Reducing the impacts of flood-induced reservoir turbidity on a regional water supply system

Advances in Water Resources 33 (2010) 146–157

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Reducing the impacts of flood-induced reservoir turbidity on a regional water supply system Frederick N.-F. Chou, ChiaWen Wu * Department of Hydraulic and Ocean Engineering, NCKU, No. 1 Dasyue Rd., Tainan City 70101, Taiwan

a r t i c l e

i n f o

Article history: Received 31 December 2008 Received in revised form 27 July 2009 Accepted 27 October 2009 Available online 31 October 2009 Keywords: Water supply Turbid reservoir High turbidity Simulation

a b s t r a c t This paper proposed an integrated simulation model to incorporate the impact of flood-induced reservoir turbidity into water supply. The integrated model includes a regional water allocation model and a onedimensional settling model of cohesive particles based on Kynch’s theory. It simulates the settling of sediment flocculation in a turbid reservoir. The restrictions of water supply during floods is mimicked by simulating turbidity profiles for control points and then quantifying the associated treatment capability of raw water in the regional water allocation model for each time step. This framework can simulate shortages caused by flood-induced high turbidity as well as extended droughts, thus provide a basis for comprehensive evaluations of emergent and regular water supply facilities. A case study of evaluating different measures to mitigate the impact of turbid reservoir on water supply in northern Taiwan is presented to demonstrate the efficacy of the proposed approach. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction The devastating Jiji earthquake occurred on September 21, 1999 in central Taiwan. This earthquake was measured 7.3 on the Richter scale. It had caused large scale landslides and avalanches which brought significant impacts on the stability of hill slopes in watersheds. After Jiji earthquake, the streamflow turbidity and suspended sediment concentration during flood both significantly rose. Along with other critical factors, such as the steep terrain and dense rainfall, floodwaters in Taiwan are often accompanied by enormous amounts of sediment. Turbidity frequently exceeds the treatment limit of treatment plants. Public water demands often suffer serious shortage due to the lack of clear raw water. High turbidity of raw water during typhoons has become one of the major threats to water resources administrators in Taiwan over the last decade. Although the flood-induced high turbidity and its impact on water supply is a world-wide problem, its severity in Taiwan is much more critical than most cases mentioned in the literature [1–5]. Typhoon Aere of 2004 constitutes a particularly representative case. It brought the heaviest precipitation of the last 40 years to the watershed of the Shihmen Reservoir, a major reservoir on the Tahan River of northern Taiwan. The peak inflow was 8500 m3/s, and the total runoff volume approached 700 million m3, which was three times the total capacity of Shihmen Reservoir. Due to the washout by extended torrential rainfall, several hillsides in * Corresponding author. Tel.: +886 6 2757575x63269; fax: +886 6 2741463. E-mail address: [email protected] (C. Wu). 0309-1708/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.advwatres.2009.10.011

the watershed of reservoir collapsed, and about 28 million m3 of sediments were flushed into the reservoir. The turbidity of streamflow and reservoir storage rose to 100,000 NTU, which significantly exceeds the treatment threshold. The muddy storage of Shihmen Reservoir clarified extremely slowly following Typhoon Aere. All regional treatment plants were unable to process raw water from the Tahan River and the Shihmen Reservoir, causing a 19-day public water supply outage in southern Taoyuan district. Severe economic losses, as well as social and political crises, ensued. In addition to the immense sediment yield, another critical cause of severe shortage was the lack of outlet work being able to withdraw clear water from the Shihmen Reservoir. The major intake where treatment plants withdraw water was originally designed for agricultural uses, which accept much lower water quality. This intake was thus set near the bottom of the reservoir to enable water withdrawal even when storage is low. Following Typhoon Aere, several comprehensive projects were proposed to resolve the sedimentation and water supply problems of Shihmen Reservoir. The major measures adopted were to improve watershed management, reconstruct sluiceway, elevate public water intake and develop backup water supply systems. The proposed backup systems include building storage ponds and expanding trans-district pipes in the public water supply system. For assessing the functions of the above water supply proposals, simulation is the major approach used in Taiwan. It entails constructing computer models to imitate the operations of a water resources system and predict the probable shortages under a given set of conditions. The backup water supply facilities can be used for mitigating emergent water shortages and may also be utilized

F.N.-F. Chou, C. Wu / Advances in Water Resources 33 (2010) 146–157

for year-round water supply. Trans-basin pipes, for example, can improve spatial allocation of available water even during normal conditions. Storage ponds may be filled during the monsoon season in order to ensure steady water supply during the dry season as well as emergent water supply during typhoons. Hence, a simulation model should be able to mimic water supply and shortage during drought as well as typhoon periods for evaluating the contributions of backup facilities. The turbidity of raw water in the system following a typhoon should be estimated to figure out the restrictions on water withdrawal and treatment. If treatment plants withdraw water from reservoirs, then the settling of sediments in the reservoir should also be modeled to understand turbidity patterns at the elevations of water intakes. For most conventional simulations of water supply in Taiwan, engineers have developed codes for specific systems on the basis of water law, agreements between purposes, rule curves of a multi-purpose reservoir, logical judgment and iterative procedures [6]. However, applying the conventional approach to a complex water resources system always compels engineers to simplify the system and analysis. Another drawback to the conventional approach is the lack of generality, which means one existing program code written by the engineer cannot be applied to other systems without considerable modification or an entire rewrite. Alternatively, one may apply commercial general water allocation simulation package, such as HEC-ResSim [7], MIKE BASIN [8], RIBASIM [9] or ARSP [10]. However, these models are still not general enough to effectively simulate certain characteristics of water resources systems in Taiwan, such as daily or even hourly simulation time step, the operating rule curves, the peak-hour hydroreleasing of reservoirs, channel losses and most importantly the impact of turbidity on water supply. This paper integrates a generalized regional water allocation simulation model, GWASIM, developed by Chou and Wu [11], with a one-dimensional sediment settling model. It proposes an integrated framework for incorporating typhoon-induced turbidity of raw water into water supply simulation. This framework facilitates evaluation of both emergent and regular water supply facilities as well as provides a basis for decision makers to develop a comprehensive master plan. This paper introduces the proposed framework for analysis. It then demonstrates the efficacy of proposed model with a case study of water supply in the Tahan River system of northern Taiwan.

2. Literature review While an extensive body of literature addresses the effects of water quality on water supply, the specific role of turbidity has been largely neglected in the field of regional water resources simulation. MODSIMQ allocates water in a manner that incorporates water quality effect by combining the generic river basin management decision-support system MODSIM [12–14] with the QUAL2E water quality model of the US Environmental Protection Agency [15]. MODSIMQ applies MODSIM to generate a water allocation scenario as the input boundary conditions of QUAL2E, which simulates contaminant concentrations at each control point in the system. An iterative procedure based on the Frank–Wolfe nonlinear programming algorithm links MODSIM and QUAL2E. This procedure retains the water allocation efficiency of MODSIM while ensuring that the solution satisfies water quality requirements. HEC-5Q analyzes the operations of large multiple reservoir systems for water quality [16]. The water quality simulation module in HEC-5Q accepts system flows generated by the flow simulation module and computes the distribution of water quality constituents in up to 20 reservoirs as well as their associated downstream reaches. For each reservoir, a port selection algorithm selects

147

which of the available gates to open and what flow rate should pass through each gate, so that the desired reservoir release quality is obtained. If the water quality objectives cannot be satisfied using the initially-computed balanced pool flows, then the model will compute the modified flow distribution necessary to satisfy all downstream objectives. The method proposed here focuses on turbidity while other water quality models such as MODSIMQ and HEC-5Q analyze a variety of contaminants. For MODSIMQ or HEC-5Q, the point or non-point sources of constituents may come from the regular return flow of irrigation, farms, ranges, domestic or industrial districts, while the turbidity of raw water is related to the sediment, phytoplankton, algae and other inorganic tripton. Among these suspended particles, sediments from erosion during torrential rainfalls in Taiwan are the essential cause for the catastrophically high turbidity and disruption of water supply. As if the case of Shihmen Reservoir, the peak turbidities of its release during typhoons usually exceeded 10,000 NTU while the treatment threshold is approximately 3000 NTU. These storages were not merely turbid but muddy, and their turbidities are incomparable to most cases in the literature. Due to the dominant role of sediment in the cause of turbidity, regression analysis by Hsu [17] showed a strong linear correlation between sediment concentration versus turbidity with the maximum turbidity sample as 128,150 NTU. This empirical relationship provides a basis for this study to model the turbidity-induced water supply restriction through simulating the sediment concentration in reservoir. Streamflow turbidity during regular periods is generally low. It does not incapacitate treatment plants and public water supply systems. For the purpose of water resources planning analysis, the turbidity of raw water need only be estimated during typhoon or storm periods. Limited space and mountainous topography restrict reservoir capacity in Taiwan, thus challenging water resources officials to operate reservoir during typhoons to alleviate the impact of high turbidity on short-term water supply. The reservoirs are typically filled during typhoons, and the capacities of sluiceways cannot fully vent the turbid inflow. The unvented turbid current in a reservoir usually creates a muddy lake after typhoon. The suspended floc in a muddy lake is comprised primarily of silt- and clay-sized sediments that adhere to each other, while most sand-sized sediments deposit in the backwater zone of the impoundment to form a delta [18]. When the concentration exceeds a specific threshold, the flocs may further link to become a flocculated-framework [19], in which particles ‘‘lose their individual identity and settle en masse” [20]. Due to the influence of inter-particle forces and the upward flux of displaced water, the flocculated-framework settles much slower than do individual particles, whose motion may be adequately predicted by Stokes’ law [21,22]. Hsu [17] also observed this phenomenon of slower settling in experiments using mud of the Shihmen Reservoir. Generally sediment movement within a reservoir can be conceptualized as contributing to delta formation via quasi-homogeneous flow, turbidity currents and settling of the sediment flocs [17,18]. This study examines how settling of sediment flocs in reservoirs affects post-typhoon public water withdrawal regardless of sedimentation processes near bottom. A one-dimensional phenomenological model was developed based on the theory of Kynch [23] to simulate the settling of sediment flocs in a muddy lake. The simulated sediment concentration profile indicates the number of days that a given typhoon will restrict treatment plants from withdrawing water from a reservoir. The water supply allocation model incorporates withdrawal limitations due to streamflow turbidity and muddy lakes. This study proposes a simulation model to facilitate water resources allocation with respect to the impact of typhoon-induced turbidity. The simulation for water resources planning is based

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on estimated reservoir capacities and demand levels for a specified target year. Although this study considers the settling of sediments in reservoirs, it is assumed that the capacities of reservoirs do not change during the target year. Historic unregulated streamflow records for the system provide a hydrologic basis for sequential routing of water supply. Simulation results quantify the probable short-term water shortages due to floods and long-term shortages due to drought conditions in every hydrologic year.

ci ¼ 1000 þ 10  pi

3. Methodology 3.1. Water allocation model GWASIM, the generalized water allocation model, is specialized by incorporating physical and operational parameters of Taiwanese water resources system. It is a network flow programming (NFP) based model and developed by consulting the water allocation philosophy and structure of MODSIM of Colorado State University [12–15]. GWASIM conceptualizes a water resources system as a flow network with continuity at nodes and capacity limits of links, thus facilitating solution by NFP. NFP, a special formulation of linear programming (LP), may be resolved by more efficient algorithms than conventional simplex method of LP. NFP minimizes the total flow cost of a network, while maintaining flow conservation at nodes and ensuring that flow in every link obeys the upper and lower limits. An NFP formulation with m nodes may be expressed mathematically as follows:

Minimize

m X m X i¼1

subject to

cij  xij

ð1Þ

j¼1

m X j¼1

flow into the terminal node by applying a large positive cost coefficient to the artificial terminal link. Successive approximation quantifies system loss components, such as channel loss, water treatment loss and reservoir evaporation, thereby improving estimates of available water supply. Artificial links divert these losses from the system to the surrounding network. The pseudo-cost of conveyance through artificial storage or demand links in GWASIM is expressed below:

xij 

m X

xki ¼ 0;

i ¼ 1; . . . ; m

ð2Þ

k¼1

lij 6 xij 6 uij ;

i; j ¼ 1; . . . ; m

ð3Þ

where m is the total number of nodes; j, k the numbering of nodes; xij the flow entering link from node i to node j; cij the costs per unit flow in links from node i to node j, lij the lower bound on flow in link from node i to node j and uij is the upper bound on flow in links from node i to node j. For water allocation analysis, pseudo-costs of links are commonly employed as a means of prioritizing the distribution of flows in the network according to water right, agreements between users, reservoir operating rule curves and other allocation mechanisms. By assigning proper priorities for demand or storage links, the NFP model can optimally allocate available water according to operating rules of the system. GWASIM conceptualizes a water resources system as a network by nodes and links. Fig. 1 depicts the basic user-specified real and model-generated artificial elements of a generalized water resources network system. The model provides seven distinct node categories – storage facilities, demand areas, diversions, hydropower plants or instream-use purposes, water treatment plants, confluence or bifurcation of river reaches, and terminal nodes – to simulate the range of significant water supply functions. Directed, capacitated links – river reaches, tunnels, canals, or pipes – convey water between these nodes. Daily simulation is performed in default. Like MODSIM, GWASIM achieves flow circulation with the surrounding water resources network by generating artificial nodes and links to convey water into and out of the system. Artificial accounting inflow links convey unregulated streamflows and initial reservoir storages into the system. Flows in other artificial links specify allocated storages, supplies or water losses of connected nodes to assure water balance. The terminal node receives all residual flows, including reservoir spill, of the physical system and conveys them to the surrounding network. GWASIM penalizes

ð4Þ

where ci is the pseudo-cost coefficient of artificial link i, and pi is the priority of artificial link i. GWASIM ensures necessary flows with priority values below 100 for artificial demand and storage links, while it penalizes artificial terminal links with priority values that exceed 100. Pseudo-cost coefficients for realistic links are assigned 0 in default. Preferred realistic links may be favored with positive or negative cost coefficients to locally direct flows. The difference of cost coefficients of artificial links is set by a value of multiple of 10 to prevent the overall allocation principles disturbed by the cost coefficients on the realistic links. GWASIM separates reservoir storage and related demand of operating rule curves into several discrete levels and assigns each level a stratified priority. Different levels of storages and demands are represented by artificial sub-storage and sub-demand links to convey water of distinct priorities. Fig. 1 illustrates a reservoir with three rule curves as severe, lower and upper limits, respectively. Suppose the operating rules prescribe that (1) if the reservoir storage is below the severe limit, only 70% of demand should be satisfied, (2) if the storage is between the severe and lower limits, only 90% of demand should be satisfied, (3) if the storage is above the lower limit, the demand should be fulfilled and (4) if the storage is above the upper limit, the reservoir can release more water to execute peak-hours hydrogeneration. Under this doctrine, four artificial sub-storage links from the reservoir node, three sub-demand links from the demand node and one from the hydro-demand node are added to represent different water allocations. Pseudo-cost coefficients of these artificial links are set as below to represent the relative priority of each respective storage or demand:

Cd1 < Cs1 < Cd2 < Cs2 < Cd3 < Cs3 < Cp < Cs4 < Ct

ð5Þ

where Cs1 ; Cs2 ; Cs3 and Cs4 are assigned for artificial storage links, Cd1 ; Cd2 ; Cd3 and Cp for artificial demand links and Ct for the terminal link. These cost coefficients provide a basis for NFP to simulate the flow allocation which conforms to the operating rule curves. GWASIM utilizes the same concept of MODSIM in simulating non-consumptive water use demand, such as instream flow requirements and hydrogenation [24]. This method operates by iteratively removing flow as a consumptive demand from the network, but then replacing those flows at one specified return node (usually the next downstream), which essentially corresponds to demand with 100% return flow without lag [14]. Fig. 1 depicts the hydropower node in its usual schematic location: just downstream of a reservoir node. This node requires water only during the period of peak-hours for each day; the exact timing and duration of hydropower demand varies from day to day. The hydrogenating rule is a component of operating rule curves of a reservoir. It may allocate surplus reservoir storage to hydrogeneration, thus allow operators to release more water than consumptive demands, to increase hydropower and lower the risk of spillage. The hydropower plant characteristics, as well as the number of peak-hours and the effective head for a given day, iteratively determine the daily water demand of a given hydropower node. Prioritization usually favors peak-hours hydrogeneration over reservoir flood storage but below domestic, industrial and agricultural demands.

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149

Fig. 1. Illustration of network structure of GWASIM.

3.2. One-dimensional settling model for cohesive particles The unidimensional settling model of this study, based on Kynch’s theory of flocculent suspension [23], simulates the settling of sediment flocs in a reservoir. Kynch’s settling theory is widely applied to fields such as chemical engineering, mineral processing, food industries and waste water treatment [25]. Concha and Bustos [26], who presented Kynch’s theory as a unified kinematic process, developed a rigorous mathematical formulation of batch settling in a cylinder. They presented the following assumptions of Kynch’s theory: 1. The solid particles are all small with respect to the container and of the same size, shape and density. 2. Solid particles in suspension and the fluid itself are incompressible. 3. There is no mass transfer between components. 4. The settling velocity, denoted as v s , at any point in the suspension is a function of the local particle concentration only. A mixture obeying such assumptions may be called an ideal suspension. 5. The movement of a suspension is one-dimensional. The field variables are functions of time and only one space variable. Thus, there is no wall effect, and the concentration of particles is constant at any cross-section of the vessel. On their basis of batch sedimentation in still water, Concha and Bustos [27] further developed the continuous Kynch settling process to the case of injecting clear water at a specific height and

allowing thickened pulp at the bottom of the container. Bürger et al. [28] extended the phenomenological theory of batch and continuous settling to vessels with non-uniform cross-sections. This study models a typhoon-affected reservoir as a large vessel with varying cross-sections and multiple intakes and outlet works at different elevations. Based on the results of Bürger et al. [28], the analysis of reservoir sedimentation simulation requires the following additional assumptions: 1. Reservoir inflow directly converges into a zone of similar concentration. 2. The inflow and outflow of a reservoir after flood do not cause significant horizontal fluid movement. The flow condition can be regarded as vertically unidimensional. The volume discharge throughout the depth is piecewise uniform. It will vary only at the location of outlets and where the inflow converges. 3. The accumulation of consolidated sediments is negligible. These assumptions allow the following continuity equations for water and sediment in a reservoir:

AðzÞ  @C=@t þ

@½AðzÞ  C  v s  ¼ qi  CI  qo  C @z

@½1  C @½AðzÞ  ð1  CÞ  v f  þ @t @z ¼ qi  ð1  CIÞ  qo  ð1  CÞ

ð6Þ

AðzÞ

ð7Þ

in which AðzÞ is the cross-sectional area of the vessel at height z (m2), C the average volumetric sediment concentration in the ves-

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sel, v f the velocities of the fluid components in the mixture (m/day), v s the velocities of the solid components in the mixture (m/day), qi the lateral inflow discharge within unit height (m2/day), qo the lateral outflow discharge within unit height (m2/day), CI is the volumetric sediment concentration of the lateral inflow. Combining (6) and (7) yields:

@ @Q ðz; tÞ fAðzÞ  ½C  v s þ ð1  CÞ  v f g ¼ ¼ qi  qo @z @z

ð8Þ

where Q ðz; tÞ is the volumetric discharge of the mixture at height z and time t. Substitution of (8) into (6) yields:

@C @½AðzÞ  C  v s  þ @t @z @C @½Q ðz; tÞ  C þ AðzÞ  C  ð1  CÞ  ðv s  v f Þ ¼ AðzÞ þ @t @z ¼ qi  CI  qo  C

( t qij

¼

QIt Dzndz

0

if j 2 ZONE if j R ZONE

ð15eÞ

where QIt is the lateral inflow discharge during iDt to t þ Dt. Thus with the necessary information known beforehand, the field variables can be obtained by solving Eqs. (8), (14) and (15). These necessary information include the initial and boundary conditions, the empirical drift flux function, the discharge and concentration of the lateral inflow, the discharge and range of the lateral outflow, and the geometric characteristics of vessel. 3.3. Model integration

AðzÞ

ð9Þ

The Kynch’s kinematical settling theory is based on the assumption that C  ð1  CÞ  ðv s  v f Þ in Eq. (9) can be expressed by an empirical drift flux density function, fbk ðCÞ. This governing equation is derived by substituting fbk ðCÞ into (9):

A

@C @½Q  C þ A  fbk ðCÞ þ ¼ qi  CI  qo  C @t @z

ð10Þ

In order to solve (10), the initial concentration of suspension, C 0 , is assumed to be constant throughout the volume at t = 0:

Cðz; 0Þ ¼ C 0

for z > 0

ð11Þ

The surface concentration is assumed to clarify immediately as settling begins:

CðZL; tÞ ¼ 0

ð12Þ

where ZL is the height of storage in the vessel. The bottom of the vessel is assumed to be a closed boundary, which reduces the sediment flux at the bottom to zero:

fbk ðCÞjz¼0 ¼ 0 for t > 0

ð13Þ

In accordance with the aforementioned initial and boundary conditions, (10) can be solved using the explicit upwind difference scheme of Bürger et al. [28]:

Aj 

h   C tþ1  C tj 1 n t j EO C tjþ1 ; C tj ¼ Q jþ1 C tjþ1  Q tj C tj þ Ajþ1 fbk 2 Dt Dz  io C tjþ1 þ C tj t EO Aj1 fbk þ qij CItj  qotj C tj ; C tj1 2 2

ð14Þ

In (14), the outflow concentration term is calculated by averaging the concentrations within the interval where the outlet vents EO in water. The numerical Kynch batch flux density function fbk (14) is given by:

      EO fbk C tjþ1 ; C tj ¼ f þ C tjþ1 þ f  C tj Z C 0 max½fbk ðxÞ; 0  dx f þ ðCÞ ¼ fbk ð0Þ þ f  ðCÞ ¼

Z

ð15aÞ ð15bÞ

0

C

0

0 min½fbk ðxÞ; 0  dx

ð15cÞ t

This study assumes that the lateral inflow term of (14), qij , directly enters the storage zone whose concentration best approximates CI. The convergence zone is formulated as follows:

ZONE ¼ fðjd; jd þ nDzÞjjCIt  C tj j < 104 for 8j 2 ðjd; jd þ nDzÞg Then

t qij

can be calculated by:

The settling model improves estimation of treated water supply by accounting for the restrictions that turbidity imposes on treatment of raw water. The settling simulation for each flood event commences immediately after the peak inflow occurs. It initializes reservoir storage at full capacity. The operation strategy of regulating large flood always requests outlet works, such as spillways and sluiceways, to release water. A sediment-rating curve is developed based on field observed data. The initial uniform sediment concentration in reservoir is estimated with the total volume of water and sediment of the rising limb. Moving from upstream to downstream, the model simulates the settling of the sediment floc and establishes vertical concentration profile for each reservoir. The settling model applies the concentration profile for each reservoir to compute the average concentration of its releases. Simulated mixing of upstream reservoir releases with lateral inflows from the downstream sub-watershed determines the sediment concentration of the downstream river reach. This well-mixed streamflow enters the downstream reservoir as the settling of its sediment floc is simulated. The above procedure repeats until the sediment concentration has been simulated for each control point in the system. An empirical relationship between sediment concentration and turbidity [17] facilitates the conversion of the simulated sediment concentration into turbidity units. The model estimates the local turbidity at the depth of each intake based on the simulated sediment concentration and the empirical turbidity conversion. During every daily simulation, GWASIM will close the link if the turbidity exceeds treatment limit. Otherwise, it reduces the capacity of the link based on the estimated turbidity. The daily water allocation is then performed subject to the restrictions of turbidity. The above procedure is sequentially routed during each post-typhoon day. The NFP model reopens restricted links as the turbidity declines to treatable levels. Then the analysis is switched to normal water supply simulation until the re-initiation of settling model after the next flood peak. The processes described above support the comprehensive analysis of turbidity estimation and water allocation of GWASIM. For each typhoon event that occurs during a simulation time frame, the model quantifies turbidity and assesses its impact throughout the system. For each time step, the upper bounds of turbidity-affected links decline in accordance with turbidity. Reference to system parameters, such as treatment plant turbidity thresholds, ensures that the model accurately simulates real-time capacity throughout the water supply network. GWASIM can thus simulate the comprehensive water supply status of a typhoon-ravaged system by evaluating turbidities in the system. 4. Model calibration 4.1. Parameterization of empirical drift flux density function

ð15dÞ

There exist various forms of the batch flux density function, fbk , in the literature [29–33]. The value of function fbk is 0 for C 6 0 or

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C P C max and less than 0 for 0 < C < C max , where C max is the maximum solids concentration. It is usually assumed to be piecewise 0 0 ð0Þ < 0 and fbk ðC max Þ > 0. differentiable, fbk For fbk functions with no more than two inflection points, Concha and Bustos [26] used the method of characteristics to present five modes of sedimentation. These five modes indicate that the zones of uniform initial concentration lie above concentration gradients; in between shocks, or sharp discontinuities in the concentration profile; or in combination. Bürger and Tory [31] proposed two additional sedimentation modes indicating that the bulk suspension could be separated from the supernatant by a rarefaction wave. The settling experiments of Hsu [17] using Shihmen Reservoir mud revealed that both upper and lower concentration gradients existed during settling. Due to the lack of a generalized fbk form to accommodate this phenomenon, this study parameterizes the fbk function by dividing the feasible concentration range between 0 and C max into 10 intervals. Each interval is represented by ½C i1 ; C i , where i ¼ 1—10; C 0 ¼ 0 and C 10 ¼ C max . A corresponding value, denoted as bi to represent fbk ðC i Þ, is assigned to the concentration C i . The bi is set to obey the following sequence:

The relationship between the original and surrogate parameters can be expressed as below:

1  C l1 þ C l1 ; for l ¼ 1—10 1 þ ePl bl1  bmin þ bmin ; for l ¼ 1—5 bl ¼ 1 þ ePlþ10 blþ4 þ blþ4 ; for l ¼ 1—4 blþ5 ¼ 1 þ ePlþ15 Cl ¼

After defining the ðC 0 ; b0 Þ; ðC 1 ; b1 Þ; . . . ; ðC 10 ; b10 Þ points, the other possible fbk values within these intervals are interpolated by the cubic spline approach during the numerical simulation. The coordinates of these pre-defined points are regarded as parameters that must be calibrated. 4.2. Calibration algorithm Calibration analysis of GWASIM was conducted based on the settling experiments by Hsu [17] using field slurry sampled from the detention pond downstream from Shihmen Reservoir. The experiments were performed in a cylindrical settling tube of uniform cross-section with height 200 cm and diameter 23.8 cm at initial concentrations of 20,000 and 70,000 ppm, respectively. There is no lateral inflow to or outflow from the tube. Applying the experimental data, the parameters of the fbk function are calibrated by the Gauss–Newton least-square method. The objective function minimizes the deviation of simulated concentrations from the corresponding experimental values:

Min Z ¼

N  2 X C obs  C sim i i

ð17Þ

i¼1

ð19cÞ

k Pkþ1 ¼ Pk  qk d

ð20Þ k

k

where q a scalar step size of kth iteration, and d is the L  1 search direction vector of kth iteration. k The search direction d in Eq. (20) is determined by solving the following linear algebraic equations:

0 ð16Þ

ð19bÞ

where Pl is the lth transformed surrogate parameter. The initial original parameters are first transformed into an initial surrogate parameter set. The Gauss–Newton algorithm is then utilized to calibrate these surrogate parameters. If P represents the vector of surrogate parameters ½P1 ; P 2 ; . . . ; PL T where L is the total number of parameters, the formula for iteratively improving P is:

b5 < b4 < b3 < b2 < b1 < b0 ¼ 0 and b5 < b6 < b7 < b8 < b9 < b10 ¼ 0

ð19aÞ

obs k C sim 1 ðP Þ  C 1

C B sim k B C ðP Þ  C obs C 2 C k k T B 2  ½J C ðP Þ  ½J C ðP Þ  d ¼ ½J C ðP Þ  B C .. C B A @ . k

T

k

where Z is the value of objective function, the ith observed conthe ith simulated concentration and N is the total centration, C sim i number of the measurement data. Beginning with assumed initial parameter values, the Gauss– Newton algorithm iteratively modifies these parameters toward local minima. Nevertheless, the ordinary Gauss–Newton leastsquare algorithm is an unconstrained nonlinear optimization approach. It cannot directly accommodate the upper and lower limit constraints of the parameters of this study as expressed below:

C l1 6 C l 6 1:0; for l ¼ 1—10 bmin 6 bl 6 bl1 ; for l ¼ 1—5

ð18aÞ ð18bÞ

blþ4 6 blþ5 6 0:0;

ð18cÞ

for l ¼ 1—4

where C l ’s and bl ’s are parameters, and bmin is a pre-defined lower limit of the fbk function. In order to incorporate the parameters of (18a)–(18c) into calibration process, this study applies a transformation procedure to convert the original parameters into unconstrained surrogate parameters to apply Gauss–Newton algorithm.

ð21aÞ

obs k C sim N ðP Þ  C N

where

2

k @C sim 1 ðP Þ

6 @P1 6 @C sim ðPk Þ 6 2 6 k J c ðP Þ ¼ 6 @P1 6 . 6 .. 4 k @C sim N ðP Þ @P 1

3

k @C sim 1 ðP Þ @P 2



k @C sim 1 ðP Þ @P L 7

k @C sim 2 ðP Þ @P 2



k @C sim 2 ðP Þ 7 7 @P L

k @C sim N ðP Þ @P 2



k @C sim N ðP Þ @P L

7 ð21bÞ

7 7 7 5

The finite-difference approximation is applied to evaluate its partial derivative elements to solve the Jacobian matrix of (21b): k k @C sim C sim ðPk þ DPl el Þ  C sim n ðP Þ n ðP Þ  n @Pl DP l

ð22Þ

in which DP l a small perturbation of the lth parameter, el a unit vector with 1 in the lth element and 0 else. Upon determining the k search direction d , the qk in Eq. (20) is then determined using the golden section method. The iterative updating of P by Eq. (20) kþ1

C obs i

1

k

Þ 6 105 . While will cease when ZðPkþ1 Þ 6 ZðPk Þ and 0 6 ZðP ZðPÞZðP kþ1 Þ

the numerical settling model is invoked during calibration to evaluate the objective function or the element of Jacobian matrix, back transformation of the unconstrained surrogate parameters through (19a)–(19c) determines the constrained original parameter values. 4.3. Calibration and validation results Experimental values yielded by both initial concentrations – 70,000 and 20,000 ppm – were used as the observed data for calibration. The discrete temporal and depth intervals for simulation were set as 5 min and 0.01 m. Fig. 2a depicts the calibrated fbk function and associated parameters. The root mean square errors (RMSE) between the observed and simulated concentrations are 34,932 and 7462 ppm, respectively, for the cases of initial concentrations of 70,000 and 20,000 ppm. The maximal measurement concentrations reach 348,900 ppm in the case of initial concentration of 70,000 and 178,000 ppm for the case of initial concentration of 20,000 ppm. Fig. 2b shows the RMSE and coefficient of efficiency

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a

0

-0.02

concentration-flux coordinates of the calibrated points: (0.006, -0.035) (0.015, -0.055) (0.021, -0.057)

fbk(C) -0.04 (m/day)

(0.029, -0.065) (0.048, -0.065) (0.053, -0.062) (0.071, -0.049)

-0.06

(0.088, -0.040) (0.281, -0.004) (0.459, 0.000) -0.08 0

0.1

0.2

0.3

0.4

0.5

Concentration (106 ppm)

CE between the observed and simulated concentration profiles

b

RMSE between the observed and simulated concentration profiles

0.8

50,000 40,000

0.6

30,000

0.4 20,000

0.2

10,000

0

Coefficient of Efficiency

Root Mean Square Error (ppm)

1 60,000

0 0

20

40

60

80

100

Time (hours)

c

Storage level of reservoir

Simulated Interface of clear-muddy storage

Elevations of turbidity measurements with numbers as turbiditiesin NTU unit

250 37

Elevation (El. m)

240

El. 236 El. 228

230

El. 220

220

41

56

210

159

68

362

54 84,400 49,400

200

52

78,200

59,600 73,400

65,400

11

13

109,000

Elevation of Shihmen Canal’s Intake

29

51

76,000

102,100 117,750

190 180 1

3

5

7

9

15

Days after Flood Peak of Typhoon Aere Fig. 2. (a) Calibrated fbk function and associated parameters. (b) RMSE and CE of the observed and simulated concentrations for the 70,000 ppm case. (c) Settling simulation result of Shihmen Reservoir after Typhoon Aere.

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(CE) between the observed and simulated concentration profiles at each time of measurement for the 70,000 ppm case. Following calibration, validation analysis was conducted to evaluate the model performance by simulating the clear–muddy interface in Shihmen Reservoir after Typhoon Aere. The simulation started from August 26 to September 11 in 2004. The initial sediment concentration of reservoir storage was set as 25,000 ppm according to the measurement of Pingcheng Treatment Plant on August 26, 2004. The sediment concentration of reservoir recession inflow was assumed to be 0. The linear relationship between sediment concentration and turbidity calibrated by Hsu [17] was employed to transform concentrations into turbidity units. This relationship equates 1 ppm concentration with approximately 1.28 NTU. The historical releasing record of each outlet work was also used as outflow conditions in the settling simulation. Fig. 2c depicts the simulated process in declining elevation of the simulated clear–muddy interface as well as the field measured turbidities. The interface is assumed to be 3000 NTU, which is the treatable threshold of the Taiwan Water Company (TWC). The result shows that the calibrated model has the tendency to overestimate the elevation of clear–muddy interface in the first few days after flood peak. This overestimation provides a satisfactory decision in withdrawing clear water from reservoir during water supply simulation. Thus it would lead to a conservative planning and design of backup water supply facilities.

5. Case study 5.1. Study area The Tahan River system of northern Taiwan was chosen as a case study. Fig. 3 maps the Tahan River water resources system. The Shihmen Reservoir, constructed in 1964, is the largest storage facility in the Tahan River system. Sediment deposition, however, has reduced its total capacity from 309 to 225 million m3 and its effective capacity from 252 down to 219 million m3, according to 2007 data. Fig. 4 shows the elevations of the major intake works. Shihmen Reservoir was designed as a multi-purpose reservoir for irrigation, hydrogeneration, public water supply, flood control and recreation. Public water supply, however, has gradually become its primary function. Weirs, including the Yuanshan Weir and the Shanshia Weir, supplement to the storage provided by the Shihmen Reservoir. Located 19 km downstream from the Shihmen Reservoir, the Yuanshan Weir intercepts releases from the Shihmen Reservoir as well as return flows from nearby irrigation areas. The water travel time from Shihmen Reservoir to Yuanshan Weir is between 2 and 3 h. The current capacity of Yuanshan Weir is 4.90 million m3. There is also a pumping station at the Shanshia Weir on the Shanshia River, which is a tributary of the Tahan River. The Shanshia Pumping Station provides raw water to Panhsin Water Treatment Plant at a capacity of 0.50 million CMD. The primary water demands in the Tahan River system are agricultural and municipal. The irrigated farmlands, concentrated in the Taoyuan Platform region as well as the downstream area of the Tahan River, comprise a total area of 36,500 ha. The net annual irrigation demand of 485.5 million m3 concentrates between February and November. The public water demand of this region includes the domestic demand of Taoyuan and Pan-Hsin districts and the industrial demand of high-tech industrial park of Taoyuan district. The domestic and high-tech industrial water supply of the Taoyuan district is managed by the second branch office of TWC; the Taoyuan district can be further divided into southern and northern Taoyuan sub-districts. The southern Taoyuan sub-district is supplied by Pingcheng, Longtang and Shihmen Treatment Plants,

153

which obtain raw water from the Shihmen Reservoir via the Shihmen Irrigation Canal. Danan Treatment Plant, which withdraws raw water from the Yuanshan Weir, supplies the northern Taoyaun sub-district. The current net demand of southern and northern Taoyuan sub-districts is 1.16 million CMD. The 12th branch office of TWC manages the water supply for the Pan-Hsin district. The water demand for Pan-Hsin district is 0.88 million CMD at year 2006. This demand is jointly supplied by the Tahan River and Hsintien River systems. The Panhsin Treatment Plant receives Tahan River water diverted from Yuanshan Weir as well as that pumped at Shanshia Weir. The Hsintien River system provides a maximum of 0.53 million CMD treated water to the Pan-Hsin district through a newly constructed trans-basin pipeline of ‘‘Pan-Hsin Water Supply Improvement Plan, Phase I” (PH-Phase I). ‘‘Pan-Hsin Water Supply Improvement Plan, Phase II” (PH-Phase II) has been planned to expand the capacities of existing treatment plants and to increase transmission mains, booster stations and connection conduits. The ultimate goal of this project is to reallocate water from the Hsintien River to fulfill the demand of the Pan-Hsin district up to 1.005 million CMD until the year 2021. 5.2. Typhoon Aere and backup water supply projects Typhoon Aere provoked severe water supply shortage as it invaded Taiwan between August 23 and 26 of 2004. The inflow of Shihmen Reservoir peaked at 8500 m3/s on August 25. During Typhoon Aere, the Shihmen Reservoir operator released water primarily through the tunnel spillway, whose crest elevation is 220 m. Hydropower gates and permanent river outlet were closed from August 29 through September 6. The turbid reservoir clarified extraordinarily slowly after Typhoon Aere. Three treatment plants in the southern Taoyuan sub-district failed to process the mud flow pumped from the Shihmen Irrigation Canal which withdraws water near the bottom of the reservoir. The southern Taoyuan sub-district suffered overwhelming water supply disruption between August 25 and September 5. From September 6 to September 12, the water outage was rotated across sections to alleviate the shortage severity. Following Typhoon Aere, the Northern Water Resources Office (NWRO) of the Water Resources Agency, Taiwan, decided to reconstruct the desiltation infrastructure for the Shihmen Reservoir [34]. The first proposal calls for the construction of a sluiceway with a maximum discharge of 300 m3/s originated from the hydropower penstock of Shihmen Power Plant. Another proposal entails building a multi-level outlet work [35] to withdraw the less turbid, higher storage of Shihmen Reservoir for public demand during typhoons. This work consists of a diversion shaft from the reservoir. The shaft will be divided into three levels, with diversion tunnels to convey water from the reservoir. The operating elevations of these tunnels will be 236, 228 and 220 m, respectively. The outlet of this shaft will be connected to the existing diversion pipes of the TWC. In response to plans for the Hsintien River system to take over the adjacent Pan-Hsin district in the future, another project has proposed to reallocate treated water from the Panhsin Treatment Plant to the northern and southern Taoyuan sub-districts. The first phase of this reallocation project (TRAP-I) will be completed by the end of 2008 with a maximum interbasin transfer capacity of 0.30 million CMD. The second phase of this reallocation project will be completed in 2011 with a maximum reallocation capacity of 0.60 million CMD in total. The final proposal calls for the construction of an off-stream, backup storage facility to be called Chongchung Regulation Pond. It is located in the abandoned river path near Yuanshan Weir, where clear water could be stored for direct conveyance to

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Fig. 3. Map of the Tahan River system.

Fig. 4. Intake works of the Shihmen Reservoir.

northern Taoyuan and Pan-Hsin districts during typhoons. Its planned capacity is 6.90 million m3, including diversion capacities of 0.3 and 0.5 million CMD, respectively, for Danan and Panhsin Treatment Plants. Fig. 5 illustrates the network structure of the Tahan River system, with dotted links and nodes representing planned backup construction. 5.3. Water supply simulation scenarios The water supply simulation was carried out with historical daily inflows to the Shihmen Reservoir and the Sanshia Weir from 1957 to 2006. The releasing policy of the Shihmen Reservoir during typhoon-period consists of the following elements: 1. The sluiceway sluices the bottom mud for the first 3–4 days following the flood peak. 2. The hydropower plant also releases turbid water since the storage is greater than the upper limit of operating rule curves of Shihmen Reservoir.

3. The tunnel spillway vents excess inflow to assist desiltation. Historic field data yield a regressive relationship between inflow discharge and sediment concentration of the Shihmen Reservoir. On the basis of the regression equation and the calibrated fbk function, the settling of sediments in Shihmen reservoir is simulated for every typhoon event between 1957 and 2006. For each of these typhoons, pattern of sediment settling restricts the magnitude and duration of discharge for every diversion tunnel or public intake pipe in the reservoir. Four scenarios, listed in Table 1, were simulated in order to evaluate current water supply status of this system as well as the functions of proposed backup water supply facilities. Simulations applied the Shihmen Reservoir operating rule curves to allocate water to each demand. The non-consumptive demand approach mentioned in Section 3.1 was applied to simulate the water use for desiltation and hydropower generation during the water supply simulation phase. The priority of storage in the backup Chongchung Pond is set below that of all other demands and Shihmen

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155

Fig. 5. Network structure of the Tahan River system.

Table 1 Simulated water supply scenarios. Scenario

Analysis conditions

ST-0 ST-0T ST-1 ST-2

The default case which does not consider the turbidity condition in the Shihmen Reservoir and streamflow ST-0T is identical to ST-0 except it restricts water withdrawal and treatment capacities according to the flood-induced turbidity of raw water ST-1 attempts to mitigate the impact of high turbidity of raw water of ST-0T by incorporating a multi-level outlet work in the Shihmen Reservoir ST-2 supplements ST-1 condition with the integration of the proposed Chongchung Pond and trans-district pipelines of TRAP-I

Reservoir during the dry season; once monsoon season begins, Chongchung Pond storage is prioritized first right before anticipated typhoon occurs, in order to accumulate stored water for typhoon conditions. After the flood peak, the diversion link of Chongchung pond from Tahan River is closed due to high turbidity, and its storage priority is moved to the last again to allow the system allocates its backup storage. Two performance indices evaluate hypothetical water supply scenarios according to duration and magnitude of shortage, respectively. The shortage index, SI, measures the extended impact of shortage for each demand node in the system:

SI ¼

2 N  100 X DF i N i¼1 Di

ð23aÞ

where SI is the shortage index for any demand, N the analysis years, Di the total demand in the ith year and DFi is the total deficits in ith year. The maximum daily deficit ratio, DR, following a typhoon measures the short-term severity of water supply shortage:

 DRj ¼ max

DFT NDj DFT 1 DFT 2 ; ;...; DT 1 DT 2 DT NDj

DR ¼ max ðDRj Þ j¼1—NT

 j ¼ 1—NT

ð23bÞ ð23cÞ

where DRj is the maximum daily deficit ratio following the jth typhoon, DFT kj the kth daily deficit following the jth typhoon, DT kj the kth daily demand following the jth typhoon, NDj the total

number of days when turbidity-affected public water supply following the jth typhoon and NT is the total number of typhoons. The duration of shortages by flood-induced turbidity is much shorter than the shortages caused by drought, which may extend to months in the dry season. Thus SI essentially measures more drought-induced total shortage, although it includes all shortages in annual temporal scale. By Eq. (23), DR focuses only on the maximum daily shortage potential by the flood-induced turbidity. It represents the severest reduction in the satisfaction ratio of a water demand following a typhoon. DR is usually required to be below 20% for domestic water users in Taiwan. It is used to evaluate the capacities of backup water supply facilities to alleviate the impact of high turbidity during short-term post-typhoon periods. 5.4. Simulation results Table 2 presents the performance indices of every simulated scenario. In scenario ST-0, public demand shortage is caused by drought during dry season as well as insufficient capacities of treatment plants in respect to the peak summer demand of Taoyuan district. Inadequate treatment plant capacity explains why the DR of Taoyuan district exceeds 0 even during wet season. On the basis of ST-0, ST-0T further considers the water withdraw and treatment limitations by high turbidities of floods. Both SI and DR increase significantly from their ST-0 value for each public district due to turbidity-induced shortage.

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Table 2 Water supply simulation results. Scenario

ST-0 ST-0T ST-1 ST-2

Demand Southern Taoyuan sub-district

Northern Taoyuan sub-district

Pan-Hsin district

Agricultural demand

SI

DR

SI

DR

SI

DR

SI

DR

0.80 1.16 0.88 0.55

0.09 1.00 1.00 0.15

1.07 1.32 1.15 0.42

0.10 0.80 0.76 0.10

0.35 0.36 0.36 0.56

0.00 0.43 0.41 0.00

1.69 1.69 1.69 1.80

0.00 0.00 0.00 0.00

The addition of the proposed multi-level outlet work, simulated by scenario ST-1, should facilitate selective withdrawal from less turbid zones in the Shihmen Reservoir. The SI’s of southern and northern Taoyaun districts decrease accordingly, yet the DR just slightly improves from its ST-0T value for each public district. This is because the clear–muddy interface of reservoir storage requires an average of 1–2 days to descend below the upmost intake of multi-level outlet work. Without other sources as emergent water supply, the Toayuan districts will still suffer overwhelming shortterm shortage while the turbidity prevents withdrawal from the Shihmen Reservoir. The last scenario, ST-2, allows TWC to transport treated Tahan River water from the Panhsin Treatment Plant through the proposed pipeline of TRAP-I to the Taoyuan districts. The TRAP-I significantly reduces the corresponding SI of Taoyuan districts, as indicated in Table 2. While shortages inevitably occur, the original supplies to Pan-Hsin district in ST-1 might be transferred to the other two domestic districts through TRAP-I to mitigate concentrated shortage. Thus the SI of Pan-Hsin district of case ST-2 increases a little from ST-1, but a more balancing status of shortage is maintained among all districts. During high-turbidity periods, the trans-district pipeline of TRAP-I can also transport those water provided by the Chongchung Pond or the adjacent Hsintein River system. These water transfers altogether apparently improve the stability of public water supply of Pan-Hsin and Taoyuan districts. 6. Conclusions and suggestions This paper presented an approach to improve short-term water supply allocation and shortage management by quantifying the level and impacts of high turbidity in reservoir. It integrates a unidimensional settling model of cohesive particles based on Kynch’s theory of sediment flocculation [23] with a regional water allocation model based on NFP [11]. Shortage scenarios based on short-term, flood-induced elevated turbidity, as well as extended droughts, can be simulated. The settling model simulates sediment flocculation in a reservoir, which is conceptualized as a large vessel of varying cross-section with multiple outflows at different elevations. The NFP model responds to problematic turbidity levels by adjusting the upper bounds of associated flow links, thus mimicking typhoon-induced restricted conveyance and treatment capacity. Simulation results reveal the severity of water supply shortage with respect to time and location. This model may also be applied to evaluate water supply shortage associated with infrastructure malfunction or temporary closure for scheduled repairs. Such scenarios must be defined according to duration and location: the user must close associated flow links for the appropriate number of time steps in GWASIM. The statistical frequency of infrastructure malfunction should be investigated first; then the timing of link closures can be modeled by the Monte Carlo method. Traditionally, water resources planning in Taiwan has focused on satisfying continuously increasing demand. The shortage index,

SI, is the most popular criterion for sizing reservoirs or other capacity expansion alternatives. Nevertheless, the importance of backup water supply is increasingly apprehended after the critical Typhoon Aere in 2004. The proposed methodology is actually a decision-support tool for planning traditional water resources projects as well as emergent backup systems. In the case study, two different indices, SI and the allowed daily shortage ratio following typhoon, were used to assess both the severity and duration of water supply shortage. Such a pair of shortage indices facilitates the evaluation of backup water supply proposals that can support regular water supply as well as short-term emergency water supply needs. The simulation results of both regular and short-term emergent water supply generated by GWASIM can assist the water resources planner drawing a comprehensive master plan. Acknowledgements This study is funded by Water Resources Planning Institute (WRPI) of the Water Resources Agency (WRA), Taiwan, with project number MOEAWRA0970051. The authors appreciate the assistance of the research personnel in WRPI: Section Chief K.L. Wang, Senior Engineers J.C. Pan and K.M. Chung, and Engineer Y.D. Du. Professor S.H. Hsu of the Feng Chia University provided the data of his settling experiments with courtesy. Former Vice Chief Engineer of Taiwan Water Company F.C. Hsieh and Former Vice Director of the Central Water Resources Office of WRA B.H. Su gave insights for water resources allocation scenarios. There were also many agencies provide operation data to accomplish the study: the Taipei Water Department, Taipei Feitsui Reservoir Administration, Shihmen Reservoir Administration of Northern Water Resources Office and the second and twelfth branch offices of Taiwan Water Company. Last but not the least, Miss Dawn Brady helped with the proofreading of this paper is very much appreciated. References [1] Sohn BY, Park TJ, Oh BS, Kwon SB, Kang JW. A case study of the DAF-based drinking water treatment plant in Korea. Sep Sci Technol 2008;15:3873–90. [2] Effler SW, Mathews DA, Kaser JW, Prestigiacomo AR, Smith DG. Runoff event impacts on a water supply reservoir: suspended sediment loading, turbid plume behavior, and sediment deposition. J Am Water Resour Assoc 2006;42(6):1697–710. [3] Li SY, Cheng XL, Xu ZF, Han HY, Zhang QF. Spatial and temporal patterns of the water quality in the Danjiangkou Reservoir, China. Hydrol Sci J 2009;54(1):124–34. [4] Gelda RK, Effler SW. Simulation of operations and water quality performance of reservoir multilevel intake configurations. J Water Resour Plan Manage 2007;133(1):78–86. [5] Wittmann E, Tazi-Pain A, Chanussot T, Patterson A, Niay R, Ga A, et al. Clarification of a highly turbid karstic water by microfiltration. Desalination 2002;145:309–13. [6] Chung KM. Development and applications of water resources adjustment model. Hydraulics 2006;16:223–34 [in Chinese]. [7] US Army Corps of Engineers. HEC-ResSim Reservoir System Simulation User’s Manual Version 3.0, Hydraulic Engineering Center, California, USA; 2007. [8] DHI Water & Environment. MIKE BASIN 2003 A versatile decision support tool for integrated water resources management planning. Denmark: DHI Water & Environment; 2003.

F.N.-F. Chou, C. Wu / Advances in Water Resources 33 (2010) 146–157 [9] van der Krogt Wil NM. RIBASIM Version 6.31 Technical Reference Manual, Delft Hydraulics, the Netherlands; 2003. [10] Sigvaldason OT. A simulation model for operating a multipurpose multireservoir system. Water Resour Res 1976;12(2):263–78. [11] Chou NF, Wu CW. A network flow model for evaluating water supply strategies in Taiwan. In: Proceedings of the international conference on water resources management, IASTED, Honolulu, Hawaii; 2007. p. 51–6. [12] Shafer JM. An interactive river basin water management model: synthesis and application. Colorado State University, Fort Collins, CO: Colorado Water Resources Research Institute; 1979. [13] Labadie JW, Bode DA, Pineda AM. Network model for decision-support in municipal raw water supply. J Am Water Resour Assoc 1986;22(6):927–40. [14] Fredericks JW, Labadie JW, Altenhofen JM. Decision support system for conjunctive stream-aquifer management. J Water Resour Plan Manage 1998;124(2):69–78. [15] Dai T, Labadie JW. River basin network model for integrated water quantity/ quality management. J Water Resour Plan Manage 2001;127(5):295–305. [16] Willey RG, Smith DJ, Duke JH. Modeling water resources systems for waterquality management. J Water Resour Plan Manage 1996;122(3):171–9. [17] Hsu SH. Settling characteristics of muddy lake and reservoir operation study for reducing deposition. Water resources agency technical report, Taiwan; 2005 [in Chinese]. [18] Toniolo H, Parker G, Voller V. Role of ponded turbidity currents in reservoir trap efficiency. J Hydraul Eng 2007;133(6):579–95. [19] Dankers PT, Winterwerp JC. Hindered settling of mud flocs: theory and validation. Cont Shelf Res 2007;27(14):1893–907. [20] Diplas P, Papanicolaou AN. Batch analysis of slurries in zone settling regime. J Environ Eng 1997;123(7):659–67. [21] Toorman EA, Berlamont JE. A hindered settling model for the prediction of settling and consolidation of cohesive sediment. Geo-Mar Lett 1991;11(3– 4):179–83. [22] Shojaeia A, Arefinia R. Analysis of the sedimentation process in reactive polymeric suspensions. Chem Eng Sci 2006;61(23):7565–78. [23] Kynch GJ. A theory of sedimentation. Trans Faraday Soc 1952;48:166–76.

157

[24] Labadie JW, Baldo M. Discussion of ‘Priority preserving unit penalties in network flow modeling’ by M. Israel and J. Lund. J Water Resour Plan Manage 2001;127(1):67–8. [25] Bürger R, Karlsen KH, Towers JD. Mathematical model and numerical simulation of the dynamics of flocculated suspensions in clarifier– thickeners. Chem Eng J 2005;111(2–3):119–34. [26] Concha F, Bustos MC. Settling velocities of particulate systems. 6. Kynch sedimentation processes: batch settling. Int J Miner Process 1991;32(3– 4):193–212. [27] Concha F, Bustos MC. Settling velocities of particulate systems. 7. Kynch sedimentation processes: continuous thickening. Int J Miner Process 1992;34(1–2):33–51. [28] Bürger R, Damasceno JR, Karlsen KH. A mathematical model for batch and continuous thickening of flocculated suspensions in vessels with varying cross-section. Int J Miner Process 2004;73(2–4):183–208. [29] Michaels AS, Bolger JC. Settling rates and sediment volumes of flocculated kaolin suspensions. Ind Eng Chem Fundam 1962;1:24–33. [30] Vesilind PA. Discussion of ‘Evaluation of activated sludge thickening theories’. J Sanit Eng Div 1968;94:185–91. [31] Bürger R, Tory EM. On upper rarefaction waves in batch settling. Powder Technol 2000;108(1):74–87. [32] Garrido P, Bürger R, Concha F. Settling velocities of particulate systems: 11. Comparison of the phenomenological sedimentation–consolidation model with published experimental results. Int J Miner Process 2000;60(3– 4):213–27. [33] Garrido P, Concha F, Bürger R. Settling velocities of particulate systems: 14. Unified model of sedimentation, centrifugation and filtration of flocculated suspensions. Int J Miner Process 2003;72(1–4):57–74. [34] G.T. International. Existing facility desilting improvement project for Shihmen Reservoir-power plant desilting project, phase 1. Water resources agency technical report, Taiwan; 2006 [in Chinese]. [35] G.T. International. Shihmen Dam permanent surface intake structure. Water resources agency technical report, Taiwan; 2005 [in Chinese].