Convection Parameterization

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I. Description of Physical Processes

II. Comparison of Model Implementations

III. Critical Evaluation


 One of the more difficult aspects of forecasting is convection.  This is especially true with computer model forecasts.  Efforts have been made to model convective outbreaks.  However, the great number of variables required to simulate convection, and the fact that it often occurs on scales too small to be tracked well by models, mean simulation of this process is virtually impossible.  Actions and motions at this scale have proved to be better handled through parameterization.  Parameterization is a way to, out of mathematical convenience and necessity, represent the physical effects of a process (in this case convection) in terms of simplified parameters, rather than actually resolving the process itself.  Thus, if the parameters satisfy certain conditions, convection is forecasted by the model.

The National Weather Service (NWS) forecast models concern themselves with convection, primarily because of the significant weather it can produce.  Models should be able to show the forecaster the following pieces of information through parameterization of convection:

    1. a quantitative measure of instability

    2. a triggering mechanism for convection

    3. the net effect of latent heating on the local atmosphere

    4. the amount of water vapor available in a convective situation

Steps are being made to improve the parameterization of convection in all models.  The result will hopefully be a reliable forecasting tool for thunderstorm genesis.

II. Comparison of Model Implementations

The various models each follow somewhat different schemes in dealing with convection.  Here's a look at how the models parameterize convection:

A. Shallow convection (Non-precipitating):

1. Medium Range Forecast Model (MRF):
This spectral model is run daily using observed data at 00Z and extends out to 16 days.  These plots are updated once a day at 10 a.m. (EST) based on the 00Z model run. (0.7 x 0.7 degree resolution)

- Shallow convection occurs where convective instability exsists but no convection occurs.

- The convection calculations are performed after each leap-frog time step and can be considered as adjustments. Deep convection is done first, then shallow convection, as is the case with the ETA.

- Effects of non-precipitating cumulus clouds, carried out in a manner similar to Tiedtke, utilize a subroutine that carries out an enhanced vertical diffusion of specific heat and humidity.

- Only model columns that contain conditionally unstable layers near the surface are eligible for this process.

- No convergence is explicitly required, more vigorous vertical mixing of water vapor occurs (in synoptically inactive regions, the water vapor would otherwise tend to accumulate near the surface).

- The shallow convective process acts to simulate the increased turbulence and attendant vertical eddy transport. These are known to be properties of shallow cumulus clouds and their local environment. This process is also treated in the same way as the model's basic vertical diffusion.

- Shallow convection calculation follows these five guidelines:

    1. Cloud base is determined from values of lifting condensation level that have been received from the deep convection subroutine, which has been previously called. A value for cloud top (the highest unstable layer) is also passed, but stronger restrictions (below) apply.
    2. In columns for which deep convection has been performed, shallow convection is not allowed.
    3. Shallow convective "clouds" may occupy, at most, sigma layers two through six, producing relatively strong diffusion within the cloud and weak diffusion above and below it, as governed by an
imposed K profile.
    4. Values of K are tapered in the vertical (to prevent development of unrealistic kinks in the T and q profiles) as follows: at the base of the cloud layer, K = 1.5m2s-1; at the top, K = 1; for the next-to-top layer, K = 3; for intermediate layers, if any: K=5 .
    5. There must be at least one potentially unstable layer within the conditionally unstable column.

Note: K = diffusion coefficient (m2s-1)

2. ETA:
This model uses a vertical coordinate system (eta coordinates) with series of steps of varying heights, allowing improved accuracy when dealing with topographic effects.  This model runs out to 60 hours. This model uses the Betts-Miller-Janjic (BMJ) scheme.  There is also an experimental run using the Kain-Fritsch (KF) scheme.  Output from the experimental runs can be found at

- Determines the mixing line between two saturation points, one at the cloud base, and one at the cloud top.  The model uses the mixing line to create modified soundings reflecting the moist mixing process.

- Determines the most unstable parcel and establishes the LCL.

- Calculates cloud depth.

- If the cloud depth resulting from lifting the most unstable parcel is >10 hPa deep, < 200 hPa deep, and covers at least 2 model layers then the shallow convection ETA is triggered.

- Modifies the temperature profile so there is no latent heat release.  (See  Figure 1 )

- Modifies moisture profile so that no precipitation will reach the ground.

- Results in condensation at cloud bottom and moisture moving upward to evaporate at cloud top.   So there will be net drying at the cloud base, and net moistening will occur at the top.

- Whole modification process takes about 40 minutes of real time.

B. Deep convection:

1. Medium Range Forecast (MRF):

This spectral model is run daily using observed data at 00Z and extends out to 16 days.  These plots are updated once a day at 10 a.m. (EST) based on the 00Z model run.

- Simplified Arakawa-Schubert (SAS) Scheme that models deep convection.  This is based on rate of destabilization or quasi-equilibrium.

- In order to be active it requires moisture convergence and deep conditional instability.

- Moisture convergence between cloud base and cloud top is separated into a rain producing portion and a humidity increasing portion. The convective heating and moistening of the environment is distributed with height between cloud base and cloud top.

- No ceiling is imposed on the deep convection. The medium range model is allowed to carry water vapor only in the lowest 12 sigma layers, which begin at the surface and gradually thicken into the mid troposphere.

- No convective moistening is allowed above layer 12 (only restriction).

- Either layer 2 (sigma = .981) or layer 3 (sigma = .960), or a combination of the two must produce the air entering the convective column.

- Layer one is not considered because it has a thickness of only 10 mb and is subject to surface processes that produce rapid variations in temperature and humidity.

- Now considers evaporation

    - ice phase
    - vertical fluxes of heat, momentum and moisture
    - the effects of water loading
    - cloud water, although the convective portion of a column is referred to as the "cloud"

2. Aviation Model (AVN):
This model currently gives forecast information out to 84 hours at 6z and 18z and 126 hours at 00z and 12z. Starting in March 2002 these lengths will increase to 384 hours (global model). Currently it uses T170L42 resolution four times a day and plots are 6 paneled, but it will change in May 2002 to T254L64 resolution.   It is the same numerical model as MRF, the only difference is in the data cutoff times.

- Uses 42 layers
- 0.7 x 0.7 degree resolution
- Uses the Simplified Arakawa-Schubert (SAS) convective parameterization scheme
- Convection initiation within a column considers time rate of change in stability as primary convective trigger
 -presence of positive buoyancy, and Cap strength
- Refer to MRF description for details.

3. Nested Grid Model (NGM):
There have been no improvements implemented since 1990 and none are planned.  The NGM differs from other models because of its use of horizontal nesting.  The model makes its own forecasts of conditions at the boundaries of the inner grids.  The NGM does not have cumulus parameterization.

- Moist convection also from modified Kuo scheme*

- Convection occurs if all of following conditions are met:

    1.  Sufficient moisture convergence in bottom six model layers
    2.  Parcel originating in any of the bottom four layers would become buoyant if lifted
    3.  Total moisture convergence into column below cloud top is positive

- Moisture is distributed in the vertical through latent heating and moistening.  Precipitation and latent heating are produced from 80% of the available moisture.  The remaining 20% is used for moistening.

- Precipitation is allowed to fall and evaporate.  If precipitation remains after evaporation has raised the relative humidity in a layer to about 48%, it is allowed to fall into the next layer.  That process continues until all of the precipitation evaporates or it reaches the ground.

- One type of vertical mixing is dry convective adjustment.  When a superadiabatic layer develops, the temperature profile is adjusted to be adiabatic so as to conserve the enthalpy of the column, a process also employed in the ETA.

* The Kuo scheme stabilizes the atmosphere at higher levels in the vertical than would be done by a grid-scale process.  This model forecasts moderate precipitation when actually it is more likely to be light or heavy.

4. ETA:
This model uses a vertical coordinate system (eta coordinates) with series of steps of varying heights, allowing improved accuracy when dealing with topographic effects.  This model runs out to 60. This model uses the Betts-Miller-Janjic (BMJ) scheme.  There is also an experimental run using the Kain-Fritsch (KF) scheme.  Output from the experimental runs can be found at

- The most unstable parcel from the LCL to the EL triggers the convective parameter

- Calculates cloud depth, deep parameterization continues if greater than 200 mb

- The BMJ deep convective scheme nudges the environment toward a well-defined reference profile (See  Figure 2 )

- Temperature profile is modified to be near that of the moist adiabat to allow for slight instability ( See  Figure 3 )

- Moisture profile defines the distance a parcel needs to be lifted to reach saturation

- Measures cloud efficiency which indicates enthalpy (heat potential) transport upward and produces as little precipitation as possible.

- Enthalpy is conserved because latent heat release will balance the net change in moisture due to condensation.

- To get precipitation, the modified moisture profile must become drier and the modified temperature profile must become warmer

- Precipitation is directly calculated from the amount of latent heat produced by the modification of the soundings

- Adjustment is made so that enthalpy is unchanged but allows for latent heat of condensation to be released and precipitation to fall.

- Entire modification process takes 40 minutes of real time

5. Rapid Update Cycle (RUC):
This model is designed for short-term forecasts and is updated frequently -- every hour (it is considered the "nowcast" of weather models).  RUC operates on sigma coordinates near the ground and on a theta coordinate system aloft. This model is sometimes more accurate than others because it uses a wider range of available observations. The RUC-2 was active as of 1998 with a 40 km resolution.  About to come out (early 2001) is the new RUC with 20 km resolution.  Since the Grell scheme operates well with resolutions of 10 to 30 km, the new RUC will forecast heavy rainfall events even better.

- Uses isentropic values

- Does have some convective parameters

- Uses Grell convective parameterization scheme- The Grell Scheme is based on the rate of destabilization or quasi equilibrium. This is a single cloud scheme with updraft downdraft fluxes and compensating motion that determines the heating and moistening profiles. This scheme is useful for smaller grid scales (e.g., 10-30km), and it tends to allow a balance between the resolved scale rainfall and the convective rainfall.  ( )

- Includes downdraft detrainment, cloud top levels, minimum cloud depth, and capping criteria

- Inclusion of downdrafts results in smaller scale details in warm season precipitation patterns

- Evaporation of precipitation occurs with convective precipitation (not stable precipitation)

- Includes analysis and forecast grids with perceptible water, CAPE (multi-layered), and CIN

-         Contains forecast sub grids for convective precipitation during last forecast period


C. WRF (Deep or Shallow Convection) The WRF model is an experimental model so it can be used in both deep and shallow convection. The NCEP and NSSL versions are included for comparison/contrast. The ability exists for both Deep and Shallow Convection to be included on either one of these models depending on the convective parameterization used in the model. The NCEP version is available on the web ( for various initializations and fields. NSSL also has its version available on the web (

1. NCEP version

Betts-Miller-Janjic convective parameterization

NCEP 3-class simple ice microphysics

MRF PBL scheme

5-layer slab ground temperature

RRTM longwave radiation

MM5 shortwave radiation

Thermal diffusion surface physics

22 km grid length, 28 vertical levels, Time step 120 s

            BMJ Convective Parametrization

               It adjusts the sounding toward a pre-determined, post-convective reference profile derived from climatology.

Trigger: Three conditions are required to trigger convection:

         At least some CAPE

         Convective cloud depth exceeding a threshold value

         Moist soundings to activate .

                 General WRF NCEP facts

                      The dynamics uses a terrain-following height-based, conservative flux-form of the fully compressible nonhydrostatic equations.

                      The numerics is 3rd order Runge-Kutta in time, 5th order horizontally and 3rd order vertically in space.

                      The model is initialized directly from the Eta analysis via the WRF Standard Initialization package.

                      The display uses NetCDF output with NCL graphics.


2. NSSL version

Modified KF convective parameterization

MRF PBL scheme

NCEP 3 class simple ice microphysics

RRTM longwave radiation

Dudhia shortwave radiation

Thermal diffusion surface physics

34 km grid length, 31 vertical levels

Time step 180s

Model domain and resolution are very similar to those of the Eta model.


KF Convective Parametrization

This is a complex scheme designed to rearrange mass in a column so that CAPE is consumed.

Trigger: The following conditions must be met for the scheme to trigger convection:

The sounding has CAPE for source parcels from a low-level layer 50 to 100 hPa thick

The cap is small enough for a parcel to penetrate given a boost of a few m/s (a function of large-scale vertical motion at LCL)

The convective cloud depth exceeds a threshold


III. Critical Evaluation

    Just as all people have unique skills and abilities, the convective parameterization schemes of the various models will do different things well and different things poorly.  Often, the skill of the model depends on the exact location and time for which it is forecasting. For example, the AVN under predicts mesoscale convective events across the Great Plains during the warmest part of the year.  The ETA parameterizes convection differently over water than land, thus it often overestimates precipitation along the Gulf and Atlantic coasts.  The ETA is also plagued by a greater amount of convective feedback than the NGM.  The MRF now accounts for factors such as evaporation of falling rain like the RUC and NGM.  The NGM and the MRF employ a variant of the Grell scheme which stabilizes the atmosphere at higher levels in the vertical than would be done by a grid-scale process causing precipitation events to be forecast as moderate when they actually are light or heavy.  Of course, no model can accurately forecast precipitation (or anything) everywhere all the time,  but the problems with the various models are fairly well documented.  Using this information and relying on more than one model can allow forecasters to predict convective precipitation events with a good degree of accuracy.  Still, any parameterization scheme is going to be flawed because it is limited in its ability to describe what truly occurs in the complex and chaotic atmosphere.


Anthes, T.A., 1977. A cumulus parameterization scheme utilizing a one dimensional cloud model.  Monthly Weather Review, 105, 270-286.

AVN Version of the Global Spectral Model web site Feb 2002

Baldwin, Mike, et. al., 1998.  Convective Parameterization in Models: Background Information.

Benjamin, Stanley G., Kevin J. Brundage, and Lauren L. Morone,  NOAA/ERL Forecast Systems    Laboratory, NWS/NOAA,  1994:  Implementation of the Rapid Update Cycle.

Black, Thomas L.,  1994:  The New NMC Mesoscale Eta Model: Description and Forecast ExamplesWeather and Forecasting, 9, 265-278.

Developing Meteorological Fields. Environmental Protection Agency. 1999

NCAR WRF web site. Weather Research and Forecasting Model. 2002 .

Grell, G. 1993.  Prognostic evaluation of assumptions used by cumulus parameterizationsMonthly Weather Review, 121, 764-787.

Hoke, James H., Norman A. Phillips, Geoffrey J. DiMego, James J. Tucillo, Joseph G. Sela,  1989:  The Regional Analysis and Forecast System of the National Meteorological CenterWeather and Forecasting, 4, 323-334.

Information about the MRF.

Kuo, H.L. 1965. On formulation and intensification of tropical cyclones through latent heat release by cumulus convectionJournal of Atmospheric Science, 22, 40-63.

NCAR WRF website. Weather Research and Forecasting Model. 2002

NOAA/NMC,  1995:  Description of Models.

NSSL WRF website. RealTime WRF model runs from NSSL. May 23. 2001

Operational Models Matrix web site. 2002

Rogers, Eric, et. al., 2000.  Changes to the NCEP Meso Eta Analysis and Forecast System: Assimilaltion of satellite radiances and increase in resolution

Staudenmaier Jr., Mike.  WR-SSD/NWSFO SLC.  The Convective Parameterization Scheme in the MESOETA Model.

Tiedtke, M.,  ECMWF, 1983.  The sensitivity of the time-mean large-scale flow to cumulus convection in the ECMWF model. Workshop on Convection in Large-Scale Numerical Models. 28 Nov - 1 Dec 1983, pp. 297-316.

UCAR website. How Models Produce Precipitation & Clouds: Convective Parameterization. .

WRF model information. Weather research and forecasting model.

Jeff Jamison, Julie Jasien, and Greg Ostermeier
April 30, 1998

Julie Slater, Dan Stillman
February 1, 1999

Brad Armstrong, Bruce Sherbon, and Christine Meleo
February 15, 2000

Dave Long, Jennifer Derrick, Nathan Cheneaux
February 14, 2001

Robert Osborn, Stephen Latimer, Travis Wyatt, and Michael Griffin
February 18, 2002

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