含有协变量的地下水动态规划管理模型研究
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摘要
在地下水系统的数值模拟和优化管理中,需要考虑地下水与其它水体的水力联系和交换。其中有一类交换量,如河水与地下水的交换量、蒸发排泄量、泉流量等,它们的共同特征是其大小都取决于补(排)点处地下水位的高低,不能人为给定,我们将这种交换量统称为协变量。将人工开采(补给)量、地下水位和协变量三者之间的关系称为互馈协变关系。
本文通过分析地下水互馈协变关系行为的作用过程和特征,提出了应用状态转移方程法构建含有协变量的地下水动态规划管理模型的理论和方法,并采用微分动态规划方法求解。首先,把描述协变量和地下水位的数学关系式代入到数值模拟模型中,完成了含有协变量的地下水模拟模型的建立,应用有限差分法求解。其次,针对一个假想例子,即一个具有互馈协变关系的假想地下水系统,运用嵌入法建立了含有协变量的地下水非线性规划管理模型,运用状态转移方程法建立了含有协变量的地下水动态规划管理模型,然后分别采用Lingo软件和微分动态规划方法进行求解。两种管理模型的计算结果基本一致。
在假想例子研究的基础上,以吉林省西部松原地区的地下水系统为研究实例,全面收集和整理资料,通过分析协变量与地下水位之间的相互作用过程和机制,完成了含有协变量的地下水数值模拟模型的建立,采用Visual MODFLOW软件求解。
针对研究区内的主要互馈协变关系问题,在数值模拟模型的基础上,以前郭县和扶余县部分地区为重点研究区,应用状态转移方程法构建了该区含有协变量的地下水动态规划管理模型,采用微分动态规划方法求解,同步获得了优化的人工开采量、地下水位和协变量。
Water resources crisis including water resources shortage and water environmental problem is one of the major issue in the 21st century. The phenomenon of water resources shortage is serious with the development of economy, increasing of population and changes of climate. As an important component part of water resource, groundwater is an important water supply source of human life and industrial and agricultural production. At present, the shortage of macroscopical programming and scientific management has leaded to groundwater over extraction in the processes of groundwater pumping and utilization in some area, and has leaded to a series of water environmental problem.
Groundwater optimization management is the application of decision science in groundwater exploitation and utilization process. It is a logistic process which is based on the inherent physical law of groundwater system, analyses and describes the groundwater system decision environment, and makes the action state and functional effect optimal though the optimum control of controllable input decision. At present, simulation and optimization of groundwater are still the main techniques of forecasting groundwater behaviors and optimizing the regulating schemes. In order to assure that the optimization process following the inherent principle and theory of groundwater system, optimal model must be on the basis of simulation model. We need to imbed the simulation model into optimization model using some approach, which makes the simulation model be a part of optimization model, implementing the connection of simulation model and optimization model. Embedding method, response matrix method and state transition equation method has been used in the past to solve how to embed and call the simulation model in the optimization model.
During the numerical simulation and optimal management of groundwater system, the hydraulic connection and exchange between groundwater and other waters need to be considered. Among them, such as exchange between surface water and groundwater, evapotranspiration, spring discharge et al, its amount is strictly dependent on the groundwater level at the recharge or discharge point, can not be given artificially, and such exchange is called covariate. The interaction among artificial pumping or recharge, groundwater level, and covariates is called relation of mutual-feed joint-variation.
In groundwater management model with covariates, the artificial pumping or recharge, groundwater level and covariates are all unknown. Moreover, these three variables inherently affect one another, resulting in such problems is difficult to resolve. Before this study is developed, embedding method and response matrix method has been used in building groundwater management model with covariates and has already got the result. However, document about treatment of groundwater dynamic programming management model with covariates and treatment of real groundwater system management problem using theory and methodology of relation of mutual-feed joint-variation has not been published, and this is the problem that the paper wants to solve.
Through the analysis of groundwater relation of mutual-feed joint-variation behavior process and its character, the expression of covariate in simulation model and the coupling technique of simulation model with covariate and optimization model as well as the solving method of this model were researched in the paper. Here, a dynamic optimization groundwater management model containing covariates is solved using dynamic differential programming method is described.
The main achievements of this research are as follows:
(1) Through the analysis of interaction process and its mechanism of covariates and groundwater table, the mathematical expressions which express the relationship of covariates and groundwater table were embedded into groundwater numerical simulation model, and then the groundwater simulation model with covariates was built, which was solved by finite difference method.
(2) The groundwater management model with covariates was built by the embedding method, the algebraic equations which obtained by discreting the groundwater simulation model with covariates was embed into optimization model as a part of constraint condition, together with other constraints and the objective functions, constitute the groundwater nonlinear programming management model with the ability to deal with relation of mutual-feed joint-variation, was solved using the Lingo software.
(3) Simulation model with covariates was coupled with optimization model using the state transition equation method. First, the state transition equation was obtained using groundwater simulation model with covariates. In other words, the water level in the end time was expressed by the initial time water level and pumping amounts, then the state transition equation was embedded into dynamic programming optimal model, together with other constraints and the objective functions, constituted the groundwater dynamic programming management model with the ability to deal with relation of mutual-feed joint-variation.
The groundwater dynamic programming management model with covariates was solved with differential dynamic programming method. Differential dynamic programming method can divide the optimal management process into several periods, the end time status variables of each period was only relevant to the initial time and decision variables, which reduce the computer load greatly. It was applicable to deal with the groundwater management problem with large scale and multi period.
(4) The above theory and method were applied to a hypothetical groundwater system with typicality relation of mutual-feed joint-variation, the groundwater nonlinear programming management model with covariates and groundwater dynamic programming management model with covariates were built respectively. The theory and method which the paper presented was applied, and reasonability analysis of the model was taken.
(5) On the basis of hypothetical instance analysis, the groundwater system of Songyuan area in western Jilin province was taken as the case study. Data was collected and sorted, through the analysis of interaction process and mechanism between covariates and groundwater level, groundwater simulation model with covariates was built, and then Visual MODFLOW was used to solve the problem.
(6) To solve the main relation of mutual-feed joint-variation problem, on the basis of simulation model, Qianguo Xian and Fuyu Xian was taken as important study area, groundwater dynamic programming management model with covariates was built using the state transition equation method, and solved using differential dynamic programming method, then the optimal pumping amounts, the amounts of covariates and groundwater levels were obtained simultaneously.
To sum up, this research expands the theory and method that dealing with relation of mutual-feed joint-variation in groundwater management model, so as to establish theoretical foundation and provide technical means for the solution of various practical problems.
本文通过分析地下水互馈协变关系行为的作用过程和特征,提出了应用状态转移方程法构建含有协变量的地下水动态规划管理模型的理论和方法,并采用微分动态规划方法求解。首先,把描述协变量和地下水位的数学关系式代入到数值模拟模型中,完成了含有协变量的地下水模拟模型的建立,应用有限差分法求解。其次,针对一个假想例子,即一个具有互馈协变关系的假想地下水系统,运用嵌入法建立了含有协变量的地下水非线性规划管理模型,运用状态转移方程法建立了含有协变量的地下水动态规划管理模型,然后分别采用Lingo软件和微分动态规划方法进行求解。两种管理模型的计算结果基本一致。
在假想例子研究的基础上,以吉林省西部松原地区的地下水系统为研究实例,全面收集和整理资料,通过分析协变量与地下水位之间的相互作用过程和机制,完成了含有协变量的地下水数值模拟模型的建立,采用Visual MODFLOW软件求解。
针对研究区内的主要互馈协变关系问题,在数值模拟模型的基础上,以前郭县和扶余县部分地区为重点研究区,应用状态转移方程法构建了该区含有协变量的地下水动态规划管理模型,采用微分动态规划方法求解,同步获得了优化的人工开采量、地下水位和协变量。
Water resources crisis including water resources shortage and water environmental problem is one of the major issue in the 21st century. The phenomenon of water resources shortage is serious with the development of economy, increasing of population and changes of climate. As an important component part of water resource, groundwater is an important water supply source of human life and industrial and agricultural production. At present, the shortage of macroscopical programming and scientific management has leaded to groundwater over extraction in the processes of groundwater pumping and utilization in some area, and has leaded to a series of water environmental problem.
Groundwater optimization management is the application of decision science in groundwater exploitation and utilization process. It is a logistic process which is based on the inherent physical law of groundwater system, analyses and describes the groundwater system decision environment, and makes the action state and functional effect optimal though the optimum control of controllable input decision. At present, simulation and optimization of groundwater are still the main techniques of forecasting groundwater behaviors and optimizing the regulating schemes. In order to assure that the optimization process following the inherent principle and theory of groundwater system, optimal model must be on the basis of simulation model. We need to imbed the simulation model into optimization model using some approach, which makes the simulation model be a part of optimization model, implementing the connection of simulation model and optimization model. Embedding method, response matrix method and state transition equation method has been used in the past to solve how to embed and call the simulation model in the optimization model.
During the numerical simulation and optimal management of groundwater system, the hydraulic connection and exchange between groundwater and other waters need to be considered. Among them, such as exchange between surface water and groundwater, evapotranspiration, spring discharge et al, its amount is strictly dependent on the groundwater level at the recharge or discharge point, can not be given artificially, and such exchange is called covariate. The interaction among artificial pumping or recharge, groundwater level, and covariates is called relation of mutual-feed joint-variation.
In groundwater management model with covariates, the artificial pumping or recharge, groundwater level and covariates are all unknown. Moreover, these three variables inherently affect one another, resulting in such problems is difficult to resolve. Before this study is developed, embedding method and response matrix method has been used in building groundwater management model with covariates and has already got the result. However, document about treatment of groundwater dynamic programming management model with covariates and treatment of real groundwater system management problem using theory and methodology of relation of mutual-feed joint-variation has not been published, and this is the problem that the paper wants to solve.
Through the analysis of groundwater relation of mutual-feed joint-variation behavior process and its character, the expression of covariate in simulation model and the coupling technique of simulation model with covariate and optimization model as well as the solving method of this model were researched in the paper. Here, a dynamic optimization groundwater management model containing covariates is solved using dynamic differential programming method is described.
The main achievements of this research are as follows:
(1) Through the analysis of interaction process and its mechanism of covariates and groundwater table, the mathematical expressions which express the relationship of covariates and groundwater table were embedded into groundwater numerical simulation model, and then the groundwater simulation model with covariates was built, which was solved by finite difference method.
(2) The groundwater management model with covariates was built by the embedding method, the algebraic equations which obtained by discreting the groundwater simulation model with covariates was embed into optimization model as a part of constraint condition, together with other constraints and the objective functions, constitute the groundwater nonlinear programming management model with the ability to deal with relation of mutual-feed joint-variation, was solved using the Lingo software.
(3) Simulation model with covariates was coupled with optimization model using the state transition equation method. First, the state transition equation was obtained using groundwater simulation model with covariates. In other words, the water level in the end time was expressed by the initial time water level and pumping amounts, then the state transition equation was embedded into dynamic programming optimal model, together with other constraints and the objective functions, constituted the groundwater dynamic programming management model with the ability to deal with relation of mutual-feed joint-variation.
The groundwater dynamic programming management model with covariates was solved with differential dynamic programming method. Differential dynamic programming method can divide the optimal management process into several periods, the end time status variables of each period was only relevant to the initial time and decision variables, which reduce the computer load greatly. It was applicable to deal with the groundwater management problem with large scale and multi period.
(4) The above theory and method were applied to a hypothetical groundwater system with typicality relation of mutual-feed joint-variation, the groundwater nonlinear programming management model with covariates and groundwater dynamic programming management model with covariates were built respectively. The theory and method which the paper presented was applied, and reasonability analysis of the model was taken.
(5) On the basis of hypothetical instance analysis, the groundwater system of Songyuan area in western Jilin province was taken as the case study. Data was collected and sorted, through the analysis of interaction process and mechanism between covariates and groundwater level, groundwater simulation model with covariates was built, and then Visual MODFLOW was used to solve the problem.
(6) To solve the main relation of mutual-feed joint-variation problem, on the basis of simulation model, Qianguo Xian and Fuyu Xian was taken as important study area, groundwater dynamic programming management model with covariates was built using the state transition equation method, and solved using differential dynamic programming method, then the optimal pumping amounts, the amounts of covariates and groundwater levels were obtained simultaneously.
To sum up, this research expands the theory and method that dealing with relation of mutual-feed joint-variation in groundwater management model, so as to establish theoretical foundation and provide technical means for the solution of various practical problems.
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