It is well known that obtaining optimal solutions for groundwater management models with covariates is a challenging task, especially for dynamic planning and management. Here, a theory and method of dealing with mutual-feed joint variation in groundwater management models is described. Specifically, an equation expressing the inherent connection between covariates and groundwater level was developed. This equation was integrated into a mathematical simulation model of groundwater, after which a groundwater dynamic optimization management model with covariates was constructed using the state transition equation method and solved with differential dynamic programming algorithms. Finally, the above theory and method were applied to a hypothetical groundwater system. For the same groundwater system, a groundwater management model with covariates was developed and the results of the two optimization methods were found to be nearly identical, which validated the theory and methods put forth here.

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