---
title: 'Simple Spectral Model (SSM): Radiative Transfer'
url: https://www.emergentmind.com/topics/simple-spectral-model-ssm
type: topic
---

# Simple Spectral Model (SSM): 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 [2508.09353]. 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** [2508.09353].

## 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** [2508.09353].

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 [2508.09353]. 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\(_2\) bands are ignored [2508.09353].

The atmospheric inputs required by the scheme are profiles of **temperature** \(T(p)\), **humidity** through water vapor specific humidity \(q_v(p)\), and **pressure** \(p\). CO\(_2\) is prescribed as a well-mixed mass-specific concentration,
\[
q_{\mathrm{CO}_2}=\text{ppmv}\times 10^{-6}\times \frac{44}{29}.
\]
For example, at \(280\) ppmv,
\[
q_{\mathrm{CO}_2}=280\times 10^{-6}\times (44/29).
\]
These assumptions define the model’s intended domain: Earth-oriented, idealized, clear-sky longwave climate calculations rather than general-purpose spectroscopic radiative transfer [2508.09353].

## 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,
\[
(T_{\mathrm{ref}},p_{\mathrm{ref}},RH_{\mathrm{ref}})=(260\ \mathrm{K},500\ \mathrm{hPa},100\%).
\]
The reference spectra are derived from **PyRADS** using **HITRAN2016** line data and the **MT\_CKD\_3.2** continuum [2508.09353].

At reference conditions, the H\(_2\)O line absorption coefficient is represented piecewise across longwave bands as
\[
\kappa^{\mathrm{ref}}_{\mathrm{H}_{2}\mathrm{O, line}}=
\begin{cases}
\kappa_{\mathrm{rot}} & \text{if } \tilde{\nu}\in [10,200)\ \mathrm{cm}^{-1} \\
\kappa_{\mathrm{rot}} \exp\left(-\frac{\tilde{\nu}-200}{l_{\mathrm{rot}}}\right) & \text{if } \tilde{\nu}\in [200,1000)\ \mathrm{cm}^{-1} \\
\kappa_{\mathrm{vr}} \exp\left(-\frac{1450-\tilde{\nu}}{l_{\mathrm{vr,1}}}\right) & \text{if } \tilde{\nu}\in [1000,1450)\ \mathrm{cm}^{-1} \\
\kappa_{\mathrm{vr}} & \text{if } \tilde{\nu}\in [1450,1700)\ \mathrm{cm}^{-1} \\
\kappa_{\mathrm{vr}} \exp\left(-\frac{\tilde{\nu}-1700}{l_{\mathrm{vr,2}}}\right) & \text{if } \tilde{\nu}\in [1700,2500]\ \mathrm{cm}^{-1}.
\end{cases}
\]
This piecewise form is intended to capture the **rotation band**, the **vibration–rotation band**, and the **combination-band tail** [2508.09353].

CO\

Source: https://www.emergentmind.com/topics/simple-spectral-model-ssm