A. Emadi; Ramin Fazloula
Abstract
Introduction: Population growth and water resource constraints make optimal operation of available resources important. Considering the utility of the stakeholders and the physical limitations of the problem, the optimal allocation of water resources is, therefore, necessary. Among the proposed strategies, ...
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Introduction: Population growth and water resource constraints make optimal operation of available resources important. Considering the utility of the stakeholders and the physical limitations of the problem, the optimal allocation of water resources is, therefore, necessary. Among the proposed strategies, the game theory is one of the methods used to improve water resources management. Also, in order to achieve the optimal and fair allocation, a model and method should be selected in accordance to the conditions. Our main purpose was to study the optimal water allocation from the dam reservoir by increasing the overall profitability of the system through forming a coalition as well as increasing the profits of each water users participated in the coalition. Increase in profits will be possible without the need for any additional costs and only with the change in the operation management. Integration of Genetic Algorithm optimization model with Shapley Crisp game theory can be considered as the innovation of this research work applied to optimally allocate water from Shahid Rajaee Dam reservoir to downstream needs.
Materials and Methods: In this study, a new methodology based on crisp Shapley games is developed for optimal water allocation from the dam reservoir. First, the standard operation policy was used to determine the volume of available water. Then, the optimization model of the Genetic Algorithm was employed for initial allocation considering an equity criterion. The Crisp Cooperative Game Theory was then applied for secondary optimization of water allocation among stakeholders. The possible coalitions for increasing the overall system profits were formed using the Shapley method and the profits of each coalition were then calculated. Finally, the Shapley's value relationship was used to reassign profits to players in order to encourage them to participate in the grand coalition. This study was carried out on Shahid Rajaee dam located in 45 kilometers southwest of Sari in Tajan basin. This dam mainly supplies agricultural and drinking water. Rice and citrus production were the largest and second largest water consumer, respectively.
Results and Discussion: In this study, the monthly amount of water released from Shahid Rajaee Dam reservoir was determined by using standard utilization policy and then the amount of initial allocation to downstream dam needs was calculated using genetic algorithm optimization model. Then, by using the players' profit coefficient and the amounts allocated from the implementation of the genetic algorithm model, the initial profit values were calculated for each stakeholder. Employing the Shapley Crisp method, the amounts of water allocated to each player and their corresponding economic benefits were obtained for the grand and two-player coalition. The results showed that the grand coalition had more benefits than the binary coalitions as well as the initial allocation. At this step, the Shapley value relationship was used to reallocate the profits among the players. After allocating water to three participants based on different coalitions, since the fair share of each was obtained in the first step, payments must be made between the players in order to be fair. The player who receives more water share determined at the first step must pay money to other players receiving water less than their fair share. The method proposed for the 18 years statistical period was used to allocate water among the stakeholder. According to the findings, the formation of a grand coalition increases overall system profit without the need for any additional costs and only with revising the operation management.
Conclusion: In this research, an integrated model of optimization was developed using Genetic Algorithm and Shapley Crisp Cooperative Game Approach. The amount of financial payments among the stakeholders in the coalition was also determined based on the Shapely value. Constituent coalitions show the management impacts on water policy and demand management in the studied area. The best results were obtained when players formed a grand coalition. In other words, by participating in the grand coalition and reallocation of water and profits among players, the overall system profits will increase by 10 % and the profits of players cultivating rice, citrus and other agricultural products will rise by 6, 16 and 15 %, respectively, as compared with the condition the players do not participate in the grand coalition and water allocation is only done using the Genetic Algorithm. Therefore, the water allocation should be based on a grand coalition requiring the cooperation and participation of all stakeholders. The results indicate that this method can be applied to allocate resources equitably. It can be also used to solve social conflicts among decision-makers.
mahsa noori; Saeed Reza Khodshenas; H. Rezaeepajand
Abstract
Introduction: Dam failure and its flooding is one of the destructive phenomena today. Therefore, estimating the peak outflow (QP) with reasonable accuracy and determining the related flood zone can reduce risks. Qp of dam failure depends on important factors such as: depth above breach (Hw), volume ...
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Introduction: Dam failure and its flooding is one of the destructive phenomena today. Therefore, estimating the peak outflow (QP) with reasonable accuracy and determining the related flood zone can reduce risks. Qp of dam failure depends on important factors such as: depth above breach (Hw), volume of water above breach bottom at failure (Vw), reservoir surface area (A), storage (S) and dam height (Hd). Various researchers have proposed equations to estimate QP. They used the regression method to obtain an appropriate equation. Regression is a mathematical technique that requires initial test and diagnosis. These researchers present a new regression model for a better estimation of Qp.
Materials and Methods: The data used in this study are related to 140 broken dams in the world for 34 of which sufficient data are available for analysis. Dam failure phenomenon is a rapidly varied unsteady flow that is explained by shallow waters equations. The equations in the one-dimensional form are known as Saint-Venant equations and are based on hydrostatic pressure distribution and uniform flow under rectangular steep assumption. Although hydraulic methods to predict the dam failure flood have been developed by different software, due to the complex nature of the problem and the impossibility of considering all parameters in hydraulic analysis, statistical methods have been developed in this field. Statistical methods determine the equations that can approximate the required factors from the observed parameters. Multiple regression is a useful technique to model effective parameters in Qp, which can examine the statistical aspects of the model. This work is done by different tests, such as the model coefficients necessity test, analysis of variance table and it creates confidence intervals. Data analysis in this paper is done by SPSS 16 software. This software can provide fit model, various characteristics and related tests in the Tables.
Results and Discussion:This paper proposes a new relationship with better estimation of discharge peak (Qp) based on Hw and Vw factors. Results showed how to choose the appropriate model (fitting the model) and the initial required tests, according to the diagnostic model. And it compares the estimated error (relative efficiency) of the researchers’ models with the proposed models. The number of models can be classified to three convenient linear, multiplicative and transformed bases on Vw, Hw and Qp (nonlinear terms Qp). The best models for each of the three models were selected. Their corrected determination coefficients (Adj R2) are close together and are between 0.86 until 0.864. The relative efficiency criteria based on the root mean square error (RMSE) was used to determine the best model. This standard was also used for other researchers’ models. RMSE of the three models presented in this article is lower than that of other models (from 745 to 759). Diagnostics analysis of the three models is not possible due to the large volume, so some statistical analysis for the model 2 are presented in detail. The results are given in the following Tables. Test level has been assumed to be 5%. From the point view of hydraulics, it can be said that the final equation for Qp should be proportional to Hw 1.5. So although the model (2) has the lowest RMSE, but the model (3) of the hydraulics viewpoint seems more logical and its RMSE is not very different from the model (2), so this model can be selected as the best model. Figure 1 show diagnostics diagrams of model (3). The right Figure shows the homogeneity of residuals (follow the normal law) as a histogram. This homogeneity is confirmed by the crouch graph (center Figure). The left graph shows the stabilization of residual variance. According to the preliminary and diagnostics tests results, the model (3) has been selected. Its determination coefficient (0.864) also shows good strength.
Table 1- Top models presented in this research
Model1
Model2
Model3
,
Note:
Table 2- Statistical characteristics of the proposed models
model Adjusted R Square Durbin
Watson F VIF Std.
Residual Cook's Distance Centered Leverage
1 0.862 1.716 104.383 1.283 [-1.975 , 2.908] [ 0,0.569] [0,0.363]
2 0.860 1.744 102.545 1.283 [-1.824 , 2.834] [0,0.608] [0,0.363]
3 0.864 1.687 211.048 1 [-2.202 , 2.699] [0,0.527] [0,0.335]
Figure 1- Model 3 diagnostics pattern diagrams: histogram (right), crouch diagram (middle) the estimated residuals (left)
Conclusion: In this study, data from 140 broken dams were used to provide an appropriate model for estimating the peak outflow of dam failure. Standard statistical principles including preliminary tests, diagnostic and the efficiency of the models are the innovations of this paper. Analysis showed that the three models are competitive, and that the best of them was selected. The determined coefficient of these models was from 0.86 to 0.864 ranges. Relative efficiency was calculated by the RMSE index. The results showed that these models are more accurate than the models presented by other researchers. The model (3) was presented in this research, the best result was estimated for Qp and its error was less than the other models.
