Spectrally uniform treatment of the atmospheric radiative transfer (RI) problem has been approached through two different techniques - very high resolution line-by-line (LBL) algorithms and lower resolution band models (BM). Each has its advantages and specific applications. However, if commonality and validation of a specific pair of RI approaches is to be mutually maintained, then these codes must be continually reevaluated against both measurements and other models.

The Moderate Resolution Atmospheric Radiance and Transmittance Model (MODTRAN3) is the developmental version of MODTRAN and MODTRAN2. The Geophysics Directorate, Phillips Laboratory, released a beta version of this model in October 1994. It encompasses all the capabilities of LOWTRAN7, the historic 20 cm{sup -1} resolution (full width at half maximum, FWHM) radiance code, but incorporates a much more sensitive molecular band model with 2 cm{sup -1} resolution. The band model is based directly upon the HITRAN spectral parameters, including both temperature and pressure (line shape) dependencies. Validation against full Voigt line-by-line calculations (e.g., FASCODE) has shown excellent agreement. In addition, simple timing runs demonstrate potential improvement of more than a factor of 100 for a typical 500 cm{sup -1} spectral interval and comparable vertical layering. Not only is MODTRAN an excellent band model for {open_quotes}full path{close_quotes} calculations (that is, radiance and/or transmittance from point A to point B), but it replicates layer-specific quantities to a very high degree of accuracy. Such layer quantities, derived from ratios and differences of longer path MODTRAN calculations from point A to adjacent layer boundaries, can be used to provide inversion algorithm weighting functions or similarly formulated quantities. One of the most exciting new applicationsmore » is the rapid calculation of reliable IR cooling rates, including species, altitude, and spectral distinctions, as well as the standard spectrally integrated quantities. Comparisons with prior line-by-line cooling rate calculations are excellent, and the techniques can be extended to incorporate global climatologies of both standard and trace atmospheric species.« less

MODTRAN2' is the most recent version of MODTRAJP, the Moderate Resolution Atmospheric Radiance and Transmittance Model, officially released by the Geophysics Directorate, Phillips Laboratory, in early 1993. It encompasses all the capabilities of LOWTRAN 73, the historic 20 cni' resolution (full width at half maximum, FWHM) radiance code, but incorporates a much more sensitive molecular band model with 2 ciii' resolution. The band model is based directly upon the HITRAN4 spectral parameters, including both temperature and pressure (line shape) dependencies. Because the band model parameters and their applications to transmittance calculations have been independently developed using equivalent width "binning" procedures, validation against full Voigtline-by-line calculations (eg. FASCODEb) is important. Extensive spectral comparisons have shown excellent agreement. In addition, simple timing runs of MODTRAN vs. FASCOD3P (released in 1992) show an improvement of more than a factor of 100 for a typical 500 cm spectral interval and comparable vertical layering. It has been previously established that not only is MODTRAN an excellent band model for "full path" calculations (that is, radiance and/or transmittance from point A to point B), but it replicates layer-specific quantities to a very high degree of accuracy6. Such layer quantities, derived from ratios and differences of longer path MODTRAN calculations from point A to adjacent layer boundaries, can be used to provide inversion algorithm weighting functions or similarly formulated quantities. One of the most exciting new applications is the rapid calculation of reliable IR cooling rates7, including species, altitude, and spectral distinctions, as well as the standard integrated quantities. Comparisons with prior line-by-line cooling rate calculations'9 are excellent, and the techniques can be extended to incorporate global climatoIogies°.

Beginning in the early 1970's, the then Air Force Cambridge Research Laboratory initiated a program to develop computer-based atmospheric radiative transfer algorithms. The first attempts were translations of graphical procedures described in a 1970 report on The Optical Properties of the Atmosphere, based on empirical transmission functions and effective absorption coefficients derived primarily from controlled laboratory transmittance measurements. The fact that spectrally-averaged atmospheric transmittance (T) does not obey the Beer-Lambert Law (T equals exp(-(sigma) (DOT)(eta) ), where (sigma) is a species absorption cross section, independent of (eta) , the species column amount along the path) at any but the finest spectral resolution was already well known. Band models to describe this gross behavior were developed in the 1950's and 60's. Thus began LOWTRAN, the Low Resolution Transmittance Code, first released in 1972. This limited initial effort has how progressed to a set of codes and related algorithms (including line-of-sight spectral geometry, direct and scattered radiance and irradiance, non-local thermodynamic equilibrium, etc.) that contain thousands of coding lines, hundreds of subroutines, and improved accuracy, efficiency, and, ultimately, accessibility. This review will include LOWTRAN, HITRAN (atlas of high-resolution molecular spectroscopic data), FASCODE (Fast Atmospheric Signature Code), and MODTRAN (Moderate Resolution Transmittance Code), their permutations, validations, and applications, particularly as related to passive remote sensing and energy deposition.

MODTRAN2 (1992) is the most recent version of MODTRAN, the Moderate Resolution Atmospheric Radiance and Transmittance Model, first released by the Geophysics Directorate, Phillips Laboratory, in 1990. It encompasses all the capabilities of LOWTRAN 7, the historic 20 cm-1 resolution radiance code, but incorporates a much more sensitive molecular band model with 2 cm-1 resolution. For inversion algorithm applications, MODTRAN2 must prove to be sufficiently accurate when calculating layer- specific perturbations. First steps in establishing this capability have recently been accomplished. DREV (Defence Research Establishment Valcartier, Canada), in conjunction with the Geophysics Directorate, has taken measurements with a surface-based Bomem interferometer (approximately 1 cm-1 resolution), with full supporting sonde profiles (z, T, p, and relative humidity). This suggests that the derivative matrices, typically required for inversion algorithms, may be readily (and rapidly) calculated using MODTRAN whenever its spectral resolution is adequate.

A formulation is developed in which the contribution of the far wings of collisionally broadened spectral lines to the water vapor continuum absorption is established. The effects of deviations from the impact (Lorentz) line shape due to duration of collision effects are treated semi-empirically to provide agreement with experimental results for the continuum absorption and its temperature-dependence. The continua due to both water-water molecular broadening (self-broadening) and water-air molecular broadening (foreign broadening) are discussed. Several atmospheric validations of the present approach are presented.

A unified approximate expression for the real part of the susceptibility for collisionally broadened transitions, including line coupling, has been developed. The Hilbert transform has been applied to the impact approximation line shape (Kramers-Kronig relationship) to obtain a result that is applicable from the microwave to the infrared. The approximate function has been compared numerically with the exact result using a newly developed algorithm. The results are applicable to spectral computations of the index of refraction and propagation delays.

In a recent paper,1 we developed a unified expression for the real part of the complex susceptibility of the atmosphere over the millimeter through the IR region from the imaginary part of the susceptibility under the impact approximation with a first-order line coupling correction. Here, two other real part expressions are derived, corresponding to the imaginary part specified by the modified Lorentz and the Gaussian line shape functions. Fundamental to our derivation is the Kramers-Kronig relationship,1 which states that the real and imaginary parts of the complex susceptibility are related through the Hilbert transform. The real part for the Gaussian case was expressed in terms of the Dawson and the modified Dawson integrals. Asymptotic expressions of the obtained real-part expressions and of the unified real part and the real part corresponding to the delta line shape1 were derived and shown to be identical. Considering the fact that the corresponding imaginary parts have entirely different asymptotic characteristics, the asymptotic behavior of the real part has depressed sensitivity to that of the corresponding imaginary part.

An atmospheric data base consisting of volume-mixing ratios (o0 to 12 okm) for 28 minor and trace gases was assembled for use with spectral-radiance transmittance models. Six reference atmospheres, each defining temperature, pressure and density as a function of altitude (selected from the U.S. Standard Supplements, 1966 and the U.S. Standard Atmosphere, 1976) provide a range of climatological choices. Analogous zonal-mean descriptions for H/sub 2/O, O/sub 3/, N/sub 2/O, CO, and CH/sub 4/ were subsequently adapted from satellite data and/or dynamical-photochemical analyses. The remaining species are defined by single profiles, usually appropriate for U.S. Standard conditions. Because the entire profile set is preferentially based on available measurements, explicit photochemical consistency between the different species has not been maintained.