Simple Spectral Model (SSM): Radiative Transfer

• SSM is a clear-sky longwave radiative transfer scheme that simulates H2O line/continuum and CO2 line absorption using analytic fits at reference conditions.
• It uses analytic fits derived from PyRADS with HITRAN2016 data to approximate the large-scale spectral structure without resolving fine line details.
• The model integrates six equations and ten physical parameters, serving both idealized climate studies and educational demonstrations in radiative transfer.

Searching arXiv for the specified paper and closely related acronym usages. The Simple Spectral Model (SSM) is a clear-sky longwave radiative transfer scheme developed for idealized climate models. It was introduced to occupy the middle ground between gray radiation schemes, which are simple but physically crude, and correlated-$k$ schemes such as RRTMG / RTE+RRTMGP, which are fast and accurate but rely heavily on lookup tables and precomputed spectroscopic information (Williams, 12 Aug 2025). In this formulation, the model represents the large-scale spectral structure of H$_2$O and CO$_2$ absorption with analytic fits at reference conditions, extends those fits to off-reference states with simple scaling laws, and couples them to a two-stream solver. The resulting scheme consists of six equations and ten physically meaningful parameters and is intended both for idealized climate modeling and for pedagogical/classroom use (Williams, 12 Aug 2025).

1. Scope, motivation, and physical assumptions

The SSM is restricted to clear-sky longwave radiative transfer. It computes upward and downward longwave fluxes through absorption and emission only; no scattering term appears. The active absorbers are limited to H$_2$O line absorption, H$_2$O continuum absorption, and CO$_2$ line absorption (Williams, 12 Aug 2025).

The model omits several processes by construction. It includes no clouds, no atmospheric absorption of solar radiation, and no ozone. In the aquaplanet GCM experiments built around the scheme, the atmospheric shortwave heating rate is therefore zero, and the same shortwave treatment is used across gray, SSM, and RRTMG comparisons (Williams, 12 Aug 2025). Fine spectral line structure is not resolved line-by-line; instead, the model keeps only the large-scale spectral envelope. For CO$_2$, only the major 15 $\mu$m bending band is retained, represented over approximately $500$–$850\ \mathrm{cm}^{-1}$, while secondary CO$_2$0 bands are ignored (Williams, 12 Aug 2025).

The atmospheric inputs required by the scheme are profiles of temperature $_2$1, humidity through water vapor specific humidity $_2$2, and pressure $_2$3. CO$_2$4 is prescribed as a well-mixed mass-specific concentration,

$_2$5

For example, at $_2$6 ppmv,

$_2$7

These assumptions define the model’s intended domain: Earth-oriented, idealized, clear-sky longwave climate calculations rather than general-purpose spectroscopic radiative transfer (Williams, 12 Aug 2025).

2. Spectral construction and fitted parameterization

The central approximation is that the large-scale spectral structure of atmospheric absorption can be represented analytically at a reference state,

$_2$8

The reference spectra are derived from PyRADS using HITRAN2016 line data and the MT_CKD_3.2 continuum (Williams, 12 Aug 2025).

At reference conditions, the H$_2$9O line absorption coefficient is represented piecewise across longwave bands as

$_2$0

This piecewise form is intended to capture the rotation band, the vibration–rotation band, and the combination-band tail (Williams, 12 Aug 2025).

CO\