Study On The Theory And Method Of The Relation Of Mutual-Feed Joint-Variation In Groundwater Management Model

Groundwater management model plays an important role in the development and management of water resources, which is coupled by the numerical simulation model and the optimization model of groundwater system. At present, numerical simulation and optimal management of groundwater are still the main techniques of forecasting groundwater behaviors and optimizing the regulating schemes. As a copy of the prototype, the evaluation criterion of the merits of model is the approximation degree of the actual problem. As groundwater is affected by many factors such as geology, climate and human activities, the cycle process and interaction relationship are extremely complex, and management model is not fully express certain aspects of the reality, resulting that the distortion degree of model is relatively large, and the application is ineffective. The relation of mutual-feed joint-variation is one of the problems to be resolved in groundwater management model.During the numerical simulation and optimal management of groundwater system, the interactions between groundwater system and surrounding environment need to be considered, especially the hydraulic connection and exchange between groundwater and other waters. Among them, one kind of exchange, its amount is strictly dependent on the groundwater level at the recharge or discharge point, can not be given artificially, and has natural attribute, such as exchange between suface water and groundwater, spring discharge, groundwater discharge to drain, evapotranspiration, such exchange is called covariate. The interaction among artificial pumping or recharge, groundwater level, and covariates is called relation of mutual-feed joint-variation. The characteristics of covariates are as follows: their amounts are dependent on the state variable of groundwater system, i.e. groundwater level; covariates and groundwater level interact with each other, that is, the level of groundwater determines the amount of covariates, in turn, covariates influence the level of groundwater through consuming groundwater storage within the groundwater system; and the amounts of some covariates, such as spring discharge, groundwater discharge to drain and evapotranspiration, become zero when groundwater level declines below a specified reference elevation. This particularity makes the treatment method in simulation model and management model of groundwater system different from artificial pumping or recharge.In groundwater simulation model with covariates, the above problem has been solved by iteration and Cauchy boundary condition, and some softwares such as MODFLOW also have the ability to solve this problem. However, in groundwater management model with covariates, in the prediction stage, the artificial pumping or recharge, groundwater level, and covariates are all unknown. Moreover, these three variables inherently affect one another. Existing management models lack of the description and treatment of this particular inherent relationship, resulting in such problems have not yet been resolved in groundwater management model. From domestic and foreign literatures, the theory and method of solving this problem successfully have yet not be seen, some avoided, and some only approximation, and neglected the dependence of covariates on the water table. The establishment of the theory and methods dealing with the relation of mutual-feed joint-variation in groundwater management model, not only can enhance the approximation degree of management model, and improve the capacity of groundwater model in coping with the complex actual problems, but also can provide a foundation for the research work of coupling groundwater system with surroundings environment. With the increasingly expanding of the development scale of water resources, and the increasingly outstanding of the problems of water resources shortage and water pollution, the optiminzaions of the development schemes of groundwater resources and remediation measures are becoming important, and the interactions among the adjacent systems will be protruding increasingly, how to describe in theory and solve these problems, and enrich and improve the theory and method of optimal management of groundwater, so as to establish theoretical foundation and provide technical means for the solution of various practical problems, and provide scientific and technological support to the sustainable use of groundwater resources. Therefore, this study has important theoretical significance and broad application prospect.Some achievements and conclusions acquired in the research of this paper are as follows:(1) An equation expressing in quantitative form the inherent connection between covariates and groundwater level is developed through analyzing the process and mechanisms of the interaction of covariates and groundwater level, and was integrated to the mathematical simulation model of groundwater system, which was solved by finite element method.(2) In groundwater management model, covariates were considered as decision variables, and the equation which describes the inherent quantitative relationships among artificial pumping or recharge, groundwater level, and the covariates has been developed using response matrix method, and was then added to the optimization model as an additional equality constraint, in order to guarantee that the relation of mutual-feed joint-variation would be maintained during the optimization calculations. These additional constraint equations, together with other constraints and the objective functions, constitute the management model of the groundwater system with covariates.(3) The programs for the simulation and management of groundwater system with covariates were developed with Fortran 90 language, and the optimal pumping amounts, groundwater levels and the amounts of covariates were obtained simultaneously.(4) The above theory and method were applied to a hypothetical groundwater system with typicality and representativeness. The groundwater management model with covariates of the hypothetical groundwater system was constituted, and was solved by simplex method, the optimal pumpings were compared with that of groundwater management model built by embedding method, and the results show that, the optimal solutions, i.e. optimal pumpings obtained by groundwater management model with covariates are almost the same with that of embedding method, thus, validated the correctness of the groundwater management model with covariations.(5) In order to solve complex and nonlinear groundwater management model, simulated annealing genetic algorithm was introduced to solve the groundwater management model with covariates, in which adaptive crossover and variation probability, elitist strategy and niche technology were used, and the treating methods of constraints were discussed. The performance of SAGA was validated through the test function of Schaffer, the results show that this algorithm not only has powerful overall optimizing capacity and local searhing ability, but also has fast convergence rate and high optimization precision.