## Goddard Space Flight Center: Model GSFC GEOS-1 (4x5 L20) 1993

### AMIP Representative(s)

Dr. Wei Min and Dr. Richard Rood, Data Assimilation Office, Mail Code 910.3, Goddard Space Flight Center, Greenbelt, Maryland 20771; Phone: +1-301-286-8695; Fax: +1-301-286-1754; e-mail: min@dao.gsfc.nasa.gov (Min) and rood@sgccp.gsfc.nasa.gov (Rood); World Wide Web URL: http://dao.gsfc.nasa.gov/### Model Designation

GSFC GEOS-1 (4x5 L20) 1993### Model Lineage

The GSFC model, equivalent to the Goddard Earth Observing System-1 (GEOS-1) model, was developed by the Data Assimilation Office of the Goddard Laboratory for Atmospheres (GLA). The GSFC/GEOS-1 model is designed for use with an optimal interpolation analysis scheme for production of multi-year global atmospheric datasets (cf. Schubert et al. 1993) [1]. The earliest model predecessor was based on the "plug-compatible" concepts outlined by Kalnay et al. (1989) [2], and subsequent refinements are described by Fox-Rabinovitz et al. (1991) [3], Helfand et al. (1991), [4] and Suarez and Takacs (1993) [5]. 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.### Model Documentation

A summary of basic model features is provided by Schubert et al. (1993) [1]. Details of the numerics are given by Suarez and Takacs (1993). The radiation scheme is that of Harshvardhan et al. (1987) [6]. The parameterizations of convection and evaporation of rainfall follow Moorthi and Suarez (1992) [7] and Sud and Molod (1988) [8] respectively. Treatment of turbulent dissipation is based on formulations of Helfand and Labraga (1988) [9] and Helfand et al. (1991) [4].## Numerical/Computational Properties

### Horizontal Representation

Finite differences on a staggered Arakawa C-grid that conserves potential enstrophy and energy (cf. Burridge and Haseler 1977 [10]).### Horizontal Resolution

4 x 5-degree latitude-longitude grid.### Vertical Domain

Surface to about 10 hPa. For a surface pressure of 1000 hPa, the lowest atmospheric level is at a pressure of about 994 hPa.### Vertical Representation

Unstaggered finite-differences in generalized sigma coordinates. The vertical differencing scheme is that of Arakawa and Suarez (1983) [11], 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.### Vertical Resolution

There are 20 unevenly spaced sigma levels. For a surface pressure of 1000 hPa, 5 levels are below 800 hPa and 7 levels are above 200 hPa.### Computer/Operating System

The AMIP simulation was run on a Cray Y/MP computer using a single processor in the UNICOS environment.### Computational Performance

For the AMIP experiment, about 4 minutes of Cray Y/MP computer time per simulated day.### Initialization

For the AMIP simulation, the model atmospheric state is initialized for 1 January 1979 from the ECMWF reanalysis of the FGGE period. The initial soil wetness fractions (see Land Surface Processes) are specified from the January 1979 estimates of Schemm et al. (1992) [12], and snow cover from a January climatology (see Snow Cover).### Time Integration Scheme(s)

The main time integration is by a leapfrog scheme with an Asselin (1972) [13] 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.### Smoothing/Filling

- Orography is smoothed (see Orography). A sixteenth-order Shapiro
(1970)
[14] 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
pressure.
- 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.

### Sampling Frequency

For the AMIP simulation, the history of prognostic atmospheric variables is produced every 6 hours at 18 pressure levels, while surface and vertically integrated diagnostics are generated every 3 hours.## Dynamical/Physical Properties

### Atmospheric Dynamics

Primitive-equation dynamics are expressed in terms of u-v winds, potential temperature, specific humidity, and surface pressure. The momentum equations are written in "vector-invariant" form (cf. Sadourny 1975b [15] and Arakawa and Lamb 1981 [16]), while the thermodynamic and moisture equations are rendered in flux form to facilitate conservation of potential temperature and specific humidity.### Diffusion

- 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) [9], which predicts turbulence kinetic energy (TKE) and determines the eddy transfer coefficients used for a bulk formulation.

### Gravity-wave Drag

Gravity-wave drag is not modeled.### Solar Constant/Cycles

The solar constant is the AMIP-prescribed value of 1365 W/(m^2). Both seasonal and diurnal cycles in solar forcing are simulated.### Chemistry

The carbon dioxide concentration is the AMIP-prescribed value of 345 ppm. Monthly zonal profiles of ozone concentrations are specified from data of Rosenfield et al. (1987) [17], with linear interpolation for intermediate time steps. Radiative effects of water vapor, but not those of aerosols, are also included (see Radiation).### Radiation

- Atmospheric radiation is simulated by the scheme of Harshvardhan et al. (1987)
[6]. The shortwave parameterization after Davies (1982)
[18] follows the approach of Lacis and Hansen (1974)
[19]. 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)
[20], based on both line-type and e-type
approximations. Absorption by carbon dioxide follows the scheme of Chou and Peng (1983)
[21], which separates the
band-wing and band-center scaled paths. Absorption by ozone applies the
Rosenfield et al. (1987)
[17] modifications of the Rodgers (1968)
[22] line width.
- Shortwave scattering by clouds (as a function of solar zenith angle) is treated by the Meador and Weaver (1980) [23] 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.

### Convection

- Penetrative and shallow cumulus convection are simulated by the Relaxed
Arakawa-Schubert (RAS) scheme of Moorthi and Suarez (1992)
[7], a modification of
the Arakawa and Schubert (1974)
[24]
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.

### Cloud Formation

- 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.

### Precipitation

- 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) [8]. 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.

### Planetary Boundary Layer

The PBL height is diagnosed as the level at which TKE is reduced to 10 percent of its surface value (see Diffusion), typically within the first 2 to 4 levels above the surface (sigma = 0.994 to 0.875). See also Surface Characteristics and Surface Fluxes.### Orography

Surface orography is determined from area-averaging the U.S. Navy topographic height data with 10-minute arc resolution (cf. Joseph 1980) [25] over the model's 4 x 5-degree grid. The resulting heights are passed through a Lanczos (1966) [26] filter to remove the smallest scales, and negative values are refilled.### Ocean

AMIP monthly sea surface temperature fields are prescribed, with linear interpolation to intermediate time steps (see Time Integration Scheme(s)).### Sea Ice

AMIP monthly sea ice extents are prescribed and linearly interpolated to intermediate time steps. The ice is assumed to have a uniform thickness of 3 m, and the heat conduction through it is accounted for as part of the surface energy budget (see Surface Fluxes), with the surface temperature over ice determined prognostically. Snow is not present on sea ice (see Snow Cover).### Snow Cover

Snow mass is not a prognostic variable. Monthly snow cover over land is prescribed from satellite-derived surface albedo estimates of Matson (1978) [27]: wherever the albedo of a grid box exceeds 0.40, that area is defined as snow-covered. (In the Southern Hemisphere, snow cover is only specified for Antarctica). If precipitation falls when the ground temperature is <0 degrees C, some thermodynamic effects of snow cover are also included. See also Surface Characteristics and Land Surface Processes.### Surface Characteristics

- Over land, monthly varying roughness lengths are specified from the data
of Dorman and Sellers (1989)
[28]. 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)
[29] for high surface
winds and of Kondo (1975)
[30] 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)
[31] data. The albedos of snow-covered
land (see Snow Cover) are specified from monthly satellite-derived
estimates of Matson (1978)
[27], 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)
[32] for further details.
- Longwave emissivity is assumed to be unity (blackbody emission) for all surfaces.

### Surface Fluxes

- 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) [33] 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)[34], 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) [35]. 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) [36] and Helfand et al. (1991) [4] for further details. See also Diffusion.

### Land Surface Processes

- 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) [12]. These are based on the procedure developed by Mintz and Serafini (1984) [37] using a single-layer "bucket" model in conjunction with monthly observed surface air temperature and precipitation for the AMIP period 1979 to 1988.

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Last update December 12, 1996. For further information, contact: Tom Phillips (phillips@tworks.llnl.gov )

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