GFS SAS-based Mass-Flux Deep Convection Scheme

The scale-aware mass-flux (SAMF) deep convection scheme is an updated version of the previous Simplified Arakawa-Schubert (SAS) scheme with scale and aerosol awareness and parameterizes the effect of deep convection on the environment (represented by the model state variables) in the following way. First, a simple cloud model is used to determine the change in model state variables due to one entraining/detraining cloud type, per unit cloud-base mass flux. Next, the total change in state variables is retrieved by determining the actual cloud base mass flux using the quasi-equilibrium assumption (for grid sizes larger than a threshold value [currently set to 8 km]) or a mean updraft velocity (for grid sizes smaller than the threshold value). With a scale-aware parameterization, the cloud mass flux decreases with increasing grid resolution. A simple aerosol-aware parameterization is employed, where rain conversion in the convective updraft is modified by aerosol number concentration. The name SAS is replaced with SAMF as for the smaller grid sizes, the parameterization does not use Arakawa-Schubert's quasi-equilibrium assumption any longer where the cloud work function (interpreted as entrainment-moderated convective available potential energy [CAPE]) by the large scale dynamics is in balance with the consumption of the cloud work function by the convection.

The SAS scheme uses the working concepts put forth in Arakawa and Schubert (1974) [7] but includes modifications and simplifications from Grell (1993) [71] such as saturated downdrafts and only one cloud type (the deepest possible), rather than a spectrum based on cloud top heights or assumed entrainment rates. The scheme was implemented for the GFS in 1995 by Pan and Wu (1995) [139], with further modifications discussed in Han and Pan (2011) [75] , including the calculation of cloud top, a greater CFL-criterion-based maximum cloud base mass flux, updated cloud model entrainment and detrainment, improved convective transport of horizontal momentum, a more general triggering function, and the inclusion of convective overshooting.

The SAMF scheme updates the SAS scheme with scale- and aerosol-aware parameterizations from Han et al. (2017) [77] based on the studies by Arakawa and Wu (2013) [9] and Grell and Freitas (2014) [70] for scale awareness and Lim (2011) by [105] for aerosol awareness. The ratio of advective time to convective turnover time is also taken into account for the scale-aware parameterization. Along with the scale- and aerosol-aware parameterizations, more changes are made to the SAMF scheme. The cloud base mass-flux computation is modified to use convective turnover time as the convective adjustment time scale. The rain conversion rate is modified to decrease with decreasing air temperature above the freezing level. Convective inhibition in the sub-cloud layer is used as an additional trigger condition. Convective cloudiness is enhanced by considering suspended cloud condensate in the updraft. The lateral entrainment is also enhanced to more strongly suppress convection in a drier environment.

In further update for FY19 GFS implementation, interaction with turbulent kinetic energy (TKE), which is a prognostic variable used in a scale-aware TKE-based moist EDMF vertical turbulent mixing scheme, is included. Entrainment rates in updrafts and downdrafts are proportional to sub-cloud mean TKE. TKE is transported by cumulus convection. TKE contribution from cumulus convection is deduced from cumulus mass flux. On the other hand, tracers such as ozone and aerosol are also transported by cumulus convection.

Occasional model crashes have been occurred when stochastic physics is on, due to too much convective cooling and heating tendencies near the cumulus top which are amplified by stochastic physics. To reduce too much convective cooling at the cloud top, the convection schemes have been modified for the rain conversion rate, entrainment and detrainment rates, overshooting layers, and maximum allowable cloudbase mass flux (as of June 2018).