The GFS Atmospheric Model
(status as of August 28, 2003)
Comprehensive documentation of the
1988 version of the model was provided by the NMC (now NCEP)
Development Division (1988), with subsequent model development summarized by
Kanamitsu(1989), Kanamitsu et al. (1991), Kalnay et al. (1990).
NCEP MRF/RSM physics status as of August 1999 is located here .
This document containing radiation, surface layer, vertical diffusion, gravity wave drag,
convective precipitation, shallow convection, non-convective precipitation and
references updates the old 1988 documentation. In addition
Office Note # 424, New Global Orography Data Sets contains documentaiton of the
higher resolution orography for the MRF. The documentation of the GFS atmospheric model
as of 2003 is in NCEP Office Note # 442 .
- Numerical/Computational Properties
Spectral (spherical harmonic basis functions) with transformation to a Gaussian grid for
calculation of nonlinear quantities and physics.
Spectral triangular 254 (T254); Gaussian grid of 768X384, roughly equivalent to 0.5 X 0.5
The vertical domain is from the earth's surface (sigma=1) to the top of the atmosphere (sigma=0).
This domain is divided into 64 layers with enhanced resolution near the bottom and the top.
For a surface pressure of 1000 hPa, the lowest atmospheric level is
at a pressure of about 997.3 hPa and the top level is at about 0.27 hPa.
Sigma coordinate. Lorenz grid. Quadratic-conserving finite difference scheme by Arakawa and
64 unequally-spaced sigma levels. For a surface pressure of 1000 hPa, 15 levels are below 800
hPa, and 24 levels are above 100 hPa.
IBM RS/6000 SP (Class VIII) in an AIX environment.
About 12 minutes computation time on the IBM per one-day forecast at T254.
Initialization is not necessary because the statistical spectral interpolation analysis scheme
eliminates the unbalanced initial state.
Time Integration Scheme(s)
The main time integration is leapfrog for nonlinear advection terms, and semi-implicit for
gravity waves and for zonal advection of vorticity and moisture. An Asselin (1972)
time filter is used to reduce computational modes. The dynamics and physics are split. The
physics are written in the form of an adjustment and executed in sequence. For physical
processes, implicit integration with a special time filter (Kalnay and Kanamitsu, 1988) is used
for vertical diffusion. In order to incorporate physical tendencies into the semi-implicit
integration scheme, a special adjustment scheme is performed (Kanamitsu et al., 1991). The
time step is 7.5 minutes for computation of dynamics and physics, except that the full calculation
of longwave radiation is done once every 3 hours and shortwave radiation every hour
(but with corrections made at every time step for
diurnal variations in the shortwave fluxes and in the surface upward longwave flux).
Mean orographic heights on the Gaussian grid are used (see Orography). Negative
atmospheric moisture values are not filled for moisture conservation, except for a temporary moisture filling that is applied in the radiation
- Dynamical/Physical Properties
Primitive equations with vorticity, divergence, logarithm of surface pressure, specific
humidity virtual temperature, and cloud condensate as dependent variables.
Scale-selective, second-order horizontal diffusion after Leith (1971) is applied to vorticity,
divergence, virtual temperature, and specific humidity and cloud condensate.
The diffusion of temperature, specific humidity, and cloud condensate are performed
on quasi-constant pressure surfaces (Kanamitsu et al. 1991).
See Planetary Boundary Layer
Gravity-wave drag is simulated as described by Alpert et al. (1988). The parameterization
includes determination of the momentum flux due to gravity waves at the surface, as well as
at higher levels. The surface stress is a nonlinear function of the surface wind speed and the
local Froude number, following Pierrehumbert (1987). Vertical variations in the momentum
flux occur when the local Richardson number is less than 0.25 (the stress vanishes), or when
wave breaking occurs (local Froude number becomes critical); in the latter case, the
momentum flux is reduced according to the Lindzen (1981) wave saturation hypothesis.
Modifications are made to avoid instability when the critical layer is near the surface, since
the time scale for gravity-wave drag is shorter than the model time step (see also Time
Integration Schemes and Orography). The treatment of the gravity-wave drag parameterization in
the lower troposphere is improved by the use of the Kim and Arakawa (1995) enhancement.
Included is a dependence of variance on wind direction relative to the mountain as well as
subgrid statisical details of mountain distribution. This improves the prediction
of lee cyclogenesis and the accompanying movement of cold outbreaks (Alpert,et al, 199x).
The longwave (LW) radiation in NCEP's operational GFS employs a Rapid Radiative Transfer
Model (RRTM) developed at AER (Mlawer et al. 1997). The parameterization scheme uses a
correlated-k distribution method and a linear-in-tau transmittance table look-up to achieve high
accuracy and efficiency. The algorithm contains 140 unevenly distributed intervals (g-point) in
16 broad spectral bands. In addition to the major atmospheric absorbing gases of ozone, water
vapor, and carbon dioxide, the algorithm also includes various minor absorbing species such as
methane, nitrous oxide, oxygen, and up to four types of halocarbons (CFCs). In water vapor
continuum absorption calculations, RRTM-LW employs an advanced CKD_2.4 scheme
(Clough et al. 1992). A maximum-random cloud overlapping method is used in the GFS
application. Cloud liquid/ice water path and effective radius for liquid water and ice are used
for calculation of cloud-radiative properties. Hu and Stamnes' method (1993) is used to treat
liquid water clouds, while Ebert and Curry's method (1992) is used for ice cloud. Atmospheric
aerosol effect is not included in the current model.
The shortwave (SW) radiative transfer parameterization (Hou et al., 2002) is based on Chou's
work (1992) and his later improvements (Chou and Lee, 1996; Chou and Suarez, 1999). The
parameterization uses a correlated-k distribution method for water vapor and transmission
function look-up tables for carbon dioxide and oxygen absorptions. The model contains eight
broad spectral bands covering ultraviolet (UV) and visible region ( < 0.7 æ), and choices of
one or three spectral bands in the near infrared (NIR) region ( > 0.7 æ). (Currently one NIR
band is used in GFS for computational economy, but may be switched to three bands in the
future.) Ten correlated-k values are used in each NIR spectral band. The model includes
atmospheric absorbing gases of ozone, water vapor, carbon dioxide, and oxygen. A delta-
Eddington approximation method is used in multi-scattering calculations. Random cloud
overlapping is assumed in the operational GFS. Cloud liquid/ice water path and effective
radius for cloud liquid water and ice are used for calculation of cloud-radiative properties. For
liquid water clouds, cloud-optical property coefficients are derived based on Slingo (1989), and
coefficients for ice clouds are based on Fu (1996). Atmospheric aerosol effect is included in
the SW radiation calculation. A global distributed seasonal climatology data from Koepke et
al. (1997) is used to form a mixture of various tropospheric aerosol components. Aerosol
optical properties and vertical profile structures are established based on Hess et al. (1998).
Horizontal distribution of surface albedo is a function of Matthews (1985) surface vegetation
types in a manner similar to Briegleb et al. (1986). Monthly variation of surface albedo is
derived in reference to Staylor and Wilbur (1990).
For both LW and SW, the cloud optical thickness is calculated from the predicted cloud
condensate path. The cloud single-scattering albedo and asymmetry factor are as functions of
effective radius of the cloud condensate. The effective radius for ice is taken as a linear
function of temperature decreasing from a value of 80 microns at 263.16 K to 20 microns at
temperatures at or below 223.16K. For water droplets with temperatures above 273.16 K an
effective radius of 5 microns is used and for supercooled water droplets between the melting
point and 253.16 K, a value between 5 and 10 microns is used. (See also Cloud Fraction).
Effects from rain drops and snow are not included in the operational GFS but may be included
in the future.
Penetrative convection is simulated following Pan and Wu (1994), which is based on Arakawa and
Schubert(1974) as simplified by Grell (1993) and with a saturated downdraft. Convection occurs when
the cloud work function exceeds a certain threshold. Mass flux of the cloud is determined using a
quasi-equilibrium assumption based on this threshold cloud work function. The cloud work
function is a function of temperature and moisture in each air column of the model gridpoint. The
temperature and moisture profiles are adjusted towards the equilibrium cloud function within a
specified time scale using the deduced mass flux. A major simplification of the original
Arakawa-Shubert scheme is to consider only the deepest cloud and not the spectrum of clouds.
The cloud model incorporates a downdraft mechanism as well as the evaporation of precipitation.
Entrainment of the updraft and detrainment of the downdraft in the sub-cloud layers are included.
Downdraft strength is based on the vertical wind shear through the cloud. The critical cloud work
function is a function of the cloud base vertical motion. As the large-scale rising motion
becomes strong, the cloud work function (similar to CAPE) is allowed to approach zero (therefore
approaching neutral stability).
Mass fluxes induced in the
updraft and the downdraft are allowed to transport
momentum. The momentum exchange is calculated through the
mass flux formulation in a manner similar to that for heat
and moisture. In order to take into account the pressure
gradient effect on momentum, a simple parameterization using
entrainment is included for the updraft momentum inside the
The entrainment rate, tuned to ensure that the tropical
easterly jet strength in the Indian monsoon flow maintains
the least drift in the forecast is set to 10-4 m-1.
This addition to the cumulus parameterization has
reduced the feedback between heating and circulation
in sheared flows.
In addition, we have made a change in the cloud top
selection algorithm in the convection parameterization. In
the current SAS scheme, the cloud top level is determined by
the parcel method. The level where the parcel becomes stable
with respect to the environment is the cloud top. When the
prognostic cloud water scheme is tested with this scheme,
there is evidence that cloud top detrainment is too
concentrated in the upper troposphere. In order to provide a
more even detrainment of cloud water in the tropics, we are
making a change to the selection algorithm. Once the highest
possible cloud top has been determined by the parcel method,
we make a random selection of the actual cloud top between
the highest possible cloud top and the level where
environmental moist static energy is a minimum. The proper
entrainment rate is computed to ensure that the parcel
becomes neutral at the new cloud top. This is very similar
to the Relaxed Arakawa-Schubert (RAS) scheme developed by S.
Moorthi. Cloud top detrained water is seperated in to condensate
and vapor with the condensate used as a source of prognostic
Following Tiedtke (1983), the simulation of shallow (nonprecipitating) convection is
parameterized as an extension of the vertical diffusion scheme. The shallow convection
occurs where convective instability exist but no convection occurs. The cloud base is
determined from the lifting condensation level and the vertical diffusion is invoked between
the cloud top and the bottom. A fixed profile of vertical diffusion coefficients is assigned for
the mixing process.
The fractional area of the grid point covered by the
cloud is computed diagnostically following the approach of
Xu and Randall (1996) using the formula
where R is the relative humidity, q* is the saturation specific humidity and qcminis a minimum threshold value of qmin. The saturation specific humidity is calculated with
respect to water phase or ice phase depending on the
temperature. Unlike the operational model, the new model
has only one type of cloud cover represented by C. In the tropics the cloudiness is primarily due to convective
anvils, the result of cumulus detrainment, whereas in the
extratropics, cloudiness is mainly through grid-scale
The fractional cloud cover C is available at all model levels. There is no cloud
cover if there is no cloud condensate. Clouds in all layers are assumed to be randomly
overlapped. Other options will be explored in the future.
(See also Radiation)
Grid-scale Condensation and Precipitation
The prognostic cloud condensate has two sources, namely convective detrainment (see
convection) and grid-scale condensation. The grid-scale condensation
is based on Zhao and Carr(1997), which in turn is based on Sundqvist et al. (1989).
The sinks of cloud condensate are grid-scale precipitation which is parameterized
following Zhao and Carr (1997) for ice, and Sundqvist et al. (1989) for liquid water,
and evaporation of the cloud condensate which also follows Zhao and Carr (1997).
Evaporation of rain in the unsaturated layers below the level of
condensation is also taken into account. All precipitation that penetrates the bottom
atmospheric layer is allowed to fall to the surface (see also Snow Cover).
Planetary Boundary Layer
A new scheme based on the Troen and Mahrt (1986) paper was implemented on
25 October, 1995. The scheme is still a first-order vertical diffusion scheme.
There is a diagnostically determined pbl height that uses the bulk-Richardson
approach to iteratively estimate a pbl height starting from the ground upward.
Once the pbl height is determined, the profile of the coefficient of diffusivity
is specified as a cubic function of the pbl height. The actual values of the
coefficients are determined by matching with the surface-layer fluxes. There is
also a counter-gradient flux parameterization that is based on the fluxes at the
surface and the convective velocity scale. (See Hong and Pan(1996) for a description of
the scheme as well as a description of the convection scheme in the model).
New orography data sets are constructed based on a United States Geological Survey (USGS)
global digital elevation model (DEM) with a horizontal grid spacing of 30 arc seconds
(approximately 1 km). Orography statistics including average height, mountain variance,
maximum orography, land-sea-lake masks are directly derived from a 30-arc second
DEM for a given resolution.
See NCEP Office Note 424
(Hong, 1999) for more details. (see also Gravity-wave Drag).
A daily OI sea surface temperature analysis that assimilates observations from past seven
days is used (Reynolds and Smith, 1994, available
The sea surface temperature anomaly is damped
with an e-folding time of 90 days during the course of the forecast.
Sea-ice is obtained from the analysis by the marine Modeling Branch, available daily. The sea
ice is assumed to have a constant thickness of 3 meters, and the ocean temperature below the
ice is specified to be 271.2 K. The surface temperature of sea ice is determined from an
energy balance that includes the surface heat fluxes (see Surface Fluxes) and the heat capacity
of the ice. Snow accumulation does not affect the albedo or the heat capacity of the ice.
Snow cover is obtained from an analysis by NESDIS (the IMS system) and the Air Force, updated daily.
When the snow cover analysis is not available, the predicted snow in the data assimilation is
used. Precipitation falls as snow if the temperature at sigma=.85 is below 0 C. Snow
mass is determined prognostically from a budget equation that accounts for accumulation and
melting. Snow melt contributes to soil moisture, and sublimation of snow to surface
evaporation. Snow cover affects the surface albedo and heat transfer/capacity of the soil, but
not of sea ice. See also Sea Ice, Surface Characteristics, Surface Fluxes, and Land Surface
Roughness lengths over oceans are determined from the surface wind stress after the method
of Charnock (1955). Over sea ice the roughness is a uniform 0.01 cm. Roughness lengths
over land are prescribed from data of Dorman and Sellers (1989) which include 12 vegetation
types. Note that the surface roughness is not a function of orography.
Over oceans the surface albedo depends on zenith angle. The albedo of sea
ice is a function of surface skin temperature and nearby atmospheric temperature as well as snow
cover (Grumbine, 1994), with values ranging from 0.65-0.8 for snow-covered sea ice and from
0.45-0.65 for bare sea ice. Albedoes for land surfaces are based on Matthews (1985) surface
vegetation distribution (See Radiation).
Longwave emissivity is prescribed to be unity (black body
emission) for all surfaces.
Soil type and Vegetation type data base from GCIP is used. Vegetation fraction
monthly climatology based on NESDIS NDVI 5-year climatology is used.
Surface solar absorption is determined from the surface albedos, and longwave emission from
the Planck equation with emissivity of 1.0 (see Surface Characteristics).
The lowest model layer is assumed to be the surface layer (sigma=0.996) and the Monin-Obukhov similarity profile relationship is applied to obtain the surface stress and sensible and latent heat
fluxes. The formulation was based on Miyakoda and Sirutis (1986) and has been modified by P.
Long in the very stable and very unstable situations. A bulk aerodynamic formula is used to calculate
the fluxes once the turbulent exchange coefficients have be obtained. Roughness length over
ocean is updated with a Charnock formula after surface stress has been obtained.
Thermal roughness over the ocean is based on a formulation derived from TOGA COARE(Zeng et al, 1998).
Land surface evaporation is comprised of three components: direct evaporation from the soil and
from the canopy, and transpiration from the vegetation. The formulation follows Pan and Mahrt
Land Surface Processes
Soil temperature and soil volumetric water content are computed in two layers at depths 0.1 and 1.0
meters by a fully implicit time integration scheme (Pan and Mahrt, 1987). For sea ice, the
layer depths were specified as 1.5 and 3 meters. Heat capacity, thermal and hydraulic diffusivity
and hydraulic conductivity coefficients are strong functions of the soil moisture content. A
climatological deep-soil temperature is specified at the third layer of 4 meters for soil and a constant
value of 272 K is specified as the ice-water interface temperature for sea ice. The vegetation
canopy is allowed to intercept precipitation and re-evaporation. Runoff from the surface and
drainage from the bottom layer are also calculated.
Ozone is a prognostic variable that is updated in the analysis and
transported in the model. The sources and sinks of ozone are computed
using zonally averaged seasonally varying production and destruction rates
provided by NASA/GSFC.
Alpert, J.C., S-Y Hong and Y-J Kim, 199x: Sensitivity of cyclogenesis to lower troposphere
enhancement of gravity wave drag using the Environmental Modeling Center medium range model.
Alpert, J.C., M. Kanamitsu, P.M. Caplan, J.G. Sela, G.H. White, and E. Kalnay, 1988:
Mountain induced gravity wave drag parameterization in the NMC medium-range model.
Preprints of the Eighth Conference on Numerical Weather Prediction, Baltimore, MD,
American Meteorological Society, 726-733.
Arakawa, A. and W. H. Shubert, 1974: Interaction of a Cumulus Ensemble with the Large-Scale
Environment, Part I. J. Atmos. Sci., 31, 674-704.
Asselin, R., 1972: Frequency filter for time integrations. Mon. Wea. Rev., 100, 487-490.
Betts, A.K., S.-Y. Hong and H.-L. Pan, 1996: Comparison of NCEP-NCAR Reanalysis
with 1987 FIFE data. Mon. Wea. Rev., 124, 1480-1498
Briegleb, B. P., P. Minnus, V. Ramanathan, and E. Harrison, 1986: Comparison of regional
clear-sky albedo inferred from satellite observations and model computations.
J. Clim. and Appl. Meteo., 25, 214-226.
Campana, K. A., Y-T Hou, K. E. Mitchell, S-K Yang, and R. Cullather, 1994: Improved diagnostic
cloud parameterization in NMC's global model. Preprints of the Tenth Conference on
Numerical Weather Prediction, Portland, OR, American Meteorological Society, 324-325.
Charnock, H., 1955: Wind stress on a water surface. Quart. J. Roy. Meteor. Soc., 81, 639-640.
Chen, F., K. Mitchell, J. Schaake, Y. Xue, H.-L. Pan, V. Koren, Q. Y. Duan, M.
Ek, and A. Betts, 1996: Modeling of land surface evaporation by four schemes
and comparison with FIFE observations. J. Geophys. Res., 101, D3, 7251-7268.
Chou, M-D, 1990: Parameterizations for the absorption of solar radiation by O2 and CO2 with
application to climate studies. J. Climate, 3, 209-217.
Chou, M-D, 1992: A solar radiation model for use in climate studies. J. Atmos. Sci., 49,
Chou, M-D and K-T Lee, 1996: Parameterizations for the absorption of solar radiation by water
vapor and ozone. J. Atmos. Sci., 53, 1204-1208.
Chou, M.D., M. J. Suarez, C. H. Ho, M. M. H. Yan, and K. T.
Lee, 1998: Parameterizations for cloud overlapping and
shortwave single scattering properties for use in general
circulation and cloud ensemble models. J. Climate, 11, 202-
Clough, S.A., M.J. Iacono, and J.-L. Moncet, 1992: Line-by-line calculations of atmospheric
fluxes and cooling rates: Application to water vapor. J. Geophys. Res., 97, 15761-15785.
Coakley, J. A., R. D. Cess, and F. B. Yurevich, 1983: The effect of tropospheric aerosols on
the earth's radiation budget: a parameterization for climate models. J. Atmos. Sci., 42,
Dorman, J.L., and P.J. Sellers, 1989: A global climatology of albedo, roughness length and
stomatal resistance for atmospheric general circulation models as represented by the Simple
Biosphere model (SiB). J. Appl. Meteor., 28, 833-855.
Ebert, E.E., and J.A. Curry, 1992: A parameterization of ice cloud optical properties for
climate models. J. Geophys. Res., 97, 3831-3836.
Frohlich, C. and G. E. Shaw, 1980: New determination of Rayleigh scattering in the terrestrial
atmosphere. Appl. Opt., 14, 1773-1775.
Fu, Q., 1996: An accurate parameterization of the solar radiative properties of cirrus clouds for
climate models. J. Climate, 9, 2058-2082.
Hess, M., P. Koepke, and I. Schult, 1998: Optical properties of aerosols and clouds: The
software package OPAC. Bull. Am. Meteor. Soc., 79, 831-844.
Grell, G. A., 1993: Prognostic Evaluation of Assumprions Used by Cumulus Parameterizations.
Mon. Wea. Rev., 121, 764-787.
Grumbine, R. W., 1994: A sea-ice albedo experiment with the NMC medium range forecast
model. Weather and Forecasting, 9, 453-456.
Hong, S.-Y. and H.-L. Pan, 1996: Nonlocal boundary layer vertical diffusion in a medium-range
forecast model. Mon. Wea. Rev., 124, 2322-2339.
Hong, S.-Y., 1999: New global orography data sets. NCEP Office Note #424.
Hou, Y-T, K. A. Campana and S-K Yang, 1996: Shortwave radiation calculations in the NCEP's
global model. International Radiation Symposium, IRS-96, August 19-24, Fairbanks, AL.
Hou, Y.-T., S. Moorthi, and K.A. Campana, 2002: Parameterization of solar radiation transfer
in the NCEP models. NCEP Office Note 441.
Hu, Y.X., and K. Stamnes, 1993: An accurate parameterization of the radiative properties of
water clouds suitable for use in climate models. J. Climate, 6, 728-742.
Joseph, D., 1980: Navy 10' global elevation values. National Center for Atmospheric Research
notes on the FNWC terrain data set, 3 pp.
Kalnay, E. and M. Kanamitsu, 1988: Time Scheme for Stronglyt Nonlinear Damping Equations.
Mon. Wea. Rev., 116, 1945-1958.
Kalnay, M. Kanamitsu, and W.E. Baker, 1990: Global numerical weather prediction at the
National Meteorological Center. Bull. Amer. Meteor. Soc., 71, 1410-1428.
Kanamitsu, M., 1989: Description of the NMC global data assimilation and forecast system.
Wea. and Forecasting, 4, 335-342.
Kanamitsu, M., J.C. Alpert, K.A. Campana, P.M. Caplan, D.G. Deaven, M. Iredell, B. Katz,
H.-L. Pan, J. Sela, and G.H. White, 1991: Recent changes implemented into the global
forecast system at NMC. Wea. and Forecasting, 6, 425-435.
Kiehl, J.T., J. J. Hack, G. B. Bonan, B. A. Boville, D. L.
Williamson, and P. J. Rasch, 1998: The national center
for atmospheric research community climate model CCM3.
J. Climate, 11,1131-1149.
Kim, Y-J and A. Arakawa, 1995: Improvement of orographic gravity wave parameterization
using a mesoscale gravity wave model. J. Atmos. Sci. 52, 11, 1875-1902.
Koepke, P., M. Hess, I. Schult, and E.P. Shettle, 1997: Global aerosol data set. MPI
Meteorologie Hamburg Report No. 243, 44 pp.
Lacis, A.A., and J. E. Hansen, 1974: A parameterization for the absorption of solar radiation
in the Earth's atmosphere. J. Atmos. Sci., 31, 118-133.
Leith, C.E., 1971: Atmospheric predictability and two-dimensional turbulence. J. Atmos. Sci.,
Lindzen, R.S., 1981: Turbulence and stress due to gravity wave and tidal breakdown. J.
Geophys. Res., 86, 9707-9714.
Matthews, E., 1985: "Atlas of Archived Vegetation, Land Use, and Seasonal Albedo Data Sets.",
NASA Technical Memorandum 86199, Goddard Institute for Space Studies, New York.
Mitchell, K. E. and D. C. Hahn, 1989: Development of a cloud forecast scheme for the GL
baseline global spectral model. GL-TR-89-0343, Geophysics Laboratory, Hanscom AFB, MA.
Mlawer, E.J., S.J. Taubman, P.D. Brown, M.J. Iacono, and S.A. Clough, 1997: Radiative
transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the
longwave. J. Geophys. Res., 102, 16663-16682.
Miyakoda, K., and J. Sirutis, 1986: Manual of the E-physics. [Available from Geophysical
Fluid Dynamics Laboratory, Princeton University, P.O. Box 308, Princeton, NJ 08542.]
NMC Development Division, 1988: Documentation of the research version of the NMC
Medium-Range Forecasting Model. NMC Development Division, Camp Springs, MD, 504 pp.
Pan, H-L. and L. Mahrt, 1987: Interaction between soil hydrology and boundary layer
developments. Boundary Layer Meteor., 38, 185-202.
Pan, H.-L. and W.-S. Wu, 1995: Implementing a Mass Flux Convection Parameterization
Package for the NMC Medium-Range Forecast Model. NMC Office Note, No. 409, 40pp.
[ Available from NCEP, 5200 Auth Road, Washington, DC 20233 ]
Pierrehumbert, R.T., 1987: An essay on the parameterization of orographic wave drag.
Observation, Theory, and Modelling of Orographic Effects, Vol. 1, Dec. 1986, European
Centre for Medium Range Weather Forecasts, Reading, UK, 251-282.
Ramsay, B.H., 1998: The interactive multisensor snow and ice mapping system.
Hydrol. Process. 12, 1537-1546.
Reynolds, R. W. and T. M. Smith, 1994: Improved global sea surface temperature analyses. J. Climate, 7, 929-948.
Roberts, R.E., J.A. Selby, and L.M. Biberman, 1976: Infrared continuum absorption by
atmospheric water vapor in the 8-12 micron window. Appl. Optics., 15, 2085-2090.
Rodgers, C.D., 1968: Some extension and applications of the new random model for
molecular band transmission. Quart. J. Roy. Meteor. Soc., 94, 99-102.
Schwarzkopf, M.D., and S.B. Fels, 1985: Improvements to the algorithm for computing CO2
transmissivities and cooling rates. J. Geophys. Res., 90, 10541-10550.
Schwarzkopf, M.D., and S.B. Fels, 1991: The simplified exchange method revisited: An
accurate, rapid method for computation of infrared cooling rates and fluxes. J. Geophys. Res.,
Sela, J., 1980: Spectral modeling at the National Meteorological Center, Mon. Wea. Rev.,
Slingo, A., 1989: A GCM parameterization for the shortwave radiative properties pf water
clouds. J. Atmos. Sci.,46, 1419-1427.
Slingo, J.M., 1987: The development and verification of a cloud prediction model for the
ECMWF model. Quart. J. Roy. Meteor. Soc., 113, 899-927.
Slingo, A., 1989: A GCM parameterization for the shortwave
radiative properties pf water clouds. J. Atmos. Sci.,46, 1419-1427.
Stephens, G. L., 1984: The parameterization of radiation for
numerical weather prediction and climate models. Mon.Wea. Rew., 112, 826-867.
Staylor, W. F. and A. C. Wilbur, 1990: Global surface albedoes estimated from ERBE data.
Preprints of the Seventh Conference on Atmospheric Radiation, San Francisco CA,
American Meteorological Society, 231-236.
Sundqvist, H., E. Berge, and J. E. Kristjansson, 1989:
Condensation and cloud studies with mesoscale numerical
weather prediction model. Mon. Wea. Rev., 117, 1641-
Tiedtke, M., 1983: The sensitivity of the time-mean large-scale flow to cumulus convection in
the ECMWF model. ECMWF Workshop on Convection in Large-Scale Models, 28
November-1 December 1983, Reading, England, pp. 297-316.
Troen, I. and L. Mahrt, 1986: A simple model of the atmospheric boundary layer;
Sensitivity to surface evaporation. Bound.-Layer Meteor., 37, 129-148
Xu, K. M., and D. A. Randall, 1996: A semiempirical
cloudiness parameterization for use in climate models.
J. Atmos. Sci., 53, 3084-3102.
Zeng, X., M. Zhao, and R.E. Dickinson, 1998: Intercomparison of bulk
aerodynamical algorithms for the computation of sea surface fluxes using TOGA
COARE and TAO data. J. Climate, 11, 2628-2644.
Zhao, Q. Y., and F. H. Carr, 1997: A prognostic cloud scheme
for operational NWP models. Mon. Wea. Rev., 125,1931-1953.
This web site and
sites that are part of the EMC distributed Web operate under
the NWS Web policy - click here
for Disclaimer click here