**The Medium-Range Forecast Model
**

status as of January 09, 2001

Model Documentation: 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).

The documentation 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**### Horizontal Representation

Spectral (spherical harmonic basis functions) with transformation to a Gaussian grid for calculation of nonlinear quantities and physics.### Horizontal Resolution

Spectral triangular 170 (T170); Gaussian grid of 512x256, roughly equivalent to 0.7 X 0.7 degree latitude/longitude.### Vertical Domain

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.### Vertical Representation

Sigma coordinate. Lorenz grid. Quadratic-conserving finite difference scheme by Arakawa and Mintz (1974).### Vertical Resolution

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.### Computer/Operating System

IBM RS/6000 SP (Class VIII) in an AIX environment.### Computational Performance

About 7 minutes computation time on the IBM per one-day forecast at T170.### Initialization

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).### Smoothing/Filling

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 calculation.

**Dynamical/Physical Properties**### Atmospheric Dynamics

Primitive equations with vorticity, divergence, logarithm of surface pressure, specific humidityn 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 of temperature and specific humidity are performed on quasi-constant pressure surfaces (Kanamitsu et al. 1991).### Vertical Diffusion

See Planetary Boundary Layer### 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). 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).### Radiation

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 Formulation.### Convection

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.### Shallow convection

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.### Cloud Formation

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

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).### Orography

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).### Ocean

A 5-day running mean sea surface temperature analysis is used. The analysis is available once a day at 00GMT.### Sea Ice

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

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 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 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 Fluxes

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 (1987).### 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.### Chemistry

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 NASA-Goddard.

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