DOI 10.1007/s11269-010-9687-8
An Integrating Approach for Conjunctive-Use Planning
of Surface and Subsurface Water System
Liang-Cheng Chang· Chih-Chao Ho · Ming-Sheng Yeh· Chao-Chung Yang
Received: 7 July 2009 / Accepted: 11 June 2010 / Published online: 17 July 2010
© Springer Science+Business Media B.V. 2010
Abstract This study proposes an integrated approach to assess the performance of a conjunctive-use surface and subsurface water system. System dynamics serves as the main framework of the proposed conjunctive-use model, simulating the interaction between surface and subsurface water and the impact of various conjunctive-use alternatives on the system as a whole. This study assumes natural groundwater recharge as a water source to the system, and estimates its volume using geographic information system (GIS) tools, a groundwater simulation model (MODFLOW), and a parameter identification model (UCODE). This study assesses various conjunctive-use alternatives and analyzes the frequency of water shortage to illus-trate how the recharge rate affects water supply reliability under the conjunctive-use framework. Simulation results indicate that conjunctive-use with artificial recharge indeed reduces the frequency of extreme water shortages. Results also reveal that artificial recharge is necessary to maintain groundwater conservation without overusing river flow. Although this study focuses on southern Taiwan, the proposed concepts and procedure are applicable to other areas with a similar conjunctive-use framework.
L.-C. Chang (
B
)· C.-C. HoDepartment of Civil Engineering, National Chiao Tung University, 1001 University Road, Hsinchu, Taiwan 300, Republic of China
e-mail: [email protected] C.-C. Ho
e-mail: [email protected] M.-S. Yeh
Hydrotech Research Institute, National Taiwan University, Taipei, Taiwan, Republic of China e-mail: [email protected]
C.-C. Yang
Construction and Disaster Prevention Research Center, Feng Chia University, Taichung, Taiwan, Republic of China
Keywords Conjunctive-use· System dynamics · Geographic Information System
(GIS)· MODFLOW · UCODE
1 Introduction
Climate changes caused by global warming have made hydrological conditions increasingly unstable spatially and temporally (Simonovic and Li 2003). Because surface water resources are highly related to climate changes, global warming in-creases the risk of water deficits. However, groundwater provides a more stable water resource, and rich groundwater areas play a vital role in regional water resources (Tsur 1990). Therefore, the conjunctive use of surface and subsurface water can enhance the water supply reliability (Fisher et al. 1995). This study proposes an integrated approach to assess the performance of a surface and subsurface water conjunctive-use system.
Water distribution models can be developed using either an optimization or a simulation approach (Yeh 1985). This study uses a simulation approach, system dynamics, to assess water distribution system behavior. Following the recommen-dations of previous studies (Brito et al.2006; Juckem et al.2006; Lin and Anderson 2003; Szilagyi et al.2005), this study uses Geographic Information System (GIS), MODFLOW and UCODE to estimate the interactions between surface and subsur-face water resources. The objective of this study is to assess various conjunctive-use alternatives and evaluate water shortage risks using the proposed developed model.
System dynamics, initially developed by Jay W. Forrester, uses information feedback and mutual or recursive causalities to understand the dynamics of com-plex physical, biological, social, and other systems (Forrester 1961). A stock-flow diagram of system dynamics not only displays the system diagram, but also presents information linkages among components or variables. In other words, the stock-flow diagram simultaneously shows the structure of the problem and the internal process of the system. Therefore, using the system dynamics approach makes the modeling process transparent.
Many system dynamics studies on water resource management focus on the global policy results of large-scale systems. These studies use system dynamics to study long-term water resource planning and policy analysis (Simonovic and Fahmy 1999; Simonovic and Li2003; Stave 2003; Xu et al.2002). However, the tendency of current research is to model systems in detail, with more emphasis on quantitative results. Ahmad and Simonovic (2000) used system dynamics to study the impacts of a gated spillway on the flood management capacity of a reservoir. Sehlke and Jacobson (2005) applied system dynamics to the conjunctive-use analysis of surface and subsurface water. They used aquifer response curves to evaluate the effects of ground water pumping on surface water flows in the Bear River, a transboundary basin that includes portions of Idaho, Utah, and Wyoming. Yang et al. (2008) combined a system dynamics approach and impact analysis to evaluate water strategy systematically and quantitatively. They formulated an appropriate strategy that strikes a balance between mitigating water shortages and limit total financial costs. These studies clearly demonstrate that the system dynamics approach is well suited to investigating detailed operation rules and complex interactions among components.
2 Methodology
Figure 1 presents the framework of the proposed conjunctive-use model, where system dynamics integrates a groundwater recharge model into a conjunctive-use distribution system. The groundwater recharges are from natural recharges (includ-ing rainfall, river interaction, and boundary recharge) and artificial recharge (com(includ-ing from non-used river flows). The natural recharges are estimated based on GIS, MODFLOW, and UCODE. The following sections describe these methods and tools in detail.
2.1 System Dynamics
System dynamics is a computer-aided approach to evaluating the interrelationships of components and activities within complex systems (Sehlke and Jacobson2005). The use of causal loops and stock-flow diagrams make system dynamics unlike other approaches. These elements help describe how a seemingly simple system can display baffling nonlinearities.
System dynamics has four basic building components: stocks, flows, converters, and connectors. Stocks and flows mostly represent variables associated with physical quantities, such as reservoir storage or reservoir release, while converters represent additional variables, such as water demands, water treatment plant capacity, or water pipe capacity. Connectors connect the dependency relationships among stocks, flows, and converters.
Figure2shows the causal loop of a single node water distribution problem. This is a negative causal loop, which implies that the system state achieves a goal or desired state (Simonovic and Fahmy1999). In other words, the loop indicates that operation behavior will trend towards a balance between supply and demand. The variables on the loop are endogenous variables that influence each other. Variables not on this loop are exogenous variables, which must be specified or estimated before endogenous variable computation.
Conjunctive-use distribution modeling (Using system dynamics software-Vensim)
Groundwater storage Surface water distribution system artificial
recharge
Groundwater recharge estimation
(Using GIS, MODFLOW and UCODE) Demand1 pumping withdraw Demand2 Nature recharge
Inflow (I)
Storage
Reserved flow (OB)
water supply (OD) Non-used flow (ON) -Demand (D) + Capacity of water treament plant (Cmax)
+ Capacity of Reservoir (Smax) -Requirment of downstream reserved flow (R) Capacity of Pipe (Pmax) +
Fig. 2 The causal loop diagram of water distribution system (single node)
2.2 MODFLOW model
The modular three-dimensional groundwater flow model (MODFLOW) was devel-oped by the United States Geological Survey (USGS) (Harbaugh and McDonald 1996). McDonald and Harbaugh (1988) were the first to document the MODFLOW model. The MODFLOW model is a physical finite-difference numerical flow model and a computer program developed by the USGS that numerically solves three-dimensional partial-differential equations for ground-water flow through a porous medium using a finite-difference method (Harbaugh and McDonald1996). Before running MODFLOW, an analyst must discretize the study area into cells and assign parameters to them to simulate confined or unconfined flows and saturated flows in one, two, or three dimensions using the finite-difference techniques.
2.3 UCODE
This study uses UCODE, developed by USGS, to perform parameter optimization (Poeter and Hill1998). UCODE is a computer code for the universal inverse model based on the nonlinear regression. UCODE minimizes a weighted least-squares objective function with respect to parameter values using the modified Gauss– Newton method or Conjugate-Direction Method. This study applies UCODE to solve an inverse problem in which the sink and source are the parameters to be identified.
3 Model Development for Study Case 3.1 Study Area Description
The study area covers the two metropolitan areas of Tainan and Kaoshing in Southern Taiwan. This area contains two major basins, the Kaopin River basin
Table 1 The capacities and demands of the main facilities in the study area
Reservoir capacity (104m3) The treatment capacity of Water Demand treatment plant (104m3/day) (104m3/day)
Nan-Hua Tseng-Wen Wu-Shan-Tou Pin-Tin Nan-Hua Wu-Shan-Tou Tainan Kaoshing Reservoir Reservoir Reservoir water water and Tan-Tin
treatment treatment water plant plant treatment
plant
3,236.9 8,708 8,376 200 110 67 172.4 228.5
and the Tseng-Wen River basin. The main surface water facilities are the Nan-Hua Reservoir, the Tseng-Wen Reservoir, the Wu-Shan-Tou Reservoir, and the Kaopin-Hsi Weir. There are four main water treatment plants, the Pin-Tin water treatment plant, the Nan-Hua water treatment plant, the Wu-Shan-Tou water treatment plant, and the Tan-Tin water treatment plant.
The main groundwater resources come from the Pingtung Plain. At 1,140 km2, the Pingtung Plain is the largest alluvial plain in Taiwan. The Central Mountain Range is the east boundary of the Pingtung Plain, while the northern and western boundaries of the plain are low hills of quaternary sediments. The southern boundary of the plain is the Taiwan Strait. Figure3depicts the study area’s location, and Table1shows the main facilities described above. Figure4shows the water distribution system.
The groundwater system of the Pingtung Plain consists of one unconfined aquifer (Aquifer 1) and two confined aquifers (Aquifer 2, and Aquifer 3). The
Tseng-Wen Reservoir Wu-Shan-Tou Reservoir Nan-Hua Reservoir Wu-Shan-Tou &
Tan-Tin WTP Nan-Hua WTP Pin-Tin WTP Chia-Hsien Weir Kaopin-Hsi Weir Formosa Strait Tainan Public Use Demand Kaohsing Public Use Demand Wu-Shan-Tou Irrigation Demand Water intake Point Aquifer Artificial recharage Pumping Existing Reservoir Existing Weir Groundwater Water Demand Water Treatment Plant Conjun-ction Legend
hydro-geological parameters such as hydraulic conductivity are adopted from the data of groundwater monitoring network. There are 41 monitoring wells at Aquifer 1, 35 monitoring wells at Aquifer 2, and 40 monitoring wells at Aquifer 3.
The basic operational concept of conjunctive use is to withdraw surface water before using groundwater to conserve groundwater and ensure efficient distribution. In this case, groundwater acts as the water supplement when the surface water supply cannot fulfill the demand for water.
The other operating rule of conjunctive use is to fulfill demand in sequence depending on water source availability. For example, when withdrawing water from the Kaopin River and aquifer, Kaoshing public use demand has a higher priority for fulfillment then Tainan public use demand. Further, when withdrawing water from reservoirs, Wu-Shan-Tou irrigation demand, Tainan public use demand, and Kaoshing public use demand should be fulfilled in sequence. The three reservoirs operate together as a multi-reservoir system and the water released from each reservoir is managed according to the index level method of storage balancing provided by the US army corps of engineers.
Additionally, conjunctive-use operation should be based on the operating curve of an equivalent reservoir. However, there is no operating curve for the conjunctive-use system. Therefore, this study applied the original reservoirs operating curve as the conjunctive-use rule guide. The original operating curve is based on the equivalent reservoir combining the Tseng-Wen Reservoir and the Wu-Shan-Tou Reservoir. The current operating curve divides this equivalent reservoir volume into five operating zones; inactive, low buffer, high buffer, conservation, and flood control zones (Fig.5). Each zone has different criteria for decreasing target demand depending on how much water has been stored in the equivalent reservoir. The available storage of the equivalent reservoir is the sum of all inflows and the initial storage of each reservoir. The public use demand should be fulfilled 100%, 100%, 100%, and 80% when the available storage of the equivalent reservoir falls within the flood control zone, conservation zone, high buffer zone, or low buffer zone, respectively. The irrigation demand should be fulfilled 100%, 100%, 75%, and 50% when the available storage of the equivalent reservoir falls within the flood control zone, conservation zone, high buffer zone, or low buffer zone, respectively. Additionally, if the available storage falls within the flood control zone, the reser-voir will operate in flood control mode and try to evacuate water as quickly as possible.
Fig. 5 Definition of reservoir
operating zones for the equivalent reservoir of the Tseng-Wen Reservoir and the Wu-Shan-Tou Reservoir
3.2 Water Distribution Model Development
Because inflow data vary unevenly, reservoir releases are difficult to predict. Hence, this study develops a water distribution model and model results describe these re-lease variations in depth. Figure6show the stock-flow diagram of water distribution for a single node.
The following equation describes variable quantification. First, define the re-served flow based on Eq.1
OBk,t= min i⊂L Ii,t+ Sk,t,Rk,t (1)
where OBk,tis the reserved flow of node k at time t, Ii,trepresents the inflow to node k at time t, and Sk,tdenotes node k storage at time t. The first suffix of all variables denotes the node number; the second suffix represents the time step. L is the set of all inflows for node k. Rk,t denotes the requirement of downstream reserved flow at node k and time t. For ensuring that the reserved flow can fulfill the ecological base streamflow after downstream, Rk,tis setting as the summation of the ecological base streamflow and priority downstream water demands that should be fulfilled prior to fulfilling the water demands of node k. The ecological base streamflow is the minimum requirement for aquatic animal survival. Equation2 defines Rk,t as follows:
Rk,t=
i⊂M
DRi,t+ Bk,t (2)
where DRi,t is the priority downstream water demand, and Bk,t represents the ecological base streamflow at node k and time t. M denotes the set of all priority downstream water demands. The value of Bk,t is estimated from the exceedance probability of a stream flow equal to 95%.
Node K Inflow (I) Reserved flow (OB) Non-used flow (ON) Water supply (OD) capacity of pipe (Pmax) Capacity of water treament plant (Cmax)
Demand (D) Capacity of reservoir (Smax) Requirement of downstream reserved flow (R) Fig. 6 The stock-flow diagram of water distribution system (single node)
Equation3illustrates the water supply: ODK,t= min ⎡ ⎣ i⊂L Ii,t+ Sk,t− OBk,t, j⊂N Dj,t, Cmaxk, Pmaxk ⎤ ⎦ (3)
where ODk,tis the water supply from node k at time t, Dj,tis the desired demand of node k at time t, N is the set of all demands of node k, Cmaxkdenotes the maximum water treatment plant capacity for node k, and Pmaxkdenotes the maximum pipe capacity for node k.
Equation4represents the unused flow of node k if node k is an impounding node. Alternately, Eq.5shows the unused flow if node k is a non-impounding node.
ONk,t = K⊂L Ik,t+ Sk,t− ODk,t− OBB,t− Smaxk, i f K⊂L Ik,t+ Sk,t− ODk,t− OBk,t> Smaxk = 0 , i f K⊂L
Ik,t+ Sk,t− ODk,t− OBk,t≤ Smaxk (4)
ONk,t=
K⊂L
Ik,t− OBK,t−ODk,t (5)
where ONk,tis the non-used flow of node k, and Smaxkdenotes the maximum storage capacity of node k.
The mass balance principle defines node k storage at the next time step (t+ 1):
Sk,t+1= Sk,t+ i⊂L Ii,t− j⊂W Oj,t (6)
where Sk,t+1denotes node k storage at time t+ 1, Oj,tis the outflow from node k at time t, which involves reserved flow, water supply, and non-used flow, and W is the set of all outflows draining from node k. If node k is a non-impounding node, Sk,tand Sk,t+1must equal zero.
It is possible to deduce the multi-nodes distribution system model based on the proposed procedure for the single node water distribution problem. Figure7shows the causal loop diagram of multi-nodes distribution system. The symbol definitions in this case are the same as mentioned above, and the number denotes the node number. The reserved flow (OB) and unused flow (ON) from the upstream node are the inflow of the downstream node.
The combined Groundwater storage levels and the remaining water treatment plant capacity determine the quantity of groundwater available. The groundwater
S1 S2 OB1 OD1 ON1 I1 OB2 OD2 ON2 S3 OB3 OD3 ON3 R1 R2 R3
Pmax1 Pmax2 Pmax3
D1 D2 D3
Cmax1 Cmax2 Cmax3
Smax1 Smax2 Smax3
Fig. 7 The causal loop diagram of multi-nodes distribution system
storage level is the groundwater storage at time t minus the initial groundwater storage. Equation7denotes the groundwater supply:
IF i⊂ G ODWi,t = min
GIi,t, Di,t−
k⊂SODk,t, Cmaxi, Pmaxi
,GIi,t > 0
ODWi,t = 0 ,GIi,t ≤ 0
(7)
where ODWi,tis the water supply from the groundwater node i at time t, GIi,t indi-cates the groundwater storage level variation, Di,tis the desired demand withdrawn from groundwater node i at time t, ODk,tis the water supply of the surface-water node k at time t, Cmaxidenotes the maximum water treatment plant capacity for node i, and Pmaxi denotes the maximum pipe capacity for node i. G means that the storage node belongs to groundwater, while S denotes the pipes connect surface water node with demand Di,t.
3.3 Groundwater Recharge/discharge Estimation
Figure 8illustrates the procedure of estimating the recharge and discharge of the groundwater system. A groundwater system typically includes into four types of recharge or discharge: area recharge from surface infiltration, river and groundwa-ter ingroundwa-teraction (recharge/discharge), recharge from the easgroundwa-tern boundary (Central Mountain Range), and area pumping. This study estimates the area recharge from surface infiltration using GIS tools, and determines the three other source and sink quantities by solving a parameter identification problem (inverse problems). The parameter identification problem in this study involves the famous finite different numerical model, MODFLOW (Harbaugh and McDonald 1996; McDonald and Harbaugh1988), and a computer code for universal inverse modeling, UCODE (Hill 1998; Poeter and Hill1998).
First, area recharge estimation requires GIS tools, a land use map, and soil type coverage. The land use map of Pingtung Plain used in this study originally had 95 land use types, which were reclassified into five classes according to the infiltration abilities of each type. Figure 9 shows the reclassified map with these five classes, including impermeable zones, river zones, paddy field zones, water body zones, and other permeable zones. Figure8shows the estimation process for these
α
Fig. 8 Procedure for Groundwater recharges/discharge estimation
five classes. The recharge quantity of each land use class is based not only on its own recharge mechanism, but also according to its type of soil coverage. Because the interaction between river and groundwater is very complex, the parameter identification procedure determines the recharge quantity of river zones, as the next step illustrates. Due to the effects of man-made structures, the recharge quantity for impermeable zones is zero. The area values of the three other zones, paddy field zones, water body zones and other permeable zones, are A1, A2, and A3, respectively. Two equations, Eqs.8and9, determine the recharge quantities for different classes. Equation8is suitable for wet land, while Eq.9is for dry land. These equations can respectively estimate the quantities of water body zones and other permeable zones:
R= A4× t × φ (8)
where A4is total area of wet land. (L2),t is time interval of each time step. (T),φ denotes the constant infiltration rate of saturated soil (L/T) varies according to soil coverage type.
Legend
Surface water body Other permeable area Impermeable area Paddy field River N W S E 0 4,125 8,250 16,500 Meters
Fig. 9 Land-use diagram of Pingtung Plain
where P is total rainfall quantity in the time interval (L), A5is total area of dry land (L2), α denotes rainfall recharge coefficient (non-dimensional), varies according to soil type.
In Eq.8, the soil is saturated and the infiltration rate relies on the soil properties, φ. The symbol φ means the constant infiltration rate of saturated soil and its value are referred to the data of a previous study of the Hydrology Agency, Ministry of Water Resources of mainland China (Assessment of China Water Resources (Chinese)
1986). Because the paddy field zones during irrigation period store specific levels of water, the mechanism is the same as one on wet land. Therefore, the total area of wet land, A4, equals the sum of A1and A2during irrigation periods, and A2during non-irrigation periods.
In Eq.9, rainfall and soil water levels determine the recharge quantities. The value of α is taken from the study of the Hydrology Agency, Ministry of Water Resources of mainland China (Assessment of China Water Resources (Chinese)1986). Because paddy field zones are dry during non-irrigation periods, this mechanism is as same as that of dry land. Therefore, the total area of dry land, A5, is equals the sum of A1 and A3during non-irrigation periods, and A3during irrigation periods. Summing the quantities of paddy field zones, water body zones and other permeable zones reveals the magnitude of area recharge.
2
zone of pumping down stream medium stream upper stream artificial well22
Legend-500 -400 -300 -200 -100 1 2 3 4 5 6 7 8 9 10 11 12 0 100 200 300 time (month)
discharge (million ton / month)
infiltrtion recharge river recharge pumping boundary recharge net recharge
Fig. 11 Results of groundwater recharge/discharge estimation
Next, this study uses MODFLOW and UCODE to solve the inverse problem (the parameter identification). The purpose of the inverse problem is to estimate the other sink and source quantities of the groundwater system, such as area pumping, recharge from the eastern boundary, and interaction between river and groundwater. Owing to a lack of raw data, such as riverbed conductance, we used the well package, instead of river package, to simulate the interaction between river and groundwater. Figure10shows the Pingtung Plain divided into 316 cells with a size of 2.0× 2.0 km each for MODFLOW modeling. The Zonation method then reduced parameter dimensions (Yeh1986). Figure10shows that the area pumping includes six zones. River and groundwater interaction is only considered in the Kaoping River, dividing it into upper, middle, and downstream sections (Fig. 10). Applying the Zonation method, cells in the same river section or the same zone were simulated with the same pumping and injecting rates. Four ‘artificial wells’ that recharge the shallow aquifer at the boundary represent recharging at the eastern boundary, making it possible to implement the well package. The number of decision variables in the parameter identification procedure is 13, including quantities for six zones, three river sections, and four artificial wells.
Figure11shows the results of recharge and pumping estimation for the groundwa-ter system at each month. This figure indicates that the net recharge is positive during February, March, May, August, September, and October. Figure12 compares the groundwater table observations and simulations using contour lines. These results demonstrate a good fit between the simulated groundwater table and observed data.
4 Simulation Results
The proposed model investigates the performance of different conjunctive-use alter-natives in southern Taiwan. This study uses two indicators, the shortage index (SI)
1999, March 1999, August Simulated water level (m)
Observed water level (m)
Simulated water level (m) Observed water level (m)
Fig. 12 Comparison of contour lines of groundwater level for simulation and observation
and the intensity of surface water use, to respectively indicate the water shortage severity and water resources depletion in Taiwan. The SI, proposed by US Army Corps of Engineers, represents water shortage impact in Taiwan. The SI is defined as SI =100 N N i=1 Sh i T i 2 (10) where N denotes number of periods, Shiis the water shortage volume during period I, and Tirepresents the demand of the water use sector (agriculture or industry) during period i. Each period in this study is 10 days, which is commonly used in Taiwan when performing long-term studies for water resource planning.
The intensity of surface water use is the ratio of annual water used to annual river flow, and indicates the depletion of surface water resources in Taiwan. A high value of this indicator represents the overuse of surface water, and may have negative impacts on river environment sustainability.
Table 2 summarizes the results of different conjunctive-use alternatives. Case 0 is the base scenario that uses only surface water, while other cases use both surface and groundwater resources with different artificial recharge capacities. The
Table 2 Summaries o f conjunctive-use operations with different artificial recharge capacities Case Conjunctive-use A rtificial A verage Average Shortage Intensity o f surface Intensity o f surface recharge groundwater artificial index w ater use for the w ater use for the capacity pumping recharge Kaopin R iver (%) Z engwen River (%) 10 4m 3/10 d ays (10 4m 3/year) (10 4m 3/year) Case 0 N o – 0 0 0.91 16.72 56.53 Case 1 Y es 0 527.35 0 0 .84 16.72 56.53 Case 2 Y es 100 611.68 220.95 0.58 17.18 56.53 Case 3 Y es 200 832.16 441.42 0.3 17.65 56.53 Case 4 Y es 300 1,049.88 661.90 0.13 18.10 56.53
water shortage (indicated by the SI) decreases as the artificial recharge capacity increases. Because the only river on the Pingtung Plain is the Kaoping River, the artificial recharge only includes the unused flow of the Kaoping River. Hence, only the intensity of surface water use for the Kaoping River varies, while that for the Zengwen River is stationary.
Figure13 indicates the variations of groundwater storage increment for various scenarios. These results indicate that all scenarios preserved the same average variations in last 8 years. Higher artificial recharge leads to higher final groundwater storage. Table 2 shows the average volume of groundwater used and artificial recharge. -70000 -60000 -50000 -40000 -30000 -20000 -10000 0 10000 20000 30000 40000 50000 60000 70000 1 37 73 109 145 181 217 253 289 Time (ten-days)
groundwater storage increasement (10000m3)
groundwater storage increasement (10000m3)
325 361 397 433 469 505 541 577 613 649 685 721 1 37 73 109 145 181 217 253 289 Time (ten-days) 325 361 397 433 469 505 541 577 613 649 685 721 -70000 -60000 -50000 -40000 -30000 -20000 -10000 0 10000 20000 30000 40000 50000 60000 70000 case0 case1
case2 case3 case4
< 400 600~800 800~1200 1200~1600 1600~200 > 2000 case0 case2 case4 0 10 20 30 40 50 60 70 The conditional probability of shortage(%)
Shortage interval( 10000ton/ten-days) case0 case1 case2 case3 case4 case5
Fig. 14 Conditional probabilities of water shortage for all cases
Furthermore, the occurrence frequency analysis of water shortage illustrates how artificial recharge capacity affects water supply reliability under the conjunctive-use framework. The analysis in this study adopts the conditional probability expressed in Eq.11:
P(SHR|SH) =
P(SHR∩ SH)
P(SH) (11)
where P(SHR|SH) indicates the probability of a specific amount (R) of water shortage based on the occurrence of a water deficit. P(SH) represents the probability of a water deficit. P(SHR∩ SH) is the joint probability, indicating the probability of two events in conjunction. Figure14represents the histogram of the conditional probability of water shortage value for all cases with six intervals. This figure shows that water supply without conjunctive-use (case 0) has the highest conditional probability of large water shortages. As the artificial recharge capacity increased, the conditional probability of large water shortages decreased. Water system managers would rather incur a sequence of smaller shortages in water supply than one potential catastrophic shortage. Hence, this conditional probability diagram can provide useful information for decision makers to avoid extreme water shortages.
5 Conclusions
This study proposes a systematic procedure to assessing the performance of po-tential planning alternatives for reducing water shortage risks in a conjunctive-use
water distribution system. The proposed procedure is based on system dynamics, groundwater model simulation, parameters identification, and GIS tools. This study uses the stock-flow diagram of system dynamics to explore the relationships among system components and provides a transparent framework for model development. Simulation results demonstrate that the proposed integrated approach is well suited for analyzing the performance and long-term effects of different water management alternatives.
The occurrence frequency analysis in this study also provides useful information for decision makers to avoid potential catastrophic shortage. These results indicate that as the artificial recharge capacity increased, the occurrence probability of extreme shortages decreased. These results also demonstrate that artificial recharge is necessary to maintain groundwater resource conservation without overusing river flow. Although this study focuses on southern Taiwan, the proposed concepts and procedures are applicable to other areas with a similar conjunctive-use framework. Acknowledgement We are grateful to the National Center for High-performance Computing for computer time and facilities and to the National Science Council of the Republic of China for supporting this research under Contract No. NSC 97-2221-E-009-084.
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