# Seasonal variations of Titan's haze and mist layers monitored by VIMS-IR onboard Cassini

Pascal Rannou, De Batz De Trenquelléon, Sébastien Rodriguez, Benoît

Seignovert

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Pascal Rannou, De Batz De Trenquelléon, Sébastien Rodriguez, Benoît Seignovert. Seasonal variations of Titan's haze and mist layers monitored by VIMS-IR onboard Cassini. Icarus, 2026, 450, pp.116949. 10.1016/j.icarus.2026.116949. hal-05484121

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Research Paper

# Seasonal variations of Titan's haze and mist layers monitored by VIMS-IR onboard Cassini

Pascal Rannou<sup>a, ∗</sup>, Bruno de Batz de Trenquelléon<sup>a</sup>, Sébastien Rodriguez<sup>b</sup>, Benoît Seignovert<sup>c</sup>

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ARTICLE INFO

Keywords:

Titan

Haze

Photometry

Cassini

Climate

A B S T R A C T

The Cassini orbiter around Saturn monitored Titan with multiple instruments 13 years, between 2004 to 2017. This is about half of a Titan year and this period included a major seasonal change at the North Spring Equinox (NSE) in 2009 that could be observed. The Visual and Infrared Mapping Spectrometer (VIMS) onboard Cassini produced a large amount of observations of Titan generally presented under the form of spectro-images. The observations with the IR part of VIMS detector are taken in a spectral range between 0.88 to 5.12 µm and with a resolving power between R= λ/Δλ = 120 and 180. The spatial resolution of the images depends on the observation and is few hundreds of meters at the best. In this study, we retrieved the distribution of the photochemical haze (above 80 km) and the condensate mist layer (below 80 km) as a function of latitude, altitude, and tile throughout the Cassini era. We found a haze latitudinal distribution with an extinction increasing from the south to the north at the beginning of the Cassini mission. The distribution evolved around the North Spring Equinox and a turnover was completely achieved at the end of the Cassini mission. This evolution is linked to the stratospheric circulation that blows from the summer hemisphere to the winter polar region. The latitudinal distribution of the mist layer evolves differently than the haze distribution because it depends on both the circulation pattern in the low atmosphere and on the conditions of condensation for several species. The distribution of the mist layer is also modulated with the seasons, but always increases from the equator and inter-tropical latitude band to the poles.

These results yield a quantitative description of the aerosol layer on Titan and its seasonal evolution. This has been compared with previous works and with the output of the Titan Planetary Climate Model. Producing such results is quite important to constrain climate models. In return, we expect from these climate models to be helpful in fully understanding the meaning of our results and more generally in characterizing Titan's climate.

**1. Introduction**

Saturn's main satellite Titan is a place of intense atmospheric activ-
ity with quite vigorous meteorology. For more than 50 years, since the
beginning of space exploration, it has been of particular interest to plan-
etologists. It is known to have an atmosphere of nitrogen and methane
denser than Earth's atmosphere. An important characteristic of Titan is
its very rich photochemistry, triggered by the photodissociation of the
main gases (nitrogen and methane). It yields a complex photochemistry
with surprisingly large molecules, even in very high altitude layers
above 1000 km. This produces a pervasive photochemical haze and,
below about 80 km, an extended layer of mist and clouds composed

of most of the minor species, such as C₂H₆, C₂H₂, C₂H₄, C₃H₄ and
methane. Some specific molecules, such as HCN, C₆H₆ or C₂H₃CN
produce discrete clouds higher in the middle stratosphere of polar
regions up to around 300 km (De Kok et al., 2014; Vinatier et al., 2018;
Le Mouélic et al., 2018).

Titan's climate is dominated in the upper stratosphere and above by
the complex interplay between the haze and the atmospheric circula-
tion through the influence of the haze on the thermal radiative balance.
In the low stratosphere and the troposphere, the interplay is more
complex and involves the gaseous methane and other photochemical

<footnote><sup>a</sup> GSMA, Université de Reims Champagne-Ardenne, UMR 7331, CNRS, Université de Reims Champagne-Ardenne, Campus Sciences Exactes et Naturelles, BP 1039, 51687 REIMS, France</footnote>

<footnote><sup>b</sup> Université de Paris Cité, Institut de Physique du Globe de Paris (IPGP), CNRS, Paris, 75005, France</footnote>

<footnote><sup>c</sup> Observatoire des Sciences de l'Univers Nantes-Atlantique (OSUNA), CNRS-3281, Nantes Université, France</footnote>

<footnote>* Correspondence to: Groupe de Spectrométrie Moléculaire et Atmosphérique (UMR CNRS 7331) UFR de Sciences Exactes et Naturelles, BP 1039 Université de Reims Champagne-Ardenne 51687 REIMS, France

E-mail address: pascal.rannou@univ-reims.fr (P. Rannou).</footnote>
byproducts, clouds, hazes and the reservoirs of liquids at the surface and in the subsurface.

During the Cassini-Huygens era (2004–2017), observations of Titan revealed a very active and complex climatic cycle, with cloud cover related to the atmospheric circulation, rain, liquid surface reservoirs, dry fluvial systems and dry seabeds reflecting an ancient humid equatorial region, dunes (e.g., Porco et al., 2005; Tomasko et al., 2005; Radebaugh et al., 2008; Brossier et al., 2018; Lopes et al., 2019, 2020; Birch et al., 2023 and Daudon et al., 2025). Instruments also monitored the seasonal evolution and the profound change in meteorology while Titan passed through the northern vernal equinox (e.g., Rodriguez et al., 2009, 2011; West et al., 2018; Turtle et al., 2018; Teanby et al., 2019; Vinatier et al., 2020; Mathé et al., 2020 and Seignovert et al., 2021).

After 13 years of observation, Cassini yielded an extraordinary amount of data. For some instruments, a large part of the data still remains to be analyzed. For instance, in addition to the descriptive analysis and discussions about color ratios of the Visual and Infrared Mapping Spectrometer (VIMS) images, it is important to analyze the spectral information with photometric models in order to obtain quantitative information on the atmospheric properties and the surface. One reason is because climate models must be compared with observations and, in particular, with quantitative analysis to fully characterize the haze and mist cycle. Also, having a better knowledge about the haze and mist layers is also the best way to study surface features. The Dragonfly mission (JHU-APL/NASA) is already scheduled to land in 2034, observations of Titan by the James Webb Space Telescope (JWST) have already started in 2022 (Nixon et al., 2016, 2025; Rannou et al., 2025) and very large terrestrial telescopes (including the European Extremely Large Telescopes of the European Southern Observatory, EELT/ESO and the NASA Thirty Meters Telescope, TMT/NASA) will have the opportunity to observe and follow the evolution of Titan's climate in the coming decades. It is then imperative to extract all the possible information from observations already acquired with Cassini.

The scope of this paper is to retrieve the haze and the mist extinction and their spatial and temporal variations with spectra collected in the infrared channel of the VIMS instrument (hereafter VIMS-IR) over the time of the Cassini mission, between 2004 and 2017. For this, we performed retrievals on a selection of observations made by VIMS-IR rather than an exhaustive study of all the dataset. We select spectroimages among the extensive dataset provided by this instrument and we characterize the extinction of the photochemical haze above 80 km and the mist layer below 80 km as a function of latitude and time. Since we are interested in the haze and the mist spatial distribution and their seasonal variations, we only used channels of VIMS-IR which are not influenced by the surface reflectivity. Only channels in the methane bands, that is at wavelengths where methane is sufficiently optically thick to not allow for seeing the surface, meet this condition. In contrast, the methane windows are defined as parts of the spectra where methane absorption is weak enough to see surface through the haze (e.g. Sotin et al., 2005). In this work, we ignore data in methane windows. Since these seasonal variations are deeply constrained by the circulation and the thermodynamical conditions, we also compare our results to the Titan Planetary Climate Model (hereafter TPCM).

The outline of the paper is as follows: Section 1, we present the main results of previous works performed about the haze seasonal cycle. We then describe in the Section 2 the physical properties of the atmosphere in our model, including the haze layer and the gaseous absorption, and we discuss our choice of parameters to retrieve the haze properties in relation with the atmosphere levels that are probed. In the Section 3, we describe the images and the pixels that we selected for our analysis and in Section 4, we describe our retrieval method. The Section 5 is dedicated to the presentation of our retrieval and the comparison with results of other works. In Section 6 we describe and discuss our results and compare with the prediction of the TPCM and then give a conclusion.

## 2. Seasonal variation of haze and mist extinction

Several recent studies have used photometrical observations of Titan to study the seasonal change of the aerosol layers. Karkoschka (2016, 2022) used observations of the Space Telescope Imaging Spectrograph (STIS) onboard the Hubble Space Telescope (HST) to characterize the haze cycle through a statistical approach. They studied the amplitude and the time phase of the haze seasonal change by analyzing the different components of the I/F signal. The first and second components describe the haze below 80 km and above 150 km respectively and they give a conversion between the components and the corresponding aerosol opacities. Ádàmkovics and de Pater (2017) retrieved the evolution of the aerosol opacity between 2006 and 2015, above and below 20 km with the OH Suppressing InfraRed Imaging Spectrograph (OSIRIS) instrument on the Keck Telescope. These two works provide interesting results to compare with since the dates of observation spanning the duration of the Cassini mission.

Vashist et al. (2023) also used the radiance factor obtained from VIMS-IR observations as a proxy for haze opacity and its seasonal variation. They mainly discuss the seasonal variation of the north-south asymmetry (NSA). They found a fairly constant NSA between 2004 and 2011, that is up two years after the North Spring Equinox in 2009, followed by a rapid change leading to a complete inversion of the NSA in 2017. They also found that the NSA is tilted relative to the equatorial plane by a fraction of degree. Snell and Banfield (2024) used Cassini Imaging Science Subsystem to characterize the albedo of the NSA, focusing on the location of the transition and its tilt relative to the polar axis as a function of season. They found a tilt around of 4° and a rapid transition around 2015, in agreement with Vashist et al. (2023). Although these features are obviously linked to the haze layer, as also reported by Kutsop et al. (2022), no quantitative evaluation of the aerosol opacity is given in these works.

Another analysis of VIMS-IR observations, the same data that we are analyzing here, to retrieve the haze and the mist layers has been released recently (Thesis report by Es-sayeh, 2023). The main motivation of this work may appear quite similar to ours. However, there are substantial differences in the scope and in the procedure that was used. Es-sayeh et al. (2023), developed a complete procedure to perform a “massive inversion” of VIMS-IR data based on look-up tables with several dimensions. It enables retrieval of the aerosol layers (reported in Es-sayeh, 2023) and the surface (Es-sayeh et al., 2023). Some dimensions of the look-up tables (incidence, emergence, and phase angles) are used as inputs since they pertains to the geometry of the observation. Proxies of the haze opacity above 55 km and the mist opacity below 55 km, using a haze profile that strictly follows Doose et al. (2016) and the surface albedos in methane windows are the outputs of the look-up tables. The haze proxies here are simply the factors $F_h$ and $F_m$ by which they multiply the haze and mist profile published by Doose et al. (2016). The principle is to compare a given observation (radiance factor in 256 channels) with a known geometry to radiance factors interpolated between the nodes of the look-up tables. In this way, they are able to retrieve the best values of the haze and the mist proxies and the surface albedo as well. The advantage of this method is the speed of the retrieval once the database is built and the ability to treat a huge amount of spectra. The drawback is the rigidity of the choices made *a priori* concerning the gas and the aerosol properties to build the look-up tables. These choices cannot be changed easily.

On the other hand, in our model, all the absorption and scattering properties are calculated at the beginning of the run and they are controlled by input parameters. This includes a description of the aerosol layers, the morphology of the aerosols, the haze and mist optical constant, the gas vertical profiles. A noticeable exception concerns the gas absorption properties that require long calculations and are stored in tables. The advantage of this model is to be very flexible and to allow for testing and to easily compare any parameters or options
in the calculations (e.g., Rannou et al., 2025). The drawback is the computational time which is of few seconds for one spectrum and a complete inversion can take several minutes. This prevents us from making a massive inversion.

The two approaches are then complementary and allow for having both common and different objectives about the haze and the mist layer on Titan. For this work, we chose to perform full retrievals and tested several setups of our model to select the best retrieval options. We then produce latitudinal profiles of haze and mist extinctions that can be compared to those of climate models.

### 3. Description of the model

In this work, we use the same model as in Rannou et al. (2025), dedicated to the retrieval of the extinction of the haze and the mist layer with observations of the Near Infrared Spectrometer (NIRSpec) onboard the James Webb Space Telescope (JWST). This model, “Tunable tool for Radiative-transfer and Inversion of Properties related to Titan” (TRIP2Titan), and the main properties of the atmosphere model setup are described in detail in this first paper. The VIMS-IR and NIRSpec made observations over about the same wavelength range (0.88 to 5.12 µm for VIMS-IR and 0.96 to 5.27 µm for NIRSpec) and the main difference between the two instruments, regarding the retrieval aspect, stands in their spectral resolutions (R = 120–180 for VIMS-IR and R = 2700 for NIRSpec). The spectral resolution has a direct consequence on the vertical resolution of the retrievals because the selective gaseous spectral signature defines how well the vertical structure of the atmosphere is described in the spectra.

To solve the radiative transfer equation, we use a combination of models depending on the incidence and emergence angles. For incidence and emergence angles, $\theta_i$ and $\theta_e$, smaller than 40°, we used the model Spherical Harmonics Discrete Ordinate Method in Plane-Parallel (SHDOMPP) (Franklin Evans, 1998). For incidence angles $\theta_i$ larger than 40° and up to 80° and emergence angles $\theta_e$ smaller than 40°, we use the model Single Precision Spherical Discrete-Ordinate-method Radiative Transfer (SPSDISORT) which solves the radiative transfer equations in pseudo-spherical geometry (Mayer and Kylling, 2005; Dahlback and Stamnes, 1991). For all the other cases, a model in spherical geometry is required because they are always close to the terminator and thus we cannot make calculation. This means that the polar regions are not studied although these are the places where the strongest radiative forcing takes place on Titan climate (Rannou et al., 2004).

#### 3.1. Haze and mist optical properties

The model is discretized into 70 layers of 10 km thickness up to 700 km. In each layer, optical properties are assumed to be constant. The layer thickness is thus smaller than the smallest atmosphere scale height (H ≈ 17 km at the tropopause). Above 80 km, the aerosols are assumed to be made of photochemical particles that constitutes the haze. Below 80 km, the aerosols are assumed to be photochemical aerosols mixed with ices or liquid condensed on photochemical aerosols that produces a mist. We choose this transition altitude because it is the altitude where observations show a change in particle optical properties (Tomasko et al., 2008; Doose et al., 2016) and this is also the altitude where minor species are expected to condense onto aerosols (e.g., Barth, 2017 and de Batz de Trenquelléon et al., 2025a,b). We use the vertical profile for the haze extinction as published by Doose et al. (2016). The mist layer is split into several sublayer and we assume a constant extinction profile in each sublayer.

The optical properties of the aerosols (cross-sections and phase functions) are computed with the Mean Field Theory model published by Botet et al. (1997) and improved in Rannou et al. (2024). However, the phase functions given by this model are modified to account for the enhanced backscattering observed for particles in Titan's particles (Rodriguez et al., 2023). We assume that the photochemical aerosols

are fractal aggregates of 3176 monomers of 50 nm with a fractal dimension ($D_f$ = 2.3). This structure have been defined by Coutelier et al. (2021) and Rannou et al. (2022) from the analysis of VIMS-IR observations in nadir viewing and in occultation mode and already used by Es-sayeh et al. (2023). Our choice of tholin refractive index differs from the choice made by Coutelier et al. (2021) and by Es-sayeh et al. (2023). In the present work, we managed to match the single scattering albedo as published by Doose et al. (2016) where their results are valid, around the wavelength 0.9 µm. At longer wavelength, the haze single scattering albedo is computed with the model of scattering by fractal aggregates. For the mist, the single scattering is scaled from those of the haze as described by Doose et al. (2016). More detail are given in Rannou et al. (2025).

#### 3.2. Gas optical properties

The gaseous absorptions are computed from the TheoRETS database (Rey et al., 2018) for methane and its main isotopologues ($^{12}$CH$_4$, $^{13}$CH$_4$ and CH$_3$D) and from the HiTRAN database for C$_2$H$_2$, HCN and CO. The gas cross-sections are computed with a convolution of each line by a Voigt profile to which a cut-off is applied at a distance $\Delta v = |v - v_0| = 26 \text{ cm}^{-1}$ from the line position $v_0$ beyond which we apply an exponential decay with a characteristic length in the wavenumber space $\sigma = 120 \text{ cm}^{-1}$ (after de Bergh et al., 2012). We calculate the gas cross-sections for the 70 layers of our model, with corresponding pressure and temperature profiles (Fulchignoni et al., 2005). In our model, the gas absorption is implemented using the correlated-k approximation with four terms. The values of the gaseous absorptions (cross-sections and correlated-k tables) for the nominal profile are those computed and used for the analysis of Coutelier et al. (2021) and by Es-sayeh et al. (2023). We set a vertical mixing ratio of methane following the results of Niemann et al. (2005) but scaled to 1% in the stratosphere (Lellouch et al., 2014; Rannou et al., 2021).

To build this reference profile, named $X_0$, we simply used a linear transformation of the profile published in Niemann et al. (2005) to stretch the methane molar fraction between ≈1% in the stratosphere and 5.9% at the surface. Other opacity sources in our model are Rayleigh scattering, that generally has a negligible effect in the infrared, and the collision induced absorptions (McKellar, 1989; Lafferty et al., 1996). The latter absorption is dominant around 4.25 µm and marginally affects the shape of the 2 µm window around 2.1 µm.

#### 3.3. Parameters of the model

In the model, the total opacity of the haze is controlled by a parameter, $F_h$. The mist layer between 0 and 80 km is subdivided and we can retrieve the opacity in each sublayer. After several tests, we found that the low resolution of VIMS-IR allows for describing the mist layer with a first mist layer between 40 km and 80 km and a second mist layer below 40 km. We defined the number of layers in this study empirically. With two layers, the opacities of the mist layers behave smoothly with latitude. Attempts to use more than two layers always result in disordered variations of opacities or extinctions with latitude, characterizing a too high correlation between the layer parameters. With two layers, the opacities of these mist layers are controlled by the parameters $F_{m1}$ and $F_{m2}$ respectively.

The $F_h$, $F_{m1}$ and $F_{m2}$ are intermediate parameters proportional to the logarithm of the extinction. Unlike previous works, such as Coutelier et al. (2021) and Es-sayeh et al. (2023), these parameters have no direct link with the opacities of the haze and mist layers published by Doose et al. (2016). This is required by the retrieval procedure that deals with intensive variables. To present our results, we directly display the opacities or the extinction which are the physical quantities of interest. A last parameter is used. The particle spectral properties are close to those found in Rannou et al. (2022) but we do not expect that they remain identical at all latitudes and dates. Therefore, we adjust the
<figure><img src="image_4.png" /><figcaption>Fig. 1. Altitude where the transmission and the effective transmission reach $e^{-1}$ as a function of the wavelength over all the complete VIMS range.</figcaption></figure>

overall spectral opacities of the haze and the two mist sublayers with a multiplying factor $(\lambda/\lambda_0)^a$. $\lambda_0$ is set to 1.4 µm and $\alpha$ is then the last free parameter of the study. Although variations in spectral the extinction spectral slope could correspond to changes in particle properties, such as the size or the optical constant, the intent of this parameters is primarily to improve the quality of the fits and offset possible minor bias in the model. This correction applies to both the haze and the mist.

### 3.4. Probed levels in atmosphere

We display the penetration depth at nadir of the light in our model as the altitude where the weighted transmission in the correlated-k model, that is $\langle T(z) \rangle = \sum_{i=1}^{N_k} T_i(z)w_i$, reaches the value $e^{-1}$ (Fig. 1). The sum corresponds to an integral calculated with a Gaussian quadrature. Here, $N_k$ is the number of correlated-k terms for each VIMS-IR channel, $w_i$ and $T_i(z)$ are the Gaussian weight and the transmission associated to the term $i$. Of course, $T_i(z) = e^{-\tau_i(z)}$ where $\tau_i(z)$ is the column optical depth above the altitude $z$. Since we are also interested in the transmission of flux into the atmosphere rather than a beam, we use an effective opacity to compute the effective transmitted flux evaluated from the 2-stream approximation, following Pollack and McKay (1985). We then define the effective optical thickness of layers as $\Delta\tau_i^{eff}(z) = ((1 - \omega_i(z))(1 - \omega_i(z)g_i(z)))^{1/2} \Delta\tau_i$, where $\omega_i(z)$ is the single scattering albedo and $g_i(z)$ the asymmetry parameter of the atmosphere at the altitude $z$. The column effective opacity $\tau_i^{eff}(z)$ is the sum of the $\Delta\tau_i^{eff}$ above the level $z$, and the effective transmission $\langle T^{eff}(z) \rangle$ is calculated with the terms $T_i^{eff}(z) = e^{-\tau_i^{eff}(z)}$. The altitude where $T_i^{eff}(z) = e^{-1}$ shows the depth of penetration of the sum of the direct and the scattered flux (Fig. 1). This will help us in defining the VIMS-IR channels to use in our study.

## 4. Selection of cubes, pixels and spectels

To perform this work, we selected several images from each flyby in order to obtain good coverage for each terrestrial year between 2004 and 2017. We selected our spectro-images through the portal of the PDS Ring-Moon System Node's OPUS search service.<fnref n="1" /> With this portal, we could filter the data as a function of the date, the spatial resolution and the phase angle. We then selected the ID of the images we want to study. We then used the Cassini VIMS Data Portal hosted at the University of Nantes<fnref n="2" /> (Le Mouélic et al., 2019) to have a detailed

preview of the selected data and finally got the selected data with the Python library `pyvims`.<fnref n="3" /> Our first criterion is to select images with body center phase angle lower than 60° in order to maximize the number of pixels having incidence and emergence angles consistent with the use of the SHDOMPP or the SPSDISORT solvers. For some period of time, as the year 2008, 2013 and 2017, all the images were chosen with phase angles up to 77° in order to obtain enough data to analyze. The second criterion is to have a large part of Titan's disk, either a full disk when possible or at least more than ≈20% of the disk, in the image to be able to retrieve the extinction over a large latitude range. The list of the 111 selected cubes is given in the Table 1 and the Fig. 2 shows the distribution of the number of images as a function of the date, of the best spatial resolution and of the phase angle. We have an average of 8 images per year and the average spatial resolution is 100 km.

In this study, we assumed that the relative error on the radiance factor is around 3.5%, following Sromovsky et al. (2013). This error is known to be not uniform in reality. It depends on the wavelength and on the observation as stated for instance by Coutelier et al. (2021). No general prescription for the actual uncertainty of VIMS-IR is given beyond the small instrumental error given by the instrumental pipeline (e.g., Es-sayeh et al., 2023). The way errors are accounted for should have a moderate impact the results. We expect the change in retrieved opacities of the different layers and in spectral corrections to be only marginally impacted and their latitudinal variations, which are the main scope of this work, to be unchanged.

For each image, we select the pixel with the lowest two-way airmass factor $f_a$ define as $f_a = 1/\cos(\theta_i) + 1/\cos(\theta_e)$, where $\theta_i$ and $\theta_e$ are the incidence and emergence angles for a given pixel. From this pixel, we choose all the other pixels of the image at the same longitude within a range of ±10°. This produces latitudinal cuts in the images and we then retrieve the haze and the mist extinction over a broad latitude range along these cuts.

Some spectra taken from VIMS-IR instrument have bad measurements in some channels. This is already known for channels at the edge of the VIMS-IR filter intervals, around 1.65, 3.0 and 3.9 µm as reported in the “VIMS Wavelength and Radiometric Calibration 19, Final Report” document<fnref n="4" /> (hereafter, RC19). However, other spurious values are also found in other channels and they can be spotted because they produce a noticeable deviation from usual spectra. In some cases, we find null or negative values for the radiance factor and this is easy

<footnote n="1">¹ https://opus.pds-rings.seti.org/opus.</footnote>

<footnote n="2">² https://vims.univ-nantes.fr/.</footnote>

<footnote n="3">³ Seignovert et al. (2023), doi:10.5281/zenodo.4708004.</footnote>

<footnote n="4">⁴ https://pds-imaging.jpl.nasa.gov/data/cassini/cassini_orbiter/vims-calibration-files/clark-et-al_vims-radiometric-calibration-pds-2018-v2.0.pdf.</footnote>
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Distribution of the number of images selected for this work as a function of the year of observation (left), of the best spatial resolution at the surface (middle) and of the phase angle of the observation.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Typical radiance factor measured by VIMS-IR, in the spectral range of our study, along with the modeled spectra shown in the methane bands (red squares) and also shown everywhere (blue line), in particular in windows (shown for information), at three periods of the Cassini mission. The shift in wavelength, observed during the time of the Cassini mission, is accounted for. The χ² value obtained for the fits of the band is indicated.</figcaption></figure>

to detect. In other cases, the defect is a too low value in a specific channel or in a group of channels, surrounded by apparently normal values in the surrounding channels. We finally noted that when such defects are spotted, this could also affect other parts of the spectra, especially in methane windows. We finally decided, as a precaution, not to use spectra where such defects are detected.

Since we are focusing exclusively our study on haze and mist properties and spatial distribution, only channels corresponding to the methane bands are used. We selected channels in the spectral range between 1.08 to 2.38 µm and, to select only methane bands, we made preliminary tests using the radiative transfer model. We made two computations with values of the surface reflectivity set at 0 and at 0.3.
Then, we determined the specific spectral ranges for which the calculated intensities do not change by more than one part per mil. Thus, only the following wavelength intervals, corresponding to radiance factor in the methane bands, were used in our study: [1.131,1.197], [1.328,1.459], [1.642,1.837] and [2.167,2.616] (Fig. 3). Once the haze and mist properties are retrieved with data in the methane bands, our model is also able to fit data in the windows by adjusting the surface reflectivity, as shown on the Fig. 3. However, we did not perform a systematic study of the surface and thus, we do not discuss this point in our paper.

## 5. Retrieval method for the haze and mist vertical profiles

We use the retrieval procedure based on the Bayesian inference described by Rodgers (2000) as the optimal method for the non-linear problems. We have completely described our method in Rannou et al. (2025) and we give here the main information.

The relation between a set of observations $y$, such as the radiance factors, and a set of parameters $x$, such as a proxy of the haze and mist extinction and the correction on the spectral slope, is formally given by $y = F(x)$. Here, $y$ and $x$ are vectors. We chose to deal with the logarithm of the extinction rather than the extinction itself to have parameters on the complete space of real numbers. The function $F$ represents the radiative transfer model. The error on the observations is assumed to be gaussian and given by $\sigma_y$. The method can be cast under the form of an iterative equation:

$$x_{i+1} = x_i + (K^T S_{\epsilon}^{-1} K + \beta H + S_a^{-1})^{-1} (K^T S_{\epsilon}^{-1} (y - F(x_i))) - S_a^{-1}(x_i - x_a) \quad (1)$$

where $x_i$ is the vector at the ith iteration, the Jacobian matrix $K$ is the set of partial derivatives $\partial F(x)/\partial x_i|_{x_i}$, $S_a$ is the diagonal error matrix for the observation values $(S_{a,(ij)}) = \delta_{i,j}/\sigma_{y_i}^2$, $S_a$ is the diagonal error matrix for the a priori terms when used $(S_{a,(ij)}) = \delta_{i,j}/\sigma_{x_a,i}^2)$. In our analysis, we also used a Tikhonov regularization that can be assimilated to a diffusion process in the $x$-space to attenuate spurious oscillations in the solution. The matrix $H$ is defined from the second order derivative matrix (e.g., Quémerais et al., 2006 and Koskinen et al., 2011) and $\beta$ is analogous to a diffusion coefficient. For practical reasons, we scale the Tikhonov matrix to largest term of the matrix $S^{-1}$ in such a way that $\beta = \gamma \Delta Z^4 \times \max(S_{i,j}^{-1})$, $\Delta Z$ as the thickness of the model layers, 10 km. $\Delta Z$ and $\max(S_{i,j}^{-1})$ contains most of the information to calculate $\beta$ and $\gamma$ is on the order of magnitude of 1 and is used as an adjustment. We actually set $\gamma \approx 0.316$.

The matrix $S = (K^T S_{\epsilon}^{-1} K)^{-1}$ is the covariance matrix and if we account for the Tikhonov term, it turns to $S^\dagger = (K^T S_{\epsilon}^{-1} K + \beta H)^{-1}$. The error on the $k$th term of the retrieved vector $x$ is given by the square root of the diagonal terms in the covariance matrix $\sigma_{x_k} = \sqrt{S_{kk}^\dagger}$. The final state of the vector $x$ and the corresponding errors in its components are finally presented in terms of haze and mist extinction with their related errors and in term of a correction and error on the extinction spectral slope (That is parameter $\alpha$).

## 6. Results and comparisons with other works

We display our results under the form of extinction panels as a function of the latitude and altitude for each year of the Cassini mission (Fig. 4). We also present the opacity of the three layers (Fig. 5) and the correction on the spectral slope (Fig. 6) as a function of the latitude and the time. This presentation allows quantifying the time evolution of the different layers in one glance. Fig. 3 shows how the model matches the data in the band and in the window as well and, for these three spectra, the value of the reduce $\chi^2$, used as a measurement of fit goodness. We find, for all the spectra selected for this study, an average value $\chi^2 = 5.42 \pm 3.16$.

Before discussing our results, we performed several validation tests with the retrieval model. These tests are less elaborated than in Rannou et al. (2025), but they allow to verify with VIMS-IR observations our previous main conclusions obtained with NIRSpec/JWST observations. First, on Titan, the haze and the mist layers are known to be quite invariant with the longitude for a given latitude band. We perform several retrievals along latitude bands (Fig. 7). This enables to check that haze and mist opacities are actually constant with longitude within the error bars, as expected. This also validates the limits we have set for the incident and emergent angles. We find variations of less than 20% and, assuming that opacities are actually constant, this gives the typical uncertainty that could be expected due to geometry. However, moderate longitude variations could also exist as already shown in other works (Hirtzig et al., 2005; Seignovert et al., 2021; Nichols-Fleming et al., 2021). But this test shows that the longitude variations that we retrieve are much smaller than the latitude variations.

The second test is performed with two different methane vertical profiles. We first use an alternative vertical profile with a methane molar fraction reduced to 3.9% near the surface and adjusted linearly to conserve the same molar fraction than previously in the stratosphere, that is 1%. The aim of this test is to mimic the consequence of a methane fraction limited by saturation in a colder environment at higher latitudes. A second vertical profile is used by changing the methane mixing ratio in the lower stratosphere. We used the methane mixing ratio profile of Huygens below 120 km then dimming it from 1.4% at 120 km to 1% at 200 km. This test is performed to mimic the variability in the low stratosphere methane mixing ratio that was observed during with Cassini mission (Lellouch et al., 2014; Rannou et al., 2021, 2022). These profiles are shown in Fig. 8, respectively profile $X_1$ and $X_2$, and the corresponding results in Fig. 9.

Using the first profile that modifies the methane molar fraction below about 25 km only changes by few percents the opacity of the deepest mist layer (below 40 km) and not at all the upper mist layer and the haze layer (Fig. 9 - left). With the second profile, the haze opacity changes by about 10% and the mist layers by less than a few percent in most cases and never more than 10% in any cases (Fig. 9 - right). The vertical profiles of methane molar fraction that we have tested, with changes in the troposphere and in the lower stratosphere compared to the nominal profile, do not produce effects that compete with latitude variations of the opacity as retrieved in this work.

From these tests along longitude scans and with alternative methane profiles, we then assume that the latitudinal variations of opacity found in this work reflects the actual variations in the haze and mist layers. We have to keep in mind that latitudinal change in the methane vertical mixing profile, especially in the lower stratosphere and in the troposphere, may modulate latitudinal variations. However, these changes are too weak to modify the overall latitudinal trends at planetary scale found in this work.

Several other works allowed for characterizing the opacity of the haze layer (photochemical haze and mist) and its seasonal evolution. We focus here on five specific works that produced quantitative value of aerosol opacity as a function of the latitude, at several moments of Titan's year and that can be directly compared with our results (Penteado and Griffith, 2010; Rannou et al., 2010; Ádàmkovics and de Pater, 2017; Nichols-Fleming et al., 2021; Karkoschka, 2016, 2022). For comparison purposes between retrieved quantities, one has to note that probed levels in the haze layer, wavelength ranges and assumed haze optical properties differ between works. We are able to cast our results for the same layers as those used in other works to make relevant comparisons. However, differences in aerosol optical properties, spectral trends and other atmosphere properties are not always explicit in publications and, in any case, cannot be easily accounted for. Then, to make comparisons, we had to scale opacities. This however preserves the latitudinal variations and the timing of the seasonal change. Figs. 10 and 11 show comparisons between opacities found in this work and retrieved in other works.
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Sum of the haze and mist extinctions retrieved from VIMS-IR observations at 2 µm for the years 2004 to 2017, that is time of the Cassini mission. The black horizontal dashed line indicates the transition in our model between the haze layer and the mist layer at 80 km.</figcaption></figure>

More specifically, in the Fig. 10, we remark that the opacity curves always fall abruptly at the edge of the latitudinal range probed by Ádàmkovics and de Pater (2017). This is probably because the limit to incidence and emergence angles, set at 50° in their work, is too large and makes the retrieved opacities to be underestimated near the edge of their intervals. In the Fig. 11, the limit set by Nichols-Fleming et al. (2021) with emergent and incident angles lower than ≈37° is strict enough and their haze factor can be considered over the whole range of retrieval. Angular limits are not to be considered for the work of Karkoschka (2022) because they use a center-to-limb correction and essentially produce a statistical treatment of their data.

Then, the two harmonic terms related to the spatial variations of the signal in their retrieval are associated to specific haze layers and to their opacities thanks to radiative transfer calculations performed by Karkoschka (2016). The haze retrieval made by Rannou et al. (2010) along a central line of a VIMS-IR image with a low phase angle also has emergence and incidence angles exceeding the limit of 40°. Therefore, this result should be considered only between about 50°S and 30°N, that is at latitudes ±40° from the central latitude of the image, around 10°S. Finally, Penteado and Griffith (2010) also use incidence angles all exceeding 40° by more than 10° with a plane-parallel model. On the other hand, the emergence angle is well below the limit, between 25°
<figure><img src="image_8.png" /><figcaption>Fig. 5. Haze opacity above 80 km (purple lines), upper mist opacity (between 40 and 80 km, blue lines) and lower mist opacity (between 40 and 80 km, black lines) for each year between 2004 to 2017 retrieved from VIMS-IR observations over all the Cassini mission. Thick lines show average values, thin lines the envelope error due to the error on VIMS-IR intensities and parameter correlations and tiny black points show individual values. We also display the result obtain with NIRSpec onboard JWST, for the same layers as those retrieved with VIMS-IR, and for the year 2022.. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

and 35°. This has, as foreseeable consequence, that their haze opacity retrievals are underestimated everywhere. However, their results are composed of 10,988 different spectra with a very narrow range of values for the incident angle (between about 53° and 57°) and with quite comparable phase angles (between 60° and 77°). Thus, we can speculate that the relative variation of the haze opacity, the only result that we consider here, is preserved.

Having that in mind, we conclude that the haze opacities found in this work are consistent with opacities retrieved from observations in other works. In the Fig. 10, we remark that the opacity curves always follow the same trend within the error bars except at the edge of the latitudinal range for the retrieval made by Ádàmkovics and de Pater (2017). We then conclude that the works are fully in agreement and

display the same seasonal variations of the haze. The comparison with opacities found by Nichols-Fleming et al. (2021) (Fig. 11) shows that the haze opacity is fairly flat in the northern hemisphere with abrupt drops at the two edges of the latitudinal range, similarly to Ádàmkovics and de Pater (2017), despite the better constraints on the incidence and emergence angles. If we focus on the central part of the latitude range, between ≈0° to ≈ + 40°N, the variation of opacity with latitude in our work appears in agreement with the retrieval of Nichols-Fleming et al. (2021). However and unfortunately, a flat behavior is not very discriminating. The comparisons with the other works shown in Fig. 11 are satisfactory since they all display similar latitudinal variations although details may differ. Thus, for validation purpose, we conclude that these comparisons show that our retrieval are consistent with
<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Adjustment of the spectral slope *α* of the haze and mist extinctions for each year between 2004 to 2017. Thick lines show average values, thin lines the envelope error due to the error on VIMS-IR intensities and parameter correlations and tiny black points show individual values. We also display the result obtained with NIRSpec onboard JWST for the year 2022.</figcaption></figure>

previous works and characterize well the seasonal evolution of the haze and the mist over the Cassini era.

# 7. Discussion

## 7.1. *Description of the results*

Extinction panels displayed as a function of the year in Fig. 4 and latitudinal variations of opacity and spectral slope (Figs. 5 and 6) show the seasonal evolution of the haze and the two mist layers considered in this work.

The haze layer, above 80 km, evolves with a well marked seasonal trend. From the Fig. 5, we note that in 2004, it increases from the south to the north due to the stratospheric circulation, as predicted by models at the South Summer Solstice. The circulation is known to reverse at the equinox (e.g., Rannou et al., 2004; Lebonnois et al., 2012; Larson

et al., 2014) and our retrievals show that the haze starts to reverse in 2008 and it is well observed in 2009. After the equinox of 2009, the latitudinal variation in haze opacity shows a marked step between 20°S and the equator that is similar to observations of Voyager one Titan year before (Sromovsky et al., 1981). This step lasts and gradually fades away by 2011 and yields an almost flat haze layer in 2012. After that year, that is three years after the northern spring equinox, the opacity latitudinal gradient is reversed and increases from north to south. This type of evolution was long expected (e.g., Sromovsky et al. (1981)) and monitored (e.g., Lorenz et al. (1999, 2004) and Karkoschka (2016, 2022)).

In 2014, peaks in haze opacity emerge and should produce circum-planetary rings at 20°N, 45°N and 70°N similarly to those detected by Kutsop et al. (2022). Other similar features in the haze opacity also appear after that year, in 2016 and 2017, for instance. Such structures are probably linked to dynamical processes after the equinox but these are not modeled by the TPCM thus their formation mechanism
<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Haze opacity above 80 km (purple lines), upper mist opacity (between 40 and 80 km, blue lines) and lower mist opacity (between 40 and 80 km, black lines) as a function of the longitude for four selected years, retrieved from VIMS-IR observations. All the plots are centered in longitude in order to plot the results around the central meridian 0°. The plain circles indicate the results for emergent and incidence angle within the limit of the plane-parallel approximation. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

remains unknown for the moment. An alternative possible origin could be overshooting clouds above the tropopause but one should find a mechanism able to produce clouds under the form of a circumplanetary ring at mid-latitude as reported by Kutsop et al. (2022). This is not the most likely option since clouds outside of the polar regions are rather localized (Roe et al., 2005; Griffith et al., 2005; Rodriguez et al., 2009, 2011; Turtle et al., 2011; Nixon et al., 2025) and air above the tropopause is undersaturated.

Below 80 km, the evolution of the mist layer is a combination of influences due to the circulation and to thermodynamical conditions that control condensation and evaporation. The upper mist layer between 40

and 80 km appears modulated with seasons and has a north to south variation which is comparable, although not identical, to the haze layer. In this upper mist layer, the distinction between photochemical haze and condensate is complicated because the transition is not well defined and the vertical resolution allowed by VIMS-IR data is quite coarse. The lower mist (below 40 km) appears to have no strongly marked seasonal cycle and systematically has a minimum opacity between tropics (around ±30°) that increases at higher latitudes beyond around ±50° by a factor of about 3.

Fig. 6 shows that the correction brought to the spectral slope of the haze and mist optical properties is always around the value 0
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Reference methane molar fraction in our model (profile $X_0$), and methane molar fraction used to test the sensitivity of the retrieval to change in the low troposphere (profile $X_1$), due to lower temperatures at higher latitude yielding lower saturation threshold for methane and to a change in the lower stratosphere as observed by Lellouch et al. (2014) and Rannou et al. (2021) (profile $X_2$).</figcaption></figure>

within the error bars except at some specific periods and locations. These variations may reflect changes in particle size. We observe these features on the spectral slope after the year 2011 and with well marked features in 2013 and 2014. An increase in opacity spectral slope, with a reference value of $\alpha = -2.18$ for the choice we made about particle structure (Rannou et al., 2022, 2025), corresponds to a flatter spectral opacity. This indicates an increase in the particle size that may be due dynamical processes.

## 7.2. Description of the circulation with GCMs

Several climate models help to characterize Titan's seasonal variation of the circulation (e.g. Lebonnois et al., 2012; Larson et al., 2014; Lora et al., 2015; Lora, 2024; de Batz de Trenquelléon et al., 2025ba and de Batz de Trenquelléon et al., 2025ab). Titan's circulation is composed of two main cell systems. Most of the time, there is a planetary scale direct cell in the stratosphere, above about 80 km that rises at the summer hemisphere and plunges into the winter polar region. The lower branch of this cell returns to the summer hemisphere in the lower stratosphere or descends into the troposphere near to the pole. This cell transports heat, gaseous species and aerosols from the summer to the winter haze. At the equinoxes, the ascending branch of this unique cell moves from one hemisphere to the other, triggered by the subsolar latitude crossing the equinox. This produces two transient opposite cells with an ascending branch that moves from one hemisphere to the other through the equator and descending branches at the two poles. These changes take about three years and then the opposite summer to winter cell becomes stable while the seasons have changed in both hemisphere.

Below 80 km, a much more complex cell system, analogous to the Hadley cell on Earth, takes place. The main action of this cell is to distribute heat at the planetary scale and, in the same way, it also transports the haze and the mist. It rises in the summer tropical region, triggered by the diabatic heating of the sun. This is also where convective clouds are generally observed (e.g., Griffith et al., 2005). Climate models show ascending winds around 30–60° in the summer hemisphere, often in multiple adjacent cells (e.g. Larson et al., 2014; Lora et al., 2015, 2019 and de Batz de Trenquelléon et al., 2025ba). The

upper branches of this cell, above 40 km, are directed toward the polar regions. The lower branches below 40 km return from the polar regions to the ascending branch that produces a kind of Tropical Convergence Zone (TCZ). This pattern is quite comparable to the Inter-Tropical Convergence Zone (ITCZ) on Earth.

This tropospheric circulation produces a complex interaction with the haze and the condensate which are described, in our results, at very low vertical resolution with only the lower mist layer. The upper and lower cells are separated by a zone of strong shear, at around 70 km, in the meridional and the zonal wind (Tomasko et al., 2005; Bird et al., 2005), probably related to strong positive vertical temperature gradients in the lower stratosphere.

Beyond the quantitative and qualitative descriptions of the haze and mist opacities shown previously, our results can then be considered along with the prediction of climate models. In the following, we present the haze and mist extinction predicted by the TPCM (de Batz de Trenquelléon et al., 2025ab) at three selected dates: 2004, 2012 and 2017. This model accounts for the microphysical processes related to haze and clouds, their transport by the dynamical processes and their feedback onto the dynamics through their effect on the thermal equilibrium. We expect such a model to yield a realistic view of the haze and the mist layer and to predict cloud events that are in agreement with observations. In addition, the origin of the opacity variations can be explained in terms of transport and condensation.

The Fig. 12 shows the seasonal variations of the haze and the mist as predicted by the TPCM along with the circulation pattern. The main characteristics of the stratospheric haze layer in the TPCM are similar to the observations, with a haze layer thicker in the southern hemisphere and then a switch starting around the equinox to finally yield a haze layer concentrated in the northern hemisphere at the end of the Cassini mission. As expected, this trend is linked to the organization of the stratospheric cell. However, the timing of the seasonal change is not exactly the same in the TPCM and for observations. The mist layer, below 80 km, is much more detailed and has a more complex structure in the TPCM than in the retrievals. Thus, to facilitate the comparison, we have to consider the integrated opacities of the TPCM mist over the same altitude ranges as in retrievals.

This layer is presumably made of photochemical aerosols and minor species condensed onto aerosols acting as nucleii seeds. The distribution of the mist depends both on the circulation that transports particles and on the thermodynamical conditions that controls the condensation of the species. We also note that the upper mist is located at the transition between the low circulation cell and the stratospheric cell around 80 km. The upper and lower mist layers are shaped by the upper branch and the lower branch of the Hadley-type cell respectively. Opacities of both mist layers increase toward the polar regions. This is due to the increased condensation at high latitude. The lower mist, is entirely comprised in the troposphere and its horizontal distribution is mainly affected by the lower branch of the lower cell that always converges to the TCZ. Thus, the distribution of the lower mist can be quite different from the distribution in the upper mist and reflect the action of the atmospheric transport and the thermodynamical conditions that apply to the condensible species and thus to the mist.

## 8. Conclusion

In this work, we used observations performed by the VIMS-IR instrument in order to monitor the seasonal evolution of the photochemical haze above 80 km and two distinct layers of mist below 80 km. Our study covers the thirteen years of the Cassini mission and we selected several spectro-images for each year to improve the sampling. We defined the actual limits of the observation geometry for the plane-parallel or the pseudo-spherical approximations to be valid. We consequently restricted our retrievals to these limits in order to avoid spurious effects at the edge of our intervals in latitude. In this work, we limited the emergence angle to 40° and the incidence angle
<figure><img src="image_12.png" /><figcaption>Fig. 9. Haze opacity above 80 km (purple lines), upper mist opacity (between 40 and 80 km, blue lines) and lower mist opacity (between 40 and 80 km, black lines) as the function of the latitude for three selected years, retrieved from VIMS-IR observations. At left, the results obtained with a methane profile limited to 3.92% (profile $X_1$ in Fig. 8). At right, results obtained with the methane profile of Huygens below 120 km and dimming linearly to 1% at 200 km (profile $X_2$). In each case, red curves show the result obtained with the reference methane profile (profile $X_0$) for the same year. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

80°. With our model, we retrieve a set of parameters that are proxies for the haze and the mist extinctions and a correction for the extinction spectral slopes for all the layers. This allows for computing the opacities of the haze and the two mist layers and to display extinction panels. We also made several sensitivity tests to verify the robustness of our retrievals.

We compared our results with other works. Infrared observations made with VIMS-IR or with other instruments have already been used to retrieve the aerosol opacities over the same period. (Penteado and Griffith, 2010; Rannou et al., 2010; Karkoschka, 2016; Ádàmkovics and de Pater, 2017; Nichols-Fleming et al., 2021; Karkoschka, 2022). It is always useful to compare the same physical quantities retrieved with different methods and with the same or with different instruments to guarantee the validity of our results.

We find that the haze layer evolves in a way that is directly linked to the stratosphere circulation and it has a north-to-south positive gradient of opacity in 2004 that gradually decreases and reverse to increase from south the north after equinox. At lower altitudes, the evolution of the mist layer is a combination of influences due to the circulation and to the thermodynamical conditions that control condensation and evaporation. The upper mist appears modulated with seasons and has a north to south variation that is similar although not identical to the haze layer. In this upper mist layer, the distinction between photochemical haze and condensate is complicated because the transition is not well defined due to the too coarse vertical resolution in retrievals allowed

by VIMS-IR data. The lower mist (below 40 km) appears to have no strongly marked seasonal cycle and systematically has a minimum between tropics (±30°) and increases at higher latitudes.

The comparison of our results with other works shows good agreements concerning the spatial distribution of the aerosol opacities. Despite that different layers are probed with different instruments, in different wavelengths intervals and with different retrieval procedures the latitudinal variations are generally consistent within the error envelope and, if not, with a good consistency in the trend.

The comparison with the TPCM gives an interpretation of the results. The distribution of the stratospheric haze is well explained by the circulation although the timing of the model is not exactly in phase with observations. The mist layer that we retrieve corresponds to a mixture of photochemical haze and condensate in the TPCM, as it was expected (e.g., Tomasko et al., 2008), below about 80 km. The upper mist layer in the TPCM appears modulated by seasons, as in observations, while the lower mist layer in the TPCM is dominated by thick sporadic clouds that produces irregular patterns. This may indicates that these prominent sporadic clouds in this layer are possibly overestimated in the climatic simulation. For this lower mist, in our retrieval, we rather find a continuous and smooth layer with a moderate modulation with time and with an opacity at minimum in the equatorial region and that increases toward the poles. In the TPCM, there is still work to perform in order to improve the results. Our retrievals should be considered as important clues for the future to help define the best setup for
<figure><img src="image_13.png" /><figcaption>**Fig. 10.** Haze and mist opacity found by Ádàmkovics and de Pater (2017) above 20 km with the InfraRed Imaging Spectrograph (OSIRIS) at the W. M. Keck Observatory shown with red, black and green lines representing the error envelope compared with opacities at 2 µm found in this work (thick purple lines and envelope with thin purple lines) between 2006 and 2015. The opacities published by Ádàmkovics and de Pater (2017) are multiplied by ≈0.4 to match our values, and we compare the latitudinal trends and not the absolute values.. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>**Fig. 11.** Haze and mist opacity found in other works compared to opacities in this work plotted in violet and blue (thick line and error envelope with thin lines). Upper graph at left: Comparison with opacity retrieved in Karkoschka (2022) for the year 2004 with the Hubble Space Telescope/Space Telescope Imaging Spectrograph (HST/STIS) in the range between 0.5 and 1.0 µm. Upper graph at right: Comparison with haze opacity retrieved with VIMS-IR observations (Rannou et al., 2010) (Black thick lines and error envelope with black thin lines). Middle row, at left: Comparison with haze opacity above 80 km retrieved with VIMS-IR by Penteado and Griffith (2010) (Black thick lines and error envelope with black thin lines). Middle row, at right: Comparison of haze and mist opacity above 40 km found by Nichols-Fleming et al. (2021) with the Spectrograph for INtegral Field Observations in the Near Infrared (SINFONI) on the Very Large Telescope (VLT) in the range 1.45–1.70 µm and 1.90–2.25 µm (black thick lines and error envelope with black thin lines). Lower graph: Comparison with opacity retrieved in Karkoschka (2022) for the year 2017.. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>**Fig. 12.** Extinction panels from the TPCM for the years 2004, 2012 and 2017 (Right) and comparisons between the opacity layers predicted by the TPCM compared with our retrievals, that is the haze above 80 km and the mist layer between 40 and 80 km (Mist 1) and 0 and 40 km (Mist 2).</figcaption></figure>

climate models dealing with haze and mist processes. With this latter point comes an important issue for the comparison due to limits in observation geometries applied in our work. We set a limit at 40° for the emergence beyond which observations cannot be treated with a plane-parallel or a pseudo-spherical model. This prevents us from investigating the polar regions where the stronger radiative forcing takes place on Titan's climate (Rannou et al., 2004). This is clearly the main improvement to bring to this kind of study in the future with, for instance, the htrdr-planet model (e.g., He et al., 2025).

### CRediT authorship contribution statement

**Pascal Rannou:** Writing – review & editing, Writing – original draft, Software, Investigation, Formal analysis. **Bruno de Batz de Trenquelléon:** Writing – review & editing, Validation. **Sébastien Rodriguez:** Writing – review & editing, Validation. **Benoît Seignovert:** Writing – review & editing, Software, Data curation.

### Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Pascal Rannou reports financial support was provided by French National Research Agency. If there are other authors, they declare that

they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

We acknowledge funding from the Programme National de Planétologie (PNP) of the CNRS-INSU, from the French National Research Agency (Project RaD3-net (ANR-21-CE49-0020-04/RAD3-NET) and EOLE (ANR-23-CE56-0008)) and from the CNES (Centre National d'études Spatiales). This work was also supported by the HPC Center ROMEO from the University of Reims Champagne-Ardenne, FRANCE.

### Appendix 9

See Table 1.

### Data availability

Data are yet publicly available.
<table><caption>**Table 1**

List of cubes selected to analyze the haze and mist extinction.</caption><thead><tr><th>Cube ID</th><th>Flyby</th><th>Date</th><th>Mean pixel scale (km/pixel)</th><th>Body center phase angle</th></tr></thead><tbody><tr><td>1477456632_1</td><td>TA</td><td>26/10/2004</td><td>108</td><td>13°</td></tr><tr><td>1477456872_1</td><td>TA</td><td>26/10/2004</td><td>108</td><td>13°</td></tr><tr><td>1477457253_1</td><td>TA</td><td>26/10/2004</td><td>106</td><td>13°</td></tr><tr><td>1477468808_1</td><td>TA</td><td>26/10/2004</td><td>53</td><td>13°</td></tr><tr><td>1477472030_1</td><td>TA</td><td>26/10/2004</td><td>49</td><td>13°</td></tr><tr><td>1481588586_1</td><td>TB</td><td>12/12/2004</td><td>87</td><td>15°</td></tr><tr><td>1481589788_1</td><td>TB</td><td>13/12/2004</td><td>85</td><td>15°</td></tr><tr><td>1481591044_1</td><td>TB</td><td>13/12/2004</td><td>78</td><td>15°</td></tr><tr><td>1509135301_1</td><td>T8</td><td>27/10/2005</td><td>79</td><td>24°</td></tr><tr><td>1514284191_1</td><td>T9</td><td>26/12/2005</td><td>82</td><td>28°</td></tr><tr><td>1515981170_1</td><td>T10</td><td>15/01/2006</td><td>95</td><td>35°</td></tr><tr><td>1519681910_1</td><td>T11</td><td>26/02/2006</td><td>108</td><td>18°</td></tr><tr><td>1519684688_1</td><td>T11</td><td>26/02/2006</td><td>101</td><td>18°</td></tr><tr><td>1519694609_1</td><td>T11</td><td>27/02/2006</td><td>73</td><td>18°</td></tr><tr><td>1519695739_1</td><td>T11</td><td>27/02/2006</td><td>67</td><td>18°</td></tr><tr><td>1553593017_1</td><td>T27</td><td>26/03/2007</td><td>86</td><td>53°</td></tr><tr><td>1554970060_1</td><td>T28</td><td>11/04/2007</td><td>85</td><td>45°</td></tr><tr><td>1556354808_1</td><td>T29</td><td>27/04/2007</td><td>105</td><td>37°</td></tr><tr><td>1557724855_1</td><td>T30</td><td>13/05/2007</td><td>86</td><td>29°</td></tr><tr><td>1559100738_1</td><td>T31</td><td>29/05/2007</td><td>80</td><td>24°</td></tr><tr><td>1560489660_1</td><td>T32</td><td>14/06/2007</td><td>109</td><td>15°</td></tr><tr><td>1561864449_1</td><td>T33</td><td>30/06/2007</td><td>98</td><td>12°</td></tr><tr><td>1567266292_1</td><td>T35</td><td>31/08/2007</td><td>87</td><td>27°</td></tr><tr><td>1570018046_1</td><td>T36</td><td>02/10/2007</td><td>69</td><td>32°</td></tr><tr><td>1576922887_2</td><td>T39</td><td>21/12/2007</td><td>106</td><td>50°</td></tr><tr><td>1578283552_1</td><td>T40</td><td>06/01/2008</td><td>63</td><td>57°</td></tr><tr><td>1578285227_1</td><td>T40</td><td>06/01/2008</td><td>72</td><td>57°</td></tr><tr><td>1578293252_1</td><td>T40</td><td>06/01/2008</td><td>92</td><td>57°</td></tr><tr><td>1582416832_1</td><td>T41</td><td>22/02/2008</td><td>61</td><td>66°</td></tr><tr><td>1582417804_1</td><td>T41</td><td>22/02/2008</td><td>64</td><td>66°</td></tr><tr><td>1582418732_1</td><td>T41</td><td>23/02/2008</td><td>66</td><td>66°</td></tr><tr><td>1608513034_1</td><td>T49</td><td>21/12/2008</td><td>122</td><td>71°</td></tr><tr><td>1608525964_1</td><td>T49</td><td>21/12/2008</td><td>87</td><td>71°</td></tr><tr><td>1608526928_1</td><td>T49</td><td>21/12/2008</td><td>84</td><td>71°</td></tr><tr><td>1616269941_1</td><td>T51</td><td>20/03/2009</td><td>504</td><td>50°</td></tr><tr><td>1619420275_1</td><td>T53</td><td>26/04/2009</td><td>379</td><td>44°</td></tr><tr><td>1621682945_1</td><td>T55</td><td>22/05/2009</td><td>125</td><td>52°</td></tr><tr><td>1623050429_1</td><td>T56</td><td>07/06/2009</td><td>101</td><td>44°</td></tr><tr><td>1624419028_1</td><td>T57</td><td>23/06/2009</td><td>78</td><td>37°</td></tr><tr><td>1625814559_1</td><td>T58</td><td>09/07/2009</td><td>126</td><td>27°</td></tr><tr><td>1629929393_1</td><td>T61</td><td>25/08/2009</td><td>81</td><td>13°</td></tr><tr><td>1634064034_1</td><td>T62</td><td>12/10/2009</td><td>89</td><td>11°</td></tr><tr><td>1639295651_1</td><td>T63</td><td>12/12/2009</td><td>57</td><td>47°</td></tr><tr><td>1639300856_1</td><td>T63</td><td>12/12/2009</td><td>74</td><td>46°</td></tr><tr><td>1639301818_1</td><td>T63</td><td>12/12/2009</td><td>77</td><td>46°</td></tr><tr><td>1640663119_4</td><td>T64</td><td>28/12/2009</td><td>25</td><td>44°</td></tr><tr><td>1642069381_1</td><td>T65</td><td>13/01/2010</td><td>101</td><td>44°</td></tr><tr><td>1643438315_1</td><td>T66</td><td>29/01/2010</td><td>70</td><td>43°</td></tr><tr><td>1649210035_1</td><td>T67</td><td>06/04/2010</td><td>88</td><td>16°</td></tr><tr><td>1653054304_1</td><td>T68</td><td>20/05/2010</td><td>89</td><td>31°</td></tr><tr><td>1654442241_1</td><td>T69</td><td>05/06/2010</td><td>113</td><td>31°</td></tr><tr><td>1655801953_1</td><td>T70</td><td>21/06/2010</td><td>64</td><td>33°</td></tr><tr><td>1657178597_1</td><td>T71</td><td>07/07/2010</td><td>58</td><td>35°</td></tr><tr><td>1657180617_1</td><td>T71</td><td>07/07/2010</td><td>65</td><td>35°</td></tr><tr><td>1664080693_1</td><td>T72</td><td>25/09/2010</td><td>87</td><td>34°</td></tr><tr><td>1676783497_1</td><td>T74</td><td>19/02/2011</td><td>116</td><td>31°</td></tr><tr><td>1681916816_1</td><td>T75</td><td>19/04/2011</td><td>89</td><td>17°</td></tr><tr><td>1683621234_1</td><td>T76</td><td>09/05/2011</td><td>83</td><td>47°</td></tr><tr><td>1687323133_1</td><td>T77</td><td>21/06/2011</td><td>89</td><td>22°</td></tr><tr><td>1702534693_1</td><td>T79</td><td>14/12/2011</td><td>87</td><td>17°</td></tr><tr><td>1706657543_1</td><td>T81</td><td>30/01/2012</td><td>84</td><td>25°</td></tr><tr><td>1716372270_1</td><td>T83</td><td>22/05/2012</td><td>75</td><td>22°</td></tr><tr><td>1717764186_1</td><td>T84</td><td>07/06/2012</td><td>109</td><td>28°</td></tr><tr><td>1717772426_1</td><td>T84</td><td>07/06/2012</td><td>132</td><td>29°</td></tr><tr><td>1721887234_1</td><td>T85</td><td>25/07/2012</td><td>84</td><td>37°</td></tr><tr><td>1731515861_1</td><td>T87</td><td>13/11/2012</td><td>52</td><td>53°</td></tr><tr><td>1739817134_1</td><td>T89</td><td>17/02/2013</td><td>203</td><td>69°</td></tr><tr><td>1739818520_1</td><td>T89</td><td>17/02/2013</td><td>154</td><td>68°</td></tr></tbody></table>

(continued on next page)

<table><caption>**Table 1 (continued).**</caption><tr><td>1739818613_1</td><td>T89</td><td>17/02/2013</td><td>155</td><td>68°</td></tr><tr><td>1739878787_1</td><td>T89</td><td>18/02/2013</td><td>219</td><td>67°</td></tr><tr><td>1743903661_1</td><td>T90</td><td>06/04/2013</td><td>31</td><td>74°</td></tr><tr><td>1743905600_1</td><td>T90</td><td>06/04/2013</td><td>36</td><td>73°</td></tr><tr><td>1743911656_1</td><td>T90</td><td>06/04/2013</td><td>51</td><td>74°</td></tr><tr><td>1743937163_1</td><td>T90</td><td>06/04/2013</td><td>119</td><td>73°</td></tr><tr><td>1760385371_1</td><td>T95</td><td>13/10/2013</td><td>92</td><td>77°</td></tr><tr><td>1764481053_1</td><td>T96</td><td>30/11/2013</td><td>189</td><td>67°</td></tr><tr><td>1764516182_1</td><td>T96</td><td>30/11/2013</td><td>91</td><td>67°</td></tr><tr><td>1764530910_1</td><td>T96</td><td>30/11/2013</td><td>43</td><td>67°</td></tr><tr><td>1767263336_1</td><td>T97</td><td>01/01/2014</td><td>113</td><td>61°</td></tr><tr><td>1770032656_1</td><td>T98</td><td>02/02/2014</td><td>76</td><td>52°</td></tr><tr><td>1772756734_1</td><td>T99</td><td>05/03/2014</td><td>154</td><td>43°</td></tr><tr><td>1772759089_1</td><td>T99</td><td>06/03/2014</td><td>148</td><td>43°</td></tr><tr><td>1775520712_1</td><td>T100</td><td>06/04/2014</td><td>130</td><td>35°</td></tr><tr><td>1775559547_1</td><td>T100</td><td>07/04/2014</td><td>31</td><td>34°</td></tr><tr><td>1796908084_1</td><td>T107</td><td>10/12/2014</td><td>92</td><td>59°</td></tr><tr><td>1796915119_1</td><td>T107</td><td>10/12/2014</td><td>80</td><td>59°</td></tr><tr><td>1796916004_1</td><td>T107</td><td>10/12/2014</td><td>76</td><td>59°</td></tr><tr><td>1799687272_1</td><td>T108</td><td>11/01/2015</td><td>33</td><td>51°</td></tr><tr><td>1799688522_1</td><td>T108</td><td>11/01/2015</td><td>29</td><td>59°</td></tr><tr><td>1799691002_1</td><td>T108</td><td>11/01/2015</td><td>23</td><td>53°</td></tr><tr><td>1802420367_1</td><td>T109</td><td>12/02/2015</td><td>86</td><td>46°</td></tr><tr><td>1805177835_1</td><td>T110</td><td>16/03/2015</td><td>83</td><td>39°</td></tr><tr><td>1814916430_1</td><td>T112</td><td>06/07/2015</td><td>88</td><td>26°</td></tr><tr><td>1826053334_1</td><td>T114</td><td>12/11/2015</td><td>85</td><td>26°</td></tr><tr><td>1826075655_1</td><td>T114</td><td>13/11/2015</td><td>31</td><td>29°</td></tr><tr><td>1831560524_1</td><td>T115</td><td>15/01/2016</td><td>115</td><td>27°</td></tr><tr><td>1832949172_1</td><td>T116</td><td>31/01/2016</td><td>85</td><td>30°</td></tr><tr><td>1834317383_1</td><td>T117</td><td>16/02/2016</td><td>111</td><td>38°</td></tr><tr><td>1838442636_1</td><td>T118</td><td>04/04/2016</td><td>132</td><td>44°</td></tr><tr><td>1841201418_1</td><td>T119</td><td>06/05/2016</td><td>121</td><td>53°</td></tr><tr><td>1853609076_1</td><td>T123</td><td>26/09/2016</td><td>87</td><td>69°</td></tr><tr><td>1857751210_1</td><td>T124</td><td>13/11/2016</td><td>62</td><td>69°</td></tr><tr><td>1859120521_1</td><td>T125</td><td>29/11/2016</td><td>78</td><td>68°</td></tr><tr><td>1859128959_1</td><td>T125</td><td>29/11/2016</td><td>57</td><td>67°</td></tr><tr><td>1859142812_1</td><td>T125</td><td>29/11/2016</td><td>25</td><td>68°</td></tr><tr><td>1871487830_1</td><td>T126</td><td>21/04/2017</td><td>122</td><td>72°</td></tr><tr><td>1871506885_1</td><td>T126</td><td>21/04/2017</td><td>75</td><td>72°</td></tr><tr><td>1871507603_1</td><td>T126</td><td>21/04/2017</td><td>72</td><td>72°</td></tr><tr><td>1872921369_1</td><td>T12+</td><td>08/05/2017</td><td>270</td><td>8°</td></tr><tr><td>1872921504_1</td><td>T12+</td><td>08/05/2017</td><td>270</td><td>8°</td></tr><tr><td>1872922906_1</td><td>T12+</td><td>08/05/2017</td><td>270</td><td>7°</td></tr></table>

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