- Second-order (del^2) horizontal diffusion is applied to spectral
vorticity, divergence, temperature, and specific humidity on constant-sigma
surfaces. All diffusivity coefficients are 10^5 m^2/s.
- Vertical diffusion is represented by the turbulence kinetic energy (TKE) closure scheme described by Benoit et al. (1989)  and Mailhot and Benoit (1982) . Prognostically determined TKE is produced by shear and buoyancy, and is depleted by viscous dissipation. Vertical (but not horizontal) transport of TKE is also modeled, and a minimum background TKE (10^-4 m^2/s^2) is always present. Diffusion coefficients for momentum and heat/moisture are determined from the current value of TKE and from a locally defined stability-dependent turbulence mixing length. See also Planetary Boundary Layer and Surface Fluxes.
- The outputs of the shortwave and longwave radiation schemes are the fluxes
at each level and the heating rates in each layer. Fluxes also interact with
the model at the surface, where the energy balance determines the surface
temperature (see Surface Fluxes and Land Surface Processes).
- The shortwave parameterization after Fouquart and Bonnel (1980)
 considers the effects of carbon dioxide and
ozone (see Chemistry), water vapor, clouds, and liquid water. When
clouds are present, liquid water is diagnosed from atmospheric temperature: a
fraction of the maximum theoretical liquid water concentration on a wet adiabat
is assumed, following Betts and Harshvardhan (1987)
. The entire visible spectrum is treated as a single interval.
- The longwave parameterizations after Garand (1983)  and Garand and Mailhot (1990)  include the same constituents as in the shortwave scheme, except that liquid water is not interactive. The frequency integration is carried out over 4 spectral intervals: the carbon dioxide 15-micron band divided into center and wing components, the 9.3-micron ozone band, and the rest of the infrared spectrum, including absorption bands for water vapor and continuum absorption. (The frequency integration is precomputed for different temperatures and absorber amounts, with the results stored in look-up tables.) All clouds are assumed to behave as blackbodies (emissivity of 1.0) and to be fully overlapped in the vertical. See also Cloud Formation.
- A modified Kuo (1974)
 scheme is used
to parameterize the effects of deep precipitation-forming convection. When the
large-scale vertical motion at the top of the planetary boundary layer (PBL) is
upward and the free atmosphere above the PBL top (at about 900 hPa) is
conditionally unstable, the assumed convective activity depends on the net
moisture accession in the atmospheric column that is provided by both surface evaporation and large-scale moisture convergence. This moisture is partitioned between a fraction b which moistens the environment, and the remainder (1 - b) which contributes to the latent heating (precipitation) rate. Following Anthes (1977)
, the moistening parameter b is
determined as a cubic function of the ratio of the mean relative humidity of
the cloud layer to a prescribed critical relative humidity threshold value; if
the cloud relative humidity is less than the threshold, b is set to unity (no
heating of the environment). The vertical distribution of the heating or
moistening is according to differences between mean-cloud and large-scale
profiles of temperature and moisture. The mean-cloud profiles are computed from
the parcel method slightly modified by an entrainment height of 20 km.
- Shallow convection is parameterized by a generalization of the PBL turbulence formulation (see Diffusion) to include the case of partially saturated air in the conditionally unstable layer above an unstable boundary layer. First, a convective cloud fraction is diagnosed from a relation based on the Bjerknes slice method; then the buoyancy and all the turbulent fluxes are calculated, assuming condensation occurs in that layer fraction. The main effect of the parameterization is to enhance the vertical moisture transport in the absence of large-scale moisture convergence. See also Planetary Boundary Layer.
- Over land, surface roughness lengths that are functions of orography and
vegetation are specified after Louis (1984)
. Over sea ice, the prescribed
roughness length ranges between 1.5 x 10^-5 and 5 x 10^-3 m. Over ocean, the
roughness length is treated as a function of the surface wind stress after the
method of Charnock (1955)
- Surface albedos do not depend on solar zenith angle or spectral interval.
On land, the surface albedo is specified from annual background values
(provided by the Canadian Climate Centre) modulated with the monthly ice
(albedo 0.70) and snow (albedo 0.80) climatology (see Snow Cover). The
albedo of ocean points is specified to be a uniform 0.07.
- The surface longwave emissivity is prescribed as 0.95 over land and sea ice and as 1.0 (blackbody emission) over ocean.
- The surface solar absorption is determined from surface albedos, and
longwave emission from the Planck equation with prescribed surface
emissivities (see Surface Characteristics).
- Following Monin-Obukhov similarity theory, the surface turbulent momentum,
sensible heat, and moisture fluxes are expressed as bulk formulae, with drag
and transfer coefficients that are functions of surface roughness length (see
Surface Characteristics) and of stability (expressed as a bulk
Richardson number computed between level sigma = 0.99 and the surface). The
same transfer coefficient is used for the heat and moisture fluxes.
- The flux of surface moisture also depends on an evapotranspiration
efficiency factor b that is unity over oceans, sea ice, and snow, but that is
prescribed as a monthly wetness fraction over land (see Land Surface Processes).
- Above the surface layer, the turbulence closure scheme after Mailhot and Benoit (1982)  and Benoit et al. (1989)  is used to determine momentum, heat, and moisture fluxes. See also Diffusion and Planetary Boundary Layer.
- The surface temperature of soil (and of sea ice) is computed by the
force-restore method of Deardorff (1978)
. The upper boundary condition is a net
balance of surface energy fluxes (see Surface Fluxes), and monthly deep
temperatures are prescribed as a lower boundary condition. The thermodynamic
properties are those characteristic of clay soil, and the depth of the soil
layer is taken to be that of the penetration of the diurnal heat wave. The same
properties are also used for predicting the temperature of sea ice (see Sea Ice).
- Soil moisture (expressed as a wetness fraction) is prescribed from monthly climatologies of Louis (1981) . Precipitation and snowmelt therefore do not influence soil moisture, and runoff is not accounted for; however, the prescribed wetness fraction does affect surface evaporation (see Surface Fluxes). Cf. Benoit et al. (1989)  for further details.
Last update April 19, 1996. For further information, contact: Tom Phillips ( firstname.lastname@example.org )