At a recent conference I was talking to a colleague about research ideas, and we kept coming back to the conclusion that we don’t know as much as we should about how clouds are treated in the various models used around the world. There are many different schemes in use today and most of them are closely related to one another, but it’s hard to keep track of the subtle differences between the approaches. Sometimes it’s hard to find any information about the particular configuration of the convective schemes in certain models. I decided to compile a list of the different types of parameterization schemes, and gather some notes on the key papers that developed these schemes.

If you’re looking for a good overview of convective parameterization, I would suggest this review article by Akio Arakawa

Arakawa, A., 2004: The cumulus parameterization problem: Past, present, and future. J. Clim., 17, 2493–2525.

Below are the list of basic concepts that convective parameterizations are built upon, followed by lists of papers that related to the development of specific parameterizations.

Cloud Model Concepts

There are a few fundamental building blocks of any parameterization.

• Steady State Entraining Plume
  • Simpson (1971)
  • Kain and Fritsch (1990)
• Buoyancy Sorting Model
  • Telford (1975)
  • Raymond and Blyth (1986)
  • Taylor and Baker (1991)
• Lattice Model
  • Khoudier et al. (2010)

Closure Assumptions 

If we write the equations for large-scale variations of temperature and humidity, there will be at least four unknown terms that describe the heating and drying from unresolved convection. As discussed in Arakawa and Chen (1987), the “closure assumption” of a convective parameterization is a way to simplify the problem such that these unknown tendencies can be estimated.

• Moist Adjustment
  • Betts (1986)
• Free Tropospheric Quasi-Equiblibrium
  • Arakawa (1969)
  • Arakawa and Schubert (1974)
• Boundary Layer Quasi-Equilibrium
  • Raymond (1997)

---

Old Schemes

• Manabe and Strickler (1964)
• Kuo (1974)

Deep Cumulus Schemes

• Moorthi and Suarez (1992)
  • Relaxed Arakawa-Schubert (RAS) – quasi-equilibrium closure with a relaxation timescale
• Pan and WU (1994)
  • Simplified Arakawa-Schubert (SAS) – includes downdrafts and parcel based trigger
• Zhang and McFarlane (1995)
  • Based on AS74 – CAPE Closure
• Betts (1986) – Both deep and shallow
  • Moist adjustment approach that uses empirical reference profiles from limited field campaign data instead of a moist adiabat
  • Betts and Miller (1986) – First implementation
  • Betts and Miller (1993) – Includes evaporatively drive downdrafts
  • Janjic (1994) – Added cloud efficiency parameter
• Grell (1993)
  • designed for mesoscale simluations
  • includes downdrafts
• Grell and Devenyi (2002)
  • A scheme designed for spreading the uncertainty of assumptions across model simulation ensembles
• Kain and Fritsch (1990)
  • designed for mesoscale simulations
  • uses a buoyancy sorting
• Emanuel (1991)
  • Based on buoyancy-sorting concept
  • Includes downdrafts
  • Closure depends on a specified “parcel precipitation efficiency”
• Pan and Randall (1998)
  • Based on AS74 with a prognostic closure (i.e. no steady-state assumption)
• Chikira (2010)
  • Based on Pan and Randall (), but with a unique “state dependent” entrainment rate
• Donner (1993) ; Donner et al. (2001)
  • Incorporates microphysical
  • considers effects of mesoscale organization
• Gregory and Rowntree (1990)
  • Previously used by the UK Met office model
  • Bulk cloud model (not spectral)
  • closure based on low-level stability
• Tiedtke (1989)
  • Mass flux scheme with 3 plumes for shallow, congestus, and deep, downdrafts included
  • Nordeng (1994) – Modified closure based on CAPE
• Kim and Kang (2012)
  • Based on Tiedkte (1989) – new closure, entrainment, and detrainment
  • Closure uses sub-cloud layer TKE
  • Entrainment depends on parcel vertcial velocity and buoyancy

Shallow Cumulus Schemes

Shallow convection is often treated separately from deep convection. I actually don’t know a whole lot about the fundamental differences between these yet, but I’m working on it.

• Albrecht et al. (1979)
• Hack (1994)
• Bretherton and Park (2008)

Experimental Schemes

• Khoudier and Majda (2006a, 2006b, 2006c)
• Romps and Kuang (2010) ; Romps (2016)
• Mapes and Neale (2011)
  • Based on Bretherton and Park (2008)
  • uses 2 plumes which can interact
  • a prognostic parameter “org” mimics convective memory thought to be associated with organized mesoscale convection through density current mechanisms (cold pools)

Stochastic Schemes

• Shutts (2005)
• Plant and Craig (2008)
• Dorrestijn et al. (2016)

Unified Convective Schemes

• Arakawa and Wu (2011; 2013; 2014)
• Park (2014a; 2014b)
• CLUBB (Storer et al. 2014)

---

These list are not meant to be exhaustive, but if you notice I’m missing any major papers, please let me know in the comments and I’ll add them in. I’ll be trying to come back and update these lists regularly.