The Medium-Range Forecast Model
status as of January 09, 2001
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.
- Numerical/Computational Properties
Spectral (spherical harmonic basis functions) with transformation to a Gaussian grid for
calculation of nonlinear quantities and physics.
Spectral triangular 170 (T170); Gaussian grid of 512x256, roughly equivalent to 0.7 X 0.7
Surface to about 2.0 hPa divided into 42 layers. For a surface pressure of 1000 hPa, the lowest atmospheric level is
at a pressure of about 996 hPa.
Sigma coordinate. Lorenz grid. Quadratic-conserving finite difference scheme by Arakawa and
42 unequally-spaced sigma levels. For a surface pressure of 1000 hPa, 12 levels are below 800
hPa, and 10 levels are above 100 hPa.
IBM RS/6000 SP (Class VIII) in an AIX environment.
About 7 minutes computation time on the IBM per one-day forecast at T170.
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
humidityn and virtual temperature as dependent variables.
Scale-selective, second-order horizontal diffusion after Leith (1971) is applied to vorticity,
divergence, virtual temperature, and specific humidity. The diffusion of temperature and
specific humidity are performed on quasi-constant pressure surfaces (Kanamitsu et al.
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).
Shortwave radiation is computed using multi-band techniques and includes absorption/scattering
by water vapor, ozone, carbon dioxide, and clouds, with future options available for aerosols and
oxygen. It is based on work by Chou (1992), Chou and Lee (1996), Chou (1990), and Hou, et al
(1996). Data for Rayleigh scattering are calculated from Frohlich and Shaw's formulation (1980).
Multi-scattering in clouds is treated using a delta-Eddington approximation with a two-stream
adding method (Coakley, etal. 1983). Horizontal distribution of surface albedo is a function
of Matthews (1985) surface vegetation types in a manner similar to Briegleb, etal (1986).
Monthly variation of surface albedo is derived in reference to Staylor and Wilbur (1990).
Longwave radiation follows the simplified exchange method of Fels and Schwarzkopf (1975)
and Schwarzkopf and Fels (1991), with calculation over spectral bands associated with carbon
dioxide, water vapor, and ozone. Schwarzkopf and Fels (1985) transmission coefficients for
carbon dioxide, a Roberts et al. (1976) water vapor continuum, and the effects of water
vapor-carbon dioxide overlap and of a Voigt line-shape correction are included. The Rodgers
(1968) formulation is adopted for ozone absorption.
Cloud radiative properties for shortwave (reflectance, absorptance) and longwave (emissivity) are
obtained from cloud thickness, cloud layer temperature, and cloud layer moisture in a manner
similar to Hashvardhan, Randall, Corsetti and Dazlich (1989). Independent cloud layered masses
(separated by one clear layer) are randomly overlapped in the vertical direction. Vertically
contiguous anvil cirrus and lower convective cloud is also randomly overlapped. See also Cloud
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 strenght 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). In 2001, we also included momentum mixing due
to convection in the same manner as the temperature and humidity. The pressure
effect on the convective air parcel is parameterized in the form of entrainment.
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 formation of stratiform clouds associated with fronts and tropical disturbances follows
Slingo (1987) and Campana, et al (1994).
Clouds are permitted to exist in most model layers (exceptions near the earth's
surface and above the model-estimated tropopause). Stratiform cloud is computed from 10-month
(March-December 1995) mean cloud/relative humidity relationships (Mitchell and Hahn, 1989),
developed from U.S.A.F. RT Nephanalysis data, for tropics, mid-latitudes, land, sea,
and vertical (high, middle, low, and 'boundary layer') regions. For the radiation computation,
vertically contiguous diagnosed-cloud layers are maximally overlapped into individual cloud masses.
The height of sub-gridscale convective cloud is determined by the
level of non-buoyancy for moist adiabatic ascent (see Convection). The convective cloud fraction
is a function of precipitation rate (Slingo, 1987). The fractional value of cloud cover is Slingo's
convective coverage algorithm and the cloud is considered one columnar mass for the radiation
calculations. Anvil cirrus also forms in the layer above the top of convection if
precipitation is intense enough! See also Radiation for cloud-radiative interactions.
Precipitation is produced both from large-scale condensation and from the convective scheme
(see Convection). The large-scale precipitation algorithm checks supersaturation in the
predicted specific humidity, and latent heat is released to adjust the specific humidity and
temperature to saturation. 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). As of July 1998,
a convective adjustment is included when the model column becomes super-saturated and
conditionally unstable. The lowest level where supersaturation occurs is the cloud base
and the cloud top is chosen as the maximum level where the theta-e from cloud base is warmer
and while the resulting column can remain saturated.
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).
Raw orography obtained from the U.S. Navy dataset with resolution of 10 minutes arc
(Joseph 1980) is area-averaged on the T126 Gaussian grid of the NMC operational model.
Orographic variances are computed from the 10-minute dataset and also area-averaged
to T126 Gaussian grid for use in the gravity-wave drag parameterization (see Gravity-wave Drag).
A 5-day running mean sea surface temperature analysis is used. The analysis is available once a
day at 00GMT.
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 now a prognostic variable that is updated in the analysis and
transported in the model with zonally averaged seasonally varying sources and sinks. For
longterm forecasts, we use a monthly zonal mean climatology obtained from
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Ek, and A. Betts, 1996: Modeling of land surface evaporation by four schemes
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Chou, M-D, 1990: Parameterizations for the absorption of solar radiation by O2 and CO2 with
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Chou, M-D, 1992: A solar radiation model for use in climate studies. J. Atmos. Sci., 49,
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Grell, G. A., 1993: Prognostic Evaluation of Assumprions Used by Cumulus Parameterizations.
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Grumbine, R. W., 1994: A sea-ice albedo experiment with the NMC medium range forecast
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Harshvardhan, D. A. Randall, T. G. Corsetti and D. A. Dazlich, 1989: Earth radiation budget and
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