Tom Phillips of PCMDI/LLNL wrote a very good description of the NCEP AMIP model.
We liked it so much that we asked Tom for a copy.  H-L Pan, M. Kanamitsu and
K. Campana updated Tom's version to describe the current operational model 
which now resides on the EMC's home page.  The latter version was then 
modified for the Reanalysis model.
                                       Thanks Tom.






Reanalysis Model status as of Jan. 10, 1995

Model Documentation

Comprehensive documentation of the 1988 version of the model is provided by the
NMC Development Division (1988), with subsequent model development summarized 
by Kanamitsu (1989), Kanamitsu et al. (1991), Kalnay et al. (1990). 

Numerical/Computational Properties

Horizontal Representation

Spectral (spherical harmonic basis functions) with transformation to a 
Gaussian grid for calculation of nonlinear quantities and physics. 
Radiation and clouds are calculated on a lower resolution Gaussian grid
and later bilinearly interpolated to the 'dynamics' Gaussian grid.


Horizontal Resolution

Spectral triangular 62 (T62). The Gaussian grid of 192x94, roughly equivalent to
2x2 degree latitude/longitude.  The radiation grid is a Gaussian grid of
dimension 128x62.

Vertical Domain

Surface to about 2.7 hPa. For a surface pressure of 1000 hPa, the lowest 
atmospheric level is at a pressure of about 995 hPa. 

Vertical Representation

Sigma coordinate. Lorenz grid. Quadratic conserving finite difference scheme by
Arakawa and Minz (1974). 

Vertical Resolution

28 unequally spaced sigma levels. For a surface pressure of 1000 hPa, 8 levels 
are below 800 hPa, and 7 levels are above 100 hPa. 

Computer/Operating System

Cray-Y/MP computer using 8 processors in a UNICOS environment. 
[The Cray-Y/MP was retired and J-16's are being used for latter years.]

Computational Performance

About 2 minutes Cray-Y/MP computation time per one day forecast. 

Initialization

Initialization is not necessary because the statistical spectral interpolation 
analysis scheme eliminated the unbalanced initial state. (This not to say
that we've eliminated all spin-up/spin-down problems.)

Time Integration Scheme(s)

The main time integration is by a leapfrog for nonlinear advection terms,
semi-implicit for gravity waves and semi-implicit for zonal advection of 
vorticity and moisture. Asselin (1972) time filter is used to reduce the 
computational mode. The dynamics and physics are split. The physics are 
written in the form of adjustment and executed in sequence. For physical 
processes, implicit integration with special time filter (Kalnay and Kanamitsu,
1988) is used for vertical diffusion. In order to incorporate physical 
tendencies into the semi-implicit integration scheme, special adjustment 
scheme is performed (Kanamitsu et al., 1991). The time step is 20 minutes
for computation of dynamics and physics, except for full calculation of 
atmospheric radiation once every 3 hours (but with corrections made at every 
time step for diurnal variations in the short wave fluxes and in the surface 
upward long wave flux). 

Smoothing/Filling

Mean orographic heights on the Gaussian grid are used (see Orography). Negative
atmospheric moisture values are not filled for moisture conservation. In the 
radiation calculation, however, the temporally moisture filling is applied for 
computation. 

Dynamical/Physical Properties

Atmospheric Dynamics

Primitive-equations with vorticity, divergence, logarithm of surface pressure,
specific humidity, and virtual temperature as dependent variables. 

Horizontal Diffusion

Scale-selective, second-order horizontal diffusion after Leith (1971) is 
applied to vorticity, divergence, virtual temperature, and specific humidity. 
The diffusion on temperature and specific humidity are performed on quasi-
constant pressure surfaces (cf. Kanamitsu et al. 1991).  This scheme has no 
horizontal diffusion for wavenumbers less than or equal to 34.

Vertical Diffusion

Richardson number-dependent vertical diffusion of momentum, virtual temperature
and moisture follows Miyakoda and Sirutis (1986). 

Gravity-wave Drag

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). 

Radiation

Short wave Rayleigh scattering and absorption in ultraviolet (wavelengths < 0.35
microns) and visible (wavelengths 0.5-0.7 microns) spectral bands by ozone, 
and in the near-infrared (wavelengths 0.7-4.0 microns) by water vapor follows 
the method of Lacis and Hansen (1974). Absorption by carbon dioxide is after 
Sasamori et al. (1972). Pressure corrections and multiple reflections between 
clouds and the surface are treated. Long wave 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 short wave (reflectance, absorptance) and long wave 
(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 
Formulation.

Convection

Penetrative convection is simulated following Pan and Wu (1994) based on Arakawa
and Schubert(1974) simplified by Grell (1993) with a saturated downdraft.
Convection occurs when 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 grid point. The 
temperature and moisture profiles are adjusted towards equilibrium cloud 
function within a specified time scale using the deduced mass flux. Major 
simplification from the original Arakawa-Shubert scheme is to consider only 
the deepest cloud and not the spectrum of clouds. The cloud model incorporates 
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. 

Shallow convection

Following Tiedtke (1983), simulation of shallow (non-precipitating) 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. 

Cloud Formation

The formation of stratiform clouds associated with fronts and tropical 
disturbances follows Slingo (1987). Clouds are permitted to exist in most model
layers (exceptions near the earth's surface and above model-estimated 
tropopause). Stratiform cloud is computed from 6-month mean cloud/relative 
humidity relationships which have been developed (Mitchel and Hahn, 1989) from 
U.S.A.F. RT Nephanalysis data, for tropics, mid-latitudes, land, sea, and 
vertical (high, middle, low) regions. For the radiation computation, vertically
contiguous diagnosed-cloud layers are maximally overlapped into individual 
cloud masses. Low frontal cloud; these clouds may be more than one layer thick,
but are excluded from the surface layer (cf. Kanamitsu et al. 1991). 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 intense-enough 
precipitation. See also Radiation for cloud-radiative interactions. 

Precipitation

Precipitation is produced both from large-scale condensation and from the
convective scheme (see Convection). The large-scale precipitation algorithm 
checks super-saturation 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). 

Planetary Boundary Layer

While in theory the model PBL can extend throughout the entire atmosphere,
typically its main effects are felt at the first 5 levels above the surface 
(at sigma= 0.995, 0.981, 0.960, 0.920, and 0.856). See also Diffusion, Surface 
Characteristics, and Surface Fluxes. 

Orography

Raw orography obtained from the U.S. Navy dataset with resolution of 10 minutes
arc (cf. Joseph 1980) is area-averaged on the T62 Gaussian grid of the NCEP
operational model. Orographic variances also are computed on the T62 Gaussian
grid for use in the gravity-wave drag parameterization (see Gravity-wave Drag). 

Ocean

Sea-surface temperatures from the UK Met office are used up to 1988.  After 
1988, SST from R. Reynolds (CPC) are used.

Sea Ice

Sea-ice is obtained from SSMR and SSM/I data that was processed by the ECMWF 
(79-92).  For later analyses, the SSM/I data will be processed internally.  For 
the pre-SSMR period, analyses will be obtained from the Joint Ice Center, 
available once a week.  The sea ice is assumed to have a constant thickness of 
2 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.   Even though the sea-ice data is given as a concentration, the model
only has two states, ice free and ice covered.  A value of 50% is the threshold
for an ice-covered sea.

Snow Cover

Snow cover is also obtained from analysis by the Joint Ice Center, updated 
once a week.  Since the model requires a snow depth, the snow cover is
converted to a depth by assuming the depth is a function of the surface
temperature. On days a new snow analysis is not available, the snow depth
is a weighted mean of the observed snow 'depth' and the predicted snow
snow depth.  The weight factor is determined by the 'age' of the last
observed snow analysis.

Precipitation falls as snow if a linear combination of ground temperature 
(weighted 0.35) and the temperature at the lowest atmospheric level (weighted 
0.65) is < 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 
Processes. 

Surface Characteristics

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 
1x10-4 m. Roughness lengths over land are prescribed from data of Dorman and 
Sellers (1989) that includes 12 vegetation types. Note that the surface 
roughness is not a function of orography. Over oceans the surface albedo 
depends on zenith angle (cf. Payne 1972). 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 snow-free land surfaces 
are obtained from Matthews (1985) and are zenith angle dependent. Snow cover 
modifies the local background albedo of land surfaces as follows (no zenith 
angle dependence). Poleward of 70 degrees latitude permanent snow with albedo 
0.75 is assumed. Equatorward of 70 degrees snow albedo is set to 0.60 if the 
snow depth is at least 0.01 m; otherwise, the albedo is a linear combination 
of the background and snow albedos weighted by the fraction of snow cover in 
the grid box (see Snow Cover). Albedos do not depend on spectral interval. 
Long wave emissivity is prescribed to be unity (black body emission) for all 
surfaces. The minimum stomatal resistance used in the transpiration calculation 
(see Land Surface Processes) is assumed to be a function of the vegetation 
only and a climatology created by Dorman and Sellers (1989) has been adopted. 
Due to the problem concerning cultivated vegetation type in the monthly 
climatology, the minimum over the year at each geographical location is used
throughout the year.

Surface Fluxes 

Surface solar absorption is determined from the surface albedos, and long wave
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=0.995) and apply the Monin-Obukhov similarity profile relationship 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. Bulk aero-dynamic formula is 
used to obtain 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. 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 
(1987). The vegetation cover is presently set as a constant of 0.7 over the 
globe. 

Land Surface Processes

Soil temperature and soil volumetric water content are computed in two layer at
depths 0.1 and 1.0 meters by a fully implicit time integration scheme (cf. Pan 
and Mahrt, 1987). For sea ice, the layer depths were specified at 1.5 and 3 
meters. Heat capacity, thermal and hydrolic diffusivity and hydrolic 
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 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 while runoff from the surface and 
drainage from the bottom layer are also calculated. The soil moisture is
relaxed to a 'climatology' with a 60-day time scale.

Chemistry

Seasonal climatological zonal profiles of ozone concentrations are prescribed 
from data of Hering and Borden (1965) and London (1962). (These Northern 
Hemisphere seasonal concentrations also are prescribed for the Southern 
Hemisphere in the corresponding season. The resulting global zone profiles are 
linearly interpolated for intermediate time points.) Radiative effects of 
water vapor, but not those of aerosol, also are included (see Radiation). 

References

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
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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. 

Charnock, H., 1955: Wind stress on a water surface. Quart. J. Roy. Meteor. Soc., 81,
639-640. 

Dorman, J.L., and P.J. Sellers, 1989: A global climatology of albedo, roughness
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Fels, S.B., and M.D. Schwarzkopf, 1975: The simplified exchange approximation: A
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Grell, G. A., 1993: Prognostic Evaluation of Assumptions Used by Cumulus
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Grumbine, R. W., 1994: A sea-ice albedo experiment with the NMC medium range
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Harshvardhan, D. A. Randall, T. G. Corsetti and D. A. Dazlich, 1989: Earth 
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Hering, W.S., and T.R. Borden, Jr., 1965: Mean distributions of ozone density 
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Joseph, D., 1980: Navy 10' global elevation values. National Center for 
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