The goal of this study is to parallelize the multidimensional positive definite advection transport algorithm (MPDATA) across a computational cluster equipped with GPUs. Our approach permits us to provide an extensive overlapping GPU computations and data transfers, both between computational nodes, as well as between the GPU accelerator and CPU host within a node. For this aim, we decompose a computational domain into two unequal parts which correspond to either data dependent or data independent parts. Then, data transfers can be performed simultaneously with computations corresponding to the second part. Our approach allows for achieving 16.372 Tflop/s using 136 GPUs. To estimate the scalability of the proposed approach, a performance model dedicated to MPDATA simulations is developed. We focus on the analysis of computation and communication execution times, as well as the influence of overlapping data transfers and GPU computations, with regard to the number of nodes.