The aim of this article is to study the asymptotical behavior, in terms of upper semi-continuous property of attractor, for small multiplicative noise of the three-dimensional planetary geostrophic equations of large-scale ocean circulation. In this article, we establish the existence of a random attractor for the three-dimensional planetary geostrophic equations of large-scale ocean circulation
... [Show full abstract] with small multiplicative noise by verifying the pullback flattening property and prove that the random attractor of the three-dimensional planetary geostrophic equations of large-scale ocean circulation with small multiplicative noise converges to the global attractor of the unperturbed three-dimensional planetary geostrophic equations of large-scale ocean circulation when the parameter of the perturbation tends to zero.