http://www.dkrz.de/.  The results of changes in model resolution and physics are described by Roeckner et al. (1992) .  and Simmons and Strüfing (1981) .  and Robert (1981 , 1982 ) is applied with an Asselin (1972)  frequency filter. The time step is 24 minutes for dynamics and physics, except for radiation which is calculated at 2-hour intervals. Orography). Negative moisture values arising from truncation of the spherical harmonic basis functions are filled for purposes of the radiation calculations, but negative moisture values are tolerated in transport algorithms (advection, convection, and diffusion). Negative cloud water values are avoided by invoking a suitable condensation term (see Cloud Formation).
- Scale-selective fourth-order (del^4) horizontal diffusion is applied to
all atmospheric prognostic variables for total spectral wave numbers >15
after the method of Laursen and Eliasen (1989)
. To avoid unrealistic results near mountains,
horizontal diffusion operates only on the deviation of the temperature field
from that of a standard atmosphere. The horizontal diffusion coefficient varies
for different variables and vertical levels, and is selected to make the slope
of the atmospheric spectral kinetic energy approximate that observed.
- Vertical diffusion operates above the planetary boundary layer (PBL) only in conditions of static instability. In the PBL, vertical diffusion of momentum, heat, cloud water, and moisture is proportional to the vertical gradient of the appropriate field. The vertically variable diffusion coefficient depends on stability (expressed as a bulk Richardson number) and the vertical shear of the u-wind, following standard mixing-length theory. See also Planetary Boundary Layer and Surface Fluxes.
- The radiation schemes follow Hense et al. (1982)
, Eickerling (1989)
, and Rockel et al. (1991)
. Radiative transfer equations are based on
the two-stream approximation of Kerschgens et al. (1978)
 and Zdunkowski et al. (1980)
, and are solved in 4 shortwave
spectral intervals (with boundaries at 0.215, 0.685, 0.891, 1.273, and 3.580
microns) and in 6 longwave spectral intervals (with boundaries at 3.96, 7.98,
8.89, 10.15, 11.76, 20.10, and 100 microns).
- Shortwave equations are expressed in terms of optical depth,
single-scattering albedo, diffuse and direct backscattering parameters, and
diffusivity factor; longwave equations (with scattering effects neglected) are
expressed in terms of the Planck function, optical depth, and diffusivity
factor. Absorbers determining shortwave and longwave optical depths include
ozone, carbon dioxide, and water vapor (with continuum absorption included).
Optical depths for diffuse shortwave and longwave absorption are calculated
using coefficients derived from "exact" reference models. Effects of pressure
broadening on longwave absorption are also treated.
- In the shortwave, optical depths for Rayleigh scattering are determined
from the molecular cross section for each gas, and those for absorption and Mie
scattering by ocean, desert, and urban aerosols are from data of Shettle and
. Single scattering albedo is
derived from the optical depths for diffuse shortwave scattering/absorption. At
a given vertical level, the total optical depth for direct shortwave radiation
(which is dependent on solar zenith angle) is obtained from linear
superposition of optical depths for scattering/absorption by gases and aerosols
summed over all the levels above.
- The shortwave optical depth for clouds is parameterized after the method of Stephens (1978) , and the single-scattering albedo and backscattering parameter follow Kerschgens et al. (1978) . Longwave emissivity is an exponential function of geometrical cloud thickness, prognostic cloud water content, and a mass absorption coefficient, following Stephens (1978). For purposes of the radiation calculations, clouds in contiguous vertical layers are treated as fully overlapped, and as randomly overlapped otherwise. Cf. DKRZ (1992)  for further details. See also Cloud Formation.
- The (stratiform) cloud-formation scheme is based on prognostic cloud
water, following Sundqvist (1978)
Roeckner and Schlese (1985)
, and Roeckner
et al. (1991)
. Subgrid-scale condensation
and cloud formation in a fraction c of each grid box are governed by transport
equations for water vapor and cloud water. The threshold relative humidity of
the cloud-free fraction (1 - c) is prescribed as a function of height and
stability: it is a minimum of 50 percent at tropopause level when penetrative
convection occurs (cf. Xu and Krueger 1991
); otherwise the threshold humidity decreases
linearly from 99 percent at the surface to 85 percent at the top of the PBL
(see Planetary Boundary Layer), above which it remains constant.
- Cloud droplets grow by condensation if the grid-mean relative humidity
exceeds this threshold relative humidity or if the relative humidity in the c
fraction of the grid box exceeds 100 percent. The condensation rate depends on
the moisture convergence into the grid box, with a fraction c of the
convergence producing more cloud, and the fraction (1 - c) increasing the
relative humidity of the cloud-free part of the grid box.
- The cloud water in the cloud-free fraction (1 - c) that increases (decreases) as a result of advective/diffusive transports into the grid cell or through numerical effects (e.g., spectral truncation) is assumed to evaporate (condense) instantaneously; explicit filling of negative cloud water values is therefore unnecessary (see Smoothing/Filling). Convective cloud water is not advected (rather, there is instantaneous precipitation and/or evaporation to the environment--see Precipitation). Cf. DKRZ (1992)  for further details. See also Radiation for treatment of cloud-radiative interactions.
- For convective precipitation, freezing and melting processes are not considered. No cloud water is stored in convective cloud (see Cloud Formation); once detrained, it evaporates instantaneously, with any portion not moistening the environment falling out as precipitation. Conversion from convective cloud droplets to rain/snow is proportional to the product of cloud water content and upward convective mass flux at cloud base, weighted by an empirical function of height (cf. Yanai et al. 1973)
. Convective snow forms if the temperature of
the cloud layer is <0 degrees C. Following Kessler (1969)
, evaporation of convective precipitation is
assumed to be proportional to the saturation deficit and the rainfall
- For stratiform mixed-phase precipitation formation (i.e., in a temperature range from 0 to -40 degrees C), the ice and liquid phases are treated independently. Growth of cloud droplets (see Cloud Formation) to precipitating raindrops occurs by autoconversion, following the exponential relationship of Sundqvist (1978) , and by collisions with larger drops, following the parameterization of Smith (1990) . Partitioning of cloud liquid vs ice is according to the temperature-dependent relation of Matveev (1984) , and the loss of ice crystals by sedimentation follows Heymsfield (1977) . Evaporation of stratiform precipitation in a layer below cloud is proportional to the saturation deficit, but cannot exceed the precipitation flux at the layer top. Stratiform snow forms if the cloud layer temperature is <0 degrees C. Falling convective and stratiform snow melts if the temperature of a layer is >2 degrees C. Cf. DKRZ (1992)  for further details. See also Snow Cover.
- The fraction of each grid box covered by vegetation is determined from
 1 x 1-degree data, but is
reduced when soil moisture available in the root zone becomes less than 40
percent of field capacity (0.20 m)--see Land Surface Processes.
- The surface roughness length is prescribed as a uniform 1 x 10^-3 meter
over sea ice; it is computed prognostically over open ocean from the surface
wind stress by the method of Charnock (1955)
, but is constrained to be a minimum of 1.5 x 10^-5 m. Over land, the roughness length is geographically prescribed as a
blended function of the local orographic variance (cf. Tibaldi and Geleyn
) and of the vegetation (cf.
Baumgartner et al. 1977
) that is
interpolated to the model grid; the logarithm of the local roughness length is
then smoothed by the same Gaussian filter as is used for orography (see
- The annual-mean surface albedo is obtained from satellite data of Geleyn and Preuss (1983)
. Over land, this
background albedo is altered by snow cover as a linear function of the ratio of
the water-equivalent snow depth to a critical value (0.01 m). Albedos of snow
(range 0.30 to 0.80), sea ice (range 0.50 to 0.75), and continental ice (range
0.6 to 0.8) vary as a function of surface temperature and forested area, as
given by Robock (1980)
 and Kukla and Robinson (1980)
. The albedo of ocean is a
constant 0.065 for diffuse radiation, while that for the direct beam depends on
solar zenith angle, but never exceeds 0.15.
- Longwave emissivity is prescribed as 0.996 for all surfaces. Cf. DKRZ 1992  for further details.
- Surface solar absorption is determined from the surface albedo, and
longwave emission from the Planck equation with prescribed uniform surface emissivity (see Surface Characteristics).
- Surface turbulent eddy fluxes of momentum, dry static energy (sensible
heat), cloud water, and moisture are simulated as stability-dependent bulk
formulae, following Monin-Obukhov similarity theory. The required near-surface
values of wind, temperature, cloud water, and humidity are taken to be those at
the lowest atmospheric level (sigma = 0.996). (At the surface, cloud water is
assumed to be zero.) Surface drag and transfer coefficients in the bulk
formulae are functions of stability and roughness length (see Surface Characteristics), following Louis (1979)
 and Louis et al. (1981)
, but with modifications by Miller et al. (1992)
 for calm conditions over the
oceans. The stability criterion is the moist bulk Richardson number, which
includes the impact of cloud processes on buoyancy (cf. Brinkop 1992)
- The surface moisture flux depends on the surface specific humidity; over ocean, snow, ice, and wet vegetation fractions of each grid box, this is taken as the saturated humidity at the surface temperature and pressure (i.e., potential evaporation is assumed). Over the bare soil fraction, the surface specific humidity is the product of relative humidity (that is a function of soil moisture--see Land Surface Processes) and the saturated specific humidity. For a dry vegetation canopy, the potential evaporation is reduced by an evapotranspiration efficiency factor beta that is the inverse sum of aerodynamic resistance and stomatal resistance; the latter 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 ).
- Soil temperature is determined after Warrilow et al. (1986)
 from the heat conduction in 5 layers
(proceeding downward, layer thicknesses are 0.065, 0.254, 0.913, 2.902, and
5.70 m), with net surface heat fluxes (see Surface Fluxes) as the upper
boundary condition and zero heat flux as the lower boundary condition at 10 m depth.
- Snow pack temperature is also computed from the soil heat equation using heat diffusivity/capacity for ice in regions of permanent continental ice, and for bare soil where water-equivalent snow depth is <0.025 m. For snow of greater depth, the temperature of the middle of the snow pack is solved from an auxiliary heat conduction equation (cf. Bauer et al. 1985
). The temperature at the upper surface is
determined by extrapolation, but it is constrained not to exceed the snowmelt
temperature of 0 degrees C.
- There are separate prognostic moisture budgets for snow, vegetation
canopy, and soil reservoirs. Snow cover is augmented by snowfall and is
depleted by sublimation and melting (see Snow Cover). Snow melts
(augmenting soil moisture) if the temperatures of the snow pack and of the
uppermost soil layer exceed 0 degrees C. The canopy intercepts precipitation
and snow (proportional to the vegetated fraction of a grid box), which is then
subject to immediate evaporation or melting.
- Soil moisture is represented as a single-layer "bucket" model (cf. Manabe 1969 ) with field capacity 0.20 m that is modified to account for vegetative and orographic effects. Direct evaporation of soil moisture from bare soil and from the wet vegetation canopy, as well as evapotranspiration via root uptake, are modeled (see Surface Fluxes). Surface runoff includes effects of subgrid-scale variations of field capacity related to the orographic variance (see Orography); in addition, wherever the soil is frozen, moisture contributes to surface runoff instead of soil moisture. Deep runoff due to drainage processes also occurs independently of infiltration if the soil moisture is between 5 and 9 percent of field capacity (slow drainage), or is larger than 90 percent of field capacity (fast drainage). Cf. Dümenil and Todini (1992)  for further details.
Last update October 22, 1996. For further information, contact: Tom Phillips ( email@example.com )