risk-based drought early warning system in reservoir operation

12
Risk-based drought early warning system in reservoir operation Wen-Cheng Huang * , Chia-Ching Chou Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung 202, Taiwan Received 9 April 2007; received in revised form 21 December 2007; accepted 27 December 2007 Available online 11 January 2008 Abstract This paper introduces a risk-based decision process integrated into a drought early warning system (DEWS) for reservoir operation. It is to support policy making under uncertainty for drought management. Aspects of posterior risk, chances of option occurrences and the corresponding options to given chances, are provided to help decision makers to make better decisions. A new risk index is also defined to characterize decision makers’ attitudes toward risk. Decision makers can understand the inclination of attitude associated with any specific probability through accuracy assessment, and learn to adjust their attitudes in decision-making process. As a pioneering exper- iment, the Shihmen reservoir in northern Taiwan was tested. Over the simulation period (1964–2005), the expected overall accuracy approximated to 77%. The results show that the proposed approach is very practical and should find good use for reservoir operations. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Drought; Early warning system; Reservoir; Risk; Decision making 1. Introduction Drought, a natural disaster, is a complex problem asso- ciated with its type, intensity, duration, frequency, and extent. Generally, a drought plan contains three main parts: monitoring and early warning, risk assessment, and mitigation and response [23]. Many drought indices have been defined to meet particular needs of different water users [16,18,15,11]. And much work has been published regarding drought watch, drought impact, drought mitiga- tion, and drought early warning [7,10,12,21,24,19,20]. However, there is little literature available on the risk- based drought early warning system to real-time reservoir operations. Water resource regulated by the Shihmen reservoir in northern Taiwan is crucial to the regional farmland of 35,000 ha [6]. The annual irrigation demand approximates 529 million cubic meters (MCM), and municipal water sup- ply with top priority demands 620 MCM annually. Since Shihmen’s small capacity (235 MCM) cannot catch enough rainfall to subsequently satisfy such large water demand of users, both spring and typhoon rains are so critical that the lack of either one will cause severe drought in its operation. In case drought occurs, water rationing and/or farmland fallow would be needed. For Shihmen’s reservoir opera- tion, by late January (the start of the spring growing sea- son) and mid-July (the start of the summer growing season), a critical decision about water release strategy should be made before implementing a scheduled irrigation project. It was found that a minimum 215 MCM in reser- voir storage would be necessary for a full supply at the end of January, and below 72 MCM would necessitate the termination of irrigation. Huang and Chou [6] presented a drought early warning system (DEWS) for reservoir operation to help the water resources agency (WRA) while confronting drought threats. A five-level, color-coded drought alert system, ranging from ‘‘greento ‘‘red, was classified in line with any specific water-cut option (see Table 1). As known, deci- sions imply act selections among alternatives. Analysts just analyze the consequences of each alternative, and then present results to decision makers to let them choose what they prefer. Indeed, it is difficult for decision makers to 0309-1708/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.advwatres.2007.12.004 * Corresponding author. E-mail address: [email protected] (W.-C. Huang). www.elsevier.com/locate/advwatres Available online at www.sciencedirect.com Advances in Water Resources 31 (2008) 649–660

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Page 1: Risk-based drought early warning system in reservoir operation

Available online at www.sciencedirect.com

www.elsevier.com/locate/advwatres

Advances in Water Resources 31 (2008) 649–660

Risk-based drought early warning system in reservoir operation

Wen-Cheng Huang *, Chia-Ching Chou

Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung 202, Taiwan

Received 9 April 2007; received in revised form 21 December 2007; accepted 27 December 2007Available online 11 January 2008

Abstract

This paper introduces a risk-based decision process integrated into a drought early warning system (DEWS) for reservoir operation. Itis to support policy making under uncertainty for drought management. Aspects of posterior risk, chances of option occurrences and thecorresponding options to given chances, are provided to help decision makers to make better decisions. A new risk index is also definedto characterize decision makers’ attitudes toward risk. Decision makers can understand the inclination of attitude associated with anyspecific probability through accuracy assessment, and learn to adjust their attitudes in decision-making process. As a pioneering exper-iment, the Shihmen reservoir in northern Taiwan was tested. Over the simulation period (1964–2005), the expected overall accuracyapproximated to 77%. The results show that the proposed approach is very practical and should find good use for reservoir operations.� 2008 Elsevier Ltd. All rights reserved.

Keywords: Drought; Early warning system; Reservoir; Risk; Decision making

1. Introduction

Drought, a natural disaster, is a complex problem asso-ciated with its type, intensity, duration, frequency, andextent. Generally, a drought plan contains three mainparts: monitoring and early warning, risk assessment, andmitigation and response [23]. Many drought indices havebeen defined to meet particular needs of different waterusers [16,18,15,11]. And much work has been publishedregarding drought watch, drought impact, drought mitiga-tion, and drought early warning [7,10,12,21,24,19,20].However, there is little literature available on the risk-based drought early warning system to real-time reservoiroperations.

Water resource regulated by the Shihmen reservoir innorthern Taiwan is crucial to the regional farmland of35,000 ha [6]. The annual irrigation demand approximates529 million cubic meters (MCM), and municipal water sup-ply with top priority demands 620 MCM annually. SinceShihmen’s small capacity (235 MCM) cannot catch enough

0309-1708/$ - see front matter � 2008 Elsevier Ltd. All rights reserved.

doi:10.1016/j.advwatres.2007.12.004

* Corresponding author.E-mail address: [email protected] (W.-C. Huang).

rainfall to subsequently satisfy such large water demand ofusers, both spring and typhoon rains are so critical that thelack of either one will cause severe drought in its operation.In case drought occurs, water rationing and/or farmlandfallow would be needed. For Shihmen’s reservoir opera-tion, by late January (the start of the spring growing sea-son) and mid-July (the start of the summer growingseason), a critical decision about water release strategyshould be made before implementing a scheduled irrigationproject. It was found that a minimum 215 MCM in reser-voir storage would be necessary for a full supply at theend of January, and below 72 MCM would necessitatethe termination of irrigation.

Huang and Chou [6] presented a drought early warningsystem (DEWS) for reservoir operation to help the waterresources agency (WRA) while confronting droughtthreats. A five-level, color-coded drought alert system,ranging from ‘‘green” to ‘‘red”, was classified in line withany specific water-cut option (see Table 1). As known, deci-sions imply act selections among alternatives. Analysts justanalyze the consequences of each alternative, and thenpresent results to decision makers to let them choose whatthey prefer. Indeed, it is difficult for decision makers to

Page 2: Risk-based drought early warning system in reservoir operation

Table 1Responses to drought alert signal

Alert signala Water-cut rate (%)

Irrigation Municipal supply

Green (0 5 DAI 5 1), G 0 0Blue (1 < DAI51.5), B 0–30 0Yellow (1.5 < DAI 5 2), Y 30–50 0–10Orange (2 < DAI 5 2.5), O >50 10–20Red (2.5 < DAI 5 3), R 100 >20

a DAI indicates a drought alert index (see Eq. (1)).

650 W.-C. Huang, C.-C. Chou / Advances in Water Resources 31 (2008) 649–660

make an appropriate decision under uncertainty, in partic-ular when alternatives differ substantially from each other[4,8,1,22,9,17]. That is, the WRA officials probably hesitateabout signal choice when signals provided by the DEWSvaried considerably. Therefore, risk assessment is furtherneeded to help decision makers to make better decisions.

2. Risk-based DEWS

2.1. Objective

Fig. 1 gives the process of the risk-based drought earlywarning system in reservoir operation. It comprises fivemain parts: (1) drought watch, (2) water consumption,(3) drought alert, (4) decision analysis, and (5) optionchoice. The ‘‘drought watch” monitors current droughtconditions including both hydrologic and water-supplydroughts. Five drought categories (D), (none, slightlysevere, fairly severe, severe, very severe), were used. The‘‘water consumption” measures possible water shortage inthe near future, based on rule curves of any specific reser-voir system. Also, five shortage categories (S), (normal,slightly high, fairly high, high, very high), were designated.By integrating both D and S, a nonlinear-scale transforma-tion was applied for drought impact assessment. That is,

Current Drought Watch (D)

Future Water Consumption (S)

Drought Alert Index ( DAI= )

Option Choice

Decision Analysis

Expected DAI (E[DAI])

Risk Analysis

AccuracyAssessment

)(log 25 DS

Fig. 1. Process of the risk-based drought early warning system.

for a given hydrologic condition (Qh), a standardizeddrought alert index was introduced (DAI) as follows:

DAI ¼ f ðD; SjQhÞ ¼ log5ðDS2Þ;D ¼ 1; 2; . . . ; 5; S ¼ 1; 2; . . . ; 5 ð1Þ

where 0 5 DAI 5 3; Qh indicates the inflow Q associatedwith the exceedence probability h% [13]. The outcome ismore favorable as DAI value approaches 0. As comparedwith DS2, the form of DSk with k > 2 appears to be unfa-vorable for the signal judgment [6]. Therefore, we choosethe form of DS2 appropriate for the drought alert here.

In this article, the ‘‘drought alert” establishes the DAI tocharacterize the alert level of drought and suggestsresponses by curtailing water demands to any specific alertsignal. Here five signals, (green, blue, yellow, orange, red),were designated to reflect the intensity of drought severity(see Table 1). Since this paper is a sequel to the authors’previous work, here we would like to avoid repeating indetailed explanation about the DEWS model. In detail,please refer to Huang and Chou [6]. The earlier one talkedabout a new methodology of drought early warning for res-ervoir operation. However, it did not investigate the prob-lem of how to pick an appropriate alert option underuncertainty, i.e., there was a gap between the drought alertindices and the option choices (see Fig. 1). The main objec-tive of this paper is to build a decision process incorporatedwith the DEWS. It aims at assisting the WRA officials inconsidering the implications of different courses of thinkingto reach best decisions.

2.2. Decision process

2.2.1. Calculation of expected DAI

Risk can be characterized by the severity of the possibleadverse alert signals with corresponding occurrence proba-bilities. Suppose that n periods are simultaneously consid-ered for future’s operation (see Table 2), where the stateof nature (hi) indicates a wide range of possible hydrologicconditions from optimistic (based on a 10% exceedenceprobability of streamflow, Q10) to pessimistic (based on95% exceedence probability, Q95). For a given hydrologiccondition in period t, DAI equals log5 ðDtS

2t Þhi. Then, the

expected DAI value over time can be expressed as

E½DAI� ¼Xn

t¼1

W t

XQ95

hi¼Q10

ptðhiÞlog5ðDtS2t Þhi

ð2Þ

Table 2Calculation of the drought alert index among periods

Inflowhi

Probabilitypt (hi)

DAI (t = 1) DAI (t = 2) � � � DAI (t = n)

Q10 pt(Q10) log5ðD1S21ÞQ10

log5ðD2S22ÞQ10

� � � log5ðDnS2nÞQ10

Q20 pt(Q20) log5ðD1S21ÞQ20

log5ðD2S22ÞQ20

� � � log5ðDnS2nÞQ20..

. ... ..

. ... ..

. ...

Q95 pt(Q95) log5ðD1S21ÞQ95

log5ðD2S22ÞQ95

� � � log5ðDnS2nÞQ95

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W.-C. Huang, C.-C. Chou / Advances in Water Resources 31 (2008) 649–660 651

where pt(hi) gives the probability distribution of hi, and Wt

shows the weight associated with the expected DAI in timet (0 5Wt 5 1). Analogous to water recession, we assume

dfdt¼ �kf ð3Þ

where f = log5(DS2) and k is a recession constant. That is,

ln f ¼ �kt þ constant ð4ÞLet f = f0 as t = 1, then

f ¼ f0e�kðt�1Þ ð5Þwhere f0 is a specified initial DAI, and f gives DAI’s reces-sion over t periods. In the meantime, the value f in Eq. (5)would decay faster with larger k. The empirical value of kcan be approximately determined in response to practicaldrought situations. With consideration of recession effect,Eq. (2) can be transformed to

E½DAI� ¼ 1Pnt¼1e�kðt�1Þ

Xn

t¼1

XQ95

hi¼Q10

ptðhiÞlog5ðDtS2t Þhi

" #e�kðt�1Þ

ð6Þwhere

W t ¼e�kðt�1ÞPnt¼1e�kðt�1Þ ð7Þ

In practice, the WRA officials analyze the impact ofwater deficit status for the next 3 months at a time, i.e.,n = 3 here. Therefore, the calculated weights in Eq. (7)are illustrated in Fig. 2. It is clear that the weights will bethe same as k equals zero (without recession), and moreweight arises on W1 as k value increases. Furthermore, toestimate the probabilities of each possible inflow state forany time period, pt(hi), we can use a matrix of transitionprobabilities. Let Pt be the matrix with elements pij, indi-cating the next inflow state in period t + 1 is at state j, giventhe current inflow in period t is at state i. It satisfies

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Recession

Wei

ght

Weight (t=1)

Weight (t=2)

Weight (t=3)

0.0 0.1 0.2 0.3 0.4 0.5

Fig. 2. Weight variation in respo

Pj pij = 1, for all i. Hence the relationship between pt and

pt+1 is given by

ptþ1 ¼ ptPt ð8Þ

2.2.2. Risk analysis

Obviously, to use the expected DAI based on Eq. (6) fora decision would probably be satisfactory if the signal alertoptions do not vary considerably. For example, it wasfound that a green level was the most suitable signal forall hydrologic conditions during the wet year [6]. In suchcases, the expected DAI would make no difference to the‘‘green” decision. On the contrary, the use of expected val-ues would be unacceptable when large variation in alert sig-nals emerges, say, in the beginning of a potential drought.Therefore taking risk into account in the decision process isneeded.

(a) Chance of optionsDecision making is the cognitive process leading to the

selection of a course of action among alternatives. It wouldbe helpful if the probability to select an option is availableto the WRA officials prior to making a decision. The prob-ability of any specific signal can be found by maximizingthe cumulative probability over the state of nature. Twophases would be needed for the searching. The first is tofind the existing inflow state which holds the maximumDAI value along with a specified signal level; subsequentlythe probabilities beyond the inflow state are accumulated.Therefore, the equations can be written as

MaximizeQ956hi6Q10

log5ðDtS2t Þhi

e�kðt�1Þ 8t ð9Þ

subject to log5ðDtS2t Þhi

e�kðt�1Þ6 DAIðjÞ 8t ð10Þ

where DAI(j) (j = 1,2,3,4,5) represents the maximum va-lue in response to each signal level (see Table 1), such asDAI(1) = 1 for ‘‘green”, DAI(2) = 1.5 for a ‘‘blue” signal,and DAI(5) = 3 for the highest alert in ‘‘red”. By using

Parameter (λ)

0.6 0.7 0.8 0.9 1.0 2.0

nse to recession parameter.

Page 4: Risk-based drought early warning system in reservoir operation

Table 3Example error matrix for the expected DAI analysis over 1964–2005

Predictedsignal

Actual signal User’sAccuracy (%)Green Blue Yellow Orange Red

Green 1088 105 34 6 0 88.24Blue 39 22 57 14 4 16.18Yellow 3 7 20 42 11 24.10Orange 0 1 2 18 25 39.13Red 1 0 0 1 12 85.71

Producer’sAccuracy (%)

96.20 16.30 17.70 22.22 23.08

652 W.-C. Huang, C.-C. Chou / Advances in Water Resources 31 (2008) 649–660

both Eqs. (9) and (10), we can find the smallest h�t in eachperiod in accordance with any specific DAI(j). Accord-ingly, the cumulative probability p�t associated with anyspecified signal alert level can be calculated as

p�t ¼XhiPh�t

ptðhiÞ 8t ð11Þ

where the state of nature (hi) appears in the ordered listfrom largest (Q10 here) to smallest (Q95 here). For this case,is the sum of the probabilities over the designated signals(G,B,Y, O,R) one by one. Therefore the difference betweentwo successive signals indicates the chance of the latter. Itappears that the accumulated probability for a ‘‘green” op-tion probably approximates to one during the wet year.Consequently the chance for the remaining signals wouldbe close to zero.

(b) Options with given chance

On the other hand, the decision makers may be of inter-est to the determination of options along with known prob-abilities. For a given probability (u), let the accumulatedprobabilities ranging from Q10 to a certain h��t approximatethe specified probability. That is,XhiPh��t

ptðhiÞ 6 u 8t ð12Þ

Then the overall DAI along with a prior probability u

equals

DAIu ¼1Pn

t¼1e�kðt�1Þ

Xn

t¼1

log5ðDtS2t Þh��t e�kðt�1Þ ð13Þ

In fact, any probability specified in Eq. (12) responds to adecision maker’s behavior toward risk. Generally, there arethree types of preferences in decision, i.e., risk-seeking,risk-neutral, and risk-averse [4]. The higher the specifiedprobabilities, the more degrees of risk aversion would takein decision making.

3. Accuracy assessment

For model validation, the accuracy analysis by using anerror matrix is effective. The error matrix represents thenumber of sample units (like drought occurrence) assignedto a particular category (signal here) relative to the actualcategory as indicated by the reference data [2,3]. It is asquare matrix. The approach has been popularly appliedon remote sensing and GIS accuracy assessment [14]. Asshown in Table 3, for example, the classified data (pre-dicted signal) represent the signal outcomes from the devel-oped decision process, and the reference data (actualsignal) express the signals based on perfect forecasts ofinflow in hindsight. The reference sources are assumed tobe correct. Subsequently, we can assess the accuracy withthe error matrix. Let xij be the number of observationsassigned to signal i (i = 1,2,3,4,5) in the DEWS classifica-

tion and to category j (j = 1,2,3,4,5) in the reference data.Clearly, the predicted signal is correct as i = j, underesti-mated as i < j, and overestimated as i > j. Then the overallaccuracy (OA), the ith user’s accuracy (UAi), and the jthproducer’s accuracy (PAj), respectively, can be computedby

OA ¼P5

i¼1xii

Nð14Þ

UAi ¼xiiP5j¼1xij

8i ð15Þ

PAj ¼xjjP5i¼1xij

8j ð16Þ

where N is the total number of observations, that is,N ¼

P5i¼1

P5j¼1xij. In this article, the user’s accuracy and

signal’s predicted accuracy are identical in meaning. Be-cause UAi and PAj represent the proportion accuracy byclasses, the indicators have direct probabilistic interpreta-tions for a given error matrix. In this study, we further de-fine the underestimated error (UE) and overestimated error(OE) as

UE ¼P8iP8jxij

N; i < j ð17Þ

OE ¼P8jP8ixij

N; i > j ð18Þ

where OA + UE + OE = 1. UE and OE, respectively,show the total errors on the upper triangle and lower trian-gle matrices. As UE > OE, it represents a risk-seeking atti-tude in decision making, whereas UE < OE means risk-averse. By taking signal deviation from reality into consid-eration, we can define a risk index (RI) further with

RI ¼X8i

X8jði� jÞ � xij ð19Þ

where ji � jj shows the weight on xij. More weight will beadded to xij along with greater signal difference betweenprediction and reality. For example, x25 shows that the pre-dicted signal appears ‘‘blue”, whereas the actual signal is‘‘red”. Obviously, the alert signal is underestimated overa span of three levels, equivalent to a weight on the errorprediction. In fact, the values with RI < 0, RI = 0, andRI > 0, respectively, may indicate risk-seeking, risk-neu-tral, and risk-averse attitudes toward decision making.

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W.-C. Huang, C.-C. Chou / Advances in Water Resources 31 (2008) 649–660 653

And higher absolute value of RI reveals a higher degree ofpreference on attitudes.

4. Model testing

In this study, historical data of 10-day-long inflow, res-ervoir storage, and water demand from 1964 through 2005are used to test the proposed decision process. Thereforethe total sample size we have here equals 1512 (36 � 42).It describes a practical reservoir management scenario inShihmen situated in northern Taiwan. In application, thematrix of transition probabilities between subsequentinflows can be built directly from the historical inflowrecord. Note that synthetic inflow generation would beneeded as historical flow sequence does not allow examina-tion of the transition matrix [13]. And the DEWS couldrenew the analysis of the situation every 10 days againstany potential droughts.

4.1. Determination of recession constant

Since the weighted drought alert index is considered inthis study, the recession parameter k, first of all, shouldbe determined according to practical drought conditions.However, the so-called drought situations are identifiedvia Eq. (1). It seems a little convoluted. The ‘‘true” signalshere in response to droughts were derived on a basis of per-fect 3-month-ahead forecasts of inflow. The determinationof k needs trial and error to match practical events.

For example, in early June of 2002, the effective storagein Shihmen approximated 8.78 MCM, around 3.1% of theactive capacity. The drought situation was extremelysevere. Fortunately, started on July 3, Typhoon Ramm-asun brought torrential rainfall over northern Taiwan.The accumulated rainfall reached 443 mm in Shihmen’sbasin within two days. The abundant rains gave a rapidincrease of reservoir storages to 183.51 MCM in Shihmen.On July 5, the end of water rationing was announced by the

Nov-00 Apr-01 Sep-01 Feb-02 Aug-02 Jan-03 Jun-03

(G)

(B)

(Y)

(O)

(R)

Sign

al

Fig. 3. Signal variation in response to recessio

WRA and the prolonged drought was finally over. Thetimely rainfall was a great contribution to drought relief.In reality, the situation approximated ‘‘yellow” level. Sup-pose that the incoming abundant inflows are known inadvance. Obviously, larger k will diminish the influenceon W2 and W3 (see Fig. 2). As a result, the alert level wouldbecome more severe along with larger k value, rangingfrom ‘‘yellow” (as k = 0.0) to ‘‘red” (as k = 2.0). Again,at the same period of 2003, the remaining volume in Shih-men equaled 48.37 MCM. In hindsight, no typhoons hadarrived yet to increase Shihmen’s storage in July. Rainfallwas probably insufficient in the coming future, and a‘‘blue” alert was more appropriate. As known, smallweight of W2 and W3 in response to large k could notreflect the impact of future’s water scarcity on alert levels.It was found that the signals in early June varied from ‘‘yel-low” (k = 0.0) to ‘‘green” (k = 2.0). As compared with real-ity, the recession constant by k = 0.2 was eventually chosenherein (see Fig. 3). Hence the weights in Eq. (7) for the nextthree consecutive months equal 0.4, 0.33, and 0.27respectively.

4.2. Example interpretation

Following with a given k value, the expected DAI valuecan be calculated for the next 3 months by using Eqs. (6)–(8). Fig. 4 shows the signal variation between actual andexpected signals over the period of 2000–2006. Obviously,there were three severe drought events during three consec-utive years (2002–2004). The authors had a detailed discus-sion on the determination of alert signals [6]. In this article,further, the authors would focus investigation on the deci-sion making under uncertainty in terms of the followingcases.

4.2.1. Decision in late February of 2002

By late February of 2002, the effective storage in Shih-men only approximated 89.20 MCM, 38.0% of the active

Nov-03 Apr-04 Sep-04 Feb-05 Jul-05 Dec-05 May-06

λ = 0.0

λ = 0.2

λ = 0.5

λ = 1.0

λ = 2.0

n parameter over the period of 2000–2006.

Page 6: Risk-based drought early warning system in reservoir operation

Nov-00 Apr-01 Sep-01 Feb-02 Jul-02 Dec-02 May-03 Oct-03 Mar-04 Aug-04 Dec-04 May-05 Oct-05 Mar-06 Aug-06

Actual signal

Expected signal

(R)

(O)

(Y)

(B)

(G)

Fig. 4. Signal variation over the period of 2000–2006.

Table 5Risk analysis in February of 2002

hi t = 1 (March) t = 2 (April) t = 3 (May)

p1(hi) DAI p2(hi) DAI p3(hi) DAI

Q10 0.00% 0.86 6.80% 0.68 12.60% 0.00Q20 1.20% 1.72 7.10% 0.86 10.40% 0.43Q30 2.30% 2.23 9.70% 1.72 7.60% 0.43Q40 5.80% 2.23 15.40% 2.23 8.30% 1.72Q50 14.00% 2.23 18.40% 2.23 12.60% 2.23Q60 16.30% 2.23 9.30% 2.23 12.00% 2.37Q70 12.80% 2.23 6.70% 2.23 11.70% 2.37Q80 18.60% 2.23 7.50% 2.23 9.00% 3.00Q90 3.50% 2.23 6.00% 2.23 7.10% 3.00Q95 25.60% 2.23 13.00% 3.00 8.60% 3.00

E[DAI]t 2.22 2.07 1.80Wt 0.40 0.33 0.27

654 W.-C. Huang, C.-C. Chou / Advances in Water Resources 31 (2008) 649–660

capacity. The DEWS based on the known exceedenceprobability of inflows (Qh) produced the alert signals insequence ranging from ‘‘green” to ‘‘red”, as shown in Table4. The accumulated amount of inflow into Shihmen in Feb-ruary retained only 27.49 MCM, in nearly 65% of theexceedence probability. Based on the transition relation-ship shown in Eq. (8), we can calculate the probabilitiesof each inflow state for the next three months (see Table5). The chance to occur in optimistically Q10 was verylow. As compared with the actual ‘‘orange” signal, theexpected DAI equaled 2.07, indicating the same ‘‘orange”

alert (see Fig. 4). Quantity reduction for water users wasprobably needed.

As seen in Table 5, the inflow conditions h�t in accordancewith ‘‘orange” level (i.e. 2 < DAI 5 2.5) reach Q95, Q90, Q70,respectively, for the next three months based on Eqs. (9),(10). Accordingly, the accumulated probabilities in Eq.(11) equal (100%, 87%, 75.3%) in sequence. Similarly, theaccumulated probabilities for ‘‘red” level (i.e. 2.5 < DAI 53.0) would become (100%, 100%, 100%) individually. Thedifference in probability between ‘‘orange” and ‘‘red” givesthe chance of ‘‘red” to (0%, 13%, 24.7%) during the periodof (March, April, May). As a result, the sequent probabili-

Table 4Signal variation in accordance with hydrologic conditions

hi Februaryof 2002

Decemberof 2003

Februaryof 2005

Februaryof 2006

Decemberof 2006

Q10 G Y G G GQ20 B O G G GQ30 Y R G B GQ40 O R G Y GQ50 O R G O GQ60 O R G O GQ70 O R G O BQ80 O R G O BQ90 O R G O BQ95 R R G O B

Expected O R G Y G

ties for ‘‘yellow” level within the same period equaled(1.2%, 9.7%, 8.3%), and (98.8%, 63.4%, 36.4%) for‘‘orange” alert. Obviously, the ‘‘orange” action would behighly suggested.

On the other hand, for any specified probability, akin todecision maker’s attitude toward risk, we could estimatethe corresponding signal on the basis of Eqs. (12) and(13). Table 6 shows the variations in signals from ‘‘green”

of u = 0.01 (extremely risk-seeking) to ‘‘red” of u = 0.99(extremely risk-averse). At this moment, the rainfall predic-tion information from the Weather Bureau will greatly helpthe WRA make a final decision on signal choice. The WRAofficials eventually chose ‘‘yellow” action instead of‘‘orange” action. In hindsight, the option was unfortu-nately identified as inappropriate. Huang and Yuan [5]had a detailed discussion on the consequences because ofthe WRA’s lack of decisive action.

4.2.2. Decision in late December of 2003

In the end of December 2003, the remaining storage inthe Shihmen reservoir had fallen to 72.8 MCM, about31% of the active capacity. The storage was close to the

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Table 6Option choice based on specified probability toward risk

Probability(u)

Februaryof 2002

Decemberof 2003

Februaryof 2005

Februaryof 2006

Decemberof 2006

0.01 G Y G G G0.1 B O G G G0.2 Y O G B G0.3 Y R G Y G0.4 O R G O G0.5 O R G O G0.6 O R G O G0.7 O R G O B0.8 O R G O B0.9 R R G O B0.95 R R G O B0.99 R R G O B

W.-C. Huang, C.-C. Chou / Advances in Water Resources 31 (2008) 649–660 655

threshold value of 72 MCM for irrigation termination. TheDEWS yielded the signals from ‘‘yellow” to ‘‘red” corre-sponding to each of the 10 inflow states (see Table 4). Obvi-ously, the WRA should put the water reduction on thealert. According to the probability distribution of potentialinflow (see Table 7), the expected DAI equal to 2.51 sug-gested to take ‘‘red” action, same as the actual signal. Itwould need to suspend all irrigation water. We found thatthe sequent probabilities for ‘‘orange” in (January, Febru-ary, March) equaled (0%, 17%, 12.4%), and the chances for‘‘red” were (100%, 72.4%, 78.7%). The probability at redlevel occurrence was high.

Moreover, as shown in Table 6, the signal swiftly chan-ged from ‘‘orange” to ‘‘red” as the designated probability uapproached 0.3, a very risk-seeking behavior. Besides, theforthcoming potential rainfall conditions were not so opti-mistic, the WRA eventually made the decision to fallow allfarmland (35,000 ha) in the mid-January of 2004, akin tothe actual ‘‘red” option. In hindsight, the action was a cor-rect decision. The remaining storage had fallen to 50.33MCM by the end of January. The irrigation project couldnot survive under such a severe drought impact.

Table 7Risk analysis in December of 2003

hi t = 1 (January) t = 2 (February) t = 3 (March)

p1(hi) DAI p2(hi) DAI p3(hi) DAI

Q10 19.30% 2.58 10.60% 1.72 8.90% 0.68Q20 12.00% 2.58 17.00% 2.23 12.40% 2.23Q30 9.60% 2.58 20.40% 2.58 16.30% 2.58Q40 8.40% 2.58 5.30% 2.58 12.80% 2.58Q50 14.50% 2.58 8.20% 2.58 11.50% 2.58Q60 3.60% 2.58 9.10% 2.58 7.80% 2.58Q70 10.80% 2.58 6.30% 2.58 7.30% 3.00Q80 8.40% 2.58 7.80% 2.58 6.00% 3.00Q90 9.60% 2.58 5.10% 2.58 3.60% 3.00Q95 3.60% 2.58 10.40% 2.58 13.50% 3.00

E[DAI]t 2.58 2.44 2.50Wt 0.40 0.33 0.27

4.2.3. Decisions in 2005

2005 was a wet year. All expected DAI values alwaysremained at ‘‘green” level from optimistic hydrologicalcondition (Q10) through pessimistic hydrological condition(Q95). For instance, in late February of 2005 there was asmuch as 220.51 MCM in Shihmen. As demonstrated inTable 8, the reservoir volume would be sufficient for allwater users’ needs if future inflow conditions were betterthan Q70. On average, a green signal was the single optionin terms of hydrologic conditions (see Table 4) and decisionmaker’s attitudes (see Table 6). Fig. 4 also illustrates thecoincidence between expectation and reality. It is clear thatthere is no difficulty in making a decision during a wet year.

4.2.4. Decision in late February of 2006

By late February of 2006, 107.25 MCM was left in theShihmen reservoir for use. Given exceedence probabilityof inflows, as Table 4 shows, the DEWS introduced the sig-nals from ‘‘green” to ‘‘orange”. There were worrying signsthat alert signal would be close to an ‘‘orange” level asinflow was less than median value. The WRA officialsshould think twice of the matter for water curtailment.The expected DAI value 1.81 suggested a ‘‘yellow” alert;thus some water reduction around 30–50% for irrigationprobably would be needed. In hindsight, the actual signalwas ‘‘blue”, requesting 30% at most to curtail irrigationdemand.

Besides, according to the inflow distribution (see Table9), the probabilities in (March, April, May) appeared toequal (1.3%, 14.9%, 31.1%) for ‘‘green”, (73.7%, 0%, 0%)for ‘‘blue”, (25%, 10%, 8.4%) for ‘‘yellow” signal, nochance for ‘‘orange”, and (0%, 75.1%, 60.5%) for ‘‘red” insequence. Meanwhile, by considering the attitude towardrisk represented with any specific probability, Table 6 alsoshows the alert signals from ‘‘green” to ‘‘orange” are pos-sible. And ‘‘orange” emerged as u = 0.4. The WRA officialsprobably encountered difficulties in making a decision withsuch information. As compared with the so-called ‘‘prior”probability distribution of inflow, the ‘‘posterior” probabil-

Table 8Risk analysis in February of 2005

hi t = 1 (March) t = 2 (April) t = 3 (May)

p1(hi) DAI p2(hi) DAI p3(hi) DAI

Q10 61.40% 0.00 17.90% 0.00 16.10% 0.00Q20 22.80% 0.00 13.00% 0.00 12.00% 0.00Q30 12.40% 0.00 13.10% 0.00 8.60% 0.00Q40 2.80% 0.00 17.20% 0.00 9.00% 0.00Q50 0.70% 0.00 16.20% 0.00 12.80% 0.43Q60 0.00% 0.00 7.60% 0.43 11.70% 0.43Q70 0.00% 0.00 4.00% 0.43 10.70% 0.43Q80 0.00% 0.00 3.90% 0.43 7.50% 2.05Q90 0.00% 0.00 2.70% 0.43 5.60% 2.58Q95 0.00% 0.00 4.60% 0.43 6.00% 2.58

E[DAI]t 0.00 0.10 0.61Wt 0.40 0.33 0.27

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Table 9Risk analysis in February of 2006

hi t = 1 (March) t = 2 (April) t = 3 (May)

p1(hi) DAI p2(hi) DAI p3(hi) DAI

Q10 1.30% 0.43 7.40% 0.68 12.90% 0.00Q20 1.30% 1.29 7.50% 0.86 10.50% 0.43Q30 6.30% 1.29 10.00% 1.72 7.70% 0.86Q40 2.50% 1.29 15.70% 2.58 8.40% 1.72Q50 21.30% 1.29 18.40% 2.58 12.60% 2.58Q60 10.00% 1.29 9.20% 2.58 12.00% 2.72Q70 17.50% 1.29 6.50% 2.58 11.60% 2.72Q80 15.00% 1.29 7.30% 2.58 8.90% 3.00Q90 10.00% 1.80 5.80% 2.58 7.00% 3.00Q95 15.00% 1.80 12.30% 2.58 8.40% 3.00

E[DAI]t 1.41 2.23 1.95Wt 0.40 0.33 0.27

Table 10Risk analysis in December of 2006

hi t = 1 (January) t = 2 (February) t = 3 (March)

p1(hi) DAI p2(hi) DAI p3(hi) DAI

Q10 16.50% 0.43 10.40% 0.43 8.80% 0.00Q20 13.50% 0.43 16.80% 0.68 12.30% 0.43Q30 10.00% 0.43 20.20% 0.68 16.30% 0.68Q40 6.50% 0.43 5.30% 0.68 12.80% 1.54Q50 12.50% 0.43 8.20% 0.68 11.50% 2.23Q60 10.00% 0.43 9.10% 0.68 7.90% 2.23Q70 8.00% 0.43 6.40% 0.68 7.30% 2.58Q80 7.50% 0.43 7.90% 0.68 6.00% 2.58Q90 9.00% 0.43 5.20% 0.68 3.60% 2.58Q95 6.50% 0.43 10.70% 1.54 13.60% 2.58

E[DAI]t 0.43 0.75 1.58Wt 0.40 0.33 0.27

656 W.-C. Huang, C.-C. Chou / Advances in Water Resources 31 (2008) 649–660

ity distribution of rainfall provided by the Weather Bureauwould be crucial at this moment.

At present, the Weather Bureau can simply provideprobabilistic rainfall prediction for the next three months,and update the information monthly. According tomonthly quantity, rainfall is classified as (less-than-normal,normal, more-than-normal). The then predicted probabili-ties in March, April, and May, respectively, were(0.4,0.4, 0.2), (0.4,0.4,0.2), and (0.2,0.5,0.3). The so-called‘‘normal” rainfall ranges between 118 and 198 mm inMarch, between 109 and 221 mm in April, and from 188to 303 mm in May. Obviously, the chance to obtain rainfallover 100 mm per month for the next 3 months would reach60%. The rainfall quantity was approximately medianvalue. As known, decision makers commonly take a moreconservative attitude toward significant risks than expectedvalue would suggest [9]. Accordingly, the WRA proclaimeda partial fallowing of 17,536 ha on March 2 of 2006, akinto an orange alert. And a total of NT$1159 million (nearlyUS$35 million) was paid to compensate the owners of idlefarmland. On the other hand, the Weather Bureau onMarch 1 predicted probably normal rainfall (estimatedprobability of 0.6 over 100 mm/month) in the comingmonths. In hindsight, the partial fallowing option wasunfortunately identified as inappropriate because consider-able sum of spring rainfall subsequently arrived. The accu-mulated rainfall over the Shihmen basin in March andApril reached 216 mm and 269 mm respectively, nearly30% exceedence probability of rainfall. The partial fallow-ing decision was a failure.

Uncertainty rules out guaranteeing that the best out-come is obtained. The risk-based DEWS, however, pro-vides a complete procedure for making a decision.Because much more rainfall fell than expected, the pre-dicted ‘‘orange” decision missed the actual ‘‘blue” level,and the cost of fallow decision in the early spring of 2006was huge. Obviously, the decision failed. The lessonpointed out that some difficulties remain in making a cor-rect decision under uncertainty. For instance, the long-termrainfall prediction information from the Weather Bureau

could yet give sound advice in decision making. If predic-tion techniques could be enhanced, the overall accuracyof the risk-based DEWS would definitely be improved.

4.2.5. Decision in December of 2006

Because of an unsuccessful decision in late February of2006, the WRA is concerned what kind of action shouldbe taken for the next growing season. In early Decemberof 2006, the remaining volume equaled 154.26 MCM inthe Shihmen reservoir along with nearly 12 cubic metersper second in inflow, where the present drought index D

remained at level 2. In accordance with various hydrologicconditions, the DEWS simply yielded ‘‘green” and ‘‘blue”

signals, where the ‘‘green” signal represented expectation.Risk analysis also showed the probabilities for ‘‘green” in(December, January, February) would equal (100%,92.4%, 52.8%). And the Weather Bureau predicted thatthe chance for the upcoming 3-month-long rainfall to reach100 mm/month probably would be over 80%. Accordingly,as from December 1, a ‘‘green” signal would be recom-mended within the next three months.

In fact, the area rainfall in December totaled up to156 mm. As of December 31, there was as much as168.69 MCM of storage in the reservoir. As a result,options ranging from ‘‘green” to ‘‘blue” are possiblechoices under the specified hydrologic conditions (seeTable 4). The expected DAI value still indicates a ‘‘green”

level. Obviously to keep going on the irrigation projectwould be available. Furthermore, the renewed probabilitieswith a ‘‘green” level in (January, February, March) reach(100%, 89.3%, 37.4%), as shown in Table 10. Comparedwith the previous estimation, the updated probabilities of‘‘green” in January and February are higher. In the mean-time, the ‘‘green” option remains as u 5 0.6 according todecision makers’ attitudes toward risk (see Table 6). On29 December of 2006, the Weather Bureau said there wasan 80% probability that potential rainfall from this comingJanuary through March would exceed 100 mm/month. Thepredicted rainfall is more than the median value. Hence theDEWS would introduce a ‘‘green” signal to the WRA.

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That is, the action to satisfy all water targets on schedulefor this coming 2007 spring growing season would be avail-able. In hindsight, the choice of ‘‘green” option is correct.

5. Model validation

5.1. Based on expected value

Table 3 presents the error matrix corresponding to theexpected DAI analysis. The overall accuracy over the sim-ulation period (1964–2005) was 76.72%. For the ‘‘green”

signal, both producer’s accuracy and user’s accuracyreached 96.20% and 88.24% respectively. Nonetheless, allthe remaining signals had producer’s accuracies thatranged from 16.30% to 23.08% and user’s accuraciesbetween 16.18% and 85.71%. Since RI < 0 (�316 here)and UE(19.71%) > OE(3.57%), it illustrated a risk-seekingbehavior herein. With scrutiny, the overall accuracies dur-ing the less-than-normal-, normal-, and more-than-normal-year conditions were 58.97%, 80.71%, and 91.16% respec-tively. The high accuracy rate occurred in wet years demon-strates that the ‘‘green” signal will prevail over mosthydrological conditions. The expected DAI calculationwould result in a unique ‘‘green” option. On the contrary,it is apparently more difficult to make decisions during adry year. The accuracies in 2002–2003, for example, merelyapproximated 36%. Obviously it is insufficient for decisionmakers to rely on the expected DAI value alone. An in-depth study about decision maker’s attitude toward riskwould be essential.

5.2. Based on decision maker’s behavior

In response to a decision maker’s behavior, Table 11shows the overall, producer’s, and user’s accuracies associ-ated with any specified probability. The highest overallaccuracy (79.17%) occurred within the range betweenu = 0.5 and u = 0.6. The overall accuracy, however, felldramatically afterward. An extremely conservative behav-ior as u = 0.99 (RI = 950) apparently led to the lowestaccuracy (58.33%) even though it attained the highest pro-ducer’s accuracy of ‘‘red” signal to 92.31%. Oppositely, anextremely risky attitude at u = 0.01 (RI = �714) obtainedthe highest producer’s accuracy of ‘‘green” signal with99.91%. Meanwhile, overall accuracy up to 74.87% can stillbe preserved. This is because the number of true ‘‘green”signal (1,131) occupied most of the total size number(1512), and ‘‘green” signal can be selected with ease byu = 0.01.

According to the user’s accuracy shown in Table 11, if arisk-averse attitude associated with u = 0.9 yields a ‘‘green”

signal, then the WRA officials could have 99% confidencefor the ‘‘green” action, such as the event in February of2005. Similarly, there would be 97% confidence by takinga ‘‘green” action along with u = 0.8 for the event in earlyDecember of 2006. On the other hand, from the producer’saccuracy, when a risk-seeking attitude by u = 0.3 suggests a

‘‘red” signal, the ‘‘red” event would be true. In this case, adecision to fallow all farmland should be made as soon aspossible, for instance, the event in late December of 2003(see Table 6). For the remaining signals (blue, yellow, andorange), the peak user’s accuracies occurred, respectively,at u = 0.7, 0.6, and 0.5 (see Table 11). The accuracies, how-ever, remained unsatisfactory. For instance, the predictedaccuracy for ‘‘orange” alert only reached 54.55%. So theevents both in late February of 2002, and of 2006, clearlyneeded more information for making final decisions.

Fig. 5, moreover, demonstrates that both underestimatedand overestimated errors will change in inverse proportionsubject to variation of probability. It clearly comes outtoo optimistic (risk-seeking) to underestimate system per-formances, and too pessimistic (risk-averse) to overestimatesystem oppositely. So, the higher the probability, largeroverestimated error will arise. It was found the point asUE = OE occurred between u = 0.6 and u = 0.7, identicalto the point with RI = 0. (see Table 11). As a result, wecan objectively define ‘‘risk-neutral” as 0.6 5 u 5 0.7,‘‘risk-seeking” as u < 0.6, and ‘‘risk-averse” as u > 0.7. Itshows extremely risk-seeking and risk-averse attitudes inDEWS decision making are not suggested. In detail, Fig. 6expresses the variation of overall accuracies toward risk,respectively, in less-than-normal-, normal-, and more-than-normal-year conditions. We found the ‘‘risk-neutral”as 0.6 5 u 5 0.7 for both normal- and more-than-normal-year conditions, whereas 0.7 5 u 5 0.8 for less-than-nor-mal-year condition. The accuracy in more-than-normal yearwas clearly the highest. And a risk-seeking attitude canobtain better performance in overall accuracy over 90% inmore-than-normal year and around 80% in normal year.On the contrary, it reached worse accuracy with a smalleru value in less-than-normal year. Extremely risk-aversebehavior, say, at u = 0.99 was not favored either.

In general, the municipal water supply takes priority,and the water for irrigation will be restricted when a watershortage occurs. Therefore, before implementing a sched-uled irrigation project, a critical decision about waterrelease strategy should be made in between January andFebruary for the spring growing season, and in mid-Julyfor the summer growing season. These are the key points.Table 12 shows that, within the period from Januarythrough February, all the overall accuracies, user’s accura-cies, and producer’s accuracies simultaneously appear bet-ter between u = 0.6 and u = 0.7. And the ‘‘risk-neutral”occurs nearby u = 0.6 in terms of RI. We also found thatno ‘‘red” level ever happened in mid-July, and an attitudeas u 5 0.7 would not yield a ‘‘red” alert, where the ‘‘risk-neutral” was close to u = 0.7.

Indeed, attitudes can be changed through advice. Thedecision process is like an analyst to play a support role,whereas the WRA official is the decision maker to seekthe best option. The former offers a rational reasoning pro-cess to the latter on the choice of signal alerts. Generallyspeaking, both extremely risk-seeking and extremely risk-averse attitudes are not recommended in decision making.

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Table 11Accuracy assessment based on specified probability over 1964–2005

Specified probability (u) Green Blue Yellow Orange Red OAc RId

UAa PAb UA PA UA PA UA PA UA PA

0.01 77.61 99.91 0.00 0.00 0.00 0.00 16.67 2.47 – 0.00 74.87 �7140.1 78.62 99.82 3.23 0.74 0.00 0.00 20.83 6.17 – 0.00 75.07 �6670.2 80.92 99.73 7.41 2.96 0.00 0.00 29.27 14.81 100.00 7.69 75.93 �5810.3 82.99 99.20 7.35 3.70 10.00 3.54 31.11 17.28 100.00 13.46 76.19 �5010.4 85.36 97.97 15.91 10.37 25.76 15.04 41.30 23.46 92.86 25.00 77.45 �3980.5 87.05 96.91 15.73 10.37 41.38 31.86 54.55 37.04 95.45 40.38 79.17 �2960.6 88.27 94.52 15.00 8.89 43.52 41.59 53.09 53.09 81.25 50.00 79.17 �1450.7 91.76 89.57 31.13 24.44 43.38 52.21 47.79 66.67 60.38 61.54 78.77 1170.8 97.03 77.98 27.83 47.41 33.14 51.33 41.88 60.49 49.38 76.92 72.29 4430.9 99.20 65.43 19.84 37.78 25.00 60.18 36.46 43.21 33.33 90.38 62.24 8410.95 99.17 63.04 17.83 34.07 23.61 60.18 32.65 39.51 32.21 92.31 59.99 9120.99 99.14 61.01 16.30 33.33 23.59 59.29 30.19 39.51 32.00 92.31 58.33 950

Expected 88.24 96.20 16.18 16.30 24.10 17.70 39.13 22.22 85.71 23.08 76.72 �316

a UA: user’s accuracy (%).b PA: producer’s accuracy (%).c OA: overall accuracy (%).d RI: risk index.

30.00

40.00

50.00

60.00

70.00

80.00

90.00

100.00

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Specified Probability (u)

Ove

rall

Acc

urac

y (%

)

Less-than-normal yearsNormal yearsMore-than-normal years

Fig. 6. Variation of overall accuracy toward risk within the given hydrologic years.

0.00

10 00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

100.00

0 0.1 0.2 0.3 0.4 0.5Specified Probability (u)

0.6 0.7 0.8 0.9 1

Acc

urac

y / E

rror

(%

)

Overall AccuracyOverestimated ErrorUnderestimated Error

Fig. 5. Accuracy variation in response to any specified probability toward risk.

658 W.-C. Huang, C.-C. Chou / Advances in Water Resources 31 (2008) 649–660

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Table 12Accuracy assessment toward risk for the spring growing season

Specified probability (u) Green Blue Yellow Orange Red OA RI

UA PA UA PA UA PA UA PA UA PA

0.01 71.37 100.00 0.00 0.00 0.00 0.00 0.00 0.00 – 0.00 64.73 �1670.1 72.49 99.40 0.00 0.00 0.00 0.00 0.00 0.00 – 0.00 64.34 �1520.2 74.77 99.40 9.09 3.45 0.00 0.00 7.69 6.67 100.00 16.67 66.28 �1240.3 77.00 98.20 7.69 3.45 7.69 3.45 13.33 13.33 100.00 22.22 66.67 �1040.4 84.24 92.81 23.33 24.14 33.33 24.14 28.57 26.67 88.89 44.44 70.16 �540.5 86.29 90.42 16.67 13.79 44.12 51.72 60.00 40.00 93.33 77.78 73.46 �220.6 88.34 86.23 25.00 24.14 52.78 65.52 78.57 73.33 94.12 88.89 76.36 60.7 97.14 81.44 42.11 55.17 51.11 79.31 80.00 80.00 85.00 94.44 79.07 490.8 98.35 71.26 33.33 51.72 41.51 75.86 61.11 73.33 80.95 94.44 71.32 850.9 100.00 61.68 15.91 24.14 35.21 86.21 53.33 53.33 72.00 100.00 62.40 1270.95 100.00 59.28 14.58 24.14 34.29 82.76 46.67 46.67 69.23 100.00 60.08 1330.99 100.00 59.28 14.58 24.14 34.78 82.76 43.75 46.67 69.23 100.00 60.08 134

Expected 89.29 89.82 21.15 37.93 12.50 6.90 23.53 26.67 80.00 22.22 66.28 �49

W.-C. Huang, C.-C. Chou / Advances in Water Resources 31 (2008) 649–660 659

As far as the examples shown in this article are concerned,this risk-based DEWS performs well in reservoir operation.

6. Conclusions

This article presents a risk-based decision process for res-ervoir operation to integrate with a drought early warningsystem (DEWS), initially developed by the authors [5,6].Since the latter did not explore the choices among alterna-tives (alert levels), this paper is further to link drought mea-sures with decisions under uncertainty, as shown in Fig. 1.The model would tell decision makers the chances of alter-native occurrences and the corresponding options to givenchances. Based on the posterior information, decision mak-ers can realize the tendency of attitude associated with anyspecified probability by means of accuracy assessment, andlearn to adjust their attitudes in decision-making process. Inaddition, we characterize decision makers’ attitudes interms of a risk index, and consider a recession effect onthe drought alert index. In practice, this developed decisionprocess provides a procedure to cut the size of the set ofsolutions and offers the most probable drought alertoptions. It can help reduce the risk of human errors. In thispaper we select a specific case study (Shihmen reservoir) as apioneering experiment. The expected overall accuracyapproximated to 77% over the simulation period (1964–2005). In fact, we have continued to test some other mainreservoirs in Taiwan and found the proposed approach isvery practical for reservoir operations. Although uncer-tainty rules out guaranteeing that the best outcome wouldbe obtained, the risk analysis greatly helps the wateragency’s officials make decisions on signal choices. Besides,new techniques on long-term rainfall prediction will be agreat benefit to the risk-based DEWS.

Acknowledgement

This research was sponsored, in part, by the Water Re-sources Agency and the National Science Council ofTaiwan.

References

[1] Bell DE. Regret in decision making under uncertainty. Oper Res1982;30(5):961–81.

[2] Congalton RG. A review of assessing the accuracy of classifications ofremotely sensed data. Remote Sens Environ 1991;37:35–46.

[3] Congalton RG, Green K. Assessing the accuracy of remotely senseddata: principles and practices. Boca Raton, FL: CRC Press; 1999.

[4] Holloway CA. Decision making under uncertainty: models andchoices. New Jersey: Prentice-Hall, Inc.; 1979.

[5] Huang WC, Yuan LC. A drought early warning system on real-timemultireservoir operations. Water Resour Res 2004;40. doi:10.1029/2003WR002910. W0641.

[6] Huang WC, Chou CC. Drought early warning system in reservoiroperation: Theory and practice. Water Resour Res 2005;41.doi:10.1029/ 2004WR003830. W11406.

[7] Johnson GE, Achutuni VR, Thiruvengadachari S, Kogan F. The roleof NOAA satellite data in drought early warning and monitoring:selected case studies. In: Wilhite DA, editor. Drought assessment,management, and planning: theory and case studies. Kluwer Aca-demic Publishers; 1993. p. 31–48.

[8] Kahneman D, Tversky A. Prospect theory: an analysis of decisionunder risk. Econometrica 1979;47(2):263–92. doi:10.2307/1914185.

[9] Kirkwood CW. Strategic decision making: multiobjective decisionanalysis with spreadsheets. CA: Duxbury Press, Wadsworth Publish-ing Company; 1997.

[10] Kogan FN. Global drought watch from space. Bull Am Meteorol Soc1997;78(4):621–36.

[11] Lawrimore J, Heim Jr RR, Svoboda M, Swail V, Englehart PJ.Beginning a new era of drought monitoring across north America.Bull Am Meteorol Soc 2002;83(8):1191–2.

[12] Lohani VK, Loganathan GV. An early warning system for droughtmanagement using the Palmer drought index. J Am Water ResourAssoc 1997;33(6):1375–86.

[13] Loucks DP, Stedinger JR, Haith DA. Water resource systemsplanning and analysis. New Jersey: Prentice-Hall, Inc.; 1981.

[14] Lunetta RS, Lyon JG, editorsRemote sensing and GIS accuracyassessment. Boca Raton, FL: CRC Press; 2004.

[15] McKee TB, Doesken NJ, Kleist J. Drought monitoring with multipletime scales. In: 9th Conference on applied climatology, Dallas, Texas,1995. p. 233–6.

[16] Palmer WC. Meteorologic drought. Research Paper No. 45, USWeather Bureau, 1965.

[17] Pappenberger F, Beven KJ. Ignorance is bliss: Or seven reasons not touse uncertainty analysis. Water Resour Res 2006;42(5). W05302.

[18] Shafer BA, Dezman LE. Development of a surface water supply index(SWSI) to assess the severity of drought conditions in snowpack

Page 12: Risk-based drought early warning system in reservoir operation

660 W.-C. Huang, C.-C. Chou / Advances in Water Resources 31 (2008) 649–660

runoff areas. In: Proceedings of the western snow conference,University of Colorado, Fort Collins, Colorado, 1982. p. 164–75.

[19] Rao Z, Moore IN, O’Connell PE, Jamieson DG. An interactivemanagement system for operational control of Kirazdere reservoir(Turkey). Water Resour Manage 2001;15(4):223–34.

[20] Vicente-Serrano SM. El Nino and La Nina influence on droughts atdifferent timescales in the Iberian Peninsula. Water Resour Res2005;41(12). W12415.

[21] Vogt JV, Somma F, editorsDrought and drought mitigation inEurope. The Netherlands: Kluwer Academic Publishers; 2000.

[22] Wernerfelt B, Karnani A. Competitive strategy under uncertainty.Strategic Manage J 1987;8(2):187–94.

[23] Wilhite DA, Svoboda MD. Drought early warning systems in thecontext of drought preparedness and mitigation. In: Wilhite DA,Sivakumar MVK, Wood DA, editors. Early warning systems fordrought preparedness and drought management, World Meteorolog-ical Organization, Geneva, 2000. pp. 1–16.

[24] Wilhite DA, Sivakumar MVK, Wood DA, editorsEarly warningsystems for drought preparedness and drought manage-ment. Geneva: World Meteorological Organization; 2000.