Cumulus convection schemes

General info

Interacts with:
- Surface Schemes though Convective Rain
- Microphysics Schemes through Cloud Detrainment
- Radiation Schemes through Convective Cloud Fraction
Use for coarse grid spacing $Λ >> I$ with $I$ as the grid spacing where convective energy is maximal ( $\sim 3 k m$ ).
No net mass flux. Updraft is compensated by subsidence aorund the clouds $M_{s} = - M_{u} : w_{s} = - σ w_{u}$ | Mass flux schemes | Adjustment schemes | |---------------------|-----------------------| |All others | Betts-Miller-Janjic | | Determines fluxes | Relaxes towards post-convective, mixed sounding |

Driving buoyancy determines cloud top and therefore detrainment level
Moisture transport to troposphere → condensation → convective rainfall
Strength depends on:
- Initial properties at updraft base
- Entrainment dilution (horizontal disturbance)
- Condensation to cloud particles and rain

cu_physics	Scheme	Reference	Added
1	Kain-Fritsch (KF)	Kain (2004, JAM)	2000
2	Betts-Miller-Janjic (BMJ)	Janjic (1994, MWR; 2000, JAS)	2002
3	Grell-Freitas (GF)	Grell and Freitas (2014, ACP)	2013
4	Old Simplied Arakawa-Schubert (SAS)	Pan and Wu (1995), NMC Office Note 409	2005/2011
5	Grell-3 (G3)	Grell (1993, MWR), Grell and Devenyi (2002, GRL)	2008
6	Tiedtke	Tiedtke (1989, MWR), Zhang et al. (2011, MWR)	2011
7	Zhang-McFarlane (ZM)	Zhang and McFarlane (1995, AO)	2011
10	KF-CuP	Berg et al. (2013, MWR)	2016
11	Multi-scale KF (MSKF)	Zheng et al. (2016, MWR)	2015
14	KIAPS SAS (KSAS)	Han and Pan (2011, Wea. Forecasting), Kwon and Hong (2017, WMR)	2018
16	New Tiedtke	Zhang and Wang (2017, JCLI)	2015
93	Grell-Devenyi (GD)	Grell and Devenyi (2002, GRL)	2002
99	Old Kain-Fritsch	Kain and Fritsch (1990, JAS; 1993, Meteo. Monogr.)	2000

CAPE-removal time scale (KF, ZM, Tiedtke, BMJ)
Quasi-equilibrium with large-scale destabilization (SAS, NSAS)
- Quasi-equilibrium maintains balance with large-scale destabilization.
Scale-awareness - Reduce deep convection mass flux based on grid size (GF, MSKF)

abbr,	Ensemble methods	Shallow Convection	Momentum transport
KF	✅	✅ - enhanced mixing	:x:
BMJ	❌	✅	:x:
GD	✅	✅ - mass-flux	:x:
SAS	:x:	✅ - enhanced mixing	✅
G3	✅	✅ - mass-flux	:x:
T	:x:	✅ - mass-flux	✅
ZM	:x:	:x:	✅
KFCP	:x:	:x:	:x:
MSKF	:x:	:x:	:x:
KSAS	:x:	✅ - enhanced mixing	✅
NT	:x:	:x:	✅
GD	✅	:x:	:x:
OKF	:x:	:x:	:x:

- Ensemble of up to 144 trigger parameters. Take mean to feed to model
** Non-precipitating shallow mixing dries PBL and moistens and cools above. May be useful at grid sizes that do not resolve shallow cumulus clouds ( $> 1 k m$ ) GAR Or may use PBL scheme with mass-flux method or standalone shallow schemes

Sources: