<figure><img src="image_1.png" /></figure>

HAL
open science

# Retrieval of H2O abundance in Titan's stratosphere: A (re)analysis of CIRS/Cassini and PACS/Herschel observations

S. Bauduin, P.G.J. Irwin, E. Lellouch, V. Cottini, R. Moreno, C.A. Nixon, N.A. Teanby, T. Ansty, F.M. Flasar

<figure><img src="image_2.png" /></figure>

► To cite this version:

S. Bauduin, P.G.J. Irwin, E. Lellouch, V. Cottini, R. Moreno, et al. Retrieval of H2O abundance in Titan's stratosphere: A (re)analysis of CIRS/Cassini and PACS/Herschel observations. Icarus, 2018, 311, pp.288-305. 10.1016/j.icarus.2018.04.003. hal-02291429

HAL Id: hal-02291429

https://hal.science/hal-02291429v1

Submitted on 19 Jun 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_3.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Bauduin, S., Irwin, P. G. J., Lellouch, E., Cottini, V., Moreno, R., Nixon, C. A., Teanby, N. A., Ansty, T., & Flasar, F. M. (2018).

Retrieval of H₂O abundance in Titan's stratosphere: A (re)analysis of CIRS/Cassini and PACS/Herschel observations. *Icarus*, *311*, 288-305.

https://doi.org/10.1016/j.icarus.2018.04.003

Peer reviewed version

License (if available):

CC BY-NC-ND

Link to published version (if available):

10.1016/j.icarus.2018.04.003

Link to publication record on the Bristol Research Portal

PDF-document

This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Elsevier at https://www.sciencedirect.com/science/article/pii/S0019103517308096. Please refer to any applicable terms of use of the publisher.

**University of Bristol – Bristol Research Portal**

**General rights**

This document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/red/research-policy/pure/user-guides/brp-terms/
Retrieval of H₂O abundance in Titan's stratosphere: a
(re)analysis of CIRS/Cassini and PACS/Herschel
observations¹*

S. Bauduin<sup>a</sup>, P.G.J. Irwin<sup>a</sup>, E. Lellouch<sup>b</sup>, V. Cottini<sup>c</sup>, R. Moreno<sup>b</sup>, C.A. Nixon<sup>d</sup>, N.A. Teanby<sup>e</sup>, T. Ansty<sup>f</sup>

<sup>a</sup>Atmospheric, Oceanic and Planetary Physics, University of Oxford, Parks Road, Oxford
OX1 3PU, UK

<sup>b</sup>LESIA-Observatoire de Paris, CNRS, Université Paris 06, Université Paris-Diderot, 5
Place Jules Janssen, 92195 Meudon, France

<sup>c</sup>Department of Astronomy, University of Maryland at College Park, College Park, MD
20742, USA

<sup>d</sup>Planetary Systems Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD
20771, USA

<sup>e</sup>School of Earth Sciences, University of Bristol, Wills Memorial Building, Queens Road,
Bristol BS8 1RJ, UK

<sup>f</sup>Department of Space Science, Cornell University, Ithaca, NY 14853, USA

**Abstract**

Since its first measurement 20 years ago by the Infrared Space Observatory
(ISO), the water (H₂O) mole fraction in Titan's stratosphere remains un-
certain due to large differences between the determinations from available
measurements. More particularly, the recent measurements made from the
Herschel observatory (PACS and HIFI) estimated the H₂O mole fraction to be
0.023 ppb at 12.1 mbar. A mixing ratio of 0.14 ppb at 10.7 mbar was, how-
ever, retrieved from nadir spatially-resolved observations of Cassini/CIRS.
At the same pressure level (10.7 mbar), this makes a difference of a factor of
5.5 between PACS and CIRS measurements, and this has notably prevented
current models from fully constraining the oxygen flux flowing into Titan's
atmosphere. In this work, we try to understand the differences between

Preprint submitted to Icarus

March 13, 2018
the H₂O mole fractions estimated from Herschel/PACS and Cassini/CIRS
observations. The strategy for this is to 1) analyse recent disc-averaged ob-
servations of CIRS to investigate if the observation geometry could explain
the previous observed differences, and 2) (re)analyse the three types of ob-
servation with the same retrieval scheme to assess if previous differences in
retrieval codes/methodology could be responsible for the previous discrepan-
cies. With this analysis, we show that using the same retrieval method bet-
ter reconcile the previous measurements of these instruments. However, the
addition of the disc-averaged CIRS observations, instead of confirming the
consistency between the different datasets, reveals discrepancies between one
of the CIRS disc-averaged set of observations and PACS measurements. This
raises new questions regarding the possibility of latitudinal variations of H₂O,
which could be triggered by seasonal changes of the meridional circulation.
As it has already been shown for nitriles and hydrocarbons, this circulation
could potentially impact the latitudinal distribution of H₂O through the sub-
sidence or upwelling of air rich in H₂O. The possible influence of spatial/time
variations of the OH/H₂O input flux in Titan's atmosphere is also discussed.
The analysis of more observations will be needed in future work to address
the questions arising from this work and to improve the understanding of the
sources of H₂O in Titan's atmosphere.

<footnote n="18">¹⁸ *Keywords:* Titan, atmosphere, Atmosphere, composition, Spectroscopy,
Infrared observations, Satellite, atmosphere</footnote>

<footnote n="1">¹ Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.</footnote>
## 1. Introduction

Since the discovery of carbon dioxide (CO₂) more than 30 years ago (Samuelson et al., 1983), the presence of oxygen compounds has been firmly demonstrated in Titan's atmosphere. Among these, water vapour (H₂O) is deposited in the high atmosphere by external sources. It was measured for the first time in Titan's stratosphere around 20 years ago by the Infrared Space Observatory (ISO), using the Short Wavelength Spectrometer (SWS) (Coutenis et al., 1998). The two lines recorded at 227.8 and 254 cm⁻¹ by this instrument were effectively modelled using a H₂O profile of 0.4 ppb above some cut-off altitude and were mainly sensitive to H₂O in the pressure range 1–1 × 10⁻⁵ mbar. After this first detection, de Kok et al. (2007a) made a first attempt to measure stratospheric H₂O with the Composite Infrared Spectrometer (CIRS) on board the NASA Cassini spacecraft. Due to a poor signal-to-noise ratio (SNR), this first analysis of CIRS spectra was unsuccessful, and only an upper limit of 0.9 ppb was determined, which was consistent with ISO observations. These results were, however, later challenged by measurements from the Photodetector Array Camera and Spectrometer (PACS) and the Heterodyne Instrument for the Far-Infrared (HIFI) onboard the Herschel observatory (Moreno et al., 2012). Using both instruments, Moreno et al. (2012) constrained the vertical profile of H₂O, showing that it increases with height, which is consistent with a high altitude source and low-level sink (condensation and photolysis). They retrieved a H₂O volume mixing ratio (VMR) of 0.023 ppb at 12.1 mbar, which is 20-times lower than the VMR (assumed constant with altitude above the saturation level) determined from ISO. Furthermore, Moreno et al. (2012) reanalysed SWS/ISO spectra and
showed that the H₂O abundance inferred from those observations needed a downward revision to 0.06 ppb (uniform profile). Almost at the same time, Cottini et al. (2012) performed a second attempt to measure H₂O from nadir and limb CIRS observations. By averaging a large number of nadir spectra recorded over 4 years, they determined a H₂O VMR of 0.14 ppb at 10.7 mbar. From limb observations, they retrieved 0.13 ppb at 115 km (around 6 mbar) and 0.45 ppb at 230 km (around 0.35 mbar), which confirmed that the H₂O mole fraction increases with height. The retrieved abundance, however, differed by about a factor of 4 from the results of Moreno et al. (2012).

These uncertainties on the H₂O mole fraction have prevented photochemical models from constraining the flux of OH/H₂O into Titan's atmosphere. As a result, it is currently not determined whether the main source of H₂O comes from micrometeorite ablation (English et al., 1996) or from local sources, such as the cryovolcanic activity on Enceladus (e.g. Hansen et al., 2006; Waite et al., 2006; Hansen et al., 2008, 2011). Using HIFI onboard Herschel, Hartogh et al. (2011) detected the Enceladus H₂O torus and proposed that the latter could be the main source of H₂O in Saturn's atmosphere. Based on the OH/H₂O input flux required by the model of Hörst et al. (2008) to reproduce the H₂O abundance retrieved from ISO observations, Hartogh et al. (2011) concluded that the Enceladus influx rates at Titan's atmosphere are too small to explain the observed H₂O abundance. However, with the retrieval of H₂O from Herschel, Moreno et al. (2012) estimated new input fluxes and showed that Enceladus surface activity is a viable source of H₂O in Titan's atmosphere. This was confirmed by the recent model of Dobrijevic et al. (2014), coupling oxygen, nitrogen and hydrocarbon chemistry,
which was able with an Enceladus source to reproduce the H₂O abundance retrieved by either Moreno et al. (2012) or Cottini et al. (2012). Note that if the H₂O abundance retrieved by Cottini et al. (2012) is taken as the reference, Dobrijevic et al. (2014) overestimated the thermospheric H₂O mole fraction when compared with the upper limit estimated by Cui et al. (2009) from the Cassini/INMS (Ion Neutral Mass Spectrometer) data. The OH/H₂O input flux determined is, however, very different depending on the reference chosen. More particularly, if the flux is determined using the results of Moreno et al. (2012), both Moreno et al. (2012) and Dobrijevic et al. (2014) could not reproduce H₂O and CO₂ abundances at the same time. They respectively obtained CO₂ mole fractions 10 and 4 times lower than the observed abundance (de Kok et al., 2007a). Based on the large difference in the atmospheric lifetimes of CO₂ (several hundred years) and H₂O (around 10 years), Moreno et al. (2012) invoked a variable OH/H₂O input flux over long timescales to explain this difference. This scenario has been explored by the recent model of Lara et al. (2014). They showed, however, that when results of Moreno et al. (2012) are considered, a time-dependent input flux does not solve alone the H₂O/CO₂ problem and the addition of another loss term for H₂O, such as a loss to the haze, is required. Understanding the discrepancies between the H₂O mole fractions measured from Herschel and CIRS is therefore crucial to better constrain the existing photochemical models, and to improve the knowledge of the source and chemistry of oxygen compounds in Titan's atmosphere.

In this work, we aim to investigate and understand these previous reported differences. For this, we analyse recent disc-averaged observations
of Titan (2013-2015) made with the CIRS/Cassini instrument and retrieve
new H₂O mole fractions. The use of disc-averaged observations allows an
easier comparison with Herschel measurements, which share the same view-
ing geometry. In addition to a difference in observation geometry, Moreno
et al. (2012) and Cottini et al. (2012) also applied distinct retrieval meth-
ods and used different *a priori* information and radiative transfer modelling
codes to retrieve H₂O. The goal of this work is also to (re)analyse the CIRS
and Herschel datasets with the same retrieval scheme. This will allow us to
distinguish if the observed discrepancies are due to modelling/retrieval differ-
ences or due to other possible sources. In the case of Herschel, we focus only
on PACS observations, which have a very similar vertical sensitivity to H₂O
as the CIRS measurements. Among the spectra analysed by Cottini et al.
(2012), we only consider the nadir spectrum for the same reasons. These
observations are presented in more details in section 2. Sections 3 and 4
describe, respectively, the forward modelling settings and the retrieval strat-
egy developed to analyse all observations. The results are then discussed in
section 5.

## 2. Instruments and observations

### 2.1. CIRS

The CIRS instrument is a Fourier transform spectrometer. It is composed
of three separate focal planes (FP1, FP3 and FP4) that measure together
spectra in the far- and mid-infrared (IR) (full range: 10–1400 cm⁻¹) with
an adjustable apodised resolution between 0.5 and 15.5 cm⁻¹. The FP1
covers the far-IR spectral range (10–600 cm⁻¹). It has a circular field-of-view
(FOV) of 3.9 mrad diameter, whose half of the integrated response is located
within 2.5 mrad. The FP3 and FP4 focal planes consist of collinear arrays
of 10 pixels each that record spectra in the mid-IR range (respectively 600–
1100 cm⁻¹ and 1100–1400 cm⁻¹). The size of each FOV is 0.27 × 0.27 mrad.
More details about the instrument can be found elsewhere (e.g. Flasar et al.,
2004; Jennings et al., 2017).

In this work, four sets of FP1 observations recorded between February 2013 and July 2015 at a spectral resolution of 0.5 cm⁻¹ are analysed. They were acquired during four different observations at more than 1.5 million kilometres from Titan (Titan Explorations at Apoapse, TEA), and each set include around 800 disc-averaged spectra. The first observation (rev 182) lasted 20 hours whereas the three next ones (revs 202, 206, 209) lasted around 12 hours. The sub-spacecraft latitudes of these observations are -41.43°, 50.73°, 48.58° and -0.02° respectively for sets 182, 202, 206 and 219. Details of these four sets are given in Table 1.

Because H₂O lines are very weak in the FP1 range, an averaged spectrum
has been calculated for each set of observations to increase the SNR. They are
shown in Figure 1 for the 125–260 cm⁻¹ spectral range. The associated noise
has been evaluated using the same method as Teanby et al. (2006). Briefly,
two types of standard error are calculated for each set: 1) the standard
deviation on the averaged spectrum, and 2) the standard error related to the
noise equivalent spectral radiance (NESR) measured from deep space spectra.
The maximum of these standard errors is then taken as the measurement
error on the averaged spectrum. This measurement error is similar for the
four sets, with the minimum found for the 182 (around 1 nW cm⁻² sr⁻¹ cm
for the spectral range shown in Figure 1) and the maximum for the 206 and 219 sets (around 1.4 nW cm⁻² sr⁻¹ cm). Noise spikes are however located in different ranges: 140–150 cm⁻¹ for 182, 152–164 cm⁻¹ for 202, 212–227 cm⁻¹ for 206, and 240–265 cm⁻¹ for 219. A spike at 191.25 cm⁻¹ is common to all sets.

From Figure 1, we can see that H₂O lines are at most barely detected. This is not surprising given the small number of spectra averaged together. For comparison, Cottini et al. (2012) averaged thousands of nadir spectra to achieve a sufficient SNR. Among the four sets analysed here, the SNR seems to vary, with only set 182 showing clear H₂O lines. For this set, the SNR of the H₂O lines is estimated to be around 2 for the lines located above 200 cm⁻¹ and around 3 for the ones below. The difference observed with the other sets is unlikely to be attributable to measurement error differences, the latter being small. The possibility of latitudinal variations will be discussed in section 5.2.4. Note that in section 5.2.1, we will assess if H₂O lines are present in the sets 202, 206 and 219. Note also that the retrieval scheme, which is described in the following sections, has been developed using set 182 only.

Finally, the nadir spectrum studied previously by Cottini et al. (2012) is reanalysed. This spectrum is an average of around 7000 spectra acquired between December 2004 and December 2008 in a latitudinal bin of 0–30°N (see Figure 1). More details are given in Cottini et al. (2012). This averaged spectrum will be called “CIRS NA” hereafter.
## 2.2. PACS/Herschel

PACS is one of the three science instruments onboard the Herschel observatory. It is composed of an imaging photometer, covering the spectral range 60–210 µm (47.6–181.8 cm⁻¹) over a FOV of 1.75' × 3.5', and of a grating spectrometer, providing observations in the range 55–210 µm at a spectral resolving power between 1000 and 4000 and over a FOV of 47" × 47", resolved in 5 × 5 pixels. More details about the instruments can be found in Poglitsch et al. (2010).

In this work, we reanalyse the spectra recorded by the PACS spectrometer that were previously studied by Moreno et al. (2012). These consist of disc-averaged observations of three H₂O lines at 66.43 µm (150.5 cm⁻¹), 75.38 µm (132.7 cm⁻¹) and 108.07 µm (92.5 cm⁻¹), expressed as line/continuum ratios. They were recorded on 22nd June 2010 when the apparent distance between Titan and Saturn was close to the maximum elongation (see Moreno et al. (2012) for more details about the observations and their reduction). In addition to H₂O lines, observations of CH₄ lines acquired by PACS at around the same time are also analysed to retrieve temperature information. These were recorded in the range 102–146 µm using the chopped-nodded PACS range spectroscopy mode with a small chopper throw (see PACS observers’ manual 2013, http://herschel.esac.esa.int/Docs/PACS/pdf/pacs_om.pdf). In this spectral range, two CH₄ lines have been used in this work, at 106.43 µm (94 cm⁻¹) and 119.63 µm (83.6 cm⁻¹). These CH₄ spectra have been reduced from Level 0 to Level 2 within HIPE 15.0.0 (Herschel Interactive Processing Environment), using the Telescope Normalization pipeline (see PACS Data Reduction Guide 2017 for details, http://herschel.esac.esa.int/twiki/pub/Pu
blic/PacsCalibrationWeb/pacs_spec15.pdf), and the final spectrum has been rebinned close to the Nyquist sampling. Note that spectra (CH₄ lines only) reduced in such a way have units of Janskys (Jy) and have been converted to spectral radiance units of W cm⁻² sr⁻¹ cm. Table 2 summarizes the PACS observations analysed in this work, which are shown in Figure 1.

## 3. Forward model

### 3.1. Reference atmosphere and spectroscopic data

A reference atmosphere has been defined for the analysis of all the observations considered. It is composed of 99 levels distributed between 1457 and $1.01 \times 10^{-5}$ mbar. The far-infrared spectrum of Titan's atmosphere, and more especially the continuum level, is affected by collision-induced absorption (CIA) between pairs of N₂, CH₄ and H₂ molecules. The CIA coefficients have been calculated using the work of Borysow and Frommhold (1986a,b,c, 1987), Borysow (1991) and Borysow and Tang (1993). The reference vertical profiles of the 3 gases included are shown in Figure 2.a. The profile of CH₄ has been defined according to Niemann et al. (2010) with a volume mixing ratio of around 5.6% close to the surface and of 1.48% in the stratosphere. For H₂, the mixing ratio has been set at 0.101% at all pressure levels (Niemann et al., 2010). In addition to CIA, the continuum shape is also impacted by aerosol absorption. The assumed haze vertical profile is shown in Figure 2.b and is a simplified version built from previous results (de Kok et al., 2007b, 2010b; Tomasko et al., 2008). The haze relative absorption cross-sections adopted were previously used by Teanby et al. (2013) and derived from the volume absorption coefficients of Anderson and Samuelson (2011). Finally, emission
lines of different gases are present in the far-infrared range and are mainly
those of CO, HCN, CH₄, H₂O, C₄H₂ and C₂N₂. The spectral ranges used in
the different steps of our retrieval scheme have, however, been selected to only
include either CH₄ and its isotopologues (CH₃D and ¹³CH₄) or H₂O lines.
The vertical profiles of CH₃D and ¹³CH₄ we have considered are shown in
Figure 2.a and have been calculated using the isotopic ratios determined by
Niemann et al. (2010). The choice of the temperature and the H₂O *a priori*
profiles will be discussed in the following sections. Note finally that line data
were taken from the HITRAN 2004 database (Rothman et al., 2005) and
CH₄ line intensities have been revised according to Wishnow et al. (2007).
For CIRS, these have been used to calculate k-tables (Lacis and Oinas, 1991)
of gaseous opacities (see Teanby et al. (2013) for details) and line-by-line
calculations have been performed for the H₂O retrieval. For PACS, given
its high spectral resolution, line-by-line calculations have been preferred to
the correlated-k method. To decrease the computation time, pre-calculated
tables of monochromatic absorption coefficients (hereafter.lbl-tables) have
been built using the same pressure/temperature grids as for calculating the
k-tables.

## 3.2. *Disc-averaged radiance*

To analyse both CIRS FP1 (except the nadir spectrum) and PACS ob-
servations, it has been necessary to accurately model the disc-averaged radi-
ance. More especially, in the case of CIRS, the inhomogeneous response of
the FP1 detector has to be taken into account. It has been shown that the
disc-averaged spectrum can be calculated using a weighted sum of spectra
simulated for discrete FOV located at increasing offsets from Titan’s centre
(Teanby and Irwin, 2007; Teanby et al., 2013). In this work, a total of 20 synthetic spectra distributed from the centre of Titan to the top of the atmosphere has been used to calculate the expected disc-averaged radiance of Titan. The weights applied to the sum are calculated as explained in Teanby et al. (2013). In the case of CIRS observations, these weights are multiplied by the FP1 spatial sensitivity response determined while Cassini was en route to Saturn (Flasar et al., 2004).

## 4. Analysis strategy

The retrieval of H₂O abundance has been performed using the NEMESIS software (Irwin et al., 2008). This code includes a forward model which can be solved either using a line-by-line model or the correlated-k method (Lacis and Oinas, 1991) according to the spectral resolution of the measurement. A retrieval method is also implemented and is based on the optimal estimation formalism (Rodgers, 2000). The idea of this inverse method is to determine the most probable atmospheric state that is consistent with both the spectrum and the knowledge of the atmosphere prior to the measurement. This is done by minimising a cost function $\phi$ of the form

$$ \phi = (\mathbf{y} - \mathbf{F}(\mathbf{x}))^{\mathrm{T}} \mathbf{S}_{\epsilon}^{-1} (\mathbf{y} - \mathbf{F}(\mathbf{x})) + (\mathbf{x} - \mathbf{x}_{\mathrm{a}})^{\mathrm{T}} \mathbf{S}_{\mathrm{a}}^{-1} (\mathbf{x} - \mathbf{x}_{\mathrm{a}}), \quad (1) $$

where $\mathbf{y}$ is the measured spectrum, $\mathbf{x}$ is the atmospheric state vector, $\mathbf{x}_\mathrm{a}$ is the a priori state vector, $\mathbf{S}_\epsilon$ is the measurement covariance matrix (including measurement errors), $\mathbf{S}_\mathrm{a}$ is the a priori covariance matrix (including the uncertainties on the a priori state), and $\mathbf{F}$ is the forward model. The
minimisation is performed using an iterative scheme based on the Levenberg-Marquardt method (see Irwin et al. (2008) for more details). Note that in this work, the *a priori* uncertainties are chosen to avoid unconstrained (elements of $S_a$ are too large) or over-constrained (elements of $S_a$ are too small) solutions (Irwin et al., 2008).

To analyse CIRS and PACS observations, we have developed a retrieval scheme relying on three successive steps: 1) the retrieval of the tropospheric and stratospheric temperatures, 2) the adjustment of the continuum level in the vicinity of the targeted H₂O lines, and 3) the retrieval of H₂O stratospheric abundance. Because the stratospheric temperatures and the continuum level affect the retrieval of H₂O abundance (see below), their associated uncertainties have been evaluated and then propagated to evaluate the total error on the retrieved H₂O abundance. Each step of the analysis is described in more details in the following sections.

## 4.1. Step 1: Temperature retrieval

Because it affects the strength of H₂O emission lines along with the H₂O abundance itself, stratospheric temperatures have to be retrieved. As well as affecting the strength of H₂O emission lines, the temperature profile also impacts the vertical sensitivity to H₂O. The lower boundary of this sensitivity is indeed determined by the condensation level of H₂O, whose height depends on the assumed temperature profile. Colder temperatures move this level towards higher altitudes and inversely. For these two reasons, the temperature profile has to be determined before the H₂O retrieval, and more especially in
the pressure range of maximal sensitivity to H₂O. From the H₂O Jacobians<fnref n="2" /> shown in Figure 3 (b,d), this range is found to be between 12 and 1 mbar for both disc-averaged CIRS and PACS observations (Jacobians calculated for the CIRS NA spectrum are similar to those of CIRS disc-averaged observations). The temperature over this range of pressure levels is usually retrieved for CIRS observations using the CH₄ ν₄ band of spatially-resolved observations recorded with the FP4 focal planes (e.g. Achterberg et al., 2008, 2011; Vinatier et al., 2010). If these observations are used to build a disc-averaged temperature profile, they have to sample a sufficiently large range of different latitudes and have to be recorded in a same time interval, close to the time of the FP1 disc-averaged observations. This was found to be difficult to achieve. Therefore, we decided to retrieve the whole temperature profile from the far-IR spectrum only. Pure rotational CH₄ lines along with small parts of the continuum level in their vicinity have been used to retrieve stratospheric and tropospheric temperatures. Although this spectral range is mainly sensitive to tropospheric temperatures (Figure 3.a and 3.c), we can see from Figure 3 that the temperature Jacobians calculated for the pure CH₄ rotational lines for both instruments are not null in the 12-1 mbar range, especially close to the level where the Jacobians of H₂O are the largest. CH₄ rotational lines are thus partly sensitive to temperatures in this region and this is what has been exploited in the retrieval. The vertical sensitivity of the temperature retrieval will be discussed in section 5.1. In the case of the CIRS NA spectrum, the temperature is not disc-averaged but has been retrieved using the

<footnote n="2">²Derivatives of the calculated top-of-atmosphere radiance with respect to the H₂O abundances at the 99 levels of the reference atmosphere</footnote>
same method. In the next subsections, the retrieval settings are described
and the method used to assess the errors on the retrieved temperature profile
is presented.

4.1.1. Retrieval settings

For CIRS FP1 observations, the continuous temperature profile has been
retrieved using six CH₄ lines, which have the largest sensitivity to strato-
spheric temperature (Figure 5), and including the continuum level in their
vicinity (Figure 5). In the case of PACS, fewer lines were available and the
temperature has been retrieved from the lines located at 106.43 µm (94 cm⁻¹)
and 119.63 µm (83.6 cm⁻¹). In both cases, the retrieval range has been cho-
sen to not include any other lines than CH₄.

Depending on the type of observation, we have considered different a pri-
ori temperature profiles taking into account the time and the sub-spacecraft
latitude at which they were recorded. For CIRS NA and PACS spectra,
the a priori temperature profile has been set to the temperature profiles
respectively assumed by Cottini et al. (2012) and Moreno et al. (2012). Cot-
tini et al. (2012) adopted the temperature profile determined by Anderson
and Samuelson (2011) at 15°N. The profile used by Moreno et al. (2012)
was a combination of 1) the temperatures measured by the Huygens Atmo-
spheric Structure Instrument (HASI) between 0 km and 140 km (Fulchignoni
et al., 2005), 2) the disc-averaged temperatures measured from CIRS (140–
500 km) by Vinatier et al. (2010), 3) temperatures retrieved from INMS
(1000–1500 km) (De La Haye et al., 2007), and 4) a decreasing temperature
from 165 K to 155 K between 500 km and 1000 km. For the disc-averaged
CIRS observations, the a priori temperature profile has been built using
retrieved profiles from nadir and limb mid-IR CIRS observations (see Fig-
ure 6) (Teanby et al., 2016). Briefly, temperature has been retrieved at four
pressure levels (5.6, 1 mbar from nadir, 0.1 and 0.01 mbar from limb) and
interpolated in time and space to acquire a more global coverage. The tem-
peratures estimated at the sub-spacecraft latitude and at the time of the
disc-averaged observations have been interpolated onto a finer pressure grid
and have been joined onto the HASI profile (Fulchignoni et al., 2005). The
a priori
uncertainty has been taken at 1% on the whole profile for all the
observations.

The measurement covariance matrix $\mathbf{S}_{\epsilon}$ has been considered diagonal and includes the measurement noise associated with each observations. For CIRS observations, the retrieval has been performed using the correlated-k method. Lbl-tables have been used for PACS spectra. To take into account slight differences between these methods and line-by-line calculations, forward modelling errors have been added to the diagonal elements of the $\mathbf{S}_{\epsilon}$. They have been estimated from differences between spectra simulated with the different methods using the reference atmosphere described is section 2.

4.1.2. Error analysis

When using the optimal estimation method, the assessment of the retrieval uncertainties is usually performed using the total error covariance matrix, $\mathbf{S} = (\mathbf{K}^{\mathrm{T}} \mathbf{S}_{\epsilon}^{-1} \mathbf{K} + \mathbf{S}_{\mathrm{a}}^{-1})^{-1}$, whose square roots of the diagonal elements correspond to the standard deviation of each retrieved variable included in the retrieved state vector $\mathbf{x}_{\mathrm{ret}}$ (i.e., temperature at each pressure level). The use of these errors implies that the elements of the *a priori* covariance matrix are very well known and representative of the real uncertainties on the
a priori profile, which is not the case here. The retrieval random errors have therefore been evaluated using another method. Here, 35 different temperature profiles, covering a large range of temperatures, have been built for each observation. Using these profiles and the reference atmosphere defined in section 3.1, synthetic spectra have been generated and random noise has been added (assuming a normal distribution with a standard deviation equal to the noise associated to the observation). The retrieval procedure described in the previous subsection has then been applied to the 35 spectra and the error has been estimated from the differences between the retrieved and real temperature profiles.

The systematic error related to the choice of the CH₄ profile used in the retrieval has not been estimated from the above analysis. As already mentioned, the CH₄ lines are also sensitive to CH₄ abundance and the latter has been fixed to the profile determined by Niemann et al. (2010). The uncertainties on this profile propagate to the retrieved temperature profile and have to be taken into account. To assess the error propagation, we have shifted the CH₄ profile by ±11% (Niemann et al., 2010) and retrieved the temperature profile again. The systematic errors are taken as the temperature difference between the retrieval with and without applying the shift. It is also worth mentioning that the CH₄ profile determined by Niemann et al. (2010) is measured at one specific location and is not necessarily representative of the observations analysed here. More especially, Lellouch et al. (2014) have observed latitudinal variations of CH₄ stratospheric mole fraction and have estimated that the latter can be as low as 0.01 at some latitudes. For the sake of completeness we have also evaluated the difference in the retrieved
383 temperature profile if the true stratospheric CH₄ mole fraction is equal to 384 0.01. These different effects will be discussed in section 5.1. Note finally that 385 there is some error on the intensities of the CH₄ pure rotational lines that 386 we have considered. More especially, there is a 10% reduction of the CH₄ 387 line intensities between Wishnow et al. (2007) and the more recent values 388 reported by Boudon et al. (2010). However, we have evaluated that this 389 difference leads to a maximum uncertainty of 0.06 K on the temperature 390 profile. This uncertainty is insignificant compared with the other sources of 391 error described above, and will be therefore neglected in the calculation of 392 the total uncertainty on the retrieved H₂O abundance. 393

393 4.2. Step 2: Continuum

394 4.2.1. CIRS

395 The second step of the retrieval scheme consists of properly modelling 396 the continuum level, especially in the vicinity of H₂O lines. Indeed, an 397 under(over)-estimation of this level leads to an over(under)-estimation of the 398 H₂O abundance. This level is mainly affected by tropospheric temperatures, 399 aerosols distribution and absorption, and by the CIA between pairs of N₂, 400 CH₄ and H₂ molecules. The retrieval of the temperature profile described in 401 previous section has partly adjusted this level but we have noticed that dif- 402 ferences remain between the simulated and the observed spectra, especially 403 above 120 cm⁻¹ where most of the targeted H₂O lines are located. To reduce 404 these differences, we have retrieved a continuous profile of aerosols in a first 405 stage. The *a priori* profile considered is shown in Figure 2.b and the related 406 uncertainties have been set to 20%. The retrieval has been performed using 407 the correlated-k method for the spectral ranges 70-100 cm⁻¹ and 130-245
cm⁻¹, avoiding emission lines of gases and noise spikes. As for temperature, forward modelling errors have been included in the Sₑ matrix.

The retrieval of aerosols profile brings a slight improvement to the fit of the continuum level but the latter remains unsatisfactory above 120 cm⁻¹. We have assumed that this was due to uncertainties in the spectral dependence of the absorption cross-sections of haze that we have considered. To properly fit the observed continuum, keeping the retrieved aerosol profile, we have smoothly adjusted the spectral variations of the aerosol absorption cross-sections in the range 120–255 cm⁻¹. Note that apart from variations of haze properties, another possible source for the observed continuum residual is the deficiencies in the modelled CIA (de Kok et al., 2010a), which have not been considered here. However, both aerosols and CIA contribute to the radiance mostly below the emitting level of H₂O and, as long as the continuum level is properly fitted, their values should therefore not impact the H₂O retrieval. Example fits to the CIRS spectra are shown in Figure 5.

### 4.2.2. PACS/Herschel

Because they are expressed as line/continuum ratios, the analysis performed on CIRS spectra does not need to be applied to PACS H₂O observations. These ratios have however to be converted into disc-averaged radiances. For this, a continuum level has been simulated using the reference atmosphere and using the temperature profile retrieved after the first step. The ratios have then been rescaled using the modelled continuum.
430 4.3. Step 3: H₂O retrieval

431 4.3.1. Retrieval settings and a priori choice

432 The last step of the retrieval scheme consists of determining the strato-
spheric H₂O abundance. For CIRS observations, this is done using 5 H₂O
lines: 132.75, 170.25, 202.75, 208.5, 254 cm⁻¹ (identified in Figure 1 and
Figure 5), using line-by-line calculations. In the case of PACS, only three
lines are used (described in Table 2) and the retrieval is performed using
lbl-tables.

438 According to the optimal estimation method, the *a priori* H₂O profile
439 should represent the best knowledge of the H₂O abundance prior to the mea-
surement. The choice of this profile is important as it will affect directly the
440 H₂O retrieved abundance. This choice is, however, in this case difficult be-
441 cause the uncertainties on the H₂O abundance are large, and their reduction
442 is at the centre of this work. Table 3 and Figure 4 present several profiles
443 that could be used as *a priori*. They are either consistent with previous
444 CIRS observations (Cottini et al., 2012) or with the profile determined from
445 Herschel measurements (Moreno et al., 2012). Because it is impossible to
446 establish which of these is the most representative of the true profile, all
447 of them have been considered as *a priori*. This allows us 1) to assess the
448 effect of the *a priori* profile on the retrieval of H₂O abundance, and 2) to
449 determine if one of them is better suited. Note that we have considered only
450 profiles that differ in values and shape. We have therefore not considered
451 the profiles modelled by Dobrijevic et al. (2014) assuming an external source
452 of CO, which are similar to the “IM1”, “IE1” and “IM2” profiles listed in
453 Table 3. The H₂O profiles simulated by Lara et al. (2014) for the comet
454
impact scenario have not been used because this scenario is very unlikely. To take into account the condensation of H₂O in the low atmosphere, H₂O has been set to its saturation vapor pressure<fnref n="3" /> below the condensation level for all the *a priori* profiles. A scaling factor, set at 1 as a first guess, is retrieved for each of them considering 100% of *a priori* uncertainties.

### 4.3.2. Error analysis - CIRS

The retrieved H₂O abundance is associated to two types of error: 1) the error on the abundance itself, and 2) the uncertainty on the height at which this abundance is located. The first one has been evaluated by propagating the uncertainties of different parameters, and this has been done for the retrieval case using the “IM2” H₂O profile as *a priori*. We have first considered the propagation of the random errors on the retrieved temperature profile and of the measurement noise. For this, the temperature random errors are incorporated in the measurement covariance matrix S<sub>ε</sub> as follows:

$$S'_{\epsilon} = S_{\epsilon} + K_{Tp} S_{Tp} K_{Tp}^{T}, \qquad (2)$$

where K<sub>Tp</sub> are the temperature Jacobians calculated for the H₂O retrieval range, S<sub>Tp</sub> includes the random errors on temperature estimated according to the method described in subsection 4.1.2. The matrix S<sub>ε</sub>' has then been used in the retrieval of H₂O, and the uncertainties on the latter are calculated from the matrix S.

<footnote n="3">³The saturation vapor pressure (P) has been calculated by assuming an expression of the form P = exp (a + b/T + cT + dT²), where T is the temperature and the coefficients a, b, c, d for H₂O are taken equal to 15.278, -5980.3 K, 8.8294×10⁻³ K⁻¹ and -1.2169×10⁻⁵ K⁻².</footnote>
We have then evaluated the error on the retrieved H₂O mole fraction coming from the uncertainty on the continuum level. For this, we have applied a shift to the continuum, representative of the uncertainty of the latter, and retrieved a new H₂O mole fraction. The uncertainty on the continuum has been estimated as the 1σ significance level (68.3%) of the fit described in section 4.2, which is determined by a Δχ² that depends on the number of retrieved cross-sections (Press et al., 2007).

The last source of errors propagated to the H₂O abundance is the temperature systematic errors coming from the choice of the CH₄ profile. It has been evaluated by shifting the stratospheric temperature by the systematic uncertainties estimated in section 4.1.2 following a change of ±11% of the CH₄ profile. The H₂O retrieval is then performed with the new temperature profile. The difference in the H₂O mole fraction retrieved with and without the shift of temperature is taken as the systematic uncertainty on the H₂O abundance. Note that the H₂O retrieval has also been performed using the stratospheric temperatures retrieved using a CH₄ mole fraction of 0.01. The impact of this change on the determined H₂O abundance will be discussed separately from the systematic errors.

The total uncertainty is finally calculated considering that the random uncertainties (noise, temperature and continuum) are not fully independent of each other, but are independent of the systematic ones resulting from the uncertainty on the CH₄ profile. The random errors have been thus linearly summed and then added to systematic errors by quadrature.

Finally, the height at which H₂O is retrieved is taken as the pressure level at which the Jacobians of H₂O are maximum, which is different for the
499
500
501

different assumed H₂O a priori profile listed in Table 3. The full width at
half maximum of these functions has been used to define the uncertainty on
that level.

502

4.3.3. Error analysis - PACS

503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520

The assessment of the error on the H₂O abundance retrieved from the PACS observations is very similar to the one applied for CIRS observations, apart from the evaluation of the continuum uncertainty. Because PACS spectra are scaled by a modelled continuum, the continuum level does not need to be fitted and there is no “retrieval” error on this level. However, the modelled continuum is associated with a systematic uncertainty related to the choice of the reference atmosphere, which propagates to the H₂O abundance. To evaluate the propagation of this uncertainty, we have to estimate the error on the modelled continuum, and thus on the parameters affecting this level. For tropospheric temperature, random errors calculated as described in section 4.1.2 are taken into account. For the aerosols distribution and the associated absorption cross-sections, based on the retrieval performed on CIRS spectra, we have estimated that their uncertainties are reasonably around 10% and 20% respectively. A new continuum level has then been modelled by scaling these parameters by their respective uncertainties, and the H₂O abundance has been retrieved from the new radiance spectra computed. The H₂O difference obtained between the two modelled continuum is taken as the systematic uncertainty on H₂O due to the continuum.
## 5. Results

### 5.1. Temperature

#### 5.1.1. CIRS disc-averaged

Figure 6 (a-d) shows the *a priori* and retrieved temperature profiles for the four CIRS disc-averaged observations. For all of them, the retrieved profile departs from the *a priori* by about 1.5 K in the troposphere (at pressure levels larger than 100 mbar) and by up to 4 K in the stratosphere (between 100 and 1 mbar) for the 182, 202, 206 observations, and by up to 7 K for the set 219. Figure 5 shows the fit to the set 182 as an example. The vertical sensitivity of the temperature retrieval can be discussed using the associated averaging kernel (AVK) functions (Figure 6 (e-h)). The AVK functions represent the sensitivity of the retrieved state $x_{\text{ret}}$ to the true state $x_{\text{tr}}$ (Rodgers, 2000). The height at which they reach their largest value provides an estimation of the height of the retrieval maximum sensitivity. The AVK are included in a matrix ($\mathbf{A}$) calculated according to:

$$ \mathbf{A} = \frac{\partial x_{\text{ret}}}{\partial x_{\text{tr}}} = (\mathbf{K}^{\text{T}} \mathbf{S}_{\epsilon}^{-1} \mathbf{K} + \mathbf{S}_{\text{a}}^{-1})^{-1} \mathbf{K}^{\text{T}} \mathbf{S}_{\epsilon}^{-1} \mathbf{K}, \quad (3) $$

where $\mathbf{K}$ is the Jacobian matrix of the retrieval. From Figure 6 (e-h), we can see that for the four disc-averaged observations the maximum sensitivity to temperature is found between 400 and 200 mbar as it was expected from the Jacobians (Figure 3.a). The temperature sensitivity stays large up to 70 mbar and then starts to decrease as moving upwards in the atmosphere. In the pressure range of sensitivity to H$_2$O, the AVK functions still present non-zero values and show that the retrieval is also partly sensitive to temperatures
543

in this region. At pressure levels lower than 1 mbar, where CH₄ lines are not
sensitive to temperature (from Jacobians and AVK), the retrieved profile
stays close to the *a priori* profile.

544

545

546

The random retrieval error on the temperature profile is shown in Fig-
ure 7.a, and has been calculated for the set 182. Given the very similar noise
levels and retrieval diagnostics (AVK, DOFS,...), we can reasonably assume
that the error will be of the same order of magnitude for the four sets. It
decreases from 1 K at the surface to about 0.3 K around 100 mbar, where
the maximal sensitivity to temperature is found. It increases then to 0.4 K
and stays constant up to 7 mbar, where it starts to increase again to 1 K at
1 mbar. From this level, as the sensitivity of CH₄ lines to temperature de-
creases, it increases and reaches more than 2 K. The systematic errors on the
retrieved temperature profile are shown in Figure 7.b in absolute value for
the set 182. We can see that the choice of CH₄ stratospheric abundance has a
significant impact on the retrieved temperatures. This is especially the case
in the range of sensitivity to H₂O, where the differences reach around 2 K
when the CH₄ profile is shifted by ±11% (mole fraction of CH₄ equals 1.32%
and 1.64%). In the case where the CH₄ mole fraction is reduced to 0.01, these
differences are even larger and reach more than 5 K in the 12-1 mbar range.
Note that in this case the retrieved temperature profile is warmer than the
*a priori* profile. The impact of the assumed CH₄ profile is of the same or-
der of magnitude for the three other sets. The impact of these temperature
differences on the H₂O retrieval will be assessed in subsection 5.2.1.

547

548

549

550

551

552

553

554

555

556

557

558

559

560

561

562

563

564

565
5.1.2. CIRS nadir

Figure 8.a shows the temperature profile retrieved from the CIRS NA
spectrum and the fit is shown in Figure 5. In the troposphere, it is very
similar to the *a priori* profile and this was expected since tropospheric tem-
peratures were retrieved by Cottini et al. (2012) using CH₄ pure rotational
lines. However, in the 12-1 mbar region, the retrieved profile is significantly
different from the profile used by Cottini et al. (2012), which was taken from
Anderson and Samuelson (2011) and was not retrieved from the analyzed
spectrum. The differences are up to 8 K. Such temperature difference very
likely impacts the retrieval of the stratospheric H₂O abundance and this will
be investigated in subsection 5.2.2.

As seen from the AVK functions shown in Figure 8.b, the vertical sen-
sitivity of the retrieval is very similar to the one observed for disc-averaged
CIRS spectra. The AVK functions reach their maximum values between 400
and 200 mbar, where the sensitivity to temperature is maximal. Their values
then start to decrease, but the retrieval still show sensitivity to temperature
in the pressure range of maximum sensitivity to H₂O.

The random uncertainties on the temperature profile are shown in Fig-
ure 8.c. They are well below 1 K in the troposphere, especially in the range
400-30 mbar, where the sensitivity to temperature is maximal. In the re-
gion of sensitivity to H₂O, these errors are within 0.9-1.6 K, which is slightly
larger than the ones estimated for disc-averaged observations. As already
noticed in the previous subsection, the CH₄ profile has a large influence on
the retrieved profile in the range 12-1 mbar (Figure 8.d). The systematic
errors are estimated at around 2 K in absolute value if we consider ±11%
of uncertainty on the CH₄ profile. If the stratospheric CH₄ mole fraction is reduced to 0.01, the retrieved temperature profile is warmer by up to 8 K than the one shown in Figure 8.a.

5.1.3. PACS

Figure 9 presents the temperature profile retrieved from PACS observations along with the associated error and vertical sensitivity diagnostics. As observed for the CIRS NA case, the retrieved profile is significantly colder, by up to 9 K, from the temperature profile considered by Moreno et al. (2012) in the range of H₂O sensitivity. As a reminder, Moreno et al. (2012) did not determine the temperature profile from PACS spectra but built one based on several retrievals performed in different studies. The observed difference could possibly lead to the retrieval of a larger H₂O abundance, and then therefore to a better agreement between CIRS and Herschel measurements. This will be discussed in more details in subsection 5.2.3. The fit to the spectrum is shown in Figure 5.

From the AVK functions shown in Figure 9.b, we can see that the retrieval has less vertical resolution than those performed on CIRS observations. The maximum sensitivity to temperature is found to be within 200 and 70 mbar and thus show lower sensitivity to temperature in the lower troposphere. This was expected from the temperature Jacobians (Figure 3.c) and explains that the retrieved profile stays close to the *a priori* in the low atmosphere. As observed for CIRS observations, the retrieval, however, shows sensitivity to temperature in the pressure range of maximum sensitivity to H₂O. The smaller vertical resolution likely explains the larger random errors on the profile in the 12-1 mbar range, which reach more than 4 K (Figure 9.c).
Systematic errors (absolute value) are within 2-3 K in the same range when the uncertainty on CH₄ profile is assumed to be ±11%. If the stratospheric CH₄ mole fraction is reduced to 0.01, the retrieved temperature profile is warmer by up to 9 K. The propagation of these uncertainties to the H₂O abundance will be discussed in section 5.2.3.

## 5.2. H₂O abundance

Table 4 shows a summary of the H₂O retrievals performed on the different observations analysed in this work. For comparison, the H₂O abundances retrieved when the stratospheric temperatures are determined assuming 1.00% of stratospheric CH₄ are also indicated. Note that they are calculated for the pressure range indicated. Example fits are shown in Figure 5. The following subsections discuss first of all the retrieval for each type of observation and then compare the retrieved H₂O abundances.

### 5.2.1. CIRS disc-averaged

#### 5.2.1.1 CIRS 182

From Table 4, considering all the different *a priori* H₂O profiles, we can see that the H₂O VMR retrieved from the set 182 is found to be within 0.120 ppb and 0.215 ppb in the 8.2–5.1 mbar pressure range. This shows that the choice of the *a priori* profile has a significant impact on the retrieved H₂O abundance. The total column of H₂O above the condensation level is, however, less affected by the H₂O vertical profile assumptions and is determined to be within 3.5–3.8×10¹⁴ molecules/cm². Because the *a priori* profiles have different slopes (Figure 4), they have also an effect on the height of maximum sensitivity to H₂O, which varies from 8.2 mbar to 5.1 mbar. For all
640 retrievals, the fits are reasonably good with associated $\chi^2$ around 1.48–1.49.

641 Given these very similar values, it is therefore impossible to determine which 642 *a priori* profile is the most appropriate, and all of them are kept in the fol- 643 lowing discussions. The total error has been estimated at -43%/+44%. The 644 largest contribution to the total error is the uncertainty on the continuum 645 level, which is estimated at ±27%. Finally, when the stratospheric temper- 646 atures retrieved using a CH$_4$ mole fraction of 0.01 are considered, the H$_2$O 647 VMRs are around 40% smaller and fall within 0.072–0.131 ppb.

648 5.2.1.2 Other sets

649 Compared to the set 182, the three other disc-averaged spectra do not show 650 clear H₂O lines as can be seen in Figure 1. Before performing the retrieval, we 651 have first of all assessed if the presence of H₂O lines is statistically attested. 652 To do this, we have calculated the misfit χ² as a function of the scaling factor 653 (MF) applied to the H₂O profile (the “IM2” *a priori* profile is considered), 654 starting at MF=0. If H₂O emission lines are present in the spectrum, the χ² 655 function should show a minimum at the best fitting scaling factor. Because 656 we are adjusting one parameter (the scaling factor), a 3σ detection requires 657 a χ² decrease of 9 compared to the case assuming no H₂O. Figure 10 shows 658 the Δχ²(χ² - χ²(MF = 0)) functions calculated for each sets. For all of 659 them, the minimum is found below the limit Δχ² = -9, meaning that H₂O 660 is detected at the 3σ level. The minimum χ² is found at MF=0.75 for the 661 set 202, and at MF=0.55 for the sets 206 and 219.

662 As the presence of H₂O emission lines has been statistically confirmed, 663 we have applied the retrieval scheme to the three sets in a second stage. The
results are summarized in Table 4. The retrieved scaling factors are very close to those determined from the $\chi^2$ analysis: they are equal to 0.76, 0.58 and 0.59 respectively for the sets 202, 206 and 219. These correspond to respective H$_2$O VMRs of 0.129 ppb, 0.099 ppb, and 0.100 ppb at 5.6 mbar.

As seen for the set 182, the choice of the *a priori* H$_2$O profile has a strong influence, leading to retrieved VMRs varying within 0.080–0.151 ppb for the set 202, 0.059–0.119 ppb for the set 206, and 0.054–0.120 ppb for the set 219, mainly between 8 mbar and 5 mbar. The total columns of H$_2$O are more stable against the choice of the *a priori* H$_2$O profile and are found to be within 2.3–2.6×10$^{14}$ molecules/cm$^2$, 1.7–2.0×10$^{14}$ molecules/cm$^2$, 1.6–2.1×10$^{14}$ molecules/cm$^2$ respectively for sets 202, 206, and 219. The assessment of the most appropriate *a priori* is impossible for the three sets because all profiles lead to very similar quality of fit. The reduced $\chi^2$ values are found to be 1.65–1.66, 1.40 and 1.20–1.21 respectively for sets 202, 206 and 219.

The estimated total errors are larger than those assessed for the set 182. This was expected given the smaller SNR of the averaged spectra for the three other sets. These errors are equal to -56%/+57%, ±65%, and -70%/+78% respectively for sets 202, 206 and 219. Finally, as seen for set 182, when using the stratospheric temperature profile determined for a stratospheric CH$_4$ mole fraction of 0.01, the retrieved H$_2$O VMRs are smaller. They fall within 0.038–0.081 ppb, 0.038–0.082 ppb and 0.032–0.075 ppb respectively for sets 202, 206 and 219.

### 5.2.2. CIRS nadir

Using the scheme developed for disc-averaged CIRS spectra, the H$_2$O VMR retrieved from the CIRS NA spectrum falls within 0.058 ppb–0.109 ppb
in the 9.6–5.4 mbar pressure range. This VMR is smaller by a factor 1.3–
2.4 than the one determined by Cottini et al. (2012) (0.14 ppb) and this
shows the influence of the chosen retrieval scheme on the evaluation of the
H₂O abundance. This difference is mostly associated with the choice of the
*a priori* profile. Indeed, by redoing the retrieval using a constant H₂O *a
priori* profile of 0.1 ppb above the saturation level as Cottini et al. (2012),
we retrieve a H₂O VMR of 0.138 ppb, which is in very good agreement with
the value reported by Cottini et al. (2012). However, because the H₂O mole
fraction has been firmly demonstrated to increase with height, a H₂O profile
constant at all altitudes is not the best option for the *a priori* profile and
was therefore not considered in this work. Note that if the total errors are
taken into account (-42%/+44% for this work, ±0.05 ppb for Cottini et al.
(2012)), the largest H₂O abundances determined in this work agree within
the error bars with the results of Cottini et al. (2012). Note finally that the
discrepancies mentioned above are even larger when the H₂O abundance is
retrieved using the stratospheric temperatures determined for a stratospheric
CH₄ mole fraction of 0.01. The retrieved H₂O VMRs are in this case a factor
of 1.7–3.2 smaller than the one reported by Cottini et al. (2012).

As we already mentioned, the assumed temperature profile affects the
height of the H₂O condensation level and therefore the vertical sensitivity
to H₂O. Because the temperature profile we retrieved is colder than the one
assumed by Cottini et al. (2012), the maximum sensitivity to H₂O is found
to be higher in the atmosphere (9.6–5.4 mbar) than determined by Cottini
et al. (2012) (maximum sensitivity at 10.7 mbar). Note also that, as seen for
CIRS disc-averaged observations, determining the most appropriate H₂O *a*
priori profile is impossible based on the $\chi^2$ values (0.67–0.68 for the reduced $\chi^2$).

### 5.2.3. PACS

Before applying the retrieval scheme described in section 4 to the PACS observations, we have determined if differences in retrieval codes might have a significant impact on the H$_2$O abundance. For this, we first retrieved H$_2$O using very similar retrieval assumptions as those used by Moreno et al. (2012), i.e., using the same temperature profile and considering the “Sa” profile as a priori (Table 3 and Figure 4). With these settings, we retrieve a scaling factor of 0.96 to be applied to the “Sa” profile, which is in excellent agreement with the results of Moreno et al. (2012). To investigate the effect of the choice of the a priori profile, we then performed the retrievals using the different profiles shown in Table 3. The retrieved H$_2$O abundances vary between 0.015–0.031 ppb, and fall well within the error bars estimated by Moreno et al. (2012).

Since differences in retrieval codes do not affect the retrieved H$_2$O abundance, we have investigated in a second stage if differences in the retrieval method, especially differences in the temperature profile, significantly affect the retrieved H$_2$O abundance from PACS. For this, we have applied the analysis described in section 4 and the results are shown in Table 4. The retrieved VMRs are found to be within 0.024–0.052 ppb and are slightly larger than those determined by Moreno et al. (2012). This shows the impact of the temperature profile retrieved from PACS CH$_4$ lines, which was found to be colder than the one assumed by Moreno et al. (2012). This temperature profile also explains that the H$_2$O maximum sensitivity is found higher in the
atmosphere (8.2–5.6 mbar) because the condensation level moves upwards.

The H₂O VMRs retrieved when considering the stratospheric temperature profile determined using 1.00% for the stratospheric CH₄ mole fraction are, however, in good agreement with those determined by Moreno et al. (2012).

This is explained by the fact that this temperature profile is very similar to the one considered by Moreno et al. (2012). In this case, the retrieved H₂O VMRs fall within 0.020–0.030 ppb.

As already observed for the other types of observations, the H₂O total column is more stable against the choice of the *a priori* H₂O profile and is determined to be within 0.8–0.9×10¹⁴ molecules/cm². The total errors are estimated to be -15%/+12%. These errors are significantly smaller than those estimated for CIRS. This can be explained by the better SNR of PACS observations. Note that the reduced χ² values are very similar for all the *a priori* profiles and are within 1.49–1.51.

### 5.2.4. Comparison and discussion

Figure 11 compares the H₂O VMRs retrieved for all observations using the same analysis scheme as a function of the H₂O *a priori* profile considered. We can see that the comparison changes slightly depending on the chosen *a priori*, which directly impacts the retrieved abundance. The lowest VMRs are retrieved using the “Sa” profile of Moreno et al. (2012) (0.029–0.120 ppb), and the largest using the “L3” profile of Lara et al. (2014) (0.052–0.215 ppb). Because it affects the H₂O retrieved abundance, the choice of the *a priori* profile seems to impact the relative agreement between the different observations. Indeed, the best agreement is found for the “Sa” profile, whereas the retrieved VMRs show larger discrepancies in case of “L1”, “L2”, and
“L3” profiles. Note that in the case of the H₂O total column abundance, there is much less impact of the *a priori* profile on the relative agreement between the different datasets. However, despite the differences due to the choice of the H₂O *a priori* profile and whether the total column abundances or the volume mixing ratios are considered, the same general trend is observed. For each case, the smallest H₂O abundance is retrieved from PACS spectra confirming the initial discrepancy between Moreno et al. (2012) and Cottini et al. (2012). The CIRS disc-averaged set 182 is associated with the largest H₂O abundance, and a very good agreement is found between the three other disc-averaged sets and the CIRS NA observations. Note that the *a priori* profile also impacts the height of maximum sensitivity (Table 4). For each *a priori*, when taking into account the FWHM of the Jacobians (not shown), PACS and CIRS seem to sound a very similar pressure region, and the small differences do not explain the variation of the retrieved H₂O VMRs between the different observations.

By analysing PACS observations with the same assumptions than Moreno et al. (2012) but with the NEMESIS retrieval code, we have shown that differences in the retrieval codes used by Moreno et al. (2012) and Cottini et al. (2012) hardly explain the differences observed previously between CIRS and PACS measurements. Applying the same retrieval method and making the same H₂O *a priori* assumptions for both PACS and CIRS observations has, on the contrary, decreased the discrepancies observed previously between these instruments (Moreno et al., 2012; Cottini et al., 2012). However, the analysis of the CIRS disc-averaged dataset has brought new differences. Whereas the sets 202, 206, and 219 are in good agreement with the CIRS
NA observation and consistent within the error bars with PACS measurements, the H₂O VMRs retrieved from the set 182 are significantly larger and especially differ from PACS measurements. This is confirmed by Figure 12, which shows a comparison between observed PACS H₂O lines and lines simulated using the H₂O profiles retrieved for the different observations considering the “Sa” *a priori* profile. Indeed, we can see that the profile retrieved for set 182 strongly overestimates PACS H₂O lines. Also from Figure 12 we can see that, although a relative agreement is found within the error bars between the other CIRS and PACS measurements, the H₂O profiles retrieved from CIRS observations are inconsistent with PACS H₂O lines. This confirms that H₂O is less abundant for PACS observations. Based on this, the hypothesis of natural variations of the H₂O abundance, triggered by the global circulation in Titan’s atmosphere, can be envisaged. Similarly to nitriles and some hydrocarbons, H₂O shows an increasing mole fraction with height, resulting from a source at high altitudes (either micrometeorite ablation or Enceladus) and a sink in the low atmosphere (condensation and photolysis). The meridional circulation could thus possibly affect the latitudinal distribution of H₂O abundance. This has been observed for nitriles and hydrocarbons, for which subsidence of air rich in these gases leads to an enrichment in the stratosphere, and inversely upwelling leads to the depletion of their stratospheric abundance (e.g. Coustenis et al., 2007, 2016; Teanby et al., 2006, 2008, 2009, 2010). The observations analysed in this work are recorded at different sub-spacecraft latitudes and at different periods in Titan’s year (see Figure 11), and are therefore subject to different meridional circulation. The CIRS disc-averaged set 182 is recorded in the
late southern autumn-early southern winter, when according to dynamical
models (e.g. Hourdin et al., 2004) the meridional circulation is dominated
by a single Hadley cell with subsidence at the South Pole (Teanby et al.,
2012) and upwelling at the North Pole. The sub-spacecraft latitude of this
set is -41° but because of its disc-averaged nature, the observation includes
the South Pole. It is therefore sensitive to the possible H₂O enhancement
brought by the subsidence of air rich in H₂O occuring at the South Pole,
and this could explain the larger stratospheric VMRs retrieved for this set
(see also Coustenis et al. (2016)). On the contrary, PACS observations were
recorded close to the northern spring equinox, for which dynamical models
predict a transitional circulation state, in which two cells develop with up-
welling at the equator and subsidence at both poles (Hourdin et al., 2004;
Vinatier et al., 2015). The PACS sub-spacecraft latitude is close to the equa-
tor, where upwelling could cause H₂O depletion and explain the low H₂O
abundance retrieved from PACS spectra. Note that the variations of H₂O
could be very similar to those observed for C₂H₂, which has a comparable
lifetime of around 10 years. Another origin that could contribute to explain
the H₂O VMRs differences is the spatial/time variation of the input OH/H₂O
flux in Titan's atmosphere. Depending on its source, H₂O is likely deposited
at different locations (heights but also latitudes) in Titan's atmosphere. The
idea of time variations on scales of decades/centuries has already been put
forward by Moreno et al. (2012) to explain the difference of the input flux
needed to explain current H₂O and CO₂ abundances. Time variations of
the H₂O source rate at Enceladus, although previously debated, have been
reported by some recent studies (Hedman et al., 2013; Nimmo et al., 2014;
Teolis et al., 2017, e.g.). These variations occur on timescales of a few months or years, which is smaller than the H₂O lifetime, and unlikely explain the H₂O differences observed in this work. Variations on longer timescales cannot be ruled out, but do not provide a complete satisfactory explanation for the differences observed in this work. Indeed, if such variations existed, the H₂O abundance would react over periods of around 10 years. The variations of the H₂O abundance reported in this work occur, however, on shorter timescales. Moreover, assuming that a change of the OH/H₂O flux is responsible for the difference between the H₂O mole fractions retrieved from PACS and the set 182 of CIRS, the good agreement observed between the CIRS NA measurement and the three other CIRS disc-averaged sets becomes then more difficult to understand. For this reason, the meridional circulation and its seasonal variations seem at this stage to provide the most reasonable explanation for the H₂O abundance differences observed in this work. Note also that longitudinal variations of H₂O are barely possible given the lifetime of H₂O and the strong stratospheric zonal winds that rapidly homogenize gas abundances. Finally, following the work of Coustenis et al. (1998), Moreno et al. (2012) reanalysed SWS/ISO observations and determined a H₂O VMR of 0.06 ppb. Most of the H₂O VMRs determined in this work are in good agreement with this reanalysis.

The hypotheses discussed above are hardly proved with the results of this work, given the very few analysed measurements and the large errors associated with the CIRS observations. The analysis of more observations will be needed in future work to better understand the observed H₂O variations. We also believe that the development of 2D-3D photochemical models, cou-
pling Titan's oxygen chemistry and general circulation, could help address the new issues highlighted in this work. Note that if H₂O is retrieved using stratospheric temperatures determined for a stratospheric CH₄ mole fraction of 0.01, the H₂O VMRs evaluated for the set 182 and for PACS observations remain significantly different, and thus the above discussion still holds. It is worth, however, assessing if this discussion still holds when the CH₄ latitudinal variability is taken into account. Indeed, we have considered a constant stratospheric CH₄ mole fraction for all the observations (either 1.48% or 1.00%). Based on Lellouch et al. (2014), 1.48% seems to be a relatively good assumption for the CIRS disc-averaged set 182. On the contrary, a mole fraction of 1.00% is best suited for the set 219, the CIRS NA observation and for PACS data. If these CH₄ mole fractions are assumed for these observations, the difference in the retrieved H₂O VMRs between set 182 and the three other observations is larger than when considering constant CH₄ abundance, and this strengthens the idea of latitudinal variations of the H₂O abundance. Regarding the sets 202 and 206, it is more difficult to assess what CH₄ mole fraction is the most appropriate, given the large error bars reported by Lellouch et al. (2014). If it is assumed to be in between the extreme values considered in this work, significant differences in the retrieved H₂O VMRs should remain. In future work, attempts to reduce the uncertainty on the stratospheric CH₄ mole fraction, but also on other parameters such as the continuum level, should be undertaken to reduce the total uncertainty on the retrieved H₂O abundance.
887 6. Conclusions

888 The goal of this work was to understand the differences in H₂O abundances retrieved previously by Moreno et al. (2012) from Herschel disc-averaged observations, and by Cottini et al. (2012) from the average of a
889 large number of spectra recorded in a 0–30° latitudinal bin. The strategy
890 for this was to 1) analyse disc-averaged observations of CIRS to investigate
891 if the observation geometry could explain the differences, and 2) (re)analyse
892 the three types of observation with the same retrieval scheme to assess if dif-
893 ferences in retrieval codes/methodology could be responsible for the previous
894 discrepancies. For this purpose, four sets of CIRS disc-averaged observations
895 taken between 2013–2015 were analysed. A retrieval scheme composed of
896 three successive steps was also set up. It comprises the retrieval of the tem-
897 perature profile (step 1), the adjustment of the continuum level in the vicinity
898 of H₂O lines (step 2), and the retrieval of the H₂O abundance (step 3). A
899 rigorous error assessment was performed and included the propagation of
900 the uncertainties of key parameters: measurement noise, temperature, CH₄
901 profile (for temperature retrieval), and continuum level. Different H₂O *a pri-
902 ori* profiles, either consistent with PACS or CIRS measurements, have been
903 considered for the H₂O retrieval from all observations.
904
905

906 With this analysis, we have first of all shown that differences in the re-
907 trieval codes used by Moreno et al. (2012) and Cottini et al. (2012) do not
908 explain the discrepancies observed previously between PACS and CIRS mea-
909 surements. Applying the same retrieval method, including the temperature
910 retrieval, and making the same H2O a priori assumptions for both PACS and
911 CIRS has, on the contrary, better reconciled the measurements of these in-
struments, with the agreement depending on the chosen *a priori* H₂O profile.

The retrieved H₂O abundances are also in good agreement with the reanal-
ysis of ISO observations performed by Moreno et al. (2012). The addition of
the disc-averaged CIRS observations, instead of confirming the consistency
between the different datasets, has revealed discrepancies mainly between the
set 182 and PACS observations. This makes us question the idea that the
datasets should be in agreement. The instruments measured H₂O at differ-
ent sub-observer latitudes and at different periods in Titan's year which are
associated with different meridional circulation. This circulation is shown to
affect the latitudinal distribution of nitriles and hydrocarbons, through the
subsidence or upwelling of air rich in these gases. As discussed in this work,
the meridional circulation could potentially impact the latitudinal distribu-
tion of H₂O as well and explain the differences between the CIRS set 182
and PACS measurements. On the contrary, time variations of the OH/H₂O
input flux in Titan's atmosphere, which were shown to occur on timescales
of a few months or years by recent studies, unlikely explain the observed
differences given the H₂O lifetime of around 10 years. Given the few H₂O
measurements and the large uncertainties associated with the CIRS observa-
tions, these hypotheses are, however, impossible to evaluate with the results
obtained so far.

To validate these assumptions, the analysis of more observations will be
required in future work. More especially, the NASA Cassini mission covers
now almost the half of a Titan year. CIRS FP1 observations of Titan recorded
between 2004 and 2017 could be used to determine if the H₂O abundance
varies with time and/or latitude. The photochemical models describing the
oxygen chemistry in Titan's atmosphere developed until now are 1D models, considering only the vertical transport of gases. In the future 2D-3D models, coupling the oxygen chemistry with the general circulation, should be developed to address the questions arising from this work. Finally, efforts should be undertaken to decrease the uncertainties on the retrieved H₂O abundances, which are revealed to be large for CIRS observations. Reducing the uncertainty of the stratospheric CH₄ mole fraction or on the continuum level, which were shown to significantly affects the H₂O retrieval, should be a priority of any future study.

## Acknowledgements

S. Bauduin would like to thank the Wiener-Anspach Foundation (Belgium) for her postdoctoral fellowship. N. Teanby is funded by UK Science Technology and Facilities Council. The authors would like to thank the Cassini and CIRS teams involved in building and testing the instrument, planning data acquisition sequences and calibration of the data. PACS has been developed by a consortium of institutes led by MPE (Germany) and including UVIE (Austria); KU Leuven, CSL, IMEC (Belgium); CEA, LAM (France); MPIA (Germany); INAF-IFSI/OAA/OAP/OAT, LENS, SISSA (Italy); IAC (Spain). This development has been supported by the funding agencies BMVIT (Austria), ESA-PRODEX (Belgium), CEA/CNES (France), DLR (Germany), ASI/INAF (Italy), and CICYT/MCYT (Spain). HCSS / HSpot / HIPE is a joint development (are joint developments) by the Herschel Science Ground Segment Consortium, consisting of ESA, the NASA Herschel Science Center, and the HIFI, PACS and SPIRE consortia.
References
---

Achterberg, R. K., Conrath, B. J., Gierasch, P. J., Flasar, F. M., Nixon, C. A., 2008. Titan's middle-atmospheric temperatures and dynamics observed by the Cassini Composite Infrared Spectrometer. Icarus 194 (1), 263–277.

Achterberg, R. K., Gierasch, P. J., Conrath, B. J., Flasar, F. M., Nixon, C. A., 2011. Temporal variations of Titans middle-atmospheric temperatures from 2004 to 2009 observed by Cassini/CIRS. Icarus 211 (1), 686–698.

Anderson, C. M., Samuelson, R. E., 2011. Titans aerosol and stratospheric ice opacities between 18 and 500m: Vertical and spectral characteristics from Cassini CIRS. Icarus 212 (2), 762–778.

Borysow, A., 1991. Modeling of collision-induced infrared absorption spectra of H<sub>2</sub>-H<sub>2</sub> pairs in the fundamental band at temperatures from 20 to 300 K. Icarus 92 (2), 273–279.

Borysow, A., Frommhold, L., 1986a. Collision-induced rototranslational absorption spectra of N<sub>2</sub>-N<sub>2</sub> pairs for temperatures from 50 to 300 K. The Astrophysical Journal 311, 1043–1057.

Borysow, A., Frommhold, L., 1986b. Theoretical collision-induced rototranslational absorption spectra for modeling Titan's atmosphere: H<sub>2</sub>-N<sub>2</sub> pairs. The Astrophysical Journal 303, 495–510.
982

Borysow, A., Frommhold, L., 1986c. Theoretical collision-induced rototranslational absorption spectra for the outer planets: H₂-CH₄ pairs. The Astrophysical Journal 304, 849–865.

983

984

985

Borysow, A., Frommhold, L., 1987. Collision-induced rototranslational absorption spectra of CH₄-CH₄ pairs at temperatures from 50 to 300 K. The Astrophysical Journal 318, 940–943.

986

987

988

Borysow, A., Tang, C., 1993. Far Infrared CIA Spectra of N₂-CH₄ Pairs for Modeling of Titan's Atmosphere. Icarus 105 (1), 175 – 183.

989

990

Boudon, V., Pirali, O., Roy, P., Brubach, J.-B., Manceon, L., Auwera, J. V., 2010. The high-resolution far-infrared spectrum of methane at the SOLEIL synchrotron. Journal of Quantitative Spectroscopy and Radiative Transfer 111 (9), 1117 – 1129, special Issue Dedicated to Laurence S. Rothman on the Occasion of his 70th Birthday.

991

992

993

994

995

Cottini, V., Nixon, C., Jennings, D., Anderson, C., Gorius, N., Bjoraker, G., Coustenis, A., Teanby, N., Achterberg, R., Bézard, B., de Kok, R., Lellouch, E., Irwin, P., Flasar, F., Bampasidis, G., 2012. Water vapor in Titans stratosphere from Cassini CIRS far-infrared spectra. Icarus 220 (2), 855 – 862.

996

997

998

999

1000

Coustenis, A., Achterberg, R. K., Conrath, B. J., Jennings, D. E., Marten, A., Gautier, D., Nixon, C. A., Flasar, F. M., Teanby, N. A., Bzard, B., Samuelson, R. E., Carlson, R. C., Lellouch, E., Bjoraker, G. L., Romani, P. N., Taylor, F. W., Irwin, P. G., Fouchet, T., Hubert, A., Orton, G. S., Kunde, V. G., Vinatier, S., Mondellini, J., Abbas, M. M., Courtin, R.,

1001

1002

1003

1004
1005 2007. The composition of Titan's stratosphere from Cassini/CIRS mid-infrared spectra. Icarus 189 (1), 35-62.

1007 Coustenis, A., Jennings, D. E., Achterberg, R. K., Bampasidis, G., Lavvas, P., Nixon, C. A., Teanby, N. A., Anderson, C. M., Cottini, V., Flasar, F. M., 2016. Titans temporal evolution in stratospheric trace gases near the poles. Icarus 270, 409-420.

1011 Coustenis, A., Salama, A., Lellouch, E., Encrenaz, T., Bjoraker, G., Samuelson, R., de Graauw, T., Feuchtgruber, H., Kessler, M., 1998. Evidence for water vapor in Titan's atmosphere from ISO/SWS data. Astronomy Astrophysics 336, L85-L89.

1015 Cui, J., Yelle, R., Vuitton, V., Waite, J., Kasprzak, W., Gell, D., Niemann, H., Mller-Wodarg, I., Borggren, N., Fletcher, G., Patrick, E., Raaen, E., Magee, B., 2009. Analysis of Titan's neutral upper atmosphere from Cassini Ion Neutral Mass Spectrometer measurements. Icarus 200 (2), 581-615.

1020 de Kok, R., Irwin, P., Teanby, N., 2010a. Far-infrared opacity sources in Titans troposphere reconsidered. Icarus 209 (2), 854-857.

1022 de Kok, R., Irwin, P., Teanby, N., Lellouch, E., Bzard, B., Vinatier, S., Nixon, C., Fletcher, L., Howett, C., Calcutt, S., Bowles, N., Flasar, F., Taylor, F., 2007a. Oxygen compounds in Titan's stratosphere as observed by Cassini CIRS. Icarus 186 (2), 354-363.

1026 de Kok, R., Irwin, P., Teanby, N., Nixon, C., Jennings, D., Fletcher, L., Howett, C., Calcutt, S., Bowles, N., Flasar, F., Taylor, F., 2007b. Char-
acteristics of Titan's stratospheric aerosols and condensate clouds from
Cassini CIRS far-infrared spectra. Icarus 191 (1), 223 – 235.

1029

de Kok, R., Irwin, P., Teanby, N., Vinatier, S., Tosi, F., Negrao, A., Osprey, S., Adriani, A., Moriconi, M., Coradini, A., 2010b. A tropical haze band in Titans stratosphere. Icarus 207 (1), 485 – 490.

1030

1031

1032

De La Haye, V., Waite, J. H., Johnson, R. E., Yelle, R. V., Cravens, T. E., Luhmann, J. G., Kasprzak, W. T., Gell, D. A., Magee, B., Leblanc, F., Michael, M., Jurac, S., Robertson, I. P., 2007. Cassini Ion and Neutral Mass Spectrometer data in Titan's upper atmosphere and exosphere: Observation of a suprathermal corona. Journal of Geophysical Research: Space Physics 112 (A7), A07309.

1033

1034

1035

1036

1037

1038

Dobrijevic, M., Hébrard, E., Loison, J., Hickson, K., 2014. Coupling of oxygen, nitrogen, and hydrocarbon species in the photochemistry of Titan's atmosphere. Icarus 228, 324 – 346.

1039

1040

1041

English, M., Lara, L., Lorenz, R., Ratcliff, P., Rodrigo, R., 1996. Ablation and chemistry of meteoric materials in the atmosphere of Titan. Advances in Space Research 17 (12), 157 – 160.

1042

1043

1044

Flasar, F. M., Kunde, V. G., Abbas, M. M., Achterberg, R. K., Ade, P., Barucci, A., Bézard, B., Bjoraker, G. L., Brasunas, J. C., Calcutt, S., et al., 2004. Exploring the Saturn System in the Thermal Infrared: The Composite Infrared Spectrometer. Space Science Review 115, 169–297.

1045

1046

1047

1048

Fulchignoni, M., Ferri, F., Angrilli, F., Ball, A., et al., 2005. In situ mea-

1049
surements of the physical characteristics of Titan's environment. Nature
438 (7069), 785-91.

Hansen, C., Esposito, L., Stewart, A., Meinke, B., Wallis, B., Colwell, J.,
Hendrix, A., Larsen, K., Pryor, W., Tian, F., 2008. Water vapour jets
inside the plume of gas leaving enceladus. Nature 456 (27), 477-479.

Hansen, C. J., Esposito, L., Stewart, A. I. F., Colwell, J., Hendrix, A., Pryor, W., Shemansky, D., West, R., 2006. Enceladus' Water Vapor Plume. Science 311 (5766), 1422-1425.

Hansen, C. J., Shemansky, D. E., Esposito, L. W., Stewart, A. I. F., Lewis, B. R., Colwell, J. E., Hendrix, A. R., West, R. A., Waite, J. H., Teolis, B., Magee, B. A., 2011. The composition and structure of the Enceladus plume. Geophysical Research Letters 38 (11), L11202.

Hartogh, P., Lellouch, E., Moreno, R., Bockelée-Morvan, D., Biver, N., Cas-
sidy, T., Rengel, M., Jarchow, C., Cavali, T., Crovisier, J., Helmich, F.,
Kidger, M., 2011. Direct detection of the Enceladus water torus with Her-
schel. A&A 532, L2.

Hedman, M. M., Gosmeyer, C. M., Nicholson, P. D., Sotin, C., Brown, R. H., Clark, R. N., Baines, K. H., Buratti, B. J., Showalter, M. R., 2013. An observed correlation between plume activity and tidal stresses on Enceladus. Nature 500 (7461), 182-184.

Hörst, S. M., Vuitton, V., Yelle, R. V., 2008. Origin of oxygen species in Titan's atmosphere. Journal of Geophysical Research: Planets 113 (E10), E10006.
1073 Hourdin, F., Lebonnois, S., Luz, D., Rannou, P., 2004. Titan's stratospheric composition driven by condensation and dynamics. Journal of Geophysical Research: Planets 109 (E12), E12005.

1074
1075
Research: Planets 109 (E12), E12005.

1076 Irwin, P., Teanby, N., de Kok, R., Fletcher, L., Howett, C., Tsang, C., Wilson, C., Calcutt, S., Nixon, C., Parrish, P., 2008. The NEMESIS planetary atmosphere radiative transfer and retrieval tool. Journal of Quantitative Spectroscopy and Radiative Transfer 109 (6), 1136–1150.

1077
1078
atmosphere radiative transfer and retrieval tool. Journal of Quantitative
1079
Spectroscopy and Radiative Transfer 109 (6), 1136 – 1150.

1080 Jennings, D. E., Flasar, F. M., Kunde, V. G., Nixon, C. A., Segura, M. E., 1081 Romani, P. N., Gorius, N., Albright, S., Brasunas, J. C., Carlson, R. C., 1082 Mamoutkine, A. A., Guandique, E., Kaelberer, M. S., Aslam, S., Achterberg, R. K., Bjoraker, G. L., Anderson, C. M., Cottini, V., Pearl, J. C., 1083 Smith, M. D., Hesman, B. E., Barney, R. D., Calcutt, S., Vellacott, T. J., 1084 Spilker, L. J., Edgington, S. G., Brooks, S. M., Ade, P., Schinder, P. J., 1085 Coustenis, A., Courtin, R., Michel, G., Fettig, R., Pilorz, S., Ferrari, C., 1086 Jun 2017. Composite infrared spectrometer (cirs) on Cassini. Appl. Opt. 1087 56 (18), 5274-5294.

1081
Romani, P. N., Gorius, N., Albright, S., Brasunas, J. C., Carlson, R. C.,
Mamoutkine, A. A., Guandique, E., Kaelberer, M. S., Aslam, S., Achter-

1083
berg, R. K., Bjoraker, G. L., Anderson, C. M., Cottini, V., Pearl, J. C.,
1084
Smith, M. D., Hesman, B. E., Barney, R. D., Calcutt, S., Vellacott, T. J.,

1085
Spilker, L. J., Edgington, S. G., Brooks, S. M., Ade, P., Schinder, P. J.,
1086
Coustenis, A., Courtin, R., Michel, G., Fettig, R., Pilorz, S., Ferrari, C.,

1087
Jun 2017. Composite infrared spectrometer (cirs) on Cassini. Appl. Opt.
1088
56 (18), 5274-5294.

1088
Lacis, A. A., Oinas, V., 1991. A description of the correlated k distribution
1089
method for modeling nongray gaseous absorption, thermal emission, and
1090
multiple scattering in vertically inhomogeneous atmospheres. Journal of
1091
Geophysical Research: Atmospheres 96 (D5), 9027-9063.

1091
Geophysical Research: Atmospheres 96 (D5), 9027-9063.

1092

1093 Lara, L., Lellouch, E., González, M., Moreno, R., Rengel, M., 2014. A time-
dependent photochemical model for Titan's atmosphere and the origin of
1094
H₂O. A&A 566, A143.

1095
H₂O. A&A 566, A143.
1096 Lellouch, E., Bézard, B., Flasar, F., Vinatier, S., Achterberg, R., Nixon, C., Bjoraker, G., Gorius, N., 2014. The distribution of methane in Titan's stratosphere from Cassini/CIRS observations. Icarus 231, 323–337.

1097
1098

1099 Moreno, R., Lellouch, E., Lara, L. M., Feuchtgruber, H., Rengel, M., Hartogh, P., Courtin, R., 2012. The abundance, vertical distribution and origin of H₂O in Titan's atmosphere: Herschel observations and photochemical modelling. Icarus 221 (2), 753–767.

1101
1102

1103 Niemann, H. B., Atreya, S. K., Demick, J. E., Gautier, D., Haberman, J. A., Harpold, D. N., Kasprzak, W. T., Lunine, J. I., Owen, T. C., Raulin, F., 2010. Composition of Titan's lower atmosphere and simple surface volatiles as measured by the Cassini-Huygens probe gas chromatograph mass spectrometer experiment. Journal of Geophysical Research: Planets 115 (E12).

1104
1105

1106
1107
1108

1109 Nimmo, F., Porco, C., Mitchell, C., 2014. Tidally Modulated Eruptions on Enceladus: Cassini ISS Observations and Models. The Astronomical Journal 148 (3), 46.

1110
1111

1112 Poglitsch, A., Waelkens, C., Geis, N., Feuchtgruber, H., Vandenbussche, B., Rodriguez, L., Krause, O., Renotte, E., van Hoof, C., Saraceno, P., et al., 2010. The Photodetector Array Camera and Spectrometer (PACS) on the Herschel Space Observatory. A&A 518, L2.

1113
1114

1115

1116 Press, W. H., Teukolsky, S. A., Vetterling, W. T., Flannery, B. P., 2007. Numerical Recipes: The Art of Scientific Computing, 3rd Edition. Cambridge University Press.

1117
1118
1119 Rodgers, C., 2000. Inverse methods for atmospheric sounding: theory and practice. World Scientific.

1121 Rothman, L., Jacquemart, D., Barbe, A., Benner, D. C., Birk, M., Brown, L., Carleer, M., Chackerian, C., Chance, K., Coudert, L., Dana, V., Devi, V., Flaud, J.-M., Gamache, R., Goldman, A., Hartmann, J.-M., Jucks, K., Maki, A., Mandin, J.-Y., Massie, S., Orphal, J., Perrin, A., Rinsland, C., Smith, M., Tennyson, J., Tolchenov, R., Toth, R., Auwera, J. V., Varanasi, P., Wagner, G., 2005. The HITRAN 2004 molecular spectroscopic database. Journal of Quantitative Spectroscopy and Radiative Transfer 96 (2), 139–204.

1129 Samuelson, R. E., Maguire, W. C., Hanel, R. A., Kunde, V. G., Jennings, D. E., Yung, Y. L., Aikin, A. C., 1983. CO₂ on Titan. Journal of Geophysical Research: Space Physics 88 (A11), 8709–8715.

1132 Teanby, N., Irwin, P., de Kok, R., Nixon, C., 2009. Dynamical implications of seasonal and spatial variations in Titan's stratospheric composition. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 367 (1889), 697–711.

1136 Teanby, N., Irwin, P., de Kok, R., Nixon, C., Coustenis, A., Bézard, B., Calcutt, S., Bowles, N., Flasar, F., Fletcher, L., Howett, C., Taylor, F., 2006. Latitudinal variations of HCN, HC₃N, and C₂N₂ in Titan's stratosphere derived from Cassini CIRS data. Icarus 181 (1), 243–255.

1140 Teanby, N., Irwin, P., de Kok, R., Nixon, C., Coustenis, A., Royer, E., Calcutt, S., Bowles, N., Fletcher, L., Howett, C., Taylor, F., 2008. Global and
1142 temporal variations in hydrocarbons and nitriles in Titan's stratosphere
1143 for northern winter observed by Cassini/CIRS. Icarus 193 (2), 595–611.

1144 Teanby, N., Irwin, P., Nixon, C., Courtin, R., Swinyard, B., Moreno, R., Lellouch, E., Rengel, M., Hartogh, P., 2013. Constraints on Titan's middle atmosphere ammonia abundance from Herschel/SPIRE sub-millimetre spectra. Planetary and Space Science 75, 136–147.

1148 Teanby, N., Irwin, P., Nixon, C., de Kok, R., Vinatier, S., Coustenis, A., Sefton-Nash, E., Calcutt, S., Flasar, F., 2012. Active upper-atmosphere chemistry and dynamics from polar circulation reversal on Titan. Nature 491, 732–735.

1152 Teanby, N. A., Irwin, P., 2007. Quantifying the effect of finite field-of-view size on radiative transfer calculations of Titan's limb spectra measured by Cassini-CIRS. Astrophysics and Space Science 310 (3-4), 293–305.

1155 Teanby, N. A., Irwin, P. G. J., de Kok, R., Nixon, C. A., 2010. Seasonal Changes in Titan's Polar Trace Gas Abundance Observed by Cassini. The Astrophysical Journal Letters 724 (1), L84.

1158 Teanby, N. A., Vinatier, S., Sylvestre, M., de Kok, R., Nixon, C., Irwin, P., 2016. Titan's south polar stratospheric vortex evolution. In: DPS48, 509.08.

1161 Teolis, B. D., Perry, M. E., Hansen, C. J., Waite, J. H., Porco, C. C., Spencer, J. R., Howett, C. J. A., 2017. Enceladus Plume Structure and Time Variability: Comparison of Cassini Observations. Astrobiology 17 (9), 926–940.
1164 Tomasko, M., Doose, L., Engel, S., Dafoe, L., West, R., Lemmon, M., Karkoschka, E., See, C., 2008. A model of Titan's aerosols based on measurements made inside the atmosphere. Planetary and Space Science 1165
1166
1167 56 (5), 669–707.

1168 Vinatier, S., Bézard, B., Lebonnois, S., Teanby, N. A., Achterberg, R. K., Gorius, N., Mamoutkine, A., Guandique, E., Jolly, A., Jennings, D. E., Flasar, F. M., 2015. Seasonal variations in Titan's middle atmosphere during the northern spring derived from Cassini/CIRS observations. Icarus 1169
1170
1171
1172 250, 95–115.

1173 Vinatier, S., Bézard, B., Nixon, C. A., Mamoutkine, A., Carlson, R. C., Jennings, D. E., Guandique, E. A., Teanby, N. A., Bjoraker, G. L., Flasar, F. M., Kunde, V. G., 2010. Analysis of Cassini/CIRS limb spectra of Titan acquired during the nominal mission. Icarus 205 (2), 559–570.

1177 Waite, J. H., Combi, M. R., Ip, W.-H., Cravens, T. E., McNutt, R. L., Kasprzak, W., Yelle, R., Luhmann, J., Niemann, H., Gell, D., Magee, B., Fletcher, G., Lunine, J., Tseng, W.-L., 2006. Cassini Ion and Neutral Mass Spectrometer: Enceladus Plume Composition and Structure. Science 1178
1179
1180
1181 311 (5766), 1419–1422.

1182 Wishnow, E., Orton, G., Ozier, I., Gush, H., 2007. The distortion dipole rotational spectrum of CH₄: A low temperature far-infrared study. Journal of Quantitative Spectroscopy and Radiative Transfer 103 (1), 102–117.
<table><caption>Table 1: Sets of CIRS FP1 disc-averaged observations analysed in this work. The start and end times are in UTC and Titan radius is the projected angular radius of the solid surface. The sub-spacecraft latitudes and Titan radius are the average of each sequence. TEA stands for Titan Explorations at Apoapse.</caption><thead><tr><th>TEA</th><th>Start date</th><th>End date</th><th>No. spectra</th><th>Sub-spacecraft<br>latitude</th><th>Titan radius<br>(mrad)</th></tr></thead><tbody><tr><td>182-001</td><td>21/02/2013<br>8:31:38</td><td>22/02/2013<br>04:21:23</td><td>712</td><td>-41.43°</td><td>1.64</td></tr><tr><td>202-001</td><td>02/03/2014<br>22:47:21</td><td>03/03/2014<br>11:56:10</td><td>898</td><td>50.73°</td><td>1.69</td></tr><tr><td>206-001</td><td>10/07/2014<br>00:50:30</td><td>10/07/2014<br>12:29:06</td><td>793</td><td>48.58°</td><td>1.67</td></tr><tr><td>219-001</td><td>23/07/2015<br>13:57:21</td><td>24/07/2015<br>01:35:55</td><td>792</td><td>-0.02°</td><td>1.63</td></tr></tbody></table>
<table><caption>Table 2: PACS observations of CH$_4$ and H$_2$O (see also Moreno et al. (2012)) analysed in this work.</caption><thead><tr><th>Gas</th><th>Line<br>(μm)</th><th>Spectral<br>resolution (μm)</th><th>Start date</th><th>Duration<br>(sec)</th><th>Sub-observer<br>lat/lon</th></tr></thead><tbody><tr><td rowspan="3">H<sub>2</sub>O</td><td>66.43</td><td>0.0169</td><td>22/06/2010<br>23:49:52</td><td>3071</td><td>2.10°/283.74°</td></tr><tr><td>75.38</td><td>0.039</td><td>22/06/2010<br>22:56:26</td><td>3079</td><td>2.10°/282.91°</td></tr><tr><td>108.07</td><td>0.1127</td><td>22/06/2010<br>22:56:26</td><td>3079</td><td>2.10°/282.91°</td></tr><tr><td rowspan="2">CH<sub>4</sub></td><td>106.43</td><td>0.1120</td><td>23/06/2010<br>00:43:14</td><td>1140</td><td>2.10°/284.59°</td></tr><tr><td>119.63</td><td>0.1176</td><td>23/06/2010<br>00:43:14</td><td>1140</td><td>2.10°/284.59°</td></tr></tbody></table>
<table><caption>Table 3: A priori profiles considered for the H₂O retrieval (see also Figure 4).</caption><thead><tr><th>Reference</th><th>Name</th><th>Type</th><th>Agreement</th><th>Comments</th></tr></thead><tbody><tr><td>Moreno et al. (2012)</td><td>Sa</td><td>Measured</td><td>Herschel</td><td>Parametrized profile: q = q<sub>0</sub> × (p<sub>0</sub>/p)<sup>n</sup><br>with n the power law index</td></tr><tr><td>Dobrijevic et al. (2014)</td><td>IM1</td><td>Modelled</td><td>Herschel</td><td>Origin H<sub>2</sub>O: micrometeorite ablation<br>OH flux: 5.7 × 10<sup>5</sup> cm<sup>-2</sup> s<sup>-1</sup></td></tr><tr><td>Dobrijevic et al. (2014)</td><td>IM2</td><td>Modelled</td><td>CIRS</td><td>Origin H<sub>2</sub>O: micrometeorite ablation<br>OH flux: 2.6 × 10<sup>6</sup> cm<sup>-2</sup> s<sup>-1</sup></td></tr><tr><td>Dobrijevic et al. (2014)</td><td>IE1</td><td>Modelled</td><td>Herschel</td><td>Origin H<sub>2</sub>O: Enceladus<br>OH flux: 1.4 × 10<sup>6</sup> cm<sup>-2</sup> s<sup>-1</sup></td></tr><tr><td>Lara et al. (2014)</td><td>L1</td><td>Modelled</td><td>Herschel</td><td>Time-dependent model, initial OH flux:<br>5.1 × 10<sup>6</sup> cm<sup>-2</sup> s<sup>-1</sup> + loss to the haze</td></tr><tr><td>Lara et al. (2014)</td><td>L2</td><td>Modelled</td><td>CIRS</td><td>Time-dependent model, initial OH flux:<br>5.1 × 10<sup>6</sup> cm<sup>-2</sup> s<sup>-1</sup> + loss to the haze</td></tr><tr><td>Lara et al. (2014)</td><td>L3</td><td>Modelled</td><td>CIRS</td><td>Time-dependent model, initial<br>OH flux: 1.0 or 2.0 × 10<sup>7</sup> cm<sup>-2</sup> s<sup>-1</sup></td></tr></tbody></table>

<table><caption>Table 4: Retrieved H₂O abundances and associated errors for the different observations analysed. The retrieved abundances are indicated for the two temperature profiles considered in this work. The given ranges describe the results arising from using the different a priori H₂O profiles listed in Table 3. Note that the pressure range is defined using the pressure levels at which the H₂O sensitivity is maximum (based on H₂O Jacobians). The total column of H₂O is calculated above the condensation level. For the comparison, the reported H₂O VMRs for the case using 1.00% of stratospheric CH₄ are given for the same pressure range.</caption><thead><tr><th>Observation</th><th>H₂O VMR<br>(ppb)</th><th>Total error</th><th>Pressure<br>(mbar)</th><th>H₂O total column<br>(molec/cm²)</th><th>H₂O VMR (ppb)<br>if 1.00% CH₄</th><th>Previous retrieved H₂O</th></tr></thead><tbody><tr><td>CIRS 182</td><td>0.120–0.215</td><td>-43%/+44%</td><td>8.2–5.1</td><td>3.5–3.8×10<sup>14</sup></td><td>0.072–0.131</td><td>/</td></tr><tr><td>CIRS 202</td><td>0.080–0.151</td><td>-56%/+57%</td><td>8.2–5.1</td><td>2.3–2.6×10<sup>14</sup></td><td>0.038–0.081</td><td>/</td></tr><tr><td>CIRS 206</td><td>0.059–0.119</td><td>-65%/+65%</td><td>8.0–5.1</td><td>1.7–2.0×10<sup>14</sup></td><td>0.038–0.082</td><td>/</td></tr><tr><td>CIRS 219</td><td>0.054–0.120</td><td>-70%/+78%</td><td>8.2–4.7</td><td>1.6–2.1×10<sup>14</sup></td><td>0.032–0.075</td><td>/</td></tr><tr><td>CIRS NA</td><td>0.058–0.109</td><td>-42%/+44%</td><td>9.6–5.4</td><td>2.0–2.2×10<sup>14</sup></td><td>0.044–0.082</td><td>0.14±0.05 ppb at 10.7 mbar</td></tr><tr><td>PACS</td><td>0.024–0.052</td><td>-15%/+12%</td><td>8.2–5.6</td><td>0.8–0.9×10<sup>14</sup></td><td>0.020–0.030</td><td>0.023±0.006 ppb at 12.1 mbar</td></tr></tbody></table>
<figure><img src="image_4.png" /><figcaption>Figure 1: CIRS and PACS spectra analysed in this work. For display purposes, CIRS disc-averaged spectra have been offset vertically as indicated. H₂O lines, which are used for the retrieval, are identified for CIRS spectra with vertical dashed lines. PACS spectra are expressed in radiance units (µW cm⁻² sr⁻¹ µm⁻¹) as explained in the text.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Figure 2: Main reference atmospheric vertical profiles used to simulate CIRS and PACS spectra: (a) Mole fraction of gases (Niemann et al., 2010), (b) Haze specific density (de Kok et al., 2007b, 2010b; Tomasko et al., 2008). See text for details.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Figure 3: Jacobians of temperature and H₂O (color scales) calculated for disc-averaged observations of CIRS (a,b) and PACS (c,d). The Jacobians of H₂O are calculated for the “IM2” *a priori* profile (see Table 3 and Figure 4). For CIRS, the H₂O lines used in the retrieval are indicated with the vertical black lines.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Figure 4: A *priori* profiles of H₂O considered in this work (see Table 3 for details).</figcaption></figure>
<figure><img src="image_8.png" /></figure>

Figure 5: Example fits to the observed CIRS (set 182 and CIRS NA) and PACS spectra. For CIRS observations, they include the fits of the temperature retrieval, of the continuum and of the H₂O retrieval (considering the “IM2” *a priori* profile). Vertical lines indicate the fitted H₂O lines. For display purposes, the CIRS NA spectrum has been offset vertically as indicated. For PACS, the fits are shown for the H₂O and CH₄ lines analysed (considering the “Sa” *a priori* profile).
<figure><img src="image_9.png" /><figcaption>Figure 6: Retrieved and *a priori* temperature profiles (a-d) and associated averaging kernels functions (e-h) for the four sets of disc-averaged CIRS spectra. The black dashed lines delimit the region of maximum sensitivity to H~2~O (12-1 mbar). For clarity, only one in every two averaging kernel functions until 0.2 mbar are shown. The dots indicate the pressure levels associated to each of these functions and a different colour is associated to each AVK function.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Figure 7: (a) Random error and its standard deviation calculated from retrievals on synthetic spectra. (b) Systematic errors (absolute values) on the retrieved temperature profile associated with the choice of CH$_4$ profile. The black dashed lines delimit the stratospheric region of sensitivity to H$_2$O abundance.</figcaption></figure>
<figure><img src="image_11.png" /></figure>

Figure 8: Temperature retrieval from the CIRS NA spectrum: (a) *A priori* and retrieved profile, (b) AVK functions associated to the retrieved profile, (c) Random errors and its standard deviation calculated from retrievals on synthetic spectra, and (d) Systematic errors (absolute values) on the retrieved temperature profile associated to the choice of CH₄ profile. The black dashed lines delimit the stratospheric region of sensitivity to H₂O abundance.
<figure><img src="image_12.png" /><figcaption>Figure 9: Same as Figure 8 but for PACS observations.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>Figure 10: $\Delta\chi^2(\chi^2 - \chi^2(\text{MF} = 0))$ as a function of the scaling factor applied to the “IM2” H$_2$O *a priori* profile for the CIRS sets 202 (a), 206 (b), and 219 (c). The horizontal dashed line indicates the level of $3\sigma$ detection ($\Delta\chi^2 = -9$).</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Figure 11: Retrieved H₂O VMRs for all observations as a function of latitude, of time (color scale) and of the *a priori* H₂O profile. These VMRs are retrieved using the stratospheric temperature profile determined using 1.48% for the stratospheric CH₄ mole fraction. The circles represent CIRS disc-averaged observations, the upward-pointing triangle the CIRS nadir observation, and the left-pointing triangle PACS observations.</figcaption></figure>
<figure><img src="image_15.png" /></figure>

Figure 12: Comparison between observed PACS H₂O lines (black) and lines simulated using the H₂O profiles retrieved for the different observations (colored lines). The case using the “Sa” *a priori* profile has been considered (the profile has been scaled by the retrieved scaling factors) and using the stratospheric temperature profile determined using a stratospheric CH₄ mole fraction of 1.48%.