Documentation of the PMIP models (Bonfils et al. 1998)

PMIP Documentation for LMD5

Laboratoire de Météorologie Dynamique: Model LMCE LMD5.3 (sin(lat)x5.6 L11) 1994

PMIP Representative(s)

for 0fix and 6fix:

Dr. Pascale Braconnot, Laboratoire des Sciences du Climat et de l´Environnement, Bat 709 CEA-DSM, Orme des Merisiers, F 91191 Gif-sur-Yvette cedex, France, Phone: 33 (1) 69 08 77 11; Fax 33 (1) 69 08 77 16;

for 21fix:

Dr. Gilles Ramstein Laboratoire des Sciences du Climat et de l´Environnement, Bat 709 CEA-DSM, Orme des Merisiers, F 91191 Gif-sur-Yvette cedex, France, Phone: 33 (1) 69 08 77 11; Fax 33 (1) 69 08 77 16;


Model Designation

LMCE LMD5.3 (sin(lat)x5.6 L11) 1994

Model Identification for PMIP


PMIP run(s)

0fix, 6fix, 21fix

Number of days in each month: 30 30 30 30 30 30 30 30 30 30 30 30

Model Lineage

The LMD model derives from an earlier version developed for climate studies (cf. Sadourny and Laval 1984) . 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.

Model Documentation

Harzallah A. and R. Sadourny, 1995 : Internal versus SST-forced atmospheric variability as simulated by an atmospheric general circulation model, J. Climate, Vol.8, 474-495.

Sadourny R., Laval K., 1984, January and July performance of the LMD general circulation model. In New Perspectives in Climate Modelling, A. Berger and C. nicolis (eds), Developments in Atmospheric Science, 16,

Elsevier, pp 173-198

Numerical/Computational Properties

Horizontal Representation

Finite differences on a uniform-area, staggered C-grid (cf. Arakawa and Lamb 1977) .

The model has a regular grid in longitude and in SINE OF THE LATITUDE

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. )

dim_longitude*dim_latitude: 64*50

Vertical Domain

Surface to about 4 hPa. For a surface pressure of 1000 hPa, the lowest atmospheric level is at 979 hPa.

Vertical Representation

Finite-difference sigma coordinates.

Vertical Resolution

There are 11 unevenly spaced sigma levels: the model uses a sigma-coordinate in the vertical with the following levels: 0.991, 0.967, 0.914, 0.830, 0.708, 0.566, 0.411, 0.271, 0.150 0.07, 0.01.

For a surface pressure of 1000 hPa, 3 levels are below 800 hPa and 2 levels are above 200 hPa.

Computer/Operating System

The PMIP simulation was run on a CRAY C94 under the UNICOS operating system.

Computational Performance

For the PMIP experiment, about 3 hours Cray C94 computation time per simulated year.


For the PMIP experiment, the model atmosphere, soil moisture, and snow cover/depth are initialized for 1 January 1979 from a previous model simulation.

Time Integration Scheme(s)

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) 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.

Sampling Frequency

For the PMIP simulation, the model history is written once every 24 hours.

Dynamical/Physical Properties

Atmospheric Dynamics

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 , b ). Total energy is also conserved for irrotational flow (cf. Sadourny 1980) . 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 Ñ (Ñ *Ñ *)Ñ , where Ñ denotes a first-order difference on the model grid, while Ñ * 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) 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) . Estimation of TKE involves calculation of a countergradient term after Deardorff (1966) and comparison of the bulk Richardson number with a critical value. Cf. Sadourny and Laval (1984) for further details. See also Planetary Boundary Layer and Surface Fluxes.

Gravity-wave Drag

The formulation of gravity-wave drag closely follows the linear model described by Boer et al. (1984) . 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.

Solar Constant/Cycles

The solar constant is the PMIP-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.


Carbon dioxide concentration is of prescribed value of 345, 280 and 200 ppm for control, 6ka and 21ka, respectively. Three-dimensional ozone concentration is diagnosed as a function of the 500 hPa geopotential heights following the method of Royer et al. (1988) . 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) . 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) 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) 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) .

Longwave radiation is modeled in six spectral intervals between wavenumbers 0 and 2.82 x 105 m-1 after the method of Morcrette (1990, 1991 ). Absorption by water vapor (in two intervals), by the water vapor continuum (in two intervals in the atmospheric window, following Clough et al. 1980) , 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) . 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) 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) 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) . See also Cloud Formation.

Cloud Formation

Cloud cover is prognostically determined, as described by Le Treut and Li (1991) . 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).

Cloud water content and cloud fraction are interactively used in the radiative code through the calculation of cloud optical thickness and cloud emissivity (Le Treut 1994).

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) 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) for further details. See also Precipitation.


Both convective and large-scale precipitation are linked to cloud LWC (see Cloud Formation). For warm clouds, the precipitation is parameterized using the relationship proposed by Sundqvist (1981) in which Cl = 2 x 104 kg per kg and Ct = 5.5 10-4 s-1. For cold clouds, we use a relationship that takes into account the terminal falling speed of the crystals as described in Starr and Cox (1985).

Planetary Boundary Layer

The PBL is represented by an whole atmospheric column. At the end of the atmosphere, 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) 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). The rugosity is also linked to orographic variance.

For LGM, we add the anomaly of Peltier (Peltier(21k) -Peltier(0k)) to the control run.


For control: SSTs and sea ice extent are specified from the climatolgy of the 79-88 Reynold?s data (1988) used in AMIP (10 years mean).

For 6 fix: SSTs and sea-ice prescribed at their present day value, as in the control run.

For 21 fix: SSTs and sea-ice: the change in SSTs (LGM minus present-day) given by CLIMAP (1981), available at NGDC rather than the LGM absolute values in order to avoid differences due to differences in present day climatologies, was used. When points remain ocean, to obtain seasonally varying SSTs and sea ice edge from data for February and August, a simple sinusoidal variations, with extrems in February and August, is used. When points are ocean in summer and ice in winter (for Nothern Hemisphere), a "trapezoidal" function is used with an ad-hoc duration of the sea-ice deduced from present-day temperatures equivalent.

For computed SSTs experiments, the AGCM was coupled to a mixed layer ocean (50m) (Le Treut et al. 1994). The ocean heat transport is daily prescribed using the present-day diagnosed ocean heat transport accounting for the sea level drop (105m.) as described in the PMIP Newsletter (Webb et al. 1997).

Sea Ice

For 0fix and 6fix, sea ice extents are prescribed monthly. 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.

For 21fix, sea ice edge of CLIMAP data is used for February and August.There is not any percent of sea ice for each grid box. When the CLIMAP 21k sea-ice extent is interpolated over the model grid 48x36 if the result is higher than 50%, we consider that the grid box is sea ice. When the result is lower than 50%, the whole box is free of ice.

For computed SSTs experiments, the sea ice appears when the temperature is lower than -2°C and disappear when it is higher.

Snow Cover

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.

Surface Characteristics

For each grid box, 8 coexisting land surface types are specified from aggregation of the data of Matthews (1983; 1984): 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) , and their seasonal modulation is inferred following Dorman and Sellers (1989) . Roughness lengths over ice surfaces are a uniform 1 x 10-2 m. Over ocean roughness length using coefficients (see Surface Fluxes) are determined using Charnock?s relationship.

Surface albedos for oceans and snow-free sea ice are prescribed from monthly data of Bartman (1980) , and for snow-free continents from monthly data of Dorman and Sellers (1989) . When there is snow cover, the surface albedo is modified according to the parameterization of Chalita and Le Treut (1994) , 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.

Surface Fluxes

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 involving drag/transfer coefficients that are functions of wind speed, stability, and 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. At the surface, the ECMWF (1992) parametrization of momentum, heat and moisture transfer is included in the model.

Above the surface layer, but only within the PBL, turbulent eddy fluxes are represented as diffusive processes (see Diffusion and Planetary Boundary Layer).

As in the baseline model, the bare soil and vegetation in each grid box are treated as a single medium for calculations of the surface radiative budget and the sensible heat flux. The parameterization of evaporation from the oceans is also unchanged, but the evaporation from land surfaces is determined by the SECHIBA model rather than by the "bucket" scheme.

In SECHIBA, the evaporative flux is calculated separately for each of the 8 coexisting surface types (bare ground plus 7 vegetation classes with fractional areas specified according to grid box). The total evaporative flux in each grid box then is computed as an area-weighted average of the individual fluxes. The total flux includes sublimation from snow, evaporation from bare soil and from moisture intercepted by the canopy of each vegetation class, and transpiration from the dry foliage of each class. Sublimation and evaporation from intercepted canopy moisture occur at the potential rate, while canopy transpiration and evaporation from bare soil depend on the surface relative humidity which is parameterized in terms of soil moisture. Evaporation from sub-canopy soil is neglected.

In SECHIBA, the surface moisture flux is computed by a bulk method that depends on the moisture gradient between the surface and the overlying air and on resistances of different kinds (aerodynamic, soil, architectural, and canopy) that vary according to surface type and/or the nature of the moisture flux (sublimation, evaporation, transpiration). Cf. Ducoudré et al. (1993) for further details. See also Surface Characteristics and Land Surface Processes.

Land Surface Processes

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) , includes as forcing the surface heat fluxes (see Surface Fluxes) and the heat of fusion of snow and ice.

Soil hydrology is simulated using the land-surface scheme SECHIBA (Schématisation des Echanges Hydriques à l' Interface entre la Biosphère et l'Atmosphère) of Ducoudré et al. 1993. The total depth of the soil column (corresponding to the vegetation root zone) is a constant 1.0 m. Soil moisture is computed in two layers, the upper layer being the most reactive: when precipitation exceeds evapotranspiration, the upper layer fills first; when the reverse is true, it empties first. Runoff occurs whenever the soil column is completely saturated (water depth 0.15 m). The remaining prescribed parameters for bare soil are a constant evaporative resistance and an empirical constant used to compute surface relative humidity for calculation of evaporation.

In SECHIBA, each of the 7 prescribed vegetation classes interact individually with the soil hydrology and contribute individually to the surface moisture flux. All the vegetation is assumed to have a single-story canopy that transpires or intercepts precipitation, but the canopy moisture capacity varies with the leaf area index, which is prescribed differently for each vegetation class. Different architectural and canopy resistances for evaporation/transpiration also are prescribed for each vegetation class. Cf Ducoudré et al. 1993 for further details. See also Surface Characteristics and Surface Fluxes.

Last update November 9, 1998. For further information, contact: Céline Bonfils ( )