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This research analysed the action and characteristics of the relationship between mutual-feed joint-variations of the groundwater. On this basis, a theory and method for constructing a dynamic programming management model for groundwater with covariates was proposed which used the state transition equation method. The model was solved using the differential dynamic programming (DDP) method. Thereafter, the groundwater system of Songyuan area in western Jilin Province, was treated as a interest area to study the major problem of the relationships governing mutual-feed joint-variation. Based on the numerical simulation model, the research paid more attention to Qianguo County and Fuyu County and established a dynamic programming management model of the groundwater with covariates for these areas. Then the optimised amount of pumping, the groundwater level, and the covariates were solved simultaneously. To sum up, this research was enriched the theory and method for dealing with mutual-feed joint-variations in the groundwater management model. Therefore, it established a theoretical foundation and provided technical support for the solution of various practical problems.

The dynamic programming management model of groundwater with covariates: a case study for the Songyuan area, Jilin Province, China