Dr. Jan Polcher, Laboratoire de Météorologie Dynamique du Centre National de la Recherche Scientifique, Ecole Normale Superieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France; Phone: +33-1-44322243; Fax: +33-1-43368392; e-mail: polcher@lmd.ens.fr; WWW URL: http://www.lmd.ens.fr/
LMD LMD5 (3.6x5.6 L11) 1991
The LMD model derives from an earlier version developed for climate studies (cf. Sadourny and Laval 1984)
[1]. Subsequent
modifications principally include changes in the representation of radiation
and horizontal diffusion, and inclusion of parameterizations of gravity-wave
drag and prognostic cloud formation.
Overall documentation of the LMD5 model is provided by Polcher et al. (1991)[32]. Other key model documents include publications by Sadourny and Laval (1984)
[1],
Laval et al. (1981)
[2], and Le Treut and Li
(1991)
[3]. Details of computational aspects are
described by Butel (1991)
[4].
Finite differences on a uniform-area, staggered C-grid (cf. Arakawa and Lamb
1977)
[5], with points equally spaced in sine of
latitude and in longitude. Horizontal advection of moisture is by a semi-upstream advection scheme. See also Horizontal Resolution.
There are 50 grid points equally spaced in the sine of latitude and 64 points
equally spaced in longitude. (The mesh size is 225 km north-south and 625 km
east-west at the equator, and is about 400 x 400 km at 50 degrees latitude. )
Surface to about 4 hPa. For a surface pressure of 1000 hPa, the lowest
atmospheric level is at 979 hPa.
Finite-difference sigma coordinates.
There are 11 unevenly spaced sigma levels. For a surface pressure of 1000 hPa,
3 levels are below 800 hPa and 2 levels are above 200 hPa.
The AMIP simulation was run on a Cray 2 computer, using a single processor in
the UNICOS operating environment.
For the AMIP experiment, about 2 minutes Cray 2 computation time per simulated
day.
For the AMIP experiment, the model atmosphere, soil moisture, and snow
cover/depth are initialized for 1 January 1979 from a previous model
simulation.
The time integration scheme for dynamics combines 4 leapfrog steps with a
Matsuno step, each of length 6 minutes. Model physics is updated every 30
minutes, except for shortwave/longwave radiative fluxes, which are calculated
every 6 hours. For computation of vertical turbulent surface fluxes and
diffusion, an implicit backward integration scheme with 30-minute time step is
used, but with all coefficients calculated explicitly. See also Surface Fluxes and Diffusion.
Orography is area-averaged on the model grid (see Orography). At the
four latitude points closest to the poles, a Fourier filtering operator after
Arakawa and Mintz (1974)
[6] is applied to the
momentum, thermodynamics, continuity, and water vapor tendency equations to
slow the longitudinally propagating gravity waves for numerical stability.
Negative moisture values (arising from vertical advection by the centered
nondiffusive scheme) are filled by borrowing moisture from the level below.
For the AMIP simulation, the model history is written once every 24 hours.
Primitive-equation dynamics are expressed in terms of u and v winds, potential
enthalpy, specific humidity, and surface pressure. The advection scheme is
designed to conserve potential enstrophy for divergent barotropic flow (cf.
Sadourny 1975a [7], b [8]). Total energy is also conserved for
irrotational flow (cf. Sadourny 1980)
[9]. The
continuity and thermodynamics equations are expressed in flux form, conserving
mass and the space integrals of potential temperature and its square. The water
vapor tendency is also expressed in flux form, thereby reducing the probability
of spurious negative moisture values (see Smoothing/Filling).
- Linear horizontal diffusion is applied on constant-pressure surfaces to
potential enthalpy, divergence, and rotational wind via a biharmonic operator
del(del*del*)del, where del denotes a first-order difference on the model grid,
while del* is a formal differential operator on a regular grid without
geometrical corrections. Because of the highly diffusive character of the
flux-form water vapor tendency equation (see Atmospheric Dynamics), no
further horizontal diffusion of specific humidity is included. Cf. Michaud
(1987)
[10] for further details.
- Second-order vertical diffusion of momentum, heat, and moisture is applied
only within the planetary boundary layer (PBL). The diffusion coefficient
depends on a diagnostic estimate of the turbulence kinetic energy (TKE) and on
the mixing length (which decreases up to the prescribed PBL top) that is
estimated after Smagorinsky et al. (1965)
[11].
Estimation of TKE involves calculation of a countergradient term after
Deardorff (1966)
[12] and comparison of the
bulk Richardson number with a critical value. Cf. Sadourny and Laval (1984)
[1] for
further details. See also Planetary Boundary Layer and Surface Fluxes.
The formulation of gravity-wave drag closely follows the linear model described by Boer et al. (1984)
[13]. The drag at any
level is proportional to the vertical divergence of the wave momentum stress,
which is formulated as the product of a constant aspect ratio, the local
Brunt-Vaisalla frequency, a launching height determined from the orographic
variance over the grid box (see Orography), the local wind velocity, and
its projection on the wind vector at the lowest model level. The layer where
gravity-wave breakdown occurs (due to convective instability) is determined
from the local Froude number; in this critical layer the wave stress decreases
quadratically to zero as a function of height.
The solar constant is the AMIP-prescribed value of 1365 W/(m^2). A
seasonal, but not a diurnal cycle in solar forcing, is simulated.
The carbon dioxide concentration is the AMIP-prescribed value of 345 ppm.
Three-dimensional ozone concentration is diagnosed as a function of the 500 hPa
geopotential heights following the method of Royer et al. (1988)
[14]. Radiative effects of water vapor, but not
those of aerosols, are also included (see Radiation).
- Shortwave radiation is modeled after an updated scheme of Fouquart and Bonnel (1980)
[15]. Upward/downward shortwave
irradiance profiles are evaluated in two stages. First, a mean photon optical
path is calculated for a scattering atmosphere including clouds and gases. The
reflectance and transmittance of these elements are calculated by,
respectively, the delta-Eddington method (cf. Joseph et al. 1976)[16] 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 two spectral intervals (0.30-0.68 micron and 0.68-4.0 microns) using more exact gas transmittances (Rothman 1981)[17] and with adjustments made for the presence of clouds (see Cloud Formation). For clouds, the asymmetry factor is prescribed, and the optical depth and single-scattering albedo are functions of cloud liquid water content after Stephens (1978)
[18].
- Longwave radiation is modeled in six spectral intervals between
wavenumbers 0 and 2.82 x 10^5 m^-1 after the method of Morcrette
(1990[19], 1991
[20]). Absorption by water vapor (in two
intervals), by the water vapor continuum (in two intervals in the atmospheric
window, following Clough et al. 1980)
[21], by
the carbon dioxide and the rotational part of the water vapor spectrum (in one
interval), and by ozone (in one interval) is treated. The temperature and
pressure dependence of longwave absorption by gases is included. Clouds are
treated as graybodies in the longwave, with emissivity depending on cloud
liquid water path after Stephens (1978)
[18]. 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,
all clouds are assumed to overlap randomly in the vertical. See also Cloud Formation.
- When the temperature lapse rate is conditionally unstable, subgrid-scale
convective condensation takes place. If the air is supersaturated, a moist
convective adjustment after Manabe and Strickler (1964)
[22] is carried out: the temperature profile is
adjusted to the previous estimate of the moist adiabatic lapse rate, with total
moist static energy in the column being held constant. The specific humidity is
then set to a saturated profile for the adjusted temperature lapse, and the
excess moisture is rained out (see Precipitation).
- If the temperature lapse rate is conditionally unstable but the air is
unsaturated, condensation also occurs following the Kuo (1965)
[23] cumulus convection scheme, provided there is
large-scale moisture convergence. In this case, the lifting condensation level
is assumed to be at the top of the PBL, and the height of the cumulus cloud is
given by the highest level for which the moist static energy is less than that
at the PBL top (see Planetary Boundary Layer). It is assumed that all
the humidity entering each cloudy layer since the last call of the convective
scheme (30 minutes prior) is pumped into this cloud. The environmental humidity
is reduced accordingly, while the environmental temperature is taken as the
grid-scale value; the cloud temperature and humidity profiles are defined to be
those of a moist adiabat.
- The fractional area of the convective cloud is obtained from a suitably
normalized, mass-weighted vertical integral (from cloud bottom to top) of
differences between the humidities and temperatures of the cloud vs those of
the environment. As a result of mixing, the environmental (grid-scale)
temperature and humidity profiles evolve to the moist adiabatic values in
proportion to this fractional cloud area, while the excess of moisture
precipitates (see Precipitation). Mixing of momentum also occurs.
- There is no explicit simulation of shallow convection, but the moist
convective adjustment produces similar effects in the moisture field (cf. Le
Treut and Li 1991)
[3]. See also Cloud Formation.
- Cloud cover is prognostically determined, as described by Le Treut and Li (1991)
[3]. Time-dependent cloud liquid water content (LWC) follows a conservation
equation involving rates of water vapor condensation, evaporation of cloud
droplets, and the transformation of small droplets to large precipitating drops
(see Precipitation). The LWC also determines cloud cover (see below) and
cloud optical properties (see Radiation).
- The fraction of convective cloud in a grid box is unity if moist
convective adjustment is invoked; otherwise, it is given by the surface
fraction of the active cumulus cloud obtained from the Kuo (1965)
[23] scheme (see
Convection). Cloud forms in those layers where there is a decrease in
water vapor from one call of the convective scheme to the next (every 30
minutes), and the cloud LWC is redistributed in these layers proportional to
this decrease.
- The fraction of stratiform cloud in any layer is determined from the
probability that the total cloud water (liquid plus vapor) is above the
saturated value. (A uniform probability distribution is assumed with a
prescribed standard deviation--cloud typically begins to form when the relative
humidity exceeds 83 percent of saturation.) This stochastic approach also
crudely simulates the effects of evaporation of cloud droplets. Cf. Le Treut
and Li (1991)
[3] for further details. See also Precipitation.
Both convective and large-scale precipitation are linked to cloud LWC (see
Cloud Formation). If the LWC exceeds a threshold value, all liquid water
is assumed to precipitate. (For water clouds, the LWC threshold is set to 1 x
10^-4 kg liquid per kg dry air; for ice clouds with tops at temperatures
below -10 degrees C, the threshold is set to the minimum of 5 percent of the
water vapor mixing ratio or 1 x 10^-5 kg per kg.) Evaporation of falling
convective and large-scale precipitation is not explicitly modeled, but
evaporation of small stratiform cloud droplets making up the LWC is simulated
stochastically.
The PBL is represented by the first 4 levels above the surface (at sigma =
0.979, 0.941, 0.873, and 0.770). The PBL top is prescribed to be at the sigma =
0.770 level; here vertical turbulent eddy fluxes of momentum, heat, and
moisture are assumed to vanish. See also Diffusion, Surface Fluxes, and
Surface Characteristics.
Raw orography obtained at 10 x 10-minute resolution from the U.S. Navy dataset
(cf. Joseph 1980)
[24] is area-averaged over
the model grid boxes. The orographic variance about the mean value for each
grid box is also computed from the same dataset for use in the gravity-wave
drag parameterization (see Gravity-wave Drag).
AMIP monthly sea surface temperature fields are prescribed, with daily values
determined by a cubic-spline interpolation which preserves the mean.
AMIP monthly sea ice extents are prescribed. The surface temperature of the ice
is predicted from the balance of energy fluxes (see Surface Fluxes) that
includes conduction heating from the ocean below. This conduction flux is
proportional to the difference between the surface temperature and that of
melting ice (271.2 K), and is inversely proportional to the ice thickness
(prescribed to be a uniform 3 m). Snow that accumulates on sea ice modifies its
albedo and thermal properties. See also Snow Cover and Surface Characteristics.
If the air temperature at the first level above the surface (at sigma = 0.979)
is <0 degrees C, precipitation falls as snow. Prognostic snow mass is
determined from a budget equation, with accumulation and melting over both land
and sea ice. Snow cover affects the surface albedo and the heat capacity of the
surface. Sublimation of snow is calculated as part of the surface evaporative
flux, and snowmelt contributes to soil moisture. See also Surface Characteristics, Surface Fluxes, and Land Surface Processes.
- For each grid box, 8 coexisting land surface types are specified from aggregation of the data of Matthews (1983[40]; 1984[41]): bare soil, desert, tundra, grassland, grassland with shrub cover, grassland with tree cover, deciduous forest, evergreen forest, and rainforest. The fractional areas of each surface type vary according to grid box.
- The surface roughness lengths over the continents are prescribed as a
function of orography and vegetation from data of Baumgartner et al. (1977)
[25], and their seasonal modulation is inferred
following Dorman and Sellers (1989)
[26].
Roughness lengths over ice surfaces are a uniform 1 x 10^-2 m. Over
ocean, the surface drag/transfer coefficients (see Surface Fluxes) are
determined without reference to a roughness length.
- Surface albedos for oceans and snow-free sea ice are prescribed from
monthly data of Bartman (1980)
[27], and for
snow-free continents from monthly data of Dorman and Sellers (1989)
[26]. When there
is snow cover, the surface albedo is modified according to the parameterization
of Chalita and Le Treut (1994)
[28], which
takes account of snow age, the eight designated land surface types, and spectral
range (in visible and near-infrared subintervals).
- The longwave emissivity is prescribed as 0.96 for
all surfaces.
- The surface solar absorption is determined from surface albedos, and
longwave emission from the Planck equation with prescribed emissivity of 0.96
(see Surface Characteristics).
- In the lowest atmospheric layer, surface turbulent eddy fluxes of
momentum, heat, and moisture are expressed as bulk formulae multiplied by
drag/transfer coefficients that are functions of wind speed, stability, and
(except over ocean) roughness length (see Surface Characteristics). The
transfer coefficient for the surface moisture flux also depends on the vertical
humidity gradient. Over the oceans, the neutral surface drag/transfer is corrected according to the local condition of surface winds. For strong surface winds, the drag/transfer coefficients are determined
(without reference to a roughness length) as functions of surface wind speed
and temperature difference between the ocean and the surface air, following
Bunker (1976)
[29]. For conditions of light surface winds over the oceans, functions of Golitzyn and Grachov (1986)[33] that depend on the surface temperature and humidity gradients are utilized. In the transition region between these wind regimes, surface drag/transfer coefficients are calculated as exponential functions of the surface wind speed.
- In addition, the momentum flux is proportional to the wind vector
extrapolated to the surface. The sensible heat flux is proportional to the
difference between the potential temperature at the ground and that
extrapolated from the atmosphere to the surface. The surface moisture flux is
proportional to the potential evaporation (the difference between the saturated
specific humidity at the surface and the extrapolated atmospheric humidity)
multiplied by an evapotranspiration efficiency beta. Over oceans, snow, and ice, beta is set to unity, while over land it is a function of soil moisture (see Land Surface Processes).
- Above the surface layer, but only within the PBL, turbulent eddy fluxes
are represented as diffusive processes (see Diffusion and Planetary Boundary Layer).
- Ground temperature and bulk heat capacity (with differentiation for bare
soil, snow, and ice) are defined as mean quantities over a single layer of
thickness about 0.15 m (over which there is significant diurnal variation of
temperature). The temperature prediction equation, which follows Corby et al. (1976)
[30], includes as forcing the surface
heat fluxes (see Surface Fluxes) and the heat of fusion of snow and ice.
- Prognostic soil moisture is represented by a single-layer "bucket" model
after Budyko (1956)
[31], with uniform field
capacity 0.15 m. Soil moisture is increased by both precipitation and snowmelt,
and is decreased by surface evaporation, which is determined from the 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 maximum of unity or twice the ratio
of local soil moisture to the constant field capacity. Runoff occurs implicitly
if the soil moisture exceeds the field capacity. Cf. Laval et al. (1981)
[2] for further details.
Go to LMD References
Last update August 13, 1996. For further information, contact: Tom Phillips (
phillips@tworks.llnl.gov)
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