http://people.csail.mit.edu/jaffer/SimRoof/NRT  
SimRoof: Net Radiative Transfer 
99% of the sun's radiance is at wavelengths shorter than 4 µm; while 99% of a 25°C blackbody's radiance is at wavelengths longer than 4.8 µm. So we can consider solar and thermal radiance separately. The three quantities to compute for a prototypical square meter of roof are:
More problematic may be emission and scattering by clouds. The sections Weather, Cloudless Sky, and Cloudy Sky discuss these models.
Kirchhoff's Law of Thermal Radiation dictates that in every band, a body must emit the same proportion of thermal radiation as it absorbs. The Infrared Scattering page establishes that thermalinfrared radiation is not significantly scattered by clear air. Without scattering (or reflection), the correspondence between absorption and emission is of interest because it allows the use of atmospheric transmission data to calculate emissivity of cloudless atmosphere: That portion of mid and farinfrared radiation which isn't transmitted is absorbed.
The Infrared Scattering by Water Clouds page argues that water and ice clouds can be treated as (opaque) blackbodies. The infrared transparency of the atmosphere between the ground and cloudbase is no different than that for cloudless sky. The cloudbase is modeled as the remaining moisture in a layer of liquid at the cloudbase height.
In the tropics, ice clouds occur at high altitudes. They will play a role only if there are not opaque clouds below them. Because high ice clouds are at cold temperatures (as estimated by the lapserate), treating them as cloudless sky will not introduce large errors.
The angledependence is the angle from zenith. Angledependent optical functions allow modeling of the aperturerestriction discussed in Optics for Passive Radiative Cooling.
Angledependent optical functions can model when buildings or terrain
obstruct the horizon. This can be done in a manner analogous to the
way clouds are treated: for each angle near the horizon, the
obstruction percentage of the incoming radiation comes from a
blackbody at a temperature at or above ambient through the average
distance to the obstructions. During the day, the temperature of
obstructed horizons is greater than ambient due to solar heating.
Introduced is a solartemperaturegain (stg) parameter which is the
temperature increment (°C) per 1000 W of TMY3
GlobalHorizontalIrradiance (ghi). For an angle h above the
horizon (π/2−h from the zenith), the solid angle to
the horizontal plane is
π·sin^{2}(h)=(π/2) (1−cos(h)).
For a given solid angle γ, the h having the same solid
angle is cos^{1}(1−(2/π)·γ).
If the roof has a small tilt t, then the airmass over most of
the hemisphere is not much different than for a horizontal roof. The
difference is that a spherical wedge between the plane of the roof and
the horizontal plane receives thermal radiation from the ground or
buildings. The solid angle subtended by tilt angle t is
2t (radians).
Lambertian Roof  Angle Dependent  Angle and Wavelength Dependent 

The simplest configuration is a horizontal, Lambertian surface under a full hemisphere of unobstructed sky.  Aperture restricted to a cone around the zenith; also handles obstructed horizons and small roof tilts (less than 15°).  Spectral optical function, horizon obstructions, and daylight spectra must be compiled into the NIRT array, making it specific to a single configuration. 
Lambertian Roof  Angle Dependent  Angle and Wavelength Dependent 

Roof Solar Absorption  
The fraction of solar power absorbed; between 0 and 1.  
Roof Aperture Cone Angle  Roof Solar Optical Absorption Function  
The angle centered on the zenith of the cone from which solar radiation is absorbed. The angle is between 0° and 180°.  Function of solarelevation (angle) and wavelength.  
TMY3 Global horizontal irradiance  TMY3 Direct normal irradiance  
Total amount of direct and diffuse solar radiation received on a horizontal surface during the 60minute period.  Amount of solar radiation (modeled) received in a collimated beam on a surface normal to the sun during the 60minute period.  
TMY3 Diffuse horizontal irradiance  
Amount of solar radiation received from the sky (excluding the solar disk) on a horizontal surface during the 60minute period.  
SolarElevation  
Computed from:

Lambertian Roof  Angle Dependent  Angle and Wavelength Dependent 

Roof Emissivity  
The fraction of possible blackbody power radiated; between 0 and 1.  
Roof Aperture Cone Angle  Emissivity Function  
The angle centered on the zenith of the cone from which thermal radiation is absorbed. The angle is between 0° and 180°.  function of angle and wavelength.  
TMY3 Drybulb  
Ambient temperature in °C. 
Lambertian Roof  Angle Dependent  Angle and Wavelength Dependent 

Roof Emissivity  
The fraction of possible blackbody power radiated; between 0 and 1.  
Roof Aperture Cone Angle  Emissivity Function  
The angle centered on the zenith of the cone from which thermal radiation is absorbed. The angle is between 0° and 180°.  function of angle and wavelength.  
TMY3 Drybulb  
Ambient temperature in °C. Ignoring outlying negative temperatures from 3 sites, the tropical TMY3 range is 12.8°C to 36.6°C.  
TMY3 Opaque sky cover  
Amount of sky dome covered by clouds or obscuring
phenomena that prevent observing the sky or higher cloud layers at
the time indicated. Range is 0% to 100% at 20% resolution.  
TMY3 Ceiling height  
Height of the cloud base above local terrain. Tropical TMY3 range is 0 m to 21999 m.  
TMY3 Precipitable water  
The total precipitable water contained in a column of
unit cross section extending from the earth's surface to the top
of the atmosphere. Tropical TMY3 range is 11 mm to 65 mm.  
TMY3 Atmospheric Pressure  
Station pressure at the time indicated;
101.325 kPa in the
International Standard Atmosphere. Tropical TMY3 range is 95800 Pa to 103600 Pa.  
Atmospheric Transparency  
Valued 0 to 1, a function of precipitablewater and wavelength.  
Z  
Height of the tropopause (top of the troposphere); 16 km in the tropics; 11 km in ISA.  
L  
Troposphere lapserate; 6.5 K/km (ISA). 
All the inputs for computing upwardthermalradiation are also inputs for computing downwardthermalradiation; and computing upwardthermalradiation is an order of magnitude simpler than downwardthermalradiation. So the upward and downward thermal radiation computations can be combined.
troposphere.pdf gives the mathematical details of the thermal radiation calculation.
For Lambertian roofs (described in Simulation Inputs), a single table can be used to simulate any TMY3 (whose values are within its range). For rotationalsymmetry cases a single table which stores values for each rayangle can be used, 5850 values in the example below. For the generalcase (wavelengthdependent emissivity), a table must be calculated for each emissivityfunction. But that table is valid for any TMY3 (whose values are within its range).
The CoolRoof page shows the results of running the tropical model with Guam TMY3 data.
Copyright © 2010 Aubrey Jaffer
I am a guest and not a member of the MIT Computer Science and Artificial Intelligence Laboratory.
My actions and comments do not reflect in any way on MIT.  
SimRoof  
agj @ alum.mit.edu  Go Figure! 