The concept of IDEMIX was recently developed to simulate and parameterize the effect of gravity waves on the large-scale circulation. It is applied here to Rossby waves. Since gravity wave drag is formally identical to baroclinic instability it appears possible to parameterize the effect of baroclinic and barotropic instability on the large-scale circulation following the IDEMIX concept which is based here on the Rossby wave energy equation in physical and phase space. The dimensions of that equation are reduced by assuming a fixed shape of the energy spectrum with respect to horizontal wave number. The result is a set of coupled conservation equations for Rossby wave energy compartments resolved in horizontal direction and wave vector angle. Using simple parameterisations for wave-wave interaction, the performance of the closure is tested in an idealized model of baroclinic and barotropic instability where the Rossby waves are assumed to contain the subgrid-scale energy.