  We study the long time behavior of the solutions to the 2D stochastic
quasi-geostrophic equation on $\mathbb{T}^2$ driven by additive noise and real
linear multiplicative noise in the subcritical case (i.e. $\alpha>1/2$) by
proving the existence of a random attractor. The key point for the proof is the
exponential decay of the $L^p$-norm and a boot-strapping argument. The upper
semicontinuity of random attractors is also established. Moreover, if the
viscosity constant is large enough, the system has a trivial random attractor.
