http://www.cnrm.meteo.fr/  and Geleyn et al. 1988 ), but with adaptations made for climate simulation. , Cariolle and Déqué (1986) , Cariolle et al. (1990) , Clary (1987) , Geleyn (1987) , Geleyn and Preuss (1983) , Ritter and Geleyn (1992) , and Royer et al. (1990) . The surface schemes follow the methods of Bhumralkar (1975)  and Deardorff (1977 , 1978 ). ). Above 165 hPa all levels are in constant pressure coordinates (cf. Cariolle et al. 1990 ). Vertical Representation). For a surface pressure of 1000 hPa, 4 levels are below 800 hPa and 20 levels are above 200 hPa (cf. Cariolle et al. 1990 ). Radiation). The vorticity, specific humidity, and prognostic ozone mixing ratio are integrated by a leapfrog scheme that is dampled with a weak Asselin (1972)  frequency filter. The soil temperature and moisture are integrated explicitly, while the tendencies due to horizontal diffusion and the linear part of vertical diffusion are calculated implicitly.Orography). Filling of negative values of atmospheric moisture follows the global horizontal borrowing scheme of Royer (1986) , which ensures conservation of total moisture in each of the model's atmospheric layers. Chemistry ).
- Linear fourth-order (del^4) horizontal diffusion is applied on hybrid sigma-pressure surfaces to vorticity, divergence, temperature, and specific humidity. The diffusion coefficient is a prescribed function of height.
- Stability-dependent vertical diffusion of momentum, heat, and moisture after Louis et al. (1981)  is applied at levels up to 25 hPa. The diffusion coefficients depend on the bulk Richardson number and, following standard mixing-length theory, the vertical wind shear.
- Radiation is modeled by a simplified version of the scheme of Ritter and Geleyn (1992)
. All flux calculations follow the delta-two-stream approach (cf. Zdunkowski et al. 1980
) applied in one shortwave interval between 0.25 and 4.64 microns, and in one longwave interval between 4.64 and 104.5 microns. Differential fluxes are calculated by subdividing the atmosphere into layers of constant optical properties (optical depth, single-scattering albedo, asymmetry factor) with linear relationships assumed (cf. Geleyn and Hollingsworth 1979
). Optical properties are specified after Rothman et al. (1983)
 for gases, after Tanré et al. (1983)
 for five types of aerosol, and after Stephens (1979)
 for water clouds with eight different droplet-size distributions that are related to diagnostic cloud liquid water content (LWC) following Betts and Harshvardhan (1987)
. Optical properties of ice clouds are not specifically included.
- Gaseous optical depths are first evaluated with band-model calculations along idealized photon paths, and then are reused in multiple scattering calculations for both shortwave and longwave fluxes in a manner similar to that of Geleyn and Hollingsworth (1979)
. Continuum absorption is treated by including a special term in the equivalent width for a modified Malkmus (1967)
- Partial cloudiness in each layer is treated by specifying separate sets of optical properties and fluxes for the cloudy and cloud-free portions. Cloud layers are assumed to overlap randomly in the vertical. See also Cloud Formation.
- The effects of sub-gridscale cumulus convection on the gridscale heat and water budgets are represented by the bulk mass flux scheme of Bougeault (1985)
. The cloud profile is determined from a moist adiabat, with incorporation of entrainment of environmental air. The scheme also predicts the convective mass inside the cloud, assuming the vertical mass flux profile varies as the square root of the moist static energy excess (with a proportionality coefficient determined after Kuo (1965)
 from the large-scale moisture convergence and turbulent water transport at the cloud base). Convective detrainment is proportional to the excess of cloud temperature and moisture over their environmental values (the detrainment coefficient being determined from conservation of moist static energy in the column). The convective precipitation rate is given by the difference between the total moisture convergence and the environmental moistening due to detrainment, under the assumption of no evaporation of precipitation below the cloud base (see Precipitation).
- Following Geleyn (1987) , shallow convection is accounted for by modifying the bulk Richardson number to include the gradient of specific humidity deficit in computing vertical stability.
- The surface roughness length over the oceans is prognostically determined from the wind stress after the Charnock (1955)
 relation with a coefficient of 0.19. The roughness length over ice surfaces is specified as a constant 0.001 m. Over land, the surface roughness is a function of the variance of the orography and vegetation cover that is prescribed from data of Baumgartner et al. (1977)
. The roughness length of land and ice surfaces also varies with snow depth.
- Surface albedos are prescribed from monthly satellite data of Geleyn and Preuss (1983)
. The albedos are also a function of solar zenith angle, but not spectral interval. Prognostic snow cover modifies the albedo of land and ice surfaces according to the depth of snow.
- Longwave emissivity is specified from CLIMAP (1981) data for all surfaces.
- The surface solar absorption is determined from surface albedos, and longwave emission from the Planck equation with prescribed emissivities (see Surface Characteristics).
- In the lowest atmospheric layer, turbulent eddy fluxes of momentum, heat, and moisture follow Monin-Obukov theory, and are expressed as bulk formulae multiplied by drag or transfer coefficients that depend on stability (bulk Richardson number) and surface roughness length (see Surface Characteristics) after the formulation of Louis et al. (1981)
. The surface wind, temperature, and humidity required for the bulk formulae are taken to be the values at the lowest atmospheric level (at sigma = 0.99527, or about 40 m above the ground), and the same transfer coefficient is used for the heat and moisture fluxes.
- The effective ground value of humidity also required for determination of the surface moisture flux is obtained as a fraction alpha of the saturated humidity at the ground temperature; alpha is unity over oceans, snow, and ice, but it is a function of the surface soil moisture over land (see Land Surface Processes).
- Above the surface layer, turbulent eddy fluxes are represented as stability-dependent diffusive processes following the method of Louis et al. (1981) --see Diffusion.
- Soil temperature is prognostically determined in two layers after the method of Bhumralkar (1975)
 with time constants of 1 day and 5 days, respectively. Relaxation (with time constant 20 days) toward a climatological deep soil temperature is also imposed, while the boundary condition at the soil-atmosphere interface is the net balance of the surface energy fluxes (see Surface Fluxes). Soil heat capacity and conductivity are spatially invariant and are not affected by snow cover, but their values are different from those used for sea ice.
- Soil moisture is prognostically determined by the force-restore method of Deardorff (1977)  in two layers: a shallow surface reservoir of capacity 0.02 m to capture diurnal variations, and an underlying reservoir of 0.10 m capacity to simulate the effects of longer-term variations. Both precipitation and snowmelt contribute to soil moisture, while evaporation depletes it. The fraction alpha of ground saturation humidity that is available for evaporation (see Surface Fluxes) is determined from an empirical function of the ratio of soil moisture in the shallow upper layer to its saturation value. Runoff occurs if soil moisture exceeds the maximum capacity for each layer.
Last update July 2, 1996. For further information, contact: Tom Phillips ( firstname.lastname@example.org )