Optimal tree-based release rules for real-time flood control operations on a multipurpose multireservoir system

Journal of Hydrology 365 (2009) 213–224

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Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol

Optimal tree-based release rules for real-time flood control operations on a multipurpose multireservoir system Chih-Chiang Wei a, Nien-Sheng Hsu b,* a b

Department of Information Management, Toko University, No. 51, Sec. 2, University Rd., Pu-Tzu City, Chia-Yi County 61363, Taiwan Department of Civil Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei 106, Taiwan

a r t i c l e

i n f o

Article history: Received 24 November 2007 Received in revised form 20 November 2008 Accepted 25 November 2008

Keywords: Flood control Decision-tree algorithm Release rules Reservoir operation

s u m m a r y This study presents a methodology to establish a set of optimal operation release rules which are treebased rules for real-time flood control on a multipurpose multireservoir system. The derived rules can be used to determine the optimal real-time releases during flood periods. Steps of the proposed methodology involve: (1) collection of data, (2) building of flood database, (3) generation of optimal input– output patterns by running the flood control optimization model, (4) classification of training and testing data, (5) extraction of tree-based release rules for designed scenarios using the decision-tree algorithm (C5.0), (6) determination of optimal tree-based rules, (7) generation of the real-time forecast data by using the hydrological forecast model, (8) processing of reservoir real-time releases by simulating the reservoir real-time flood control operation, and (9) verification of the superior release rules through comparisons of tree-based rules, regression-based rules derived from a multiple-linear regression model and existing release rules. The developed methodology is applied to the Tanshui River Reservoir System in Taiwan to extract the decision trees for each scenario and then select the best ones with highest accuracy as the optimal tree-based rules. The derived optimal tree-based rules, regression-based rules and existing rules are compared by conducting the real-time operations in three historical typhoons, including Aere, Haima and Nock-ten in 2004. Results demonstrate that the solution using the derived tree-based rules have better performance than the regression-based rules and the existing rules in terms of reducing the peak stage at downstream control points, and meeting the target reservoir storage at the end of flood. Ó 2008 Elsevier B.V. All rights reserved.

Introduction Taiwan has subtropical climate and high mountains with steep slopes all over the island. The most severe disaster in Taiwan is flooding caused by typhoons. Once a typhoon strikes, due to receiving voluminous rainfalls from upstream watersheds, considerable upstream flows usually converge downstream within a few hours. To reduce the downstream peak flow, reservoirs have been built to serve for flood control purpose during typhoon. However, the water level at the downstream may rise abnormally if the upstream reservoirs are not operated properly. With all these unfavorable conditions, it has been one of the challenges for engineers to release such voluminous water wisely from the multireservoir systems into ocean to mitigate the downstream flood disaster. Currently, the most common release strategy for reservoir flood control operations in Taiwan involves predefined operation rules, such as the release look-up tables for flood control, where * Corresponding author. Tel.: +886 2 33662640; fax: +886 2 33665866. E-mail addresses: [email protected], [email protected] (N.-S. Hsu). 0022-1694/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2008.11.038

releases are expressed as a function of reservoir variables (water levels) and hydrological inputs (reservoir inflows). As an example, Water Resources Agency (WRA, 1984) stipulated flood control operation rules for the Shihmen Reservoir in order to mitigate flood damage. The flood control operation rules (called the ‘‘existing rules” in this paper) adopt the release look-up tables for each of two flood stages (i.e., peak-flow-preceding stage and the peakflow-proceeding stage) to standardize the water releases during typhoon periods. These release tables are graded by total forecasted rainfall, the observed storage level, and the reservoir inflow during flood periods. Although, using these predefined operation rules is straightforward, the ranges between the release look-up tables are too large to operate the release of a reservoir precisely (Chang and Chang, 2001). Another problem is that in the multiple-reservoir systems each reservoir usually has individual release rules for its operation purposes; for example, in Tanshui River Reservoir System, the two reservoirs (i.e., Shihmen and Feitsui reservoirs) stipulated the release rules separately. During extreme flood events, it has difficulty for operators in identifying the best joint release policy to mitigate downstream flood hazard.

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To derive the operation rules for a reservoir system, the decision-tree algorithm is one of the novel technologies. The decisiontree algorithm is a powerful and popular approach for classification and prediction (Apté and Weiss, 1997; Bradford and Fortes, 2001). Decision trees extracted by the decision-tree algorithm can be used to assist decision-makers to make proper decisions. It has been widely applied to decision judgments, screening images, load forecasting, diagnosis, marketing and sales and so on (Witten and Frank, 1999). In the field of water resources management, Solomatine et al. (2000) built decision trees in classifying surge water levels in the coastal zone depending on the hydrometeorological data. Bessler et al. (2003) built the release operation rules of water supply for a multireservoir system using the decision-tree algorithm. In order to establish the optimal operation rules of flood control during typhoon periods for a multipurpose multireservoir system, a methodology for deriving tree-based rules is developed in this article. The derived optimal tree-based rules are compared with classical regression-based rules and existing rules by conducting the real-time operations in historical typhoons. In this study, the tree-based rules are extracted by the decision-tree algorithm (i.e., induction tree technique, C5.0, the C4.5 commercial version) as described in Quinlan (1993, 1996). The developed methodology is applied to the Tanshui River Reservoir System in Taiwan.

Development of methodology Procedures of the methodology In this section, a methodology is presented for extracting the optimal release rules of real-time flood control for a multipurpose multireservoir system. Fig. 1 illustrates the flowchart of the proposed method. Each step in Fig. 1 can be thoroughly described as follows. Step 1: collect data. The related data collected include reservoir data, historical flood events, and existing reservoir release rules. Reservoir data involve the capacities of the hydraulic facilities and the relationships between storage and water level. Historical flood events comprise hydrological hydrographs (including reservoir storage levels, reservoir inflows and outflows, lateral flows, water levels of downstream control points and estuary). Step 2: build flood database. This database is built to refine the collected data (from Step 1). The data mining process requires the domain expert to perform good selection and preprocessing of data (Fayyad et al., 1996). That is to say, an important step to ensure the success of extracting release rules is to identify the selection and preprocessing steps for the data set. Step 3: construct the flood control optimization model to obtain the optimal input–output patterns. The formulation of this deterministic model formulated as the mixed-integer linear programming (MILP) problem is described in ‘‘Flood-control optimization model”. Then, the optimization model using the data from Step 2 runs to obtain the optimal release hydrographs. The optimization model is carried out by the LINGO solver (Lindo Systems Inc., 2001). Step 4: Classify the optimal patterns into training and testing datasets. The optimal patterns obtained from Step 3 are separated into two datasets. The first dataset is used for training rules and the second dataset is used for testing the extracted tree-based rules. Step 5: Construct the decision-tree model to extract the treebased release rules for designed scenarios using training dataset. Two terms are defined in this study. The ‘‘attribute” (or called ‘‘variable”) refers to a single data item common to all cases under consideration, and the ‘‘case” (or called ‘‘record”) is the collection of attribute values of a specific case. To train a C5.0 decision-tree model, one or more In attributes (inputs) and one Out attribute

Fig. 1. Flowchart of the developed methodology for extracting optimal reservoir release rules.

(output or target) are needed. For C5.0, the In attribute can be numerical or symbolic (or categorical and nominal) type but the Out attribute must be symbolic. The principle of constructing decision trees is described in ‘‘Decision-tree model”. The C5.0 algorithm is performed using the Clementine software (SPSS Inc., 2002). In this step, to extract the release rules for flood control, three sub-steps are described as follows. 5a. Find the attributes that possibly affect the behavior of reservoir releases during flood, such as water storage and reservoir inflow. 5b. Design various scenarios under the considerations of different combinations of attributes. 5c. Utilize the C5.0 algorithm to extract the graphical ‘‘tree” (the tree-based rules) for each scenario using the training dataset. Step 6: Determine the optimal tree-based rules by using testing dataset. In order to determine the optimal rules, three sub-steps are made as follows. 6a. Define the performance criterion ‘‘Accurate” as

Accurate ð%Þ ¼

Correct trials Total simulation trials

ð1Þ

where ‘‘Accurate” is the percentage of correct classification for total trials; ‘‘Total simulation trials” denotes the total number of simulation trials (cases); and ‘‘Correct trials” is the number of simulation

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runs that match the optimal obtained by running the optimization model. 6b. Utilize the testing dataset (from Step 4) as inputs to the derived tree-based rules of each scenario (from Step 5). 6c. Determine the optimal scenario (trees) according to the highest accuracy of all scenarios. Step 7: Construct multiple-linear regression model. For comparisons with the optimal tree-based rules, the multiple-linear regression model is used. The variables of the multiple-linear regression equations are the same as those attributes of the tree-based rules. Step 8: Determine the regression-based rules by using testing dataset. Using these generated regression-based rules, we can solve the best fitting for predicting the outputs (releases) according to the inputs (see ‘‘Regression-based rules generated by multiplelinear regression model”). Step 9: Construct the hydrological forecast model to obtain the hydrological forecast data. In order to simulate the reservoir realtime operations during flood periods, generation of hydrological forecasts in advance is necessary. To obtain the hydrological forecasts, the real-time recurrent learning (RTRL) neural network algorithm (see ‘‘Hydrological forecast model”) is employed. The RTRL model is carried out by the MATLAB software. Step 10: Simulate the reservoir real-time flood control operations to obtain reservoir real-time releases. For conducting the processes of reservoir real-time release by using the derived optimal tree-based rules, regression-based rules and existing rules, several historical typhoons are employed. The steps of processing realtime release operations are described in ‘‘Real-time operation procedure”. Step 11: Verify the superior release rules for flood control. The results conducted by the three rules (i.e., optimal tree-based rules, regression-based rules, and existing rules) are compared to verify the superiority of the rules. In the following sections, the above-mentioned flood control optimization model, decision-tree model and hydrological forecast model are described. Flood control optimization model This deterministic linear programming model is employed to identify the optimal reservoir release hydrographs during flood. Wei and Hsu (in press) formulated a mixed-integer linear programming (MILP) model to determine the optimal real-time reservoir releases for a reservoir system during typhoon in Taiwan. This study employs their proposed model. The formulation can be summarized as below. Objective function The two objectives considered in the model are: (1) reducing downstream floodwaters at control points, and (2) meeting reservoir target storage at the end of flood. The composite objective function using dimensionless method can be formulated as

Min

X k;k2X

Lpk

þ bank

Lk

X Esi;t i;i2K

Starget i

ð2Þ

where k is the index of the control points; i is the index of reservoir; t is the index of time point; X is the set of control points; K is the set of reservoirs; Lpk is the maximum water level at the selected control points during flood; Esi;t is the target storage error, which is the difference between storage and target value during the specific time is the elevation of interval at the flood ending periods; Lbank k is the target storage in embankment at control point k; and Starget i normal periods at reservoir i.

The above two min–max problems (sub-objectives) should be subjected to

Lk;t 6 Lpk

k 2 X;

t 2 ½t 0 ; T

 Esi;t 6 Si;t  Starget 6 Esi;t i

i 2 K; t 2 ½t b ; T

ð3Þ ð4Þ

where t0 is the starting time for operation; tb is the starting time for regulating storage; T is the flood duration; Lk,t is the water level at control point k; and Si,t is the reservoir storage. Note that the time tb is between the ending time of the peak-flow-preceding stage (ta) and flood duration (T). Constraints (1) Reservoir routing  Continuity constraints The general form of reservoir continuity constraints associated with natural inflow (Ii,t), artificial inflow (from upstream reservoir release) (Q iu ;t ), release (Ri;t ) and storage (Si;t ) can be expressed as the finite difference formula

ðIi;t þ Ii;tþ1 Þ þ ðQ iu ;t þ Q iu ;tþ1 Þ  ðRi;t þ Ri;tþ1 Þ ¼

2 ðSi;tþ1  Si;t Þ i 2 K; t 2 ½t 0 ; T Dt

ð5Þ

where iu is the index of upstream reservoir which is connected to downstream reservoir i; and Dt is a time interval in hours for routing. The whole control horizon is the time length between t0 and T.  Physical constraints ) to dead The reservoir storage ranges from full storage (Smax i ) over the control horizon, that is storage (Sdead i

Sdead 6 Si;t 6 Smax i i

i 2 K; t 2 ½t 0 ; T

ð6Þ

 Institutional constraints In order to implement the reservoir flood operations in Taiwan, the reservoir release guidelines (WRA, 2002; TCG, 2004), describing the release rate of change, are employed. There are two release policies in two flood stages, as below Peak-flow-preceding stage: releases are for mitigating disaster and maintaining dam safety. Two release policies are stipulated: (1) the reservoir release is less than or equal to the reservoir inflow and (2) the release of the current period is greater than that of the previous period. The constraints can be integrated as

Ri;t1 6 Ri;t 6 Ii;t

i 2 K; t 2 ½t 0 þ 1; t a 

ð7Þ

where ta is the ending time of the peak-flow-preceding stage when reservoir peak inflow occurs. Peak-flow-proceeding stage: releases are to regulate the storage for future water use. Two release policies are stipulated: (1) the release at each period is less than the reservoir peak inflow and (2) the release of the current period is less than that of the previous period. The constraints can be integrated as

Ri;t 6 Ri;t1 6 Ipeak i where

Ipeak i

i 2 K; t 2 ½ta þ 1; T

ð8Þ

is the peak inflow at reservoir i.

(2) River routing The river routing incorporated in the model can be divided into: routing without tidal effects and routing with tidal effects.

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 Routing without tidal effects To deal with stream flow routing along a reach without tidal effects such as river movement between two reservoirs, the Muskingum linear channel routing (McCarthy, 1938) is employed, that is

When routing along a reach close to the coast under tidal influence, the variations of the water level (Lk,t) in the downstream station can be a function of the reservoir releases (Ri;tdi ), local flows (Il;tdl ), estuary levels (Lm;tdm ), control point levels (Lk;tdk ), and time delay. From Eq. (11), the formula of the linear channel level routing can be expressed as

Q i;t ¼ c0  Ri;t þ c1  Ri;t1 þ c2  Q i;t1

Lk;t ¼

i 2 K; t 2 ½t 0 þ 1; T

ð9Þ

where c0, c1, and c2 are channel routing coefficients. The summation of c0, c1, and c2 should be equal to 1.

XX i;i2K

þ

wk;di Ri;tdi þ

di

X

XX l;l2C

wk;dk Lk;tdk

wk;dl Il;tdl þ

dl

k2X

X

wk;dm Lm;tdm

dm

ð12Þ

dk

 Routing with tidal effects To solve the complicated flow routing under the interaction between upstream flows and tidal effects, Lai (1986, 1999, 2002) developed a gradually varying unsteady flow model, which deals with the Compound-Complex Channel (network or dendritic) system according to the Multimode Method Of Characteristics (in short, CCCMMOC; for details, see Wei and Hsu (in press)). The CCCMMOC model demonstrates that it is good at analyzing accurately the variations in water surface elevation under unsteady channel flow. The physical-based model however is mathematically a highly complicated, non-linear numerical model in space and time. Therefore, it is not suitable for embedding it into the proposed linear multireservoir operation model. Wei and Hsu (in press) proposed a neural-based linear channel level routing algorithm. Their routing developed from the feed-forward back-propagation neural network (BPNN) is employed to estimate the downstream water levels under tidal effects. Fig. 2 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 with N1 input nodes, N2 hidden nodes, and N3 output nodes, can be expressed as (Xu and Li, 2002)

yr ¼ f2

N2 X

w2qr

q¼0

 f1

N1 X

!! w1pq

 xp

r 2 ½1; N3 

ð10Þ

p¼0

where p is the index of input nodes, q is the index of hidden nodes, r is the index of output nodes, xp is the input node of the input layer, w1pq is the weight set connecting the input layer and hidden layer, w2qr is the weight set connecting the hidden layer and output layer, yr denotes the outputs from the network, f1() is the activity function of the hidden layer, and f2() is the activity function of the output layer. The commonly used activity function includes linear, sigmoid and hyperbolic tangent. Wei and Hsu (in press) introduce the linear activity function for this algorithm. Thus, Eq. (10) can be rewritten as

yr ¼

N2 X N1 X

w2qr  w1pq  xp

r 2 ½1; N3 

q¼0 p¼0

ð11Þ

where l is the index of the local flows; m is the index of the estuary; C is the set of local flows; di, dl, dm, and dk are the lag-time indices of reservoir releases, local flows, tidal forces, and control point levels, respectively, and wk;di ; wk;dl ; wk;dm ; and wk;dk are the weighting coefficients for reservoir releases, local flows, tidal levels, and control point levels, respectively. Wei and Hsu (in press) pointed out that, in comparison, the results of the linear channel level routing are slightly less accurate than those obtained by the CCCMMOC model. However, the neural-based linear channel level routing demonstrates that it is still a good alternative method. Decision-tree model Decision-tree algorithm identifies nuggets of information in bodies of data and extracts information in such a way that it can be used in areas such as decision support, prediction, forecasts, and estimation (SPSS Inc., 2002). There are various decision-tree algorithms, such as ID3, CART, OC1, and C4.5, which are greed local search algorithms with trees constructed top-down (Rissanen and Wax, 1998; Sreerama, 1998). They are usually constructed beginning with the top of the tree and proceeding down to its leaves. Each branch represents a decision and each leaf (or node) has a classifier value. C4.5 uses a divide-and-conquer approach to growing decision trees that was pioneered by Hunt and his co-workers (Hunt et al., 1966). Only a brief description of the method is given here; see Quinlan (1993) for a more complete treatment. The default splitting criterion used by C4.5 is gain ratio, an information-based measure that takes into account different numbers (and different probabilities) of test outcomes. Let C denote the number of classes and p(D, j) the proportion of cases in a set D of cases that belong to the jth class. Some test T with mutually exclusive outcomes T1, T2, . . ., Tk is used to partition D into subsets D1, D2, . . ., Dk, where Di contains those cases that have outcome Ti. The tree for D has test T as its root with one subtree for each outcome Ti that is constructed by applying the same procedure recursively to the cases in Di (Quinlan, 1996). The residual uncertainty about the class to which a case in D belongs can be expressed as

InfoðDÞ ¼ 

C X

pðD; jÞ  log2 ðpðD; jÞÞ

ð13Þ

j¼1

and the corresponding information gained by a test T with k outcomes as

GainðD; TÞ ¼ InfoðDÞ 

Fig. 2. Architecture of BPNN.

k X jDi j  InfoðDi Þ jDj i¼1

ð14Þ

The information gained by a test is strongly affected by the number of outcomes and is maximal when there is one case in each subset Di. On the other hand, the potential information obtained by partitioning a set of cases is based on knowing the subset Di into which a case falls; this split information

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SplitðD; TÞ ¼

  k X jDi j jDi j  log2 jDj jDj i¼1

ð15Þ

tends to increase with the number of outcomes of a test. The gain ratio criterion assesses the desirability of a test as the ratio of its information gain to its split information, as below

GainRatioðD; TÞ ¼

GainðD; TÞ SplitðD; TÞ

Hydrological forecast model The real-time recurrent learning (RTRL) algorithm proposed by Williams and Zipser (1989) includes dynamic internal feedback loops to train the weighting parameters; that is, the output values out of the hidden layer can return to input layer as new input data. Recently, RTRL neural network has been demonstrated the efficiency and practicability in a variety of hydrological prediction problems (Chang et al., 2002; Chiang et al., 2004; Hsu and Wei, 2007; Karamouz et al., 2008). Consider a three-layer fully interconnected recurrent neural network as shown in Fig. 3, which includes M external inputs, N hidden neurons and K outputs (Chang et al., 2002). Let x(t) denote the M  1 input vector to the network at discrete time t, z(t + 1) denote the corresponding K  1 output vector and y(t + 1) denote the corresponding N  1vector one-step later at time t + 1 in the processing layer. The input x(t) and one-step delayed output vector in the processing layer y(t) are concatenated to form the (M + N)  1 vector l(t), in which the ith element is denoted by li(t). Let A denote the set of indices i for which xi(t) is an external input, and B denote the set of indices i for which yi(t) is the output of a unit in the network. That is

li ðtÞ ¼

xi ðtÞ if i 2 A yi ðtÞ if i 2 B

X

netj ðtÞ ¼

ð17Þ

wji ðt  1Þ  li ðt  1Þ

ð18Þ

i2A[B

ð16Þ

The gain ratio of every possible test is determined and, among those with at least average gain, the split with maximum gain ratio is selected. In other words the gain ratio expresses the number of bits gained divided by the number of bits consumed by using a certain input variable for partitioning. The variable having the highest gain ratio is considered to be best. The recursive partitioning strategy above results in trees that are consistent wit the training data, if this is possible. In practical applications data are often noisy, that is, attribute values are incorrectly recorded and cases are misclassified. Noise leads to overly complex trees that attempt to account for these anomalies. Most systems prune the initial tree, identifying sub-trees that contribute little to predictive accuracy and replacing each by a leaf.



The network is fully interconnected. There are M  N forward connections and N  M feedback connections. Let V and W denote the N  K weight matrix and N  (M + N) recurrent weight matrix, respectively. The net activity of neuron j at time t, for j e B, is computed by

The output of neuron j in the processing layer is given by passing netj(t) through the non-linear transfer function f(), yielding

yj ðtÞ ¼ f ðnetj ðtÞÞ

ð19Þ

The net output of neuron k in the output layer at time t is computed by

netk ðtÞ ¼

X

kkj ðtÞ  yj ðtÞ

ð20Þ

zk ðtÞ ¼ f ðnetk ðtÞÞ

ð21Þ

Detailed information on the RTRL algorithm can be found in Williams and Zipser (1989) and Chang et al. (2002). In this study, RTRL model is applied to predict hourly data of upstream inflows (including reservoir inflows and local inflows) and estuary water levels. For prediction of upstream inflows, the hourly data of time-delay inflows are used as inputs. Briefly, the RTRL models can be represented as

9 > > > > > > =

^Ij;s ¼ RTRL1 ðIj;s1 ; Ij;s2 ; . . . ; Ij;sD Þ j ^Ij;sþ1 ¼ RTRL2 ð^Ij;s ; Ij;s1 ; . . . ; Ij;sD þ1 Þ j

ð22Þ

.. .. > > > . . > > ; ^Ij;sþK1 ¼ RTRLK ð^Ij;sþK2 ; ^Ij;sþK3 ; . . . ; ^Ij;sþKD 1 Þ > j

where ^Ij;s is the predicted inflow j at time period s; Ij;s1 is the observed inflow j at time period s  1; Dj is the delay time of upstream inflow j; and K is the number of hours of foresight on inflows (let K = 6). For prediction of estuary water levels, the hourly data of timedelay water levels are used as inputs. Similarly, the RTRL models can be represented as

^Lm;s ¼ RTRL0 ðLm;s1 ; Lm;s2 ; . . . ; Lm;sD Þ m 1 ^Lm;sþ1 ¼ RTRL0 ð^Lm;s ; Lm;s1 ; . . . ; Lm;sD þ1 Þ

9 > > > > > =

.. . ^Lm;sþK1

> > > > > ;

2

m

.. . ¼ RTRL0K ð^Lm;sþK2 ; ^Lm;sþK3 ; . . . ; ^Lm;sþKDm 1 Þ

ð23Þ

where Lm;s1 is the estuary water level at time period s  1; ^Lm;s is the predicted estuary water level at time period s; and Dm is the delay time of the estuary m. Application of methodology In this section, the application of the developed methodology to the Tanshui River Reservoir System is demonstrated. By adopting the proposed method, this study establishes separate tree-based rules for both peak-flow-preceding stage and peak-flow-proceeding stage in the Shihmen and Feitsui Reservoirs. Study area

Fig. 3. Architecture of RTRL network.

The Tanshui River Reservoir System located in northern Taiwan is shown in Fig. 4. Tanshui River with a drainage area of 2726 km2 comprises three major tributaries: Tahan River, Hsintien River and Keelung River. In Tanhan River, there are the Shihmen Reservoir and three creeks; and in Hsintien River, there are the Feitsui Reservoir and three creeks. The major stream flows of Tanshui River go through Taipei Bridge Station and Tudigong Station, and finally

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Fig. 4. Map of Tanshui River Basin.

reach the estuary (Hsu and Cheng, 2002). For the two stations (i.e., Taipei Bridge and Tudigong), the variations in water level are strongly affected by tide (since close to estuary). In this basin, the parallel Shihmen and Feitsui Reservoirs, currently managed by the Water Resources Agency (WRA) and Taipei City Government (TCG), have been used for joint flood control operations in the Taipei Metropolitan Area with a population of six million. The characteristics of the two reservoirs are as follows.  The Shihmen Reservoir was completed in 1964. The maximum water volumes for normal and flood-mitigation operations are 254.0  106 m3 and 280.8  106 m3, respectively.

 The Feitsui Reservoir was completed in 1987. The maximum water volumes for normal and for flood-mitigation operations are 388.2  106 m3 and 397.3  106 m3, respectively.

Existing operation rules In order to mitigate flood damage, WRA (1984) and TCG (2004) stipulated flood control operation rules for the Shihmen and Feitsui Reservoirs, respectively. As mentioned previously, the existing rules include two main flood stages: the peak-flow-preceding stage and the peak-flow-proceeding stage. These release tables are first

Table 1 Part of Shihmen Reservoir operation rules in flood periods (Peak-flow-preceding stage, rainfall level II). Reservoir release (m3/s)

Reservoir inflow (m3/s)

Storage level, m

<237.5 237.5–240 240–243 243–245 >245

<600

600–1100

1100–1600

1600–2100

2100–2600

2600–3100

3100–3600

3600–4100

4100–4600

>4600

0 0 0 0 0

0 600 600 600 600

0 600 600 600 800

100 600 600 1000 1200

100 600 1000 1000 1200

200 1000 1000 1500 1800

500 1000 1500 1500 1800

600 1500 1500 2000 2500

600 1500 1800 2000 2500

Switch to rainfall level III.

219

4 3

10 10 10

Class Class Class ... Class Class 990 990 990 ... 310 295

5 8 9 11 11 11 Class Class Class Class Class Class 488 789 822 1087 1087 1087

Feitsui Reservoir release amountb

Target

graded by the rainfall levels of 200 mm. There are six rainfall levels (IVI) and their corresponding precipitation ranges are: 0–200 mm, 200–400 mm, 400–600 mm, 600–800 mm, 800–1000 mm, and >1000 mm, respectively. At each rainfall level, the predefined releases are classified by the several intervals of both storage level and reservoir inflow (such as Table 1). Table 1 shows part of the operation rules for Shihmen Reservoir in flood periods (WRA, 1984). The predefined rules are usually derived through simulation using the historic observed flows prior to the construction of the reservoir. With these existing release lookup tables (i.e., operation rules), reservoir operators can easily obtain the real-time releases during flood. However, as mentioned before, the operation release rules for the two reservoirs are not joint flood control policies in reducing the downstream flood. That is to say, the floodwater from upstream reservoir operations does not take the lag effects into consideration at downstream control points.

Feitsui Reservoir release

C.-C. Wei, N.-S. Hsu / Journal of Hydrology 365 (2009) 213–224

-0.45 -0.39 -0.33 ... 0.37 0.32 0.38 -0.02 -0.34 ... 0.44 0.78 2109 1896 1581 ... 153 148 251.0 257.7 262.9 ... 258.9 258.2 380.7 383.8 386.2 ... 388.2 388.2 1409 1306 999 ... 314 291 h. m3/s. 106 m3. m. m/h. e

c

d

Unit: Unit: Unit: Unit: Unit: a

b

8 9 10 ... 41 42 Peak-flowproceeding

0.51 0.53 0.54 ... 0.99 1.00

0.38 0.35 0.24 0.08 -0.16 -0.25 0.18 0.54 0.80 0.96 0.93 0.74 2428 2020 2135 2344 2393 2358 219.9 221.8 226.7 232.3 237.4 243.5 360.9 362.8 365.3 368.6 372.7 377.0 800 934 1078 1418 1545 1622 1 2 3 4 5 6 Peak-flowpreceding

0.08 0.17 0.25 0.33 0.42 0.50

C-1 (lateralflow)b B-1 (storage)c A-2 (inflow)b A-1 (time)

Group-A (Feitsui Reservoir)

Attribute

Time perioda Flood stage

Fig. 5. Precipitation of 36 collected typhoon events from 1987 to 2004.

Table 2 Example of the attributes and target on Feitsui Reservoir.

Optimal input–output patterns According to ‘‘Flood control optimization model”, the reservoir flood control optimization model is applied to Tanshui River Basin

A-3 (storage)c

Group-C (Downstream)

Optimal tree-based rules

Group-B (Shihmen Reservoir)

In Tanshui River Basin, 18 years (1987–2004) of fully hourly historical hydrological data are available. During these years, 36 flood events, including typhoons and tropical storms have occurred. The average precipitation for each typhoon in Tanshui River Basin can be seen in Fig. 5. From the collected water level data, however, one can find that the reservoir water levels are often high (greater than the maximum normal level) at the starting operating time when a typhoon is approaching. That is because typhoons often occur during the wet season (from May through October). If the recorded water levels are used to generate the decision trees, it would not provide enough ‘‘good information” for proper database generation. That is to say, the critical situations (such as lower reservoir water levels) will never be considered when training trees. To create artificial lower water levels, this study sets four different water levels of starting operations, including maximum flood level, upper limit level, lower limit level, and extreme lower limit level, where the last three known limit levels are called ‘‘rule curves” which are used for the purposes of water supply and hydropower generation during normal periods in Taiwan (Hsu and Cheng, 2002).

C-2 (estuarylevel)d

C-3 (estuarytendency)e

Data preparation

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to generate the optimal reservoir release hydrographs for all datasets. Taipei Bridge and Tudigong Stations (see Fig. 4) are selected as the downstream control points in the model. It is noted that since the reservoir inflow distributions during flood are different in the Shihmen and Feitsui Reservoirs, the starting and ending operation times for the two reservoirs are not uniform. This condition causes difference in the total periods during the two flood stages (peak-flow-preceding and peak-flow-proceeding) for the reservoirs, as shown in Table 2. For all the optimal patterns of Shihmen Reservoir, 4603 hourly records (cases) are for the peak-flow-preceding stage and 12,293 hourly records are for the peak-flow-proceeding stage. For Feitsui Reservoir, 4577 hourly records are for the peak-flow-preceding stage and 15,539 hourly records are for the peak-flow-proceeding stage. Selected attributes For the complicated operation system, this study preliminarily selects several attributes to extract the rules for each of the two reservoirs. For Feitsui Reservoir, the selected input attributes are sorted into three groups: Feitsui Reservoir, Shihmen Reservoir, and downstream. Table 2 describes these attributes for a typical flood event (Typhoon Zeb in 1998) in the Feitsui Reservoir under optimized operation. The definitions of these attributes for each group and the target are described as follows.  Feitsui Reservoir (denoted as ‘‘Group-A”) Attribute time (denoted as ‘‘A-1”): Because the flood duration (T) of every typhoon varies greatly, ranging generally from 12 h to 5 days. To deal with such time scale, the flood period need to be non-dimensionalized. The attribute time is defined as

TimeðtÞ ¼ TimeðtÞ ¼

t 2t a 

1  t  ta

t  ta 2ðT  t a Þ

 þ 0:5 ta < t  T

Scenario

Attribute lateral-flow (C-1): The downstream lateral flows include Shanshia Creek, Heng Creek, Nanshih Creek, Gingmei Creek and Keelung River (see Fig. 4). For simplicity, this study lets the sum of these flows at each time period as an attribute. The unit of this attribute is in m3/s. Wang (1998) indicated that when the amounts of reservoir release are 20,008,000 m3/s, it takes around 3.85.5 h and 3.74.7 h for the floodwater released by Shihmen and Feitsui Reservoirs, respectively, to reach the estuary. His study revealed that the tidal table will be influenced during the time period between 3 and 6 h after the two reservoirs release. In view of this, the two tide-related attributes are considered as follows. Attribute estuary-level (C-2): This attribute is the average of estuary level from 3 to 6 h ahead, defined as 6 1X Ltþi 4 i¼3

where Ltþi is the estuary level at time period (t + i). Attribute estuary-tendency (C-3): This attribute is the average rate of change of estuary level from 3 to 6 h ahead. Here, the tendency values can be simply assumed as the average of the difference between the levels of third hour and of sixth hour (the time interval is 3 h), that is

Shihmen Reservoir

Feitsui Reservoir

Stage 1a

Stage 2b

Stage 1a

Stage 2b

88.32% 88.23% 91.85%

83.46% 87.09% 88.22%

92.15% 95.29% 97.42%

93.57% 95.25% 96.01%

Testing

1 2 3

56.46% 62.36% 63.22%

72.34% 71.37% 75.82%

67.29% 68.77% 73.41%

78.88% 80.42% 82.76%

Peak-flow-preceding. Peak-flow-proceeding.

 Downstream (Group-C)

ð25Þ

1 2 3

a

Attribute storage (B-1): When the Feitsui Reservoir releases water during flood, the status of the Shihmen Reservoir should be taken into consideration simultaneously for coordinated flood control operations. Here, the Shihmen Reservoir storage during the same time increment is selected as an attribute. The unit is in 106 m3.

Estuary-level ðtÞ ¼

Training

b

 Shihmen Reservoir (Group-B)

ð24Þ

Table 3 Accuracy for training and testing phases. Phase

where ta is the ending time at the peak-flow-preceding stage. From Eqs. (24 and 25), the time of the two flood stages are bounded in the range of [0, 0.5] and [0.5, 1], respectively. Attribute inflow (A-2): This attribute is the Feitsui Reservoir inflow during the same time increment. The unit is in m3/s. Attribute storage (A-3): This attribute is the Feitsui Reservoir storage during the same time increment. The unit is in 106 m3.

Estuary-tendency ðtÞ ¼

1 ðLtþ6  Ltþ3 Þ 3

ð26Þ

ð27Þ

 Target The Feitsui Reservoir release serves as the target for extracting Feitsui Reservoir rules. As mentioned in ‘‘Procedures of the methodology”, as the numerical-type target cannot be directly employed for the C5.0 algorithm, the target (i.e., release) should be treated as the symbolic type. For this purpose, this study divides the Feitsui Reservoir releases by 100 (m3/s) and rounds the quo-

Fig. 6. Flowchart of real-time flood control operation using release rules.

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Extracted optimal tree-based rules The data from the previous optimal input–output patterns are split into two parts: the training datasets (1987–2001, comprising 29 flood events) and testing datasets (2002–2004, comprising seven flood events). When using the Clementine software, the two important parameters are set as below.  Minimum records per child branch = 3, where the sizes of subgroups can be used to limit the number of splits in any branch of the tree. Increase this value to help prevent overtraining with noisy data.  Pruning severity = 75%, which determines the extent to which the generated decision tree will be pruned. Increase this value to obtain a small, more concise tree. Decrease it to obtain a more accurate tree. Table 3 lists the classification accuracy of the three scenarios analyzed. Overall, in both training and testing phases, the percentage of correctly classified records in Scenario 3 is the highest of these scenarios. As a result, the decision trees derived from Scenario 3 are chosen as the optimal tree-based rules. Four trees are extracted under Scenario 3, including rules with respect to two flood stages (peak-flow-preceding and peak-flow-proceeding) for the Shihmen and Feitsui Reservoirs. It is noted that Table 3 also shows results for the testing phase significantly lesser than the ones obtained for the training phase. The situation might be caused by the lack of sufficient historical typhoon records (reservoir inflows have been recorded since the Feitsui Reservoir was completed in 1987) for extracting more accurate decision trees. Regression-based rules generated by multiple-linear regression model Classically, regression techniques have been used to derive reservoir release rules for water use that are functions of presently knowable conditions, such as current season, storage, and inflows, and sometimes inflow forecasts (Young, 1967; Bhaskar and Whitlatch, 1980; Karamouz and Houck, 1982; Lund and Ferreira, 1996). For the flood control problem, in this study, the variables of the multiple-linear regression equations are the same as the attributes of the afore-derived optimal tree-based rules. The release regression equations for the two flood stages of the Shihmen and Feitsui Reservoirs can be formulated as Fig. 7. Observed hydrological data and six-hour hydrological data forecasts at each time step for Typhoon Aere.

tient up to an integer, which is then preceded by the word ‘‘Class.” For example, if the release is 488 m3/s, then the symbolic-type target is ‘‘Class 5.” In a similar way, this study selects the related attributes and target for Shihmen Reservoir. Scenarios Using the selected attributes, this study designs three scenarios for extracting the Feitsui Reservoir release rules, as below Scenario 1: Group-A (including attributes A-1, A-2 and A-3), Scenario 2: Group-A + Group-B (including attributes A-1, A-2, A-3 and B-1), Scenario 3: Group-A + Group-B + Group-C (including attributes A-1, A-2, A-3, B-1, C-1, C-2 and C-3). The target for each of the three scenarios is the Feitsui Reservoir release. For the Shihmen Reservoir rules, this study designs the scenarios in a similar way.

Shihmen-releaseðtÞ ¼ a1  timeðtÞ þ a2  Shihmen-inflowðtÞ þ a3  Shihmen-storageðtÞ þ a4  Feitsui -storageðtÞ þ a5  lateral-flowðtÞ þ a6  Estuary-levelðtÞ þ a7  Estuary-tendencyðtÞ

ð28Þ Feitsui-releaseðtÞ ¼ b1  timeðtÞ þ b2  Feitsui-inflowðtÞ þ b3  Feitsui-storageðtÞ þ b4  Shihmen-storageðtÞ þ b5  lateral-flowðtÞ þ b6  Estuary-levelðtÞ þ b7  Estuary-tendencyðtÞ ð29Þ

where a1a7 and b1b7 are coefficients, which are regressed using the least-squares method. It is noted that the release in the above equations are of numerical type. Real-time operation procedure Fig. 6 illustrates the flowchart of real-time flood control operation with a series of repetitive calculating steps at each hourly period. The steps of processing real-time simulating runs comprise:

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Table 4 Simulation results for three typhoons. Storage at the end of flood (106 m3)

Typhoon

Rule

Maximum water table (m)

Shihmen Reservoir

Feitsui Reservoir

Taipei Bridge

Tudigong

Aere

Tree-based rules Regression-based rules Existing rules

251.7 248.9 246.1

372.2 364.2 365.8

6.02 6.25 6.13

2.77 2.96 2.91

Haima

Tree-based rules Regression-based rRules Existing rules

250.2 248.3 245.5

383.8 358.8 365.4

1.67 1.93 2.14

1.56 1.68 1.78

Nock-Ten

Tree-based rules Regression-based rules Existing rules

247.3 241.3 237.9

367.5 352.7 360.3

1.45 1.65 1.62

1.42 1.57 1.56

Fig. 8. Simulation results of reservoir real-time operations in Typhoon Aere.

Step 1: receiving the hydrological information (data of attributes) at flood period t, while the forecast data is predicted,

Step 2: using the above attribute data as inputs to the release rules to solve real-time releases at time period t,

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Step 3: recording the real-time releases at the end of the period t, Step 4: updating the reservoir storage after releasing at the end of the period t, Step 5: repeating Steps 14 until flood ends. In Step 1, as mentioned in ‘‘Procedures of the methodology”, the RTRL model is used as real-time hydrological predictors. Fig. 7 shows the forecasted reservoir inflows and estuary water levels by RTRL models of Typhoon Aere (plotting 6-hour forecasts at each time period) along with the observed hydrological data. By using the obtained hydrological forecasts, processing reservoir real-time operations simulating runs can be fulfilled. In Step 2, the inputs for these release rules should include hydrological information and reservoir storage. Noted that (1) for tree-based rules and regression-based rules, the hydrological information involves the predictions of upstream inflows (including reservoir inflows and local inflows) and estuary water levels and (2) for existing rules, the hydrological information only involves the predictions of reservoir inflows (because, as mentioned before, the release look-up tables are function of the observed storage level and the reservoir inflow).

223

mance of three rules in three typhoons and average criterion values. One can see that the average results of tree-based rules, regression-based rules and existing rules in three typhoons are: (1) in Shihmen Reservoir for criterion TM by 98.3, 96.9 and 95.7%, respectively (Fig. 9a); (2) in Feitsui Reservoir for criterion TM by 96.5, 92.4 and 93.7%, respectively (Fig. 9b); (3) in Taipei Bridge Station for criterion LR by 18.9, 10.3 and 8.4%, respectively (Fig. 9c) and (4) in Tudigong Station for criterion LR by 10.5, 3.1 and 2.0%, respectively (Fig. 9d). Clearly, the release rules derived by decision-tree algorithm demonstrate theirs effectiveness in estimating real-time releases. It should be pointed out that because the two existing reservoir rules are not joint flood control operation, the results from Table 4 and Fig. 9 demonstrate the poor efficiency in reducing the downstream control point levels. In addition, one can find that the values of water level reduction rate (LR) at Tudigong Station are limited

Performance of three rules To verify the optimal rules, the derived tree-based rules, regression-based rules and existing rules are compared by conducting the real-time operations in three historical typhoons: Typhoons Aere (2004/8/23), Haima (2004/9/11) and Nock-ten (2004/10/24). Table 4 lists the results of processing real-time simulating runs in the three typhoons. Additionally, Fig. 8a and b plot the reservoir release hydrographs in Typhoon Aere, Fig. 8c and d are the reservoir storage hydrographs, and Fig. 8e and f are the control point water level hydrographs. From Table 4 and Fig. 8, one can find that the tree-based rules produce much better performance of these three rules, in terms of (1) reducing the downstream floodwaters at control points, and (2) meeting the reservoir’s target storage at the end of flood where the target storage of the Shihmen Reservoir is 254.0  106 m3 and that of the Feitsui Reservoir is 388.2  106 m3. Consequently, the optimal tree-based rules derived from C5.0 algorithm demonstrate good performance for determining the real-time releases for flood control. In order to assess the performance of the three rules, two criteria are taken into account (Wei and Hsu, in press), defined as follows:  Reservoir target storage meeting rate (TM)

TMð%Þ ¼

Send  100 Starget

ð30Þ

where Send is the reservoir storage at the end of flood, and Starget is the target storage in normal periods. For Shihmen and Feitsui Reservoirs, the target storage Starget ¼ 254:0  106 m3 and 6 3 388:2  10 m , respectively.  Control point maximum level reduction rate (LR)

LRð%Þ ¼

L  Lmax  100 L

ð31Þ

max

where L is the control point maximal level during flood, and L is the control point maximal level based upon supposing no building upstream reservoir. The L can be derived from linear channel level routing (i.e., Eq. (9)) by substituting reservoir inflows for reservoir releases. Generally, the higher the criterion is, the greater the performance is. Fig. 9 shows that the bar charts concerning the perfor-

Fig. 9. Comparisons of performances concerning release rules at reservoirs and control points.

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(roughly 015%). The reason is that Tudigong Station is close to the estuary, resulting in the influence of tide being much greater than that of upstream floodwater movement. Conclusions This article proposes a methodology to establish a set of optimal operation release rules which are tree-based rules for flood control on a multipurpose multireservoir system. The derived rules can be used to determine the optimal real-time releases during flood periods. The developed methodology incorporates with (1) collecting flood events to build flood database, (2) running flood control optimization model to generate the optimal input–output patterns, (3) building decision-tree algorithm (C5.0) to extract the optimal treebased release rules for flood control, (4) generating forecast data by using the hydrological forecast model, (5) processing the reservoir real-time releases by simulating the reservoir real-time flood control operation and (6) verifying the superior release rules through comparisons of optimal tree-based rules, regression-based rules and existing rules. The developed methodology is successfully implemented for the Tanshui River Reservoir System in Taiwan, and its performance based on 18 years of historical typhoon data. The data are divided into two independent sets, namely training and testing. The treebased rules are extracted through (1) the optimal input–output patterns obtained by the flood control optimization model, (2) tree-based rules for designed scenarios extracted by the decisiontree algorithm and (3) optimal tree-based rules determined according to the accurate performance. The derived optimal tree-based rules, regression-based rules and existing rules are compared by conducting the real-time operations in three typhoons, i.e., Aere, Haima and Nock-ten in 2004. Results demonstrate that the solution using the derived tree-based rules have better performance of these three rules in terms of reducing the peak stage at downstream control points, and meeting the target reservoir storage at the end of flood. Acknowledgements The support under Grant No. NSC 97-2218-E-464-001 and NSC 97-2111-M-464-001 by the National Science Council, Taiwan is greatly appreciated. The writers are also grateful for the constructive comments of the referees. References Apté, C., Weiss, S., 1997. Data mining with decision trees and decision rules. Future Generation Computer System 13, 197–210. Bessler, F.T., Savic, D.A., Walters, G.A., 2003. Water reservoir control with data mining. Journal of Water Resources Planning and Management 129, 26–34. Bhaskar, N.R., Whitlatch Jr., E.E., 1980. Derivation of monthly reservoir release policies. Water Resources Research 16 (6), 987–993. Bradford, J.P., Fortes, J.A.B., 2001. Characterization and parallelization of decisiontree induction. Journal of Parallel and Distributed Computing 61, 322–349.

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