# Radiative Transfer and Inversion Codes for Characterizing Planetary
Atmospheres: An Overview

###### Abstract

The study of planetary atmospheres is crucial for understanding the origin,
evolution, and processes that shape celestial bodies like planets, moons and
comets. The interpretation of planetary spectra requires a detailed
understanding of radiative transfer (RT) and its application through
computational codes. With the advancement of observations, atmospheric
modelling, and inference techniques, diverse RT and retrieval codes in
planetary science have been proliferated. However, the selection of the most
suitable code for a given problem can be challenging. To address this issue,
we present a comprehensive mini-overview of the different RT and retrieval
codes currently developed or available in the field of planetary atmospheres.
This study serves as a valuable resource for the planetary science community
by providing a clear and accessible list of codes, and offers a useful
reference for researchers and practitioners in their selection and application
of RT and retrieval codes for planetary atmospheric studies.
Keywords: atmospheres, radiative transfer, planets and satellites, retrieval,
exoplanets

Authors: Rengel, M. 111Max-Planck-Institut für Sonnensystemforschung, Justus-
von-Liebig-Weg 3, 37077 Göttingen, Germany, Adamczewski, J. 1,222Georg-August-
Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany

Correspondence<EMAIL_ADDRESS>
## Introduction

Planetary science, including the study of exoplanets, is currently a very
active and fascinating multi-disciplinary field covering astronomy,
astrophysics, geophysics, astrobiology, among other fields. By studying
planets, we can answer fundamental questions about their origin, formation,
evolution, potential for life, and physico-chemical processes. The spectrum of
a planet contains valuable information about its atmospheric chemical
composition and physical processes. Deriving atmospheric properties like the
vertical thermal structure, chemical composition and dynamics is essential to
understand the origin, evolution, and how the atmospheres are influenced by
physical and chemical mechanisms.

Numerous physico-chemical problems in planetary atmospheres require a detailed
understanding of radiative transfer (RT) of photons in different environments.
Detailed solutions of the RT equation demand high computational capabilities.
The technical implementation of these solutions in codes is a rapidly
developing area, and numerous RT approaches have been attempted in recent
years. Several groups then attacked the problem from a variety of perspectives
by using completely different, independent and dedicated numerical algorithms.
Some atmospheric RT codes have been developed with a particular aim or for the
interpretation of a particular planet. Later on, in some cases, their
functionalities have been extended beyond their original purposes but still
limited to the study of a specific type of planets. In recent years,
breakthroughs in atmospheric retrieval have been made possible through a
combination of advancements in instrumentation, computational resources,
sophisticated atmospheric modelling, and powerful statistical inference
techniques.

There are varying levels of complexity in atmospheric models and the physico-
chemical processes considered in RT and inversion codes, motivated by
atmospheric observations. As a result, a significant number of RT and
inversion codes have been developed and widely used in different atmospheric
contexts, depending on whether the planet being studied is Earth, another
planet or body in the Solar System, or an exoplanet. Spectra of Solar System
planets can be spatially distributed and have a high signal-to-noise ratio,
and can be supplemented with in situ measurements or a priori knowledge.
However, exoplanetary spectroscopy currently lacks this observational
capability, and retrievals must navigate a much larger parameter space for
exoplanetary atmospheres than that for Solar System planets.

The selection of a particular code may depend on various factors, such as the
physical problem to face, the estimation technique, computation time,
flexibility, user-friendliness, among others. The selection of the most
appropriate code suited for a specific problem may result in more accurate and
reliable results, highlighting the importance of having a comprehensive list
of available codes. This mini-review provides a comprehensive overview of the
current RT and inversion codes used in the planetary and exoplanetary
communities, as seen from the perspective of a user. These codes are crucial
in predicting and interpreting spectra of planetary atmospheres, both in
hydrostatic equilibrium and in expanding comas. The quality and extent of
these codes are critical for the effective use of space and ground-based
telescopes facilities. [94] has already provided a review of exoplanetary
atmospheric retrieval, some existing retrieval codes, and a description of
their differences, [3] provides a discussion of open problems in retrieval
analysis, and more recently, [89] provides a catalogue of the atmospheric
retrieval codes for exoplanets published to date. In this mini-review, we
expand and update the codes list, including a large new generation of RT and
atmospheric retrieval codes for Solar System and exoplanets.

## RT and inversion codes

One commonly used way to interpret the measured spectra is calculating a
synthetic spectrum for comparison with that measured by solving the radiative
transfer (forward model) -i.e., computation of the outgoing radiation from the
planetary surface for a given set of free parameters-, and inferring
parameters like temperature and chemical abundance profiles. This last step is
called inversion or retrieval and consists in comparing the measured and best
modelled/synthetic spectra adjusting the atmospheric parameters in such a way
as to minimise any discrepancy. A number of radiative transfer codes or
forward models and inversion algorithms are already constructed, and generally
available and used by the planetary and exoplanetary characterisation
communities. A comprehensive list of RT and retrieval codes in the literature
is shown in Table 1, indicating where to find them (if available) and the
estimation technique employed (Sect. 3).

Retrieval codes can use either parametric models or self-consistent
equilibrium models to estimate the composition and pressure-temperature (P-T)
profiles from spectral data. Parametric models do not make any assumptions
about thermochemical and radiative-convective equilibrium, using instead
parametric forms for the P-T profile and composition. Self-consistent models
compute profiles based on assumptions of the atmosphere’s physical and
chemical properties and processes, with varying levels of complexity from 1-D
atmospheres to full 3-D general circulation models. We do not cover 3-D
general circulation codes specifically in this paper, they are complex and
couple many processes together in a three-dimensional time-marching
calculation. For a discussion of the principles of atmospheric retrievals of
exoplanets see [51]. When calculating a synthetic atmospheric spectrum, lines
are read from atomic and molecular databases -databases differ in completeness
and accuracies-, and opacities are calculated via diverse approaches [117].

Some RT models used for Solar System planets and exoplanets have their roots
in Earth codes. There are several RT codes used in the Earth atmospheric
community but they are just listed here: 4A/OP [[129, 130]], 6S [[79]],
AccuRT333http://www.geminor.com/accurt.html [[140]], ARMS [163],
BIRRA444https://www.dlr.de/eoc/en/desktopdefault.aspx/tabid-5447/9970_read-20673/
[[53]], BTRAM555https://blueskyspectroscopy.com/?page_id=21 [[26]], DISORT
[[139]], Eradiate666https://www.eradiate.eu/site/ [[57]], FASCODE [[134, 28]],
FUTBOLIN [[99]], GARLIC [[127]], GENLN2 [[38]], IMAP-DOAS [[50]], IMLM [54],
KCARTA777http://asl.umbc.edu/pub/packages/kcarta.html,888https://github.com/sergio66/kcarta_gen
[[35]],
LBLRTM999http://rtweb.aer.com/lblrtm.html,101010https://github.com/AER-
RC/LBLRTM [[29]], LEEDR [[45]],
LinePak111111https://spectralcalc.com/info/about [[55]],
libRadtran121212http://www.libradtran.org/doku.php [[102]],
MODTRAN131313http://modtran.spectral.com [[12]],
MPI141414https://mitpress.mit.edu/9780262571234/mpi-the-complete-reference/
[[58]], PUMAS151515https://psg.gsfc.nasa.gov/ [[154, 156]],
RFM161616http://eodg.atm.ox.ac.uk/RFM/ [[37]], RTMOM [[56]],
RTTOV171717https://nwp-saf.eumetsat.int/site/software/rttov/ [[125, 101]],
SARTA181818https://github.com/strow/sarta191919https://github.com/clhepp/sarta
[[145]], SARTre [[103]], SASKTRAN202020https://arg.usask.ca/docs/sasktran/
[[16, 166]], SBDART212121https://github.com/paulricchiazzi/SBDART [[119]],
SCIATRAN222222https://www.iup.uni-bremen.de/sciatran/ [[123, 124]],
SICOR232323https://pypi.org/project/sicor/ [[14, 15]],
SKIRT242424https://skirt.ugent.be/root/_home.html [[2]],
SMART-G252525https://www.hygeos.com/smartg [[115]], TOMRAD [[34]], VDISORT
[[82]], VLIDORT/LIDORT262626http://www.rtslidort.com/about_overview.html
[[137]], WFM-DOAS [[18, 19]] as well as models by [62], [148, 147] and [122].

## Retrieval or parameter fitting or estimation techniques

The objective of an optimization algorithm is to extensively and efficiently
sample a high-dimensional parameter space to find the best solution space
given the data. The retrieval or parameter fitting or estimation techniques
commonly used are Optimal Estimation (OE) algorithm ($\dagger$), nested
sampling ($\ddagger$), Markov chain Monte Carlo (MCMC) method
($\blacktriangle$), Grid search ($\bullet$), and more recently, data-driven
Machine Learning (ML) approaches ($\blacklozenge$). OE is popular in the Solar
System community and assumes Gaussian statistics. It is fast and efficient and
applicable to exoplanets under some specific conditions (e.g. [118, 61, 78,
83, 132, 116, 156]. Grid search is simple and computationally cheap, but it
can be inefficient (e.g. Madhusudhan & Seager 2009). MCMC provides a better
parameter exploration of the parameter space but with limitations in
calculating the model evidence for model comparison and can be computationally
expensive (e.g. [9, 96, 159, 13, 31, 43, 157, 75]). Nested sampling algorithm
facilitates efficient parameter space exploration and calculation of model
evidence (e.g. [11, 160, 51, 114, 105, 17, 46, 133, 104, 131]). ML algorithms
can be computationally efficient, but they require large amounts of training
data and can be sensitive to biases in the training set (e.g. [158, 98, 169,
135, 30, 47, 110, 63]). An example of an application of the forward model and
retrieval technique is provided in Figure 1.

## Verification and validation of RT and retrieval codes

The retrieval problem is a challenging one due to its ill-posed and ill-
conditioned nature. This means that even a small change in measurements can
result in a significant deviation in the estimated model, making the inverse
solution computation extremely unstable (e.g. [69]). Currently, each retrieval
code has its unique method for computing opacities and input models, lacking
community standards. Furthermore, models continue to become more complex and
data quality improves, retrieval codes face increasingly complex and
degenerate problems (e.g. [161]).

Verification and validation of planetary retrieval codes is an important
aspect. Verification can be readily accomplished using synthetic measurements
and code inter-comparison. Inter-model comparisons of forward and retrieval
suites have already been underway, with notable studies by [27, 8, 128, 4, 5].
Validation is challenging due to the lack of reference “truth” data (e.g. in
situ measurements). Thus, for an assessment of exoplanet atmospheric remote
sensing, data dedicated to solar system planets like Earth, Mars and Venus is
an ideal test case. To our knowledge, this kind of data have been rarely used
to demonstrate the capabilities of exoplanet atmospheric studies. Observing
planetary transits in our own Solar System for example can serve as an
invaluable benchmark and can provide crucial information for future exoplanet
characterizations (e.g. [40, 41, 106, 85, 128]).

Results from inter-comparison show that that small differences in the forward
model setup can lead to noticeable differences in the retrieval outcome ([4]).
These efforts are crucial for improving the field and providing a clearer
understanding of the sources of variability and their impact on the results.
Such comparisons provide a roadmap for future advancements and refinements in
modelling, enabling us to compare theoretical predictions with observations.
They also offer an opportunity to identify any remaining problems, leading to
the improvement of existing codes and the development of more reliable and
consistent codes. The continued pursuit of inter-model comparisons will drive
the field forward towards a better understanding of the retrieval problem.
Furthermore, the inherent similarities in methods was investigated ([84]), and
there is now considerable work to understand and quantify the role of
different modelling choices affecting accuracy and precision on constraints
([4]).

## Final remarks

Our current understanding of planetary atmospheres is limited by model
completeness and robustness. Forward modelling and spectral retrieval is the
leading technique for interpretation of spectra and is employed by various
teams using a variety of forward models and parameter estimation algorithms.
Numerous codes are available and continue been developed. The code employed
which contain the complexity of models should be chosen with care depending on
the specific questions whose answer is sought and on the nature of the data at
hand (considering spectral coverage and region, resolution, precision, signal-
to-noise ratio, etc.). The efficiency of these codes is a critical issue, but
beyond the scope of this paper.

The study of RT in planetary atmospheres is a rapidly developing field, with
numerous advances being made in both the understanding of the RT process and
in the development of RT codes. With continued research and development
including the improving of observational capabilities, it is likely that even
more sophisticated RT codes and inversion algorithms will be developed in the
future, enabling us to better understand the diversity of planetary systems
beyond our own and the mechanisms shaping their atmospheres.

## Author Contributions

MR wrote the first draft of the manuscript. All authors contributed to
manuscript revision, read, and approved the submitted version.

## Funding

Authors acknowledge the support by the DFG priority program SPP 1992
“Exploring the Diversity of Extrasolar Planets” (DFG PR 36 24602/41).

## Acknowledgments

This research has made use of NASA’s Astrophysics Data System Bibliographic
Services.

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Table 1: Some radiative transfer and inversion codes used in the (exo) planetary community. Symbols: OE algorithm ($\dagger$), nested sampling ($\ddagger$), MCMC method ($\blacktriangle$), Grid search ($\bullet$), and ML approaches ($\blacklozenge$). Code name |  Link | Reference
---|---|---
Alfnoor ‡ |  - | [25]
APOLLO ▲ |  https://github.com/alexrhowe/APOLLO | [67, 68]
ARCiS ‡ |  http://www.exoclouds.com | [104]
ARTS † |  https://radiativetransfer.org/ | [20]
ASIMUT † |  - | [152, 151]
ATMO ${}^{\blacktriangle}\ddagger\bullet$ |  https://www.erc-atmo.eu/?page_id=322 |  |  [149];
---
[157];
[43]
AURA ‡ |  - |  e.g. [114]
Aura-3D ‡ |  - | [111]
Aurora ‡ |  - | [162]
BART ▲ |  https://github.com/exosports/BART | [13]
Benneke & Seager ‡ |  - | [11]
Brewster ‡▲ |  - | [21]
Carrión-González et al. ▲ |  - | [23]
Cerberus ▲ |  - | [146]
CCF-sequence ◆ |  - | [47]
CHIMERA ${}^{\dagger\text{ }\blacktriangle\text{ }\ddagger}$ |  https://github.com/mrline/CHIMERA | [84]
DISORT |  http://www.rtatmocn.com/ | [138]
Dynesty ‡ |  https://dynesty.readthedocs.io/en/stable/ | [136]
Ehrenreich et al. |  - | [39]
exoCNN ◆ |  https://gitlab.astro.rug.nl/ardevol/exocnn | [100]
ExoGAN ◆ |  https://osf.io/6dxps/ | [169]
ExoJAX ▲ |  https://github.com/HajimeKawahara/exojax | [73]
ExoReLR‡ |  - | [33]
exoretrievals ‡ |  - | [42]
Exo-REM |  https://gitlab.obspm.fr/Exoplanet-Atmospheres-LESIA/exorem |  |  [7];
---
[8]
Fortney et al. ∙ |  - | [48, 49]
gCMCRT |  https://github.com/ELeeAstro/gCMCRT | [77]

Code name |  Link | Reference
---|---|---
Gibson et al.▲ |  - | [52]
HARP |  https://github.com/luminoctum/athena-harp | [81]
HELA ◆ |  https://github.com/exoclime/HELA | [98]
HELIOS-R ‡ |  https://github.com/exoclime/HELIOS |  |  [76];
---
[112]
Helios-r2 ‡ |  https://github.com/exoclime/Helios-r2 |  | [74]
---
Home made (MPS) † |  - | [71]
HRCCS ‡ |  https://www.dropbox.com/sh/0cxfolfmrs8ip37/AABZYoHr8nuRlHJG84dArX4ea?dl=0 | [17]
HyDRA ‡ |  - | [51]
HyDRo ‡ |  - | [113]
INARA ◆ |  https://gitlab.com/frontierdevelopmentlab/astrobiology/inara | [135]
Johnson & Marley ◆ |  https://github.com/WreckItTim/MLP-Estimating-Exoplanet-Parameters | [72]
KOPRA |  https://www.imk-asf.kit.edu/english/312.php |  |  [65];
---
[141];
[142]:
[143]
Lellouch et al. † |  - | [80]
Lupu et al. ▲‡ |  - | [87]
Madhusudhan & Seager ∙▲ |  - | [92]
Madhusudhan et al. ▲ |  - |  | [93]
---
[95]
MARGE ◆ |  github.com/exosports/marge | [64]
Marley & McKay |  - | [97]
MassSpec ▲ |  - | [164]
MERC ‡ |  - | [131]
METIS ▲ |  - | [75]
MOLIERE † |  - | [150]
Moreno et al. |  - | [108, 107]
NEMESIS †‡ |  https://users.ox.ac.uk/~atmp0035/nemesis.html | [70]
Nixon & Madhusudhan ◆ |  - | [110]
PETRA ${}^{\bullet\text{ }\blacktriangle}$ |  - | [86]

Code name |  Link | Reference
---|---|---
petitRADTRANS ‡▲ |  https://petitradtrans.readthedocs.io/en/latest/ | [105]
PICASO |  https://github.com/natashabatalha/picaso |  | [120]
---
[6]
plan-net ◆ |  https://github.com/exoml/plan-net | [30]
PLATON ‡ |  https://github.com/ideasrule/platon | [167]
PLATON II ‡ |  https://github.com/ideasrule/platon | [168]
PolyChord ‡ |  https://github.com/PolyChord/PolyChordLite | [59, 60]
POSEIDON ‡ |  https://github.com/MartianColonist/POSEIDON | [91]
PSG †‡ |  https://github.com/nasapsg | [155]
Pyrat-Bay ▲ |  https://pyratbay.readthedocs.io/en/latest/ | [32]
Pytmosph3R |  https://pypi.org/project/pytmosph3r/ | [22, 44]
p-winds▲ |  https://github.com/ladsantos/p-winds | [36]
REDFOX |  - | [126]
rfast▲ |  https://github.com/hablabx/rfast | [121]
SCARLET ‡▲ |  - | [10]
smarter ‡ |  - | [88]
species ‡∙▲ |  https://github.com/tomasstolker/species | [144]
Tau |  https://cpc.cs.qub.ac.uk/summaries/AEPN_v1_0.html | [66]
TauREx 2.6 ‡▲ |  https://github.com/ucl-exoplanets/TauREx_public |  |  [159];
---
[160]
TauREx 3.1 ‡ |  https://taurex3-public.readthedocs.io/en/latest/ | [1]
ThERESA ▲ |  - | [24]
tierra ▲ |  https://github.com/disruptiveplanets/tierra | [109]
TRIDENT |  - | [90]
Vasist et al. ◆ |  - | [153]
VI-retrieval ◆ |  - | [165]

Figure 1: Example of forward model and retrieval applied to the case of HCN in
Titan: Left: comparison between observed and best-fit simulated HCN (3-2)
lines (black and red, respectively, upper panel), and the difference between
the observed and fitted spectra (lower panel). Right: retrieved temperature
and HCN distribution derived from the spectrum. The black and red lines, and
the pink shadow show the initial and retrieved profiles, and the error bars,
respectively. Figure based on Fig. 1 in [116]

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