Vertically resolved minimal-set k-distribution for thermal infrared absorption: an application to the atmosphere of Venus

TL;DR

The paper develops a vertically resolved minimal-set $k$-distribution (FKDM) parameterization for longwave absorption in Venus' lower and middle atmosphere, built from line-by-line Monte-Carlo references to control accuracy. It constructs height-dependent $k(z)$ terms for 16 bands (10--$6000$ cm$^{-1}$) yielding 32 $k$-terms, band-averaged Planck values, and per-band cloud inputs, enabling direct use in radiative transfer solvers without inter-layer correlation assumptions. Validation shows upward fluxes agree with the line-by-line reference to within $<2\%$ below 95 km and cooling rates stay within acceptable error across the lower to middle atmosphere, with substantially fewer $k$-terms than correlated-$k$ implementations. A Fortran driver and public repository provide tools to generate $k(z)$ for arbitrary Venus profiles, facilitating integration into Venus GCMs and radiative–convective models, with potential applicability to other planetary atmospheres. Future work will extend to shortwave spectral ranges and incorporate updated continuum and $\chi$-factor treatments.

Abstract

The FKDM $k$-distribution technique is applied to parameterize absorption of thermal radiation in the lower and middle atmosphere of Venus, targeting modeling scenarios where the cost of full radiative transfer calculations necessitates efficient parameterizations (e.g. climate modeling). Line-by-line reference modeling based on a Monte Carlo method for radiative transfer is built into the $k$-distribution terms construction process, explicitly controlling accuracy. From 16 bands across $10$--$6000~\mathrm{cm^{-1}}$, the method produces 32 $k$-terms, band-averaged Planck function values and per-band spectral points for computing Venus cloud optical properties. The FKDM $k$-distribution technique does not require the inter-level correlation assumption common for the correlated $k$-distribution method. We supply height-dependent $k(z)$ functions tabulated on the same vertical grid as the input temperature-pressure profile, designed for direct use in radiative transfer solvers and avoiding additional remapping of the pre-tabulated $k$-data. Our implementation of the technique yielded acceptable accuracy below 90~km ($<1.2~\mathrm{K\,day^{-1}}$ for cooling rates; $<2\%$ for fluxes), while requiring substantially fewer $k$-terms than recent implementations of the correlated-$k$ method. A Fortran driver that generates $k(z)$ functions for an arbitrary Venus atmospheric profile is provided in a public repository.

Figures (3)

• Figure 1: Representative Venus atmospheric temperature profiles (Seiff, 1983; VIRA-1 day- and night-side at $75^\circ$ latitude) used for the construction and sensitivity analysis of the FKDM $k$-distribution.
• Figure 2: Vertical profiles of upward longwave radiative fluxes computed with the FKDM $k$-distribution scheme (dashed lines) and the line-by-line Monte-Carlo reference model (solid lines) for several representative Venus atmospheric profiles.
• Figure 3: Comparison of radiative cooling rate profiles obtained with the FKDM $k$-distribution scheme (dashed lines) and the line-by-line Monte-Carlo reference calculations (solid lines) for the same set of Venus atmospheric profiles as in Fig. \ref{['fig:Fup']}.