- RADIATION

The radiation calculations are computationally quite expensive. Using compiler optimized CYBER 205 coding, the average radiation computation time for one 18 layer column of atmospheric data is .0031 seconds. This requires approximately 40 seconds of computation time for a rhomboidal-40 grid array. The faster shortwave calculations account for only 18% of this time. Because of their computational expense, radiation calculations are made only once every 12 hours. Longwave heating rates are held fixed for the entire 12 hours; however, provision is made within the forecast model for an approximate diurnal cycle, so shortwave heating rates and surface radiative fluxes are allowed to change during this interval.

The first part of this report describes the necessary alteration of model temperature and moisture data for the radiation parameterization. Then, climatological surface albedo, ozone concentration, and cloudiness are discussed. Finally, basic techniques which are used to model both shortwave and longwave processes are described. A schematic of the radiation calculations, including basic subroutine names, is shown in Fig 3.1.

- Preprocessing Input Data
- Atmospheric Temperature

where *q* is layer specific humidity. This calculation is made only for the forecast model's lower
12 moisture bearing layers. The extrapolated moisture in the upper model layers (described
below) is small and is neglected in eqn (3.1).

- Moisture Extrapolation

where *qk,pk* are dry layer values and* qm,pm* are uppermost moist layer (currently layer 12)
values of specific humidity and pressure. The exponent, l, is computed at each model grid
point by inverting eqn (3.2) , assuming *qk*=3.x10-6 g/g at* pk*=5 cb. Moisture is assumed
constant for pressures less than 5 cb. Relative humidity is constrained to 100% to avoid
excessive extrapolated *q* in tropical regions.

- Initial Land Surface Temperature

(1) Assuming an initial value of 290K at all land points, compute the radiative fluxes and, then, solve a surface energy balance equation for surface temperature. With these new land temperatures, make another pass through the radiation scheme.

(2) Extrapolate (linear in pressure) temperature down to the earth's surface from the lowest two forecast model layers.

There are several problems with the first option. The surface energy balance algorithm
is not the same as being used in the forecast model and produces too large initial surface
temperatures in regions where the sun is "high in the sky". Additionally, the process of solving
for an energy balanced temperature and recomputing radiative heating rates should be
iterated more than once (at least 2 or 3 iterations seem necessary). Shortcomings of both
methods can be neglected in most regions, because the forecast model's "memory" of the
initial surface temperature is quite short once the sun rises*.*

- Climatological Input Data
- Surface Albedo

- Ozone

- Clouds

- Shortwave Processes

In order to model the wavelength dependent absorption coefficients for water vapor
across the solar spectrum, a probability distribution,* p(k)*, is assumed for the absorption
coefficients in a manner virtually identical to the work of Lacis and Hansen (l974). As in eqns
(28) and (29) of Lacis and Hansen the absorption,* A*, by water vapor is:

where* * is water vapor amount, *k* is the absorption coefficient for water vapor, *p(k) dk* is the
fraction of incident solar flux associated with an absorption coefficient between *k* and *k+dk,
p(kn) *is the discrete probability distribution for* N *subintervals over the solar spectrum, and *kn*,
is the mean absorption coefficient for each subinterval. In order to overlap ozone absorption
with water vapor processes in the ultraviolet part of the solar spectrum, Lacis and Hansen's
first subinterval is split in two, giving* N*=9 (table 3.1). Thus* O3 *and *H2O* overlap is assigned
to the *n*=1 subinterval, and *CO2 *and *H2O* overlap is assigned to* n*=2,3,...,9. Since *O3 *and *CO2
*are each relegated to intervals covering 1/2 the solar spectrum, their respective absorptions
will be weighted by 1/2 (the* p(kn)*'s), so a compensating multiplication by 2 is necessary.

Absorber amounts (cm) for each of the three gases are computed as total amounts from
top of the atmosphere down to each model level (using model layer values of *H2O*,*O3,CO2*),
plus, for reflected paths from the earth's surface, additional amounts up to each model level.
Thus for a model with* j* levels, there are (2*j*-1) total amounts of each absorbing gas. For the
downward radiation path, total absorber amount, *xl,* between the top of the atmosphere and
the *l*th model level, traversed by the direct solar beam and by diffuse solar radiation below the
top of the highest cloud (if any), *lc*, is:

where *ak* is amount of an absorber in the *k*th model layer, *M* is a magnification factor accounting
for slant path and refraction, and *m* is an effective magnification (diffusivity) factor for diffuse
radiation. For the three absorbing gases,* M *and* m* are defined as:

where * *is the cosine of the solar zenith angle, *M* is from Rodgers (l967), and* m *is from Lacis
and Hansen (l974).

For the upward returning path, where* ls* is the level of the earth's surface, total absorber
amount is:

Transmission functions for each of the three gases are computed from the top of the
atmosphere to a particular model level. Shortwave flux at each level is obtained by weighting
solar flux at the top of the atmosphere by *p(kn)* and multiplying it by the transmission functions.
The solar flux at the top of the atmosphere is , where *S*=1367.4 Watts/m2, and , is the
cosine of the solar zenith angle. Net fluxes (upward-downward) are computed at each model
level and the layer heating rates, ,are computed from the vertical component of radiative
flux divergence:

where *F *and *p* are level values of net radiative flux and pressure respectively.

- Ozone

For the ultraviolet bands:

Total ozone absorption ,, is . Ozone transmission down to each
model level, , is computed and later multiplied by *H2O* transmission in the *n*=1
subinterval (table 3.1) to account for absorption band overlap.

Ozone absorption occurs primarily in the high atmospheric layers, where molecular
concentration is low enough to neglect scattering. Most of the scattering occurs in the lower
atmosphere where there is little ozone absorption. Thus Lacis and Hansen model the
scattering process by assuming a simple 2 layer atmosphere; a purely absorbing layer on top
of a purely reflecting layer. The albedo of the earth surface region, , is a combination of
the reflectivity of the earth's surface, *Rg*, and the effective albedo of the non-absorbing lower
atmosphere, , while accounting for multiple reflections between ground and the
atmosphere:

where is the average of over all solar zenith angles. Simple expressions for the various reflectivities are obtained, in a least squares sense, for clear skies by Lacis and Hansen (their cloudy sky formulation is not used):

- Water Vapor

where* kn* is the mean absorption coefficient for each subinterval in Table 3.1.

- Carbon Dioxide

Transmission functions to each model level, , are computed and later multiplied
by *H2O* transmission functions in subintervals 2 through 9 to account for absorption band
overlap.

- Clouds

For convenience, the top of the atmosphere and earth's surface are considered cloud
layers. If one makes the additional assumption that the reflectivity of both top and bottom of
the 3 physical clouds are equal, then 5 values of cloud reflectivity and transmissivity define the
entire cloud system. Reflectivity,* (CR)i*, and transmissivity, *(CT)i*, weighted for fractional
cloudiness are defined:

where *Ci* is fractional cloud amount, *(alb)i* and *(abs)i* are cloud albedo and absorptivity (Table
3.2), and* i* is cloud type. At the earth's surface (*i*=5), *(CR)i *is calculated as in eqn (3.14); with
*C5*=1., *(alb)5*=*Rg* for the second through ninth subinterval of the solar spectrum, and
*(alb)5*= for the first subinterval (see eqn (3.10)).

The calculation of shortwave fluxes in the presence of clouds entails a computation of
both upward and downward radiative fluxes at, potentially, 8 reflecting surfaces (defined
above). There is provision for multiple reflections, and, of course, the downward flux at the
top of the atmosphere is known. Consider two clouds of index *i *and* i*+1 as depicted in Fig 3.5.
Assuming the downward flux at the top of *ith* cloud ( *) *is known,* *the following fluxes are
defined:

where *ti *and* bi* represent model levels of top and bottom for cloud index * i*; and represents
clear sky transmission function from level *ti *to level* bi*. Manipulation of eqns (3.15-3.18)
yields equations for upward flux at the top of cloud index *i* and downward flux at the top of the
next lower cloud:

Now assume that the transmissivities between two surfaces are independent of direction (i.e.
) and that (*i.e*. the transmissions are exponential). Both assumptions
are exactly true for bands 2-9 (disregarding the *CO2* transmissivity) and are assumed true in
the *O3* band 1. Bearing this in mind, define

where* (TCLU)i* represents the transmission between tops of adjacent reflecting surfaces and
*(TCLD)i* is clear sky transmission between the bottom of cloud index *i* and the top of the next
lower reflecting surface,* i*+1 (Fig 3.5). Using the above definitions as well as the assumption
about the exponential nature of the transmission functions, eqns ( 3.19, 3.20) may be rewritten
as:

Recalling that is known, and that for the earth's surface (*i*=5) the relation between
and is

one obtains (after suitably manipulating eqns (3.23-3.25) for *i*=4):

Simplifying (3.26):

The quantity *(ALFA4+(CR)4)* thus represents the effective albedo of the low cloud-ground
system accounting for multiple reflections from below the cloud. Perhaps this can be visualized
by looking at the low cloud/earth surface region below level* t4* in Fig 3.5. For one reflection
at the ground

With an additional reflection off the bottom of the low cloud

where* (CR)4 (CR)5 (TCLD4)2 * accounts for clear sky transmission to the base of the low cloud,
a reflection off it, then transmission back and a subsequent reflection off the earth's surface.
With "*n*" reflections

Since *(CR)4 (CR)5 (TCLD4)2 * < l, the series in parentheses converges in the limit as *n*
approaches infinity and can be written as:

The term in parentheses is a multiple reflection factor and is seen in eqn (3.26). One may now
proceed to solve eqns (3.23,3.24) for the next surface, *i*=3, using the lower boundary condition
(3.27) in place of eqn (3.25). The resulting solution for is the same form as (3.26), with
all indices decremented by l and* (CR)5 *replaced by *(ALFA4+(CR)4)* :

For the *nth* cloud, the *ALFA* term may be generalized (*n*=l-4):

where *ALFA5*=0.

The above procedure is repeated until the upward flux has been calculated for the top
of the highest physical cloud (*i*=2). Since is a clear sky flux, and is already known, eqns
3.30, 3.23, 3.24, 3.15-3.18, may be employed to obtain upward and downward fluxes for all
reflecting surfaces. Fluxes for a model level between the clouds are easily obtained using
clear-sky transmittances between the appropriate cloud top and bottom and the desired level.
Finally, for cases where the cloud is more than one model layer thick (currently low cloud),
linear interpolation of transmission functions between cloud top and bottom produces values
at model levels inside the cloud. Application of eqn (3.7) results in identical shortwave heating
rates for these internal model layers.

- Surface Albedo Adjustment

A zenith angle dependent surface albedo over open water is obtained from Payne's (l972) tabulated data. Payne accounts for the effect of atmospheric scattering and absorption on the surface albedo by tabulating the data as a function of atmospheric transmittance, TRANS, as well as zenith angle. The radiation parameterization uses a value of TRANS = .537 for all grid points, where TRANS=1. represents clear atmosphere.

- Approximate Diurnal Cycle

where *S* is the solar constant, *t* is time, and* Tr* is the atmospheric transmissivity. *Tr* is a function
of *H2O, CO2, O3*, other trace gases and aerosols (not considered here), and clouds. Holding
these atmospheric profiles fixed (), the SW flux integrated over a complete day is:

where the final equality exists because at night.

Ideally, one could simulate the diurnal cycle at a grid point by making radiation
calculations each model time step, thereby accounting for changes in zenith angle, *H2O*,
temperature (for longwave computations) and clouds. This is computationally prohibitive
however, so some approximations must be made. For example, one could either calculate the
"less expensive" SW effects more frequently than longwave (LW) processes, or calculate both
SW and LW effects more frequently on a coarse subset of the grid and interpolate to the full
grid. An alternative approximation, developed by Ellingson (U of Md) and Campana, for SW
processes adds little computational overhead (Campana, l986). A mean cosine of the solar
zenith angle, , computed for each model latitude as in eqn (3.34) of Manabe and Strickler
(1964), and is used to calculate the SW fluxes at each model "grid point".

Shortwave radiative fluxes are computed every 12 hours at all grid points using this mean cosine of the zenith angle, , as well as atmospheric transmissivities valid at those times (eqn (3.36)).

For the nondiurnal option these fluxes are fixed, but for the diurnal cycle option, grid point values of SW fluxes (and thus heating rates) are weighted by the exact cosine of the zenith angle, , at each forecast model time step, as in eqn (3.35):

where

and whererepresents grid point transmissivity at the beginning of a 12-hour interval.
Though changes in *H2O* will occur during the 12-hour interval, a (reasonable) assumption is
made that changes in are much more important than changes in water vapor profiles in
determining SW fluxes. Integration of this SW flux over 24 hours, again holding fixed,
yields the same result as eqn (3.33)

- Longwave Processes

As in the parameterization of shortwave processes, the desired output from the
longwave scheme are net radiative fluxes at all model levels which then are used to compute
model layer heating rates (eqn (3.7)). Appropriate radiative transfer equations for the
calculation of upward (*F*" ) and downward (*F*# ) longwave flux at a specified atmospheric level,
*z*, are (see Stephens, l984, p. 828):

where n is wavenumber (i. e., wavelength-1),* B*n is the Planck function,* zT* is top of the
atmosphere, and is the longwave transmission function between level and *z* . is
defined over all zenith angles along an optical path, *du*, in eqn (3.40):

where is cosine zenith angle and is the absorption coefficient (for an absorber
concentration, *u*) which varies with pressure,* p*, and temperature, *T*, along the path from to*
z*. The four integrals imbedded in eqns (3.38) - (3.40) make the numerical calculation of
longwave effects quite expensive.

One can rewrite the radiative flux equations in a more convenient form by integrating eqns (3.38) - (3.39) by parts to obtain:

The net flux at level *z*, using eqns (3.41) - (3.42) is:

Changing vertical coordinate from *z* to pressure, *p*, noting that* p=0* at* z=zT* and *p=psfc* at *z=0*,
the net longwave flux equation (3.44) is virtually identical to eqn (1) in Fels and Schwarzkopf
(l975):

Computation of net flux at each model level requires the evaluation of integrals in eqn (3.40) and (3.44) for

1. zenith angle (),

2. absorber optical path (),

3. spectral interval (), and

4. transmission from all levels ().

Fels and Schwarzkopf parameterize longwave processes using techniques designed to reduce
the computational overhead inherent in these integrals, while, at the same time, retaining
accuracy in the calculations. The integral over zenith angle ( ) is removed by scaling the
gaseous absorber path (i.e., amount) by a diffusivity factor of 1.66. In this manner diffuse
transmission from to *p* is represented, with little loss of accuracy (Rodgers and Walshaw,
l966), as a beam of radiation along a path whose zenith angle,, is
approximately 53_.

The integral over optical path (*du* in eqn (3.40)) is difficult to compute because the
absorption coefficient depends upon pressure and temperature, both of which can change
rapidly along *du*. There are techniques which account for these inhomogeneous paths by
adjusting pressure and path length to create a homogeneous path having a mean absorption
coefficient. Fels and Schwarzkopf use two methods for their water vapor calculations. A
simple scaling of the optical path by is used in their emissivity heating rate computations
(discussed below), where =1013.25 mb. A more accurate scaling is the 2 parameter
Curtis-Godson approximation where both pressure and absorber amount are adjusted to
create the homogeneous path. Fels and Schwarzkopf employ this technique with the *H2O*
random band model used for their exact heating rate calculations (discussed below).

The integral over spectral interval ( in eqn. (3.44)) is quite difficult to calculate
because the fine scale of the absorption lines must be multiplied by the vertical derivative of
the much smoother Planck function, *B*n. Typically, methods are used which separate the
longwave spectrum into spectral intervals small enough both to consider the Planck function
a constant and to produce transmission functions which are exponential in nature (Stephens,
l984). Though *O3 *and *CO2* are evaluated as one band, *H2O* processes are complex enough to
require the smaller intervals. Using statistical properties for groups of absorption lines, an
absorption coefficient can be defined as a function of the strengths, separations, and positions
of the detailed line structure within each spectral interval (or band). In "exact" calculations
for water vapor, Fels and Schwarzkopf use the Rodgers and Walshaw (1966) random band
model distribution of absorption lines and spectral intervals. In order to simplify the
overlapping region of *H2O* and *CO2* absorption (15), the Rodgers and Walshaw bands
6,7,and 8 have been restructured to place all of the* CO2 *effects in band 7 (see table 3.3, where,
is mean line strength, is mean distance between absorption lines, andis (Lorenz) line
width).

A less accurate but computationally more efficient alternative to the band model
approximation for is the emissivity approximation (see Stephens, l984; Paltridge and
Platt, l976, p. 173). This treats the absorption as a constant for all wavelengths within each
spectral band and allows the integral over the entire spectrum to be performed once, thus
saving computer time. Fels and Schwarzkopf apply the emissivity approximation to eqn (3.44)
and obtain the following flux equation (for *H2O*):

where are pre-calculated tables for temperature between 100K - 370K (every 10K)
and for water vapor amount between 10-16 and 102 g/cm2 (180 values, equal spacing in ln *u*):

where *n* is the number of spectral intervals for *H2O* and is the transmission function for each
band. The integral in eqn (3.45) is evaluated as

where *j*,* j*+1 refer to model levels and* j*+1/2, *i*+1/2 refer to model midlayers. For nearby layers,
where , a precomputed array, *G3*, is used to evaluate the integral:

Further details may be found in Fels and Schwarzkopf (l975).

One integral remains to be discussed - the integration over all atmospheric layers ( in eqn (3.44)). Fels and Schwarzkopf simplify this integration by separating the net radiative flux equation (3.44) into two terms (Green, l967):

1. Cooling to space (*CTS*), which is longwave emission from level *p* directly to
space , and

2. Internal *EXCHANGE* between atmospheric levels, accounting for absorption
and re-emission. Stephens (1984) notes that this process primarily occurs in "nearby" layers,
because at greater distances its importance drops with the exponential decrease of the
transmission function.

In an isothermal atmosphere , and eqn (3.44) can be written as:

where *Bn *is the Planck function for each spectral interval, *n*, in the band model representation
of the longwave spectrum. The *CTS *approximation assumes that (3.48) can be used to
calculate flux at all model levels even though the atmosphere is not isothermal. The simplicity
of this scheme can be seen in the representation of transmission functions in (3.44) and (3.48);
the matrix calculation implied by in (3.44) is replaced by a function in (3.48) which
depends only on absorber amount above level *p*. Of course, the *CTS* approximation is not
accurate enough by itself and the* EXCHANGE* term must be added.

Fels and Schwarzkopf treat the cooling-to-space and exchange calculations in
different manners in order to obtain quite accurate results with a computationally efficient
method. Recall from eqn (3.7) that the heating rate, *Q*, is the vertical component of the
radiative flux divergence. Computation of *F(p)* from eqn (3.44) produces a total heating rate,
*QTOTAL*. Separation of the flux calculation into two terms can be used to obtain a *CTS* heating
rate, *QCTS* (using eqn 3.48) and an exchange rate, *QEXCHANGE* (ie. the integral term in eqn
3.44). Thus

Noting that the latter term is simply

Fels and Schwarzkopf find that the* EXCHANGE *is relatively insensitive to the method of
calculation. Thus they compute *QEXCHANGE* using the computationally more efficient
emissivity () method (3.45). The calculation of *QCTS* (in eqn (3.49) however is done more
accurately - via either the Rodgers and Walshaw random band (*RB*) model for *H2O* or
accurate pre-calculated transmission functions for *CO2*. The "exact" *CTS* calculation adds
relatively little overhead to the efficient computation for the *EXCHANGE* term because the
former is a vector, not matrix, operation. The approximation to total longwave heating rate
for each model layer, using (3.49, 3.50), now becomes:

Heating rate calculations for both* H2O *and *CO2 *employ equation (3.51), however *O3*
processes are calculated exactly, using eqn (3.44), for a one band model.

- Water Vapor

where , is absorber amount and (the diffusivity factor).
More details can be found in Paltridge and Platt (l976), chapter 7. For the water vapor rotation
bands (1-10), the Curtis-Godson approximation is employed to remove the effects of
pressure on the transmission function along the optical path, *du* (see eqns (7.47) - (7.51)
Paltridge and Platt, l976). An additional term is added to eqn (3.52) for bands 7-11, which
partially covers the region of the water vapor continuum (band 21 completes the continuum
region but is not included here, see section 3.4.2),

Note that the first term in (3.53) is zero for *n*=11, because *A11*=0. Eqn (3.53) is equivalent
to a multiplication of exponential transmission functions, where the pressure weighting
accounts for pressure effects on the continuum absorption coefficient along the optical path
and

where *(SK)n* = 38.483, l6.288, 11.312, 7.428, 4.913 *, *for * n*=7,...,11. Equation (3.54) is from
Roberts, et al. (l976) and accounts for the temperature, *T*, dependence of the absorption
coefficient.

For the emissivity calculations (in eqn 3.51), equations (3.45) - (3.47)
are used, where *G1, G2, G3* are precomputed in tabular form using the Rogers and Walshaw
parameters in Table 3.3 for *strong *absorption line transmission (see Paltridge and Platt, l976,
eqn 7.38):

Water vapor amount scaled by is used during the table "look-up" for *G1, G2*, and *G3*.
Water vapor rotational band 7 for these emissivity calculations is handled in the *CO2 *overlap
(section 3.4.3). The contribution due to lines in bands 8-11 and 21 is neglected in eqn (3.55),
however the effect of lines in bands 8-11 is included in the "exact" *CTS* computation (eqn
3.53). For the emissivity calculations, the continuum effects in bands 8-11 are included as a
one broad band calculation and added to and , after the *G1, G2, G3* table
"look-up". Transmission in this one band continuum is:

where 8.6658 is a frequency weighted mean of the *(SK)n* (*n*=8-11) in eqn (3.54). Emissivity
calculations for the continuum in band 7 are included in the *CO2* overlap (section 3.4.3).

- Ozone

where *p* is pressure in units of atmospheres, =1.66, and and are absorber amounts.
Using Rodgers notation

with =.28 cm-1, =.1 cm-1, * k*=208. cm g-1. The overlap with water vapor continuum (thus
treated "exactly") is included as the last term in eqn (3.56) where

- Carbon Dioxide

where and represent the two model profiles available in block data. The interpolation of transmission functions to the temperature profile of the particular grid point is made from a second order expansion below:

where is from (3.57) and (eqn (33) in Fels and Schwarzkopf (1981)) is

Numerical experimentation shows that

where *po*=30 mb and* p* is model level pressure using* psfc*=1013.25 mb. The function *G(p)* is
precomputed and resides in block data, BD2 (GTEMP).

A temperature correction to in (3.58) is necessary because the spectral interval (band 7) is not really narrow enough to consider the Planck function a constant. The final transmission function, is (eqn (7) in Schwarzkopf and Fels (l985)):

where

For the "exact" *CTS *heating rate calculation, in eqn (3.51), *CO2 *transmission is
multiplied by the *H2O* band transmission (eqn 3.53)) to account for absorption overlap. For
the emissivity *EXCHANGE* heating rate calculation,, in eqn (3.51), a one band
version of eqn (3.44) is used. Overlapping *H2O* transmission is computed as (see eqn (3.54)
and (3.55)):

where *C7* is defined in eqn (3.54), and the *strong line* approximation is used for *H2O *band 7.

- Clouds

In the case of thick (i.e., greater than one model layer) low cloud, longwave processes result in strong cooling in the upper cloud layer and much less cooling in the lower cloud layer. This produces a strong destabilizing effect, which could be harmful when used with the fixed zonal mean cloud climatology. An adjustment is made to the vertical gradient of longwave flux in the thick cloud (a smoothing!) so that it is constant for the cloudy part of the column. For completely overcast low cloud situations (i.e., cloud fraction =1), the resulting model layer longwave heating rates within the cloud will be identical.

- Adjustment to the Surface Downward Flux

**Table 3.1**

Discrete probability distribution,, of water vapor absorption coefficients, *kn*, for *N*=9
subintervals of the solar spectrum (see Lacis and Hansen (l974), table 1)

**Table 3.2**

Shortwave radiative properties of clouds for the 9 subintervals of the solar spectrum

**Table 3.3**

Water vapor band parameters used for exact *CTS* calculations. Bands (7-11,21) are *H2O*
continuum and band 21 is for exact *O3 *computation, but neither is part of Rodgers and
Walshaw (1966) model. * H2O *rotation bands (1-10) and 6.3 bands (12-20) from Rodgers
and Walshaw. Adjustments made to bands 6-8 so that *CO2* effects lie entirely within band 7.

Fels, S. B. and M. D. Schwarzkopf, l975: "The Simplified Exchange Approximation - A New
Method for Radiative Transfer Calculations",* J. of Atmos. Sci.*, pp.1475-1488.

Fels, S. B. and M. D. Schwarzkopf, l981: "An Efficient, Accurate Algorithm for Calculating
CO2 15Band Cooling Rates", *J. of Geophys. Res.*, pp. 1205-1232.

Green, J. S. A, l967: "Division of Radiative Streams into Internal Transfer and Cooling to
Space", *Quart. J. of Roy. Met. Soc.*, pp. 371-372.

Hering, W. S. and T. R. Borden, Jr., l965: "Mean Distribution of Ozone Density over North America, l963-l964", Environmental Research Papers, Report 162 USAF Cambridge Research Laboratory.

Lacis, A. A. and J. E. Hansen, l974: "A Parameterization for the Absorption of Solar
Radiation in the Earth's Atmosphere", *J. of Atmos. Sci.*, pp. 118-133.

London, J., l962: "Mesospheric Dynamics, 3, the Distribution of Total Ozone in the Northern Hemisphere, Final Report", Dept. of Meteorology/Oceanography, New York University.

Manabe, S. and R. F. Strickler, l964: "Thermal Equilibrium of an Atmosphere with a
Convective Adjustment", *J. of Atmos. Sci.*, pp. 361-385.

Matthews, E., l985: "Atlas of Archived Vegetation, Landuse, and Seasonal Albedo Data Sets", NASA Technical Memorandum 86199, Goddard Institute for Space Studies, New York.

Paltridge, G. W. and C. M. R. Platt, l976: "Radiative Processes in Meteorology and Climatology, Elsevier Scientific Publishing Company.

Payne, R. E., l972: "Albedo of the Sea Surface", *J. of Atmos. Sci.*, pp. 959-970.

Roberts, R., J. Selby, and L. Biberman, l976: "Infrared Continuum Absorption by
Atmospheric Water Vapor in the 8-12Window", *Applied Optics*, pp. 2085-2090.

Rodgers, C. D. and C. D. Walshaw, l966: "The Computation of Infrared Cooling Rate in
Planetary Atmospheres", *Quart. J. of Roy. Met. Soc.*, pp. 67-92.

Rodgers, C. D., l967: "The Radiative Heat Budget of the Troposphere and Lower Stratosphere", Report No. A2, Planetary Circulations Project, Dept. of Meteorology, M. I. T.

Rodgers, C. D., l968: "Some Extensions and Applications of the New Random Model for
Molecular Band Transmission", *Quart. J. of Roy. Met. Soc*., pp. 99-102.

Sasamori, T., J. London and D. Hoyt, l972: "Radiation Budget of the Southern Hemisphere", Meteorological Monagraphs, vol. 13, number 35, pp. 9-23.

Schwarzkopf, M. D. and S. B. Fels, l985: "Improvements to the Algorithm for Computing CO2
Transmissivities and Cooling Rates",* J. of Geophys. Res.*, pp. 10541-10550.

Stephens, G. L, l984: "The Parameterization of Radiation for Numerical Weather Prediction
and Climate Models," *Mon. Wea. Rev.*, pp. 826-867.

Telegadas, K and J. London, l954: "A Physical Model of the Northern Hemisphere Troposphere for Winter and Summer," Sci. Rpt. 1, Research Division, College of Engineering New York University, 55 pp.

Fig 3.1 Schematic of radiation calculations, with subroutine names.

Fig 3.2 Seasonal zonal mean ozone (parts per million) in upper nine layers of the 18 layer model. Mean layer pressure (mb) for surface pressure=1000 mb. Contour interval = 0.5 ppm.

Fig 3.3 Seasonal zonal mean cloud fraction for high, middle, and low cloud climatology. (a) Northern hemisphere winter. (b) Northern hemisphere spring. Values hemispherically flipped for opposite season.

Fig 3.4 Seasonal cloud thickness in model sigma layers (surface pressure = 1000 mb). High and middle clouds are one layer thick. (a) Northern hemisphere winter. (b) Northern hemisphere spring. Data hemispherically flipped for opposite season.

Fig 3.5 Multiple reflections for the short wave cloud calculation. Subscripts for *TCLU* and *TCLD* are inverted in subroutine SWR983 ; i.e. *TCLU4* becomes *TCLU1 *, etc...

Fig 3.6 Model clouds. (a) Schematic representation of cloud bounding surfaces for short wave (SW) and long wave (LW) processes. (b) Cloud overlap, where H, M, L are cloud fraction for high, middle, and low cloud respectively.