducing the downstream floodwaters, and meeting targetreservoir storage at the end of flood. The first objective is satisfied by Eq. 2, while the othertwo objectives can be considered in the objective function.

First, the objective of reducing downstream floodwaters can be expressed as minimizingthe maximal water level at the selected downstream control points during flood, that is

Min max XLk;t

� �n ok 2 Ω ; t 2 t0; tT½ � ð14Þ

The nonlinear min-max function of Eq. 14 can be equivalently expressed as a linearproblem, that is

Min XLPk

� �k 2 Ω ð15Þ

subject to

XLk;t � XLP

k k 2 Ω; t 2 t0; tT½ � ð16Þ

where XLpk is the maximal water level at Control-point k.

Second, the objective of meeting target reservoir storage at the end of flood can beexpressed as minimizing the maximal deviation of storage from its target value during thespecific time interval at the end of flood (i.e., [tb, tT]), that is

Min max X Si;t � Stargeti

� �n oi 2 <; t 2 tb; tT½ � ð17Þ

The min-max problem of Eq. 17 can be equivalently expressed as

Min XEPi

� �i 2 < ð18Þ

subject to

�XEPi � X S

i;t � Stargeti � XEPi i 2 <; t 2 tb; tT½ � ð19Þ

where XEp

i is the maximal target storage deviation of storage from its target value atreservoir i.


From Eqs. 15 and 18, the overall objective function can be formulated as

MinXk2Ω

XLPk þ

Xi2<

XEPi

( )ð20Þ

In the above objective function, there exists a problem with different scales between thetwo objectives. The dimensionless method is employed to tackle this problem. Thus, Eq. 20can be rewritten as

MinXk2Ω

XLPk

Lbankk

þXi2<

XEPi

Stargeti

( )ð21Þ

where Lbankk is the elevation of embankment at control-point k.

4 Model Settings

Prior to application of the proposed model, this section concentrates on setting theparameters and calibrating the weights.

4.1 Setting Parameters

For the Tanshui River Basin system, the reservoir characteristics are listed in Table 1. Currently,the embankment elevations of control-points 1 to 4 are at the altitude of 48.0, 15.0, 10.0 and4.8 m, respectively. The time period between subsequent interventions in the proposed modelis 1 h. The setup of time phases regarding the peak-flow-preceding stage and the peak-flow-proceeding stage are defined as:

& For reservoir 1: According to theWater Resources Agency (2002), the initial operatingtime t0 is at 600 m3/s inflow. In addition, the starting regulating storage time tb at400 m3/s inflow and the flood ending time tT at 300 m3/s inflow are assumed.

& For reservoir 2: According to the Taipei City Government (2004), the initial operatingtime t0 is at 500 m3/s inflow. Moreover, both the starting regulating storage time tb at150 m3/s inflow and the flood ending time tT at 100 m3/s inflow are assumed.

In order to choose the suitable lag-time lengths from various hydrological sources of thechannel level routing, for simplicity, the travel time caused by propagating flood wave froma source point to the specific control point has been regarded as the lag-time length. Forexample, empirically, the travel time (ζ1) of reservoir release from reservoir 1 to control-point 4 takes 4 h roughly when flood occurs. Table 2 lists all the lag-time lengths obtained

Table 1 Characteristics of two reservoirs

Reservoir Full storage (106 m3) Normal storage (106 m3) Dead storage (106 m3)

Reservoir 1 280.8 254.0 18.3Reservoir 2 397.3 388.2 8.7


empirically in a similar way. It is noted that for control-point 2, the local flow involves onlylateral 2 in its corresponding control-point level formula.

4.2 Channel Level Routing Validation

In this section, the weights within the neural-based linear channel level routing formula(i.e., Eq. 13) are first calibrated. Then, the linear channel level routing is compared with theCCCMMOC model.

To train the weights, the collected data for 36 typhoons (1987–2004), published by theWater Resources Agency, are divided into two independent subsets: the training andvalidating subsets. The training subset includes 26 typhoons (1,564 hourly records) and thevalidating subset has 10 typhoons (620 hourly records). According to these datasets, fourweight sets by BPNN are trained with the number of three-layer nodes (see Table 3). TheBPNN is trained using the BFGS Quasi-Newton algorithm with training cycles = 8,000 andlearning rate = 0.2 as implemented within the software Matlab. The performance is assessedusing the criterion of root mean square error (RMSE), that is

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNj¼1

LsimðjÞ � LobsðjÞð Þ2

N

vuuutð22Þ

where Lsim(j) is the simulated water level at record j, Lobs(j) is the observed water level atrecord j, and N is the number of hourly records.

During the training processes, the weights gradually converge to values in which inputvectors produce output values as close as possible to the target output desired. The resultsof training and validation can be seen in Table 3. Moreover, Fig. 6 depicts the scattered

Table 2 Various lag-time lengths at control points

Gauge station Lag-time length (h)

ζ1 ζ2 ζ3 ζ4 ζ5 ζ6

Control-point 1 2 0 0 0 0 2Control-point 2 0 1 0 1 0 2Control-point 3 3 2 0 2 2 2Control-point 4 4 3 1 3 1 2

Table 3 BPNN parameters and performances for four control points

Gauge station Number of nodes Root mean square error (RMSE)

Input layer Hidden layer Output layer Training phase Validation phase

Control-point 1 4 6 1 0.119 0.298Control-point 2 4 6 1 0.116 0.200Control-point 3 11 8 1 0.104 0.143Control-point 4 14 10 1 0.085 0.087



plots of observation versus simulation of training and validation. By means of weightcalibration, the linear channel level routing formulas at the four control points are obtained.

5 Comparison with CCCMMOC Model

Prior to making the comparison, the CCCMMOC model is briefly introduced. As describedin Section 1, the CCCMMOC model is a powerful model for simulating river flow. Asmentioned above, the CCCMMOC model deals with the compound–complex channelsystem according to the multimode method of characteristics. Essentially, the governingequations of this one-dimensional model are derived from Saint–Venant equations, whichconsist of the two following partial differential equations (i.e., continuity and motion;Lai 1986):

B@h

@tþ @Q

@x¼ q ð23Þ

@Q

@tþ Q

A

@Q

@xþ Q

@

@x

Q

A

� �þ gA

@h

@x¼ gA Sb � Sf

� �þ qu' ð24Þ

where B is the width of the river cross-section, h is the flow depth (i.e., the difference inelevation between water surface and channel bottom), Q is the river flow, q is the lateral flowper unit length, A is the cross-sectional area, g is the acceleration of gravity, Sb is the bed slopeof channel, Sf is the slope of energy gradient, and u′ is the lateral flow velocity in the x-direction. In order to solve this problem, Lai developed the multimode method of character-istics for multiple-reach rivers and estuaries. The details can be found in Lai (1965, 1986, 1988).

In here, the CCCMMOC model is applied to the Tanshui River system, which is dividedinto 17 reaches. Each reach corresponds to a resistance coefficient, which has beencalibrated and verified by Lai (1999). The Hsinhai Bridge, Showlan Bridge, Bao Bridgeand Tawa Bridge (the locations see Fig. 1) are used as the upstream boundaries, and Hekouis the only downstream boundary. Typhoon Xangsane in 2000 is used for simulating thevariations in water level at control-points 3 and 4. Figure 7 shows the simulation results ofthe CCCMMOC model as well as the neural-based linear channel level routing. Incomparison, the results of the linear channel level routing are slightly less accurate thanthose obtained by the CCCMMOC model. However, the neural-based linear channel levelrouting demonstrates that it is still a good alternative method.

6 Application

Typhoons Aere in 2004 and Nari in 2001 are first selected for applying the proposedoptimization model. Both typhoons were unusually extreme typhoons attacking Taiwan.Table 4, Figs. 8 and 9 display the related hydrological characteristics of the two typhoons inTanshui River Basin system. Typhoon Aere contains a single peak event in the tworeservoir inflow hydrographs (see Fig. 8a,b) while typhoon Nari has two peak events (seeFig. 9a,b).

�Fig. 6 Comparisons of observation vs. simulation in training and validation phases: (a), (c), (e), and (g) aretraining of Control-points 1, 2, 3 and 4, respectively; (b), (d), (f), and (h) are validation of Control-points 1,2, 3 and 4, respectively


The two typhoon cases are solved by the commercial optimization software, LINGO. Itis capable of solving linear, nonlinear, and integer programming problems. LINGO uses thebranch-and-bound algorithm to deal with the integer variables (LINGO 2001). Thecomputing time of each typhoon case with a Pentium M 1.70 GHz processor is 70 sapproximately. Comparisons are made between the records and results obtained by theoptimization model. Figures 10, 11, 12 and 13 show the results of typhoons Aere and Nari

Fig. 7 Comparisons of neural-based channel routing and CCCMMOC model running during typhoonXangsane: (a) is water-level hydrograph at Control-point 3; (b) is water-level hydrograph at Control-point 4

Table 4 Characteristics of six typhoons

Typhoon Date Floodduration(h)

Reservoir 1 Reservoir 2 Estuaryhighestlevel (m)Maximum

inflow (m3/s)Initialstorage (106 m3)

Maximuminflow (m3/s)

Initialstorage (106 m3)

Herb 1996/07/30 93 6360 153.2 2590 276.8 2.51Zeb 1998/10/15 85 4650 214.0 2640 342.7 2.51Xangsane 2000/10/31 61 1850 193.0 2640 300.9 1.55Nari 2001/9/16 106 4110 187.2 3500 261.8 2.07Aere 2004/8/23 82 8600 234.4 2650 294.9 1.78Haima 2004/09/11 53 1640 229.0 1340 331.3 1.56


with respect to the reservoir storage and release hydrographs as well as the control-pointlevel hydrographs, respectively.

In Figures 11 and 13, the model results of the maximal levels of control-points 1 to 4exhibit more positive findings than the records in reducing the downstream floodwaters.Moreover, for meeting reservoir target storage at the end of flood, Figs. 10a,b and 12a,bshow the results derived from the proposed model for reservoirs 1 and 2.

It should be pointed out that for the water level at control-points 3 and 4 (i.e., TaipeiBridge and Tudigong, respectively) in Typhoons Aere and Nari (see Figs. 11c,d and 13c,d),the difference between records and optimal values are limited. The reason, as mentioned

Fig. 8 Hydrologic observations during typhoon Aere: (a), (b), (c) and (d) are inflow hydrographs at Inflow1, Inflow 2, Tributary, and all laterals, respectively; (e) is water-level hydrograph at Estuary


above, is that control-points 3 and 4 are close to the estuary, resulting in the influence oftide being much greater than that of upstream floodwater movement. On the contrary, thewater level at control-points 1 and 2 (i.e., Sanying and Showlan Bridge, respectively) aresensitive to reservoir releases, but are not sensitive to tidal effect. In order to justify thisphenomenon, the simple sensitivity analysis can be made. For example, in typhoon Aere,provided that the maximum releases from reservoir 1 (i.e., 6,210 cm of maximum release inFig. 10c) are changed from 4,000 cm to 9,000 (if the upstream reservoir operations are notconsidered), results of sensitivity analysis can be plotted in Fig. 14. As can be seen, themaximum water-level variations are from 36.64 to 41.54 m (the difference is 4.90 m) in

Fig. 9 Hydrologic observations during typhoon Nari: (a), (b), (c) and (d) are inflow hydrographs at Inflow1, Inflow 2, Tributary, and all laterals, respectively; (e) is water-level hydrograph at Estuary


control-point 1, from 5.02 to 5.85 m (the difference is 0.83 m) in control-point 3, and from2.48 to 2.70 m (the difference is 0.22 m) in control-point 4. Apparently, the maximumwater-level variations in upstream control-point (i.e., control-point 1) are more sensitivethan those in downstream control-points (i.e., control-points 3 and 4).

Additionally, this paper analyzes other four typhoons, including Herb of 1996, Zeb of1998, Xangsane of 2000, and Haima of 2004 (for hydrological characteristics, see Table 4).In order to assess the performance of the optimization model, several criteria are taken intoaccount, which are defined as follows.

& Control-point maximum level reduction rate (LR)

LR %ð Þ ¼ L*� Lmax

L*� 100 ð25Þ

where Lmax is the control-point maximal level during flood, and L* is the control-pointmaximal level under the assumption that there is no upstream reservoir. L* can be

Fig. 10 Comparisons with optimization model running and historical records for reservoirs during typhoonAere: (a) and (c) are storage and release hydrographs at Reservoir 1, respectively; (b) and (d) are storage andrelease hydrographs at Reservoir 2, respectively


derived from linear channel level routing (i.e., Eq. 13) by substituting reservoir inflowsfor reservoir releases.

& Reservoir target storage meeting rate (TM)

TM %ð Þ ¼ Send

Starget� 100 ð26Þ

where Send is the reservoir storage at the end of flood, and Starget is the target storageduring normal periods.

Generally, the higher the criterion is, the greater the performance is. Figure 15 shows thebar charts concerning the performance of optimization model and records of six typhoons.Clearly, the results obtained by the proposed model are better than the records.

Fig. 11 Comparisons with optimization model running and historical records for control-points duringtyphoon Aere: (a), (b), (c) and (d) are water-level hydrographs at Control-points 1, 2, 3 and 4, respectively


7 Conclusions

This paper develops a multipurpose multireservoir optimization model which is formulatedas a mixed-integer linear programming (MILP) for basin-scale flood control. The modelobjectives include preventing reservoir dam from overflow, reducing the downstreamfloodwaters, and meeting reservoir target storage at the end of flood. The optimizationmodel is employed to determine the reservoir releases. The model constraints includereservoir multipurpose flood control operation and channel routing under tidal effects. Thispaper presents a neural-based linear channel level routing algorithm developed from artificialneural networks (ANN) for estimating the water level of downstream. In order to formulate alinear channel level routing, the proposed neural-based linear channel level routing algorithmdemonstrates a good alternative method in comparison with the CCCMMOC model.

The paper makes two main contributions. First, the estuary tidal effects in theoptimization model are considered. Second, a neural-based linear channel level model forreplacing the simulation model, such as the CCCMMOC model, for optimization isdeveloped.

Fig. 12 Comparisons with optimization model running and historical records for reservoirs during typhoonNari: (a) and (c) are storage and release hydrographs at Reservoir 1, respectively; (b) and (d) are storage andrelease hydrographs at Reservoir 2, respectively


Fig. 13 Comparisons with optimization model running and historical records for control-points duringtyphoon Nari: (a), (b), (c) and (d) are water-level hydrographs at Control-points 1, 2, 3 and 4, respectively

Fig. 14 Sensitivity analysis onmaximum release from reservoir 1


Fig. 15 Comparisons of performance in six typhoons: (a), (b), (c) and (d) are results of LR at Control-points1, 2, 3 and 4, respectively; (e) and (f) are results of TM at Reservoirs 1 and 2, respectively


The developed model has been applied to the Tanshui River Basin system in Taiwanusing the observed hydrological data of six typhoons. The optimization model demonstratessuccessfully its practicability for the problem of multipurpose multireservoir flood controlunder tidal effects in contrast to records. For future studies, this paper suggests that theproposed generalized optimization model can be used in real-time flood control operationsto identify the multireservoir real-time releases at each flood period.

Acknowledgement This work was partially supported by the National Science Council, Taiwan (grant no.NSC93–2625-Z-231-001). We would like to thank Professor Lai (National Taiwan University) for hisassistance in this study. In addition, the authors are indebted to the reviewers for their valuable comments andsuggestions.

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Multireservoir Flood-Control Optimization with Neural-Based Linear Channel Level Routing Under Tidal Effects