An improved framework for superparameterization

This paper discusses a large-scale modeling system with explicit representation of small-scale and mesoscale processes provided by a cloud-resolving model embedded in each column of a large-scale model, the super-parameterization. In the original formulation, referred to as the cloud-resolving convection parameterization (CRCP), thermodynamic variables were coupled using appropriate averaging procedure, but horizontal momenta were coupled only through the relaxation approach. The improved system is based on the general formulation of the coupling between the two models, and the relaxation technique is abandoned. A simple but robust time integration scheme for the system is developed using the nonoscillatory forward-in-time approach applied in both the large-scale and cloud-scale models. The improved formulation is applied to the problem, previously studied by the author, of large-scale organization of equatorial convection on a rotating constant sea surface temperature (SST) aquaplanet in convective-radiative quasi equilibrium. Three simulations are performed using 2D small-scale models as in the original CRCP approach. In the first two simulations, the 2D models have zonal orientation. The first simulation applies the new coupling scheme in the physical setup, which does not include surface drag. Tight coupling between large-scale and small-scale horizontal momenta results in rapid organization of Madden-Julian oscillation (MJO)-like coherent structures and development of strong superrotation. In the second simulation, surface drag is added into 2D small-scale model physics. This results in the development of MJO-like coherent structures with weak superrotation and more realistic strength of the westerly wind burst when compared to the terrestrial MJO. Surface drag is also included in the third simulation, where the coupling is formulated in such a way that orientation of 2D small-scale model domains is along the lower-tropospheric winds and thus it varies in space and time. Results from the third simulation are qualitatively similar to the simulation with surface drag and zonal orientation of small-scale models.