http://www.ecmwf.int/ , 1991 ) and a series of Research Department memoranda from 1988 to 1990 that are summarized in ECMWF Technical Attachment (1993) .  and Simmons and Strüfing (1981) . Horizontal Resolution).  scheme with Asselin (1972)  frequency filter is used for the time integration, with a time step of 30 minutes for dynamics and physics, except for radiation/cloud calculations, which are done once every 3 hours. Orography). Negative values of atmospheric specific humidity (due to truncation errors in the discretized moisture equation) are filled by borrowing moisture from successive vertical levels below until all specific humidity values in the column are nonnegative. Any borrowing from the surface that may be required does not impact the moisture budget there.
- Fourth-order (del^4) horizontal diffusion is applied in spectral space on hybrid vertical surfaces to vorticity, divergence, moisture, and on pressure
surfaces to temperature.
- Second-order vertical diffusion (K-closure) operates above the planetary boundary layer (PBL) only in conditions of static instability. In the PBL, vertical diffusion of momentum, heat, and moisture is proportional to the vertical gradients of the wind, specific humidity, and dry static energy, respectively (see Planetary Boundary Layer). The vertically variable diffusion coefficient depends on stability (bulk Richardson number) as well as the vertical shear of the wind, following standard mixing-length theory.
- Atmospheric radiation is simulated after the method of Morcrette (1989
). For clear-sky conditions, shortwave
radiation is modeled by a two-stream formulation in spectral wavelength
intervals 0.25-0.68 micron and 0.68-4.0 microns using a photon path
distribution method to separate the effects of scattering and absorption
processes. Shortwave absorption by water vapor, ozone, oxygen, carbon monoxide,
methane, and nitrous oxide is included using line parameters of Rothman et al. (1983)
. Rayleigh scattering and Mie
scattering/absorption by five aerosol types are treated by a delta-Eddington
- The clear-sky longwave scheme employs a broad-band flux emissivity method
in six spectral intervals from wavenumbers 0 to 2.6 x 10^5 m^-1,
with continuum absorption by water vapor included from wavenumbers 3.5 x 10^4 to 1.25 x 10^5 m^-1. The temperature/pressure
dependence of longwave gaseous absorption follows Morcrette et al. (1986)
. Aerosol absorption is also modeled by an emissivity formulation.
- Shortwave scattering and absorption by cloud droplets is treated by a delta-Eddington approximation; radiative parameters include optical thickness, single-scattering albedo linked to cloud liquid water path, and prescribed asymmetry factor. Cloud types are distinguished by defining shortwave optical thickness as a function of effective droplet radius. Clouds are treated as graybodies in the longwave, with emissivity depending on cloud liquid water path after Stephens (1978) . Longwave scattering by cloud droplets is neglected, and droplet absorption is modeled by an emissivity formulation from the cloud liquid water path. For purposes of the radiation calculations, clouds of different types are assumed to be randomly overlapped in the vertical, while convective cloud and nonconvective cloud of the same type in adjacent layers are treated as fully overlapped. See also Cloud Formation.
- Cloud formation follows the diagnostic method of Slingo (1987)
. Clouds are of three types: shallow,
midlevel, and high convective cloud; cloud associated with fronts/tropical
disturbances that forms in low, medium, or high vertical layers; and low cloud
associated with temperature inversions.
- The height of midlevel/high convective cloud is determined by the level of
non-buoyancy for moist adiabatic ascent (see Convection), and the cloud
amount (fractional area 0.2-0.8) from the scaled logarithm of the convective
precipitation rate. If this convective cloud forms above 400 hPa and the
fractional area is > 0.4, anvil cirrus cloud also forms. Shallow convective
cloud amount is determined from the difference between the moisture flux at
cloud base and cloud top.
- Frontal cloud is present only when the relative humidity is > 80 percent, the amount being a quadratic function of this humidity excess. Low frontal cloud is absent in regions of grid-scale subsidence, and the amount of low and middle frontal cloud is reduced in dry downdrafts around subgrid-scale convective clouds. In a temperature inversion, low cloud forms if the relative humidity is > 60 percent, the amount depending on this humidity excess and the inversion strength. See also Radiation for treatment of cloud-radiative interactions.
- Freezing/melting processes in convective clouds are not considered.
Conversion from cloud droplets to raindrops is proportional to the cloud liquid
water content. No liquid water is stored in a convective cloud, and once
detrained, it evaporates instantaneously with any portion not moistening the
environment falling out as subgrid-scale convective precipitation. Evaporation
of convective precipitation is parameterized (following Kessler 1969)
 as a function of convective rain intensity
and saturation deficit (difference between saturated specific humidity and that
- Precipitation also results from gridscale condensation when the local specific humidity exceeds the saturated humidity at ambient temperature/pressure; the amount of precipitation depends on the new equilibrium specific humidity resulting from the accompanying latent heat release. Before falling to the surface, gridscale precipitation must saturate all layers below the condensation level by evaporation. See also Convection and Cloud Formation.
- The fractional area of vegetation (undistinguished by type) on each grid
square is determined from Matthews (1983)
1 x 1-degree data, as modified by Wilson and Henderson-Sellers (1985)
- The roughness length is prescribed as 1 x 10^-3 m over sea ice. It
is computed over open ocean from the variable surface wind stress by the method of Charnock (1955)
, but is constrained to
be at least 1.5 x 10^-5 m. Over land, the roughness length is prescribed
as a blended function of local orographic variance, vegetation, and
urbanization (cf. Tibaldi and Geleyn 1981
, Baumgartner et al. 1977
, and Brankovic and Van Maanen 1985
) that is interpolated to the model grid. The logarithm of local
roughness length then is smoothed by the same Gaussian filter used for the
orography (see Orography).
- Annual means of satellite-observed surface albedo (range 0.07 to 0.80)
from data of Preuss and Geleyn (1980)
Geleyn and Preuss (1983)
 are interpolated
to the model grid and smoothed by the same Gaussian filter as for orography
(see Orography). Snow cover alters this background albedo: snow albedo (maximum 0.80) varies depending on depth, masking by vegetation, temperature,
and the presence of ice dew (see Snow Cover). Sea ice albedo is prescribed as 0.55, and ocean albedo as 0.07. Albedos do not depend on solar zenith angle or spectral interval.
- Longwave emissivity is prescribed as 0.996 on all surfaces. Cf. ECMWF Research Department (1991)  for further details.
- Surface solar absorption is determined from surface albedo, and longwave emission from the Planck equation with prescribed constant surface emissivity (see Surface Characteristics).
- Surface eddy fluxes of momentum, heat, and moisture are expressed as bulk formulae, following Monin-Obukhov similarity theory. The near-surface wind,
temperature, and moisture required for the bulk formulae are taken to be the
values at the lowest atmospheric level (at about 996 hPa for a surface pressure
of 1000 hPa). The drag and transfer coefficients are functions of stability
(bulk Richardson number) and roughness length (see Surface Characteristics), following the method of Louis (1979)
 and Louis et al. (1981)
, but with modifications by Miller et al. (1992)
 for calm conditions over the
oceans. The transfer coefficient for moisture is the same as that for heat.
- The surface specific humidity over the ocean and snow-covered areas is the saturated value for the local surface temperature and pressure; over bare soil it is the product of the local saturated value and the surface relative humidity. The moisture flux over vegetation is given by the vertical difference of the specific humidity at the lowest atmospheric level and the saturated value at the surface temperature and pressure, all multiplied by an evapotranspiration efficiency factor beta (cf. Budyko 1974) . This efficiency is the inverse sum of the aerodynamic resistance (surface drag) and the stomatal resistance, which depends on radiation stress, canopy moisture, and soil moisture stress in the vegetation root zone (cf. Sellers et al. 1986 , Blondin 1989 , and Blondin and Böttger 1987). See also Land Surface Processes.
- Soil temperature and moisture are predicted in two layers of thicknesses 0.07 m and 0.42 m that overlie a deep layer (of thickness 0.42 m) in which temperature and moisture are prescribed from monthly climatologies (cf. Blondin and Böttger 1987
, Brankovic and Van Maanen 1985
, and Mintz and Serafini 1981
). The upper boundary condition for the soil heat diffusion is the net surface energy balance (see
Surface Fluxes). Soil heat capacity and diffusivity are functions of snow cover, and the diffusivity is also a function of vegetation canopy area.
- The vegetation canopy also intercepts a fraction of the total precipitation (which is subject to potential evaporation) that would otherwise infiltrate the soil. The infiltrated soil moisture obeys a simple diffusion equation modified by gravitational effects (Darcy's Law), and is also affected by evaporation from the bare soil portion of each grid box as well as evapotranspiration by vegetation (see Surface Fluxes). Runoff occurs if the maximum soil moisture capacity of the surface layer (0.02 m) or middle layer (0.12 m) is exceeded; the fraction of infiltrated moisture associated with the surface runoff due to sloping terrain is also simulated using orographic variance data (see Orography).
Last update April 19, 1996. For further information, contact: Tom Phillips (firstname.lastname@example.org )