Uncertainties associated with theoretically calculated N₂-broadened half-widths of H₂O lines

With different choices of the cut-offs used in theoretical calculations, we have carried out extensive numerical calculations of the N₂-broadend Lorentzian half-widths of the H₂O lines using the modified Robert–Bonamy formalism. Based on these results, we are able to thoroughly check for convergence. We find that, with the low-order cut-offs commonly used in the literature, one is able to obtain converged values only for lines with large half-widths. Conversely, for lines with small half-widths, much higher cut-offs are necessary to guarantee convergence. We also analyse the uncertainties associated with calculated half-widths, and these are correlated as above. In general, the smaller the half-widths, the poorer the convergence and the larger the uncertainty associated with them. For convenience, one can divide all H₂O lines into three categories, large, intermediate, and small, according to their half-width values. One can use this division to judge whether the calculated half-widths are converged or not, based on the cut-offs used, and also to estimate how large their uncertainties are. We conclude that with the current Robert–Bonamy formalism, for lines in category 1 one can achieve the accuracy requirement set by HITRAN, whereas for lines in category 3, it is impossible to meet this goal.

Keywords

• theoretical calculation of half-widths,
• temperature-dependent exponent in HITRAN,
• Robert–Bonamy theory,
• convergence of half-width calculations,
• interaction potential for H₂O–N₂ pairs

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