Recherche en Prévision Numérique: Model RPN NWP-D40P29 (T63 L23) 1993

Recherche en Prévision Numérique: Model RPN NWP-D40P29 (T63 L23) 1993

AMIP Representative(s)

Dr. Harold Ritchie, Recherche en Prévision Numérique, 2121 Trans-Canada Highway, Room 500, Dorval, Quebec, Canada H9P 1J3; Phone: +1-514-421-4739; Fax: +1-514-421-2106; e-mail:

Model Designation

RPN NWP-D40P29 (T63 L23) 1993

Model Lineage

The RPN model derives from research on application of the semi-Lagrangian method (cf. Ritchie 1985 [1], 1986 [2], 1987 [3], 1988 [4], 1991 [5]), and from physical parameterizations in use in other models at this institution.

Model Documentation

The semi-Lagrangian numerics are described by Ritchie (1991) [1], and the finite element discretization by Beland and Beaudoin (1985) [6]. Descriptions of some physical parameterizations are provided by Benoit et al. (1989) [7].

Numerical/Computational Properties

Horizontal Representation

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

Horizontal Resolution

Spectral triangular 63 (T63), roughly equivalent to 1.9 x 1.9 degrees latitude-longitude.

Vertical Domain

Surface to about 10 hPa. For a surface pressure of 1000 hPa, the lowest atmospheric level is at 1000 hPa (using a nonstaggered vertical grid).

Vertical Representation

Finite-element sigma coordinates. (Some changes in the form of the vertical discretization of the model equations are required to produce a formulation appropriate for use of the semi-Lagrangian method--cf. Ritchie 1991 [1].)

Vertical Resolution

There are 23 unevenly spaced sigma levels. For a surface pressure of 1000 hPa, 7 levels are below 800 hPa and 7 levels are above 200 hPa.

Computer/Operating System

The AMIP simulation was run on a NEC SX-3 computer using a single processor in a UNIX operating environment.

Computational Performance

For the AMIP experiment, about 4 minutes computation time per simulated day.


For the AMIP simulation, the model atmosphere, soil moisture, and snow cover/depth are initialized for 1 December 1978 from FGGE analyses and climatological datasets. An adiabatic nonlinear normal mode initialization after Machenauer (1977) [8] is also applied. The model is then integrated forward to the nominal AMIP start date of 1 January 1979.

Time Integration Scheme(s)

A semi-implicit, semi-Lagrangian time integration scheme with an Asselin (1972) [9] frequency filter is used (cf. Ritchie 1991) [1]. Vertical diffusion and surface temperatures and fluxes are computed implicitly (cf. Benoit et al. 1989) [7]. The time step is 30 minutes for dynamics and physics, except for full calculations of shortwave and longwave radiative fluxes, which are done every 3 hours.


Orography is smoothed (see Orography). Negative values of atmospheric specific humidity are temporarily zeroed for use in physical parameterizations, but are not permanently filled. The solution in spectral space imposes an approximate conservation of total mass of the atmosphere.

Sampling Frequency

For the AMIP simulation, the model history is written every 12 hours.

Dynamical/Physical Properties

Atmospheric Dynamics

Primitive-equation dynamics expressed in terms of the horizontal vector wind, surface pressure, specific humidity, and temperature are formulated in a semi-Lagrangian framework (cf. Ritchie 1991) [1].


  • Second-order (del^2) horizontal diffusion is applied to spectral vorticity, divergence, temperature, and specific humidity on constant-sigma surfaces. All diffusivity coefficients are 10^5 m^2/s.

  • Vertical diffusion is represented by the turbulence kinetic energy (TKE) closure scheme described by Benoit et al. (1989) [7] and Mailhot and Benoit (1982) [10]. Prognostically determined TKE is produced by shear and buoyancy, and is depleted by viscous dissipation. Vertical (but not horizontal) transport of TKE is also modeled, and a minimum background TKE (10^-4 m^2/s^2) is always present. Diffusion coefficients for momentum and heat/moisture are determined from the current value of TKE and from a locally defined stability-dependent turbulence mixing length. See also Planetary Boundary Layer and Surface Fluxes.

Gravity-wave Drag

Subgrid-scale parameterization of gravity-wave drag follows the method of McFarlane (1987) [11]. Deceleration of resolved flow by breaking/dissipation of orographically excited gravity waves is a function of atmospheric density and the vertical shear of the product of three terms: the Brunt-Vaisalla frequency, the component of local wind in the direction of a near-surface reference level, and a displacement amplitude that is bound by the lesser of the subgrid-scale orographic variance (see Orography) or a wave-saturation value.

Solar Constant/Cycles

The solar constant is the AMIP-prescribed value of 1365 W/(m^2). Both seasonal and diurnal cycles in solar forcing are simulated.


The carbon dioxide concentration is the AMIP-prescribed value of 345 ppm. Monthly climatological zonal profiles of ozone are prescribed after data of Kita and Sumi (1986) [12]. Radiative effects of water vapor are also included, but not those of other greenhouse gases or of aerosols (see Radiation).


  • The outputs of the shortwave and longwave radiation schemes are the fluxes at each level and the heating rates in each layer. Fluxes also interact with the model at the surface, where the energy balance determines the surface temperature (see Surface Fluxes and Land Surface Processes).

  • The shortwave parameterization after Fouquart and Bonnel (1980) [13] considers the effects of carbon dioxide and ozone (see Chemistry), water vapor, clouds, and liquid water. When clouds are present, liquid water is diagnosed from atmospheric temperature: a fraction of the maximum theoretical liquid water concentration on a wet adiabat is assumed, following Betts and Harshvardhan (1987) [14]. The entire visible spectrum is treated as a single interval.

  • The longwave parameterizations after Garand (1983) [15] and Garand and Mailhot (1990) [16] include the same constituents as in the shortwave scheme, except that liquid water is not interactive. The frequency integration is carried out over 4 spectral intervals: the carbon dioxide 15-micron band divided into center and wing components, the 9.3-micron ozone band, and the rest of the infrared spectrum, including absorption bands for water vapor and continuum absorption. (The frequency integration is precomputed for different temperatures and absorber amounts, with the results stored in look-up tables.) All clouds are assumed to behave as blackbodies (emissivity of 1.0) and to be fully overlapped in the vertical. See also Cloud Formation.


  • A modified Kuo (1974) [17] scheme is used to parameterize the effects of deep precipitation-forming convection. When the large-scale vertical motion at the top of the planetary boundary layer (PBL) is upward and the free atmosphere above the PBL top (at about 900 hPa) is conditionally unstable, the assumed convective activity depends on the net moisture accession in the atmospheric column that is provided by both surface evaporation and large-scale moisture convergence. This moisture is partitioned between a fraction b which moistens the environment, and the remainder (1 - b) which contributes to the latent heating (precipitation) rate. Following Anthes (1977) [18], the moistening parameter b is determined as a cubic function of the ratio of the mean relative humidity of the cloud layer to a prescribed critical relative humidity threshold value; if the cloud relative humidity is less than the threshold, b is set to unity (no heating of the environment). The vertical distribution of the heating or moistening is according to differences between mean-cloud and large-scale profiles of temperature and moisture. The mean-cloud profiles are computed from the parcel method slightly modified by an entrainment height of 20 km.

  • Shallow convection is parameterized by a generalization of the PBL turbulence formulation (see Diffusion) to include the case of partially saturated air in the conditionally unstable layer above an unstable boundary layer. First, a convective cloud fraction is diagnosed from a relation based on the Bjerknes slice method; then the buoyancy and all the turbulent fluxes are calculated, assuming condensation occurs in that layer fraction. The main effect of the parameterization is to enhance the vertical moisture transport in the absence of large-scale moisture convergence. See also Planetary Boundary Layer.

Cloud Formation

Convective and stable cloud fractions are diagnosed separately and then combined to interact with the radiative fluxes (see Radiation). In supersaturated, absolutely stable layers, a stable cloud fraction of unity is assigned. In layers where shallow or deep convection is diagnosed, the cloud fraction is determined from the pertinent portion of the convective scheme (see Convection).


Large-scale precipitation forms as a result of condensation in supersaturated layers that are absolutely stable, and shallow convective precipitation in conditionally unstable layers. Deep convective precipitation also forms in association with latent heating in the Kuo (1974) [17] scheme (see Convection). There is subsequent evaporation of large-scale precipitation only.

Planetary Boundary Layer

The depth of the unstable PBL is determined from the profile of static stability. The depth of the stable PBL is diagnosed using the Monin-Obukhov length. See also Diffusion and Surface Fluxes.


The raw topography are from the U.S. Navy data with 10-minutes arc resolution (cf. Josseph 1980) [19] obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF). These heights are spectrally filtered and truncated at the T63 model resolution. The orographic variances required for the gravity-wave drag parameterization (see Gravity-wave Drag) are also determined from the same dataset. Cf. Pellerin and Benoit (1987) [20] for further details.


AMIP monthly sea surface temperature fields are prescribed, with daily values determined by linear interpolation.

Sea Ice

AMIP monthly sea ice extents are prescribed. The surface temperature of sea ice is predicted by the force-restore method of Deardorff (1978) [21] in the same way as for land points (see Land Surface Processes), without consideration of subsurface heat conduction through the ice. Snow cover is not accounted for on sea ice (see Snow Cover). Cf. Benoit et al. (1989) [7] for further details.

Snow Cover

Snow mass is not a prognostic variable, and a snow budget is therefore not included. Snow cover over land is prescribed from the monthly climatology of Louis (1984) [22], but snow is not specified on sea ice (see Sea Ice). Snow cover alters the albedo (see Surface Characteristics), but not the heat capacity/conductivity of the surface. Sublimation of snow contributes to surface evaporation (see Surface Fluxes), but soil moisture is not affected by snowmelt (see Land Surface Processes). Cf. Benoit et al. (1989) [7] for further details.

Surface Characteristics

  • Over land, surface roughness lengths that are functions of orography and vegetation are specified after Louis (1984) [22]. Over sea ice, the prescribed roughness length ranges between 1.5 x 10^-5 and 5 x 10^-3 m. Over ocean, the roughness length is treated as a function of the surface wind stress after the method of Charnock (1955) [23].

  • Surface albedos do not depend on solar zenith angle or spectral interval. On land, the surface albedo is specified from annual background values (provided by the Canadian Climate Centre) modulated with the monthly ice (albedo 0.70) and snow (albedo 0.80) climatology (see Snow Cover). The albedo of ocean points is specified to be a uniform 0.07.

  • The surface longwave emissivity is prescribed as 0.95 over land and sea ice and as 1.0 (blackbody emission) over ocean.

Surface Fluxes

  • The surface solar absorption is determined from surface albedos, and longwave emission from the Planck equation with prescribed surface emissivities (see Surface Characteristics).

  • Following Monin-Obukhov similarity theory, the surface turbulent momentum, sensible heat, and moisture fluxes are expressed as bulk formulae, with drag and transfer coefficients that are functions of surface roughness length (see Surface Characteristics) and of stability (expressed as a bulk Richardson number computed between level sigma = 0.99 and the surface). The same transfer coefficient is used for the heat and moisture fluxes.

  • The flux of surface moisture also depends on an evapotranspiration efficiency factor b that is unity over oceans, sea ice, and snow, but that is prescribed as a monthly wetness fraction over land (see Land Surface Processes).

  • Above the surface layer, the turbulence closure scheme after Mailhot and Benoit (1982) [10] and Benoit et al. (1989) [7] is used to determine momentum, heat, and moisture fluxes. See also Diffusion and Planetary Boundary Layer.

Land Surface Processes

  • The surface temperature of soil (and of sea ice) is computed by the force-restore method of Deardorff (1978) [21]. The upper boundary condition is a net balance of surface energy fluxes (see Surface Fluxes), and monthly deep temperatures are prescribed as a lower boundary condition. The thermodynamic properties are those characteristic of clay soil, and the depth of the soil layer is taken to be that of the penetration of the diurnal heat wave. The same properties are also used for predicting the temperature of sea ice (see Sea Ice).

  • Soil moisture (expressed as a wetness fraction) is prescribed from monthly climatologies of Louis (1981) [24]. Precipitation and snowmelt therefore do not influence soil moisture, and runoff is not accounted for; however, the prescribed wetness fraction does affect surface evaporation (see Surface Fluxes). Cf. Benoit et al. (1989) [7] for further details.

Go to RPN References

Return to RPN Table of Contents

Return to Main Document Directory

Last update April 19, 1996. For further information, contact: Tom Phillips ( )

LLNL Disclaimers