Interference coefficients for overlapping oxygen lines in air

Abstract Interference coefficients describe the non-Lorentzian effect that arises as pressure broadening causes lines to overlap. These coefficients, one for each line, are at moderate pressures related linearly to absorption and dispersion. They are determined here for the 5-mm wavelength oxygen lines broadened by air. The method includes four a priori constraints on off-diagonal elements of the relaxation matrix, which produce the interference effect: (1) detailed balance; (2) intra-branch submatrices are assumed to be identical; (3) coupling between the + and - branches is ignored; (4) coupling between the (positive-frequency) resonances and the nonresonant and negative-resonant branches is represented by a small bias term in the interference coefficients. The linear equations relating measured dispersion to the interference coefficients are solved by the Twomey-Tikhonov method, which minimizes a cost function, subject to the condition of constant measurement-error variance. The cost function is chosen to minimize the variation of elements along diagonals of the intra-branch relaxation submatrix. Implications for atmospheric radiative transfer are briefly discussed.

[1]  H. Liebe,et al.  Atmospheric oxygen microwave spectrum--Experiment versus theory , 1977 .

[2]  H. Pickett,et al.  PRESSURE BROADENING MEASUREMENTS OF THE 118.750 GHz OXYGEN TRANSITION , 1977 .

[3]  Earl W. Smith.  Absorption and dispersion in the O2 microwave spectrum at atmospheric pressures , 1981 .

[4]  H. J. Liebe,et al.  Pressure‐scanning mm‐wave dispersion spectrometer , 1975 .

[5]  F. Shimabukuro,et al.  Attenuation and emission of the atmosphere at 3.3 mm , 1970 .

[6]  U. Mingelgrin.  The microwave dispersion spectrum of O2 , 1974 .

[7]  E. Altshuler,et al.  Atmospheric effects on propagation at millimeter wavelengths , 1968, IEEE Spectrum.

[8]  P. Rosenkranz.  Shape of the 5 mm oxygen band in the atmosphere , 1975 .

[9]  T. Howell,et al.  Attenuation of radio waves by the troposphere over the frequency range 0.4–10 GHz , 1967 .

[10]  H. Liebe,et al.  Calculation of clear air EHF refractivity , 1978 .

[11]  U. Fano.  Pressure Broadening as a Prototype of Relaxation , 1963 .

[12]  G. J. Rosasco,et al.  Line interference effects in the vibrational Q-branch spectra of N2 and CO , 1983 .

[13]  A. Ben-Reuven.  Impact Broadening of Microwave Spectra , 1966 .

[14]  H. Griem,et al.  Theory of Line Broadening in Multiplet Spectra , 1958 .

[15]  D. Robert,et al.  Line coupling in the temperature and frequency dependences of absorption in the microwindows of the 4.3 μm CO2 band , 1986 .

[16]  K. Lam.  Application of pressure broadening theory to the calculation of atmospheric oxygen and water vapor microwave absorption , 1977 .

[17]  Roy G. Gordon,et al.  On the Pressure Broadening of Molecular Multiplet Spectra , 1967 .

[18]  Hans J. Liebe,et al.  An updated model for millimeter wave propagation in moist air , 1985 .

[19]  N. Grody.  Severe Storm Observations Using the Microwave Sounding Unit , 1983 .

[20]  D. Hogg,et al.  Emission measurements of 31.6 GHz absorption by atmospheric water vapor , 1983 .

[21]  E. E. Reber,et al.  Absorption of the 4‐ to 6‐millimeter wavelength band in the atmosphere , 1972 .

[22]  J. H. Van Vleck,et al.  The Absorption of Microwaves by Oxygen , 1947 .

[23]  N. N. Filippov,et al.  Influence of line interference on the vibration-rotation band shapes , 1984 .

[24]  M. Baranger.  Problem of Overlapping Lines in the Theory of Pressure Broadening , 1958 .

[25]  Hans J. Liebe,et al.  Modeling attenuation and phase of radio waves in air at frequencies below 1000 GHz , 1981 .

[26]  C. Rodgers,et al.  Retrieval of atmospheric temperature and composition from remote measurements of thermal radiation , 1976 .

[27]  S. Twomey,et al.  On the Numerical Solution of Fredholm Integral Equations of the First Kind by the Inversion of the Linear System Produced by Quadrature , 1963, JACM.