Olga B. Rodimova

On the correlated k-distribution approximation in atmospheric calculations

Water vapor transmission function calculations are performed in the case of nonhomogeneous atmospheric paths based on the exact formulas for the coefficients of expansion into the series of exponents that we obtained earlier. A comparison of the results obtained with the exact formulas and those obtained in the context of the correlated k distribution (CKD) approximation shows that the CKD approximation is successful due to the fact that the optical thicknesses are the real correlating values in the Earth atmosphere, whereas the differences in the absorption coefficient behavior for various thermodynamic conditions are not of great importance in this problem. Situations in which the CKD approximation may break down are pointed out. It is noted that the accuracy of the expansion into a series of exponents depends on the accuracy of the absorption coefficient corresponding to the abscissas of the quadrature formulas more than on the number of points. Cases are mentioned in which the CKD approximation gives results far from the line-by-line results, whereas a calculation that uses exact formulas works well in these cases.

k-distribution of transmission function and theory of Dirichlet series

Abstract A representation of the transmission function by a series of exponents is discussed in the context of the Dirichlet series theory. A rigorous expression for the distribution function of the absorption coefficient is obtained for a homogeneous medium. In this case it is a formalization of the ordering procedure for absorption coefficients. A rigorous extension of this expression to the case of a nonhomogeneous medium, overlapping spectra and integrals with the source function is also performed. The resulting relations can be used to derive approximate formulas. Thus, such a formula whose accuracy can be evaluated is written for a nonhomogeneous medium and in relation to this formula, the meaning of the correlation of k -distributions is discussed. It is shown that the number of terms in the series of exponents used for the transmission function can be greatly reduced by means of the foregoing results. As a general conclusion, it follows that transmission functions should be represented by series of exponents using the distribution function for absorption coefficients rather than the distribution function density for absorption coefficients.

Theory of series of exponents and their application for analysis of radiation processes

Academician K. Ya. Kondratyev in one of his first monographs (Kondratyev, 1950) stressed the availability of the idea put forward by Academician V.A. (1968) which is associated now with the term “series of exponents”. This involves computation of values integrated over the frequency spectrum necessary for analysis of radiation processes: in this case, a “palisade” of a great number of spectral lines gives rise to not purely technical difficulties.

Statistical approximation in line wing theory

I t i 5 we 1 1 known t hat the spectral 1 i ne shape i s def i ned as F(w) = :f P(WWjf)I<fXi<I (1) where i,f denote the initial and final states of the absorbing system, w= wi_ W is the transition frequency, X is the dipole moment operator, p is the density matrix of the system. The system under consideration is the molecular gas in a volume treated as a unified quantum-mechanical object. It can be seen from Eq. ( 1 ) that the 1 me shape is the result of stat ist ical averaging of the delta-function of the argument representing the energy conservation law under the absorption. For calculating F(w) the exact state energies and wave functions of the system or, after transition to the binary approximation, the wave functions and states of two interacting molecules and the characteristics of the statistical ensemble should be available. Usually the expression describing F(c) in term of the correlation function c(t) is used in calculat ions

Effect of variations of the greenhouse gas concentrations on the solar shortwave radiation transfer

Estimate is made of conditions which could lead to a possibility of solar radiation penetration to the Earth surface in the UV region. The altitude behaviour of the transmission for some frequencies is considered under variations of absorbing species concentrations. The value of the O2 absorption coefficient is diminished by a factor 10 for modelling the absorption in the transparency microwindows, therewith the ozone and water vapour content is varied. At variations of concentrations of absorbing species the transmission function of the solar radiation calculated from the upper bound of the atmosphere downward remains zero near the surface in microwindows of the Schumann-Runge bands. It appears, however, that near 210 nm the solar radiation may reach the surface at definite variations of concentrations of absorbing species.

Co2 line shape in far wings: From virial coefficients to radiation fluxes

Intermolecular interaction potential appears to be a value which performs the relationship between divisions of physics seemingly far from each other. Accurate consideration of the quantum problem of interacting molecules allows one to refine the employment of theoretical expressions for the potential describing one or other type ofprocesses. Thus, the potential which can be named classical one is common for the absorption coefficient in the line wing and for the second virial coefficient. This fact provides a possibility of using the temperature dependent classical potential obtained from the line wing absorption coefficient data for the calculation of the second virial coefficient. The use of the line wing absorption coefficient following from the line wing theory, which is appreciably defined by the behaviour of the classical intermolecular interaction potential, leads to noticeable changes in the cooling rates at large heights in some spectral regions.

Possible impact of the atmospheric water vapor absorption on the total ozone amount

The total ozone amount (TOA) is determined as a rule by classic spectrophotometric method: TOA is found from a measured difference of the atmospheric optical thicknesses at two specially selected wavelengths in the region 305-340 nm. In this region the aerosol and molecular scattering takes place and it is traditionally believed, that the molecular absorption in this spectral region is conditioned only by ozone. Researches performed in the Institute of Atmospheric Optics SB RAS at the end of 1980s have shown, that there is also gentle absorption of a water vapor in this region, which can make a contribution to the measured difference of atmospheric optical thicknesses and can result in some methodical error. Thus, the TOA value which is determined without considering the water vapor, may be overstated.

Estimates of integral transmission functions of solar radiation inthe near-infrared region of the spectrum for different models of the atmosphere

Integral transmission functions in near infrared region of spectrum were extracted from the benchmark calculations of the solar radiation fluxes for the mid-latitude summer atmosphere. Their comparison with the values obtained from empirical formulas shows a good agreement. Hence, the transmission functions resulting from both ways can be used in climate modeling.

Spectral behavior of the intermediate part of line contour at different pressures

Within the framework of the line wing theory the peculiarities of line shape behavior in the intermediate part appear as a result of specific construction of the profile transitional from the line center to the line wing. In this paper it is shown that the experimental data in this case are satisfactorily explained.

Absorption coefficient in the infrared CO2 Q-branch

The values of absorption coefficient κ in the wings of the infrared CO2 Q-branches significantly differ from those isolated Lorentzian lines. It becomes now traditional to explain these deviations by line-mixing. Actually, presence of the small line separations in the Q-branches are greatly conductive to this point of view. It can be noted, however, that the largest deviations from the Lorentzian line calculations are observed in spectral regions comparatively far from the line centers. Therefore it would be interesting to know whether the line wing theory can be used to describe the observed frequency dependence of κ or not. The present study concerns with the CO2 Q-branch at 1932cm-1.