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# A reversed Monte Carlo radiative transfer model for Titan PCM

**Anthony Arfaux**¹, **Sandrine Vinatier**¹, **Vincent Eymet**², **Vincent Forest**², **Zili He**¹, **Bruno de Batz de Trenquelléon**¹, **Pascal Rannou**³, **Ehouarn Millour**⁴, and **Sébastien Lebonnois**⁴

¹LIRA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, 5 place Jules Janssen, 92195 Meudon, France

²Méso-Star, Toulouse, France

³Université de Reims Champagne-Ardenne, CNRS, GSMA, Reims, France

⁴Laboratoire de Météorologie Dynamique (LMD/IPSL), Sorbonne Université, ENS, PSL Research University, Ecole Polytechnique, IP Paris, CNRS, 4 Place Jussieu, 75252 Paris Cedex 05, France

Titan and particularly its thick atmosphere, unique among solar system objects, has been a center of interest for many decades. Titan's atmosphere has been thoroughly studied, notably with the use of Global Climate Models (GCM) (Lebonnois et al. 2012; Lora et al. 2015; de Batz de Trenquelléon et al. 2025a;

de Batz de Trenquelléon et al. 2025b). All of them currently consider a plane-parallel atmosphere for the radiative transfer calculation (Lora et al. 2015; de Batz de Trenquelléon et al. 2025a). However, this assumption has limitations in the case of Titan.

First, its thick atmosphere makes sphericity effects prominent. For instance, the Titan PCM (Planetary Climate Model, developed mainly at IPSL) simulates up to 500 km altitude, while Titan radius is 2575 km, therefore the atmosphere extension is not negligible, representing 20% of Titan's radius. In such a case,

sphericity effects are important, especially at high altitudes, and may result in variations of the radiative budget with retroactions on the circulation and cloud formation. Another effect from sphericity is the absence of polar night above 300 km altitude, matching the altitude of the polar cloud observed by West

et al. 2016. We also note that the multiple scattering in a 3D atmosphere can allow for the propagation of light into the polar night at lower altitudes. Both effects can affect the thermal properties of the polar regions with implications for the formation of the polar clouds.

Additionally, the horizontal heterogeneity of the atmosphere can have a role in the radiative transfer. Indeed, the radiative budget can be affected by the optical properties of neighboring columns, which is not accounted for in GCMs, where the radiative transfer calculations are performed independently for each

column. For instance, the shadowing produced by large polar clouds or sharp haze variations in the optical properties affecting the horizontal propagation of light, can reduce or increase the radiative budget in the neighboring columns.

Therefore accounting for those effects necessitates a more sophisticated approach. We have developed a new 3D radiative transfer model, with spherical geometry and heterogeneous layers: htrdr-planets (https://www.meso-star.com/projects/htrdr/htrdr.html; He et al. submitted), to be implemented in Titan

PCM and study its atmosphere. This model is based on a reversed Monte Carlo algorithm incorporating recent developments in computing science (Villefranque et al. 2019), able to calculate radiative budget within each GCM cell with very little approximations.
We present here comparisons between simulated radiative budget computed with the new model and the two stream plane-parallel model used in the Titan PCM and we explore the expected effects on the cloud microphysics and atmospheric circulation.

### Acknowledgements:

This work is supported by the Agence National de la Recherche (ANR) through the RaD³-net project (ANR-21-CE49-0020-01).

### References:

de Batz de Trenquelléon, Bruno et al. (Apr. 2025a). "The New Titan Planetary Climate Model. I. Seasonal Variations of the Thermal Structure and Circulation in the Stratosphere". In: The Planetary Science Journal 6, p. 78. issn: 2632-3338. doi: 10.3847/PSJ/adbbe7.

de Batz de Trenquelléon, Bruno et al. (Apr. 2025b). "The New Titan Planetary Climate Model. II. Titan's Haze and Cloud Cycles". In: The Planetary Science Journal 6, p. 79. issn: 2632-3338. doi: 10.3847/PSJ/adbb6c.

He, Zili et al. (submitted). "Simultaneous Estimation of Radiance and Its Sensitivities to Radiative Properties in a Spherical- Heterogeneous Atmospheric Radiative Transfer Model by Monte Carlo Method: Application to Titan".

Lebonnois, Sébastien et al. (Mar. 2012). "Titan Global Climate Model: A New 3-Dimensional Version of the IPSL Titan GCM". In: Icarus 218.1, pp. 707-722. issn: 0019-1035. doi: 10.1016/j.icarus.2011.11.032.

Lora, Juan M., Jonathan I. Lunine, and Joellen L. Russell (Apr. 2015). "GCM Simulations of Titan's Middle and Lower Atmosphere and Comparison to Observations". In: Icarus 250, pp. 516-528. issn: 0019-1035. doi: 10.1016/j.icarus.2014.12.030.

Villefranque, Najda et al. (2019). "A Path-Tracing Monte Carlo Library for 3-D Radiative Transfer in Highly Resolved Cloudy Atmospheres". In: Journal of Advances in Modeling Earth Systems 11.8, pp. 2449-2473. issn: 1942-2466. doi: 10.1029/2018MS001602.

West, R. A. et al. (May 2016). "Cassini Imaging Science Subsystem Observations of Titan's South Polar Cloud". In: Icarus. Titan's Surface and Atmosphere 270, pp. 399-408. issn: 0019-1035. doi: 10.1016/j.icarus.2014.11.038.