The so called Lorenz-84 model has been used in climatological studies, for example by coupling it with a low-dimensional model for ocean dynamics. The behaviour of this model has been studied extensively since its introduction by Lorenz in 1984. In this paper we study the asymptotic
behaviour of a non-autonomous Lorenz-84 version with several types of nonautonomous
features. We prove the existence of pullback and uniform attractors for the process associated to this model. In particular we consider that the non-autonomous forcing terms are more general than almost periodic. Finally, we estimate the Hausdor dimension of the pullback attractor. We illustrate
some examples of pullback attractors by numerical simulations
