and Boer et al. (1992)  describe the features and equilibrium climate of the CCC model, and its simulation of greenhouse gas-induced climate change. Some properties remain the same as those of the first-generation CCC model documented by Boer et al. (1984a , 1984b ). ).  frequency filter is used. The time step is 20 minutes for dynamics and physics, except for full calculations of radiative fluxes and heating rates. Shortwave radiation is calculated every 3 hours, and longwave radiation every 6 hours, with interpolated values used at intermediate time steps (cf. McFarlane et al. 1992) . Orography). Negative values of atmospheric specific humidity (which arise because of numerical truncation errors in the discretized moisture equation) are filled in a two-stage process. First, all negative values of specific humidity are made slightly positive by borrowing moisture (where possible) from other layers in the same column. If column moisture is insufficient, a nominal minimum bound is imposed, the moisture deficit is accumulated over all atmospheric points, and the global specific humidity is reduced proportionally. This second stage is carried out in the spectral domain (cf. McFarlane et al. 1992) .
- Horizontal diffusion follows the scale-dependent eddy viscosity formulation of Leith (1971)
 as described by Boer et al. (1984a)
. Diffusion is applied to spectral modes of divergence, vorticity, temperature, and moisture, with total wavenumbers >18 on hybrid vertical surfaces.
- Second-order vertical diffusion of momentum, moisture, and heat operates above the surface. The vertically varying diffusivity depends on stability (gradient Richardson number) and the vertical shear of the wind, following standard mixing-length theory. Diffusivity for moisture is taken to be the same as that for heat. Cf. McFarlane et al. (1992)  for details. See also Surface Fluxes.
- Shortwave radiation is modeled after an updated scheme of Fouquart and Bonnel (1980)
. Upward/downward shortwave irradiance profiles are evaluated in two stages. First, a mean photon optical path is calculated for a scattering atmosphere including clouds, aerosols, and gases. The reflectance and transmittance of these elements are calculated by, respectively, the delta-Eddington method (cf. Joseph et al. 1976
) and by a simplified two-stream approximation. The scheme evaluates upward/downward shortwave fluxes for two reference cases: a conservative atmosphere and a first-guess absorbing atmosphere; the mean optical path is then computed for each absorbing gas from the logarithm of the ratio of these reference fluxes. In the second stage, final upward/downward fluxes are computed for visible (0.30-0.68 micron) and near-infrared (0.68-4.0 microns) spectral intervals using more exact gas transmittances (cf. Rothman 1981
), and with adjustments made for the presence of clouds. The asymmetry factor is prescribed for clouds, and the optical depth and single-scattering albedo are functions of cloud liquid water content (cf. Betts and Harshvardhan 1987
) and ice crystal content (cf. Heymsfield 1977
- Longwave radiation is modeled in six spectral intervals between wavenumbers 0 to 2.82 x 10^5 m^-1 after the method of Morcrette (1984 , 1990 , 1991 ), which corrects for the temperature/pressure dependence of longwave absorption by gases and aerosols. Longwave absorption in the water vapor continuum follows Clough et al. (1980) . Clouds are treated as graybodies in the longwave, with emissivity depending on optical depth (cf. Platt and Harshvardhan 1988 ), and with longwave scattering by cloud droplets neglected. The effects of cloud overlap in the longwave are treated following a modified scheme of Washington and Williamson (1977) : upward/downward irradiances are computed for clear-sky and overcast conditions, and final irradiances are determined from a linear combination of these extreme cases weighted by the actual partial cloudiness in each vertical layer. For purposes of the radiation calculations, clouds occupying adjacent layers are assumed to be fully overlapped, but to be randomly overlapped otherwise. Cf. McFarlane et al. (1992)  for further details.
- Local roughness lengths are derived (cf. Boer et al. 1984a)
 from prescribed neutral surface drag coefficients (see Surface Fluxes).
- The 1 x 1-degree Wilson and Henderson-Sellers (1985)
 data on 24 soil/vegetation types are used to determine the most frequently occurring primary and secondary types (weighted 2/3 vs 1/3) for each grid box. Averaged local soil/vegetation parameters include field capacity and slope factor for predicting soil moisture (see Land Surface Processes), and snow masking depth for the surface albedo (see below). These are obtained by table look-up based on primary/secondary vegetation types.
- Over bare dry land, the surface background albedo is determined from a weighted average for each of 24 vegetation types in the visible (0.30-0.68 micron) and near-infrared (0.68-4.0 microns) spectral bands; for wet soil, albedos are reduced up to 0.07. For vegetated surfaces, albedos are determined from a 2/3 vs 1/3 weighting of albedos of the local primary/secondary vegetation types. The local land albedo also depends on the fractional snow cover and its age (fractional coverage of a grid box is given by the ratio of the snow depth to the specified local masking depth); the resulting albedo is a linear weighted combination of snow-covered and snow-free albedos. Over the oceans, latitude-dependent albedos which range between 0.06 and 0.17 are specified independent of spectral interval. The background albedos for sea ice are 0.55 in the near-infrared and 0.75 in the visible; these values are modified by snow cover, puddling effects of melting ice (a function of mean surface temperature), and by the fraction of ice leads (a specified function of ice mass).
- The longwave emissivity is prescribed as unity (i.e., blackbody emission is assumed) for all surfaces. Cf. McFarlane et al. (1992)  for further details.
- The surface solar absorption is determined from surface albedos, and the longwave emission from the Planck equation with prescribed emissivity of 1.0 (see Surface Characteristics).
- The surface turbulent eddy fluxes of momentum, heat, and moisture are expressed as bulk formulae following Monin-Obukhov similarity theory. The momentum flux is a product of a neutral drag coefficient, the surface wind speed and wind vector (see Planetary Boundary Layer), and a function of stability (bulk Richardson number). Drag coefficients over land and ice are prescribed after Cressman (1960)
, but over the oceans they are a function of surface wind speed (cf. Smith 1980
). The flux of sensible heat is a product of a neutral transfer coefficient, the surface wind speed, the difference in temperatures between the surface and that of the lowest atmospheric level, and the same stability function as for the momentum flux. (The transfer coefficient has the same value as the drag coefficient over land and ice, but is not a function of surface wind over the oceans.)
- The flux of surface moisture is a product of the same transfer coefficient and stability function as for sensible heat, an evapotranspiration efficiency (beta) factor, and the difference between the specific humidity at the lowest atmospheric level (see Planetary Boundary Layer) and the saturation specific humidity at the temperature/pressure of the surface. Over the oceans and sea ice, beta is prescribed as 1; over snow, it is the lesser of 1 or a function of the ratio of the snow mass to a critical value (10 kg/m^2). Over land, beta depends on spatially varying soil moisture and field capacities (see Land Surface Processes), and on slope factors for primary/secondary vegetation and soil types (see Surface Characteristics). For grid boxes with fractional snow coverage, a composite beta is obtained from a weighted linear combination of snow-free and snow-covered values. Cf. Boer et al. (1984a)  and McFarlane et al. (1992)  for further details.
- Soil heat storage is determined as a residual of the surface heat fluxes and of the heat source/sink of freezing/melting snow cover and soil ice (see below). Soil temperature is computed from this heat storage in a single layer, following the method of Deardorff (1978)
 which accounts for both diurnal and longer-period forcing. The composite conductivity/heat capacity of the soil in each grid box is computed as a function of soil type, soil moisture, and snow cover.
- Soil moisture is predicted by a single-layer "bucket" model with field capacity and slope factors varying by primary/secondary soil and vegetation types for each grid box (see Surface Characteristics). Soil moisture budgets include both liquid and frozen water. The effective local moisture capacity is given by the product of field capacity and slope factor, with evapotranspiration efficiency beta a function of the ratio of soil moisture to the local effective moisture capacity (see Surface Fluxes). Runoff occurs implicitly if this ratio exceeds 1 (which is more likely the higher the local slope factor and the lower the local field capacity). Cf. McFarlane et al. (1992)  and Boer et al. (1984a)  for further details.
Last update April 19, 1996. For further information, contact: Tom Phillips ( email@example.com )