These cloud fractions are suppressed, however, in regions where the convective subcloud layer is conditionally unstable. The functional form of is shown in Figure (6.9).
The total cloud fraction in a grid box is determined by the larger of the two cloud fractions:
Finally, cloud fractions are timeaveraged between calls to the radiation packages. Radiation: The parameterization of radiative heating in the fizhi package includes effects from both shortwave and longwave processes. Radiative fluxes are calculated at each model edgelevel in both up and down directions. The heating rates/cooling rates are then obtained from the vertical divergence of the net radiative fluxes. The net flux is
where is the net flux, is the upward flux and is the downward flux. The heating rate due to the divergence of the radiative flux is given by
or
where is the accelation due to gravity and is the heat capacity of air at constant pressure. The time tendency for Longwave Radiation is updated every 3 hours. The time tendency for Shortwave Radiation is updated once every three hours assuming a normalized incident solar radiation, and subsequently modified at every model time step by the true incident radiation. The solar constant value used in the package is equal to 1365 and a mixing ratio of 330 ppm. For the ozone mixing ratio, monthly mean zonally averaged climatological values specified as a function of latitude and height (Rosenfield et al. [1987]) are linearly interpolated to the current time.
6.5.3.2.3 Shortwave RadiationThe shortwave radiation package used in the package computes solar radiative heating due to the absoption by water vapor, ozone, carbon dioxide, oxygen, clouds, and aerosols and due to the scattering by clouds, aerosols, and gases. The shortwave radiative processes are described by Chou [1990,1992]. This shortwave package uses the DeltaEddington approximation to compute the bulk scattering properties of a single layer following King and Harshvardhan (JAS, 1986). The transmittance and reflectance of diffuse radiation follow the procedures of Sagan and Pollock (JGR, 1967) and Lacis and Hansen [1974]. Highly accurate heating rate calculations are obtained through the use of an optimal grouping strategy of spectral bands. By grouping the UV and visible regions as indicated in Table 6.13, the Rayleigh scattering and the ozone absorption of solar radiation can be accurately computed in the ultraviolet region and the photosynthetically active radiation (PAR) region. The computation of solar flux in the infrared region is performed with a broadband parameterization using the spectrum regions shown in Table 6.14. The solar radiation algorithm used in the fizhi package can be applied not only for climate studies but also for studies on the photolysis in the upper atmosphere and the photosynthesis in the biosphere.
Within the shortwave radiation package, both ice and liquid cloud particles are allowed to coexist in any of the model layers. Two sets of cloud parameters are used, one for ice paticles and the other for liquid particles. Cloud parameters are defined as the cloud optical thickness and the effective cloud particle size. In the fizhi package, the effective radius for water droplets is given as 10 microns, while 65 microns is used for ice particles. The absorption due to aerosols is currently set to zero. To simplify calculations in a cloudy atmosphere, clouds are grouped into low ( mb), middle (700 mb mb), and high ( mb) cloud regions. Within each of the three regions, clouds are assumed maximally overlapped, and the cloud cover of the group is the maximum cloud cover of all the layers in the group. The optical thickness of a given layer is then scaled for both the direct (as a function of the solar zenith angle) and diffuse beam radiation so that the grouped layer reflectance is the same as the original reflectance. The solar flux is computed for each of eight cloud realizations possible within this low/middle/high classification, and appropriately averaged to produce the net solar flux.
6.5.3.2.4 Longwave RadiationThe longwave radiation package used in the fizhi package is thoroughly described by Chou and M.J.Suarez [1994]. As described in that document, IR fluxes are computed due to absorption by water vapor, carbon dioxide, and ozone. The spectral bands together with their absorbers and parameterization methods, configured for the fizhi package, are shown in Table 6.15.
The longwave radiation package accurately computes cooling rates for the middle and lower atmosphere from 0.01 mb to the surface. Errors are 0.4 C day in cooling rates and 1% in fluxes. From Chou and Suarez, it is estimated that the total effect of neglecting all minor absorption bands and the effects of minor infrared absorbers such as nitrous oxide (N O), methane (CH ), and the chlorofluorocarbons (CFCs), is an underestimate of 5 W/m in the downward flux at the surface and an overestimate of 3 W/m in the upward flux at the top of the atmosphere. Similar to the procedure used in the shortwave radiation package, clouds are grouped into three regions catagorized as low/middle/high. The net clear lineofsite probability between any two levels, and , assuming randomly overlapped cloud groups, is simply the product of the probabilities within each group:
Since all clouds within a group are assumed maximally overlapped, the clear lineofsite probability within a group is given by:
where is the maximum cloud fraction encountered between and within that group. For groups and/or levels outside the range of and , a clear lineofsite probability equal to 1 is assigned.

Surface Type Designation

The fizhi package employs the gravity wave drag scheme of Zhou et al. [1995]). This scheme is a modified version of Vernekar et al. (1992), which was based on Alpert et al. (1988) and Helfand et al. (1987). In this version, the gravity wave stress at the surface is based on that derived by Pierrehumbert (1986) and is given by:
(6.38) 
where is the Froude number, is the Brunt  Väisälä frequency, is the surface wind speed, is the standard deviation of the subgrid scale orography, and is the wavelength of the monochromatic gravity wave in the direction of the lowlevel wind. A modification introduced by Zhou et al. allows for the momentum flux to escape through the top of the model, although this effect is small for the current 70level model. The subgrid scale standard deviation is defined by , and is not allowed to exceed 400 m.
The effects of using this scheme within a GCM are shown in Takacs and Suarez [1996]. Experiments using the gravity wave drag parameterization yielded significant and beneficial impacts on both the timemean flow and the transient statistics of the a GCM climatology, and have eliminated most of the worst dynamically driven biases in the a GCM simulation. An examination of the angular momentum budget during climate runs indicates that the resulting gravity wave torque is similar to the datadriven torque produced by a data assimilation which was performed without gravity wave drag. It was shown that the inclusion of gravity wave drag results in large changes in both the mean flow and in eddy fluxes. The result is a more accurate simulation of surface stress (through a reduction in the surface wind strength), of mountain torque (through a redistribution of mean sealevel pressure), and of momentum convergence (through a reduction in the flux of westerly momentum by transient flow eddies).
Boundary Conditions and other Input Data:
Required fields which are not explicitly predicted or diagnosed during model execution must either be prescribed internally or obtained from external data sets. In the fizhi package these fields include: sea surface temperature, sea ice estent, surface geopotential variance, vegetation index, and the radiationrelated background levels of: ozone, carbon dioxide, and stratospheric moisture.
Boundary condition data sets are available at the model's resolutions for either climatological or yearly varying conditions. Any frequency of boundary condition data can be used in the fizhi package; however, the current selection of data is summarized in Table 6.17. The time mean values are interpolated during each model timestep to the current time.
Fizhi Input Datasets

Surface geopotential heights are provided from an averaging of the Navy 10 minute by 10 minute dataset supplied by the National Center for Atmospheric Research (NCAR) to the model's grid resolution. The original topography is first rotated to the proper gridorientation which is being run, and then averages the data to the model resolution.
The standard deviation of the subgridscale topography is computed by interpolating the 10 minute data to the model's resolution and reinterpolating back to the 10 minute by 10 minute resolution. The subgrid scale variance is constructed based on this smoothed dataset.
NAME  UNITS  LEVELS  DESCRIPTION  
UFLUX  1 


VFLUX  1 


HFLUX  1 


EFLUX  1 


QICE  1 


RADLWG  1 


RADSWG  1 


RI  Nrphys 


CT  1 


CU  1 


ET  Nrphys 


EU  Nrphys 


TURBU  Nrphys 


TURBV  Nrphys 


TURBT  Nrphys 


TURBQ  Nrphys 


MOISTT  Nrphys 


MOISTQ  Nrphys 


RADLW  Nrphys 


RADSW  Nrphys 


PREACC  1 


PRECON  1 


TUFLUX  Nrphys 


TVFLUX  Nrphys 


TTFLUX  Nrphys 

NAME  UNITS  LEVELS  DESCRIPTION  
TQFLUX  Nrphys 


CN  1 


WINDS  1 


DTSRF  1 


TG  1 


TS  1 


DTG  1 


QG  1 


QS  1 


TGRLW  1 


ST4  1 


OLR  1 


OLRCLR  1 


LWGCLR  1 


LWCLR  Nrphys 


TLW  Nrphys 


SHLW  Nrphys 


OZLW  Nrphys 


CLMOLW  Nrphys 


CLDTOT  Nrphys 


LWGDOWN  1 


GWDT  Nrphys 


RADSWT  1 


TAUCLD  Nrphys 


TAUCLDC  Nrphys 

NAME  UNITS  LEVELS  DESCRIPTION  
CLDLOW  Nrphys 


EVAP  1 


DPDT  1 


UAVE  Nrphys 


VAVE  Nrphys 


TAVE  Nrphys 


QAVE  Nrphys 


OMEGA  Nrphys 


DUDT  Nrphys 


DVDT  Nrphys 


DTDT  Nrphys 


DQDT  Nrphys 


VORT  Nrphys 


DTLS  Nrphys 


DQLS  Nrphys 


USTAR  1 


Z0  1 


FRQTRB  Nrphys1 


PBL  1 


SWCLR  Nrphys 


OSR  1 


OSRCLR  1 


CLDMAS  Nrphys 


UAVE  Nrphys 

NAME  UNITS  LEVELS  DESCRIPTION  
VAVE  Nrphys 


TAVE  Nrphys 


QAVE  Nrphys 


RFT  Nrphys 


PS  1 


QQAVE  Nrphys 


SWGCLR  1 


PAVE  1 


DIABU  Nrphys 


DIABV  Nrphys 


DIABT  Nrphys 


DIABQ  Nrphys 


RFU  Nrphys 


RFV  Nrphys 


GWDU  Nrphys 


GWDU  Nrphys 


GWDUS  1 


GWDVS  1 


GWDUT  1 


GWDVT  1 


LZRAD  Nrphys 

NAME  UNITS  LEVELS  DESCRIPTION  
SLP  1 


CLDFRC  1 


TPW  1 


U2M  1 


V2M  1 


T2M  1 


Q2M  1 


U10M  1 


V10M  1 


T10M  1 


Q10M  1 


DTRAIN  Nrphys 


QFILL  Nrphys 

NAME  UNITS  LEVELS  DESCRIPTION  
DTCONV  Nr 


DQCONV  Nr 


RELHUM  Nr 


PRECLS  1 


ENPREC  1 

Fizhi Diagnostic Description:
In this section we list and describe the diagnostic quantities available within the GCM. The diagnostics are listed in the order that they appear in the Diagnostic Menu, Section 6.5.3.3. In all cases, each diagnostic as currently archived on the output datasets is timeaveraged over its diagnostic output frequency:
where , NQDIAG is the output frequency of the diagnostic, and is the timestep over which the diagnostic is updated.
UFLUX Surface Zonal Wind Stress on the Atmosphere ( )
The zonal wind stress is the turbulent flux of zonal momentum from the surface.
where = the atmospheric density at the surface, is the surface drag coefficient, is the dimensionless surface exchange coefficient for momentum (see diagnostic number 10), is the magnitude of the surface layer wind, and is the zonal wind in the lowest model layer.
VFLUX Surface Meridional Wind Stress on the Atmosphere ( )
The meridional wind stress is the turbulent flux of meridional momentum from the surface.
where = the atmospheric density at the surface, is the surface drag coefficient, is the dimensionless surface exchange coefficient for momentum (see diagnostic number 10), is the magnitude of the surface layer wind, and is the meridional wind in the lowest model layer.
HFLUX Surface Flux of Sensible Heat ( )
The turbulent flux of sensible heat from the surface to the atmosphere is a function of the gradient of virtual potential temperature and the eddy exchange coefficient:
where = the atmospheric density at the surface, is the specific heat of air, is the dimensionless surface heat transfer coefficient, is the magnitude of the surface layer wind, is the dimensionless surface exchange coefficient for momentum (see diagnostic number 10), is the dimensionless surface exchange coefficient for heat and moisture (see diagnostic number 9), and is the potential temperature at the surface and at the bottom model level.
EFLUX Surface Flux of Latent Heat ( )
The turbulent flux of latent heat from the surface to the atmosphere is a function of the gradient of moisture, the potential evapotranspiration fraction and the eddy exchange coefficient:
where = the atmospheric density at the surface, is the fraction of the potential evapotranspiration actually evaporated, L is the latent heat of evaporation, is the dimensionless surface heat transfer coefficient, is the magnitude of the surface layer wind, is the dimensionless surface exchange coefficient for momentum (see diagnostic number 10), is the dimensionless surface exchange coefficient for heat and moisture (see diagnostic number 9), and and are the specific humidity at the surface and at the bottom model level, respectively.
QICE Heat Conduction Through Sea Ice ( )
Over sea ice there is an additional source of energy at the surface due to the heat conduction from the relatively warm ocean through the sea ice. The heat conduction through sea ice represents an additional energy source term for the ground temperature equation.
where is the thermal conductivity of ice, is the ice thickness, assumed to be where sea ice is present, is 273 degrees Kelvin, and is the temperature of the sea ice.
NOTE: QICE is not available through model version 5.3, but is available in subsequent versions.
RADLWG Net upward Longwave Flux at the surface ( )
RADSWG Net downard shortwave Flux at the surface ( )
RI Richardson Number ( )
The nondimensional stability indicator is the ratio of the buoyancy to the shear:
Negative values indicate unstable buoyancy AND shear, small positive values ( ) indicate dominantly unstable shear, and large positive values indicate dominantly stable stratification.
CT Surface Exchange Coefficient for Temperature and Moisture ( )
The surface exchange coefficient is obtained from the similarity functions for the stability dependant flux profile relationships:
where is the surface layer nondimensional temperature change and is the viscous sublayer nondimensional temperature or moisture change:
and: with a maximum value over land of 0.01
is the similarity function of
, which expresses the stability dependance of
the temperature and moisture gradients, specified differently for stable and unstable
layers according to Helfand and Schubert [1995]. k is the Von Karman constant,
is the
nondimensional stability parameter, Pr is the Prandtl number for air,
is the molecular
viscosity,
is the surface roughness length,
is the surface stress velocity
(see diagnostic number 67), and the subscript ref refers to a reference value.
CU Surface Exchange Coefficient for Momentum ( )
The surface exchange coefficient is obtained from the similarity functions for the stability dependant flux profile relationships:
where is the surface layer nondimensional wind shear:
is the similarity function of , which expresses the stability dependance of the temperature and moisture gradients, specified differently for stable and unstable layers according to Helfand and Schubert [1995]. k is the Von Karman constant, is the nondimensional stability parameter, is the surface stress velocity (see diagnostic number 67), and is the magnitude of the surface layer wind.
ET Diffusivity Coefficient for Temperature and Moisture ( )
In the level 2.5 version of the MellorYamada (1974) hierarchy, the turbulent heat or moisture flux for the atmosphere above the surface layer can be expressed as a turbulent diffusion coefficient times the negative of the gradient of potential temperature or moisture. In the Helfand and Labraga [1988] adaptation of this closure, takes the form:
where is the turbulent velocity, or , is the turbulence velocity derived from the more simple level 2.0 model, which describes equilibrium turbulence, is the master length scale related to the layer depth, is a function of and , the dimensionless buoyancy and wind shear parameters, respectively, or a function of and , the equilibrium dimensionless buoyancy and wind shear parameters. Both and , and their equilibrium values and , are functions of the Richardson number.
For the detailed equations and derivations of the modified level 2.5 closure scheme, see Helfand and Labraga [1988].
In the surface layer, is the exchange coefficient for heat and moisture, in units of , given by:
where is the dimensionless exchange coefficient for heat and moisture from the surface layer similarity functions (see diagnostic number 9), is the surface friction velocity (see diagnostic number 67), is the heat transfer coefficient, and is the magnitude of the surface layer wind.
EU Diffusivity Coefficient for Momentum ( )
In the level 2.5 version of the MellorYamada (1974) hierarchy, the turbulent heat momentum flux for the atmosphere above the surface layer can be expressed as a turbulent diffusion coefficient times the negative of the gradient of the uwind. In the Helfand and Labraga [1988] adaptation of this closure, takes the form:
where is the turbulent velocity, or , is the turbulence velocity derived from the more simple level 2.0 model, which describes equilibrium turbulence, is the master length scale related to the layer depth, is a function of and , the dimensionless buoyancy and wind shear parameters, respectively, or a function of and , the equilibrium dimensionless buoyancy and wind shear parameters. Both and , and their equilibrium values and , are functions of the Richardson number.
For the detailed equations and derivations of the modified level 2.5 closure scheme, see Helfand and Labraga [1988].
In the surface layer, is the exchange coefficient for momentum, in units of , given by:
where is the dimensionless exchange coefficient for momentum from the surface layer similarity functions (see diagnostic number 10), is the surface friction velocity (see diagnostic number 67), is the surface drag coefficient, and is the magnitude of the surface layer wind.
TURBU Zonal UMomentum changes due to Turbulence ( )
The tendency of UMomentum due to turbulence is written:
The Helfand and Labraga level 2.5 scheme models the turbulent flux of umomentum in terms of , and the equation has the form of a diffusion equation.
TURBV Meridional VMomentum changes due to Turbulence ( )
The tendency of VMomentum due to turbulence is written:
The Helfand and Labraga level 2.5 scheme models the turbulent
flux of vmomentum in terms of
, and the equation has the form of a diffusion
equation.
TURBT Temperature changes due to Turbulence ( )
The tendency of temperature due to turbulence is written:
The Helfand and Labraga level 2.5 scheme models the turbulent
flux of temperature in terms of
, and the equation has the form of a diffusion
equation.
TURBQ Specific Humidity changes due to Turbulence ( )
The tendency of specific humidity due to turbulence is written:
The Helfand and Labraga level 2.5 scheme models the turbulent
flux of temperature in terms of
, and the equation has the form of a diffusion
equation.
MOISTT Temperature Changes Due to Moist Processes ( )
where:
and
The subscript
refers to convective processes, while the subscript
refers to large scale
precipitation processes, or supersaturation rain.
The summation refers to contributions from each cloud type called by RAS.
The dry static energy is given
as
, the convective cloud base mass flux is given as
, and the cloud entrainment is
given as
, which are explicitly defined in Section 6.5.3.2,
the description of the convective parameterization. The fractional adjustment, or relaxation
parameter, for each cloud type is given as
, while
is the rain reevaporation adjustment.
MOISTQ Specific Humidity Changes Due to Moist Processes ( )
where:
and
The subscript refers to convective processes, while the subscript refers to large scale precipitation processes, or supersaturation rain. The summation refers to contributions from each cloud type called by RAS. The dry static energy is given as , the moist static energy is given as , the convective cloud base mass flux is given as , and the cloud entrainment is given as , which are explicitly defined in Section 6.5.3.2, the description of the convective parameterization. The fractional adjustment, or relaxation parameter, for each cloud type is given as , while is the rain reevaporation adjustment.
RADLW Heating Rate due to Longwave Radiation ( )
The net longwave heating rate is calculated as the vertical divergence of the net terrestrial radiative fluxes. Both the clearsky and cloudysky longwave fluxes are computed within the longwave routine. The subroutine calculates the clearsky flux, , first. For a given cloud fraction, the clear lineofsight probability is computed from the current level pressure to the model top pressure, , and the model surface pressure, , for the upward and downward radiative fluxes. (see Section 6.5.3.2). The cloudysky flux is then obtained as:
Finally, the net longwave heating rate is calculated as the vertical divergence of the net terrestrial radiative fluxes:
or
where is the accelation due to gravity, is the heat capacity of air at constant pressure, and
RADSW Heating Rate due to Shortwave Radiation ( )
The net Shortwave heating rate is calculated as the vertical divergence of the net solar radiative fluxes. The clearsky and cloudysky shortwave fluxes are calculated separately. For the clearsky case, the shortwave fluxes and heating rates are computed with both CLMO (maximum overlap cloud fraction) and CLRO (random overlap cloud fraction) set to zero (see Section 6.5.3.2). The shortwave routine is then called a second time, for the cloudysky case, with the true timeaveraged cloud fractions CLMO and CLRO being used. In all cases, a normalized incident shortwave flux is used as input at the top of the atmosphere.
The heating rate due to Shortwave Radiation under cloudy skies is defined as:
or
where is the accelation due to gravity, is the heat capacity of air at constant pressure, RADSWT is the true incident shortwave radiation at the top of the atmosphere (See Diagnostic #48), and
PREACC Total (Largescale + Convective) Accumulated Precipition ( )
For a change in specific humidity due to moist processes, , the vertical integral or total precipitable amount is given by:
A precipitation rate is defined as the vertically integrated moisture adjustment per Moist Processes
time step, scaled to
.
PRECON Convective Precipition ( )
For a change in specific humidity due to subgrid scale cumulus convective processes, , the vertical integral or total precipitable amount is given by:
A precipitation rate is defined as the vertically integrated moisture adjustment per Moist Processes
time step, scaled to
.
TUFLUX Turbulent Flux of UMomentum ( )
The turbulent flux of umomentum is calculated for from the eddy coefficient for momentum:
where
is the air density, and
is the eddy coefficient.
TVFLUX Turbulent Flux of VMomentum ( )
The turbulent flux of vmomentum is calculated for from the eddy coefficient for momentum:
where
is the air density, and
is the eddy coefficient.
TTFLUX Turbulent Flux of Sensible Heat ( )
The turbulent flux of sensible heat is calculated for from the eddy coefficient for heat and moisture:
where
is the air density, and
is the eddy coefficient.
TQFLUX Turbulent Flux of Latent Heat ( )
The turbulent flux of latent heat is calculated for from the eddy coefficient for heat and moisture:
where
is the air density, and
is the eddy coefficient.
CN Neutral Drag Coefficient ( )
The drag coefficient for momentum obtained by assuming a neutrally stable surface layer:
where is the Von Karman constant, is the height of the surface layer, and is the surface roughness.
NOTE: CN is not available through model version 5.3, but is available in subsequent
versions.
WINDS Surface Wind Speed ( )
The surface wind speed is calculated for the last internal turbulence time step:
where the subscript
refers to the lowest model level.
DTSRF Air/Surface Virtual Temperature Difference ( )
The air/surface virtual temperature difference measures the stability of the surface layer:
where
is the surface potential evapotranspiration coefficient (
over oceans),
is the saturation specific humidity at the ground temperature
and surface pressure, level
refers to the lowest model level and level
refers to the surface.
TG Ground Temperature ( )
The ground temperature equation is solved as part of the turbulence package using a backward implicit time differencing scheme:
where is the net surface downward shortwave radiative flux, is the net surface upward longwave radiative flux, is the heat conduction through sea ice, is the upward sensible heat flux, is the upward latent heat flux, and is the total heat capacity of the ground. is obtained by solving a heat diffusion equation for the penetration of the diurnal cycle into the ground (Blackadar [1977]), and is given by:
Here, the thermal conductivity, , is equal to , the angular velocity of the earth, , is written as divided by , and the expression for , the heat capacity per unit volume at the surface, is a function of the ground wetness, .
TS Surface Temperature ( )
The surface temperature estimate is made by assuming that the model's lowest layer is wellmixed, and therefore that is constant in that layer. The surface temperature is therefore:
DTG Surface Temperature Adjustment ( )
The change in surface temperature from one turbulence time step to the next, solved using the Ground Temperature Equation (see diagnostic number 30) is calculated:
where superscript
refers to the new, updated time level, and the superscript
refers to the value at the previous turbulence time level.
QG Ground Specific Humidity ( )
The ground specific humidity is obtained by interpolating between the specific humidity at the lowest model level and the specific humidity of a saturated ground. The interpolation is performed using the potential evapotranspiration function:
where
is the surface potential evapotranspiration coefficient (
over oceans),
and
is the saturation specific humidity at the ground temperature and surface
pressure.
QS Saturation Surface Specific Humidity ( )
The surface saturation specific humidity is the saturation specific humidity at the ground temprature and surface pressure:
TGRLW Instantaneous ground temperature used as input to the Longwave radiation subroutine (deg)
where is the model ground temperature at the current time step .
ST4 Upward Longwave flux at the surface ( )
where is the StefanBoltzmann constant and T is the temperature.
OLR Net upward Longwave flux at ( )
where top indicates the top of the first model layer. In the GCM, = 0.0 mb.
OLRCLR Net upward clearsky Longwave flux at ( )
where top indicates the top of the first model layer. In the GCM, = 0.0 mb.
LWGCLR Net upward clearsky Longwave flux at the surface ( )
LWCLR Heating Rate due to Clearsky Longwave Radiation ( )
The net longwave heating rate is calculated as the vertical divergence of the net terrestrial radiative fluxes. Both the clearsky and cloudysky longwave fluxes are computed within the longwave routine. The subroutine calculates the clearsky flux, , first. For a given cloud fraction, the clear lineofsight probability is computed from the current level pressure to the model top pressure, , and the model surface pressure, , for the upward and downward radiative fluxes. (see Section 6.5.3.2). The cloudysky flux is then obtained as:
Thus, LWCLR is defined as the net longwave heating rate due to the vertical divergence of the clearsky longwave radiative flux:
or
where is the accelation due to gravity, is the heat capacity of air at constant pressure, and
TLW Instantaneous temperature used as input to the Longwave radiation subroutine (deg)
where is the model temperature at the current time step .
SHLW Instantaneous specific humidity used as input to the Longwave radiation subroutine (kg/kg)
where is the model specific humidity at the current time step .
OZLW Instantaneous ozone used as input to the Longwave radiation subroutine (kg/kg)
where is the interpolated ozone data set from the climatological monthly mean zonally averaged ozone data set.
CLMOLW Maximum Overlap cloud fraction used in LW Radiation ( )
CLMOLW is the timeaveraged maximum overlap cloud fraction that has been filled by the Relaxed Arakawa/Schubert Convection scheme and will be used in the Longwave Radiation algorithm. These are convective clouds whose radiative characteristics are assumed to be correlated in the vertical. For a complete description of cloud/radiative interactions, see Section 6.5.3.2.
CLDTOT Total cloud fraction used in LW and SW Radiation ( )
CLDTOT is the timeaveraged total cloud fraction that has been filled by the Relaxed Arakawa/Schubert and Largescale Convection schemes and will be used in the Longwave and Shortwave Radiation packages. For a complete description of cloud/radiative interactions, see Section 6.5.3.2.
CLMOSW Maximum Overlap cloud fraction used in SW Radiation ( )
CLMOSW is the timeaveraged maximum overlap cloud fraction that has been filled by the Relaxed Arakawa/Schubert Convection scheme and will be used in the Shortwave Radiation algorithm. These are convective clouds whose radiative characteristics are assumed to be correlated in the vertical. For a complete description of cloud/radiative interactions, see Section 6.5.3.2.
CLROSW Random Overlap cloud fraction used in SW Radiation ( )
CLROSW is the timeaveraged random overlap cloud fraction that has been filled by the Relaxed Arakawa/Schubert and Largescale Convection schemes and will be used in the Shortwave Radiation algorithm. These are convective and largescale clouds whose radiative characteristics are not assumed to be correlated in the vertical. For a complete description of cloud/radiative interactions, see Section 6.5.3.2.
RADSWT Incident Shortwave radiation at the top of the atmosphere ( )
where , is the extraterrestial solar contant, is the earthsun distance in Astronomical Units, and is the cosine of the zenith angle. It should be noted that RADSWT, as well as OSR and OSRCLR, are calculated at the top of the atmosphere (p=0 mb). However, the OLR and OLRCLR diagnostics are currently calculated at (0.0 mb for the GCM).
EVAP Surface Evaporation ( )
The surface evaporation is a function of the gradient of moisture, the potential evapotranspiration fraction and the eddy exchange coefficient:
where = the atmospheric density at the surface, is the fraction of the potential evapotranspiration actually evaporated ( over oceans), is the turbulent eddy exchange coefficient for heat and moisture at the surface in and and are the specific humidity at the surface (see diagnostic number 34) and at the bottom model level, respectively.
DUDT Total Zonal UWind Tendency ( )
DUDT is the total timetendency of the Zonal UWind due to Hydrodynamic, Diabatic, and Analysis forcing.
DVDT Total Zonal VWind Tendency ( )
DVDT is the total timetendency of the Meridional VWind due to Hydrodynamic, Diabatic, and Analysis forcing.
DTDT Total Temperature Tendency ( )
DTDT is the total timetendency of Temperature due to Hydrodynamic, Diabatic,
and Analysis forcing.
DQDT Total Specific Humidity Tendency ( )
DQDT is the total timetendency of Specific Humidity due to Hydrodynamic, Diabatic, and Analysis forcing.
USTAR SurfaceStress Velocity ( )
The surface stress velocity, or the friction velocity, is the wind speed at the surface layer top impeded by the surface drag:
is the nondimensional surface drag coefficient (see diagnostic number 10), and is the surface wind speed (see diagnostic number 28).
Z0 Surface Roughness Length ( )
Over the land surface, the surface roughness length is interpolated to the local time from the monthly mean data of Dorman and Sellers [1989]. Over the ocean, the roughness length is a function of the surfacestress velocity, .
where the constants are chosen to interpolate between the reciprocal relation of
Kondo [1975] for weak winds, and the piecewise linear relation of Large and Pond [1981]
for moderate to large winds.
FRQTRB Frequency of Turbulence ( )
The fraction of time when turbulence is present is defined as the fraction of
time when the turbulent kinetic energy exceeds some minimum value, defined here
to be
. When this criterion is met, a counter is
incremented. The fraction over the averaging interval is reported.
PBL Planetary Boundary Layer Depth ( )
The depth of the PBL is defined by the turbulence parameterization to be the depth at which the turbulent kinetic energy reduces to ten percent of its surface value.
where
is the pressure in
at which the turbulent kinetic energy
reaches one tenth of its surface value, and
is the surface pressure.
SWCLR Clear sky Heating Rate due to Shortwave Radiation ( )
The net Shortwave heating rate is calculated as the vertical divergence of the net solar radiative fluxes. The clearsky and cloudysky shortwave fluxes are calculated separately. For the clearsky case, the shortwave fluxes and heating rates are computed with both CLMO (maximum overlap cloud fraction) and CLRO (random overlap cloud fraction) set to zero (see Section 6.5.3.2). The shortwave routine is then called a second time, for the cloudysky case, with the true timeaveraged cloud fractions CLMO and CLRO being used. In all cases, a normalized incident shortwave flux is used as input at the top of the atmosphere.
The heating rate due to Shortwave Radiation under clear skies is defined as:
or
where is the accelation due to gravity, is the heat capacity of air at constant pressure, RADSWT is the true incident shortwave radiation at the top of the atmosphere (See Diagnostic #48), and
OSR Net upward Shortwave flux at the top of the model ( )
where top indicates the top of the first model layer used in the shortwave radiation routine. In the GCM, = 0 mb.
OSRCLR Net upward clearsky Shortwave flux at the top of the model ( )
where top indicates the top of the first model layer used in the shortwave radiation routine. In the GCM, = 0 mb.
CLDMAS Convective Cloud Mass Flux ( )
The amount of cloud mass moved per RAS timestep from all convective clouds is written:
where is the entrainment, normalized by the cloud base mass flux, and is the cloud base mass flux. and are defined explicitly in Section 6.5.3.2, the description of the convective parameterization.
UAVE TimeAveraged Zonal UWind ( )
The diagnostic UAVE is simply the timeaveraged Zonal UWind over the NUAVE output frequency. This is contrasted to the instantaneous Zonal UWind which is archived on the Prognostic Output data stream.
VAVE TimeAveraged Meridional VWind ( )
The diagnostic VAVE is simply the timeaveraged Meridional VWind over the NVAVE output frequency. This is contrasted to the instantaneous Meridional VWind which is archived on the Prognostic Output data stream.
TAVE TimeAveraged Temperature ( )
The diagnostic TAVE is simply the timeaveraged Temperature over the NTAVE output frequency. This is contrasted to the instantaneous Temperature which is archived on the Prognostic Output data stream.
QAVE TimeAveraged Specific Humidity ( )
The diagnostic QAVE is simply the timeaveraged Specific Humidity over the NQAVE output frequency. This is contrasted to the instantaneous Specific Humidity which is archived on the Prognostic Output data stream.
PAVE TimeAveraged Surface Pressure  PTOP ( )
The diagnostic PAVE is simply the timeaveraged Surface Pressure  PTOP over
the NPAVE output frequency. This is contrasted to the instantaneous
Surface Pressure  PTOP which is archived on the Prognostic Output data stream.
QQAVE TimeAveraged Turbulent Kinetic Energy
The diagnostic QQAVE is simply the timeaveraged prognostic Turbulent Kinetic Energy produced by the GCM Turbulence parameterization over the NQQAVE output frequency. This is contrasted to the instantaneous Turbulent Kinetic Energy which is archived on the Prognostic Output data stream.
SWGCLR Net downward clearsky Shortwave flux at the surface ( )
DIABU Total Diabatic Zonal UWind Tendency ( )
DIABU is the total timetendency of the Zonal UWind due to Diabatic processes and the Analysis forcing.
DIABV Total Diabatic Meridional VWind Tendency ( )
DIABV is the total timetendency of the Meridional VWind due to Diabatic processes and the Analysis forcing.
DIABT Total Diabatic Temperature Tendency ( )
DIABT is the total timetendency of Temperature due to Diabatic processes
and the Analysis forcing.
where . Thus, DIABT may be written as
DIABQ Total Diabatic Specific Humidity Tendency ( )
DIABQ is the total timetendency of Specific Humidity due to Diabatic processes and the Analysis forcing.
If we define the timetendency of Specific Humidity due to Diabatic processes as
then, since there are no surface pressure changes due to Diabatic processes, we may write
Thus, DIABQ may be written as
VINTUQ Vertically Integrated Moisture Flux ( )
The vertically integrated moisture flux due to the zonal uwind is obtained by integrating over the depth of the atmosphere at each model timestep, and dividing by the total mass of the column.
Using , we have
VINTVQ Vertically Integrated Moisture Flux ( )
The vertically integrated moisture flux due to the meridional vwind is obtained by integrating over the depth of the atmosphere at each model timestep, and dividing by the total mass of the column.
Using , we have
VINTUT Vertically Integrated Heat Flux ( )
The vertically integrated heat flux due to the zonal uwind is obtained by integrating over the depth of the atmosphere at each model timestep, and dividing by the total mass of the column.
Or,
VINTVT Vertically Integrated Heat Flux ( )
The vertically integrated heat flux due to the meridional vwind is obtained by integrating over the depth of the atmosphere at each model timestep, and dividing by the total mass of the column.
Using , we have
CLDFRC Total 2Dimensional Cloud Fracton ( )
If we define the timeaveraged random and maximum overlapped cloudiness as CLRO and CLMO respectively, then the probability of clear sky associated with random overlapped clouds at any level is (1CLRO) while the probability of clear sky associated with maximum overlapped clouds at any level is (1CLMO). The total clear sky probability is given by (1CLRO)*(1CLMO), thus the total cloud fraction at each level may be obtained by 1(1CLRO)*(1CLMO).
At any given level, we may define the clear lineofsite probability by appropriately accounting for the maximum and random overlap cloudiness. The clear lineofsite probability is defined to be equal to the product of the clear lineofsite probabilities associated with random and maximum overlap cloudiness. The clear lineofsite probability associated with maximum overlap clouds, from the current pressure to the model top pressure, , or the model surface pressure, , is simply 1.0 minus the largest maximum overlap cloud value along the lineofsite, ie.
Thus, even in the timeaveraged sense it is assumed that the maximum overlap clouds are correlated in the vertical. The clear lineofsite probability associated with random overlap clouds is defined to be the product of the clear sky probabilities at each level along the lineofsite, ie.
The total cloud fraction at a given level associated with a line ofsite calculation is given by
The 2dimensional net cloud fraction as seen from the top of the atmosphere is given by
QINT Total Precipitable Water ( )
The Total Precipitable Water is defined as the vertical integral of the specific humidity,
given by:
U2M Zonal UWind at 2 Meter Depth ( )
The uwind at the 2meter depth is determined from the similarity theory:
where
is the nondimensional wind shear at two meters, and the subscript
refers to the height of the top of the surface layer. If the roughness height
is above two meters,
is undefined.
V2M Meridional VWind at 2 Meter Depth ( )
The vwind at the 2meter depth is a determined from the similarity theory:
where
is the nondimensional wind shear at two meters, and the subscript
refers to the height of the top of the surface layer. If the roughness height
is above two meters,
is undefined.
T2M Temperature at 2 Meter Depth ( )
The temperature at the 2meter depth is a determined from the similarity theory:
where:
where
is the nondimensional temperature gradient at two meters,
is
the nondimensional temperature gradient in the viscous sublayer, and the subscript
refers to the height of the top of the surface layer. If the roughness height
is above two meters,
is undefined.
Q2M Specific Humidity at 2 Meter Depth ( )
The specific humidity at the 2meter depth is determined from the similarity theory:
where:
where
is the nondimensional temperature gradient at two meters,
is
the nondimensional temperature gradient in the viscous sublayer, and the subscript
refers to the height of the top of the surface layer. If the roughness height
is above two meters,
is undefined.
U10M Zonal UWind at 10 Meter Depth ( )
The uwind at the 10meter depth is an interpolation between the surface wind and the model lowest level wind using the ratio of the nondimensional wind shear at the two levels:
where
is the nondimensional wind shear at ten meters, and the subscript
refers to the height of the top of the surface layer.
V10M Meridional VWind at 10 Meter Depth ( )
The vwind at the 10meter depth is an interpolation between the surface wind and the model lowest level wind using the ratio of the nondimensional wind shear at the two levels:
where
is the nondimensional wind shear at ten meters, and the subscript
refers to the height of the top of the surface layer.
T10M Temperature at 10 Meter Depth ( )
The temperature at the 10meter depth is an interpolation between the surface potential temperature and the model lowest level potential temperature using the ratio of the nondimensional temperature gradient at the two levels:
where:
where
is the nondimensional temperature gradient at two meters,
is
the nondimensional temperature gradient in the viscous sublayer, and the subscript
refers to the height of the top of the surface layer.
Q10M Specific Humidity at 10 Meter Depth ( )
The specific humidity at the 10meter depth is an interpolation between the surface specific humidity and the model lowest level specific humidity using the ratio of the nondimensional temperature gradient at the two levels:
where:
where
is the nondimensional temperature gradient at two meters,
is
the nondimensional temperature gradient in the viscous sublayer, and the subscript
refers to the height of the top of the surface layer.
DTRAIN Cloud Detrainment Mass Flux ( )
The amount of cloud mass moved per RAS timestep at the cloud detrainment level is written:
where is the detrainment level, is the cloud base mass flux, and is the entrainment, defined in Section 6.5.3.2.
QFILL Filling of negative Specific Humidity ( )
Due to computational errors associated with the numerical scheme used for the advection of moisture, negative values of specific humidity may be generated. The specific humidity is checked for negative values after every dynamics timestep. If negative values have been produced, a filling algorithm is invoked which redistributes moisture from below. Diagnostic QFILL is equal to the net filling needed to eliminate negative specific humidity, scaled to a perday rate:
where