http://dao.gsfc.nasa.gov/. The earliest model predecessor was based on the "plug-compatible" concepts outlined by Kalnay et al. (1989) , and subsequent refinements are described by Fox-Rabinovitz et al. (1991) , Helfand et al. (1991),  and Suarez and Takacs (1993) . The GSFC/GEOS-1 model represents a different historical line of development from that of the GLA model, which is also in use at the Goddard Laboratory for Atmospheres. The GSFC/GEOS-1 and GLA models differ substantially, especially in their dynamical formulations and numerics, as well as in physical parameterizations pertaining to the treatment of convection and land surface processes. . Details of the numerics are given by Suarez and Takacs (1993). The radiation scheme is that of Harshvardhan et al. (1987) . The parameterizations of convection and evaporation of rainfall follow Moorthi and Suarez (1992)  and Sud and Molod (1988)  respectively. Treatment of turbulent dissipation is based on formulations of Helfand and Labraga (1988)  and Helfand et al. (1991) . ). , which conserves the global mass integral of potential temperature for adiabatic processes, and ensures an accurate finite-difference analogue of the energy-conversion term and the pressure gradient force. Land Surface Processes) are specified from the January 1979 estimates of Schemm et al. (1992) , and snow cover from a January climatology (see Snow Cover).  time filter. Turbulent surface fluxes and vertical diffusion (see Diffusion and Surface Fluxes) are computed by a backward-implicit iterative time scheme. The time step for dynamics is 5 minutes. To avoid introducing shocks and imbalances in the dynamics, diabatic increments are added at each dynamical time step. The tendencies of diabatic processes are updated at time steps of 10 minutes for moist convection, 30 minutes for turbulent dissipation, and 3 hours for radiative fluxes.
- Orography is smoothed (see Orography). A sixteenth-order Shapiro
 filter is applied to the winds,
potential temperature, and specific humidity in order to damp small-scale
dispersive waves. (The filter is applied fractionally at every 5-minute
dynamical time step such that the amplitude of the two-grid interval wave is
reduced by half in two hours.) A high-latitude Fourier filter also is used to
avoid violation of the Courant-Friedrichs-Lewy (CFL) condition for the Lamb
wave and internal gravity waves. This polar filter is applied only to the
tendencies of the winds, potential temperature, specific humidity, and surface
- Negative values of specific humidity in a vertical column are filled by borrowing from below, with negative moisture points in the lowest layer set to zero.
- Horizontal diffusion is not modeled.
- Above the surface layer (see Surface Fluxes), turbulent fluxes of momentum, heat, and moisture are calculated by the level-2.5 closure scheme of Helfand and Labraga (1988) , which predicts turbulence kinetic energy (TKE) and determines the eddy transfer coefficients used for a bulk formulation.
- Atmospheric radiation is simulated by the scheme of Harshvardhan et al. (1987)
. The shortwave parameterization after Davies (1982)
 follows the approach of Lacis and Hansen (1974)
. Absorption by water vapor in
near-infrared (0.70 to 4.0 microns) spectral ranges, and by ozone in the
visible (0.45 to 0.75 micron) and ultraviolet (0.24 to 0.36 micron) is treated.
- The parameterization of longwave radiation employs a wide-band model, with
four broad-band transmissions. Water vapor absorption in two bands centered at
9.6 and 15 microns is calculated after the method of Chou (1984)
, based on both line-type and e-type
approximations. Absorption by carbon dioxide follows the scheme of Chou and Peng (1983)
, which separates the
band-wing and band-center scaled paths. Absorption by ozone applies the
Rosenfield et al. (1987)
 modifications of the Rodgers (1968)
 line width.
- Shortwave scattering by clouds (as a function of solar zenith angle) is treated by the Meador and Weaver (1980)  modified delta-Eddington approximation; cloud albedo and transmissivity are obtained from specified single-scattering albedo and optical thickness. Cloud-water absorption is determined from a multiple-scattering computation with k-distribution functions. In the longwave, all clouds act as blackbodies (emissivity = 1.0). The cloud fractions produced by moist convective processes (see Convection) are used to evaluate clear line-of-site probabilities and effective optical thicknesses. For purposes of the radiation calculations, deep convective cloud is fully overlapped in the vertical, while shallow convective and nonconvective clouds are randomly overlapped. See also Cloud Formation.
- Penetrative and shallow cumulus convection are simulated by the Relaxed
Arakawa-Schubert (RAS) scheme of Moorthi and Suarez (1992)
, a modification of
the Arakawa and Schubert (1974)
parameterization. The RAS scheme predicts mass fluxes from convective cloud
types that have different entrainment rates and levels of neutral buoyancy. The
predicted convective mass fluxes are used to solve budget equations that
determine the impact of convection on the grid-scale fields of temperature
(through latent heating and compensating subsidence) and moisture (through
precipitation and detrainment).
- The mass flux for each cloud type in RAS is predicted from an equation for the cloud work function, defined as the tendency of cumulus kinetic energy (CKE). The equation is solved by assuming that the rate of generation of CKE by the large-scale environment is balanced by dissipation at the scale of the cumulus subensemble (that is, a quasi-equilibrium condition). To approximate full interaction between the different cloud types, many clouds are simulated frequently; each modifies the environment by some fraction of the total adjustment, with a relaxation towards neutrality. See also Cloud Formation and Precipitation.
- Convective cloud is determined diagnostically as part of the RAS scheme
(see Convection). The lowest two model layers are regarded as a single
subcloud layer (nominally 50 hPa thick); then, if detrainment occurs in the
next two higher layers when the RAS scheme is invoked (every 10 minutes of the
integration), the convection is defined as shallow with randomly overlapped
cloud, and a fractional cloudiness of 0.5 is assigned at the detrainment level.
In addition, 10 other cloud-top levels are randomly chosen between cloud base
and the top layer; if deep convection with a cloud-top pressure <400 hPa
occurs, the associated cloud is treated as fully overlapped with a fractional
cloudiness of unity at the detrainment level.
- Large-scale randomly overlapped cloud is prescribed when grid-scale supersaturation occurs in the absence of deep convective cloud (to ensure that total cloud fraction does not exceed unity). Under such conditions, the grid box is assumed to be instantaneously covered with the large-scale cloud (cloudiness fraction of 1). See also Radiation for cloud-radiative interactions.
- Convective precipitation results from operation of the cumulus convection
scheme (see Convection). Large-scale precipitation forms under
supersaturated conditions (see Cloud Formation).
- Both large-scale and convective precipitation may evaporate in falling to the surface (cf. Sud and Molod 1988) . The evaporation parameterization takes into account rainfall intensity, drop size distribution, and the temperature, pressure, and relative humidity of the ambient air; the moisture deficit of a layer is treated as a free parameter.
- Over land, monthly varying roughness lengths are specified from the data
of Dorman and Sellers (1989)
. A uniform
roughness of 1 x 10^-4 m is prescribed for ice surfaces. Over the
oceans, the roughness is computed as an interpolation between the functions of
Large and Pond (1981)
 for high surface
winds and of Kondo (1975)
 for weak winds.
- The surface albedo is specified as a uniform 0.80 over ice surfaces, but over the oceans it is a function of solar zenith angle. Monthly varying surface albedos of snowfree land are specified following modified Posey and Clapp (1964)
 data. The albedos of snow-covered
land (see Snow Cover) are specified from monthly satellite-derived
estimates of Matson (1978)
, and depend on the surface type (with seven types distinguished), but not spectral interval. Monthly albedos are linearly interpolated to intermediate time steps. Cf. Kitzmiller (1979)
 for further details.
- Longwave emissivity is assumed to be unity (blackbody emission) for all surfaces.
- Surface solar absorption is determined from albedos, and longwave emission
from the Planck equation with prescribed emissivity of 1.0 (see Surface Characteristics).
- Turbulent eddy fluxes of momentum, heat, and moisture in the extended surface layer are calculated from stability-dependent bulk formulae based on Monin-Obukhov similarity functions. For an unstable surface layer, the chosen stability functions are the KEYPS function for the momentum flux (cf. Panofsky 1973)  and its generalization for heat and moisture (which assures nonvanishing fluxes as the surface wind speed approaches zero). For a stable surface layer, the stability functions are those of Clarke (1970), but they are slightly modified for the momentum flux. The vertical gradients in temperature and moisture are based on the relation of Yaglom and Kader (1974) . The surface moisture flux also depends on the evapotranspiration efficiency beta, which is specified as unity over oceans, but which over land is given by the locally prescribed monthly soil wetness fraction (see Land Surface Processes). Cf. Helfand (1985)  and Helfand et al. (1991)  for further details. See also Diffusion.
- Soil temperature is determined from a surface energy balance (see
Surface Fluxes), excluding provision for subsurface heat storage. When
precipitation falls on ground with temperature <0 degrees C, the conductance
of the soil is modified to partially account for the thermodynamic effects of
snow (see Snow Cover).
- The spatially variable soil wetness fraction (ratio of local soil moisture content to a uniform field capacity of 0.15 m of water) is prescribed from monthly estimates of Schemm et al. (1992) . These are based on the procedure developed by Mintz and Serafini (1984)  using a single-layer "bucket" model in conjunction with monthly observed surface air temperature and precipitation for the AMIP period 1979 to 1988.
Last update December 12, 1996. For further information, contact: Tom Phillips (email@example.com )