Optimization of Water Allocation using Cooperative Game Theory Case Study: Zayandehrud Basin

Introduction:
When there is no determined value for water (as a public asset) by its trustees and beneficiaries and its allocation method is more dependent on the requirements of water consumers than comparing water affairs benefits with its real value, decision making on which interested group, when and to what extent can use water is a game. This study is aimed to determine sustainable policies for water allocation to interested groups such that high quality sufficient water is available to survive water bodies and economic purposes of interested groups are satisfied by sustainability agreement with the environment. For this, the environment is recognized as an independent water user in optimization model and as an independent player in the game theory. Thereby, Zayandehrud basin has been studied as a case study.
 
Materials and Methods:
In this study was first dealt with optimizing the allocation of water output from the reservoir to consumptions including drinking, agriculture, industry and environment by means of genetic algorithm. To get the most desirable possible state of water provision for consumptions, 4 approaches have been considered, as described briefly below.
The first includes providing biological current for the river which is in an equilibrium using Tenant (Montana) method and available data (providing 2.06 (MCM) for each month in the cold season and 6.18 (MCM) for each month in the warm season). The second has been formulated by providing minimum water requirement for lagoon survival and considering protection and provision of minimum survival requirements for this valuable water ecosystem in the area. Continuity of natural life in the swamp depends completely on water depth. The lowest possible depth for vital activities is in about depth of 15cm. This depth can be achieved by importing 75 MCM per year water to the swamp. Benthos is hardly survived in this depth. The third includes providing desirable quality for the lagoon based on TDS such that the water requirements for TDS dilution have been assumed as a biological requirement. In the fourth, provision of minimum water requirement for the lagoon is considered and with regard to the studies on Gavkhoony swamp, desirable performance occurs with provision of 140MCM per year water. This amount provides depth of 30cm for the swamp. Then, having estimated benefits of each beneficiary, their interactions in the basin have economically investigated by cooperative games. The percentages of requirement provision for beneficiaries and annual water allocations have presented in Table 1 for different approaches. The benefits of each beneficiary and the results of cooperative game have been provided in Figure 1.
Tabel - Gross profit of water user in each approach





4^th approache


3^rd approache


2^nd approache


1^st approache


User




Benefit ($)


Water use (MCM)


Benefit ($)


Water use (MCM)


Benefit ($)


Water use (MCM)


Benefit ($)


Water use (MCM)




2057.38


8756.8


2032.89


8652.6


2157.34


9182.32


2057.89


8759


Agriculture




622.55


924.3


622.09


923.61


622.49


924.21


622.47


924.17


Industry




208


1747.2


124.4


1044.98


106.03


890.71


117.16


985.05


Environment





 




 
 



2^nd Approach


1^st Approach



 
 



4^th Approach


3^rd Approach





Figure 1. Results of cooperative games in different approaches
 
Discussion and Conclusion:
With regard to data from the studied area, in spite of various managerial plans to increase water provision for the basin, it no longer satisfies the requirements of water consumers. Specially, it is the case in the environmental sector where because of ignorance and devoting water allocation priorities in the recent years, it has been deficient in its life and is completely dependent on seasonal currents and rainfalls. According to the designed approaches in the environmental sector of this study, more than 85% of its requirements can be eliminated in allocations. With water provision approach for environment sector, 3-8% of agricultural and 8% of industrial requirements are deficient. From environmental requirement provision point of view which has been distinctively defined in every approach, the model has shown the best performance in the first approach such that 100% of environmental requirements are satisfied. Of course, considering that this approach has accounted minimum requirements for the environment, minimum deficiencies in agricultural and industrial allocations have been observed. Maximum water requirement has been considered in the fourth approach in which optimization model can allocate 87% of environmental requirements. The fourth approach, from water allocation to the environment view point, is the best approach because of water allocation to the environment with regard to water content as well as positioning the lagoon in a desirable state for survival.
It can be concluded from economic analyses of model approaches that the industry has the same benefit in all approaches despite 8% change in water allocation respect to unfair allocation and low or high environmental utility in different approaches has no influence on economic performance of the industry. The second approach has the most benefit in agricultural sector and it has the best performance in environmental sector because of the most desirable state for the river and lagoon survival. Economic analysis shows that agricultural sector has more benefit in second approach than other states. From model allocations, it can be said monthly allocation and distribution model has impressive effect in agricultural sector. With constant optimization procedure in allocations, agricultural sector incurs severe pressures but considering allocated water and benefits in the agricultural sector, first, second and fourth approaches have little differences because of monthly water distribution procedure in firth and third approaches.
From game theory, benefits from player cooperation in agricultural and environmental sector have been more than no cooperation. The industry earns the same benefit from both states, except for third approach. Proportional Nucleolus game has maximum benefit in agricultural sector, except in the first approach. Weak Nucleolus has shown better performance in benefit calculation in the environmental sector, except for fourth approach. Therefore, there is no specified procedure for games but because of more benefit from cooperation in agricultural and environmental sectors than no cooperation both sectors will get more benefits from cooperation beside water requirement provision. Best benefit allocation has respectively occurred in fourth, second, third and first approaches.
Finally, it is clear that considering the environment as a beneficiary of basins and planning for water resource management makes always more benefit the system, although less water allocation to consumers makes less benefit. Because of no profit in environment sector and no protest except in critical conditions, there is ignorance in this sector while water ecosystems are most valuable resources that their economic value estimation is complicated and far from reality but with these economic methods it is seen that the aggregate benefit and profit is in the environment protection and survival.