A variety of models have been developed which allow computations of the radiance at the top of the atmosphere or at the surface under clear conditions, given a description of the surface and the state of the atmosphere. The most detailed of these models (narrow band models) have been intercompared as part of the ICRCCM project (Intercomparison of Radiative Codes in Climate Models) in their estimation of the surface downward shortwave flux. Substantial discrepancies exist among models for water-vapor absorption with 1 to 3% for downward fluxes at the surface and 6 to 11% for total atmospheric absorption (clear cases). In cloudy cases, there is a 4 to 10% difference depending on cloud optical thickness (Fouquart et al. 1991).
Lowtran-6 (Kneizys et al. 1983) is a well-known narrow band radiative transfer model usable for such radiance computations. Another such narrow band model
(20 cm-1 resolution) is 5-S (Tanre et al. 1990), also now commonly used in a variety of applications involving signal simulation, atmospheric corrections or
instrument calibration. Differences of less than 1.5% exist between Lowtran-6 and 5-S on gaseous transmittance computations. All the available models require
the knowledge of 1) the surface bidirectional reflectance properties over the spectral interval of interest, 2) 
, 
and 
mixing ratios, and 3) aerosol
distribution or, alternatively, surface visibility. The advantage of 5-S over most other available models is that it is well-documented (so is Lowtran-6) but,
in addition, it is constantly improved, including additional physics with each new version. For instance, the next version will include radiation polarization
effects.
The validation of any of these models can be made with radiance observations from a variety of satellite sensors. These include Channel 1 and 2 of AVHRR, the
visible part of VISSR/VAS, and the shortwave channel on ERBE. One such model validation has already been performed by Frouin et al. 1990, but from the surface
perspective. Computations of the surface solar irradiance with the 5-S model have been compared with measurements from a set of two pyranometers during the
FIFE experiment. Clear-sky conditions (< 5% cloud cover) have been selected from photographs taken by a camera in the vicinity of the two pyranometers. Aerosol
optical thicknesses have been inferred from sun photometer measurements at different wavelengths during one day of the experiment and assumed constant for
the eight days analyzed because of the high noise in the aerosol property estimations. Under these conditions the comparison between the model computations
and the observations for half-hour intervals shows a 23 
standard deviation (or about 3% of the average value) and a bias of 13 . Different signs in
bias are found for the different time periods which, together with measured changes in aerosols properties, suggest that the assumption of constant aerosols
properties is not appropriate. This validation, which is not fully satisfactory in terms of accuracy, was however facilitated by the fact that the surface
reflectance plays a minimal role on the surface solar irradiance, and therefore the uncertainties in its description (i.e., bidirectional properties) only
minimally affect the results.
For cloudy conditions, the situation is much more difficult because only plane-parallel cloud models, merely adequate for homogeneous cloud conditions over the satellite field of view, are really available for spectral or broadband radiance computations. This will initially limit the applications of the proposed approach to just a few cases (homogeneous conditions over the field-of-view of the satellite radiometer whose radiances are simulated). The treatment of real clouds will require more complex models capable of handling non-homogeneous cloud conditions (e.g., Monte-Carlo computations); these types of models are, however, not yet available. They are expected to become available as a result of the ARM program.
In the IR, the situation is more complex than in the shortwave range. Line-by-line models exist but disagree with each other when different assumptions (still unresolved) are made on line shape, line cutoff and continuum absorption. When these assumptions are homogenized, however, the intercomparisons provide improved agreement but with the drawback that the line-by-line models can no longer be considered as absolute standards (Ellingson et al. 1991).
A dozen narrow-band to broadband radiative transfer models are available for clear sky computations. Their accuracies (by comparison with line-by-line models) vary with their linewidth. Some commonly used for satellite retrievals are the 3 R model of Chedin et al. (1990), the band model of Susskind et al. (1983, 1984) and the model of Fleming and McMillin (1977) and McMillin and Fleming (1976) used in Smith's (1983) retrieval. All of these models are fast models that use pre-calculated transmittances for specific satellite sensor channels (e.g., the HIRS-2).
In the case of cloudy conditions, the situation is often simplified since the effects of cloud inhomogeneities can be less dramatic on the upwelling radiance. Up to a level of accuracy of several percent, it is sufficient to treat cloud surfaces as a boundary surface with emissivity properties (which could vary with cloud inhomogeneities, for instance) and therefore treat the cloud problem as that of clear conditions but with the cloud top replacing the surface. In this case, a partial cloudiness parameter needs to be introduced. It is usually handled through a cloud fraction parameter which is an effective parameter accounting for emissivity, edge effects etc. Since these simple cloud representations may not provide radiance computations accurate to the level of the satellite observations, however, more complex models capable of handling non-homogeneous cloud conditions will be need.
