A mass flux closure function in a GCM based on the Richardson number

A mass flux closure in a general circulation model (GCM) was developed in terms of the mean gradient Richardson number (GRN), which is defined as the ratio between the buoyancy and the shear-driven kinetic energy in the planetary boundary layer. The cloud resolving model (CRM) simulations using the tropical ocean and global atmosphere-coupled ocean-atmosphere response experiment forcing show that cloud-base mass flux is well correlated with the GRN. Using the CRM simulations, a mass flux closure function is formulated as an exponential function of the GRN and it is implemented in the Arakawa-Schubert convective scheme. The GCM simulations with the new mass flux closure are compared to those of the GCM with the conventional mass flux closure based on convective available potential energy. Because of the exponential function, the new closure permits convective precipitation only when the GRN has a sufficiently large value. When the GRN has a relatively small value, the convection is suppressed while the convective instability is released by large-scale precipitation. As a result, the ratio of convective precipitation to total precipitation is reduced and there is an increase in the frequency of heavy precipitation, more similar to the observations. The new closure also improves the diurnal cycle of precipitation due to a time delay of the large GRN with respect to convective instability.