New efficient sparse space-time algorithms for superparameterization on mesoscales

Superparameterization (SP) is a large-scale modeling system with explicit representation of small-scale and mesoscale processes provided by a cloud-resolving model (CRM) embedded in each column of a large-scale model. New efficient sparse space-time algorithms based on the original idea of SP are presented. The large-scale dynamics are unchanged, but the small-scale model is solved in a reduced spatially periodic domain to save the computation cost following a similar idea applied by one of the authors for aquaplanet simulations. In addition, the time interval of integration of the small-scale model is reduced systematically for the same purpose, which results in a different coupling mechanism between the small- and large-scale models. The new algorithms have been applied to a stringent two-dimensional test suite involving moist convection interacting with shear with regimes ranging from strong free and forced squall lines to dying scattered convection as the shear strength varies. The numerical results are compared with the CRM and original SP. It is shown here that for all of the regimes of propagation and dying scattered convection, the large-scale variables such as horizontal velocity and specific humidity are captured in a statistically accurate way (pattern correlations above 0.75) based on space-time reduction of the small-scale models by a factor of ¹/3; thus, the new efficient algorithms for SP result in a gain of roughly a factor of 10 in efficiency while retaining a statistical accuracy on the large-scale variables. Even the models with ¹/6 reduction in space-time with a gain of 36 in efficiency are able to distinguish between propagating squall lines and dying scattered convection with a pattern correlation above 0.6 for horizontal velocity and specific humidity. These encouraging results suggest the possibility of using these efficient new algorithms for limited-area mesoscale ensemble forecasting.