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 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. 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 length and stomatal resistance for atmospheric general circulation models as represented by the Simple Biosphere model (SiB). J. Appl. Meteor., 28, 833-855. Fels, S.B., and M.D. Schwarzkopf, 1975: The simplified exchange approximation: A new method for radiative transfer calculations. J. Atmos. Sci., 37, 2265-2297. Grell, G. A., 1993: Prognostic Evaluation of Assumptions 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. Harshvardhan, D. A. Randall, T. G. Corsetti and D. A. Dazlich, 1989: Earth radiation budget and cloudiness simulation with a general circulation model. J. Atmos. Sci., 46, 1922-1942. Hering, W.S., and T.R. Borden, Jr., 1965: Mean distributions of ozone density over North America 1963-1964. Environ. Res. Pap. 162, U.S. Air force Cambridge Research Laboratory, Hanscom Field, Bedford, MA, 19 pp. 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 Strongly 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. 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., 28, 145-161. Lindzen, R.S., 1981: Turbulence and stress due to gravity wave and tidal breakdown. J. Geophys. Res., 86, 9707-9714. London, J., 1962: Mesosphere Dynamics, 3: The distribution of total ozone in the Northern Hemisphere. Final Report, Department of Meteorology/Oceanography, New York University. 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. 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, 1994: Implementing a Mass Flux Convection Parameterization Package for the NMC Medium-Range Forecast Model. Submitted for publication in Mon. Wea. Rev. Payne, R.E., 1972: Albedo of the sea surface. J. Atmos. Sci., 29, 959-970. 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. 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. Sasamori, T., J. London, and D.V. Hoyt, 1972: Radiation budget of the Southern Hemisphere, in Meteorology of the Southern Hemisphere, Meteorological Monographs No. 35, American Meteorological Society, 9-22. 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., 96, 9075-9096. Sela, J., 1980: Spectral modeling at the National Meteorological Center, Mon. Wea. Rev., 108, 1279-1292. 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. 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.