In this work the theoretical relationship between the clear-sky outgoing infrared radiation and the surface upward radiative flux is explored by using a realistic finite semi-transparent atmospheric model. We show that the fundamental relationship between the optical depth and source function contains real boundary condition parameters. We also show that the radiative equilibrium is controlled by a special atmospheric transfer function and requires the continuity of the temperature at the ground surface. The long standing misinterpretation of the classic semi-infinite Eddington solution has been resolved. Compared to the semi-infinite model, the finite semi-transparent model predicts much smaller ground surface temperature and a larger surface air temperature. The new equation proves that the classic solution significantly overestimates the sensitivity of greenhouse forcing to optical depth perturbations. In Earth-type atmospheres sustained planetary greenhouse effect with a stable ground surface temperature can only exist at a particular planetary average flux optical depth of 1.841. Simulation results show that the Earth maintains a controlled greenhouse effect with a global average optical depth kept close to this critical value. The broadband radiative transfer in the clear Martian atmosphere follows different principle resulting in different analytical relationships among the fluxes. Applying the virial theorem to the radiative balance equation, we present a coherent picture of the planetary greenhouse effect.

In this paper, we discuss the computational difficulties of merging line-mixing models into line-by-line computations. We present the technical details of the upgrade of the High-resolution Atmospheric Radiative Transfer Code (HARTCODE) into an accurate reference line-by-line code for line mixing computations in the Q branches of the CO₂. The implementation of line mixing was based on the model, database, and software that were developed at the Laboratoire de Physique Moleculaire et Applications (LPMA), and the HITRAN2K database absorption line compilation. In the recent version of the line mixing database 306 vibrational bands of eight CO₂ isotopes are included, and there are provisions for calculations using the first order and the more accurate relaxation operator method. The successful integration of the line mixing computations has been validated using airborne and ground‑based high‑resolution HIS radiance measurements. This exercise can also be regarded as the validation of the line mixing database for high resolution, nadir viewing thermal emission measurements.

In this paper the clear-sky infrared radiation field of the Earth-atmosphere system is characterized by the spectral decomposition of the simulated upward and downward flux density components into three distinct wave number regions. The relative contributions of the far infrared, middle infrared and windows spectral regions to the total longwave flux densities have been established. The approximate qualitative description of the meridional distributions of the zonal averages gave us a detailed insight into the role of the less explored far infrared spectral region. We demonstrate that on a global scale, the far infrared contribution to the clear-sky normalized greenhouse factor is significantly increasing toward the polar regions. Accurate computation of the transmitted and re-emitted part of the outgoing longwave radiation showed that in the far infrared the normalized upward atmospheric emittance increases poleward. This phenomenon is the direct consequence of the downward shift of the peak of the weighting functions in the strongly absorbing opaque spectral regions. The clear-sky total longwave terrestrial flux transmittance seems to be well correlated with the far infrared flux transmittance which implies the possibility of inferring total longwave flux densities solely from far infrared observations. The zonal averages of the total normalized atmospheric upward emittances are almost independent of the water vapor column amount, they have no meridional variation, and they are constantly about fifty percent of the surface upward flux density, an indication, that the gray atmosphere in the IR is in radiative equilibrium. The meridional distribution of the greenhouse temperature change and its dependence on the atmospheric water vapor content were also evaluated. Solving the Schwarzschild-Milne equations for the bounded atmosphere the infrared atmospheric transfer and greenhouse functions were derived. The theoretically predicted greenhouse effect in the clear atmosphere are in perfect agreement with simulation results and measurements.

The increasing number of IR spectral channels of recent satellite imagers implies the more accurate retrieval of surface skin temperature. In this paper the theoretical accuracy limits as a function of channel numbers, viewing angles and noise equivalent radiances have been studied. Based on LBL computations of the channel radiances regression type relationships have been established between the brightness temperatures and the skintemperatures. In this study model filter functions of the 7 IR channels of the GLI imager of the ADEOS-I have been used with a large set of temperature profiles. The global and seasonal distribution of temperature profiles were considered by groups of climatologically representative temperature profiles. Standard singular value decomposition program package was used to solve the multivariable linear regression problem. Results show that the accuracy limits of the skin temperature retrievals are depending mainly on the noise equivalent radiances and up to around 60 degree viewing angles remaining in the range of 0.1–0.2 K.