# Reflectance study of ice and Mars soil simulant associations – I. H2O ice.

Zuriñe Yoldi1 Antoine Pommerol1 Olivier Poch1,2 Nicolas Thomas1
1Physikalisches Institut, Universität Bern and NCCR PlanetS, Sidlerstrasse 5,
3012 Bern, Switzerland.  2Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble,
France  * Now at the section for the Physics of Ice, Climate and Earth at the
Niels Bohr Institute, University of Copenhagen.

###### Abstract

The reflectance of water ice and dust mixtures depends, amongst other
parameters, on how the components are mixed (e.g. intimate mixture, areal
mixture or coating) (Clark, 1999). Therefore, when inverting the reflectance
spectra measured from planetary surfaces to derive the amount of water ice
present at the surface, it is critical to distinguish between different mixing
modes of ice and dust. However, the distinction between mixing modes from
reflectance spectra remains ambiguous. Here we show how to identify some water
ice/soil mixing modes from the study of defined spectral criteria and colour
analysis of laboratory mixtures. We have recreated ice and dust mixtures and
found that the appearance of frost on a surface increases its reflectance and
flattens its spectral slopes, whereas the increasing presence of water ice in
intimate mixtures mainly impacts the absorption bands. In particular, we
provide laboratory data and a spectral analysis to help interpret ice and soil
reflectance spectra from the Martian surface.

###### keywords:

Reflectance , Water-ice , Mixture , Mars , Frost

††journal: Icaruslabel0label0footnotetext: Formal publication in
Icarus:label1label1footnotetext: https://doi.org/10.1016/j.icarus.2020.114169

##  1 Introduction

Water has played a key role in the early evolution of Mars. It has shaped its
surface at various scales, carving valley networks terminated by deltas, and
producing large outflow channels leading to the shorelines of a putative ocean
that may have covered a significant fraction of the northern hemisphere (Carr
and Head, 2010). Liquid water has also altered the mineralogical composition
of the primordial mafic crust of Mars over depths of kilometres (Bibring et
al., 2006, Ehlmann et al., 2011) and might have made and maintained Mars
habitable during part of its first billion years (Vago et al., 2017). In the
current cold and dry Amazonian climate, water is only present at the surface
and in the close subsurface in the form of ice and as a trace gas in the
atmosphere (Lasue et al., 2013). The evidence for liquid water (Recurring
Slope Lineae) remains controversial (McEwen et al., 2014, Ojha et al., 2015,
Dundas et al., 2017). Ice is nevertheless still thought to play an active role
in the current Amazonian area, the ice being regularly redistributed between
various reservoirs following astronomical forcing of the climate (Head et al.,
2003).

The largest known reservoirs of ice are the permanent polar caps which are
kilometres-thick layered deposits of ice mixed with dust in various
proportions that cover each Martian pole (Smith et al., 2020). A major
difference between the two polar caps is that the northern polar cap is
exposed whereas the southern polar cap is covered by a layer of dust that
masks, almost entirely, the water ice (Bibring et al., 2004, Plaut et al.,
2007). A small permanent cap of CO2 ice is present directly above the south
pole (Thomas et al., 2020). The exposed water ice of the Northern permanent
polar cap is the main source of water vapor which has been found in highly
variable, trace amounts in the martian atmosphere (Smith, 2002). The active
seasonal cycle characterised by the extension and recession of the metre-thick
seasonal polar caps, down to latitudes of $\sim$50∘, is dominated by the
condensation/sublimation equilibrium between atmospheric CO2 and solid CO2 ice
at the surface (Leighton and Murray, 1966). Water ice is only present in low
amounts in the northern hemisphere and at a few locations in the southern
hemisphere but its presence still influences strongly the recession of the cap
in Spring (Appéré et al., 2011, Pommerol et al., 2013).

In addition to the yearly seasonal cycle, the accumulation and sublimation of
surface ice responds to longer term climatic cycles controlled by the periodic
and secular variations of astronomical parameters (Laskar et al., 2004). In
particular, large excursions of the obliquity are responsible for a
redistribution of the ice between the thick, permanent, polar caps observed
today and metre-thick accumulations of dusty ice over significant fractions of
mid- and high-latitudes in both hemispheres (Head et al., 2003, Levrard et
al., 2004). Various morphological features provide evidence of recent
redistribution of water ice to mid-latitudes. These include near-surface
ground ice (Mustard et al., 2001), gullies (Conway et al., 2019), polygons and
other patterned ground (Mangold et al., 2004), viscous flow features (Milliken
et al., 2003), and rocky glaciers (Head et al., 2003). Water ice in the close
subsurface below a thin desiccated layer of dust is found at latitudes
poleward of 60∘ in both hemispheres with a concentration often exceeding 50
wt$\%$ (Feldman et al., 2008).

While geophysical techniques such as neutron spectroscopy (Feldman et al.,
2008) and ground penetrating radar (Plaut et al., 2007) are used to detect and
characterize ice in the subsurface, most of our knowledge about surface ice is
gained by optical remote-sensing. High-resolution visible imaging and infrared
spectroscopy and spectral imaging are techniques of choice to identify water
ice at the surface and decipher some of its properties both from orbit and in-
situ. Visible imaging provides the highest spatial resolution and the contrast
between bright ice and the dark surface at the shortest wavelength makes it
particularly sensitive to ice, even in low amounts. As the seasonal cycle of
volatiles on Mars is dominated by CO2, not H2O, the infrared spectral range is
particularly useful to distinguish H2O from CO2 from their distinctive
spectral features (Langevin et al., 2007b).

Recent examples of detection of ice reservoirs by optical remote-sensing on
Mars include orbital observations of ground ice at mid-latitudes revealed by
recent impact craters (Byrne et al., 2009) and pits with scarps exposing ice
near 55∘N latitude (Dundas et al., 2018). In both cases, the presence of ice
was inferred from high-albedo bluish patches on high-resolution visible images
and confirmed by the observation of diagnostic absorption bands of solid H2O
at 1.5 and 2 µm. The presence of ice at these latitudes could be the result of
the deposition of ice-rich mantling units, possibly as snowfall, in conditions
of higher obliquity.

Water ice has also been observed at the surface by two landed missions: Viking
2 in 1976 (Jones et al., 1979) and Phoenix in 2008 (Mellon et al., 2009). At
48∘N latitude, the Viking 2 camera observed diurnal frost deposited at night
that rapidly sublimed after sunrise. Although the nature of the frost (H2O or
CO2) had initially been debated, surface energy balance calculations show that
this behaviour is only consistent with H2O and not CO2 (Hart and Jakosky,
1986, Svitek and Murray, 1990). At 68∘N latitude, Phoenix used a robotic scoop
to excavate up to 20 cm of dust, revealing below the ice-rich ground first
detected from orbit by neutrons spectroscopy. During late summer, both
snowfall and surface frost were also observed (Smith et al., 2009).

Beyond the detection and identification of ices, either through reflectance
contrast or distinctive spectral fingerprints, optical reflectance data should
also provide information on various properties of the ice itself and its mode
of association to other constituents of the surface. Mars is a dusty planet
and the abundant red oxidized dust transported by the winds contaminates at
various levels all occurrences of ice found at the surface and, over history,
has led to contaminated sub-surface layers. Variable levels of contamination
by dust are for instance responsible for the layering seen in the polar
layered deposits of the permanent polar caps. The variable dust-to-ice ratios
are interpreted in terms of sublimation-condensation equilibrium and hence
past insulation history at the pole. The dust-to-ice ratio in the Martian
subsurface is also key to understanding the origin and emplacement mechanism
of the ice. If the amount of ice is below the open porosity of the regolith,
the ice can have been emplaced by diffusion of water from the atmosphere. If
the concentration of ice is found to be in excess of the porosity however, it
requires a different deposition mechanism such as a snowfall, which has strong
implication for past climate.

The scattering of light by ice and its contaminants is the fundamental
physical process that permits all identification and characterisation by
optical remote-sensing. In all situations investigated in this work, binary
mixtures and associations between H2O ice and dust are considered. If such a
system might seem simple at first glance, a huge level of complexity resides
in the multiple ways the ice and the dust can be associated and the resulting
multiple scattering by the two types of materials. A well-known effect of
mixing ice with a fine-grained dark contaminant is the strong darkening of the
sample, out of proportion with the concentration of the dark contaminant
(Yoldi et al., 2015). This is well studied on the Earth where minute amounts
of fine dark soot particles are known to be able to darken snow considerably
(Yasunari et al., 2011, He et al., 2019).

Despite constant progress over the past decades, physical modeling of the
light scattering process remains difficult, both because of challenges
associated with the physics and its mathematical implementation and because of
the difficulty in describing and representing the complexity of natural
samples. Even for a binary system with water ice as one component and mineral
dust as the other component, calculating the reflectance of the mixture
requires detailed knowledge of various properties of the particles which are
often out of reach in the case of planetary remote-sensing. Laboratory
experiments with well-controlled samples are therefore of considerable value
in testing models and results can also be used for direct comparison with
planetary data.

While spectro-photometric measurements with refractory materials such as rock
or mineral powders abound in the literature and in open databases, good-
quality measurements with icy samples are more difficult to find. The reason
is not merely the need for the measurement equipment to work at low
temperature but rather the challenge to produce the ice-bearing samples in a
reproducible way and characterize them thoroughly. While it is possible to
gain additional understanding of the scattering process by using stable
analogues for ice such as glass beads or other transparent particles (Jost et
al., 2013), the unique properties of the water molecule such as high surface
tension, capillarity… make the interactions between ice and dust unique and
experimentation with actual material necessary.

Clark (1981) has measured the reflectance of red cinder from Mauna Kea spread
over water frost as well as frost grown on the same red cinder and charcoal.
Strong differences between the behaviour at visible and near-infrared
wavelengths are visible as the effect of frost growth is more obvious at the
shortest wavelengths where the reflectance of the cinder is the lowest. Hart
and Jakosky (1986) have used these experimental spectra to estimate the
thickness of frost seen by Viking 2 to 50 µm on the basis of the observed
relative increase of reflectance at 0.8 µm. Unfortunately, spectral data were
restricted to wavelengths greater than 0.65 µm and the blue wavelengths where
the contrast of reflectance is the highest was not covered. In the continuum
of the near-infrared, little change is visible for the red cinder, which is
very bright but strong differences are visible for the charcoal, which
develops a blue slope over the entire spectrum. The asymmetric absorption
bands of water-of-hydration at 1.5 and 2.0 µm progressively become more
symmetric and shift their centres towards longer wavelengths. These data are
very useful to understand the spectral effects of frost growth over two very
different substrates but these substrates are relatively poor analogues of
actual Martian surfaces. Indeed, the Mauna Kea red cinder is brighter than the
brightest Martian surfaces by a factor of two and the charcoal is darker than
the darkest Martian areas by a factor of two and lacks the prominent visible
red slope seen everywhere on Mars.

Clark (1981) and Clark and Lucey (1984) also produced mixtures of the same
dust analogue from the Mauna Kea as well as a clay mineral (kaolinite) and
charcoal with water ice. These mixtures were produced by fast freezing a
suspension of dust particles into liquid water. Roush et al. (1990) modified
the sample preparation protocol by grinding and sieving the dusty ice produced
to isolate particles with a diameter of about 100 µm. The spectral data were
extended to the mid-infrared but lack the visible range ($<$ 0.65 µm).

Pommerol et al. (2013) have measured the bidirectional visible reflectance of
a few plausible analogues for Martian icy surfaces, including frost and frozen
soils. They found that, beyond differences in overall albedo, the different
types of associations between ice and mineral dust result in totally different
angular dependencies of the reflectance.

Yoldi et al. (2015) have shown that two models used in planetary sciences,
(Hapke, 1993, Hiroi and Pieters, 1994), can accurately predict the reflectance
of a mixture of spherical water ice particles and irregular basalt particles,
but only if the properties of the particles are known, including some
parametrization of their complex shape. This study was performed at a single
wavelength however and spectral or colour effects were not studied.

Kaufmann and Hagermann (2015) studied the penetration of solar radiation into
both pure and dust-contaminated snow and pointed out the major role played by
small-scale inhomogeneities in the way light penetrates an ice-dust mixture.

Recently, Gyalay et al. (2019) have measured the reflectance of intimate
mixtures of water ice and JSC Mars-1 in the visible spectral range (400-1000
nm) and use the results to estimate the amount of water ice in the Martian
soils from the images taken in-situ by the multispectral camera of the Phoenix
lander. They reached conclusions about the presence of both pore-filling ice
which diffused into the regolith from the atmosphere and ice in excess of the
porosity which could have evolved from past ice-rich deposits.

Here, we present measured reflectance spectra of different types of
associations between water ice and dust analogues that are relevant for the
different ways in which ice occurs, that have been presented briefly above.
Binary intimate mixtures (i.e. mixtures at the scale of the individual grains)
of granular ice and dust are first-order analogues for the dusty granular ice
which can be found at the surface of the permanent Northern polar cap (the
water-rich annulus around the northern seasonal cap or exposed mid-latitude
icy deposits). We produce these well-characterized samples using the equipment
and protocols developed over a decade at the The Laboratory for Outflow
Studies of Sublimating icy materials (or LOSSy) at the University of Bern
(Pommerol et al., 2019). Here, our approach is similar to the one followed by
Clark (1981) and Clark and Lucey (1984) but our mixtures are actual intimate
particulate mixtures of ice and dust and strongly differ from the frozen
suspensions used by Clark (1981). Our intimate mixtures resemble closely the
ones of Gyalay et al. (2019) with the difference that they use grinded and
sieved ice particles, probably irregular, while we use spherical particles.

In addition to these well-characterized binary mixtures which are ideal for
comparisons with physical models, we produce two additional types of
associations between water ice and dust analogues: frost growing over the
mineral substrates and dust grains embedded into a matrix of ice. We simulate
the process of direct frost growth over cold mineral substrates as analogues
to the diurnal and seasonal frosting occur on Mars. This approach is again
relatively similar to the one adopted by Clark (1981) but we extend the
spectral range to shorter visible wavelengths where the contrast is the
highest and where visible colour cameras can detect the smallest amounts of
frost. We also produce icy soils with their porosity saturated by ice by
freezing wet soils. Although the production process itself is not
representative of any contemporary Martian surface process, the structure of
the resulting samples is probably representative of small Martian icy soils
where the entire porosity has been filled by ice.

Two types of dust analogues are chosen which represent the two end-members of
surfaces found on Mars: bright and red soils and dark basaltic terrains. For
the bright red soils, the widely used JSC Mars-1 Hawaiian palagonite (Allen et
al., 1997) was used. For dark basaltic terrains, powder produced from Hawaiian
basalts identical to the one used by Pommerol et al. (2013) was used.

A versatile VIS-NIR (0.4 - 2.4 µm) hyperspectral imaging system allows us to
produce spectral and imaging data that mimic the ones acquired on Mars by
different colour imagers and imaging spectrometers. Hence, we can assess the
usefulness of various spectral/colour criteria in both spectral ranges and
explore the complementarity between the two techniques. These spectral data
are useful for the direct interpretation of optical remote-sensing of Mars as
well as the calibration and verification of physical models. In addition to
presenting the samples and the spectral data that are also made available in
open databases, we study the behaviour of a range of spectral criteria and
discuss how the different types of associations between ice and dust can be
distinguished and characterized using reflectance spectroscopy and colour
imaging.

##  2 Setup, material and data analysis

###  2.1 Instrument description

All the measurements were made in the Simulation Chamber for Imaging the
Temporal Evolution of Analogue Samples (SCITEAS), at LOSSy. SCITEAS is a
thermal vacuum chamber in which large samples are exposed to low pressure and
temperature conditions (secondary vacuum of 10-6 mbar and samples kept at
about 220 K) if desired. The chamber is equipped with a large quartz window at
the centre of its upper lid, which is used for optical observations of the
surface of the sample. Here, we have used a hyperspectral imaging system to
characterize the surfaces and their evolution. This original spectral imaging
system is made of two cameras, a CCD (silicon Charge Coupled Device) camera
for the visible spectral range (0.4-1 µm) and an MCT (Mercury Cadmium
Telluride) for the near-infrared range (0.8-2.5 µm). The difference of
resolution between the 1392 x 1040 pix VIS camera and 320 x 256 pix NIR camera
mimic the typical differences of resolutions between visible colour imagers
and infrared imaging spectrometers on-board planetary missions. The scene is
illuminated by a monochromatic light source made of a QTH (Quartz Tungsten
Halogen) lamp coupled to a multiple-gratings monochromator and a large fiber
bundle pointed at the sample. The spectral resolution is controlled by the
opening of two slits at the entrance and exit of the monochromator while the
spectral sampling can be commanded to any arbitrary value larger than 1 nm. We
refer to the spectral products as hyperspectral when the sampling is higher
than the resolution (the spectrum is fully covered with overlapping
bandpasses) and as multispectral when the sampling is lower than the
resolution (discrete non-overlapping bands are selected through the spectrum).

Multi- or hyperspectral cubes are acquired by sequentially changing the
bandpass of the monochromator and then taking an image with one or both
camera(s). A full description of an early version of the instrument can be
found in Pommerol et al. (2015). Compared to this earlier description, the
setup has been improved to increase the spectral resolution, which is now 7 nm
in the visible and 15 nm in the near-infrared. This optimisation of the Full
Width at Half Maximum (FWHM) of the monochromator bandpass led to a decrease
of 50$\%$ of the incident luminous flux, which we compensated for by
optimising the exposure time of the cameras for each wavelength. To further
enhance the signal-to-noise ratio (SNR) of the measurements, we have
implemented an image averaging system. Hence, we average three pictures per
wavelength in the visible and a hundred of pictures per wavelength in the
near-infrared.

As noted in Pommerol et al. (2015), the level of the dark signal of the NIR
camera is significantly influenced by room temperature. We have mitigated this
impact by increasing the frequency of acquisition of dark images, which allows
us to track the fluctuation of the temperature of the room. We interpolate the
dark images, and we subtract the level of dark from the signal during the
calibration of the data. This set of improvements has enhanced our SNR to 400
in optimal cases (i.e. bright and dry samples), as shown already in El-Maarry
et al. (2015).

Unfortunately, the modifications implemented to improve our spectral
resolution, sampling and SNR have boosted the time needed for the acquisition
of a cube, which was an average of 20 minutes in 2015 Pommerol et al. (2015).
With the configuration used in this study, the acquisition of a cube lasts 70
minutes. To slow down the evolution of ice during this time, we cool the
sample down radiatively. This is achieved by maintaining a continuous
circulation of liquid nitrogen through a cylindrical shroud that surrounds the
sample holder at a distance of 20 mm.

The conditions of temperature and pressure at which each experiment was
performed are specified in Table 1.

####  2.1.1 Light geometry

We have performed the measurements at an incidence angle of about 20∘ and an
emission angle of 30∘. The phase angle is of about 50∘ in the visible and 10∘
in the near-infrared (Pommerol et al., 2015). We do not expect significant
variations in the reflectance resulting from these different phase angles
(Yoldi et al., 2015).

####  2.1.2 Frost condensation on the samples

The protocols developed at LOSSy guarantee frost-free intimate mixtures.
Nevertheless, between the insertion of the sample holder into SCITEAS and
reaching stable conditions within the chamber, the samples and sample holder
can cold-trap atmospheric water. If the experiments are performed under low-
pressure conditions, frost sublimates. Otherwise, it condenses again on the
shroud as the samples and sample holder get warm.

####  2.1.3 Ice sublimation from the samples

The cooling system of SCITEAS is not powerful enough to stop the sublimation
of surface-ice in every case, especially when working at low-pressure
conditions. Sublimation decreases the ice-to-dust ratio of the first
micrometres of the sample; the depths from which light scattering occurs in
this spectral range. As a precaution, the concentrations of water ice in the
SPIPA-B and dark basalt intimate mixtures should, therefore, be considered as
upper limits.

While working on developing protocols to avoid this scenario, we have found a
temporary solution in turning SCITEAS into a multispectral imager, that is, an
imager with larger spectral sampling than resolution. In this configuration,
we select strategic wavelengths (e.g.on the continuum and on absorption bands)
at which we measure the reflectance instead of covering the whole spectral
range with small steps between wavelengths. Hence, the acquisition time of
each spectrum is reduced from 70 to 5 minutes. In this study, we have used
this procedure with the frozen soils samples, the reflectance of which has
been measured at the following wavelengths (in µm) : 0.490, 0.670, 0.835,
0.985, 1.348, 1.402, 1.438, 1.498, 1.582, 1.624, 1.702, 1.852, 1.990, 1.996,
2.098 and 2.200.

###  2.2 Data processing

The physical calibration of the spectral data allows us to convert the raw
camera units into reflectance factor (REFF) units, according to the definition
of Hapke (1993). This reflectance unit is also generally referred to as
I/F.cos i in the remote sensing community. According to this definition, a
perfect lambertian surface would have a constant reflectance factor REFF=1
independent of the incidence, emission and phase angles. The calibration
procedure consists of acquiring regularly, before and/or after the measurement
of actual samples, similar measurements (same cameras settings, spectral
ranges and sampling, sample position) with a large surface of SpectralonTM
(Labsphere) covering the field-of-view of the camera. This material shows a
nearly Lambertian behaviour and a constant hemispheric reflectance of 0.99
over the VIS-NIR spectral range. The raw data acquired with the sample are
then divided pixel-per-pixel and for every wavelength by the corresponding raw
data acquired with the Spectralon surface. On average, it is enough to acquire
one calibration cube per day to correct for most artefacts arising from the
monochromator.

A major issue with infrared MCT sensors in general, and our NIR camera in
particular, is the high and variable thermally generated dark signal. We have
mitigated this issue by installing a motorized shutter on the monochromator.
Regularly during the measurements of the spectral cubes, dark images are
acquired by shortly closing the shutter to acquire dark images with the exact
same settings as the actual images. Temporal interpolation between the
measured darks and pixel-per-pixel subtractions are then performed to correct
the variations of the dark signal. This procedure is very efficient in the
conditions that dark images are acquired and is usually sufficient to
represent accurately the variations of the dark current.

A detailed explanation of this process is given in Pommerol et al. (2015). The
only significant addition to the procedure is a correction for the small
absorption of SpectralonTM around 2.1-2.2 µm (Zhang et al. (2014)).

The calibration procedure outputs a hyperspectral reflectance cube in which we
define Regions of Interest (ROIs) to extract averaged reflectance spectra from
specific areas. The ROIs are defined trying to include as much of the sample
as possible, without touching the pixels corresponding to the sample holders.

####  2.2.1 Uncertainties

Even though dividing the sample cube by a reference removes systematic errors,
other sources of uncertainties are not accounted for. Some of these sources
are the read-noise of the cameras, changes in the illumination of the sample
or reference cubes due to an unexpected behaviour of the monochromator (such
as partial blocking of filters or gratings), multiple reflections between the
sample and the quartz window (generating ghosts and straylight) and the
uncertainties related to the calibration procedure (e.g. positioning or
cleanliness of the reference).

To assess the precision and accuracy of our measurements, our sample holders
contain -along with the samples- a small SpectralonTM (Labsphere) calibration
target.

To assess the precision of our measurements, we compare the reflectance
spectra of each pixel within a ROI with the spatial variation of the mean
spectra of that ROI (that is, we compute a standard deviation within each
ROI). We average the results to obtain a relative error of 0.3$\%$ in the VIS
and a 2$\%$ in the NIR, that is, signal-to-noise ratios (SNRs) of 333 and 50,
respectively.

A part of this noise is photon noise and varies as the square root of the
signal that is proportional to the reflectance of the sample. Another fraction
of the noise, such as read noise, is independent of the reflectance of the
sample. Assuming as the worse case that the entire error found with the white
reflectance target is due to photon noise, we can extrapolate to the
observations of darker samples. With a reflectance of 0.1, the SNR drops to 95
in VIS (relative error of 1$\%$) and 16 in NIR (relative error of 6$\%$).

These values apply to individual pixels. When pixels are averaged within a ROI
however, the photon noise decreases proportionally to the square root of the
number of pixels within the ROI. The number of pixels that we average depends
on the size of our samples. On average, our ROIs have 9000 pixels in the VIS
(with a minimum of 1150 pixels and a maximum of 30000) and 800 in the NIR
(with a minimum of 100 pixels and a maximum of 3000). The SNRs of our
measurements increase in average to almost 10000 in the VIS and 500 in the
NIR.

We assess the accuracy of our measurements by comparing the theoretical
reflectance of the references with our measurements. When performing this
analysis with a set of 10 measurements, we observe 6$\%$ of variability with
the visible camera and 3$\%$ with the near-infrared. These values do not
appear to be dependent on the signal as they show no variability with
wavelength and hence the level of the signal.

Accuracy limits, mostly, the uncertainty of our reflectance measurements.
Nevertheless, the SNR and absolute accuracy have very different implications
on our spectral analyses. Many spectral criteria used are relative criteria,
where ratios between wavelengths of the same spectra are computed (slopes,
band depths, etc., see Section 2.2.2). As the main limitations of the absolute
accuracy (illumination homogeneity and stability) are multiplicative factors
in terms of reflectance and affect all wavelengths in the same way, relative
spectral criteria are independent on the absolute accuracy and are only
influenced by the SNR.

####  2.2.2 Spectral analysis

We perform a qualitative evaluation of the reflectance spectra by analysing
the reflectance of the continuum, the spectral slopes of the spectra, and the
shape and depth of the absorption bands. We also conduct a colour analysis
based on the spectral response of the Colour and Stereo Surface Imaging System
(CaSSIS) (Thomas et al., 2017).

##### Reflectance of the continuum

Since H2O ice shows a high albedo in the visible range, the first signature to
examine when looking for ice is the overall brightness of the soil. Some Mars-
related studies use 1.08 µm (Langevin et al., 2007a, Appéré et al., 2011) as
the wavelength of reference to study the reflectance of the soil. This choice
is made for both scientific (e.g. the atmosphere shows a transmittance window)
and technical reasons (e.g. the instrument used to look at the surface has a
high SNR at that wavelength). In this study, we use the same wavelength for
comparison purposes. Because of our 0.006 µm-sampling in this range, the exact
wavelength used as a reference for the continuum is 1.078 µm. The maximum
relative uncertainty of these measurements is 3$\%$.

##### Band depth

Several parameters control the strength of the absorption bands (Pommerol and
Schmitt, 2008). The main influences are the shape and size of the ice grains
and the amount of ice present on the surface.

The definition of band depth is not unique and affects the derived values
(Pommerol and Schmitt, 2008). To refer to a particular way of assessing the
depth of the absorption bands and to avoid a sense of absoluteness, some
authors use the term H2O index (Langevin et al., 2007b, Brown et al., 2014).
This term can only be understood with the formula used to define it. For
comparison purposes, we work with formulae already in use by other authors.

To assess the water index around 1.5 µm, we use the formula proposed by
Langevin et al. (2007a), often employed in Martian spectrometry studies
(Appéré et al., 2011, Pommerol et al., 2011, Brown et al., 2014) and
reproduced in Equation 1.

$Water\>index(1.5\>\mu m)=1-\frac{R(\lambda_{0})}{R(\lambda_{1})^{0.7}\times
R(\lambda_{2})^{0.3}}$ (1)

In this formula, the shoulders of the bands are fixed at $\lambda_{1}$ = 1.385
and $\lambda_{2}$ = 1.772 µm, since those wavelengths present weak atmospheric
CO2 signatures. Using the sampling of SCITEAS, we have set the shoulders at
$\lambda_{1}$ = 1.384 and $\lambda_{2}$ = 1.774 µm. For the 2.0 µm-index, we
work with the definition proposed by Massé et al. (2008) and reproduced in
Equation 2.

$Water\>index(2.0\>\mu m)=1-\frac{R(\lambda_{0})}{\frac{W_{1}}{W}\times
R(\lambda_{2})+\frac{W_{2}}{W}R(\lambda_{1})}$ (2)

Where $\lambda_{1}$ = 1.834, $\lambda_{2}$ = 2.248 µm, W=($\lambda_{2}$ \-
$\lambda_{1}$), W1=($\lambda_{0}$ \- $\lambda_{1}$) and W2=($\lambda_{2}$ \-
$\lambda_{0}$). For both formulae, $\lambda_{0}$ refers to the position of the
reflectance minimum within the band (that is, not at 1.5 and 2.0 µm
systematically).

To assess whether a band is present, we trace the continuum (as a line)
between the previously mentioned shoulders: if the majority of the reflectance
points between the shoulders fall under that linear fit, then we assume the
existence of a band.

Figure 1: (Comparison of the water indexes obtained by assessing them at 1.5
µm (y-axis) and the minimum of reflectance of the band (x-band). The grey line
indicates the perfect correlation.

The shifts of the positions of the minima of the bands introduce errors in the
evaluation of the water indices when assessed at 1.5 and 2.0 µm instead of at
the minimum of reflectance in hydrated minerals. Figure 1 shows that this only
happens when there is not enough water ice to shift the band towards 1.5 and
2.0 µm, that is, in the experiments with frost. From Figure 1 we deduce that,
in the worst case scenario, measuring the water index at 1.5 µm can lead to
underestimates of their values by up to 50$\%$.

The uncertainty in the derived depth of a band propagates from the
uncertainties on the reflectance values used in its calculation. As the band
depth is defined as a ratio of two values of reflectance, the relative
uncertainty of the band depth is equal to the sum of the relative
uncertainties of the two values of reflectance used in the calculation. The
absolute accuracy, that affects the entire spectra with a multiplicative
factor and independent on the wavelength, does not affect the band depth. The
uncertainty on the band depth is therefore only affected by the SNR.

##### Position of barycentre of the bands

Adding hydrated minerals to pure water ice introduces an asymmetry into the
absorption band of water at 2.0 µm (Horgan et al., 2009), and a shift in the
positions of the minima of both bands at 1.5 µm and 2.0 µm. We have evaluated
the shift of the shape of the bands by tracking their barycentres (a.k.a.
centroids).

To define the barycentre, we first define the continuum as a straight line
between the shoulders of a band. Then, we apply Equation 3, where stands for
the wavelength, RC() is the reflectance of the continuum at that wavelength
and R() is the reflectance measured at that wavelength. We have used the same
shoulders as for the calculation of the band depths: 1.384 and 1.774 µm for
the absorption band at 1.5 µm, and 1.834 and 2.248 µm for the band at 2.0 µm.

$Barycentre=\frac{\sum_{i=0}^{n}\lambda_{i}(R_{C}(\lambda_{i})-R(\lambda_{i}))}{\sum_{i=0}^{n}(R_{C}(\lambda_{i})-R(\lambda_{i}))}$
(3)

##### Spectral Slope

We have determined the relative spectral slope of our samples both in the
visible and in the near-infrared following Equation 4.

$S_{r}=\frac{R_{\lambda_{2}}-R_{\lambda_{1}}}{R_{\lambda_{1}}(\lambda_{2}-\lambda_{1})}\times
10^{4}\quad\quad(\%/100nm)$ (4)

$\lambda_{1}$ and $\lambda_{2}$ have been set to 0.445 and 0.745 µm in the
visible and 1.1 and 1.7 µm in the near-infrared. R${}_{\lambda_{1}}$ and
R${}_{\lambda_{2}}$ refer to the values of reflectance at $\lambda_{1}$ and
$\lambda_{2}$ respectively.

As for the band depth calculation, the relative uncertainties are therefore
only affected by the SNR.

####  2.2.3 Colour analysis

Figure 2: CaSSIS colour composites of Figure 5d, that is, JSC Mars-1 frozen
soils. Labels refer to the size fraction of JSC Mars-1. a) NIR-RED-PAN
composite b) RED-PAN-BLU composite.

CaSSIS is the high signal-to-noise ratio (SNR) camera on board ESA’s Trace Gas
Orbiter (TGO). TGO follows a non-Sun-synchronous orbit around Mars. This type
of orbit allows us to observe diurnal phenomena, and therefore is of
particular interest for frost detection. For this reason, we use as colours of
reference CaSSIS’ four bands BLU, PAN, RED and NIR (which have their nominal
effective centre at 485, 675, 840 and 985 nm respectively (Thomas et al.,
2017)).

We have convolved the signal measured from our samples with the spectral
response of CaSSIS to obtain a colour image of our sample as it would have
been seen by CaSSIS. All technical and calibration details of CaSSIS needed to
convolve our signal have been published in Roloff et al. (2017). Below, we
explain the steps taken to simulate what we have called the CaSSIS colours.

  1. 1.

We first scale the solar radiance to an average Sun-Mars distance of 1.52 a.u.
Then, we multiply it by the cosine of the simulated incidence angle (we have
chosen i=60∘), the angular aperture of the telescope (i.e, 0.023 rad) and by
the area of the primary mirror, which has a radius of 0.07 meters.

  2. 2.

We divide the total power received by the sensor by the number of pixels and
multiply it by the exposure time.

  3. 3.

The previous result is divided by the throughput of the telescope, whose
spectral characteristics are determined by the reflectivity of the mirror. The
number of photons received is converted to electrons through the quantum
efficiency.

  4. 4.

For each colour filter, we calculate the instrument spectral response and the
electrons we would detect for a lambertian white surface (maximum amount of
electrons).

  5. 5.

We multiply the VIS-NIR reflectance measured with SCITEAS with the spectral
response of each filter and normalise it by the maximum amount of electrons
(analogue to Lambertian surface) to have units of REFF. We can now produce
colour images such as the ones in Figure 2, which shows NIR-RED-PAN and RED-
PAN-BLU CaSSIS composites of the JSC Mars-1 frozen soils shown in Figure 5d.

  6. 6.

We extract the reflectance in a filter of a given area by defining ROIs, as
performed for the spectral analysis. The different BLU/PAN/RED/NIR signals can
be combined to retrieve different band ratios.

In order to assess the uncertainties of the CaSSIS colours, we have proceeded
in the same way as in Section 2.2.1, that is, we have analysed the reflectance
of the reference sample (Spectralon) in the BLU, PAN, RED and NIR products. On
average, we have obtained an uncertainty in the precision and accuracy of
4.5$\%$ and 0.58$\%$ respectively. With a mean of 9000 pixels averaged per
ROI, the SNR of the derived colours is over 500, for both bright and dark
samples.

###  2.3 Samples

Figure 3: Soil simulants used in the experiments of this study. a) Optical
microscope image of JSC Mars-1 b) SEM image of JSC Mars-1 (80-200 µm fraction)
reproduced from Brouet (2013) c) Reflectance spectra of the size distributions
of JSC Mars-1 d) Optic microscope image of dark basalt e) SEM image of dark
basalt, acquired in the Institute of Geography of the University of Bern f)
Reflectance spectra of the size distributions of the dark basalt. Stars
indicate artefacts from the calibration process.

####  2.3.1 Martian analogues

JSC Mars-1 is the Martian regolith simulant distributed by NASA Johnson Space
Center (see Figure 3, left). As explained in Allen et al. (1997), JSC Mars-1
is the $<$1 mm fraction of weathered volcanic ash from Pu’u Nene, a cinder
cone on the Island of Hawaii. Even though JSC Mars-1 matches the visible and
near-infrared reflectance spectra of the bright regions of Mars, it is more
hydrated than actual Martian soil (see Figure 1 in Allen et al. (1997)). In
terms of particle size, JSC Mars-1 ranges from 1000 µm down to less than 20 µm
(Allen et al., 1997). To vary the size of grain of JSC Mars-1, we dry sieved
it to obtain four distribution sizes: particles bigger than 400 µm; particles
between 200 µm and 400 µm; particles between 100 µm and 200 µm, and particles
smaller than 100 µm. From now on, we will refer to these size fractions as
$>$400 µm; [200,400] µm; [100,200] µm and $<$ 100 µm respectively. Figures 3a,
3c and 3d show optical and scanning electron microscope images of non-sieved
JSC Mars-1 —extracted from Brouet (2013)—, as well as the reflectance spectra
of the different size distributions. Only the smallest size distribution shows
a noticeable rise in reflectance; up to 50$\%$ in the near-infrared. The
reflectance of the original size distribution is lower than the one of the
sieved fractions, which may be due to different preparations of the samples,
as already studied by Pommerol et al. (2013). The reflectance we measured
agrees with the one published therein.

Other regions of Mars show lower albedo along with a basaltic composition
(Bandfield, 2002, Christensen et al., 2003, Bibring et al., 2005, Poulet et
al., 2007). We have therefore used, as a second analogue, a dark, basaltic
sample. This sample was collected from active dunes in the Ka’u Desert region
in Hawaii by C. Okubo and will be further on referred to as dark basalt. More
information about this material can be found in Pommerol et al. (2013).

We sieved the sample to obtain the same size distributions used with the JSC
Mars-1, that is, $>$400 µm; [200,400] µm; [100,200] µm and $<$ 100 µm. Figures
3d, 3e and 3f show optical and scanning electron microscope images of the non-
sieved dark basalt, together with the reflectance spectra of the different
size distributions.

####  2.3.2 Ice

Figure 4: Water ice used in the intimate mixtures. a) and b) Pictures of
SPIPA-A (left) and -B (right) in a sample holder c) and d) Cryo-SEM images of
SPIPA-A (left) and -B (right) acquired at the CSEM (Switzerland) e) and f)
Reflectance spectra of SPIPA-A (left) and -B (right)

We have used the Setups for Production of Icy Planetary Analogues (SPIPA) at
LOSSy (Pommerol et al., 2019) to produce the particulate water ice used in the
preparation of intimate mixtures. In this study, we have used two grain
distributions, which will be referred to as SPIPA-A and SPIPA-B. SPIPA-A are
spherical water ice particles with a mean diameter of 4.5 µm and a standard
deviation of 2.5 µm, while SPIPA-B consists of particles that have a mean
diameter of 67 µm with 31 µm of standard deviation. Both SPIPA ices were
produced by freezing nebulised, deionised water. We obtained different size
distributions by using two different systems to nebulise the water. For
details on the preparation of the SPIPA ices, see Pommerol et al. (2019). The
diameters of the ice particles have been measured from cryo-scanning electron
microscope (cryo-SEM) images. Surface water ice on Mars is expected to be in
the micron range (Cull et al., 2010), except for the ice grains in the polar
caps, which can be millimeter sized (Barr and Milkovich, 2008). Figures 4a and
4b show pictures of sample holders filled with SPIPA A and B. Figures 4c and
4d show cryo-SEM pictures of both type of ices. Finally, we show in Figures 4e
and 4f the reflectance spectra of the pure samples.

####  2.3.3 Ice-dust mixtures.

Figure 5: Optical images of some of the mixtures characterised in this study.
a) JSC Mars-1 and SPIPA-A intimate mixtures. The weight percentage of water
ice is indicated next to each sample. The picture with 50 wt$\%$ ice shows a
shadow; the mixture is homogeneous b) Frost over intimate mixtures of Dark
Basalt and SPIPA-B ice. The weight percentage of water ice contained in the
intimate mixtures is indicated next to each sample c) Step 3 of frost
deposition on different size distributions (indicated next to each sample) of
dark basalt d) Frozen soils of different size distributions (indicated next to
each sample) of JSC Mars-1 after 17h of sublimation. The ice of the bottom
left sample holder has sublimated, revealing the dust underneath, which
appears on the picture as a bright rectangle.

We have produced three different types ice-dust mixtures: frost, intimate
mixtures, and frozen soils. A view of the samples can be found in Figure 5.

Mixing
Mode |  Water ice |  Regolith Simulant |  Size of
regolith |  Ice
Content |  Acquisition
mode |  Time of acquisition |  TShroud
(K) |  P
(mbar)
---|---|---|---|---|---|---|---|---
Frost Deposition |  Condensed atmospheric
water |  JSC Mars-1 |  $>$400 µm |  See
Table 2 |  Hyperspectral
0.4-2.4 µm |  Step 1: 10 min condensation \+ 70 min measurement Step 2: Step 1 \+ 10 min cond. \+ 70 min measurement Step 3: Step 2 \+ 10 min cond. \+ 70 min meas. |  $\sim$110 |  1000
[200,400] µm
[100,200] µm
$<$100 µm
Dark
Basalt |  $>$400 µm |  $\sim$100
[200,400] µm
[100,200] µm
$<$100 µm
Intimate mixture |  SPIPA-A |  JSC Mars-1 |  71.7$\%>$ 150µm 28.3$\%<$ 150µm1 |  10wt$\%$,35wt$\%$ 50wt$\%$,75wt$\%$ |  Hyperspectral 0.4-2.4 µm |  70 min |  $\sim$90 |  $\sim$20
SPIPA-B |  JSC Mars-1 |  10wt$\%$,35wt$\%$ 50wt$\%$ 75wt$\%$ |  $\sim$100 |  $\sim$20
Dark Basalt |  50$\%>$ 109µm
50$\%<$ 109µm |  35wt$\%$,50wt$\%$ 75wt$\%$ |  $\sim$120 |  $\sim$1
Intimate mixture \+ Frost |  SPIPA-B + Atmospheric water |  Dark Basalt |  50$\%>$ 109µm 50$\%<$ 109µm |  35wt$\%$ \+ Frost 50wt$\%$ \+ Frost 75wt$\%$ \+ Frost |  Hyperspectral 0.4-2.4 µm |  70 min |  $\sim$120 |  1000
Water saturated Frozen soil |  Slab |  JSC Mars-1 |  $<$100 µm |  87wt$\%$ |  Int.1: x3 Hyper
Int.2: x2 Hyper
Int.3: x4 Hyper
Int.4: x1 Hyper |  Int.1: 0-3h
Int.2: 4-7h
Int.3: 9-14h
Int.4: 17h |  Int.1: 90-140 Int.2: 160 Int.3: 220-260 Int.4: 280 |  Int.1:70-2e-4 Int.2: 2e-4 Int.3:0.01-0.03 Int.4: 2
Dark
Basalt |  $<$100 µm |  90wt$\%$ |  Int.1: x2 Hyper
Int.2: x4 Multi
Int.3: x4 Multi
Int.4: x4 Multi
Int.5: x2 Multi |  Int.1: 0-3h
Int.2: 3-3.5h
Int.3: 3.5-4h
Int.4: 4-4.5h
Int.5: 4.5-4.6h |  Int.1: $\sim$125
Int.2: 150-190
Int.3: $\sim$195
Int.4: 195-210
Int.5: 210-235 |  Int.1: 70-4e-4
Int.2: 5e-4
Int.3: 6e-4
Int.4: 6e-4-0.01
Int.5: 0.015
Table 1: Summary of the composition, concentrations, mixture types and
acquisition conditions of the experiments reported in this study. The
abbreviation Int. stands for interval. 1(Allen et al., 1997)

##### Intimate mixtures

In intimate mixtures, the grains of the end-members are mixed to the particle
scale (Poch et al., 2016a). At LOSSy, we work with protocols designed to
obtain homogeneous and reproducible mixtures that have already been shown to
be successful in studies such as Yoldi et al. (2015) and Poch et al. (2016a,
b). These papers also provide detailed information about the mixing procedure.
In summary, both materials are blended with the help of a vortex mixer while
they are repeatedly plunged into liquid nitrogen to avoid sublimation and
metamorphism of ice during the process.

Because porosity influences the reflectance of the samples, we always fill the
sample holders without compressing the samples: the sample holders are first
overfilled and then the excess is removed with a spatula. In this way, we
obtain non-compacted samples with flat surfaces. For reference, the porosity
of non-compacted SPIPA-A ice is 80.6 $\pm$ 0.9 $\%$ and the one of non-
compacted SPIPA-B, 49.3 $\pm$ 1.4 $\%$ (Brouet et al., 2016).

We have found difficulties, however, in mixing the dark basalt with SPIPA-A;
we could not combine the dark basalt homogeneously with such small ice
particles because the basalt tended to group in conglomerates. We also noticed
rapid warming of the dark basalt grains, probably caused by their low albedo,
which provoked the sublimation of the surface ice before the entire
acquisition of the hyperspectral cube. This problem appeared as well when
producing intimate mixtures of dark basalt with only 10 wt$\%$ of SPIPA-B. For
that reason, neither intimate mixtures of dark basalt with SPIPA-A nor with a
10 wt$\%$ of SPIPA-B are shown in this study.

Figure 5a shows four sample holders filled up with intimate mixtures of JSC
Mars-1 and SPIPA-A. The sample holders are rectangular containers of
dimensions 2x4x1 cm. The different contents of ice, ranging from 10 wt$\%$ to
75 wt$\%$, are indicated next to each sample holder. An overview of the ice-
to-dust ratios of the mixtures analysed in this paper is given in Table 1.

Figure 6: Sample holder to cold-trap frost. The sample holder consists of two
pieces; a) a cylinder that contains liquid nitrogen and b) the cover of the
cylinder pierced by a copper piece. c) Put together, the copper disks are
plunged into liquid nitrogen. The powder is spread in the blue part in c),
which remains cold enough for atmospheric water to condense on it. d) Example
of frost condensing over the JSC Mars-1 powder in contact with the copper
surface. An insulating black foam covers the rest of the remaining metallic
surface.

##### Water Frost

Throughout this study, we refer to frost as the low-density, fresh ice that
results from both the direct condensation of atmospheric water onto a cold
surface and the deposition onto a surface of ice particles condensed in the
atmosphere above the surface. To simulate the appearance of frost onto a
granular surface, we have designed and constructed a sample holder that allows
cold-trapping of atmospheric water onto a specific surface.

The sample holder consists of two parts (Figure 6). The first part is a
cylindrical container made of aluminium (Figure 6a). The second part is the
container’s cover, coloured in pink in Figure 6b. This cover is perforated by
a rectangular, copper-made piece, coloured in blue in Figure 6b. Above the
cover, the copper piece is a cuboid of 8x6x2 cm. Below the cover, the cuboid
vertebrates an array of discs. To create a cold trap, we fill up the cylinder
(Figure 6a) with liquid nitrogen and cover it with the element shown in Figure
6b, bringing the copper element (coloured blue in Figures 6b and 6c) in
contact with the liquid nitrogen. As a result of the high thermal conductivity
of copper and the large contact surface of the copper discs with the liquid
nitrogen, the entire copper element is kept at very cold temperatures. Hence,
the exposed part of the copper element remains below 220 K for an hour when in
contact with an atmosphere at around 290 K. Figure 6c shows the sample holder
once its two parts are mounted together. We then spread the dusty sample over
the copper surface in layers of about 2 mm to ensure good thermal contact of
the dust and the surface, minimising thermal gradients inside the layer. We
cover the rest of the sample holder with an isolating foam to make sure that
water condenses preferentially on the sample in contact with the metallic
surface (black area in Figure 6d). 3D model files of this sample holder are
available to share under request.

When we insert the sample holder into our simulation chamber, we use the lid
of the chamber to control the deposition of frost; we open the lid to expose
the sample to the atmosphere and close it to limit the water vapour available
to condense. Because of the constant sublimation of liquid nitrogen from
inside the sample holder, the atmosphere around the surface remains totally
dry when the lid is closed and very dry when the lid is open as the sublimated
nitrogen expands into the atmosphere of the lab, leaving only minute amounts
of water vapor to reach the cold surface. This limits the frost growth rates
to very low values and mimics the Martian situation with a very cold surface
and very dry atmosphere, although the major inert gas is nitrogen in the lab
and CO2 on Mars. Away from the simulation chamber, the atmosphere of the lab
has an average relative humidity of $\sim$30$\%$ and temperature of 293 K.

In this article, we show several steps of frost deposition on the samples;
each step equates to ten minutes of exposure to the atmosphere followed by the
acquisition of a hyperspectral cube. Figure 5c shows the state of the
different size distributions of dark basalt after the third step of
deposition.

The amount of frost that condenses on a sample at a given pressure depends on
the conditions of humidity in the room and the temperature of the sample,
which in turn depends on the properties of the material (heat capacity and
grain-size). Thus, when we expose different size fractions of the same
material to the atmosphere, not every size fraction necessarily cold-traps the
same amount of water. Therefore, in this study, it is more straightforward to
compare spectra of different steps of frost deposition on a single size
distribution than it is to compare the same deposition-steps between different
size distributions.

With the current setup of SCITEAS, we do not have the means of quantifying the
amount and thickness of frost condensed onto the samples, especially during
early stages of deposition. The 10 minutes of exposure were chosen because
this duration produces a small but recognizable change of albedo by eye. The
results of Clark (1981) however, offer us a possibility to estimate indirectly
the thickness of frost deposited. Indeed, Clark (1981) measured both the frost
thickness and the near-infrared spectra of two samples for several steps of
frost deposition. The samples, red cinder from Mauna Kea and charcoal have
high contrast in albedo. The analysis of these data show that for the first
two to three depositions of frost (first 100 to 150 µm of frost), the band
depth at 2 µm shows a nearly linear relation with frost thickness, independent
of the nature and albedo of the sample. As our two analogues fall in between
the samples studied by Clark (1981) in terms of albedo and colour, we assume
that this relation is also true for our samples and apply it to estimate our
deposited frost thickness (Thickness [µm] = 3.2 + 412.9 x BD(2 µm), where BD(2
µm) stands for the band depth at 2 µm). Note that as our thickness estimates
rely entirely on the results of Clark (1981), they should not be considered as
a confirmation of the previous work or as a new way of relating the spectro-
photometric data to the frost thickness. For future experiments, an
independent way of measuring accurately the thickness of the frost to verify
this relation, as well as other properties of the frost layer such as density,
texture… would be highly desirable.

Interestingly, no particular trend between deposited frost thickness and
particle size of the substrate was observed for our two samples. To reduce the
dispersion in values, we therefore averaged all four size fractions to obtain
the averaged estimates of deposited frost thickness shown in Table 2. Given
the uncertainties and potential differences in the procedures used by Clark
(1981) and our own procedures, these values should be considered as indicative
estimates rather than precise data.

Sample | First Step | Second Step | Third Step
---|---|---|---
JSC Mars-1 | 14 $\mu$m | 33 $\mu$m | 50 $\mu$m
Basalt | 13 $\mu$m | 52 $\mu$m | 75 $\mu$m
Basalt + SPIPA-B | 80 $\mu$m | – | –
Table 2: Averaged estimates of deposited frost thickness onto different
samples.

We also present in this study reflectance measurements of intimate mixtures of
dark basalt and SPIPA-B covered by water frost (Figure 5b). This sample was
produced unwittingly when, at the time we were about to measure the
reflectance of the intimate mixtures, our vacuum pump stopped working
correctly. Consequently, the water of the atmosphere in the chamber condensed
on the sample. We acquired the reflectance cube of the intimate mixtures with
frost before resuming the pumping and removing this superficial frost by
sublimation. This serendipitous measurement is shown to be rather useful. From
the work Clark (1981), we estimate the amount of frost deposited onto our
samples to be around 80 $\mu$m.

##### Frozen soil

We prepared what we refer to as frozen soils by pouring deionised water onto
the powders until the pores saturated and a layer of water appeared on top of
the dusts. The sample holders used for these samples were slightly thicker
than the ones previously used, i.e. 2x4x2 cm. For each dust, we produced four
different samples, one per size distribution. The sample holders were then
introduced into a freezer (230 K) and left to freeze through the night.
Because of the expansion of the ice, the samples lost the flat surfaces they
used to have when water was in its liquid state. The frozen soils were exposed
to low pressures to monitor the evolution of their reflectance as ice
sublimated. Hence, we observed the sample change from the form of ice over
soil to one in the form of ice in soil. The conditions of pressure and
temperature at which the spectra were acquired are specified in Table 1.

Figure 5d shows an example of JSC Mars-1 frozen soils after 17h of
sublimation. It can be noticed that the ice on top of the finest fraction
(bottom-left sample holder, with dust smaller than 100 micrometres) has
already sublimated, revealing the regolith inside. The other sample holders
still have a layer of ice covering the regolith. There were no spectral
differences in the evolution of the reflectance of the samples with dusts of
different sizes. Therefore, we only show here the spectra of the sample with
the finest dust, where the dust was revealed by the end of the experiment. In
some of the sample holders, e.g. the top right one, cracks are still visible.
Since particles with lower density floated in the water, the ice on top of the
samples was not pure.

##  3 Results

###  3.1 Reflectance spectra

####  3.1.1 Frost

Figure 7: Reflectance spectra of JSC Mars-1 (left) and Dark Basalt (right)
samples covered by water frost. Each step corresponds to 10 minutes of
exposure to the atmospheric water. Each row corresponds to different size
fractions of the regolith; from top to bottom, >400 µm, [200,400] µm,
[100,200] µm, and <100 µm.

Figure 7 shows the reflectance spectra of three condensations of atmospheric
water on different size-distributions of JSC Mars-1 (left) and Dark Basalt
(right). While the first step of frost deposition doubles the reflectance of
the Dark Basalt, it has limited impact on the spectra of the JSC Mars-1: the
hydration bands slightly weaken and shift towards longer wavelengths.

By the second step of frost deposition, both materials reflect, at the bluest
wavelengths, between six and eight times more than when they were frost-free.
The growth in the near-infrared reflectance is nevertheless much slower:
around 2.4 µm, the reflectance of the Dark Basalt has increased by about
50$\%$, while the one of the JSC Mars-1 remains roughly the same as without
frost. The differences in the reflectance rise between spectral ranges results
in bluer visible and near-infrared slopes for both materials. On the other
hand, the last deposition of frost strengthens the absorption bands more than
it increases the overall reflectance.

####  3.1.2 Intimate mixtures

Figure 8: Reflectance spectra of intimate mixtures of JSC Mars-1 (average
size, 24 µm) and Dark Basalt (50wt$\%$ of the particles >109 µm and 50 $\%$
<109 µm) with water ice (SPIPA-A: 4.5$\pm$2.5 µm; SPIPA-B: 67$\pm$31 µm).
Different colours represent different percentages of water ice within the
mixture. a) JSC Mars-1 mixed with SPIPA-A b) Dark Basalt and SPIPA-B mixtures
with water frost condensed on it. The star indicates an artefact caused by the
instrument c) JSC Mars-1 mixed with SPIPA-B d) Dark Basalt and SPIPA-B.

Because small particles have a greater surface-to-volume ratio than large
particles, mixtures with SPIPA-A are expected to be brighter than with SPIPA-B
(Yoldi et al., 2015). Spectra in Figures 8a and 8c show this behaviour, except
for the samples with less ice. The reason for this could be the sublimation of
the ice at the surface since the small SPIPA-A particles sublimate much faster
than the SPIPA-B particles.

The addition of SPIPA-A to a sample of JSC Mars-1 progressively increases the
reflectance of the continuum and the H2O indices. An increasing concentration
of SPIPA-B also increases the water index. Nevertheless, it seems to affect
the continuum of JSC Mars-1 in three phases; a first doubling of the
reflectance value, followed by a stage of no change (35-50wt$\%$) and finally
a new increase in the reflectance of about 50$\%$. We observe a similar
sequence in dark basalt and SPIPA-B intimate mixtures (Figure 8d); a first
increase of reflectance at 35wt$\%$ of ice is followed by a phase where the
absorption bands become deeper in the near-infrared without significant
changes in the visible reflectance. The sample with 75wt$\%$ of ice doubles
the reflectance of that with 50wt$\%$ of ice in the visible and shows distinct
absorption bands in the near-infrared.

##### Frost over an intimate mixture

Figure 8b shows the reflectance spectra of frost over the intimate mix of
SPIPA-B and Dark Basalt. As observed in Section 3.1.1, frost increases further
the reflectance at shorter wavelengths, turning the slopes to blue in both the
visible and near-infrared. Furthermore, the absorption bands of water deepen
because of the deposition of frost.

####  3.1.3 Frozen soil

Figure 9: Evolution of reflectance spectra of frozen soils of JSC Mars-1
(left) and Dark Basalt (right) through 17 and almost 5 hours of sublimation
respectively. The reflectance spectra have been grouped into Intervals. In the
Dark Basalt plots, the solid lines represent hyperspectral measurements, and
the points represent the reflectance measured at specific wavelengths in the
multispectral mode.

Frozen soils prepared with JSC Mars-1 and Dark Basalt were exposed to vacuum
and left to sublimate for 17 hours and almost 5 hours respectively; Figure 9
shows the evolution of their spectra during that time. To simplify the
figures, we have grouped the spectra in intervals. The duration of these
intervals, the pressure and temperature conditions, and the number of spectra
measured per interval is specified in Figure 9 and Table 1.

Regardless of what the spectrum of the underlying material was, the layer of
ice that covered it was thick enough to reduce its reflectance and to saturate
the spectra at wavelengths longer than 1.4 µm, as seen previously in Clark et
al. (1986). For both simulants, reflectance seems to fall more in the near-
infrared than in the visible. Furthermore, the absorption bands at 1.5 µm and
2.0 µm are saturated, leaving the near-infrared spectra featureless.

Both in the VIS and the NIR, the reflectance of the JSC Mars-1 samples
decreases from the first to the second interval. We explain that by the
presence of cracks within the ice, which increase the interfaces within the
ice layer. Once the cracks anneal, the reflectance drops. From interval 2, the
progressive sublimation of ice increases the reflectance of the samples in the
NIR. In the VIS, the reflectance spectra start to adopt the shape of the JSC
Mars-1 as the ice sublimates. Hence, the reflectance only increases as ice
sublimates at wavelengths longer than 0.5 µm. We observe in Figure 9a that JSC
Mars-1 has adsorbed water and is now highly hydrated.

###  3.2 Spectral and Colour analysis

Figure 10 shows the evolution of the spectral parameters defined in Section
2.2.2 as a function of the ice content of the sample. The experiments with JSC
Mars-1 are shown on the left and the ones with the Dark Basalt are shown on
the right. Figures 10i and 10ii contain the legends applicable to each column.
We do not show the frozen samples in these figures since there is not an
assumed linearity in the content of water: we cannot measure the content of
water per interval and the intervals do not have the same duration (see Table
1).

Figure 10: Spectral criteria as the amount of water ice increases for JSC
Mars-1 (left) and Dark Basalt (right) samples. This figure continues in
Fig.11. The points that correspond to frost experiments follow the X-axis at
the bottom, whereas the points that correspond to intimate mixtures follow the
X-axis at the top of the graphs (in blue). The top X-axis (in blue, wt $\%$ of
water) and the top X-axis (in black, Frost Step) are not to be compared in
terms of water content. i), ii) Legends for the JSC Mars-1 and Dark Basalt
measurements respectively a), b) H2O index at 1.5 µm (top) and 2.0 µm
(bottom). c), d) Barycentre position for the band at 1.5 µm (top) and 2.0 µm
(bottom)

####  3.2.1 H2O index

Figures 10a and 10b show the H2O indexes as a function of the amount of water.
We have explained in Section 2.2.2, the methodology to assess the presence of
a band; the lack of a point implies the lack of a band. We confirm the
different impact of the intimate mixtures and the frost depositions on the H2O
indices; samples covered by less than 100 $\mu$m of frost show similar H2O
indices than intimate mixtures with a 10 wt$\%$ of water. When condensed upon
the intimate mixtures of Dark Basalt and SPIPA-B, frost affects the water
indexes of the samples at 2.0 µm in different ways.

Coarse ice particles (SPIPA-B) intimately mixed with JSC Mars-1 produce
slightly higher H2O indices at 1.5 µm than the fine ice particles (SPIPA-A)
do. We do not observe such a trend at 2.0 µm. In the experiments of frost
deposition, we see no substantial influence of the particle size of the
substratum in the H2O indices. Only at the first frost deposition over JSC
Mars-1, we measure different indices at 2.0 µm. This may suggest that the
different size-distributions trapped different amount of frost in the first
step.

####  3.2.2 Position of the barycentre

In Figures 10c and 10d, we show the position of the barycentres for the bands
around 1.5 and 2.0 µm.

The bands of the intimate mixtures with JSC Mars-1 quickly move towards the
positions of the barycentre of water ice, measured for both SPIPA -A and -B at
1.55 and 2.02 µm. SPIPA -A and -B seem to be equally efficient in shifting the
bands, except for the sample with a 10 wt $\%$ of ice, in which the samples
with SPIPA -A centre at shorter wavelengths than the ones with SPIPA-B. Frost
also shifts the position of the barycentres towards long wavelengths, at
different rhythms depending on the band. Hence, Step 1 of frost deposition
shifts the band around 1.5 µm as much as the intimate mixture with 10 wt $\%$
of ice. By the third deposition, that band is already centred at 1.55 µm. The
barycentre of the band around 2.0 µm shifts more slowly, so that by the third
step of deposition the band has shifted less than the one of any intimate
mixture. For both bands, the positions we get for the JSC Mars-1 spread with
the size of the dusts. The same spread is observed during the first frost
deposition over JSC Mars-1. Intimate mixtures with Dark Basalt also align
quickly around 1.55 µm, with no difference if frost is present on the samples.
Even if pure Dark Basalt and pure Dark Basalt with frost seem to centre around
slightly longer wavelengths than pure ice (1.571 and 1.569 µm respectively),
the result lies in the range of our uncertainties, so no conclusions can be
drawn. The band around 2.0 µm, not present for Dark Basalt, appears when frost
is deposited on it. As the concentration of ice within the intimate mixtures
grows, the barycentres shift towards 2.02 µm, more slowly if frost covers the
mixtures. Regarding the frost experiments, and following the criteria
explained in Section 2.2.2, the bands only appear on the second step of the
deposition. The positions of the barycentres for Step 2 of deposition spread
with the size of the dust. As observed with the JSC Mars-1, Step 3 centres the
first band at 1.55 µm, whereas the second band remains at shorter wavelengths
than the band of the intimate mixtures.

Figure 11: (Continuation of Figure 10) Spectral criteria as the amount of
water ice increases for JSC Mars-1 (left) and Dark Basalt (right) samples. i),
ii) Legends for the JSC Mars-1 and Dark Basalt measurements, respectively e),
f) VIS (top) and NIR (bottom) spectral slopes. The points that correspond to
frost experiments follow the X-axis at the bottom, whereas the points that
correspond to intimate mixtures follow the X-axis at the top of the graphs (in
blue). Both X-axis are not to be compared in terms of water content. g), h)
Reflectance measured with the CaSSIS filters for the frost experiments (top)
and the intimate mixtures (bottom).

####  3.2.3 Spectral Slope

In its dry form, JSC Mars-1 shows a steep red slope in the visible and a
plateau in the near-infrared (Figure 11e). In comparison, the slope of the dry
Dark Basalt is two to six times bluer in the visible and three to seven times
redder in the near-infrared, depending on the size distribution (Figure 11f).
Nevertheless, regardless of the initial value of the visible slope, roughly
100 $\mu$m of water frost are enough to achieve similar slopes as the ones of
pure particulate ice. Ice particles in intimate mixtures also reduce the
initial red slopes of the materials; nevertheless, concentrations of water ice
higher than 80wt$\%$ are needed to flatten the visible slope as much as tens
of micrometres of frost would do. In the visible range, smaller particles
flatten the slope more effectively.

In the near-infrared, all the slopes have turned to blue — as expected from
water ice. At similar concentrations of water ice, intimate mixtures look
bluer with JSC Mars-1 than with Dark Basalt. At the second frost deposition,
both materials already show the same spectral slope. The drop in the spectral
slope of the Dark Basalt and intimate ice mixtures caused by frost confirms
that, in the near-infrared, frost acts as well as an efficient slope
flattener, as it does in the visible range.

####  3.2.4 Colour Analysis

Simulating the reflectance values measured in the different filters of CaSSIS
(Figures 11g and 11h) allows us to distinguish between the experiments with
JSC Mars-1 and Dark Basalt. Because of the steep slope in the visible of the
JSC Mars-1 analogue, we would measure different values of reflectance in each
filter, whereas the reflectance of the Dark Basalt with ice would be the same
in every filter.

Through successive frost deposition steps, the reflectance of both materials
rises similarly. In the case of JSC Mars-1, less than 100 $\mu$m of frost
deposited over a sample would produce an increase in the reflectance two times
greater in the BLU than in the RED filter. Hence, the values of reflectance in
the different channels converge progressively to similar values as the
condensation of frost increases. The condensation of frost on the intimate
mixtures levels out the reflectance, which hampers the estimation of the
amount of ice underneath.

The curve drawn by the increasing reflectance with the growing concentration
of ice differs slightly from material to material: while in the JSC
Mars-1–mixtures the reflectance increases gradually from 10wt$\%$ ice content,
that of the Dark Basalt– blends only varies significantly from 75wt$\%$ of
water ice. Even though pure SPIPA-A and -B are blue (i.e., the highest
reflectance is measured in the BLU filter), the intimate mixtures with
75wt$\%$ of ice still show weaker values of reflectance in the BLU filter.
Also for intimate mixtures of JSC Mars-1 and water ice, the filters become
sensitive to the size of the ice particles as from concentrations of
35-50wt$\%$ of water ice.

###  3.3 Comparison of criteria

In Figures 12 and 13, we compare, two-by-two, spectral parameters for the
different mixtures. We aim to identify trends in the reflectance of the dusts
when mixed in different ways with various amounts of water ice. Here, unlike
in Section 3.2, the focus lies on the mixing style rather than on the amount
of water contained in the sample; we want to identify the best spectral
parameters to identify the mixing styles. We only indicate with an arrow, for
orientation, the direction of increasing ice content within the sample.

The spectral parameters that we compare here provide us with a good overview
of what can be done with laboratory data. For clarity, we have split the plots
between JSC Mars-1 and Dark Basalt experiments, shown on the left and right
column, respectively. Both Figures 12 and 13 i) show the legend to follow the
plots.

Figure 12: Comparison of various spectral parameters of the laboratory samples
for different ice and dust mixing modes. Experiments with JSC Mars-1 and Dark
Basalt are shown on the left and right column, respectively. i) Legend. Arrows
indicate the direction of increasing content of ice in the samples. a), b)
Reflectance at 1.08 µm versus the H2O index at 1.5 µm (top) and 2.0 µm
(bottom) c), d) H2O index at 1.5 µm (top) and 2.0 µm (bottom) compared to the
VIS spectral slope e), f) H2O index at 1.5 µm (top) and 2.0 µm (bottom)
compared to the NIR spectral slope.

####  3.3.1 Spectral parameters

In Figures 12a and 12b, we compare the reflectance of the continuum of our
samples (JSC Mars-1 in Figure 12a and Dark Basalt in Figure 12b) with the H2O
indices at 1.5 and 2.0 µm. We observe different trends depending on the mixing
modes.

Frost experiments on dusts cluster around relatively weak water indices (i.e,
<0.2 at 1.5 µm and <0.3 at 2.0 µm) and values of reflectance ranging from 0.1
to 0.5. The growing condensation of frost on dust increases the reflectance
and the water indices linearly; on hydrated minerals (JSC Mars-1), the
reflectance rise is faster than that of the water index, whereas in the dry
minerals (Dark Basalt) water indices increase faster than the reflectance of
the continuum.

For intimate mixtures, the reflectance of the continuum does not increase
linearly with the water indices (Figures 12a and 12b) . Instead, we observe
the same regimes as in the reflectance spectra (Figures 8a, 8c and 8d); a
first one where the reflectance of the samples rises, a second one in which
the water indices increase while the reflectance remains constant, and a third
one where the reflectance increases exponentially with water indices. Where
the transition between regimes two and three happens depends on the grain size
of the ice and the albedo of the regolith. Back in Figure 12b, intimate
mixtures with frost on them show a parallel trend to the intimate mixtures
without frost, only shifted in reflectance due to the reflectance of frost.
Finally, frozen soils show generally low reflectance and a wide range of water
indices that can go up to 0.5 for the 1.5 µm band of JSC Mars-1 frozen soils.
In frozen soils experiments, the water index is not proportional to the amount
of water since when a thick layer of ice covers the dust, the absorption bands
saturate. In the plots of JSC Mars-1 (that is, left-hand column plots) in
Figures 12 and 13, we have marked a point with an orange square filled with
purple: this point represents the last measurement of the frozen soil, in
which JSC Mars-1 was exposed and ice-free but, because the regolith had been
in liquid water, the dust adsorbed water and is highly hydrated.

By comparing these parameters (reflectance of the continuum and water
indices), we can distinguish intimate mixtures with at least 35wt$\%$ of water
ice from other mixing types. By looking at the band at 1.5 µm, we can also
distinguish between frozen soils and frost-covered soils.

We plot in Figures 12c and 12d the H2O index as a function of the visible
slope. We observe once again the flattening effect of frost: as from the
second step of frost condensation, all the frost experiments gather in the
region of spectral slopes weaker than 15 $\%$/100 nm. This behaviour of frost
allows us to distinguish intimate mixtures with frost on them from frost-free
intimate mixtures, which could not be done in Figure 12b. Nevertheless, it is
still impossible to distinguish the smallest amounts of frost on dusts from
intimate mixtures with 10wt$\%$ of water. Finally, looking at the band at 1.5
µm we can distinguish frozen soils from frost experiments, while the band at
2.0 µm allows us to distinguish frozen soils from intimate mixtures with more
than 10wt$\%$ of water.

To distinguish between frozen soils and other samples, we plot in Figures 12e
and 12f the H2O indices versus the spectral slopes in the near-infrared.
Compared to other experiments that contain JSC Mars-1, frozen soils show blue
slopes (between -5 and -10 $\%$/100 nm) at low water indices (0.2-0.3). This
clustering around blue spectral slopes and weak water indices allows us to
distinguish frozen soils from the rest of experiments. Because frozen soils of
dark basalt do not reach blue slopes more pronounced that -5 $\%$/100 nm, this
comparison of only NIR parameters does not allow us to pinpoint those
experiments. Finally, we show a comparison between the VIS and NIR spectral
slopes in Figures 13g and 13h. This comparison is useful to identify the
experiments with smallest amounts of frost from the dry powders.

Figure 13: (Continuation of Figure 12). Comparison of various spectral
parameters of the laboratory samples for different ice and dust mixing modes.
Experiments with JSC Mars-1 and Dark Basalt are shown on the left and right
column, respectively. i) Legend. Arrows indicate the direction of increasing
content of ice in the samples. g),h) Comparison of the spectral slopes in the
VIS and the NIR i), j) Reflectance measured in the RED channel of CaSSIS
compared to the band-ratios PAN/RED (top) and BLU/RED (bottom)

####  3.3.2 Colour analysis

The reflectance of our samples as would have been measured with CaSSIS is
shown in Figures 13i and 13j. In this case, we compare the signal measured in
the RED filter with two band ratios: PAN/RED and BLU/RED. Ratios lower than
one correspond to red slopes between the centre of the considered bands,
ratios higher than one indicate blue slopes and ratios around one flat slope.

In this plot, mixtures with JSC Mars-1 and mixtures bearing Dark Basalt are
easy to separate, since they have different spectral slopes in the visible. We
also see that the BLU/RED plot looks like a stretched version of the PAN/RED
one, which indicates a linear correlation between the reflectance measured in
the BLU and PAN filters.

In the BLU/RED plot, we can see that CaSSIS is sensitive enough to detect the
lowest amounts of frost. The arrow indicates the direction of increasing
abundance of ice; we are therefore able to distinguish the first step of frost
deposition from the dry samples and from the other deposition steps, which
cluster between 0.7 and 0.9 BLU/RED ratio. However, frost experiments cannot
be discerned from intimate mixtures only with CaSSIS.

##  4 Discussion.

###  4.1 Effect of the mixing mode in the reflectance spectra.

So far, we have seen the reflectance of various ice and dust mixtures. We have
also observed how the way in which end members mix affects some specific
spectral parameters. Now, we discuss further this effects and how to take
advantage from them to identify different mixing modes from their reflectance
spectra.

####  4.1.1 Frost

We have identified three spectral regimes as frost condenses on a surface. In
the first regime, frost covers almost homogeneously the substrate with fine
particles (on the order of microns). Hence, the probability for a photon to
encounter a grain of ice is large, and because of the great surface-to-volume-
ratio of tiny particles, the reflectance of the surface rises slightly. This
is what we see in the Step 1 of our frost depositions. Since the transition
from Rayleigh to a more efficient particulate scattering occurs more rapidly
at short wavelengths (Kieffer, 1970), at this stage the reflectance increases
faster at short wavelengths. We observe this behaviour in the transition
between Steps 1 and 2. The deepening of the absorption bands of the spectrum
at this stage of frost deposition is limited, because of the small size of the
particles of frost.

In a second stage, ice grows thick. This does not significantly increase the
probabilities for photons to encounter ice, but the path length of photons
inside ice does increase. The second stage is, therefore, characterised by a
deepening of the absorption bands rather than an increase in reflectance, as
see in our third step of deposition. Finally, at some point, the layer of ice
becomes optically thick enough to cover the spectral signature of the material
underneath. However, we have not explored this stage in our experiments, and
such amount of frost is not expected in frost depositions over the Martian
nights. The frost that condenses at the beginning of fall and stays over the
winter, a.k.a seasonal frost, is expected to sinter and grow into large
crystals that do not show the same spectral properties as the light frosts
that we observe in here. It should be debated whether the seasonal frost
should be referred to as frost.

####  4.1.2 Intimate mixtures

Previous laboratory work has shown that the reflectance of water ice and dust
intimate mixtures does not increase linearly with the amount of water ice
(Yoldi et al., 2015, Gyalay et al., 2019). Instead, it is dominated by the
most absorptive component until the least absorptive material exceeds a
threshold relative abundance, which is determined by the grain-size and albedo
of the components. If we take the example of our ice and JSC Mars-1 intimate
mixtures, JSC Mars-1 is the absorptive material except around 1.5 and 2.0
microns, where water ice is more absorptive than JSC Mars-1. As the amount of
water ice increases from 0wt$\%$ to 100wt$\%$, we identify three phases.

The first one can be seen in the mixtures with JSC Mars-1 and 10wt$\%$ of
water ice, where the reflectance of the sample doubles since ice scatters the
incoming photons more efficiently than JSC Mars-1 does. In a second phase, the
spectra are characterised by different behaviour in the visible and the near-
infrared, as can be seen in the intimate mixtures with 35-50wt$\%$. When we
increase the amount of ice in one of our mixtures, the relative abundance of
absorptive particles decreases in the visible but increases at some
wavelengths in the NIR (around the absorption bands of water). Because the
most absorptive component dominates the reflectance of an intimate mixture,
the spectrum of JSC Mars-1 dominates in the VIS region whereas the spectrum of
water ice dominates in the NIR regions: the reflectance in the VIS stays
constant or rises smoothly (depending on the size of the ice) whereas the
absorption bands deepen steadily. In a final, third step, the abundance of ice
is enough to dominate both the VIS and NIR spectra.

####  4.1.3 Frozen soils

Layers of ice over soils are challenging to detect since water ice is almost a
continuum medium, and therefore frozen soils can be transparent in the visible
range and saturated—and therefore featureless—in the near-infrared. When
cracks appear in the ice, they create interfaces within the ice layer that
increase the reflectance. As the layer of ice on top of the soil gets thin,
the spectrum of the soil is revealed; if this soil is bright or has
characteristic features, it will be detectable. Otherwise, as in the case of
the dark basalt, frozen soils—both as ”ice-covered soil” and ”dust included in
a matrix of ice”— are nearly indistinguishable from the dry soil.

###  4.2 Discriminating spectral/colour criteria to identify different
ice/dust mixing modes.

We propose now the following scenario: if we were given a random point from
Figures 12 and 13, how could we identify to what type of mixture it
corresponds?

First, we could take advantage of the saturated near-infrared spectra of
frozen soils to identify them. Indeed, frozen soils show blue slopes akin to
the ones of fine-grained ice but their H2O indexes up to three and even eight
times weaker (at 1.5 µm and 2.0 µm respectively). Furthermore, unlike intimate
mixtures, frozen soils conserve the water absorption band at 1.03 µm when they
have a thick layer of water ice on top, which differentiates them from the
other mixing modes.

In order to identify frost deposits, it is a good strategy to compare the
water indexes with the spectral slopes; frost neutralises the slopes without
deepening the absorption features, while other forms of water ice also deepen
the absorption bands (Figures 12c, 12d). Frost is easier to detect when the
substrate has a steep slope, as seen in experiments with JSC Mars-1. Intimate
mixtures with frost on them can also be identified in this comparison. Early
stages of frost deposition can be differentiated from dry soils by comparing
the visible and the near-infrared spectral slopes.

It has been shown that it is not always possible to detect water ice
intimately mixed with soil in the visible range at specific geometries (Yoldi
et al., 2015). Instead, comparing that reflectance to the H2O index depths of
water represents a good alternative to identify intimate mixtures of ice and
dust. This comparison does not allow one to rule out the presence of frost
over icy intimate mixtures; they appear like intimate mixtures of fine-ice
particles (Figure 12a).

For our laboratory samples, we could guarantee the identification of frost-
free intimate mixtures by process of elimination: we could first rule out
frozen soils and frost by the methods explained above, leaving the intimate
mixtures as the remaining option. In natural surfaces, this process is not
that straightforward, because other dust and ice mixtures, such as intra-
mixtures (i.e., when dust grains are included in the ice grains), can have
similar reflectance spectra to those of the intimate mixtures. Other studies
have shown that inter- and intra-mixtures could be distinguished in the
visible range (Jost et al., 2017) and, if the ice at the surface sublimates,
by the evolution of their bands (Jost et al., 2017) or the properties of the
sublimation residues (Poch et al., 2016a).

###  4.3 Frost and intimate mixtures VS hydrated minerals

Identifying from remote sensing whether an absorption band is caused by
structural water or the deposition of frost (or even low contents of
intimately mixed water ice) on the surface remains a challenge. With an a
priori knowledge of the ice-free spectrum of a hydrated material, some of the
comparisons between parameters allow one to identify early stages of frost
deposition (e.g., Figures 12b, 12d), but none of them is conclusive without
the prior knowledge of the hydration state.

The study of the position of the barycentres provides us with a good way of
differentiating hydration from frost (see 10c). Nevertheless, the way in which
we compute the barycentre in this paper requires a high sampling and spectral
resolution. Instruments like OMEGA or CRISM are needed to conduct such
analysis.

###  4.4 On the pertinence of the laboratory samples

Here, we discuss the extent to which the samples that we have produced in the
laboratory match the features of Martian ices.

The nature of Martian frost is not yet well known. It follows that a direct
comparison between Earth- and Mars-grown frosts can, at the moment, be only
speculative. However, there are some points that we can already take into
consideration. Kieffer (1968) stated that, for a process limited by diffusion,
the size of the frost crystals is proportional to the relative concentration
of the condensible gas. Hence, we can expect the Martian frost to be finer
than the ones grown in the terrestrial atmosphere for a same period of
deposition. Furthermore, it has to be taken into account that in the case of
our laboratory experiments, the cooling comes from beneath the sample, and
therefore the dust is colder than the atmosphere. This is not always true on
Mars, where the atmosphere is in general colder than the regolith. If the
atmosphere is cooler that the substrate, the grains of frost tend to grow tall
towards the cold, irradiating the heat into space and cooling down through
radiative cooling. If the substrate is colder than the atmosphere, as it is in
our laboratory setup, the grains of frost cool down by conducting the heat
into the substrate: since the efficiency of this cooling depends on the
thermal contact of the frost grains with the substrate, the grains of frost
will tend to grow larger than the ones that cool down radiatively (Kieffer,
1968). Considering these points, one could expect the Martian grains of frost
to be finer than the terrestrial frosts and to gather into filament-like
structures. Would this be the case, Martian frosts would scatter light more
efficiently than terrestrial ones, and the observed differential spectral
behaviour between the VIS the NIR would be even stronger.

Regarding the frozen soils, we do not expect to find on Mars soils produced by
the process used to create the laboratory analogues. Nevertheless, these
samples might be good analogues for packed snow (or ice) with dust grains in
it, as we can find in the water ice sheets found under the Martian surface
that sublimate when exposed to the atmosphere (Dundas et al., 2018), or the
exposed dusty ice on the polar deposits. In both these examples, the snow has
likely metamorphosed into firn or ice (as it happens on terrestrial ice sheets
(Blunier and Schwander, 2000), and therefore the path of the photons within
the ice is longer than within the SPIPA-A and -B ice grains. That is precisely
the interest of the frozen soil samples: unlike the frosts and intimate
mixtures, the ice is not a particulate medium but a continuum, which, for the
mentioned examples, constitutes a better approximation than the rest of the
samples. We also note that our frozen soils analogues resemble more closely
the ice-dust mixtures from Clark (1981) and Clark and Lucey (1984) than our
own intimate particulate mixtures.

##  5 Conclusion and perspectives

We have conducted a series of laboratory experiments to measure the VIS and
NIR reflectance of various water ice and regolith mixtures. The dry members of
the mixtures are the Martian regolith analogue JSC Mars-1 and a more pristine
dark basalt to simulate the observed red and black terrains from Mars. We have
performed spectral and colour analysis on  1) cold-trapped atmospheric water
onto regolith to simulate frost deposition,  2) intimately mixed dust and ice,
and  3) frozen, water-saturated regolith samples.

The main results are summarised below:

  * •

We have identified three spectral regimes as frost grows on a dusty surface.
There is an initial increase in the reflectance preferentially at short
wavelengths; second, an increase in reflectance accompanied by a deepening of
the absorption bands and finally, a masking of the surface underneath.

  * •

We have identified three spectral regimes as the abundance of water ice in an
ice/dust intimate mixture grows. These three regimes are the result of a
competition between the single scattering albedo of the materials, their
relative abundance and the size of their particles. In the first regime, small
amounts of water ice increase the reflectance of the mixture. In the second
regime, the spectrum of the absorptive material dominates the reflectance
spectrum of the mixture; there is a modest increase of reflectance in the non-
absorptive spectral range of water and the absorption bands deepen
proportionally to the abundance of water. In the third regime, there is enough
water ice so that its reflectance spectrum dominates the spectrum of the
mixture.

  * •

Frozen soils are challenging to detect since the formation of a layer of water
ice on top of the regolith can drop the reflectance of the ground if the ice
is translucent (i.e., it does not have cracks) and if the reflectance is
measured outside specular geometry.

  * •

We have shown how a strategic comparison of spectral and colour criteria
provides crucial information about the mixing mode of ice and dust.

  * •

We have compared a set of parameters in the visible and near-infrared spectral
ranges. This is key to making our data useful for a maximum of Martian imagers
since some of them observe only in the VIS or in the NIR, or in cases where
failures cripple the capability of instruments to image the full spectral
range.

  * •

To differentiate intimate mixtures from frost experiments, the best is to
compare VIS and NIR parameters. Intimate mixtures will, as a general rule,
have more impact in the NIR, whereas frost will affect the VIS rapidly. To
identify frost on an intimate mixture —even in layers of tens of micrometres,
it is useful to compare their water index to their visible spectral slope.

  * •

The study of the position of the barycentres allows us to differentiate
hydrated minerals from early stages of frost deposition on dust.

The future steps of our work are to study the effect of a Martian-like
atmosphere in the reflectance and detectability of our samples. The first
attempts to compare our laboratory data to Martian surfaces have been
presented in planetary conferences and have given promising results (Yoldi et
al., 2018a, b). In the companion paper, we have added CO2 ice to our
experiments and conducted a similar spectral and colour analysis.

Data availability All the reflectance spectra presented here are available on
the Bern icY Planetary Analogues Solid Spectroscopy (BYPASS) database, hosted
on the Solid Spectroscopy Hosting Architecture of Databases and Expertise
(SSHADE) .

Acknowledgements The authors want to thank Daniele Piazza and the Workshop
team of the University of Bern for helping in the design and construction of
the frost sample-holder. The authors also want to thank Martin Grosjean and
Tobias Schneider from the Oeschger Centre for Climate Change Research and
Institute of Geography, University of Bern, for allowing us to use their SEM.
Z. Yoldi wants to thank Panagiotis Theologou for his help formatting Table 1.
This work has been developed in the framework of the National Center for
Competence in Research PlanetS funded by the Swiss National Science Foundation
(SNSF). Olivier Poch acknowledges funding from CNES and European Research
Council under grant SOLARYS (77169). The authors want to thank Ken Herkenhoff,
Vincent Chevrier and the anonymous reviewers for their constructive and
helpful inputs.

## References

  * Allen et al. (1997) C. C. Allen, R. V. Morris, D. J. Lindstrom, M. M. Lindstrom, and J. P. Lockwood.  Jsc mars-1: Martian regolith simulant.  _Lunar and Planetary Science_ , XXVIII, 1997.
  * Appéré et al. (2011) T. Appéré, B. Schmitt, Y. Langevin, S. Douté, A. Pommerol, F. Forget, A. Spiga, B. Gondet, and J.-P. Bibring.  Winter and spring evolution of northern seasonal deposits on mars from omega on mars express.  _Journal of Geophysical Research: Planets_ , 116(E5):n/a–n/a, 2011.  ISSN 2156-2202.  doi: 10.1029/2010JE003762.  URL http://dx.doi.org/10.1029/2010JE003762.  E05001.
  * Appéré et al. (2011) T. Appéré, B. Schmitt, Y. Langevin, S. Douté, A. Pommerol, F. Forget, A. Spiga, B. Gondet, and J. P. Bibring.  Winter and spring evolution of northern seasonal deposits on Mars from OMEGA on Mars Express.  _Journal of Geophysical Research (Planets)_ , 116(E5):E05001, May 2011.  doi: 10.1029/2010JE003762.
  * Bandfield (2002) J. Bandfield.  Global mineral distributions on mars.  _Journal of Geophysical Research_ , 107, 2002.  doi: https://doi.org/10.1029/2001JE001510.  URL https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2001JE001510.
  * Barr and Milkovich (2008) A. C. Barr and S. M. Milkovich.  Ice grain size and the rheology of the martian polar deposits.  _Icarus_ , 195:513–518, 2008.
  * Bibring et al. (2004) J.-P. Bibring, Y. Langevin, F. Poulet, A. Gendrin, B. Gondet, M. Berthé, A. Soufflot, P. Drossart, M. Combes, G. Bellucci, V. Moroz, N. Mangold, B. Schmitt, OMEGA Team, S. Erard, O. Forni, N. Manaud, G. Poulleau, T. Encrenaz, T. Fouchet, R. Melchiorri, F. Altieri, V. Formisano, G. Bonello, S. Fonti, F. Capaccioni, P. Cerroni, A. Coradini, V. Kottsov, N. Ignatiev, D. Titov, L. Zasova, P. Pinet, C. Sotin, E. Hauber, H. Hoffman, R. Jaumann, U. Keller, R. Arvidson, J. Mustard, T. Duxbury, and F. Forget.  Perennial water ice identified in the south polar cap of Mars.  _Nature_ , 428(6983):627–630, Apr. 2004.  doi: 10.1038/nature02461.
  * Bibring et al. (2005) J.-P. Bibring, Y. Langevin, A. Gendrin, B. Gondet, F. Poulet, M. Berthé, A. Soufflot, R. Arvidson, N. Mangold, J. Mustard, and P. Drossart.  Mars surface diversity as revealed by the omega/mars express observations.  _Science_ , 307(5715):1576–1581, 2005.  ISSN 0036-8075.  doi: 10.1126/science.1108806.  URL https://science.sciencemag.org/content/307/5715/1576.
  * Bibring et al. (2006) J.-P. Bibring, Y. Langevin, J. F. Mustard, F. Poulet, R. Arvidson, A. Gendrin, B. Gondet, N. Mangold, P. Pinet, F. Forget, OMEGA Team, M. Berthé, C. Gomez, D. Jouglet, A. Soufflot, M. Vincendon, M. Combes, P. Drossart, T. Encrenaz, T. Fouchet, R. Merchiorri, G. Belluci, F. Altieri, V. Formisano, F. Capaccioni, P. Cerroni, A. Coradini, S. Fonti, O. Korablev, V. Kottsov, N. Ignatiev, V. Moroz, D. Titov, L. Zasova, D. Loiseau, P. Pinet, S. Doute, B. Schmitt, C. Sotin, E. Hauber, H. Hoffmann, R. Jaumann, U. Keller, R. Arvidson, T. Duxbury, and G. Neukum.  Global Mineralogical and Aqueous Mars History Derived from OMEGA/Mars Express Data.  _Science_ , 312(5772):400–404, Apr. 2006.  doi: 10.1126/science.1122659.
  * Blunier and Schwander (2000) T. Blunier and J. Schwander.  Gas enclosure in ice : age difference and fractionation.  2000\.
  * Brouet (2013) Y. Brouet.  _Contribution rà la détermination de la permittivité des noyaux cométaires et des astéroides_.  PhD thesis, 2013.
  * Brouet et al. (2016) Y. Brouet, L. Neves, P. Sabouroux, A. C. Levasseur-Regourd, O. Poch, P. Encrenaz, A. Pommerol, N. Thomas, and W. Kofman.  Characterization of the permittivity of controlled porous water ice-dust mixtures to support the radar exploration of icy bodies.  _Journal of Geophysical Research: Planets_ , 121(12):2426–2443, 2016.  ISSN 2169-9100.  doi: 10.1002/2016JE005045.  URL http://dx.doi.org/10.1002/2016JE005045.  2016JE005045.
  * Brown et al. (2014) A. Brown, W. M. Calvin, P. McGuire, and S. L. Murchie.  CRISM south polar mapping: First Mars year of observations.  _arXiv.org_ , pages 1–31, 2014.
  * Byrne et al. (2009) S. Byrne, C. M. Dundas, M. R. Kennedy, M. T. Mellon, A. S. McEwen, S. C. Cull, I. J. Daubar, D. E. Shean, K. D. Seelos, S. L. Murchie, B. A. Cantor, R. E. Arvidson, K. S. Edgett, A. Reufer, N. Thomas, T. N. Harrison, L. V. Posiolova, and F. P. Seelos.  Distribution of mid-latitude ground ice on mars from new impact craters.  _Science_ , 325(5948):1674–1676, 2009.  ISSN 0036-8075.  doi: 10.1126/science.1175307.  URL http://science.sciencemag.org/content/325/5948/1674.
  * Carr and Head (2010) M. H. Carr and J. W. Head.  Geologic history of Mars.  _Earth and Planetary Science Letters_ , 294(3-4):185–203, June 2010.  doi: 10.1016/j.epsl.2009.06.042.
  * Christensen et al. (2003) P. R. Christensen, J. L. Bandfield, J. F. Bell III, N. Gorelick, V. E. Hamilton, A. Ivanov, B. M. Jakosky, H. H. Kieffer, M. D. Lane, M. C. Malin, T. McConnochie, A. S. McEwen, H. Y. McSween, G. L. Mehall, J. E. Moersch, K. H. Nealson, J. W. Rice, M. I. Richardson, S. W. Ruff, M. D. Smith, T. N. Titus, and M. B. Wyatt.  Morphology and composition of the surface of mars: Mars odyssey themis results.  _Science_ , 300(5628):2056–2061, 2003.  ISSN 0036-8075.  doi: 10.1126/science.1080885.  URL https://science.sciencemag.org/content/300/5628/2056.
  * Clark (1981) R. Clark.  The spectral reflectance of water-mineral mixtures at low temperatures.  _Journal of Geophysical Research: Solid Earth_ , 86(B4):3074–3086, 1981.  doi: 10.1029/JB086iB04p03074.  URL https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/JB086iB04p03074.
  * Clark and Lucey (1984) R. Clark and P. G. Lucey.  Spectral properties of ice-particulate mixtures and implications for remote sensing. 1. intimate mixtures.  _Journal of Geophysical Research_ , 89:6341–6348, 1984\.
  * Clark (1999) R. N. Clark.  _Spectroscopy of Rocks and Minerals, and Principles of Spectroscopy, Volume 3, Remote Sensing for the Earth Sciences_ , volume 3, chapter 1: Spectroscopy of Rocks and Minerals, and Principles of Spectroscopy, pages 3– 58.  (A.N. Rencz, ed.) John Wiley and Sons, 1999.
  * Clark et al. (1986) R. N. Clark, F. P. Fanale, and M. J. Gaffey.  _Surface composition of natural satellites_ , pages 437–491.  1986\.
  * Conway et al. (2019) S. J. Conway, T. de Haas, T. N. Harrison, P. A. Carling, and J. Carrivick.  Martian gullies and their Earth analogues: introduction.  _Geological Society of London Special Publications_ , 467(1):1–6, Jan. 2019.  doi: 10.1144/SP467.15.
  * Cull et al. (2010) S. Cull, R. Arvidson, R. Morris, M. Wolff, M. Mellon, and M. Lemmon.  Seasonal ice cycle at the mars phoenix landing site: 2. postlanding crism and ground observations.  _Journal of Geophysical Research: Planets_ , 115(E5), 2010\.
  * Dundas et al. (2017) C. M. Dundas, A. S. McEwen, M. Chojnacki, M. P. Milazzo, S. Byrne, J. N. McElwaine, and A. Urso.  Granular flows at recurring slope lineae on mars indicate a limited role for liquid water.  _Nature Geoscience_ , 10:903–907, 2017.  doi: 10.1038/s41561-017-0012-5.  URL https://doi.org/10.1038/s41561-017-0012-5.
  * Dundas et al. (2018) C. M. Dundas, A. M. Bramson, L. Ojha, J. J. Wray, M. T. Mellon, S. Byrne, A. S. McEwen, N. E. Putzig, D. Viola, S. Sutton, E. Clark, and J. W. Holt.  Exposed subsurface ice sheets in the martian mid-latitudes.  _Science_ , 359(6372):199–201, 2018.  ISSN 0036-8075.  doi: 10.1126/science.aao1619.  URL http://science.sciencemag.org/content/359/6372/199.
  * Ehlmann et al. (2011) B. L. Ehlmann, J. F. Mustard, S. L. Murchie, J.-P. Bibring, A. Meunier, A. A. Fraeman, and Y. Langevin.  Subsurface water and clay mineral formation during the early history of Mars.  _Nature_ , 479(7371):53–60, Nov. 2011.  doi: 10.1038/nature10582.
  * El-Maarry et al. (2015) M. R. El-Maarry, W. A. Watters, Z. Yoldi, A. Pommerol, D. Fischer, U. Eggenberger, and N. Thomas.  Field investigation of dried lakes in western united states as an analogue to desiccation fractures on mars.  _Journal of Geophysical Research: Planets_ , 120(12):2241–2257, 2015.  ISSN 2169-9100.  doi: 10.1002/2015JE004895.  URL http://dx.doi.org/10.1002/2015JE004895.  2015JE004895.
  * Feldman et al. (2008) W. C. Feldman, J. L. Bandfield, B. Diez, R. C. Elphic, S. Maurice, and S. M. Nelli.  North to south asymmetries in the water-equivalent hydrogen distribution at high latitudes on Mars.  _Journal of Geophysical Research (Planets)_ , 113(E8):E08006, Aug. 2008.  doi: 10.1029/2007JE003020.
  * Gyalay et al. (2019) S. Gyalay, E. Z. Noe Dobrea, K. Chu, and K. M. Pitman.  Nonlinear spectral mixture modeling to estimate water-ice abundance of Martian regolith.  _Icarus_ , 329:79–87, Sept. 2019.  doi: 10.1016/j.icarus.2019.02.033.
  * Hapke (1993) B. Hapke.  _Theory of reflectance and emittance spectroscopy_.  1993\.
  * Hart and Jakosky (1986) H. M. Hart and B. M. Jakosky.  Composition and stability of the condensate observed at the Viking lander 2 site on Mars.  _Icarus_ , 66(1):134–142, Apr. 1986.  doi: 10.1016/0019-1035(86)90013-8.
  * He et al. (2019) C. He, K.-N. Liou, Y. Takano, F. Chen, and M. Barlage.  Enhanced Snow Absorption and Albedo Reduction by Dust-Snow Internal Mixing: Modeling and Parameterization.  _Journal of Advances in Modeling Earth Systems_ , 11(11):3755–3776, Nov. 2019.  doi: 10.1029/2019MS001737.
  * Head et al. (2003) J. W. Head, J. F. Mustard, M. A. Kreslavsky, R. E. Milliken, and D. R. Marchant.  Recent ice ages on Mars.  _Nature_ , 426(6968):797–802, 2003.  ISSN 00280836.  doi: 10.1038/nature02114.
  * Hiroi and Pieters (1994) T. Hiroi and C. M. Pieters.  Estimation of grain sizes and mixing ratios of fine powder mixtures of common geologic minerals.  _Journal of Geophysical Research_ , 99(E5):10867–10880, May 1994.  doi: 10.1029/94JE00841.
  * Horgan et al. (2009) B. H. Horgan, J. F. Bell, E. Z. Noe Dobrea, E. A. Cloutis, D. T. Bailey, M. A. Craig, L. H. Roach, and J. F. Mustard.  Distribution of hydrated minerals in the north polar region of mars.  _Journal of Geophysical Research: Planets_ , 114(E1):n/a–n/a, 2009.  ISSN 2156-2202.  doi: 10.1029/2008JE003187.  URL http://dx.doi.org/10.1029/2008JE003187.  E01005.
  * Jones et al. (1979) K. L. Jones, R. E. Arvidson, E. A. Guinness, S. L. Bragg, S. D. Wall, C. E. Carlston, and D. G. Pidek.  One mars year: Viking lander imaging observations.  _Science_ , 204:799–806, 1979.  doi: 10.1126/science.204.4395.799.
  * Jost et al. (2013) B. Jost, B. Gundlach, A. Pommerol, J. Oesert, S. N. Gorb, J. Blum, and N. Thomas.  Micrometer-sized ice particles for planetary-science experiments - II. Bidirectional reflectance.  _Icarus_ , 225(1):352–366, July 2013.  doi: 10.1016/j.icarus.2013.04.007.
  * Jost et al. (2017) B. Jost, A. Pommerol, O. Poch, Z. Yoldi, S. Fornasier, P. H. Hasselmann, C. Feller, N. Carrasco, C. Szopa, and N. Thomas.  Bidirectional reflectance and vis-nir spectroscopy of cometary analogues under simulated space conditions.  _Planetary and Space Science_ , 145:14 – 27, 2017.  ISSN 0032-0633.  doi: https://doi.org/10.1016/j.pss.2017.07.009.  URL http://www.sciencedirect.com/science/article/pii/S0032063317300168.
  * Kaufmann and Hagermann (2015) E. Kaufmann and A. Hagermann.  Penetration of solar radiation into pure and mars-dust contaminated snow.  _Icarus_ , 252(Supplement C):144 – 149, 2015\.  ISSN 0019-1035.  doi: https://doi.org/10.1016/j.icarus.2015.01.007.  URL http://www.sciencedirect.com/science/article/pii/S0019103515000135.
  * Kieffer (1968) Kieffer.  _Near infrared spectral reflectance of simulated Martian frosts_.  PhD thesis, California Institute of Technology, 1968.
  * Kieffer (1970) Kieffer.  Spectral reflectance of co2-h2o frosts.  _Journal of Geophysical Research_ , 75:501–509, 1970.
  * Langevin et al. (2007a) Y. Langevin, J.-P. Bibring, F. Montmessin, F. Forget, M. Vincendon, S. Douté, F. Poulet, and B. Gondet.  Observations of the south seasonal cap of mars during recession in 2004–2006 by the omega visible/near-infrared imaging spectrometer on board mars express.  _Journal of Geophysical Research: Planets_ , 112(E8):n/a–n/a, 2007a.  ISSN 2156-2202.  doi: 10.1029/2006JE002841.  URL http://dx.doi.org/10.1029/2006JE002841.  E08S12.
  * Langevin et al. (2007b) Y. Langevin, J.-P. Bibring, F. Montmessin, F. Forget, M. Vincendon, S. Douté, F. Poulet, and B. Gondet.  Observations of the south seasonal cap of mars during recession in 2004–2006 by the omega visible/near-infrared imaging spectrometer on board mars express.  _Journal of Geophysical Research: Planets_ , 112(E8):n/a–n/a, 2007b.  ISSN 2156-2202.  doi: 10.1029/2006JE002841.  URL http://dx.doi.org/10.1029/2006JE002841.  E08S12.
  * Laskar et al. (2004) J. Laskar, A. C. M. Correia, M. Gastineau, F. Joutel, B. Levrard, and P. Robutel.  Long term evolution and chaotic diffusion of the insolation quantities of Mars.  _Icarus_ , 170(2):343–364, Aug. 2004.  doi: 10.1016/j.icarus.2004.04.005.
  * Lasue et al. (2013) J. Lasue, N. Mangold, E. Hauber, S. Clifford, W. Feldman, O. Gasnault, C. Grima, S. Maurice, and O. Mousis.  Quantitative assessments of the martian hydrosphere.  _Space Science Reviews_ , 174(1):155–212, Jan 2013.  ISSN 1572-9672.  doi: 10.1007/s11214-012-9946-5.  URL https://doi.org/10.1007/s11214-012-9946-5.
  * Leighton and Murray (1966) R. B. Leighton and B. C. Murray.  Behavior of carbon dioxide and other volatiles on mars.  _Science_ , 153(3732):136–144, 1966.  ISSN 0036-8075.  doi: 10.1126/science.153.3732.136.  URL https://science.sciencemag.org/content/153/3732/136.
  * Levrard et al. (2004) B. Levrard, F. Forget, F. Montmessin, and J. Laskar.  Recent ice-rich deposits formed at high latitudes on Mars by sublimation of unstable equatorial ice during low obliquity.  _Nature_ , 431(7012):1072–1075, Oct. 2004.  doi: 10.1038/nature03055.
  * Mangold et al. (2004) N. Mangold, S. Maurice, W. C. Feldman, F. Costard, and F. Forget.  Spatial relationships between patterned ground and ground ice detected by the Neutron Spectrometer on Mars.  _Journal of Geophysical Research (Planets)_ , 109(E8):E08001, Aug. 2004.  doi: 10.1029/2004JE002235.
  * Massé et al. (2008) M. Massé, S. L. Mouélic, O. Bourgeois, J. Combe, L. L. Deit, C. Sotin, J. Bibring, B. Gondet, and Y. Langevin.  Mineralogical composition, structure, morphology, and geological history of aram chaos crater fill on mars derived from omega mars express data.  _Journal of Geophysical Research: Planets (1991–2012)_ , 113(E12), 12 2008.  ISSN 2156-2202.  doi: 10.1029/2008JE003131.  URL http:https://doi.org/10.1029/2008JE003131.
  * McEwen et al. (2014) A. S. McEwen, C. M. Dundas, S. S. Mattson, A. D. Toigo, L. Ojha, J. J. Wray, M. Chojnacki, S. Byrne, S. L. Murchie, and N. Thomas.  Recurring slope lineae in equatorial regions of mars.  _Nature Geoscience_ , 7:53–58, 2014.  doi: 10.1038/ngeo2014.  URL https://doi.org/10.1038/ngeo2014.
  * Mellon et al. (2009) M. T. Mellon, R. E. Arvidson, H. G. Sizemore, M. L. Searls, D. L. Blaney, S. Cull, M. H. Hecht, T. L. Heet, H. U. Keller, M. T. Lemmon, W. J. Markiewicz, D. W. Ming, R. V. Morris, W. T. Pike, and A. P. Zent.  Ground ice at the phoenix landing site: Stability state and origin.  _Journal of Geophysical Research: Planets_ , 114(E1), 2009\.  doi: 10.1029/2009JE003417.  URL https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2009JE003417.
  * Milliken et al. (2003) R. E. Milliken, J. F. Mustard, and D. L. Goldsby.  Viscous flow features on the surface of Mars: Observations from high-resolution Mars Orbiter Camera (MOC) images.  _Journal of Geophysical Research (Planets)_ , 108(E6):5057, June 2003.  doi: 10.1029/2002JE002005.
  * Mustard et al. (2001) J. F. Mustard, C. D. Cooper, and M. K. Rifkin.  Evidence for recent climate change on Mars from the identification of youthful near-surface ground ice.  _Nature_ , 412(6845):411–414, July 2001.
  * Ojha et al. (2015) L. Ojha, M. B. Wilhelm, S. L. Murchie, A. S. McEwen, J. J. Wray, J. Hanley, M. Masse, and M. Chojnacki.  Spectral evidence for hydrated salts in recurring slope lineae on mars.  _Nature Geoscience_ , 8:829–832, 2015.  doi: 10.1038/ngeo2546.  URL https://doi.org/10.1038/ngeo2546.
  * Plaut et al. (2007) J. J. Plaut, G. Picardi, A. Safaeinili, A. B. Ivanov, S. M. Milkovich, A. Cicchetti, W. Kofman, J. Mouginot, W. M. Farrell, R. J. Phillips, S. M. Clifford, A. Frigeri, R. Orosei, C. Federico, I. P. Williams, D. A. Gurnett, E. Nielsen, T. Hagfors, E. Heggy, E. R. Stofan, D. Plettemeier, T. R. Watters, C. J. Leuschen, and P. Edenhofer.  Subsurface Radar Sounding of the South Polar Layered Deposits of Mars.  _Science_ , 316(5821):92, Apr. 2007.  doi: 10.1126/science.1139672.
  * Poch et al. (2016a) O. Poch, A. Pommerol, B. Jost, N. Carrasco, C. Szopa, and N. Thomas.  Sublimation of water ice mixed with silicates and tholins: Evolution of surface texture and reflectance spectra, with implications for comets.  _Icarus_ , 267:154 – 173, 2016a.  ISSN 0019-1035.  doi: https://doi.org/10.1016/j.icarus.2015.12.017.  URL http://www.sciencedirect.com/science/article/pii/S0019103515005709.
  * Poch et al. (2016b) O. Poch, A. Pommerol, B. Jost, N. Carrasco, C. Szopa, and N. Thomas.  Sublimation of ice–tholins mixtures: A morphological and spectro-photometric study.  _Icarus_ , 266:288 – 305, 2016b.  ISSN 0019-1035.  doi: https://doi.org/10.1016/j.icarus.2015.11.006.  URL http://www.sciencedirect.com/science/article/pii/S0019103515005163.
  * Pommerol and Schmitt (2008) A. Pommerol and B. Schmitt.  Strength of the h2o near-infrared absorption bands in hydrated minerals: Effects of particle size and correlation with albedo.  _Journal of Geophysical Research: Planets_ , 113(E10):n/a–n/a, 2008.  ISSN 2156-2202.  doi: 10.1029/2007JE003069.  URL http://dx.doi.org/10.1029/2007JE003069.  E10009.
  * Pommerol et al. (2011) A. Pommerol, G. Portyankina, N. Thomas, K.-M. Aye, C. J. Hansen, M. Vincendon, and Y. Langevin.  Evolution of south seasonal cap during martian spring: Insights from high-resolution observations by hirise and crism on mars reconnaissance orbiter.  _Journal of Geophysical Research: Planets_ , 116(E8):n/a–n/a, 2011.  ISSN 2156-2202.  doi: 10.1029/2010JE003790.  URL http://dx.doi.org/10.1029/2010JE003790.  E08007.
  * Pommerol et al. (2013) A. Pommerol, T. Appéré, G. Portyankina, K. M. Aye, N. Thomas, and C. J. Hansen.  Observations of the northern seasonal polar cap on Mars III: CRISM/HiRISE observations of spring sublimation.  _Icarus_ , 225(2):911–922, Aug. 2013.  doi: 10.1016/j.icarus.2012.08.039.
  * Pommerol et al. (2013) A. Pommerol, N. Thomas, B. Jost, P. Beck, C. Okubo, and A. S. McEwen.  Photometric properties of mars soils analogs.  _Journal of Geophysical Research: Planets_ , 118(10):2045–2072, 2013.  ISSN 2169-9100.  doi: 10.1002/jgre.20158.  URL http://dx.doi.org/10.1002/jgre.20158.
  * Pommerol et al. (2013) A. Pommerol, N. Thomas, B. Jost, P. Beck, C. Okubo, and A. S. McEwen.  Photometric properties of Mars soils analogs.  _Journal of Geophysical Research (Planets)_ , 118(10):2045–2072, Oct. 2013.  doi: 10.1002/jgre.20158.
  * Pommerol et al. (2015) A. Pommerol, B. Jost, O. Poch, M. El-Maarry, B. Vuitel, and N. Thomas.  The {SCITEAS} experiment: Optical characterizations of sublimating icy planetary analogues.  _Planetary and Space Science_ , 109–110:106 – 122, 2015\.  ISSN 0032-0633.  doi: https://doi.org/10.1016/j.pss.2015.02.004.  URL http://www.sciencedirect.com/science/article/pii/S0032063315000380.
  * Pommerol et al. (2019) A. Pommerol, B. Jost, O. Poch, Z. Yoldi, Y. Brouet, A. Gracia-Berná, R. Cerubini, A. Galli, P. Wurz, B. Gundlach, J. Blum, N. Carrasco, C. Szopa, and N. Thomas.  Experimenting with mixtures of water ice and dust as analogues for icy planetary material.  _Space Science Reviews_ , 215(5):37, Jun 2019\.  ISSN 1572-9672.  doi: 10.1007/s11214-019-0603-0.  URL https://doi.org/10.1007/s11214-019-0603-0.
  * Poulet et al. (2007) F. Poulet, C. Gomez, J.-P. Bibring, Y. Langevin, B. Gondet, P. Pinet, G. Belluci, and J. Mustard.  Martian surface mineralogy from observatoire pour la minéralogie, l’eau, les glaces et l’activité on board the mars express spacecraft (omega/mex): Global mineral maps.  _Journal of Geophysical Research: Planets_ , 112(E8), 2007\.  doi: 10.1029/2006JE002840.  URL https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2006JE002840.
  * Roloff et al. (2017) V. Roloff, A. Pommerol, L. Gambicorti, A. Servonet, N. Thomas, M. Brändli, A. Casciello, G. Cremonese, V. Da Deppo, M. Erismann, I. Ficai Veltroni, M. Gerber, M. Gruber, P. Gubler, T. Hausner, M. Johnson, P. Lochmatter, E. Pelò, B. Sodor, S. Szalai, G. Troznai, D. Vernani, T. Weigel, R. Ziethe, and C. Zimmermann.  On-ground performance and calibration of the exomars trace gas orbiter cassis imager.  _Space Science Reviews_ , 212(3):1871–1896, Nov 2017.  ISSN 1572-9672.  doi: 10.1007/s11214-017-0404-2.  URL https://doi.org/10.1007/s11214-017-0404-2.
  * Roush et al. (1990) T. L. Roush, J. B. Pollack, F. C. Witteborn, J. D. Bregman, and J. P. Simpson.  Ice and minerals on Callisto: A reassessment of the reflectance spectra.  _Icarus_ , 86(2):355–382, Aug. 1990.  doi: 10.1016/0019-1035(90)90225-X.
  * Smith et al. (2020) I. B. Smith, P. O. Hayne, S. Byrne, P. Becerra, M. Kahre, W. Calvin, C. Hvidberg, S. Milkovich, P. Buhler, M. Land is, B. Horgan, A. Kleinböhl, M. R. Perry, R. Obbard, J. Stern, S. Piqueux, N. Thomas, K. Zacny, L. Carter, L. Edgar, J. Emmett, T. Navarro, J. Hanley, M. Koutnik, N. Putzig, B. L. Henderson, J. W. Holt, B. Ehlmann, S. Parra, D. Lalich, C. Hansen, M. Hecht, D. Banfield, K. Herkenhoff, D. A. Paige, M. Skidmore, R. L. Staehle, and M. Siegler.  The Holy Grail: A road map for unlocking the climate record stored within Mars’ polar layered deposits.  _Planetary and Space Science_ , 184:104841, May 2020.  doi: 10.1016/j.pss.2020.104841.
  * Smith (2002) M. D. Smith.  The annual cycle of water vapor on Mars as observed by the Thermal Emission Spectrometer.  _Journal of Geophysical Research (Planets)_ , 107(E11):5115, Nov. 2002.  doi: 10.1029/2001JE001522.
  * Smith et al. (2009) P. H. Smith, L. K. Tamppari, R. E. Arvidson, D. Bass, D. Blaney, W. V. Boynton, A. Carswell, D. C. Catling, B. C. Clark, T. Duck, E. DeJong, D. Fisher, W. Goetz, H. P. Gunnlaugsson, M. H. Hecht, V. Hipkin, J. Hoffman, S. F. Hviid, H. U. Keller, S. P. Kounaves, C. F. Lange, M. T. Lemmon, M. B. Madsen, W. J. Markiewicz, J. Marshall, C. P. McKay, M. T. Mellon, D. W. Ming, R. V. Morris, W. T. Pike, N. Renno, U. Staufer, C. Stoker, P. Taylor, J. A. Whiteway, and A. P. Zent.  H2o at the phoenix landing site.  _Science_ , 325(5936):58–61, 2009.  ISSN 0036-8075.  doi: 10.1126/science.1172339.  URL https://science.sciencemag.org/content/325/5936/58.
  * Svitek and Murray (1990) T. Svitek and B. Murray.  Winter frost at Viking Lander 2 site.  _Journal of Geophysical Research_ , 95:1495–1510, Feb. 1990\.  doi: 10.1029/JB095iB02p01495.
  * Thomas et al. (2017) N. Thomas, G. Cremonese, R. Ziethe, M. Gerber, M. Brändli, G. Bruno, M. Erismann, L. Gambicorti, T. Gerber, K. Ghose, M. Gruber, P. Gubler, H. Mischler, J. Jost, D. Piazza, A. Pommerol, M. Rieder, V. Roloff, A. Servonet, W. Trottmann, T. Uthaicharoenpong, C. Zimmermann, D. Vernani, M. Johnson, E. Pelò, T. Weigel, J. Viertl, N. De Roux, P. Lochmatter, G. Sutter, A. Casciello, T. Hausner, I. Ficai Veltroni, V. Da Deppo, P. Orleanski, W. Nowosielski, T. Zawistowski, S. Szalai, B. Sodor, S. Tulyakov, G. Troznai, M. Banaskiewicz, J. C. Bridges, S. Byrne, S. Debei, M. R. El-Maarry, E. Hauber, C. J. Hansen, A. Ivanov, L. Keszthelyi, R. Kirk, R. Kuzmin, N. Mangold, L. Marinangeli, W. J. Markiewicz, M. Massironi, A. S. McEwen, C. Okubo, L. L. Tornabene, P. Wajer, and J. J. Wray.  The colour and stereo surface imaging system (cassis) for the exomars trace gas orbiter.  _Space Science Reviews_ , 212(3):1897–1944, Nov 2017.  ISSN 1572-9672.  doi: 10.1007/s11214-017-0421-1.  URL https://doi.org/10.1007/s11214-017-0421-1.
  * Thomas et al. (2020) P. C. Thomas, W. M. Calvin, and P. B. James.  Debris accumulations of CO2 ice in the south polar residual cap of mars: Longevity and processes.  _Icarus_ , 341:113625, May 2020.  doi: 10.1016/j.icarus.2020.113625.
  * Vago et al. (2017) J. L. Vago, F. Westall, Pasteur Instrument Team, Pasteur Landing Team, A. J. Coates, R. Jaumann, O. Korablev, V. Ciarletti, I. Mitrofanov, J.-L. Josset, M. C. De Sanctis, J.-P. Bibring, F. Rull, F. Goesmann, H. Steininger, W. Goetz, W. Brinckerhoff, C. Szopa, F. Raulin, F. Westall, H. G. M. Edwards, L. G. Whyte, A. G. Fairén, J.-P. Bibring, J. Bridges, E. Hauber, G. G. Ori, S. Werner, D. Loizeau, R. O. Kuzmin, R. M. E. Williams, J. Flahaut, F. Forget, J. L. Vago, D. Rodionov, O. Korablev, H. Svedhem, E. Sefton-Nash, G. Kminek, L. Lorenzoni, L. Joudrier, V. Mikhailov, A. Zashchirinskiy, S. Alexashkin, F. Calantropio, A. Merlo, P. Poulakis, O. Witasse, O. Bayle, S. Bayón, U. Meierhenrich, J. Carter, J. M. García-Ruiz, P. Baglioni, A. Haldemann, A. J. Ball, A. Debus, R. Lindner, F. Haessig, D. Monteiro, R. Trautner, C. Voland, P. Rebeyre, D. Goulty, F. Didot, S. Durrant, E. Zekri, D. Koschny, A. Toni, G. Visentin, M. Zwick, M. van Winnendael, M. Azkarate, C. Carreau, and ExoMars Project Team.  Habitability on Early Mars and the Search for Biosignatures with the ExoMars Rover.  _Astrobiology_ , 17(6-7):471–510, July 2017.  doi: 10.1089/ast.2016.1533.
  * Yasunari et al. (2011) T. J. Yasunari, R. D. Koster, K. M. Lau, T. Aoki, Y. C. Sud, T. Yamazaki, H. Motoyoshi, and Y. Kodama.  Influence of dust and black carbon on the snow albedo in the NASA Goddard Earth Observing System version 5 land surface model.  _Journal of Geophysical Research (Atmospheres)_ , 116(D2):D02210, Jan. 2011.  doi: 10.1029/2010JD014861.
  * Yoldi et al. (2015) Z. Yoldi, A. Pommerol, B. Jost, O. Poch, J. Gouman, and N. Thomas.  Vis-nir reflectance of water ice/regolith analogue mixtures and implications for the detectability of ice mixed within planetary regoliths.  _Geophysical Research Letters_ , 42(15):6205–6212, 2015.  ISSN 1944-8007.  doi: 10.1002/2015GL064780.  URL http://dx.doi.org/10.1002/2015GL064780.  2015GL064780.
  * Yoldi et al. (2015) Z. Yoldi, A. Pommerol, B. Jost, O. Poch, J. Gouman, and N. Thomas.  VIS-NIR reflectance of water ice/regolith analogue mixtures and implications for the detectability of ice mixed within planetary regoliths.  _Geophysical Research Letters_ , 42(15):6205–6212, Aug. 2015.  doi: 10.1002/2015GL064780.
  * Yoldi et al. (2018a) Z. Yoldi, A. Pommerol, O. Poch, and N. Thomas.  Laboratory hyperspectral study of ice and mars soil simulant associations. comparison with crism observations of icy surfaces.  2018a.  URL https://www.hou.usra.edu/meetings/lpsc2018/pdf/2158.pdf.
  * Yoldi et al. (2018b) Z. Yoldi, A. Pommerol, and N. Thomas.  Experimental, spectral and colour analysis of h2o and co2 ices and dust samples. application to martian icy surfaces.  2018b.  URL https://meetingorganizer.copernicus.org/EPSC2018/EPSC2018-805.pdf.
  * Zhang et al. (2014) H. Zhang, Y. Yang, W. Jin, C. Liu, and W. Hsu.  Effects of Spectralon absorption on reflectance spectra of typical planetary surface analog materials.  _Optics Express_ , 22(18):21280, Sept. 2014.  doi: 10.1364/OE.22.021280.