Department of Numerical Mathematics: Model DNM A5421 (4x5 L21) 1998a

Contact Information

Experimental Implementation

Model Output Description

Model Characteristics

Contact Information

Modeling Group

AMIP Representative(s)

• AMIP representatives: Dr. Vener Galin, Dr. Eugeny Volodin, and Dr. Valentin Dymnikov
• Mail address: Institute of Numerical Mathematics, Russian Academy of Sciences, 8 Gubkina Str., Moscow, 117333, Russia
• Phone: +7-095-938-39-04
• Fax: +7-095-938-18-21
• Internet e-mail: galin@inm.ras.ru

Experimental Implementation

Simulation Period

Earth Orbital Parameters

Calendar

Radiative Boundary Conditions

• As specified for AMIP II, the solar constant is 1365 Wm^-2 (with both seasonal and diurnal cycles present).

• The carbon dioxide concentration is the AMIP-specified 348 ppmv.  Concentrations of other included green house gases are as recommended: 1650 ppbv for methane and 306 ppbv for nitrous oxide.

• The monthly ozone concentration is the recommended zonal mean climatology of Wang et al. (1995)[66].

• The aerosol concentration follows the zonal-average climatology of Barker and Li (1995)[29].  See also Chemistry.

Ocean Surface Boundary Conditions

Orography/Land-Sea Mask

• The model orography is derived from the 1x1-degree topographic height data of Gates and Nelson (1975)[16] which are averaged over each 4x5 grid box.  Then a 9-point filter is applied to further smooth data from surrounding grid cells. Finally, poleward of 69 degrees, the orography is filtered by the method of Burridge and Haseler (1977)[30] to eliminate high-frequency variability near the Poles in the longitudinal direction. The global-average height of model orography is 231.07 m.

• The land-sea mask is derived from the 1x1-degree topography data of Gates and Nelson (1975)[16]. A model 4x5-degree grid box is defined as land if more than 50% of the included topography heights are positive-valued; otherwise the grid box is defined as ocean.

Atmospheric Mass

Spinup/Initialization

Computer/Operating System

Computational Performance

Model Output Description

Calculation of Standard Output Variables

• Method for calculation of percentage time that a pressure surface is below ground: Every hour surface pressure is compared with the values of standard pressures. The number of times when the surface pressure is greater than the standard pressure, divided by the number of hours in a month and multiplied by 100, is the estimated percentage time.

• Method for calculation of monthly mean tendencies at 17 WMO standard pressure levels: All temperature and moisture tendencies due to physical processes are calculated every hour on sigma-surfaces. Then they are accumulated, and every 6 hours interpolated onto standard pressure levels. These 6-hour tendencies again are accumulated to obtain monthly mean values.

• Method for calculation of cloud properties: Total cloud water content is simulated according to Lemus et al. (1997)[31]. The liquid and ice fractions of the in-cloud water content are given by Matveev (1984)[32] and by Rockel et al. (1991)[35]. Extinction coefficients for the liquid water path are after Slingo (1989)[33], and for the ice water path, after Ebert and Curry (1992)[34]. Cloud emittance is calculated according to Rockel et al. (1991)[35]. The effective radius of the liquid droplets is fixed at 10 microns, and that of the ice crystals at 30 microns.

• Method for calculation of surface variables:  The 10 m winds and 2 m temperature and humidity are calculated using the Monin-Obukhov similarity theory for the gradients of dimensionless winds, potential temperature and humidity. Universal empirical functions taken as in Businger et al. (1971)[36], are matched with a -1/3 power-law dependence for strong instability, following Kazakov and Lykossov (1982)[6].

• Method for calculation of sea-level pressure P_s:  P_s = P_surf*exp(g*Z_s/(R*T(nlev) + k*Z_s/2)), where P_surf is the surface pressure, g is the gravitational  acceleration, Z_s is the surface height, R is the universal gas constant, T(nlev) is the temperature of the lowest model level, and k = 0.006 K m^-1 is the mean vertical temperature gradient.

• The recommended procedure of Potter et al.(1992)[37] is followed for calculation of clear-sky radiation and cloud radiative forcing.

• Potential vorticity is not calculated.

• The top of the planetary boundary layer (PBL) is determined as the greater of the height predicted from Ekman theory versus a convective height that depends on dry static energy in the vertical.

Sampling Procedures

Interpolation Procedures

• Output variables are interpolated to 17 standard pressure surfaces linearly in the vertical coordinate ln (sigma). For pressure levels below ground, u, v, and w velocities are defined as zero, temperature is linearly extrapolated, and all other values are equated to those at the lowest vertical level.

• Vertical interpolation is done every 6 hours, with values accumulated to compute monthly means.

Output Data Structure/Format/Compression

Model Characteristics

AMIP II Model Designation

Model Lineage

• Inclusion of irregular vertical representation and increases in vertical resolution of the stratosphere and PBL.

• Inclusion of a spectral, instead of a bulk integral, radiation scheme.

• Use of Betts-Miller[42] convection in place of another convective adjustment scheme.

• Calculation of horizontal diffusion on constant pressure surfaces instead of sigma surfaces.

• Inclusion of gravity wave drag.

• Use of a complex soil model in place of a simple 1-layer scheme.

Model Documentation

Numerical/Computational Properties

Horizontal Representation

Horizontal Resolution

4x5 degrees latitude-longitude.

Vertical Domain

Vertical Representation

Vertical Resolution

Time Integration Scheme(s)

Smoothing/Filling

• Orography is smoothed (see Orography/Land-Sea Mask). Atmospheric temperature, specific humidity, winds and surface pressure are filtered at latitudes poleward of 69 degrees by the method of Burridge and Haseler (1977)[30]. Heat, moisture and momentum fluxes from the surface are smoothed by a 9-point filter.

• Negative moisture values are filled by borrowing from nearest neighbors in the vertical.

• Atmospheric mass is corrected by multiplying the surface pressure by an appropriate factor.

Dynamical/Physical Properties

Equations of State

Diffusion

• Non-linear, fourth-order horizontal diffusion is applied on constant pressure surfaces to u and v winds, temperature and specific humidity. The diffusion coefficient is independent of the height, but is proportional to Del³.

• Second-order local vertical diffusion operates throughout the PBL, and above for conditions of dry static instability. It is applied to potential temperature, specific humidity, and u-v winds. The vertically variable diffusion coefficient depends on stability, expressed as a bulk Richardson number, and on the vertical wind shear, following standard mixing-length theory.

Gravity Wave Drag

Chemistry

Radiation

• Shortwave scattering/absorption is parameterized by the delta-Eddington approximation of Joseph et al.(1976)[49] and Galin (1998)[46] applied in 18 spectral intervals, as described by Briegleb (1992)[50]. Following Slingo (1989)[33], the shortwave optical properties of clouds for the delta-Eddington method are specified for 4 spectral ranges with boundaries at 0.25, 0.69, 1.19, 2.38, and 4.0 microns.  Optical properties of aerosols are fixed according to Barker and Li (1995)[29].

• Longwave absorption by carbon dioxide, water vapor, methane, nitrous oxide, ozone, with transmission functions by Chou et al.(1991a[53], 1991b[52], 1993[51]), is calculated for ten spectral intervals with boundaries at 0.0, 3.40, 5.40, 6.20, 7.20, 8.00, 9.80, 11.00, 13.80, 19.00, and 30.00 m^-1.

• Cloud liquid water is diagnostically determined following Lemus et al. (1997)[31], and the ratio of cloud liquid water and ice following Matveev (1984)[32].  Large-scale clouds are assumed to be fully overlapped within a single layer (0-400 hPa, 400-700 hPa and 700-1000 hPa), but clouds in different layers are treated as randomly overlapped.  Convective clouds are assumed to be fully overlapped.

• Each grid box is divided into 8 sectors having the following characteristics: no clouds, only upper clouds; only middle clouds; only low clouds; upper and middle clouds; upper and low clouds; middle and low clouds; and upper, middle and low clouds together.  In each sector, clouds are treated as uniform in the horizontal direction with a fractional area that is determined from the assumptions about the cloud vertical overlap.  Radiative fluxes are calculated separately for each sector, and the overall flux for each grid box is computed as a weighted sum of the fluxes in the 8 sectors. See Galin (1998)[46] for further details.  See also Convection and Cloud Formation.

Convection

• If the temperature of the lowest atmospheric level exceeds 287K, convection after Betts and Miller (1984)[42] is simulated as a relaxed convective adjustment towards calculated temperature and humidity reference profiles that are based on observations. The relaxation time is 12 hours for precipitating deep convection and 2 hours for nonprecipitating shallow convection, which are regarded as mutually exclusive processes.

• The convection is treated as shallow if the cloud top (defined as the level of non-buoyancy) is below about 800 hPa for a surface pressure of 1000 hPa, or if there is insufficient moisture for precipitation to form; otherwise, deep convection is operative.

• If the temperature of the lowest atmospheric level is below 287K, then convective adjustment after Manabe and Strickler (1964)[10] operates. Once all types of convection are realized, the associated convective mixing by the u and v winds is calculated.

Cloud Formation

• Large-scale cloud amount C at a particular vertical level is diagnostically determined from relative humidity r: C = max[(r - r_cr)/(1 - r_cr), 0], where critical relative humidity r_cr is specified as 0.77 for high clouds (above 400 hPa), 0.75 for middle clouds (400 - 700 hPa), and 0.87 for low clouds (below 700 hPa). For the lowest layer, the cloud fraction cannot exceed r_cr.

• Convective cloud formation is parameterized according to the amount of convective precipitation, following Slingo (1987)[54]. See also Radiation and Precipitation.

Precipitation

• Precipitation, calculated by diagnostic methods, is uniformly distributed in each grid box.  Large-scale precipitation forms as a result of condensation in supersaturated layers. Temperature and humidity are adjusted by three iterations; after adjustment, the layer is completely saturated. Convective precipitation is defined by the difference in specific humidity before and after the occurence of convection.

• Evaporation of large-scale precipitation in a layer below cloud is proportional to the saturation deficit and rain intensity. Evaporation of convective precipitation is not treated.

Planetary Boundary Layer

Sea Ice

Snow Cover

• Snow falls to the surface if the temperature of the lowest atmosphere level is less then 0 deg C. Snow accumulates only on land to a depth that is determined prognostically from a budget equation, and melts if the temperature of the snow-covered surface is 0 deg C with positive heat balance. Snow density, heat capacity, and heat conductivity depend on snow depth and are defined as in Volodin and Lykossov (1997)[45].

• The fraction of land covered by snow is 0.9 if the water-equivalent snow depth is greater than 4x10^-3m, and decreases linearly below 0.9 proportional to decreasing snow depth. Sublimation of snow is calculated assuming saturated surface air humidity over the snow-covered area. The surface roughness does not depend on the presence of snow.

Surface Characteristics

• Distinguished surface types are open ocean, land, continental ice, and sea ice; each grid box includes only one of these types. If the surface type is land, then the grid box is subdivided into areas occupied by snow, bare soil, vegetation type, and canopy-intercepted or inland water.  The 11 vegetation types are as described by Dorman and Sellers (1989)[55], a reduction of the 72 types of  Wilson and Henderson-Sellers (1985)[58]. For dry conditions in the root-zone, the fractional area of  vegetation decreases, and that of the bare soil increases.

• The roughness length over the ocean is a function of the surface stress given by the Charnock (1955)[17] relation, with coefficient 0.14. Over sea ice, the roughness is prescribed to be 0.01 m; over continental ice, it is 0.05 m.  Over land, the roughness z is a linear function of the surface height Z_s: z = 0.2 + Z_s/5000, where all values are in meters.

• The seasonal-mean background land surface albedo is calculated as the maximum of that from Matthews (1983)[27] and from Geleyn and Preuss (1983)[56]. This albedo is altered by snow cover as a linear function of the ratio of the water-equivalent snow depth to a critical value (4x10^-3m). Albedos of snow in open areas range from 0.5 to 0.8 and, in forested areas from 0.5 to 0.7.  Albedos of sea ice range from 0.5 to 0.75 and those of land ice from 0.6 to 0.8; they vary as a linear function of surface temperature between 263.15K to 273.15K, and are constant for a temperature below 263.15K. The albedo of ocean is a constant 0.065 for diffuse radiation, while that for the direct beam depends on solar zenith angle, but never exceeds 0.15. Albedos do not depend on soil moisture or the wavelength of light.

• Longwave emissivity is prescribed as 1.0 for ocean, 0.99 for ice and snow, and 0.96 for land without snow. For partially snow-covered areas, the emissivity varies linearly from 0.96 to 0.99 as the snow-water equivalent depth varies from 0 to 4x10^-3m.

Surface Fluxes

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

• Surface turbulent eddy fluxes of momentum, heat and moisture are simulated as stability-dependent bulk formulae, following Monin-Obukhov similarity theory. For calculation of drag and exchange coefficients, empirical functions of Businger et al. (1971)[19] are matched with a -1/3 power-law dependence for strong instability (Kazakov and Lykossov, 1982)[6]; these are used as universal functions of roughness length and thermal stability to define the vertical profiles of wind, temperature, and humidity in the constant-flux surface layer. The required near-surface values of wind, temperature, and humidity are taken to be those at the lowest atmospheric level.

• The surface moisture flux depends on the specific humidity; over ocean, snow, ice and wet vegetated fractions, this is taken as the saturated humidity at the surface temperature and pressure. Over bare soil, the surface specific humidity is the product of relative humidity and the saturated specific humidity. Relative humidity is a function of soil moisture in the upper 0.08 m of the soil column (see Land Surface Processes). For a dry vegetation canopy, the potential evaporation is reduced by an efficiency factor that is the inverse sum of aerodynamic and stomatal resistances. The stomatal resistance depends on shortwave radiation, air temperature, humidity, and soil moisture as in Sellers et al. (1986)[59] and Dorman and Sellers (1989)[55]. See also Surface Characteristics.

Land Surface Processes

• Parameterizations of soil processes follow the method of Volodin and Lykossov (1998)[45a,b]. Surface temperature is calculated as a weighed sum of temperatures of 4 surface types: snow, bare soil, vegetation, and canopy-intercepted or inland water. The temperature of each surface type is calculated from a heat balance equation. In the soil column, equations of heat and moisture diffusion are solved, including terms that treat mutual heat/moisture diffusion and hydraulic water flux; melting/freezing of soil water is also included. The diffusion equations are solved at 24 irregularly spaced levels in the soil at depths from 0.01 m to 10 m, with zero-flux conditions at the lower boundary.  In the case of a snow pack, 3 additional regularly spaced levels are used to calculate heat diffusion. Snow heat conductivity depends on its depth, following Palagin (1981)[64].

• Soil heat capacity depends on water and ice amount, and soil heat conductivity on soil moisture (cf. McCumber and Pielke, 1981[63]).  Soil moisture conductivity and hydraulic flux depend on soil type as in Clapp and Hornberger (1978)[60]. The coefficient of mutual heat-moisture conductivity is defined as in Palagin (1981)[64].  All coefficients vary according to the 11 soil types (cf. Cosby et al., 1984)[61] that are specified from data of Zobler (1986)[65].

• Surface runoff depends on rain or snowmelt intensity, upper soil moisture and ice content.  Drainage from each layer depends on its moisture capacity (cf. Dümenil and Todini (1992)[62]).  Absorption of water by roots also is treated.  See also Surface Characteristics and Surface Fluxes.

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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