Note that we need to enforce the normalization condition nJ2j Bj(T) = aT4.
In Chapter 8 we give actual computations for the global distribution of the Earth's thermal infra-red budget.
For further reading related to band-absorptance formulations see: Goody and Yung and references therein; Cess and Trewari; Tien; and Ramanathan. For the molecular spectroscopy of rotational-vibrational bands see the classic texts by Herzberg, and also Banwell and McCash. Numerical computations of the Voigt function can be found in Humlicek and, for early tabulations, Hummer. The HITRAN (high-resolution transmission molecular absorption) database can be accessed for spectroscopic data.
For a detailed discussion of non-local thermodynamic equilibrium (non-LTE) related to atmospheric radiation see Lopez-Puertas and Taylor.
4.11.2 References and further reading
Abramowitz, M. and Stegun, I. A. (1965). Handbook of mathematical functions. Dover, New York.
Banwell, C. N. and McCash, E. M. (1994). Fundamentals of molecular spectroscopy. McGraw-Hill, London.
Cess, R. D. and Tiwari, S. N. (1972). Infrared radiative energy transfer in gases. Advances in heat transfer 8. Academic Press, New York.
Dirac, P. A. M. (1958). The Principles of Quantum Mechanics. Oxford University Press, Oxford.
Edwards, D. K. and Menard, W. A. (1964). Comparison of models for correlation of total band absorption. Appl. Opt., 3, 621-625.
Gamache, R. R., Hawkins, R. L. and Rothman, L. S. (1990). Total internal partition sums in the temperature range 70-3000 K: Atmospheric linear molecules. J. Mol. Spectrosc., 142, 205-219.
Goody, R. M. and Yung, Y. L. (1989). Atmospheric radiation. Oxford University Press, Oxford.
Herzberg, G. (1945). Molecular spectra and molecular structure. II. Infrared and raman spectra of polyatomic molecules. Van Nostrand, New York.
Herzberg, G. (1950). Molecular spectra and molecular structure. I. Spectra of diatomic molecules. 2nd edn., Van Nostrand, New York.
Humlicek, J. (1982). Optimized computation of the Voigt and complex probability functions. J. Quant. Spectrosc. Radiat. Transfer, 27, 437-444.
Hummer, D. G. (1965). The Voigt function. Mem. R. Astr. Soc., 70, 1-32.
Lopez-Puertas, M. and Taylor, F. W. (2001). Non-LTE radiation transfer in the atmosphere. World Scientific, Singapore.
Oxenius, J. (1965). Emission and absorption profiles in a scattering atmosphere. J. Quant. Spectrosc. Radiat. Transfer, 5, 771-781.
Ramanathan, V. (1976). Radiative transfer within the Earth's troposphere and stratosphere: A simplified radiative-convective model. J. Atmos. Sci., 33, 13301346.
Struve, O. and Elvey, C. T. (1934). The intensities of stellar absorption lines. Astrophys. J., 79, 409-440.
Tien, L. (1968). Thermal radiation properties of gases. Advances in heat transfer 5, Academic Press, New York.
Vardavas, I. M. and Carver, J. H. (1984). Solar and terrestrial parameterizations for radiative-convective models. Planet. Space Sci., 32, 1307-1325.
Vardavas, I. M. (1993). Fast and accurate generation of the curve of growth for the Voigt lineshape. J. Quant. Spectrosc. Radiat. Transfer, 49, 119-127.
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