the PMIP models (Bonfils et al. 1998)
PMIP Documentation for GFDL
Geophysical Fluid Dynamics Laboratory
: Model GFDL CDG (R30 L20) 1997
Anthony J. Broccoli, Geophysical Fluid Dynamics Laboratory/NOAA, Princeton
University, P.O. Box 308, Princeton, New Jersey 08540; Phone: +1-609-452-6671;
Fax: +1-609-987-5063; e-mail: email@example.com
World Wide Web URL: http://www.gfdl.noaa.gov/~ajb/
GFDL CDG (R30 L20) 1997
Model Identification for PMIP
0fix, 6fix, 0cal, 21cal
Number of days in each month: 31 28 31 30 31 30 31 31 30 31 30 31
One of several versions of global spectral models in use at the Geophysical
Fluid Dynamics Laboratory, ithis version of the GFDL model is applied primarily
to climate studies. In its treatment of atmospheric dynamics, the model
is similar to the GFDL Dynamical Extended-Range Forecasting (DERF) model
(cf. Gordon and Stern 1982 and Miyakoda and Sirutis 1986 ), but it displays
a number of differences in numerical features (e.g., use of rhomboidal
rather than triangular spectral truncation and a somewhat higher vertical
resolution), as well as in some model parameterizations (e.g., radiation,
vertical diffusion, land surface submodel, sea ice submodel).
Key documentation of dynamical features is given by Gordon and Stern (1982)
and Manabe and Hahn (1981) . Physical parameterizations are described by
Manabe (1969) , Holloway and Manabe (1971) , Manabe and Holloway (1975)
, Manabe et al. (1965) , Broccoli and Manabe (1992) , Wetherald and Manabe
(1988) , and Wetherald et al. (1991) .
Spectral (spherical harmonic basis functions) with transformation to a
Gaussian grid for calculation of nonlinear quantities and some physics.
Spectral rhomboidal 30 (R30), roughly equivalent to 2.25 x 3.75 degrees
dim_longitude*dim_latitude : 96*80
Surface to about 10 hPa. For a surface pressure of 1000 hPa, the lowest
atmospheric level is at about 997 hPa.
Finite-difference sigma coordinates.
!The model uses asigma-coordinate in the vertical with 20 levels:0.0091,
0.0308, 0.0600, 0.0976, 0.1438, 0.1982, 0.2600, 0.3281, 0.4008, 0.4765,
0.5533, 0.6291, 0.7020, 0.7701, 0.8315, 0.8847, 0.9284, 0.9618, 0.9845,
0.9966. For a surface pressure of 1000 hPa, six levels are below 800 hPa
and six levels are above 200 hPa.
The PMIP simulations were run on a Cray C90 computer using a single processor
in a UNICOS operating environment.
For the PMIP simulatons, about 1.4 minutes of Cray C90 computation time
per simulated day.
For the PMIP simulations, the model atmosphere is initialized from an idealized,
isothermal, dry, motionless state. Soil moisture is initialized at saturation,
and snow cover is absent.
Time Integration Scheme(s)
A leapfrog semi-implicit scheme similar to that of Bourke (1974) with an
Asselin (1972) frequency filter is used for time integration. The time
step is 13 minutes and 20 seconds for dynamics and physics, except for
full calculations of all radiative fluxes, which are done once every 24
Orography is smoothed (see Orography). Negative moisture values (that arise
because of spectral truncation) are filled by borrowing from nearest neighbors
in the vertical, and horizontally in the east-west direction only.
For the PMIP simulations, the model history is written once every 24 hours.
Primitive-equation dynamics are expressed in terms of vorticity, divergence,
surface pressure, specific humidity, and temperature (with a linearized
correction for virtual temperature in diagnostic quantities, where applicable).
Linear fourth-order (Ñ4) horizontal
diffusion is applied on constant pressure surfaces to vorticity, divergence,
temperature, and specific humidity.
Second-order vertical diffusion with coefficients derived from mixing-length
considerations is applied to momentum, heat, and moisture is applied at
all levels up to a height of about 5 km. The vertical diffusion is not
The parameterization of orographic gravity-wave drag follows linear theory,
as formulated by Y. Hayashi (cf. Broccoli and Manabe 1992) . The drag is
given by the vertical divergence of the wave stress, which near the surface
is equal to the product of the subgrid-scale orographic variance and a
representative mountain wavenumber with a mass-weighted average of the
atmospheric density, the Brunt-Vaisalla frequency, and the wind in the
first three layers above the surface. The wave stress is assumed to be
zero above a critical sigma level where the projection of the wind on the
surface wind vector vanishes. Below thisi level, the stress increases linearly
to its surface value as the sigma-distance from the critical level increases.
The solar constant is the AMIP-prescribed value of 1365 W/(m2).
The orbital parameters and seasonal insolation distribution are calculated
after PMIP recommendations. A seasonal, but not a diurnal cycle in solar
forcing, is simulated.
The carbon dioxide concentration used in the PMIP control simulations is
300 ppm. Zonally averaged seasonal mean ozone distributions are specified
as a function of height after data of Hering and Borden (1965) . These
data are linearly interpolated for intermediate times. Radiative effects
of water vapor, but not those of aerosols, also are included (see Radiation).
Shortwave Rayleigh scattering, and absorption in ultraviolet (wavelengths
less than 0.35 micron) and visible (wavelengths between 0.5 to 0.7 micron)
spectral bands by ozone, and in the near-infrared (wavelengths 0.7 to 4.0
microns) by water vapor are treated by a method similar to that of Lacis
and Hansen (1974) . Pressure corrections and multiple reflections between
clouds and the surface are treated, but radiative effects of aerosols are
Longwave radiation follows the method of Rodgers and Walshaw (1966)
, as modified by Stone and Manabe (1968) . Absorption by water vapor, carbon
dioxide, and ozone is included. The 6.3-micron band, the rotation band,
and the continuum of water vapor are subdivided into 19 subintervals, two
of which contain the 15-micron carbon dioxide and 9.6-micron ozone absorption
bands, with transmissions of the latter two gases multiplied together in
overlapping bands. A random model is used to represent the absorptivity
for each subinterval, and the Curtis-Godson approximation is used to estimate
the effective pressure for absorption. The temperature dependence of line
intensity is also incorporated. Carbon dioxide absorptivity is obtained
from data of Burch et al. (1961) , with its temperature dependence following
the model of Sasamori (1959) . The ozone absorptivity is obtained from
data of Walshaw (1957) .
Cloud-radiative interactions are treated as described by Wetherald and
Manabe (1988) and Wetherald et al. (1991) . Cloud optical properties (absorptivity/
reflectivity in the ultraviolet-visible and near-infrared intervals, and
emissivity in the longwave) depend on cloud height (high, middle, and low)
and thickness. The values of shortwave properties are assigned following
Rodgers (1967a) ; in the longwave, the emissivity of thin high clouds (above
10.5 km) is prescribed as 0.6 after Kondratiev (1972) , while all other
clouds are treated as blackbodies (emissivity = 1.0). No partial cloudiness
is accounted for in each grid box; clouds, therefore, are treated as fully
overlapped in the vertical. See also Cloud Formation.
Convection is simulated via the convective adjustment processes. If the
lapse rate exceeds dry adiabatic, a convective adjustment restores the
lapse rate to dry adiabatic, with conservation of dry static energy in
the vertical. A moist convective adjustment scheme after Manabe et al.
(1965) also operates when the lapse rate exceeds moist adiabatic and the
air is supersaturated. (For supersaturated stable layers, nonconvective
large-scale condensation takes place--see Precipitation). In moist convective
layers it is assumed that the intensity of convection is strong enough
to eliminate the vertical gradient of potential temperature instantaneously,
while conserving total moist static energy. It is further assumed that
the relative humidity in the layer is maintained at 100 percent, owing
to the vertical mixing of moisture, condensation, and evaporation from
water droplets. Shallow convection is not explicitly simulated.
Cloud forms when the relative humidity of a vertical layer exceeds a height-
dependent threshold, whether this results from large-scale condensation
or moist convective adjustment (see Convection). (The threshold relative
humidity varies linearly between 100 percent at the bottom of the model
atmosphere to 99 percent at its top.) It is assumed that no condensed water
is retained as cloud liquid water, but immediately precipitates (see Precipitation).
Cloud type is defined according to height: high cloud forms above 10.5
km, middle cloud between 4.0 to 10.5 km, and low cloud between 0.0 to 4.0
km. Cloud may form in a single layer or in multiple contiguous layers;
cloud occupying a single layer is treated as radiatively thin, and otherwise
as radiatively thick. Clouds are assumed to fill the whole grid box (cloud
fraction = 1), and therefore to be fully overlapped in the vertical. Cf.
Wetherald and Manabe (1988) and Wetherald et al. (1991) for further details.
See also Radiation.
Precipitation from large-scale condensation and from the moist convective
adjustment process (see Convection) forms under supersaturated conditions.
Subsequent evaporation of falling precipitation is not simulated.
Planetary Boundary Layer
The PBL is simulated only in a rudimentary way (e.g., above the surface
layer vertical diffusion of momentum, heat, and moisture are not stability-dependent
--see Diffusion). The PBL top is not computed. See also Surface Characteristics
and Surface Fluxes.
In the control integrations, raw orography data obtained from the U.S.
Navy dataset (cf. Joseph 1980 ) are smoothed by application of the method
of Lindberg and Broccoli (1996). The same procedure is applied to the PMIP
LGM topography for the 21K integration. Subgrid-scale orographic variances
required for the gravity-wave drag parameterization are obtained from the
same dataset (see Gravity-wave Drag) and used in all PMIP integrations.
Prescribed SST simulations of the modern climate use the AMIP monthly sea
surface temperature fields, with daily values determined by linear interpolation.
For the computed SST simulations, a static, isothermal "mixed layer" with
a depth of 50 m is employed. An interactive surface heat budget constitues
the forcing for this layer, with a heat convergence, varying both spatially
and seasonally, added to mimic the process of ocean heat transport.
Sea ice concentrations and thicknesses used in the prescribed SST simulation
are based on analyses from the NOAA/Navy Joint Ice Center and submarine
ice thickness data. In the computed SST simulations, the ice model of Flato
and Hibler (1992) is used. Snow may accumulate on sea ice, but does not
alter its thermodynamic properties. The surface temperature of sea ice
is prognostically determined after Holloway and Manabe (1971) from a surface
energy balance (see Surface Fluxes) that includes a conduction heat flux
from the ocean below. The conduction flux is proportional to the difference
between the surface temperature of the ice and the subsurface ocean temperature
(assumed to be at the melting temperature of sea ice, or 271.2 K), and
the flux is inversely proportional to the constant ice thickness (2 m).
The heat conductivity is assumed to be a constant equal to the value for
pure ice, and there is no heat storage within the ice.
Precipitation falls as snow if the air temperature at 350 m above the surface
is < 0 degrees C. Snow accumulates on both land and sea ice (see Sea
Ice), and snow mass is determined prognostically from a budget equation
that accounts for accumulation, melting, and sublimation. Sublimation is
calculated as part of the surface evaporative flux. Snowmelt, determined
from the excess surface energy available for a surface at temperature 273.2
K, contributes to soil moisture (cf. Holloway and Manabe 1971) . Snow cover
affects the albedo of the surface, but not its thermodynamic properties
(see also Surface Characteristics, Surface Fluxes, and Land Surface Processes).
Roughness lengths are prescribed constants for ocean (3.5 x 10-4
m) and land (0.045 m).
Over oceans, the surface albedo depends on solar zenith angle (cf. Payne
1972 ). The albedo of sea ice is a function of ice thickness and surface
temperature. Albedos for snow-free land are obtained from the modern albedo
data base of CLIMAP Project Members (1981) and do not depend on solar zenith
angle or spectral interval.
Snow cover modifies the local background albedo of the surface according
to its depth, following Holloway and Manabe (1971) . The albedo also depends
on surface temperature, with higher albedos at lower temperatures.
Longwave emissivity is prescribed as unity (blackbody emission) for
Surface solar absorption is determined from the surface albedos, and longwave
emission from the Planck equation, assuming blackbody emissivity (see Surface
Surface turbulent eddy fluxes follow Manabe (1969). The momentum flux
is proportional to the product of a drag coefficient, the wind speed, and
the wind velocity vector at the lowest atmospheric level. Surface sensible
heat flux is proportional to the product of a transfer coefficient, the
wind speed at the lowest atmospheric level, and the vertical difference
between the temperature at the surface and that of the lowest level. The
drag and transfer coefficients are functions of surface roughness length
(see Surface Characteristics) but are not stability-dependent.
The surface moisture flux is the product of potential evaporation and
evapotranspiration efficiency beta. Potential evaporation is proportional
to the product of the same transfer coefficient as for the sensible heat
flux, the wind speed at the lowest atmospheric level, and the difference
between the specific humidity at the lowest level and the saturated specific
humidity for the local surface temperature and pressure. The evapotranspiration
efficiency beta is prescribed to be unity over oceans, snow, and ice surfaces;
over land, beta is a function of the ratio of soil moisture to the constant
field capacity (see Land Surface Processes).
Land Surface Processes
Ground temperature is determined from a surface energy balance (see Surface
Fluxes) without provision for soil heat storage.
Soil moisture is represented by the single-layer "bucket" model of Manabe
(1969) , with field capacity everywhere 0.15 m. Soil moisture is increased
by precipitation and snowmelt; it is depleted by surface evaporation, which
is determined from a product of the evapotranspiration efficiency beta
and the potential evaporation from a surface saturated at the local surface
temperature and pressure (see Surface Fluxes). Over land, beta is given
by the ratio of local soil moisture to a critical value that is 75 percent
of field capacity, and is set to unity if soil moisture exceeds this value.
Runoff occurs implicitly if soil moisture exceeds the field capacity.
Last update November 9, 1998. For further information, contact: Céline