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

PMIP Documentation for CCC2.0

Canadian Centre for Climate Modelling and Analysis: Model CCCMA Version 2 (T32 L10) 1992

PMIP Representative(s)

Mr. Guido Vettoretti, 60 St. George Street, University of Toronto, Toronto, Ontario M5S 1A7, Canada

Phone: +1-416-978-5213; Fax: +1-416-978-8905; e-mail:


Dr. McFarlane Norman A., Canadian Center for Climate Research, Atmospheric Environment Service

University of Victoria, 3964 Gordon Head Road, Victoria, BC V8W 2Y2, Canada

Phone: +1-250-363-8227; Fax: +1-250-363-8247; e-mail:

Model Designation

CCCMA Version 2 (T32 L10) 1992

Model Identification for PMIP


PMIP run(s)

0fix, 6fix, 21fix, 0cal, 21cal

Number of days in each month: 31 28 31 30 31 30 31 31 30 31 30 31

Model Lineage

The CCC model is the second-generation version of a model first developed in the early 1980s for climate applications.

The model is identical to the latest AMIP model exept for different initial conditions and the Earth's orbital parameters.

Model Documentation

main reference:

McFarlane, N.A., Boer G.J., Blanchet J.-P., Lazare M., 1992: The Canadian Climate Centre Second-Generation General Circulation Model and Its Equiliubrium Climate, J. Climate, 5, 1013-1044. describe the features and equilibrium climate of the CCC model.

secondary refererence(s)

Some properties remain the same as those of the first-generation CCC model documented by Boer G.J., McFarlane, N.A., Laprise R., Henderson J.D., Blanchet J.-P., 1984a: The Canadian Climate Centre Spectral Atmospheric General Circulation Model, Atmos. Ocean, 22, 397-429.

Numerical/Computational Properties

Horizontal Representation

Spectral (spherical harmonic basis functions) with transformation to a Gaussian grid for calculation of nonlinear quantities and some physics.

Horizontal Resolution

Spectral triangular 32 (T32), roughly equivalent to 3.75 x 3.75 degrees latitude-longitude.

dim_longitude*dim_latitude: 96*48

Vertical Domain

Surface to 5 hPa. For a surface pressure of 1000 hPa, the lowest atmospheric level is at a pressure of about 980 hPa.

Vertical Representation

Piecewise finite-element formulation of hybrid coordinates (cf. Laprise and Girard 1990 ).

Vertical Resolution

There are 10 irregularly spaced hybrid levels. For a surface pressure of 1000 hPa, 3 levels are below 800 hPa and 4 levels are above 200 hPa.

The model uses an eta-coordinate in the vertical with the following levels: 0.012, 0.038, 0.088, 0.160, 0.265, 0.430, 0.633, 0.803, 0.915, 0.980

Computer/Operating System

The PMIP 0fix, 0cal and 6fix simulations were run on NEC-SX3.

The PMIP 21fix and 21cal simulations were run on a CRAY J916 8-CPU machine.

Computational Performance

For the PMIP, about 6 minutes CRAY computation time per simulation day.


The model was started from a intial conditions based on the present day climatology. The model atmosphere is initialized from FGGE III-B observational analyses for 1 January 1979. Soil moisture and snow cover/depth are initialized from January mean values obtained from an earlier multiyear model simulation.

Time Integration Scheme(s)

A semi-implicit time integration scheme with an Asselin (1972) frequency filter is used. The time step is 20 minutes for all dynamics and physics fields, except for full calculations of radiative fluxes and heating rates. Shortwave radiation is calculated every timestep, and longwave radiation every 3 hours, with interpolated values used at intermediate time steps (cf. McFarlane et al. 1992) . Full Longwave Radiative Heating Calculation is twice daily.


Orography is truncated at spectral T32 (see Orography). Negative values of atmospheric specific humidity (which arise because of numerical truncation errors in the discretized moisture equation) are filled in a two stage process. First, all negative values of specific humidity are made slightly positive by borrowing moisture (where possible) from other layers in the same column. If column moisture is insufficient, a nominal minimum bound is imposed, the moisture deficit is accumulated over all atmospheric points, and the global specific humidity is reduced proportionally. This second stage is carried out in the spectral domain (cf. McFarlane et al. 1992) .

Sampling Frequency

For the PMIP simulation, the model history is written every 12 hours. (However, some archived variables, including most of the surface quantities, are accumulated rather than sampled.)

Dynamical/Physical Properties

Atmospheric Dynamics

Primitive-equation dynamics are expressed in terms of vorticity, divergence, temperature, the logarithm of surface pressure, and specific humidity.


Horizontal diffusion follows the scale-dependent eddy viscosity formulation of Leith (1971) as described by Boer et al. (1984a) . Diffusion is applied to spectral modes of divergence, vorticity, temperature, and moisture, with total wavenumbers >18 on hybrid vertical surfaces.

Second-order vertical diffusion of momentum, moisture, and heat operates above the surface. The vertically varying diffusivity depends on stability (gradient Richardson number) and the vertical shear of the wind, following standard mixing-length theory. Diffusivity for moisture is taken to be the same as that for heat. Cf. McFarlane et al. (1992) for details. See also Surface Fluxes.

Gravity-wave Drag

Simulation of subgrid-scale gravity-wave drag follows the parameterization of McFarlane (1987) . Deceleration of the resolved flow by dissipation of orographically excited gravity waves is a function of the rate at which the parameterized vertical component of the gravity-wave momentum flux decreases in magnitude with height. This momentum-flux term is the product of local air density, the component of the local wind in the direction of that at the near-surface reference level, and a displacement amplitude. At the surface, this amplitude is specified in terms of the mesoscale orographic variance, and in the free atmosphere by linear theory, but it is bounded everywhere by wave saturation values. See also Orography.

Solar Constant/Cycles

The solar constant is the AMIP-prescribed value of 1365 W/(m2). The orbital parameters and seasonal insolation distribution are calculated after PMIP recommendations. Both seasonal and diurnal cycles in solar forcing are simulated.


The carbon dioxide concentration is the PMIP-prescribed value of 345, 280 and 200 ppm for 0fix, 6k and 21k run, respectively. The 0cal simulation was run with a concentration of 280 ppm. A monthly zonally averaged ozone distribution from data by Wilcox and Belmont (1977) is specified. Radiative effects of water vapor also are treated (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, aerosols, 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 visible (0.30-0.68 micron) and near-infrared (0.68-4.0 microns) spectral intervals using more exact gas transmittances (cf. Rothman 1981 ), and with adjustments made for the presence of clouds. The asymmetry factor is prescribed for clouds, and the optical depth and single-scattering albedo are functions of cloud liquid water content (cf. Betts and Harshvardhan 1987 ) and ice crystal content (cf. Heymsfield 1977 ).

Longwave radiation is modeled in six spectral intervals between wavenumbers 0 to 2.82 x 105 m-1 after the method of Morcrette (1984 , 1990 , 1991 ), which corrects for the temperature/pressure dependence of longwave absorption by gases and aerosols. Longwave absorption in the water vapor continuum follows Clough et al. (1980) . Clouds are treated as graybodies in the longwave, with emissivity depending on optical depth (cf. Platt and Harshvardhan 1988 ), and with longwave scattering by cloud droplets neglected. The effects of cloud overlap in the longwave are treated following a modified scheme of Washington and Williamson (1977) : upward/downward irradiances are computed for clear-sky and overcast conditions, and final irradiances are determined from a linear combination of these extreme cases weighted by the actual partial cloudiness in each vertical layer. For purposes of the radiation calculations, clouds occupying adjacent layers are assumed to be fully overlapped, but to be randomly overlapped otherwise. Cf. McFarlane et al. (1992) for further details.


A moist convective adjustment procedure is applied on pairs of vertical layers whenever the model atmosphere is conditionally unstable. Convective instability occurs when the local thermal lapse rate exceeds a critical value, which is determined from a weighted linear combination of dry and moist adiabatic lapse rates, where the weighting factor (with range 0 to 1) is a function of the local relative humidity. Convective instability may occur in association with condensation of moisture under supersaturated conditions, and the release of precipitation and associated latent heat (see Precipitation). Cf. Boer et al. (1984a) for further details.

Cloud Formation

The fractional cloud cover in a vertical layer is computed from a linear function of the relative humidity excess above a threshold value. The threshold is a nonlinear function of height for local sigma levels >0.5, and is a constant 85 percent relative humidity at higher altitudes. (Note that the cloud scheme uses locally representative sigma coordinates, while other model variables use hybrid vertical coordinates--see Vertical Representation). To prevent development of excessive low cloudiness, no clouds are allowed in the lowest model layer. Cf. McFarlane et al. (1992) for further details. See also Radiation for treatment of cloud-radiative interactions.


Condensation and precipitation occur under conditions of local supersaturation, which are treated operationally as part of the model's convective adjustment scheme (see Convection). All the precipitation falls to the surface without subsequent evaporation to the surrounding atmosphere. See also Snow Cover.

Planetary Boundary Layer

The depth of the PBL is not explicitly determined, but in general is assumed to be greater than that of the surface layer (centered at the lowest prognostic vertical level--about 980 hPa for a surface pressure of 1000 hPa). The PBL depth is affected by dry convective adjustment (see Convection), which simulates boundary-layer mixing of heat and moisture, and by enhanced vertical diffusivities (see Diffusion), which may be invoked in the lowest few layers that are determined to be convectively unstable (cf. Boer et al. 1984a) . Within the surface layer of the PBL, temperature and moisture required for calculation of surface fluxes are assigned the same values as those at the lowest level, but the wind is taken as one-half its value at this level (see Surface Fluxes).


Orographic heights with a resolution of 10 minutes arc on a latitude/longitude grid are smoothed by averaging over 1.8-degree grid squares, and the orographic variance about the mean for each grid box also is computed (see Gravity-wave Drag). These means and variances are interpolated to a slightly coarser Gaussian grid (64 longitudes x 32 latitudes), transformed to the spectral representation, and truncated at the model resolution (spectral T32) for control, 6fk and 21k run.

For the 0fix, 0cal and 6fix Scrippstopography (Gates, W.L., and A.B. Nelson, 1975) was used.

For 21fix and 21cal the Peltier (1994) topographic differences were used :

(Peltier(21k) - Peltier(0k)) + Scrippstopogaraphy.


The prescribed monthly climatological SSTs for 0fix and 6fix integrations were made by averaging Alexander and Mobley (1976) monthly sea surface temperature fields, with daily values determined by linear interpolation.

For 21fix, CLIMAP(21k) February and August SSTs were fit to a sinusoid to calculate mean monthly values.

For 0cal, the mixed layer model was started from modern initial conditions and run for 50 years to equilibrium.

For 21cal, the mixed layer model was started from a intial conditions based on CLIMAP 21k reconstructed SST climatology and run for 50 years to equilibrium.

Sea Ice

For the 0fix and 6fix run, Alexander and Mobley (1976) monthly sea ice extents are prescribed. Snow may accumulate on sea ice (see Snow Cover). The surface temperature of the ice is a prognostic function of the surface heat balance (see Surface Fluxes) and of a heat flux from the ocean below. This ocean heat flux depends on the constant ice thickness and the temperature gradient between the ocean and the ice.

For 21fix, CLIMAP(21k) February and August sea ice distributions were used as maxima (N.H.) and minima (N.H.), respectively, to interpolate the sea ice annual cycle.

For 21cal, CLIMAP(21k) ice distribution were allowed to evolve (receed) to equilibrium under the influence of modern day oceanic heat transport.

Snow Cover

If the near-surface air temperature is <0 degrees C, precipitation falls as snow. Prognostic snow mass is determined from a budget equation, with accumulation and melting treated over both land and sea ice. Snow cover affects the surface albedo of land and of sea ice, as well as the heat capacity of the soil. Sublimation of snow is calculated as part of the surface evaporative flux. Melting of snow, as well as melting of ice interior to the soil, contributes to soil moisture. Cf. McFarlane et al. (1992) for further details. See also Surface Characteristics, Surface Fluxes, and Land Surface Processes.

Surface Characteristics

Local roughness lengths are derived (cf. Boer et al. 1984a) from prescribed neutral surface drag coefficients (see Surface Fluxes). The 1 x 1-degree Wilson and Henderson-Sellers (1985) data on 24 soil/vegetation types are used to determine the most frequently occurring primary and secondary types (weighted 2/3 vs 1/3) for each grid box. Averaged local soil/vegetation parameters include field capacity and slope factor for predicting soil moisture (see Land Surface Processes), and snow masking depth for the surface albedo (see below). These are obtained by table look-up based on primary/secondary vegetation types.

Over bare dry land, the surface background albedo is determined from a weighted average for each of 24 vegetation types in the visible (0.30-0.68 micron) and near-infrared (0.68-4.0 microns) spectral bands; for wet soil, albedos are reduced up to 0.07. For vegetated surfaces, albedos are determined from a 2/3 vs 1/3 weighting of albedos of the local primary/secondary vegetation types. The local land albedo also depends on the fractional snow cover and its age (fractional coverage of a grid box is given by the ratio of the snow depth to the specified local masking depth); the resulting albedo is a linear weighted combination of snow-covered and snow-free albedos. Over the oceans, latitude-dependent albedos which range between 0.06 and 0.17 are specified independent of spectral interval. The background albedos for sea ice are 0.55 in the near-infrared and 0.75 in the visible; these values are modified by snow cover, puddling effects of melting ice (a function of mean surface temperature), and by the fraction of ice leads (a specified function of ice mass).

The longwave emissivity is prescribed as unity (i.e., blackbody emission is assumed) for all surfaces. Cf. McFarlane et al. (1992) for further details.

Surface Fluxes

The surface solar absorption is determined from surface albedos, and the longwave emission from the Planck equation with prescribed emissivity of 1.0 (see Surface Characteristics). The surface turbulent eddy fluxes of momentum, heat, and moisture are expressed as bulk formulae following Monin-Obukhov similarity theory. The momentum flux is a product of a neutral drag coefficient, the surface wind speed and wind vector (see Planetary Boundary Layer), and a function of stability (bulk Richardson number). Drag coefficients over land and ice are prescribed after Cressman (1960) , but over the oceans they are a function of surface wind speed (cf. Smith 1980 ). The flux of sensible heat is a product of a neutral transfer coefficient, the surface wind speed, the difference in temperatures between the surface and that of the lowest atmospheric level, and the same stability function as for the momentum flux. (The transfer coefficient has the same value as the drag coefficient over land and ice, but is not a function of surface wind over the oceans.)

The flux of surface moisture is a product of the same transfer coefficient and stability function as for sensible heat, an evapotranspiration efficiency (beta) factor, and the difference between the specific humidity at the lowest atmospheric level (see Planetary Boundary Layer) and the saturation specific humidity at the temperature/pressure of the surface. Over the oceans and sea ice, beta is prescribed as 1; over snow, it is the lesser of 1 or a function of the ratio of the snow mass to a critical value (10 kg/m2). Over land, beta depends on spatially varying soil moisture and field capacities (see Land Surface Processes), and on slope factors for primary/secondary vegetation and soil types (see Surface Characteristics). For grid boxes with fractional snow coverage, a composite beta is obtained from a weighted linear combination of snow-free and snow-covered values. Cf. Boer et al. (1984a) and details.

Land Surface Processes

Soil heat storage is determined as a residual of the surface heat fluxes and of the heat source/sink of freezing/melting snow cover and soil ice (see below). Soil temperature is computed from this heat storage in a single layer, following the method of Deardorff (1978) which accounts for both diurnal and longer-period forcing. The composite conductivity/heat capacity of the soil in each grid box is computed as a function of soil type, soil moisture, and snow cover.

Soil moisture is predicted by a single-layer "bucket" model with field capacity and slope factors varying by primary/secondary soil and vegetation types for each grid box (see Surface Characteristics). Soil moisture budgets include both liquid and frozen water. The effective local moisture capacity is given by the product of field capacity and slope factor, with evapotranspiration efficiency beta a function of the ratio of soil moisture to the local effective moisture capacity (see Surface Fluxes). Runoff occurs implicitly if this ratio exceeds 1 (which is more likely the higher the local slope factor and the lower the local field capacity). Cf. McFarlane et al. (1992) and Boer et al. (1984a) for further details.

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