Stability Analysis of Stakeholders’ Cooperation in Inter-Basin Water Transfer Projects: a Case Study

Abstract

This study investigates the conflict resolution among different stakeholders in a water transfer project. The portion of the Beheshtabad Water Transfer Project in Iran which aims to convey water from the Karun Basin to the Gavkhuni Basin is used as a case study. In this process, the initial water allocation scheme is initially determined through simulation in MODSIM ignoring the water transfer project. Then, the concepts of cooperative and non-cooperative games are used to resolve the conflict among the stakeholders. The profits of water transfer project and the payoffs for each player are calculated using an optimization model that optimizes the allocation of the conveyed water. The results of the conflict resolution model show that bilateral cooperation is the best strategy the players may adopt. In the non-cooperative model, it is found that a water transfer agreement that is incentivized by an average payment of 250.66 million US$ as compensation from the Gavkhuni basin to the Karun basin puts both basins at equilibrium with a Pareto optimal condition; in this case, none of the players will be willing to abandon the cooperation without regret. In the cooperative approach, cooperation is found to be beneficial to all the players involved.

Appendix

1.1 Model assumptions

Considering the extensive size of the study area, the modeling is performed based on the following assumptions:

• The simulation model includes only the dams and water bodies larger than 5 MCM while identical reservoir water levels are considered for the start and end of the simulation period.

• The simulation models for both basins are executed with the water demand of all the fields considered. In the optimization model, four regions in the receiving basin (Najafabad, Kuhpayeh-Sagzi, Esfahan-Borkhar, and Lenjanat) are considered because of their importance and location alongside the river.

• The water allocated to agricultural, domestic, and industrial sectors is not consumed in full; so, the return flows are incorporated into the optimization and simulation models.

• The game theory approach to conflict resolution of shared resources is based on financial payments in exchange for a reduction or non-utilization of the common source. However, given the importance attached to the full supply of the domestic and environmental demands, it is not possible to consider the stakeholders’ utilities of these sectors through game theory models. These sectors are, therefore, excluded from the game, but not from the optimization model.

• Basins are assumed to have the same agricultural productivity equal to 0.35.

1.2 Optimization model structure

1.2.1 Objective function

The objective function maximizes the difference between the benefits and the costs. In this model, the costs and benefits of the water transfer project are considered to consist of the following components:

Equation 1 expresses the benefits in US Dollars to be gained from allocation of water to the agricultural sector at the receiving basin (B₁).

$$ {\mathrm{B}}_1=\sum \limits_{\mathrm{n}=1}^{\mathrm{N}}\sum \limits_{\mathrm{s}=1}^{\mathrm{S}}\sum \limits_{\mathrm{m}=1}^{\mathrm{M}}\left({\mathrm{cpd}}_{\mathrm{n},\mathrm{s},\mathrm{m}}\ast \frac{{\mathrm{X}}_{\mathrm{n},\mathrm{s},\mathrm{m}}}{{\mathrm{D}}_{\mathrm{n},\mathrm{s},\mathrm{m}}}\ast {\mathrm{P}}_{\mathrm{s}}\right) $$

(1)

In this Equation, X, cpd, D, and P, respectively, denote the volume of water allocated (m³), yield (ton/ha), water demand (m³/ha), and net benefit of crops (US$/ton). The parameters m, n, and s are the counters of the month, field, and product.

The benefits gained from allocation of water to domestic (drinking) and industrial uses are a function of the volumes of water allocated to these demands. In this study, the equations required for estimating the benefits of water allocation to the industrial sector (B₂) and domestic use (B₃) in 10⁵ US Dollars at the receiving basin are derived by fitting the benefits of the industrial and domestic uses of water for the volumes of water consumed. In these equations, X_{ind, m} and X_{Dom, m} denote the volume of water allocated to industrial and domestic uses, respectively, in million cubic meters (MCM) at month m.

$$ {B}_2={16.308}^{\ast }\ {X^3}_{ind,m}\hbox{--} {8799.6}^{\ast }\ {X^2}_{ind,m}+{2}^{\ast }\ {10}^{6\ast }\ {X}_{ind,m}-{10}^8 $$

(2)

$$ {B}_3=-{ 3 25.53}^{\ast }\ {X}_{Dom,m}+ 109425 $$

(3)

The water transfer project will reduce the rate of withdrawal from groundwater resources at the receiving basin. The benefit to be gained from the reduced pumping costs (B₄) in US Dollars depends on the amount of water conveyed. In this equation (Karamouz et al. 2009a), ζ, W, h₂, h_s, and p represent pumping efficiency, volume of water conveyed (MCM), groundwater level relative to the surface (m), hours of pumping per month, and power price in US Dollars per kiloWatt-hour (kWh), respectively.

$$ {B}_4=\frac{1}{3.67\ast {10}^{-4}\ast \zeta}\sum \limits_{m=1}^M\left(W\ast {h}_2\ast {h}_s\ast p\right) $$

(4)

The benefit of water allocation to environmental purposes at the receiving basin is a function of volume of water diverted toward the wetland to maintain the ecosystem. In this study, the benefit of water allocation to environmental purposes is obtained from Eq. 5, where, X_ins is the amount of water allocated to environmental use (MCM) and B₅ is the benefit of water allocation to the wetland (10⁵ US Dollars).

$$ {B}_5={639.6}^{\ast }\ {X}_{ins}- 7497 $$

(5)

The transfer of water from the source basin limits the water rights and future agricultural development in its vicinity. Eq. 6 gives the loss borne by the agricultural sector (C₁) in US Dollars as a result of this limitation. In this equation, the new allocation is initially determined based on the volume of water conveyed and then compared with the original allocation to determine the extent of loss. In this eq. X^''’_{n, m, s} denotes the volume of water allocated (m³) to the crop s in field n at month m after the implementation of the water transfer project. Other variables and parameters are as previously defined.

$$ {C}_1=\sum \limits_{n=1}^N\sum \limits_{s=1}^S\sum \limits_{m=1}^M\left({cpd}_{n,s,m}^{\prime}\ast \frac{X_{n,s,m}^{\prime }}{D_{n,s,m}^{\prime }}\ast {P}_s^{\prime}\right)-\sum \limits_{n=1}^N\sum \limits_{s=1}^S\sum \limits_{m=1}^M\left({cpd}_{n,s,m}^{\prime}\ast \frac{X_{n,s,m}^{\prime \prime }}{D_{n,s,m}^{\prime }}\ast {P}_s^{\prime}\right) $$

(6)

Water transfer projects have other negative consequences for the source basin, such as elevated dredging costs, reduced hydroelectric power generation, and reduced water quality, which are incorporated into the objective function as costs. With the reduction of annual river flow due to the water transfer project, a dredging budget needs to be set aside to maintain the river bed or keep the river ready for water transportation. The additional dredging cost due to the project is a function of both the river flow and the water transfer flow. In this paper, the equation required for estimating the dredging costs is obtained by fitting the cost of dredging operations for the river flows at the source basin. In this equation, C₂ and Q₁ denote the dredging costs (10¹¹ US Dollars) and the river flow (m³/s), respectively.

$$ {C}_2=-{0.5406}^{\ast }\ {Q}_1+ 552.31 $$

(7)

>The financial loss at the source basin due to reduced hydroelectric power generation is a function of the size of power generation loss (which depends on water transfer flow) multiplied by the price of electricity. The equation of financial loss due to reduced hydroelectric power generation is obtained by fitting the annual power generation values for the transfer flows at the source basin. In this equation, C₃, Q₂, and p^′ denote financial loss (million US Dollars), water transfer flow (m³/s), and power price in US Dollars per kilowatt-hour (kWh), respectively.

$$ C3=\left(-10.653\ast Q2+3814.9\right)\ast {p}^{\prime } $$

(8)

Water transfer may also alter the water quality along the source basin and cause significant declines in quality indicators. Therefore, a price should be assigned to the preservation of environmental quality through water treatment. This cost can be defined as the product of deviation of qualitative variables from their standard values by the unit price of treatment. River quality is mostly a function of its biochemical oxygen demand (BOD) and electrical conductivity (EC); these variables can be, therefore, used as water quality indicators. Water quality preservation costs due to water transfer from the source basin are expressed by the following equation (Mojahedi 2006).

$$ {C}_4=\sum \limits_{m=1}^M\left\{\left[{RegBOD}_m\left({Q}_{headwater,m}-{Q}_{trans,\kern0.5em m},{DO}_{headwater\kern0.5em ,m}\right)-{RegBOD}_m\left({Q}_{headwater,m},{DO}_{headwater,m}\right)\right]\ast {P}_{BOD}+\left[{RegEC}_{,m}\right(\right.{Q}_{headwater,m}-{Q}_{trans,m},{EC}_{headwater,m}\left)-R{egEC}_{,m}\left({Q}_{headwater,m},{EC}_{headwater\kern0.5em ,m}\right)\right]\ast {P}_{Cond} $$

(9)

In this equation, C₄, Q_{headwater, m}, Q_{trans, m}, DO_{headwater, m}, RegBOD_m, P_BOD, RegEC_m, and P_EC are water treatment cost (US Dollars), headwater flow at month m (m³/s), transfer flow at month m (m³/s), headwater DO concentration at month m (mg/lit), BOD regression equation at month m, treatment cost for one milligram of BOD concentration (US Dollars), EC regression equation at month m, and treatment cost for one milligram EC concentration (US Dollars), respectively.

In Eqs. 10 and 11, the changes in river quality are expressed in terms of water quality indicators. The values for the coefficients in these equations for different months are derived from Mojahedi (2006).

$$ RegBOD\left(Q, BOD\right)={C}_t\ast DO+{D}_t\ast Q+{Const}_1 $$

(10)

$$ RegCond\left(Q, EC\right)={E}_t\ast EC+{F}_t\ast Q+{Const}_2 $$

(11)

Finally, the equation of the objective function will take the following form:

$$ \mathit{\operatorname{maximize}}\kern0.75em Z=\left(\sum \limits_{i=1}^I{Benefit}_i-\sum \limits_{j=1}^J{Cost}_j\right) $$

(12)

1.2.2 Constraints

Equation 13 controls the minimum and maximum cultivation areas and prevents the allocation of all the available water to only one crop. As such, the priority of this constraint is to ensure that water is at least allocated to all the crops. Equation 14 expresses the effect of irrigation efficiency on the amount of water allocated to agricultural crops. Based on the cultivation area for a 10-year period, μ₁ and μ₂ are considered to be 0.8 and 1.2, respectively. In these equations, a_s, A_n, and X_{n, s, m} represent percentage of historical cultivation area of crop s, cultivation area in field n (ha), and the amount of water allocated to crop s in field n at month m (m³) for the source basin as well as the pre- and post-water transfer conditions at the receiving basin (that is, the varaibels X, X^’ and X^”), respectively. Also, φ is agricultural productivity.

$$ \sum \limits_{n=1}^N\sum \limits_{s=1}^S\sum \limits_{m=1}^M\left({\mu}_1\ast {a}_s\ast {A}_n\ast {D}_{n,s,m}\right)\le \sum \limits_{n=1}^N\sum \limits_{s=1}^S\sum \limits_{m=1}^M{X}_{n,s,m}\le \sum \limits_{n=1}^N\sum \limits_{s=1}^S\sum \limits_{m=1}^M\left({\mu}_2\ast {a}_s\ast {A}_n\ast {D}_{n,s,m}\right) $$

(13)

$$ \sum \limits_{n=1}^N\sum \limits_{s=1}^S\sum \limits_{m=1}^M{X}_{n,s,m}=\sum \limits_{n=1}^N\sum \limits_{s=1}^S\sum \limits_{m=1}^M{x}_{n,s,m}\ast \varphi $$

(14)

The following equation is the mathematical expression of the water input of agricultural sector and includes water returned from the domestic and industrial sectors as well as that from each farm field. It may be noted that the environmental demand (equal to 140 MCM) is also considered. In this equation, R, X_{agr, i}, ins, γ₁, α₁, V_ind, and V_dom denote river flow before reaching the first farm field (m³/s), initial water allocation (the water available) to field i (m³), minimum environmental demand for water (m³), coefficients of return flow from domestic and industrial uses, and the volume of conveyed water that is allocated to industrial and domestic uses (m³), respectively.

$$ R=\left({X}_{agr,i}+V+\left({\gamma}_1-1\right)\ast {V}_{dom}+\left({\alpha}_1-1\right)\ast {V}_{ind}- ins\right) $$

(15)

Equation 16 indicates the constraint on the water allocated to the first field, which must be less than or equal to the total amount of water allocated to the agricultural sector (R). Equation 17 limits the water allocated to other fields based on the amount of water returned from the preceding fields. In this equation, k and δ represent the filed counter and the coefficient of return flows from the other fields.

$$ \sum \limits_{s=1}^S\sum \limits_{m=1}^M\left({x}_{1,s,m}\right)<=R $$

(16)

$$ \sum \limits_{k=2}^K\sum \limits_{s=1}^S\sum \limits_{m=1}^M\left({x}_{k,s,m}\right)\le R-\left(1-\delta \right)\ast \sum \limits_{k=1}^{K-1}\sum \limits_{s=1}^S\sum \limits_{m=1}^M\left({x}_{k,s,m}\right) $$

(17)

According to Eq. 18, the total amount of water allocated to the agricultural sector (R) equals the total water allocated to all fields (continuity equation). For the agricultural sector of the source basin, the continuity equations for pre- and post-water transfer conditions are expressed by Eqs. 19 and 20, in which V and C are the volumes of available and conveyed water (m³), respectively.

$$ \sum \limits_{n=1}^N\sum \limits_{s=1}^S\sum \limits_{m=1}^M\left({x}_{n,s,m}\right)=R $$

(18)

$$ \sum \limits_{n=1}^N\sum \limits_{s=1}^S\sum \limits_{m=1}^M\left({X}_{n,s,m}^{\prime}\right)=V $$

(19)

$$ \sum \limits_{n=1}^N\sum \limits_{s=1}^S\sum \limits_{m=1}^M\left({X}_{n,s,m}^{\prime \prime}\right)=V-C $$

(20)

The following equations must be incorporated to maintain the water qualitative standards at the source basin. BOD_std and EC_std denote standard BOD and EC concentrations (mg/lit), with maximum allowable values of 10 (mg/lit) and 1200 (mho/cm), respectively (Krenkel and Novotny, 1980).

$$ {RegBOD}_m\left({Q}_{headwater,m}-{Q}_{trans,m},{BOD}_{headwater\kern0.5em ,m}\right)>{BOD}_{std} $$

(21)

$$ {RegEC}_m\left({Q}_{headwater,m}-{Q}_{trans,m},{EC}_{headwater,m}\right)>{EC}_{std} $$

(22)

1.3 Simulation model results

The following Figures show the results of model calibration for the changes in aquifer volumes in the two plains of the receiving basin. Clearly, the regression errors (R² error) in the two Figures are 0.98 and 0.81, respectively, confirming the accuracy of the modeling process. Also, Table 4 reports the MODSIM results for water allocation to different sectors.

Fig. 3

Groundwater volume changes in the Chelgerd-Ghal’e Shahrokh sub-basin

Fig. 4

Groundwater volume changes in the Karvan sub-basin

Table 4 Initial allocation with MODSIM model (MCM)

Fig. 5

The effectiveness of players resulting from the differnt coalitions in each scenario

Fig. 6

Gately index for each player in different scenarios

Fig. 7

Results of non-cooperative approach under scenario 1. Note: K=Karun, G = Gavkhuni, KN=Karun Noncooperation, KC = Karun Cooperation, CGAS = Cooperation of Gavkhuni’s Agricultural Sector, CGIS = Cooperation of Gavkhuni’s Industrial Sector, CGAIS = Cooperation of Gavkhuni’s Agricultural and Industrial Sector, NGAS = Non-cooperation of Gavkhuni’s Agricultural Sector, NGIS = Non-cooperation of Gavkhuni’s Industrial Sector, NGAIS = Non-cooperation of Gavkhuni’s Agricultural and Industrial Sector

1.4 Gately index

The Gately index is expressed by the following equation, in which d_i, X_k, V(N-i), and V(i) represent the inclination to non-cooperation for player i, the allocation due to cooperation, the value of the coalition without player i, and the value of the coalition for player i, respectively.

$$ {d}_i=\frac{\sum \limits_{i\ne k}\left({X}_k\Big)-V\left(N-i\right)\right)}{X_i-V(i)} $$

(23)