Subgridscale updraft acceleration

The TKE diagnosis in the previous subsection indicated that the diurnal evolution of turbulence intensity is slower in the 4-km simulation than in the finer-grid cases. In order to enhance the boundary-layer development in the 4-km case, therefore, the subgrid-scale turbulent effects need to be intensified, which will contribute to the acceleration of convective updrafts and downdrafts. Since turbulence intensity is increased especially in the updraft regions, updraft enhancement is considered to be critical in reproducing reasonable development of the PBL.

In order to develop a representation of convection effects in cloud-resolving simulations, we apply the idea of Deng et al.23 who parameterize shallow convection in mesoscale models. They hypothesized that cloud-forming rising parcels were positively correlated with vertical velocity perturbations and proposed that an eddy vertical velocity should be added to resolved vertical motion that is related to activating cloud formation in a cloud microphysics parameterization; note that this enhanced updraft speed is not used anywhere except in this cloud activation computation. Such an adjustment to updraft velocity was also considered by Lohmann et al.24 in activating cloud droplet nucleation. A point stressed here is that incorporating the turbulent effects into updraft speeds is critical in obtaining better results in simulations with Ax of a couple of kilometers.

Motivated by these studies, we assume that updraft is enhanced if there is a significant amount of SGS turbulent intensity. This assumption for updraft enhancement is based on the fact that updrafts are generally stronger than downdrafts in a single cell of shallow and deep convective clouds in which precipitation is not strong enough to produce cold air and intense downdraft. The enhancement of updrafts is conducted by adding a forcing term to the vertical momentum equation at updraft grid points. This term is referred to as subgrid-scale updraft acceleration (SUA), and is given by where w is vertical velocity, e is TKE, and t is the timescale for the updraft acceleration. By trial and error we set t = 10min. Although this forcing term is solely artificial, it is at least useful to examine the effects of turbulent intensity and hence to give an idea for the parameterization of convection effects in dust transport simulations.

Figure 6 shows the time-height section of TKE in the case of Ax = 4 km with SUA. The result significantly improves the boundary-layer development looks quite similar to that seen in the finer-grid cases (compare with Figs. 2(b) and 5).

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