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Methods to efficiently monitor the extent of dispersion is essential to protect sensitive areas. By combining underwater robotic sampling with ocean models, we can choose informative sampling sites and adaptively change the robot\u2019s path based on in situ measurements to optimally map the tailings distribution near a seafill. This paper creates a stochastic spatio-temporal proxy model of dispersal dynamics using training data from complex numerical models. The proxy model consists of a spatio-temporal Gaussian process model based on an advection\u2013diffusion stochastic partial differential equation. Informative sampling sites are chosen based on predictions from the proxy model using an objective function favoring areas with high uncertainty and high expected tailings concentrations. 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