Parametrization of transmittance for application in atmospheric optics

An optimal approach to overlapping bands with correlated k distribution method and its application to radiative calculations

“…It may underestimate or overestimate the overlapping transmittance when the correlation among gases becomes strong [ Shi , 1984; Chou et al , 2001]. overestimates the overlapping transmission in most cases [ Firsov et al , 1998] because the hypothesis of perfect correlation is rarely satisfied in the real absorption spectrum.…”

“…The second widely adopted method combines absorption coefficients determined individually for each absorber by assuming a spectral correlation between the absorption spectra for overlapping gases [ Shi , 1981; Isaacs et al , 1987; Lacis and Oinas , 1991; Firsov et al , 1998]. The most common approach is to assume that the monochromatic transmittances or absorption spectra of the overlapping line absorbers are uncorrelated within the wavelength interval of interest [ Wang and Ryan , 1983; Lacis and Oinas , 1991; Ellingson et al , 1991].…”

“…Thus only the magnitude can be different, so only coefficients with the same quadrature index { k i 1 × k j 2 ; i = 1, …, M } need to be combined, and M ‐radiative transfer calculations are necessary in this scheme. The underlying correlation assumption, however, is unrealistic and yields a significant systematic overestimation of transmittance in most cases [ Shi , 1981, 1984; Firsov et al , 1998]. A third scheme that accounts for partial correlation between the line absorbers is worth exploring.…”

“…The present study gives two simplified schemes on partial correlation that include the correlation between different gas absorption spectra by mapping the absorption spectrum of the second or third gas to that of the primary gas [e.g., Shi , 1981, 1984; Mlawer et al , 1997]. Then, the correlation existing between the overlapping gases is automatically contained in the calculated transmittance and radiative flux; special solving as by Firsov et al [1998] is unnecessary. Therefore the optimal scheme is proposed in this study that chooses k distribution parameters for overlapping bands based on the completely uncorrelated, perfectly correlated, and partly correlated schemes, as described above.…”

Extension of the weak-line approximation and application to correlated-k methods

“…The line strengths of radiatively active gases can vary over several orders of magnitude through a band; there are often many lines in a band, making accurate and fast integration through the corresponding range of extinctions difficult. Instead, the integration through the extinctions (or frequencies) is often parameterized by a weighted sum of exponentials [4][5][6][7]. This weighted sum is called the weighted sum of gray gases, or the exponential sum fitting of transmission.…”