**PMIP Documentation for MRI2**

**Meteorological Research Institute:
Model MRI GCM-IIb (4x5 L15) 1995**

and:

Dr Hiroshi Koide, Climate Research Department, Meteorological Research Institute, 1-1, Nagamine, Tsukuba, Ibaraki, 305-0052 Japan; Phone:+81-298-53-8597 (8681); Fax: +81-298-55-2552; e-mail: hkoide@mri-jma.go.jp;

World Wide Web URL: http://www.mri-jma.go.jp.

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

Results from the AMIP simulation by the MRI model MRI GCM-IIb (4x5 L15) 1995 are discussed by Kitoh et al. (1995).

Results from the couled atmosphere/mixed-layer ocean model are given
by Kitoh (1997) and Kitoh et al. (1998).

dim_longitude*dim_latitude: 72*46

The 15 hybrid levels in pressure (modified sigma) coordinate are as the following :

912 (0.902), 741 (0.712), 589 (0.543), 457 (0.397), 335 (0.261), 237 (0.152), 168 (0.076), 119 (0.021),

72 (-0.283), 37.3 (-0.633), 19.3 (-0.815), 10 (-0.909), 5.18 (-0.958),
2.68 (-0.983), 1.39 (-0.996).

Vertical diffusion is not applied above the well-mixed PBL (see Planetary
Boundary Layer). However, momentum is redistributed vertically by cumulus
convection (see Convection).

Longwave calculations are based on the multiparameter random model of
Shibata and Aoki (1989) applied in four spectral regions (with boundaries
at 2.0 x 10^{3}, 5.5 x 10^{4}, 8.0 x 10^{4}, 1.2
x 10^{5}, and 2.2 x 10^{5} m^{-1}). Absorption
bands of carbon dioxide, ozone, and water vapor are included. Continuum
absorption of water vapor is treated after the method of Clough et al.
(1980) , but with the temperature dependency used by Roberts et al. (1976)
. Mean diffuse transmittances in each region are determined from line-by-line
calculations approximated by an exponential function including 10 or 12
parameters. Transmittances through inhomogeneous atmospheres are computed
by a modified Godson (1953) method.

In the shortwave, clouds are treated by a delta Eddington approximation
with prescribed single-scattering albedo and asymmetry factor, and with
cloud optical depth a function of height. In the longwave, clouds behave
as blackbodies, except for high (above 400 hPa) clouds, whose emissivity
is related to shortwave optical depth. For purposes of the radiation calculations,
all clouds are assumed to be randomly overlapped in the vertical. See also
Cloud Formation.

The Arakawa-Schubert scheme is modified to impose an additional constraint between the minimum entrainment rate and the prognostic depth of the PBL (cf. Tokioka et al. 1988) . The mass flux for each cumulus subensemble is predicted from an integral equation that includes a positive-definite work function (defined by the tendency of cumulus kinetic energy for the subensemble) and a negative-definite kernel which expresses the effects of other subensembles on this work function. The predicted mass fluxes are optimal solutions of this integral equation under the constraint that the rate of generation of conditional convective instability by the large-scale environment is balanced by the rate at which the cumulus subensembles suppress this instability via large-scale feedbacks (cf. Lord et al. 1982) . The mass fluxes are computed by the "exact direct method," which guarantees an exact solution within roundoff errors.

If the lapse rate becomes dry convectively unstable at any level, moisture
and enthalpy are redistributed vertically. In addition, a moist convective
adjustment simulates midlevel convection originating above the PBL. When
the lapse rate exceeds moist adiabatic under supersaturated conditions,
mass is mixed such that either the lapse rate is restored to moist adiabatic,
or the supersaturation is eliminated by formation of convective precipitation.
Cf. Tokioka et al. (1984) for further details.

The turbulence kinetic energy (TKE) also is determined. (TKE is generated
by wind shear and convective buoyancy fluxes, and is depleted by surface
dissipation, by work done against the free atmosphere, and by newly turbulent
air that is entrained into the PBL.) Because of the mutual dependence of
the entrainment rate and the turbulent fluxes at the PBL top and at the
surface, these quantities are solved iteratively under the assumption that
the generation of TKE balances its dissipation. See also Surface Characteristics
and Time Integration Scheme(s).

For 21fix run, the CLIMAP SSTs ( for February and August ) are used as a mid-month values, and interpolated with sine function. The SST of the region where temporally covered with sea ice is appropriately interpolated with assuming SST of the ice edge is -1.8 degrees C (see Sea Ice).

For 0cal and 21 cal, SST is calculated in every 5 day from the heat
balance of the 50-m depth mixed-layer (slab) ocean using the heat fluxes
at the sea surface and prescribed heat flux value (Q-flux). Monthly mean
Q-flux value is obtainedby runing the model for 3 years restoring the model
SST and sea-ice amount to observations. The same Q-flux value is used for
0cal and 21cal with some adjustment over the sea-ice area in 21k.

For 21fix run, see Ocean. The spatially variable thickness of sea ice is given by the local concentration fraction multiplied by 3.0 meters in the Northern Hemisphere and by 0.5 meter in the Southern Hemisphere. Daily values of the above quantities are determined by linear interpolation.

The ice surface temperature is predicted from the net flux of energy (see Surface Fluxes), including a subsurface conduction heat flux that is proportional to the difference between the ice surface temperature and that prescribed (271.3 K) for the ocean below. Snow may accumulate on sea ice or melt if the snow surface temperature exceeds 0 degrees C (see Snow Cover). Snow also alters the heat capacity /conductivity of the ice, but the heat capacity of snow is independent of depth.

For 0cal and 21cal, sea-ice concentration (compactness) and thinckness
are also predicted in every 5 day following Mellor and Kantha (1989). The
sea-ice model is basically the same one used in MRI coupled GCM (Tokioka
et al., 1996), but sea surface salinity is fixed at the present climatology
and advection of sea-ice is not included.

The surface roughness length is a fixed value over oceans (2 x 10^{-4}
m), sea ice (1 x 10^{-4} m), glacial ice (5 x 10^{-3} m),
and land (0.45 m); the surface drag coefficient over land is a function
of orographic variances, however (see Orography and Surface Fluxes).

Surface albedos depend on solar zenith angle (cf. Paltridge and Platt
1976) , but not on spectral interval. The ocean albedo is a maximum of
0.07. The albedo of bare sea ice ranges between a maximum of 0.50 to 0.64
as a function of surface temperature; the albedo of snow-covered sea ice
is a maximum of 0.70, depending on snow depth. Snow-covered glacial ice
albedos range between 0.70 and 0.85. Snow-free land albedos are obtained
from the data of Matthews (1983) ; with snow cover, the land albedo ranges
from its snow-free value to a maximum between 0.60 to 0.70, depending on
topographic height (see Orography). On all surfaces, the albedo of melting
snow is 0.60, and that of frost is 0.30. Longwave emissivity is prescribed
as unity (blackbody emission) for all surfaces.

Turbulent eddy fluxes of momentum, heat, and moisture are parameterized
as bulk formulae with drag and transfer coefficients that depend on vertical
stability (bulk Richardson number) and the (locally variable) depth of
the PBL normalized by the surface roughness length, following Deardorff
(1972) . The drag coefficient over land is also increased as a function
of orographic variances (see Orography and cf. Yagai and Tokioka 1987 ).
The surface atmospheric values of wind, dry static energy, and humidity
required for the bulk formulae are taken to be those predicted in the PBL
(see Planetary Boundary Layer). Because of the mutual dependence of the
turbulent fluxes at the surface and at the PBL top, these (as well as the
PBL entrainment rate) are solved by mutual iteration. See also Surface
Characteristics and Time Integration Scheme(s). The surface moisture flux
depends also on an evapotranspiration efficiency factor beta, which is
set to unity over ocean and ice surfaces and in areas of continental dew
formation; otherwise, over land, beta is a function of soil moisture (see
Land Surface Processes).

Last update November 9, 1998. For further information, contact: Céline Bonfils (pmipweb@lsce.ipsl.fr )