SummaryWe are concerned with the mapping on high performance hybrid architectures of a parallel software implementing a two level overlapping domain decomposition, that is, along space and time directions, of the four dimensional variational data assimilation model. The reference architecture belongs to the SCoPE (Sistema Cooperativo Per Elaborazioni scientifiche multidisciplinari) data center, located at University of Naples Federico II. We consider the initial boundary problem of the shallow water equation and analyse both strong and weak scaling. Keeping the efficiency always greater than and about in most cases, we experimentally find that the isoefficiency function grows a little more than linearly with respect to the number of processes. Results, obtained by using the parallel computing toolbox of MATLABR2013a, are in agreement with the algorithm's performance prevision based on the scale up factor, confirming the appropriate mapping of the algorithm on the hybrid architecture.