http://www.giss.nasa.gov/. . The current model differs from this predecessor principally in numerics and in the treatment of convection, planetary boundary layer (PBL), large-scale clouds, and ground hydrology. , with subsequent changes to the convective scheme described by Del Genio and Yao (1988) , and Yao and Del Genio (1989) . Early versions of the current large-scale cloud parameterization and ground hydrology scheme are described, respectively, by Del Genio et al. (1993)  and by Abramopoulos et al. (1988) . , which conserves mass, kinetic energy (but not angular momentum) under advection, and enstrophy in the nondivergent limit. The prognostic variable for mass (see Atmospheric Dynamics) represents a mean value over a grid box. For heat and moisture prognostics, however, the linear gradients and second-order moments in three dimensions, and the three cross-term second-order moments are included in addition to the mean quantity for each grid box. (Potential enthalpy and water vapor are advected via a stable and accurate quadratic upstream scheme that utilizes these first- and second-order moments.) Vertical Representation). For a surface pressure of 1000 hPa, 2 levels are below 800 hPa and 2 levels are above 200 hPa. Orography). An eighth-order Shapiro (1970)  filter is used to smooth the surface pressure. Because the quadratic upstream scheme (see Horizontal Representation) does not guarantee positive-definite atmospheric moisture, the first- and second-order moments of water vapor mixing ratios are minimally reduced, if necessary, at each advective step to maintain non-negative values. Vertical Representation). Convection), and the quadratic upstream advective scheme (see Horizontal Representation) is weakly diffusive as well. . . Radiative effects of water vapor, and of methane, nitrous oxide, nitric oxide, oxygen, and aerosols also are included (see Radiation).
- A correlated k-distribution method that is a generalization of the
approach of Lacis and Hansen (1974)
 is used
for both shortwave and longwave radiative calculations. The k-distribution for
a given gas and frequency interval is obtained by least-squares fitting to
calculations of line-by-line absorption for a range of temperatures and
pressures by McClatchey et al. (1973)
- The shortwave radiative fluxes are calculated after Lacis and Hansen
, but with modifications to obtain accurate results at all solar zenith
angles and optical thicknesses. Gaseous absorbers include water vapor, carbon
dioxide, ozone, oxygen, nitrous oxide, and nitric oxide. Multiple scattering
computations are made of 12 k-profiles, with strong line (exponential)
absorption of the direct solar beam computed separately for water vapor, carbon
dioxide, and oxygen. Absorption and scattering by aerosols are also included
using radiative properties obtained from Mie calculations for the global
aerosol climatology of Toon and Pollack (1976)
. The spectral dependence of Mie parameters
for clouds, aerosols, and Rayleigh scattering is specified in 6 intervals;
these are superimposed on the 12 k-profiles to account for overlapping
- In the longwave, the k-distribution method is used to model absorption by
water vapor, carbon dioxide, ozone, nitrous oxide, nitric oxide, and methane
(but with scattering effects neglected). A single k-distribution is specified
for each gas, with 11 k-intervals for water vapor, 10 for carbon dioxide, and 4
- Shortwave optical thickness of large-scale cloud is based on the prognostic cloud water path (see Cloud Formation). The required droplet effective radius is diagnosed from the cloud water content by assuming constant number concentration with different values for land/ocean cloud and liquid/ice cloud (cf. Del Genio et al. 1993) . The shortwave optical thickness of a convective cloud is proportional to its pressure depth. Cloud particle phase function and single-scattering albedo are functions of spectral interval, based on Mie computations for cloud droplet data of Squires (1958)  and Hansen and Pollack (1970) . For purposes of the radiation calculations, partial cloud cover of a grid box is represented as full cloud cover that occurs for a percentage of the time (implemented via a random number generator--cf. Hansen et al. 1983) . Longwave effects of clouds are treated by an emissivity formulation, where the longwave cloud properties are self-consistent with the shortwave properties as a result of the application of Mie theory.
- Convection is initiated only when the grid box is convectively unstable in
the mean. Dry convection can occur below the condensation level if the moist
static energy of a parcel exceeds that of the layer above. Moist convection is
triggered if the moist static energy of a parcel exceeds the saturation energy
value in the layer above and if, in addition, the implied lifting produces
saturation; this level defines the cloud base. The convective cloud top is
defined as the upper boundary of the highest vertical layer for which the cloud
parcel is buoyant.
- The amount of convective mass flux is obtained from a closure assumption that the cloud base is restored to neutral buoyancy relative to the next higher layer. The mass of the rising convective plume is changed by the entrainment of drier environmental air, with associated decreases in buoyancy. The entrainment rate is prescribed for an ensemble of two convective cloud types (entraining and non-entraining). Heating/cooling of the environment occurs through compensating environmental subsidence, detrainment of cloud air at cloud top, a convective-scale downdraft whose mass flux detrains into the cloud base layer, and evaporation of falling condensate (see Precipitation). (Latent heat release serves only to maintain cloud buoyancy.) The convective plume and subsiding environmental air transport gridscale horizontal momentum, under the assumption that exchanged air parcels carry with them the momentum of the layer of origin. Cf. Del Genio and Yao (1988)  and Yao and Del Genio (1989)  for further details.
- Clouds result from either large-scale or convective condensation (see
Convection). Condensation of cloud droplets is assumed to occur with
respect to the saturated vapor pressure of water if the local temperature is
>-35 degrees C, and with respect to the mixed-phase pseudo-adiabatic
process of Sassen and Dodd (1989)
lower temperatures. Liquid droplets form if the cloud temperature is >-4
degrees C (-10 degrees C) over ocean (land), and ice forms at temperatures <-40 degrees C. At intermediate temperatures either phase may exist, with
increasing probability of ice as temperature decreases.
- The local convective cloud fraction is given by the ratio of convective mass flux to the total atmospheric mass of the grid box (see Convection and Atmospheric Dynamics). Large-scale clouds are predicted from a prognostic cloud water budget equation, where fractional cloudiness is an increasing function of relative humidity above a 60-percent threshold. (Upper-tropospheric convective condensate is also detrained into large-scale anvil cloud.) Cloud top entrainment instability is accounted for using a restrictive instability criterion. Cf. Del Genio et al. (1993)  for further details. See also Radiation for treatment of cloud-radiative interactions.
- Precipitation can result either from large-scale or convective
condensation (see Cloud Formation and Convection); the amount of
condensate is computed from an iterative solution of the Clausius-Clapeyron
equation. For large-scale condensation, the prognostic cloud water is converted
to rainwater by autoconversion and accretion, and into snow by a seeder-feeder
- Evaporation of both the large-scale and convective condensate is modeled, with the residual falling to the surface as rain or snow (see Snow Cover). Evaporation of large-scale precipitation occurs in all unsaturated layers below its origin. The fraction of convective condensate that evaporates below cloud base is equated to the ratio of the convective mass flux to the total air mass of the grid box, while the fraction that evaporates above the cloud base is taken as half this value.
- Each grid box is assigned appropriate fractions of land and ocean, and
part of the ocean fraction may be covered by ice (see Sea Ice). In
addition, permanent ice sheets are specified for Antarctica, Greenland, and
some Arctic islands. Vegetation type is a composite over each grid-box from 32
classifications distinguished in the 1 x 1-degree data of Matthews (1983
- Over land, surface roughness is a fit to the data of Fiedler and Panofsky
 as a function of the standard
deviation of the orography (see Orography). The maximum of this
roughness and that of the local vegetation (including a "zero plane
displacement" value for tall vegetation types--cf. Monteith 1973
 determines the roughness over land. Over sea ice, the roughness length is a uniform 4.3 x 10^-4 m, after Doronin (1969)
. Over ocean, the surface roughness
is a function of the momentum flux and is used to compute the neutral drag
coefficient as well as the Stanton and Dalton numbers (see Surface Fluxes).
- The surface albedo is prescribed for ocean, land ice, sea ice, and for
eight different land surface types after the data of Matthews (1983
 , 1984
). The visible and near infrared albedos are distinguished, and seasonal variations in
the albedo for vegetated surfaces are included. The albedo of snow-covered
ground is the snow-free value modified by factors depending on snow depth, snow
age, and vegetation masking depth, which varies with vegetation type. Ocean
albedo is a function of surface wind speed and solar zenith angle after Cox and
- The spectral dependence of longwave emissivity for deserts is included from data of Hovis and Callahan (1966) , and for snow and ice from data of Wiscombe and Warren (1980) . The emissivity of the ocean is a function of the surface wind speed and of the albedo.
- The absorbed surface solar flux is determined from albedos, and the
surface longwave emission from the Planck function with spatially variable
emissivities (see Surface Characteristics).
- The surface wind stress is expressed as a product of air density, a drag
coefficient, and the surface wind speed and velocity (see Planetary Boundary Layer). The surface drag coefficient is a function of both roughness length
(see Surface Characteristics) and vertical stability.
- Over land, the latent heat flux is computed separately for bare and
vegetated surfaces (see Land Surface Processes), following Penman (1948)
 and Monteith (1981)
. Over ocean and ice surfaces, the latent
heat flux is expressed by a bulk formula that includes the product of the
surface air density, a transfer coefficient, the surface wind speed, and the
difference between the saturation value of mixing ratio at the ground
temperature and the surface atmospheric value (see Planetary Boundary Layer).
- Over land, the sensible heat flux is determined as the residual of the total net heat flux computed by the surface model (see Land Surface Processes) minus the latent heat flux. (The partitioning of the latent and sensible heat fluxes, or Bowen ratio, implies the surface temperature--see Land Surface Processes.) Over ocean and ice surfaces, the sensible heat flux is calculated from a bulk aerodynamic formula as a product of the surface air density and heat capacity, a transfer coefficient, a surface wind speed, and the difference between the skin temperature and the surface air temperature (see Planetary Boundary Layer). (The transfer coefficient is a stability-dependent function of the drag coefficient and is different from that used for the latent heat flux over ocean and ice.)
- Soil temperature is computed by solving a heat diffusion equation in six
layers. The thickness of the top layer varies, but is approximately 0.1 m. The
thicknesses of deeper layers increase geometrically, with the bottom boundary
of the soil column at a nominal bedrock depth of 3.444 m. The upper boundary
condition is the balance of surface energy fluxes (see Surface Fluxes);
at the bottom boundary, zero net heat flux is specified. The thermal
conductivity and heat capacity of the ground vary with snow cover, as well as
soil moisture amount and phase.
- Land-surface hydrology is treated after the physically based model of Abramopoulos et al. (1988) . The scheme includes a vegetation canopy, a composite over each grid box from the vegetation types of Matthews (1983 , 1984 ), that intercepts precipitation and dew. Evaporation from the wet canopy and from bare soil is treated, as well as soil-moisture loss from transpiration according to moisture availability and variable vegetation resistance and root density. Diffusion of moisture is predicted in the six soil layers, accounting for spatially variable composite conductivities and matric potentials that depend on soil type and moisture content. Infiltration of precipitation and snowmelt is explicitly calculated, with surface runoff occurring when the uppermost soil layer is saturated; underground runoff that depends on topographic slope is also included.
Last update April 19, 1996. For further information, contact: Tom Phillips ( email@example.com )