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

PMIP Documentation for BMRC

Bureau of Meteorology Research Centre: Model BMRC (R21 L9) Version 3.2 1993

PMIP Representative(s)

Dr. Bryant McAvaney, Bureau of Meteorology Research Centre, Box 1289K, GPO Melbourne, Victoria 3001,

Australia; Phone: +61-3-9669-4000; Fax: +61-3-9669-4660; e-mail:


Model Designation

BMRC 3.2 (R21 L9) 1993

Model Identification for PMIP


PMIP run(s)

0fix, 6fix

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

Model Lineage

The BMRC model is a descendant of a spectral general circulation model first developed in the 1970s (cf. Bourke et al. 1977 , and McAvaney et al. 1978 ). This version is more recent than that used for the first BMRC AMIP experiment (Version 2.7)

Model Documentation

main reference:

The model configuration for the PMIP experiment is described by :

McAvaney B.J., and Colman R.A., 1993: The BMRC Model : AMIP Configuration. BMRC Research Report No 38.

Colman R.A., and McAvaney B.J., 1995: JGR 100, 3155-3172.

McAvaney B.J., and G.D. Hess, 1996: The Revised Surface Fluxes Parametrisation in BMRC: Formulation. BMRC Research Report No 56.

secondary reference(s):

Key documentation of the BMRC model is provided by Bourke (1988) , Hart et al. (1988 , 1990 ),

Colman and McAvaney (1991) , McAvaney et al. (1991) , and Rikus (1991) .

Colman R.A., and McAvaney B.J., 1995: JGR 100, 3155-3172.

Numerical/Computational Properties

Horizontal Representation

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

Horizontal Resolution

Spectral rhomboidal 21 (R21), roughly equivalent to 3.2 x 5.6 degrees latitude-longitude.

dim_longitude*dim_latitude: 64*56

Vertical Domain

Surface to about 9 hPa. For a surface pressure of 1000 hPa, the lowest atmospheric level is at about 991 hPa.

Vertical Representation

Conservative finite differences in sigma coordinates.

Vertical Resolution

There are 9 unevenly spaced sigma levels with the following levels : 0.991 0.926 0.811 0.664 0.500 0.336 0.189 0.074 0.009

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

Computer/Operating System

The PMIP simulation was run on a Cray Y/MP 3E computer using 1 processor in a UNICOS 6.1.6 environment.

Computational Performance

For the PMIP, about 3 minutes Cray Y/MP computation time per simulation day.


The control experiment was started from an AMIP simulation. For the AMIP simulation, the model atmosphere is initialized from the ECMWF III-B analysis for 12 UT of 1 January 1979, with nonlinear normal mode initialization operative. Soil moisture is initialized from the January data of Mintz and Serafini (1989) . Snow cover is initialized from the albedo data of Hummel and Reck (1979) : albedos greater than 40 percent define areas of seasonal snow with initial depth of 5 m; in areas of permanent snow (i.e., Antarctica and Greenland) the initial depth is set to 250 m.

Time Integration Scheme(s)

A semi-implicit scheme with an Asselin (1972) frequency filter is combined with a split implicit scheme for the vertical diffusion component of the model physics. A time step of 15 minutes is used for both dynamics and physics, except that full calculations of radiative fluxes and heating rates are done once every 3 hours.


Orography is smoothed (see Orography). Filling of negative atmospheric moisture values is performed by a combination of local horizontal and vertical borrowing, and global borrowing following the method of Royer (1986) . A mass adjustment scheme is also used to prevent a slow drift in surface pressure during long integrations. Cf. McAvaney et al. (1991) for further details.

Sampling Frequency

For the PMIP simulation, the model history is written every 6 hours. (However, fields such as convective and total precipitation are accumulated over a 24-hour period; caution should therefore be exercised in interpreting such fields at subintervals of a day.)

Dynamical/Physical Properties

Atmospheric Dynamics

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


Linear second-order (del-squared) horizontal diffusion is applied for wave numbers n > 21 in the upper part of the spectral rhomboid, with a first-order sigma coordinate correction applied near topography.

Stability dependent vertical diffusion after Louis (1979) is only applied for sigma levels > 0.5 in stable layers, but it operates in all unstable layers with no separate removal of dry superadiabats, and with a minimum wind speed difference of 1 m/s assumed between model levels.

Gravity-wave Drag

Momentum transports associated with gravity waves are simulated by the method of Palmer et al. (1986) , using directionally dependent subgrid-scale orographic variances. Surface stress due to gravity waves excited by stably stratified flow over irregular terrain is calculated from linear theory and dimensional considerations. Gravity-wave stress is a function of atmospheric density, low-level wind, and the Brunt-Vaisalla frequency. The vertical structure of the momentum flux induced by gravity waves is calculated from a local wave Richardson number, which describes the onset of turbulence due to convective instability and the turbulent breakdown approaching a critical level.

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.


Carbon dioxide is assumed to be well mixed at the PMIP-prescribed concentration of 345 and 280 ppm for control and 6ka. Zonally averaged seasonal mean ozone distributions are prescribed from the data of Dopplick (1974), with linear interpolation for intermediate times. No other trace gases or aerosols are present, but the radiative effects of water vapour are included (see Radiation).


Shortwave Rayleigh scattering and absorption in ultraviolet (< 0.35 micron) and visible (0.5-0.7 micron) spectral bands by ozone, and in the near-infrared (0.7-4.0 microns) by water vapour and carbon dioxide follow the method of Lacis and Hansen (1974) . Pressure corrections and multiple reflections between clouds are treated. The radiative effects of aerosols are not included directly.

Longwave radiation follows the simplified exchange method of Fels and Schwarzkopf (1975) and Schwarzkopf and Fels (1991) , with slight modifications. (The parent code is compared against benchmark computations by Fels et al. 1991 .) Longwave calculations follow the broad-band emissivity approximation in 8 spectral intervals (with wavenumber boundaries at 0, 1.6 x 104, 5.6 x 104, 8.0 x 104, 9.0 x 104, 9.9 x 104, 1.07 x 105, 1.20 x 105, and 2.20 x 105 m-1). Another 14 bands are accounted for in the cooling-to-space corrections. Included in the calculations are Fels and Schwarzkopf (1981) transmission coefficients for carbon dioxide, the water vapour continuum of Roberts et al. (1976) , and the effects of water-carbon dioxide overlap and of a Voigt line-shape correction. , and the effects of water-carbon dioxide overlap and of a Voigt line-shape correction.

The treatment of cloud-radiative interactions is as described by Rikus (1991) and McAvaney et al. (1991) . Shortwave cloud reflectivity/absorptivity is prescribed for ultraviolet-visible and near-infrared spectral bands and depends only on the height class of the cloud (see Cloud Formation). In the longwave, all clouds are assumed to behave as black bodies (emissivity of 1). For purposes of the radiation calculations, all clouds are assumed to be randomly overlapped in the vertical.


Deep convection is simulated by the mass-flux scheme of Tiedtke (1989), but without inclusion of momentum effects. The scheme accounts for midlevel and penetrative convection, and also includes effects of cumulus-scale downdrafts. The closure assumption for midlevel/penetrative convection is that large-scale moisture convergence determines the bulk cloud mass flux. That is, a condition of moisture balance is specfified in the layer between the surface and cloud base wherby convergence by surface evaporation, turbuence or large scale advection is equated to cloud base mass flux. Entrainment and detrainment of mass in convective plumes occurs both through turbulent exchange and organized inflow and outflow. Reference should be made to Colman and McAvaney (1995) and McAvaney et al. (1995) for further details on the consequences of the use of the Tiedtke scheme in the BMRC model.

Simulation of shallow convection is parameterized in terms of the model's vertical diffusion scheme, following the method of Tiedtke (1983 , 1988 ). Shallow convection is triggered when the lower layers are conditionally unstable and have a relative humidity greater than 75%.

Cloud Formation

Stratiform cloud formation is based on the relative humidity diagnostic form of Slingo (1987) . Clouds are of 3 height classes: high (sigma levels 0.189-0.336), middle (sigma levels 0.500-0.664), and low (sigma levels 0.811-0.926). The fractional amount of each type of cloud is determined from a quadratic function of the difference between the maximum relative humidity of the sigma layer and a threshold relative humidity that varies with sigma level; for high and low cloud the threshold is 60 percent humidity, while for middle cloud it is 50 percent. In addition, following Rikus (1991) , low cloud forms when the relative humidity at the lowest atmospheric level (sigma = 0.991) exceeds 60 percent, and is capped by strong static stability in the layer immediately above (i.e., a temperature inversion is present). In this case, the amount of low cloud increases with the strength of the inversion. There is no parameterization of clouds associated with convective towers. (See Convection for the treatment of convective cloud and Radiation for cloud-radiative interactions.)


Precipitation from large-scale condensation occurs if the relative humidity exceeds 100 percent. The convective precipitation rate is determined from the Tiedtke (1989) convection scheme (see Convection). No evaporation of precipitation is simulated. See also Snow Cover.

Planetary Boundary Layer

The height of the PBL is assumed to be that of the lowest prognostic vertical level (sigma = 0.991). Winds, temperatures, and humidities for calculation of turbulent eddy surface fluxes from bulk formulae are taken to be the same values as those at this lowest atmospheric level (see Surface Fluxes). See also Diffusion and Surface Characteristics.


Orography from a 1 x 1-degree U.S. Navy dataset is grid-point smoothed using a Cressman (1959) area-averaged weighting function with a radius of influence of 3 degrees for the spectral R21 model resolution (cf. Bourke 1988) .


For control: PMIP datasets will be used for SSTs and sea-ice have been prepared at PCMDI and were calculated by averaging the 10-year AMIP datasets (1979-1988).

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

Sea Ice

For 0fix and 6fix, monthly AMIP sea ice extents are prescribed via a Cressman (1959) weighting function with a 3-degree radius of influence; these monthly ice extents are updated by interpolation every 5 days. The thickness of the sea ice is held fixed at 1 m for the Antarctic region and 2 m for the Arctic. Snow is permitted to accumulate or to melt on the ice surface, but there is no conversion of snow to ice. The surface temperature of the sea ice/snow is determined from a heat balance calculation (see Surface Fluxes) with inclusion of a conduction term from the ocean (at a fixed temperature of 271 K) below the ice.

Snow Cover

When the weighted average of the air temperature at the lowest two levels (sigma = 0.991 and 0.926) falls below 273.16 K, precipitation falls to the surface as snow. Prognostic snow mass with accumulation and melting over both land and sea ice is modelled. Snow cover affects the surface albedo and the surface roughness (see Surface Characteristics), but there is no explicit allowance for the effects of fractional snow cover. Melting of snow, which occurs when the surface temperature exceeds 0 degrees C, contributes to soil moisture (see Land Surface Processes), but sublimation of snow is not calculated as part of the surface evaporative flux (see Surface Fluxes).

Surface Characteristics

Distinguished surface types include ocean, land, land ice, and sea ice, and the presence of snow cover is also accounted for on the latter three surfaces. Soil or vegetation types are not distinguished.

The roughness length over oceans is determined from the surface wind stress, following Charnock (1955) , with a coefficient of 0.0185 assigned after Wu (1982) ; the ocean roughness is constrained to a minimum value of 1.5 x 10-5 m. Roughness lengths are prescribed uniform values over sea ice (0.001 m) and land surfaces (0.168 m), but the presence of snow cover changes the roughness to a new (fixed) value (0.001m).

Over oceans, the surface albedo depends on solar zenith angle, following Payne (1972). Seasonal climatological surface albedos of Hummel and Reck (1979) are prescribed over land. The surface albedos of sea ice and snow-covered land follow the temperature-ramp formulation of Petzold (1977) , with different values of albedo limits and a lower temperature range for sea ice and snow, as described by Colman and McAvaney (1992)

Longwave emissivity is set to unity for all surfaces (i.e., black body emission is assumed).

Surface Fluxes

Surface solar absorption is determined from surface albedos, and longwave emission from the Planck equation with prescribed constant surface emissivity of 1.0 (see Surface Characteristics).

The surface turbulent eddy fluxes of momentum, heat, and moisture follow Monin-Obukhov similarity theory, and are formulated in terms of bulk formulae with stability-dependent drag/transfer coefficients determined as in Louis (1979) . The momentum flux is given by the product of the air density, a neutral drag coefficient, wind speed and wind vector at the lowest prognostic level (sigma = 0.991), and a transfer function that depends on roughness length (see Surface Characteristics) and stability (bulk Richardson number). Surface wind speed is constrained to a minimum of 1 m/s. The flux of sensible heat is given by a product of a neutral exchange coefficient, the wind speed at the lowest prognostic level, the difference in temperatures between the ground and the first prognostic atmospheric level, and a modified form of the transfer function for unstable conditions (cf. Louis 1979) .

The flux of surface moisture is given by a product of the same transfer coefficient and stability function as for sensible heat, an evapotranspiration efficiency beta, and the difference between the specific humidity at the first prognostic level and the saturation specific humidity at the surface temperature and pressure. For calm conditions over the oceans, evaporation also is enhanced following the approximation of Miller et al. (1992) for the transfer coefficient. Over oceans, sea ice, and snow, beta is prescribed to be unity; over land, beta is a function of the ratio of soil moisture to a constant field capacity (see Land Surface Processes).

Land Surface Processes

Soil temperature is computed from heat storage in two layers with a climatological temperature specified in a deeper layer. The upper boundary condition is the surface energy balance (see Surface Fluxes). The heat conductivity of soil is fixed under all conditions.

Prognostic soil moisture is represented by a single-layer "bucket" model with uniform field capacity of 0.15 m after Manabe and Holloway (1975). . Both precipitation and snowmelt contribute to soil moisture. The evapotranspiration efficiency beta (see Surface Fluxes) is a function of the ratio of soil moisture to the field capacity. Runoff occurs implicitly if this ratio exceeds unity.

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