GFS Scale-Aware Simplified Arakawa-Schubert (sa-SAS) 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) [6] but includes modifications and simplifications from Grell (1993) [74] 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) [152], with further modifications discussed in Han and Pan (2011) [78] , 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) [80] based on the studies by Arakawa and Wu (2013) [7] and Grell and Freitas (2014) [73] for scale awareness and Lim (2011) by [114] 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).

- Version
- CCPP v6.0.0

**Scientific** **Background**

Cumulus clouds in the atmosphere can organize into a variety of sizes, ranging from small fair‐weather cumulus clouds, rain showers and thunderstorms, to larger scale weather systems. In weather and climate models, such organization is traditionally not well-represented as the motions associated with cumulus clouds are generally too small to be resolved by the numerical model. In this scheme we use a stochastic cellular automaton (CA), a mathematical model often used to describe self‐organizing behavior in physical systems to represent the effects of convective organization. The scheme addresses the effect of convective organization in a bulk-plume cumulus convection parameterizations (saSAS), where this type of organization has to be represented in terms of how the resolved flow would “feel” convection if more coherent structures were present on the subgrid.

In addition, for longer range forecasts (seasonal, decadal, climate), the relevance of stochastic cumulus convection in numerical models can also be discussed in terms of noise induced forcing. As an example, on the time scale of organized convectively coupled waves, the small scale individual convective plumes grow and decay so rapidly that they are not predictable on time-scales longer than a few hours, whereas the organized larger scale convectively coupled wave envelope can have a deterministic limit of predictability of about two weeks. Thus, for longer range forecasts, individual convective plumes can be viewed as stochastic noise - they can have an impact on the convectively coupled waves (due to noise forcing), but they are not predictable on their own. By providing the CA with a stochastic initialization, the effect of stochastic cumulus convection is also represented by the scheme.

The scientific motivation for the scheme, the CA rulesets explored, and the impact on convectively coupled equatorial waves can be found in the following references; Bengtsson et al. 2011 [17], Bengtsson et al. 2013 [18], Bengtsson and Kornich (2016) [16], Bengtsson et al 2019 [19], and Bengtsson et al. 2021 [20].

**Technical** **remarks**

The CA source code is located in the stochastic physics submodule in the ufs-weather-model: https://github.com/noaa-psd/stochastic_physics . In the UFS Weather Model, the main call to the CA routines are made from FV3/stochastic_physics_driver.F90.

There are currently two options to evolve the CA (can be done simultaneously); (`ca_global`

) a large scale global pattern which evolves the ruleset according to game of life with cell history, or (`ca_sgs`

) a sub-grid scale pattern which is conditioned on a forcing from the atmospheric model. The two options are controlled by namelist and are evolved in cellular_automata_globa.F90 and cellular_automata_sgs.F90 respectively. Both approaches use the main CA module update_ca.F90 to evolve the CA in time. Since the CA needs to know about its neighborhood it uses the halo information to gather the state in adjacent MPI domains and/or adjacent cube sphere interfaces.

**The** `ca_sgs`

**option** - **Coupled** **to** **saSAS** **cumulus** **convection** **scheme**

The evolution of the CA is an extension to the automaton family known as “Generations,” which in turn is based on the “Game of Life”(Chopard & Droz, 1998 [39]) but adds cell history to the rule set. It is a deterministic CA ruleset, initialized with Gaussian white noise. Thus, when used in an ensemble system, each ensemble member can provide a different seed to the random number generator governing the initial state to then generate a different evolution for each member. By cell history we refer to newborn cells being given a “lifetime,”τ, that is incrementally reduced by 1 each time step where the rules are not met, in contrast to going directly from 1 to 0. The CA is conditioned on a forcing from the host model through the lifetime variable τ such that:

\[ \tau =N\left( \frac{\int_{l=1}^{l=top}E\frac{dp }{g} }{\max\left( \int_{l=1}^{l=top} E\frac{d p}{g}\right)} \right) \]

here, N is an integer that when multiplied by the model time-step represents a physical time scale, such that τ is longer in regions where the forcing is larger, E is the vertically integrated convective rain evaporation from the saSAS cumulus convection scheme stored in Couplingcondition. The denominator is the maximum value of the forcing in the global domain. While the grid-scale forcing in practice could be any two-dimensional field, we choose here to set it as the vertically integrated subgrid rain evaporation amount, serving as an indicator of geographical regions where enhanced subgrid organization may arise through convective cold-pools.

The CA is evolved on a finer grid than the numerical prediction host model (size controlled by namelist), and can be either coarse grained back to the host model grid as a fraction, or (in case of `nca_plumes`

= .true.) give back the maximum number of connected “plumes” (represented by connected CA cells), and their associated size within each numerical prediction host model grid-box. nca_plumes is default true and the maximum cluster size is passed to the saSAS cumulus convection scheme in the Couplingca_deep container.

Depending on the activated namelist options, the CA can feed back to the saSAS convection scheme via the entrainment (`ca_entr`

), closure (`ca_closure`

) or convective initiation (`ca_trigger`

) in the following way:

- Entrainment (
`ca_entr`

): In entraining plume model bulk mass-flux schemes, the upward mass-flux is typically parameterized as a function of environmental air being entrained into the rising plume (as well as parcel properties at cloud base). The fractional entrainment is described as a function of the plume radius. Larger thermals (plumes) have smaller fractional entrainment, which is a consequence of the fact that larger areas have relatively smaller perimeters. In this scheme, the assumption is that subgrid organization will lead to a few larger plumes rather than several smaller plumes, such that the grid-box average fractional entrainment is reduced. Thus, after the CA is updated, we count the number of plumes, and their associated size within each NWP grid-box (`nca_plumes`

= true). If the largest cluster of cells found on the subgrid is larger than a set radius, then the fractional entrainment rate is reduced at that grid-point by 30% (selected based on experimentation) - Triggering (
`ca_trigger`

): In NWP models physical processes are parameterized in columns, and the horizontal interaction between physical processes takes place only through advection and diffusion. As the CA can organize clusters across adjacent NWP model grid-boxes, the method offers a novel approach to enhance the probability of triggering of convection in nearby areas, representing subgrid fluctuations in temperature and humidity, and triggering in premoistened regions if convection is triggered in a cluster. The stochastic nature of the CA may enhance organization in different directions within the grid-box, and across grid-boxes, depending on the initial seed. If the model is run as an ensemble, the convection scheme's stochastic triggering function can help to improve uncertainty estimates associated with subgrid fluctuations of temperature and humidity and randomness in organization. In this work, model grid boxes in which the CA's largest connecting plume exceeds a given threshold will be considered as candidates for convective activation, in addition to saSAS’s current triggering criteria. - Closure (
`ca_closure`

): We assume that convection that organizes into plumes with larger radii tends to cover a larger area fraction of the grid-box and thereby acts to enhance the cloud base mass flux. In this coupling strategy, we again count the number of plumes (represented by connected cellular automaton cells), and their associated size within each NWP grid-box. If the largest cluster of cells found on the subgrid is larger than a set radius, then the cloud base mass-flux is enhanced in that grid-box by 25% (selected based on experimentation). This option is being revisited by reformulating the entire closure using a prognostic evolution of the updraft area fraction, and is in its current formulation not recommended.

- To enhance the surface-based convective available potential energy (CAPE), more strict convection trigger conditions are applied.
- Enhanced downdraft detrainments start from 60 mb above the ground surface rather than from the cloud base.
- Reduced rain evaporation with the removal of wind shear dependency, which helps to reduce cold bias in tropospheric temperature profile especially over Tropics.
- Separation cloud depth of deep and shallow convection is increased to 200 hPa from 150 hPa.
- Updraft entrainment rates for moisture, hydrometeors, and tracers are increased by about 30%.
- A positive definite TVD (Total Variation Diminishing) mass-flux transport scheme for moisture, hydrometeors and tracers and a method for removing negative tracer mixing ratio values have been implemented.