Chance‐Constrained Model for Management of Stream‐Aquifer System

Abstract

A chance‐constrained optimization model for a stream‐aquifer system is developed using an approximate solution for the transient drawdown of the water table of an aquifer by a well operating near a river. The model explicitly considers the random nature of the hydraulic conductivity and specific yield of an unconfined aquifer. This enables the determination of the optimal groundwater pumping pattern and induced recharge from the stream to the aquifer (i.e., stream depletion rate) under specified system performance probability requirements. An application of the model is demonstrated using a hypothetical problem, and the sensitivity of the results is examined by varying probability requirements and the statistical properties of the aquifer parameters, which are: the coefficient of variation of the loghydraulic conductivity; the coefficient of variation of the log‐specific yield; and the correlation between the log‐hydraulic conductivity and log‐specific yield. The results obtained by the model indicate that the optimal pattern of pumping rates obtained by the management policy are highly sensitive to the probability levels and coefficient of variation of the log‐hydraulic conductivity. The induced rate of stream depletion is insensitive to the coefficient of variation of the log‐specific yield and is slightly sensitive to the probability levels. In contrast, the induced stream depletion rate is highly sensitive to the hydraulic conductivity statistics.