Axel Bouquety
email: a.bouquety@gmail.com

Antoine Sejourné

François Costard

Denis Mercier

Sylvain Bouley

Morphometric evidence of 3.6 Ga glacial valleys and glacial cirques in martian highlands: south of Terra Sabaea

Keywords: Glacial landscape, Late Noachian/Early Hesperian, Morphometry, Early Mars

The climate of early Mars remains unclear and the debate is topical. Recently, climatic models have suggested a cold climate during the Noachian/ Early Hesperian on Mars, which goes against the wet and warm climate often put forward. The purpose of this study is to seek geomorphologic evidence of this early cold climate. To achieve this, a step-by-step study of the geometry and morphology of several martian valleys has been done in the southern highlands. The analysis highlights the morphometric properties which enable the identication of martian glacial landscapes. We identied 100 cirques and 83 glacial valleys in two craters and on one mountain in the southern part of Terra Sabaea. The studied morphologies have the same morphometric characteristics and trends as terrestrial and martian glacial valleys and glacial cirques. In contrary, these trends are very dierent from those observed in uvial valleys on Earth and on Mars. (1) The martian glacial valleys are U-shaped with a large at oor and a V-index > 0.20. While martian and terrestrial uvial valleys are V-shaped with a V-index < 0.1. (2) The length to width ratio is >1 while for uvial valleys this ratio is > >1. (3) Finally, the cross-sectional area and the elevation are higher for the glacial valleys compared to the uvial ones. These glacial valleys often originate with a topographic hollow which have the same properties than terrestrial glacial cirque. The glacial landscapes identied in southern Terra Sabaea are restricted to elevations > 1000 m and are dated by crater counting to be 3.6 Ga. This study strongly supports glacial processes as the origin of these valleys and cirques, and is the rst morphometric evidence of glacial valleys associated with glacial cirques in the southern highlands in agreement with the climatic models. We propose that the martian climate during the late Noachian/early Hesperian was characterized by glaciated highlands at elevations greater than 1500 m and at lower elevations where uvial valley network has been identied (<1500 m) the climate was more temperate allowing liquid water to be stable and creating uvial valley

Introduction

The presence of valley network is one of the best lines of evidence for prolonged surface water on Mars, and they are located preferentially in the southern highlands. These valleys have V-shaped or U-shaped cross-prole shapes and commonly include inlet and outlet valleys of Noachian-aged basins (Fassett and Head, 2008b). The valleys width ranges is from 50 m to 10 km, their median depth is 80 m and their length is usually less than few hundred kilometers. The origin of the valley networks remains uncertain and four hypotheses are proposed: (1) precipitation-fed surface runo [START_REF] Craddock | The case for rainfall on a warm, wet early mars[END_REF]; (2) runo fed by surface ice melting [START_REF] Segura | Environmental eects of large impacts on mars[END_REF]; (3) runo fed by surface or near surface melting by magmatic intrusions [START_REF] Gulick | Origin of the valley networks on mars: a hydrological perspective[END_REF]; (4) sapping from subsurface aquifers [START_REF] Carr | The martian drainage system and the origin of valley networks and fretted channels[END_REF]. Whatever their formation process(es), the presence of valley networks similar to those on Earth [START_REF] Baker | Water and the martian landscape[END_REF][START_REF] Hynek | Updated global map of martian valley networks and implications for climate and hydrologic processes[END_REF], clay minerals [START_REF] Bibring | Global mineralogical and aqueous mars history derived from OMEGA/mars express data[END_REF], lakes, alluvial fans, and deltas [START_REF] Ramirez | The geological and climatological case for a warmer and wetter early mars[END_REF] show that during the Noachian (4.5-3.7 Ga), a hydrosphere was active on the surface of Mars with relatively warm and wet conditions. Some of these valley networks, are dated to the early Hesperian around 3.6 Ga (Fassett and Head, 2008a;[START_REF] Bouley | Age dates of valley network drainage basins and subbasins within sabae and arabia terrae, mars[END_REF]. During the Hesperian, there was the formation of outow channels [START_REF] Carr | Meter-scale characteristics of martian channels and valleys[END_REF]. The abrupt emergence of outow channels into the landscape indicates a formation by the rapid release of large volumes of water stored as subsurface groundwater or as an aquifer under pressure [START_REF] Carr | Geologic history of mars[END_REF]. In addition, the observed surface alteration products changed, the Noachian clays gave way to sulfates from the late Noachian to the Hesperian, which indicates a global change in the aqueous chemistry of Mars [START_REF] Bibring | Global mineralogical and aqueous mars history derived from OMEGA/mars express data[END_REF]. These mineralogical and geomorphological lines of evidence show that the active Noachian hydrosphere lost its intensity and changed to a cryosphere during the Hesperian [START_REF] Carr | Geologic history of mars[END_REF].

Currently, the distribution of valley networks appears to be controlled by the topography induced by the Tharsis dome. Based on this correlation, [START_REF] Phillips | Ancient geodynamics and global-scale hydrology on mars[END_REF] suggested that the valley networks were formed after the formation of Tharsis, during the Noachian. However, recent geodynamic modeling showed that without Tharsis, the valley networks would have the same distribution as observed today, in a south tropical band from 40°S to 0°S [START_REF] Bouley | Late tharsis formation and implications for early mars[END_REF]. The growth of the Tharsis dome started during the Noachian era (more than 3.7 billion years ago). Its position has induced a reorientation of the planet with respect to its spin axis (true polar wander, TPW), which is responsible for the present equatorial position of the volcanic province [START_REF] Bouley | Late tharsis formation and implications for early mars[END_REF]. It has been suggested that the Tharsis load on the lithosphere aected the orientation of the valley networks [START_REF] Bouley | Late tharsis formation and implications for early mars[END_REF]. Moreover, climate modeling has shown that with Noachian/ early Hesperian conditions, with an atmospheric pressure less than 1 bar, a reduced Tharsis bulge topography, and an obliquity of 45°, there is a preferential deposition of ice in the southern highlands in the same area as the valley networks [START_REF] Wordsworth | Global modelling of the early martian climate under a denser CO2 atmosphere: Water cycle and ice evolution[END_REF][START_REF] Bouley | Late tharsis formation and implications for early mars[END_REF]. This globally sub-zero scenario called icy-highlands for the late Noachian climate may be sucient to explain most of the uvial morphology and geology without the need to invoke additional long-term warming mechanisms or an early warm and wet Mars [START_REF] Wordsworth | Global modelling of the early martian climate under a denser CO2 atmosphere: Water cycle and ice evolution[END_REF][START_REF] Head | The climate history of early mars: insights from the antarctic McMurdo dry valleys hydrologic system[END_REF]. Therefore, it is postulated that the valley networks could have been formed in a cold climate.

So, on the one hand, several studies invoke a wet and warm climate allowing the formation of the valley networks [START_REF] Carr | The martian drainage system and the origin of valley networks and fretted channels[END_REF][START_REF] Craddock | The case for rainfall on a warm, wet early mars[END_REF][START_REF] Bibring | Global mineralogical and aqueous mars history derived from OMEGA/mars express data[END_REF][START_REF] Carr | Geologic history of mars[END_REF]. And on the other hand, the new models invoke the icy-highlands scenario for early Mars [START_REF] Wordsworth | Global modelling of the early martian climate under a denser CO2 atmosphere: Water cycle and ice evolution[END_REF][START_REF] Bouley | Late tharsis formation and implications for early mars[END_REF].

The purpose of this study is to seek geomorphologic evidence of this hypothesised cold climate in the southern highlands. To achieve this, we studied an area in Terra Sabea where ice should have been accumulated according to the models [START_REF] Wordsworth | Global modelling of the early martian climate under a denser CO2 atmosphere: Water cycle and ice evolution[END_REF][START_REF] Bouley | Late tharsis formation and implications for early mars[END_REF]. We performed a comparison between morphologies found in this area and those found in previously studied martian and terrestrial glacial and uvial valleys. By studing the geometry and the morphology of the features we can deduce whether the origin of the valleys is liquid water or owing ice.

Glacial landforms on Earth and Mars

Characteristics of glacial landforms on Earth

Glacial landforms can be recognized based on their geometry and morphology. [START_REF] Penck | Glacial features in the surface of the alps[END_REF] and de [START_REF] De Martonne | L'érosion glaciaire et la formation des vallées alpines[END_REF] were the rst to compare the morphology of alpine glacial valleys with uvial valleys. Firstly, the study of glacial valleys revealed that their morphometry is very dierent from uvial valleys (Section 4.2). Secondly, it showed that glacial valleys are often associated with other stuctures characteristic of glacial activity. These valleys are characterized by an accumulation of snow at the valley head forming a cirque. The snow then compacts and sinters to ice, and by the action of gravity the ice mass ows down the slope above the equilibrium line, the accumulation zone. Below the equilibrium line, the glacier enters in the ablation zone. Here, the ice melts and/or sublimates and meltwater and sediment are delivered on the proglacial plains [START_REF] Bennett | Glacial Geology[END_REF]. The deposital features created are: (1) moraines resulting from debris entrained during glacial erosion that are transported and deposited at the glacier side and/or the glacier front when the glacier is stable and then retreats. The frontal moraine indicates the maximum advance of the glacier [START_REF] Andersson | Genesis of hummocky moraine in the bolmen area, southwestern sweden[END_REF][START_REF] Ewertowski | Quantication of the ice-cored moraines' short-term dynamics in the high-arctic glaciers ebbabreen and ragnarbreen, petuniabukta, svalbard[END_REF]. ( 2) Eskers which are a type of straight-to-sinous ridge composed of sand and gravel resulting from the ow of glacial meltwater in predominantly subglacial and englacial conduits [START_REF] Bennett | Glacial Geology[END_REF]. Eskers are generally formed under warm-based glaciers, the core being formed in a tunnel inside the ice [START_REF] Brennand | Deglacial meltwater drainage and glaciodynamics: inferences from laurentide eskers, canada[END_REF]. At and beyond the margin of the glacier, ice blocks buried in the esker will melt and form (3) kettle holes [START_REF] Fitzsimons | Supraglacial eskers in antarctica[END_REF]. Kettle hole are enclosed topographic depression that is formed at the surface of outwash deposits in recently deglaciated surface [START_REF] Corti | Soil formation in kettle holes from high altitudes in central apennines, italy[END_REF]. This landform assemblage, making up a classic glacial landscape, is composed of a glacial cirque, a glacial valley, and associated deposits. This assemblage is found in regions which have experienced glacial activity, and their distributions is linked to paleoclimate [START_REF] Barr | Glacial cirques as palaeoenvironmental indicators: Their potential and limitations[END_REF].

Past and recent martian glaciations

Evidence of past glaciations have been extensively reported on Mars. In the southern hemisphere, at latitudes higher than 30°, some craterwall valleys have been interpreted as glacial valleys in two Noachianaged craters and in one Hesperian-aged crater [START_REF] Hobbs | Analysis of crater valleys, noachis terra, mars: Evidence of uvial and glacial processes[END_REF]Fig. 1). These glacial valleys exhibit a U-shaped cross-section and a length to width ratio >1 while uvial valleys have a length to width ratio > >1 [START_REF] Hobbs | Analysis of crater valleys, noachis terra, mars: Evidence of uvial and glacial processes[END_REF]. In addition, evidence of old glacial landsystem (3.5 Ga) in Ius Chasma and Central Candor Chasma in Valles Marineris have been identied using paraglacial structures [START_REF] Mège | Equatorial glaciations on mars revealed by gravitational collapse of valles marineris wallslopes[END_REF][START_REF] Gourronc | One million cubic kilometers of fossil ice in valles marineris: Relicts of a 3.5gy old glacial landsystem along the martian equator[END_REF].

Evidence of Amazonian glaciation has been extensively reported in the mid-latitudes. This takes the form of viscous ow features (VFF) that often appear on the slopes of high-relief features and exhibit morphologies indicative of glacial viscous ow [START_REF] Souness | Mid-latitude glaciation on mars[END_REF]. They are elongated ow-like features composed of essentially pure glacial ice below a protective layer of debris [START_REF] Holt | Radar sounding evidence for buried glaciers in the southern mid-latitudes of mars[END_REF][START_REF] Plaut | Radar evidence for ice in lobate debris aprons in the mid-northern latitudes of mars[END_REF]. VFF can be divided into three types: (1) glacier-like forms (GLF) are visually similar to terrestrial valley glaciers, showing signs of downpositive relief viscous deformation [START_REF] Hubbard | Glacier-like forms on mars[END_REF] (2) lobate debris aprons (LDA) are characterized by lobate features surrounding massifs and are often observed at the base of crater walls, in that case it is call concentric crater ll (CCF; Squyres 1979) (3) lineated valleys lls (LVF) are formed on valley oors from the convergence of two or more LDA-type ows [START_REF] Squyres | The distribution of lobate debris aprons and similar ows on mars[END_REF]. Finally, previous work has reported deposit features similar to terrestrial eskers [START_REF] Kargel | Ancient glaciation on mars[END_REF][START_REF] Fastook | Early mars climate near the noachianhesperian boundary: Independent evidence for cold conditions from basal melting of the south polar ice sheet (dorsa argentea formation) and implications for valley network formation[END_REF][START_REF] Gallagher | Eskers in a complete, wet-based glacial system in the phlegra montes region, mars[END_REF][START_REF] Butcher | Are the dorsa argentea on mars eskers?[END_REF] and moraines like-ridges (MLR) at the foot of many midlatitude crater walls [START_REF] Arfstrom | Martian ow features, moraine-like ridges, and gullies: Terrestrial analogs and interrelationships[END_REF][START_REF] Conway | Glacial and gully erosion on mars: A terrestrial perspective[END_REF]. These landforms are in many cases similar to glacial landforms on Earth and allow analogue-based comparisons to be made [START_REF] Souness | Mid-latitude glaciation on mars[END_REF].

Study area in Terra Sabaea

Description of the area

We focused our study on Terra Sabaea. Terra Sabaea is located northwest of Hellas planitia (Fig. 1a). This area is characterized by a high density of valley networks dated of the late Noachian/early Hesperian [START_REF] Hynek | Updated global map of martian valley networks and implications for climate and hydrologic processes[END_REF][START_REF] Bouley | Age dates of valley network drainage basins and subbasins within sabae and arabia terrae, mars[END_REF]Fig. 1b). The majority of these valley networks are located in the inter crater plains, but some of them are located on the inner wall of impact craters in the study area (Fig. 2a). We noted that some valley-like features, unmapped by [START_REF] Hynek | Updated global map of martian valley networks and implications for climate and hydrologic processes[END_REF], could be found on both negative relief features, such as impact craters, but also on positive relief features, such as mountains (Fig. 2b,c,d). Terra Sabaea has a mean elevation of 1740 m and is located where ice is predicted to have been deposited in the Noachian according to the models described above [START_REF] Wordsworth | Global modelling of the early martian climate under a denser CO2 atmosphere: Water cycle and ice evolution[END_REF][START_REF] Bouley | Late tharsis formation and implications for early mars[END_REF]. To seek geomorphologic evidence for this hypothesised cold climate, we studied three sites: Dawes crater, an unnamed crater we called crater 1 and a unnamed mountain we called mountain 1 (Fig. 2).

Mountain 1

This feature is an isolated mountain 2 km high with a summit at 3.5 km in elevation above the MOLA reference datum. It is located 425 km to the northeast of Dawes crater (42°17'E, 2°55'S; Fig. 2a). The south facing slope appears topographically bland and the north facing slope is dissected by valleys running from the summit to the base with lengths on the order of tens of kilometers (Fig. 2b).

Crater 1

This unnamed crater is located at 150 km to the east of Dawes crater (42°34'E, 9°10'S; Fig. 2a). It has a diameter of 74 km and a depth of 2 km. It is dated to the early Noachian [START_REF] Tanaka | Geological map of marsHttp[END_REF]. Its walls have some unmapped valleys of tens of kilometers in length (Fig. 2c).

Dawes crater

Dawes crater is a large impact crater (38°8'E, 8°55'S; Fig. 2a) with a diameter of 200 km, a depth of 2.5 km and has walls with steep inner slopes > 20°(Fig. 2d). Its walls have 35 valleys mapped by [START_REF] Hynek | Updated global map of martian valley networks and implications for climate and hydrologic processes[END_REF] as valley networks, located on the southern wall (Fig. 2a). The northern wall has some unmapped valleys. Dawes crater is dated to the late Noachian [START_REF] Tanaka | Geological map of marsHttp[END_REF].

Data and methods

Imagery

The purpose of the study is to dene if the valleys in the study area are glacial or uvial. To achieve this we compared the studied valleys with known cases on Earth and Mars. We used Context Camera image (CTX) with a resolution of 6 m/pixel (Fig. 3a; [START_REF] Malin | Mars global surveyor mars orbiter camera: Interplanetary cruise through primary mission[END_REF] to characterize the valleys. This rst step was the most important because it allowed us to identify the morphologies to be studied in more detail.

Then, to constrain their geometry, we used the Digital Terrain Map Reduced Data Record (DTMRDR) data with 1 m numeric height resolution from High-Resolution Stereo Camera (HRSC) with a resolution of 10-20 m/pixel depending on the ground resolution of the respective image [START_REF] Gwinner | The high resolution stereo camera (HRSC) of mars express and its approach to science analysis and mapping for mars and its satellites[END_REF] and MOLA gridded global digital elevation data with a resolution of 1/64°in latitude x 1/32°in longitude (Fig. 3b; [START_REF] Smith | Mars orbiter laser altimeter: Experiment summary after the rst year of global mapping of mars[END_REF]. We made our measurements using ArcGIS software. The projection systems used was SimpleCylindrical_Mars for CTX, with this projection, distortion increases as the distance from the 3). Images credit NASA/JPL/University of Arizona. standard parallels increases. We used SINUSOIDAL_MARS for DTMRDR, the scale along all parallels and the central meridian of the projection is accurate. And Mars2000_ECylindrical_clon0 for MOLA.

Our study areas are near the equator (between 2°and 9°S), which is a standard parallels so the distortions can be neglected. To measure valleys on Earth, we used data from the Institut national de l'information géographique et forestière (IGN). We used the 25m/pixel DEM. 4.2. Morphometrical analysis of terrestrial glacial landscapes 4.2.1. Terrestrial glacial and uvial valleys [START_REF] Penck | Glacial features in the surface of the alps[END_REF] showed that the cross-section area of alpine glacial valleys increases down to the equilibrium line and then decreases downstream to the end of the valley. This is the law of adjusted cross-sections [START_REF] Penck | Glacial features in the surface of the alps[END_REF]. Since 1905, numerous authors have studied the morphological and geometrical dierences between uvial and glacial terrestrial valleys using various parameters: length, width, slope, elevation, drainage area, and cross-section. The own properties of ice and liquid water (state of matter, velocity, rate of abrasion...) make that glacial valleys are dierent from uvial valleys by the footprint they leave in the landscape.

Generally, a glacial valley is U-shaped with a wide at oor, steep walls and symmetric shoulders [START_REF] Penck | Glacial features in the surface of the alps[END_REF][START_REF] Livers | An evaluation of stream characteristics in glacial versus uvial process domains in the colorado front range[END_REF]. These characteristics come from the processes of glacial erosion: (1) Glacial quarrying is the means by which a glacier removes larger chunks and fragments from its bed and walls [START_REF] Bennett | Glacial Geology[END_REF]. ( 2) Glacial abrasion is the process by which rock particles transported at the base of a glacier are moved across a bedrock surface scratching and wearing it away [START_REF] Bennett | Glacial Geology[END_REF].

A uvial valley is V-shaped with a narrow oor, gentle walls and symmetric shoulders [START_REF] Montgomery | Valley formation by uvial and glacial erosion[END_REF][START_REF] Livers | An evaluation of stream characteristics in glacial versus uvial process domains in the colorado front range[END_REF]. These characteristics come from the process of uvial erosion: (1) Water abrasion generate detachment of soil particles by owing water under the inuence of both drag and lift forces [START_REF] Léonard | Estimation of runo critical shear stress for soil erosion from soil shear strength[END_REF]. These dierences of erosion have inuences on morphology and geometry of these two kinds of valleys. Then, from literature, we created a list of morphological and geometrical characteristics that allow the distinction of glacial valleys from uvial ones (Table 1).

Terrestrial glacial cirques

Terrestrial glacial valleys have often valley heads upstream where the ice accumulates. When these valley heads are a hollow, open downstream but bounded upstream by the crest of a steep slope a `headwall' (>27°) which is arcuate in plan around a more gently sloping oor (<27°), They are called glacial cirqueIt is glacial if the oor has been aected by glacial erosion while part of the headwall has developed subaerially, and a drainage divide was located suciently close to the top of the headwall (the cirque crest) for little or none of the ice that fashioned the cirque to have owed in from outside, [START_REF] Barr | Glacial cirques as palaeoenvironmental indicators: Their potential and limitations[END_REF][START_REF] Evans | Comparability of cirque size and shape measures between regions and between researchers[END_REF]. The characteristics of cirques are readily measurable due to in the absence of ice and can include:

(1) their spatial distribution, (2) the length (L), (3) the width (W ), (4) the amplitude (A), ( 5) the height range (H ), (6) the size ( 3 √ LW H), and ( 7) the axial gradient (arctan(A/L)). This parameter approximates the surface slope of a former glacier just lling the cirque [START_REF] Barr | Glacial cirques as palaeoenvironmental indicators: Their potential and limitations[END_REF][START_REF] Evans | Comparability of cirque size and shape measures between regions and between researchers[END_REF].

Often, cirque size is calculated in order to assess whether cirques have developed isometrically (whether the rate of growth has been equal in all three orthogonal dimensions) or allometrically (whether the rate of cirque lengthening, widening and deepening has been unequal, and cirques have therefore changed shape Table 1. Morphological and geometrical criteria used to distinguish uvial and glacial valley in this study based on terrestrial studies.

during development ;[START_REF] Olyphant | Allometry and cirque evolution[END_REF][START_REF] Evans | Allometry, scaling and scale-specicity of cirques, landslides and other landforms[END_REF]). To assess this, length, width and altitudinal range are plotted against cirque size. They can provide information about the duration and intensity of the glacial conditions that formed them [START_REF] Delmas | A critical appraisal of allometric growth among alpine cirques based on multivariate statistics and spatial analysis[END_REF].

Morphometrical analysis of valleys on Mars

We used all the criteria described in Table 1 and in Table 2 to study the mapped valley networks and unmapped valleys in our study area. Authors studying terrestrial landscapes generally use only three or four parameters to characterize valleys and emphasis is placed on the shape of the valley, U-shaped for glacial valleys and V-shaped for uvial ones. The shape is an important indicator of the origin of the valley, but it is not always a discrimining parameter, for example, a V-shaped valley can be lled by deposits and become more U-shaped. In order to circumvent this problem, in this paper, we studied the morphometry of the martian valleys using as many parameters as possible to interpret the origin of the valleys.

Morphological identication of the valleys and their drainage area

The rst step in the analysis was to dene the outline of the studied valleys using two criteria: (1) The shoulders of the valley should be well preserved and should be continous over hundred of meters. As for terrestrial measurements, we chose to stop the valley when we can no longer follow the crest [START_REF] Livers | An evaluation of stream characteristics in glacial versus uvial process domains in the colorado front range[END_REF]. ( 2) The overall morphology should be the same along the whole length of the valley. For the valley networks, we do not consider the entire network as a single valley but as a set of tributary valleys. The shapele thus obtained allowed us to dene the outline of the valley, but also to obtain the drainage area within which the erosion (by ice or liquid water) took place (Fig. 4a).

Valley length and width

The length of the valley was dened using a longitudinal line extending from the furthest upstream part of the valley to the downstream part of the valley, sub-parallel to the valley shoulders (Fig. 4a). Then, in order to have a wide range of measurement, we divided the length into four segments of equal length. The width was measured at each segment boundary (5 width mesurements per valley), perpendicular to the length line and crossed the crest on each side of the valley (Fig. 4a).

Valley parameters Abbreviation Denition

Length (m) L Longitudinal line extending from the upstream part to the downstream part.

Width (m) W Perpendicular to the length line.

Slope (°) Sl

Average values of all pixel in the valley shape.

Elevation (m) El

Average values of all pixel in the valley shape.

Depth (m) Dp

Dierence between the highest and lowest point from a cross-sectional prole.

V-index (dimensionless) V-index Deviation from an ideal V-shaped valley.

Cross-section (m²) CS Calculated from the cross-sectional proles.

Length/width ratio [START_REF] Johnson | The prole of maturity in alpine glacial erosion[END_REF][START_REF] Penck | Glacial features in the surface of the alps[END_REF][START_REF] De Martonne | Fjords, cirques, vallées alpines et lacs subalpins[END_REF][START_REF] Graf | The geomorphology of the glacial valley cross section[END_REF][START_REF] Graf | Cirques as glacier locations[END_REF][START_REF] Olyphant | Allometry and cirque evolution[END_REF][START_REF] Roberts | The role of the ice contributing area in the morphology of transverse fjords, british columbia[END_REF][START_REF] Augustinus | Outlet glacier trough size-drainage area relationships, ordland, new zealand[END_REF][START_REF] Montgomery | Valley formation by uvial and glacial erosion[END_REF]Amerson et al., 2008;[START_REF] Evans | Allometry, scaling and scale-specicity of cirques, landslides and other landforms[END_REF][START_REF] Zemp | Vanishing glaciers in the european alps[END_REF][START_REF] Barr | Glacial cirques as palaeoenvironmental indicators: Their potential and limitations[END_REF][START_REF] Delmas | A critical appraisal of allometric growth among alpine cirques based on multivariate statistics and spatial analysis[END_REF][START_REF] Livers | An evaluation of stream characteristics in glacial versus uvial process domains in the colorado front range[END_REF][START_REF] Hobbs | Analysis of crater valleys, noachis terra, mars: Evidence of uvial and glacial processes[END_REF][START_REF] Evans | Comparability of cirque size and shape measures between regions and between researchers[END_REF][START_REF] Zimmer | Assessing glacial modication of bedrock valleys using a novel approach[END_REF].

Valley slope and elevation

The slope was calculated for every pixel of the HRSC DTMRDR that fell within the valleys using the ArcGIS tool slope. Then to extract the average slope and elevation values for each valley we used the ArcGIS tool extract by mask. This tool allow to compute the average values of all pixel that fell within the outline previously drawn for the valley (Fig. 4a-b).

Valley cross-sectional area and V-index

The cross-sectional area was calculated from the transverse prole at the start and end of each segment (0%, 25%, 50%, 75%, 100% of the valley length). The prole crossed the two shoulders of the valley. From this prole, we extracted the maximum depth of the valley (Fig. 4e). Five cross-sectional areas were calculated, one for each segment we measured, and the average valley cross-sectional area was calculated from these ve values. In order to characterize the shape of the valleys we used the V-index [START_REF] Zimmer | Assessing glacial modication of bedrock valleys using a novel approach[END_REF].

This V-index is the measure of the deviation from an ideal V-shaped valley. It is calculated by comparing the valley cross-sectional area (Ax) between the valley bottom and a specied height above the valley oor to that of an ideal V-shaped cross-section with the same height and width as the subject cross section (Av, [START_REF] Zimmer | Assessing glacial modication of bedrock valleys using a novel approach[END_REF].

V -index = (Ax/Av) -1

(1)

When V-index = 0, the ideal V-shaped valley is the same that the mesuread one. If the valley is U-shaped the V-index > 0 whereas V-shaped valleys have a V-index < 0 [START_REF] Zimmer | Assessing glacial modication of bedrock valleys using a novel approach[END_REF]. We chose to calculate the V-index for each valleys at 50% of the valley length.

Morphometrical analysis of valley heads on Mars

Some valley heads on Mars have an theater-like form. For these valley heads we dened the outline, using the same method as described in section 4.3.1. Then, we measured its width and length (Fig. 4c).

The altitudinal range was obtained by using the same method described previously for the valleys (Section 4.3.3; Fig. 4c,d,f ). The amplitude was obtained by mesuring the dierence in altitude between highest and lowest points on the length line [START_REF] Evans | Comparability of cirque size and shape measures between regions and between researchers[END_REF]. The size of the valley heads was calculated using the

(with L: Length, W: Width, H: Height), and the axial gradient using the relation

Axgrad = arctan(A/L) (3)
(with A: Amplitude, L: Length). The boundary between the valley head and the valley is not always very clear. To be consistent between the dierent studied valleys, we chose to set this boundary to the change in topographic break in slope that marks the transition between the upstream valley head and the downstream main valley (Fig. 4f ).

Comparative morphometrical analysis with known valleys on Earth and Mars

Comparison with Mars

Two craters in the southern highlands, that have already been studied, have been chosen as reference for our comparison (Fig. 1). Bakhuysen crater (15.39°E, 23.9°S) has 35 valley networks mapped by Hynek et al.

(2010) and are interpreted as uvial valleys by Moore (2005) (Fig. 5). A crater, refered as GLF-crater in this study (28°16'E, 31°58'S), dened by [START_REF] Souness | Mid-latitude glaciation on mars[END_REF] as a crater with Amazonian GLFs (Fig. 6). We supposed that the valleys in this crater were mainly shaped by the GLFs present in this crater.

We applied our method to the valleys in these craters. The results thus obtained allowed us to verify if our method is consistent with the interpreted origin of the valleys [START_REF] Moore | Large alluvial fans on mars[END_REF][START_REF] Hynek | Updated global map of martian valley networks and implications for climate and hydrologic processes[END_REF][START_REF] Souness | Mid-latitude glaciation on mars[END_REF]. Moreover, with the data obtained, we were able to build a database large enough to compare these known cases with the valleys in our study areas.

Comparison with the Earth

In order to compare the martian results for the valleys, we decided to apply the method described above (Section 4.3) in the area of Chamonix in the French Alps (Fig. 7). This terrestrial glacial landscape present several glaciated valleys and contrary to our study area, the glacial valleys in Chamonix still have their glacier (Mer de Glace, Argentière glacier...; [START_REF] Zemp | Vanishing glaciers in the european alps[END_REF][START_REF] Frezzotti | Glaciers and ice sheets: current status and trends[END_REF]. Then some measured parameters such as the depth and the cross-sectional are distorted, they should increase without the glacier. However, the other parameters are measurable even if a glacier is present. Indeed, the current presence of a glacier does not inuence the length and the width of the valleys because the main glacial erosion phase is over since the Holocene which correspond to the maximum glacier extent [START_REF] Zemp | Vanishing glaciers in the european alps[END_REF].

4.6. Summary of measured parameters 4.6.1. Valleys in Terra Sabaea

Using our morphometric analysis we characterized 140 valleys with dierent origins, namely 36 uvial valleys in Bakhuysen crater [START_REF] Moore | Large alluvial fans on mars[END_REF][START_REF] Hynek | Updated global map of martian valley networks and implications for climate and hydrologic processes[END_REF], 23 glacial valleys in GLF-crater [START_REF] Souness | Mid-latitude glaciation on mars[END_REF] and a suite of valleys with unknown origin: 42 from Dawes crater, 33 from Crater 1 and 6 from mountain 1. We constructed a database with more than 2500 usable measurements to determine whether the valleys of Dawes crater, Crater 1 and mountain 1 are uvial or glacial in origin. We plotted frequency distributions for each measured parameters (Fig. 8a-d). The average value for each studied parameter is presented in Table 10 in the supplementary. [START_REF] Hynek | Updated global map of martian valley networks and implications for climate and hydrologic processes[END_REF] identied 35 uvial valleys in Bakhuysen crater and 29 uvial valleys in Dawes crater. We re-examined these valleys using more morphometric parameters and we added new valleys to this dataset (Fig. 9).

Valley heads in Terra Sabaea

We identied 100 valley heads in the study area, namely 75 valley heads in Dawes crater and 25 in Crater 1. We plotted frequency distributions for each measured parameters (Fig. 10a-f ). The average value for each of the studied parameters is presented in Table 11 in the supplementary. We did not nd any valley heads in mountain 1. We constructed a database, with more than 700 usable measurements, to characterise these valley heads and to compare them with terrestrial morphologies (Fig. 11).

Glacial valleys in Chamonix valley

We identied 13 glacial valleys in Chamonix valley. The values for each studied parameter is presented in Table 9 in the supplementary. We constructed a database, with more than 250 measurements, usable as terrestrial reference from our method. The tables containing all the measured parameters for each area are in the supplementary material (Table 456789).

Age estimation of Dawes crater

In order to constrain the age of the valleys, we performed a crater size-frequency analysis, or crater counting. We measured the crater size-frequency distribution (the number and size of craters accumulated on surface units) using CTX images to estimate the age for Dawes crater [START_REF] Hartmann | Cratering chronology and the evolution of mars[END_REF][START_REF] Ivanov | Mars/moon cratering rate ratio estimates[END_REF]. We observed that the oor of Dawes crater is covered by materials that partially overlaps the base of the crater wall. This deposit partially covers the valleys showing that this material was deposited after valley formation. Hence, the valleys and valley heads are younger than the crater walls but older than the lling material that covers them. Therefore, estimating the age of the crater oor and the craters inner walls allowed us to bracket the maximum and minimum age of the valleys and valley heads. We dened two count areas, the rst one is the crater inner walls delimited by the crater rim and the break in slope with the crater oor. This area is characterized by the presence of valleys and valleys heads. The second is the crater oor characterized by a at oor, strongly cratered and the complete absence of valleys and valley heads.

We measured all impact craters > 1 km, except secondary and ghost crater using CraterTools in ArcGIS [START_REF] Kneissl | Map-projection-independent crater size-frequency determination in GIS environmentsnew software tool for ArcGIS[END_REF] in these two areas. Dawes crater has 96 superposed craters > 1 km over an area of 28439 m². The crater size-frequency distributions was plotted with Craterstats 2.1 software using a cumulative plot and using the function chronology from [START_REF] Hartmann | Cratering chronology and the evolution of mars[END_REF] and [START_REF] Hartmann | Martian cratering 8: Isochron renement and the chronology of mars[END_REF]. The crater size-frequency distribution is not signicative for crater 1, in fact, the plot obtained does not t with any of the established crater density boundaries [START_REF] Tanaka | The stratigraphy of mars[END_REF][START_REF] Hartmann | Martian cratering 8: Isochron renement and the chronology of mars[END_REF]. However, in order to constrain the age of the valley in crater 1, we counted the craters with diameter > 1 km and calculated the N(1)

to determine the formation period of the valleys using established crater density boundaries [START_REF] Bouley | Age dates of valley network drainage basins and subbasins within sabae and arabia terrae, mars[END_REF]. N(1) is the density of craters with a diameter > 1 km normalized to an area of 10 6 km².

This method was realized in two count areas in crater 1, the oor and the crater inner walls dened as the same way described above. We also applied the N(1) method to Dawes crater in order to check if the two ages found with the dierent methods are consistent. Mountain 1 only have 3 craters > 1 km it is not enough to realize a signicative crater size-frequency analysis.

Results

Morphometric comparison: Valleys

Length to Width ratio

The valleys from Dawes crater, Crater 1, mountain 1, and GLF-crater have a mean length to width ratio of 2.5, being only slightly longer than they are wide (Fig. 12). The Bakhuysen valleys are signicantly longer compared to their width, with a mean length to widtht ratio of 22 (Fig. 12). The dierence between the length to width ratio suggests that the formation process was not the same for Bakhuysen crater as for the Thus, our analysis supports the uvial interpretation for the Bakhuysen valleys and suggests the origin of the valleys from GLF-crater, Dawes crater, Crater 1, and mountain 1 are dierent.

Cross-sectional area

Based on our analysis of the valley ratio cross-sectional area/ drainage area we can distinguish two groups (Fig. 13a). The rst one is composed of Bakhuysen crater valleys, the ratio between the cross-sectional area and the drainage area is low with an average value of 0.001. The second group is composed of Dawes crater,

Crater 1, mountain 1, and GLF-crater, the ratio between the cross sectional area and the drainage area is higher than for Bakhuysen. The average values is about 0.004, that is four times higher than Bakhuysen one (Fig. 13a). On Earth, this value of four is the characteristic dierence between the glacial and uvial valleys [START_REF] Montgomery | Valley formation by uvial and glacial erosion[END_REF]. Moreover, the cross-sectional proles reveal that Bakhuysen valleys have a V-shape characteristic of a uvial erosion [START_REF] Penck | Glacial features in the surface of the alps[END_REF][START_REF] Roberts | The role of the ice contributing area in the morphology of transverse fjords, british columbia[END_REF][START_REF] Livers | An evaluation of stream characteristics in glacial versus uvial process domains in the colorado front range[END_REF] and that Dawes crater, Crater 1, mountain 1, and GLF-crater valleys have a U-shape which is characteristic of a glacial erosion (Fig. 9). In order to conrm this result, we realized a statistical test to verify if the data are statiscally dierent. The ve populations are not normally distributed so we chose to use the Mann-Whitney U test. This method is used to test whether two samples are likely to derive from the same population.

This nonparametric test is applicable when the samples are small (N<40), not normally distributed and independent which is the case for this study. To achieved this, the rst step was to rank the cross-sectionnal area/drainage area values to obtain the critical value of U and compare it with the values in Mann-Whitney table for a given N (Table 12 in supplementary). To give an example, let compare the two populations of valleys from Bakhuysen crater (N = 35) and Moutain 1 (N=6). After ranking, we obtained a critical U value of 6. For these populations, the U value in the table is 37. The critical U value from our data is strictly inferior than the U given in the Mann-Whitney table. So we can conrm that the valleys from Bakhuysen crater and Mountain 1 are statiscally separated, that mean that the cross-sectionnal area/drainage area for these two population of valley do not follow the same trend. In other words, the erosion processes between these two populations of valleys are not the same. We applied this test to the other populations and we found the same result.

The Fig. 13b shows the variation of the cross-sectionnal areas all along the valleys in the dierents areas.

From the top of the valley (100%) down to the middle of the valley (50%) the cross-sectionnal area increases and then decreases downstream to the end of the valley (0%). This variation follows the law of ajusted cross section described by [START_REF] Penck | Glacial features in the surface of the alps[END_REF] for the alpine glacial valleys on Earth.

Elevation

Based on the elevation of the valleys, we can distinguish two groups. The rst, comprises valleys in Bakhuysen crater, are found at an elevation <1000 m, 168 m on average (Fig. 14). The second group is made up of valleys from GLF-crater, Dawes crater, Crater 1 and mountain 1, where 95% the valleys are located at an elevation higher than 1000 m with an average of 1722 m (Fig. 14). These valleys are at an elevation 10 times higher than the valleys in Bakhuysen crater. On Earth, the elevation of glacial valleys is higher than uvial ones [START_REF] Roberts | The role of the ice contributing area in the morphology of transverse fjords, british columbia[END_REF][START_REF] Montgomery | Valley formation by uvial and glacial erosion[END_REF]. .

Morphometric comparison: valley heads

The valley heads in Dawes crater and Crater 1 have a sizes ranging from 372 m to 4282 m (Fig. 10 f ). Furthermore, the longitudinal prole shows a steep upstream slope, between 26°to 28°, and a gentle downstream slope between 17°to 20°(Fig. 15 a-b). On the 75 valley heads identied in Dawes crater 32

presents a topographical lip and 43 do not. For Crater 1, 13 valleys heads have a topographical lip on 25 measured valley heads. These topographical lips have a height between 20 and 100 m (Fig. 15a-b). The average value for each compared parameters is presented in Table 11 in the supplementary.

Morphometric comparison: glacial valleys in Chamonix

In order to compare the measurement made on Mars with known case on Earth, we plotted length against width for each valley in our study areas and compared them with the results we obtained on 13 glacial valleys in Chamonix (Fig. 16). This plot reveals two groups, the rst, comprises valleys in Bakhuysen crater that are longer than wider (Section 5.1.1). The second comprises valleys in Dawes crater, Crater 1, GLF-crater, moutain 1. The point here is that valleys from the second group follow the same trend than Chamonix ones. The V-index is also comparable, in fact Dawes crater, Crater 1 and moutain 1 have a mean V-index of 0.20, 0.21, 0.23 respectively and the glacial valleys from Chamonix have a mean V-index of 0.21. Moreover, the mean length to width ratio is 3.21 (Table 10 in the supplementary). These results suggest that the from [START_REF] Barr | Glacial cirques as palaeoenvironmental indicators: Their potential and limitations[END_REF] valleys from Dawes crater, Crater 1 and moutain 1 are eroded by the same processes than glacial valleys from Chamonix.

6. An interpreted glacial landscape in Terra Sabaea

Characteristics of glacial valleys in Terra Sabaea

The measured parameters of the valleys in Dawes crater, Crater 1, and on mountain 1 are similar to terrestrial glacial valleys:

1. Dawes crater, Crater 1 and mountain 1 valleys have a length to width ratio >1, which more similar to the GLF-crater valleys than to Bakhuysen uvial valley which have a length to width ratio > >1 (Fig. 12b)

2. Dawes crater, Crater 1 and mountain 1 valleys have a cross-sectional areas that are four times larger than Bakhuysen uvial valleys and a similar cross-sectional area to the GLF-crater valleys (Fig. 13a) Fig. 16. Length versus width for all the valleys from the dierent study areas.

3. Dawes crater, Crater 1 and mountain 1 valleys have a V-index around 0.20 while Bakhuysen uvial valleys have a V-index around 0.07 (Fig. 8b) 4. Dawes crater, Crater 1 and mountain 1 valleys have an elevation 10 time higher than Bakhuysen and a similar elevation to GLF-crater valleys (Fig. 14) 5. Dawes crater, Crater 1 and mountain 1 valleys have a U-shape while Bakhuysen morphologies have a V-shape (Fig. 9c-e) 6. Dawes crater, Crater 1 and mountain 1 valleys respect the cross-section law characteristic of terrestrial glacial valleys (Fig. 13b)

Characteristics of valley heads in Terra Sabaea

The longitudinal proles of valley heads in Dawes crater and Crater 1 are similar to typical longitudinal proles of glacial cirques on Earth (Fig. 15c). They have a steep upstream slope of about 28°in the headwall, then a gentle downstream slope about 20°on the oor, with a topographic lip marking the end of the feature (Fig. 15). The other measured parameters, reported in Fig. 10 and in Table 11 in the supplementary, are within the range of the highest terrestrial glacial cirques measured [START_REF] Barr | Glacial cirques as palaeoenvironmental indicators: Their potential and limitations[END_REF][START_REF] Evans | Comparability of cirque size and shape measures between regions and between researchers[END_REF]. The mean axial gradient measured is low, 9.97°in Dawes crater valley heads and 13.18°in Crater 1 valley heads (Fig. 10e) compared to the mean axial gradient measured on Earth but still in the range of terrestrial glacial cirque [START_REF] Barr | Glacial cirques as palaeoenvironmental indicators: Their potential and limitations[END_REF][START_REF] Evans | Comparability of cirque size and shape measures between regions and between researchers[END_REF]. The width to length ratio is around one, which correspond to terrestrial glacial cirque (Fig. 17a) and the length to height ratio is in the range of terrestrial glacial cirques measured on Earth by [START_REF] Barr | Glacial cirques as palaeoenvironmental indicators: Their potential and limitations[END_REF] and [START_REF] Evans | Comparability of cirque size and shape measures between regions and between researchers[END_REF] Fig. 17b).

The morphological and geometrical similarities of the valley heads and the valleys to terrestrial glacial cirques and valleys, strongly suggests that the origin of the valleys in Dawes crater, Crater 1 and on mountain 1 is glacial. Moreover, the fact that the valleys in Dawes crater and Crater 1 are also associated with features strongly resembling glacial cirques strengthens the interpretation that Dawes crater and Crater 1 exhibit relict glacial landscapes (Fig. 18a-f ).

Timing of the formation of the glacial landscape

In order to constrain the potential age of the glacial landscape, undertook an analysis of the crater-size frequency distribution for Dawes crater. The crater size-frequency distribution for the oor of Dawes crater gives a best-t age of 3.52 ± 0.05 Ga and 3.66 ± 0.03 Ga for the inner wall with [START_REF] Hartmann | Cratering chronology and the evolution of mars[END_REF] chronology function (Fig. 19a). With [START_REF] Hartmann | Martian cratering 8: Isochron renement and the chronology of mars[END_REF] chronology function, the best-t age is 3.34 ± 0.06 Ga for the oor, and 3.57 ± 0.03 Ga for the inner wall (Fig. 19b). So the age of the Dawes crater glacial landscape is probably between 3.34 and 3.66 Ga (Late Noachian/ Early Hesperian).

Dawes crater has N(1) = 4579 for the walls and N(1) = 2291 for the oor. We applied this method to

Crater 1 and we found N(1) = 4167 for the walls and N(1) = 3297 for the oor. In the two craters, the crater densities correspond to the Late Noachian/Early Hesperian for the inner walls and to the Hesperian for the oor according to the established crater density boundaries [START_REF] Tanaka | The stratigraphy of mars[END_REF][START_REF] Hartmann | Martian cratering 8: Isochron renement and the chronology of mars[END_REF]. These ages are consistent with the age found by [START_REF] Bouley | Age dates of valley network drainage basins and subbasins within sabae and arabia terrae, mars[END_REF] with the basin age-dating method for the basins and subbasins within Terra Sabaea of 3.61 ± 0.02 Ga. So, we hypothesize that from the Late Noachian to the Early Hesperian, the climate was cold enough to have deposition and preservation of ice leading to formation of glaciers and for the crater walls to be shaped by ice processes and form a glacial landscape.

7. Discussion

Allometry and origin of the glacial cirque in Terra Sabaea

The glacial cirque distribution in Dawes crater and Crater 1 shows that some of them are located at lower elevations than some glacial valleys. On Earth, glacial cirques are usually at higher elevations than the downstream glacial valleys. The sizes and allometric coecients of the cirques provides information which can explain the dierences in the topographic characteristic of cirques on Mars compared to the Earth. Cirque size is calculated in order to assess whether cirques have developed isometrically or allometrically and it is plotted against the length, width and altitudinal range [START_REF] Barr | Glacial cirques as palaeoenvironmental indicators: Their potential and limitations[END_REF]. The allometric coecients of logarithmic regressions indicate if the cirque growth equaly in the three dimensions (isometric) or unequaly (allometric), when the allometric coecients are close to 1 the cirque population displays isometric properties and when they are signicantly dierent from 1 the cirque population displays allometric properties. The sum of these coecients must be 3 [START_REF] Evans | Allometry, scaling and scale-specicity of cirques, landslides and other landforms[END_REF][START_REF] Barr | Glacial cirques as palaeoenvironmental indicators: Their potential and limitations[END_REF][START_REF] Delmas | A critical appraisal of allometric growth among alpine cirques based on multivariate statistics and spatial analysis[END_REF]. The allometric coecients for all the three dimension are close to 1 in Dawes crater and Crater 1 and they sum to 3 (Fig. 20a-b). So the glacial cirques identied in Dawes crater and Crater 1 are isometric. The apparent isometry of cirque indicate that former glacier rarely extended beyond their cirques because a glacier conned to its cirque may naturally result in isometric developement, but, on Earth, glaciers often grow beyond cirque connes and shape glacial valley downstream [START_REF] Barr | Glacial cirques as palaeoenvironmental indicators: Their potential and limitations[END_REF]. In our study, we found both, cirques connected and unconnected to a glacial valley. [START_REF] Delmas | A critical appraisal of allometric growth among alpine cirques based on multivariate statistics and spatial analysis[END_REF] proposed that the isometric character of cirques could be interpreted as a process by which nonglacial topographic depressions with allometric properties were progressively shaped by ice to form isometric landforms. We proposed that on Mars, this nonglacial topographic depressions could be a pre-existant impact crater lled later by the ice. This hypothesis could explain (1) the isolated cirques which are not linked with a glacial valley and ( 2) the fact that some glacial cirques are found at lower elevations than glacial valleys. Moreover, if some of glacial cirques have an impact crater as origin, the impact crater diameter should be >2 km (Fig. 10a-b, Table 11). These craters later lled by the ice became glacial cirques with high size. So this hypothesis can also explain (3) the fact that the measured parameters are high but within the range of the highest terrestrial glacial cirques.

Type of glaciation

On Earth, cold-based glaciers have temperatures below the pressure-melting point at near their base [START_REF] Nagle | Cold Environments: Processes and Outcomes (Epics)[END_REF][START_REF] Cogley | Glossary of glacier mass balance and related terms[END_REF]. Their movement is a result of internal plastic deformation inside the ice, and only little, if any, basal abrasion occurs. Warm-based glaciers have at their base temperatures at pressure melting points, they melt from their bed, resulting in basal sliding in which a water lm lubricates the surface. Extensive basal abrasion occurs (Hargitai and Kereszturi, 2015). These dierences of erosion involve that glacial depositional features such as moraines, kames, eskers, or kettles hole are generally typical When a glacier melts, a large amount of liquid water ows down the slope. We propose that the water thus liberated could have eroded and transported away these characteristic depositional features. Therefore, it is dicult to infer if the glaciers that created these valleys were warm or cold based. However, the morphometric properties highlighted in this study allow us to dierentiate between the types of glaciation responsible for there valleys (alpine glacier or ice cap). Our morphological and geometrical results are consistent with terrestrial alpine glaciers as dened by [START_REF] Jackson | Glossary of geology, 5th Edition[END_REF] as any glacier in a mountain range except an ice cap, ice sheet, or ice eld. Such glaciers usually originate in a cirque and may ow down into a valley (Section 6.2).

Late Noachian/early Hesperian glacial landscape versus Amazonian VFFs

An important point to discuss is the dierence between late Noachian/early Hesperian glacial landscape versus Amazonian VFFs. Even if they are both form by glacial processes, their distribution and their formation conditions are dierent. These dierences are mainly controled by the orbital parameters and atmospheric conditions that are completely dierent between the late Amazonian and the late Noachain/early Hesperian. Several studies indicate that the formation of VFF seems to be linked with an orbital obliquity increase [START_REF] Madeleine | Amazonian northern mid-latitude glaciation on mars: A proposed climate scenario[END_REF][START_REF] Hubbard | Geomorphological characterisation and interpretation of a mid-latitude glacier-like form: Hellas planitia, mars[END_REF][START_REF] Souness | Mid-latitude glaciation on mars[END_REF]. In fact, Amazonian climatic models suggested that an atmospheric pressure of 0.007 bar and high (45°) to medium obliquity (30°) are favourable conditions to form VFFs [START_REF] Montmessin | Origin and role of water ice clouds in the martian water cycle as inferred from a general circulation model[END_REF][START_REF] Forget | Formation of glaciers on mars by atmospheric precipitation at high obliquity[END_REF]. Moreover, the geomorphologic mapping of these features, show that they are only locally found between 30°to 50°in latitudes, on crater slopes > 20° [START_REF] Milliken | Viscous ow features on the surface of mars: Observations from high-resolution mars orbiter camera (MOC) images[END_REF][START_REF] Hubbard | Geomorphological characterisation and interpretation of a mid-latitude glacier-like form: Hellas planitia, mars[END_REF][START_REF] Souness | Mid-latitude glaciation on mars[END_REF][START_REF] Hubbard | Glacier-like forms on mars[END_REF].

So the VFFs have a latitudinal and slope dependence and are formed under particular conditions. The late Noachain/early Hesperian glacial landscape we found in the three sites are at elevations > 1000 m (Fig. 14). Climatic models suggested that, with an obliquity of 45°and under a 1 bar CO 2 atmosphere with cloud, radiative eects and active water cycle, water ice could deposit in area > 1000 m in elevation without latitudinal dependence [START_REF] Forget | 3d modelling of the early martian climate under a denser co2 atmosphere: Temperatures and co2 ice clouds[END_REF][START_REF] Wordsworth | Global modelling of the early martian climate under a denser CO2 atmosphere: Water cycle and ice evolution[END_REF]. At this high obliquity, the exchange in water ice and CO 2 become more intense, and surface ice are predicted to become stable even at equatorial latitudes [START_REF] Conway | Glacial and gully erosion on mars: A terrestrial perspective[END_REF]. Moreover, even if we analyzed only three sites on Terra Sabaea, a preliminary mapping of the whole area seems to indicate that more structures seems to have glacial landscape.

A futur detailed study of these features will be done in order to characterize the regional distribution of these landscapes. However, our observations linked with the climatic models suggested that the late Noachian/early Hesperian glacial landscape have an altitudinal dependence and are formed under less particular conditions and on larger scale than VFFs.

Paleoclimatic implications

Almost all the valleys identied in this study as being glacial in origin are located at elevations between 1000 m and 3000 m (Fig. 14). The glacial valley elevations we found are consistent with the previous modeling studies which predicted the deposition of water ice at elevations > 1000 m during the late Noachian [START_REF] Wordsworth | Global modelling of the early martian climate under a denser CO2 atmosphere: Water cycle and ice evolution[END_REF][START_REF] Bouley | Late tharsis formation and implications for early mars[END_REF]. Nevertheless, on Earth, the equilibrium line altitude (ELA) for a glacier, which separates area where the ice is stable (upper accumulation zone) from the area where the ice is not stable (lower ablation zone), is approximated as the elevation which corresponds to the 1/3 of the length of the valley [START_REF] Anderson | Features of glacial valley proles simply explained[END_REF]. If we apply this rule to Terra Sabaea, we nd that the elevation of the ELA is at about 1800 m for Dawes crater and 2000 m for Crater 1. These paleo-ELA are higher than the predicted 1000 m elevation stability of ice in the climatic models [START_REF] Wordsworth | Global modelling of the early martian climate under a denser CO2 atmosphere: Water cycle and ice evolution[END_REF][START_REF] Bouley | Late tharsis formation and implications for early mars[END_REF]. [START_REF] Ramirez | The geological and climatological case for a warmer and wetter early mars[END_REF] reviewed the debate between the wet and warm early martian climate versus the icy highlands scenario. They suggested that the icy highlands scenario is not possible because of the complete absence of glacial features in Noachian terrains. However, our study demonstrates, for the rst time the presence of a glacial landscape composed of glacial valleys associated with glacial cirques in Noachian terrains in the south of Terra Sabaea (Fig. 18). The observed sequence of Al-bearing clays being deposited over Mg-Fe-bearing clays in ancient terrains has also been interpreted to be consistent with a frozen early martian surface [START_REF] Ehlmann | Subsurface water and clay mineral formation during the early history of mars[END_REF].

Independently of the debate, we suggest that these two climates could have coexisted. On the Earth, it is common to nd places where the ice is stable at high elevation and not stable at lower elevation. The southern highlands have evidence of glacial landscape at elevations > 1000 m, but also some nearby uvial valley networks at elevations < 1000 m, these two kinds of landscapes seem to be linked together by their ages and their distribution. The catchment of Naktong Vallis, one of the biggest valley networks on Mars (located at 850 km at the north of Dawes crater at an elevation of 1200 m), extends up to a large plateau located at more than 2000 m elevation near Dawes crater [START_REF] Bouley | Fluvial morphology of naktong vallis, mars: A late activity with multiple processes[END_REF] and is dated at 3.6 Ga (Fassett and Head, 2008a;[START_REF] Bouley | Fluvial morphology of naktong vallis, mars: A late activity with multiple processes[END_REF][START_REF] Bouley | Age dates of valley network drainage basins and subbasins within sabae and arabia terrae, mars[END_REF]. This age is consistent with the age found for the glacial landscape in Dawes crater and show that the liquid and water ice could have coexisted. Moreover, the glacial landscapes are located at altitudes where the valley network density is known to be low (elevations > 1500 m; Table 10 and Fig. 2a). For elevations < 1500 m the valley network density is known to be higher (Fig. 2a; [START_REF] Bouley | Fluvial morphology of naktong vallis, mars: A late activity with multiple processes[END_REF]. In order to explain this altitudinal relationship between the glacial landscape and the valley networks we propose two hypotheses:

(1) These two climates scenarios are complementary, indeed to form these two types of valley morphologies, a high atmospheric humidity is necessary. Several studies have proposed snowfall and melting snow as the source of water for the valley networks [START_REF] Head | Tropical to mid-latitude snow and ice accumulation, ow and glaciation on mars[END_REF][START_REF] Bouley | Fluvial morphology of naktong vallis, mars: A late activity with multiple processes[END_REF][START_REF] Fastook | Early mars climate near the noachianhesperian boundary: Independent evidence for cold conditions from basal melting of the south polar ice sheet (dorsa argentea formation) and implications for valley network formation[END_REF]. Moreover, at the lowest elevations (<1500 m), the high density of V-shaped valleys, suggests that precipitation played a role in their formation [START_REF] Carr | The martian drainage system and the origin of valley networks and fretted channels[END_REF][START_REF] Baker | Water and the martian landscape[END_REF][START_REF] Bibring | Global mineralogical and aqueous mars history derived from OMEGA/mars express data[END_REF][START_REF] Ramirez | The geological and climatological case for a warmer and wetter early mars[END_REF]. Thus, at higher elevations (> 1500 m), snow could have accumulated to form glaciers. We propose that the martian climate during the late Noachian/early Hesperian was characterized by glaciated highlands at > 1500 m according to the glacial landscape we highlighted and temperate lowlands at < 1500 m where liquid water was stable. Thus, a water cycle similar to the Earth could have existed allowing the deposition of snow and glacier formation in the highlands and the precipitation of liquid water for an elevation < 1500 m.

(2) The variations in Mars' orbital obliquity could have changed the global climate and created glacialinterglacial cycles [START_REF] Laskar | Long term evolution and chaotic diusion of the insolation quantities of mars[END_REF]. During cold climate periods accumulation and preservation of large amount of water ice could have occured thus forming glacial landscape at elevations > 1500 m. Then during interglacial periods this ice could have melted and liquid water owed down shaping the valley networks at an elevations < 1500 m.

In any case, we suggest that the melting of ice could be an important factor to consider for valley network formation. The glaciated highlands could allow the formation of local ice sheet around craters where we found glacial landsapes. We suggest that, the ice owed down on the inner crater slopes to form alpine glacier and shaped the glacial valleys. But outside the crater, where the slope is gentle and where we did not observe alpine glacier morphologies, these supposed local ice sheet could have melted [START_REF] Fastook | Glaciation in the late noachian icy highlands: Ice accumulation, distribution, ow rates, basal melting, and top-down melting rates and patterns[END_REF]. This melting water could be a source and/or a reservoir of lowest elevations valley networks and feed the open-bassin lake observed in this area by Fassett and Head (2008b). These scenarios would be sucient to explain most of the valley networks, glacial landscape, and geology in Terra Sabaea. The water liberated could have contributed to the formation of valley networks and the hydration of the soil. Our geomorphological observations provide evidence for a glaciated highlands > 1500 m and temperate lowlands < 1500 m during the late Noachian/ early Hesperian in Terra Sabaea. These results and interpretations are veried in our study area, and bring new elements to the debate about the early Mars climate, but we did not apllied our method to the entire highlands in Terra Sabaea. However, a preliminary mapping have been done and it seems like other impact crater presents morphologies similar to those described in this study. A future study in the whole highlands > 1500 m, applying this method, will be done to better constrain the distribution of this supposed glacial landscape and the link they could have with the martian paleo-climate.

Conclusion

Our morphometrical analyses allowed us to identify glacial valleys and glacial cirques distributed across three sites in Terra Sabaea. These glacial landforms have similar characteristics to glacial landforms on Earth.

The altitude of this glacial landscape is > 1000 m in agreement with numerical climate simulations that have predicted deposition of ice in the southern hemisphere during the late Noachian. We constrain the timing of the formation of these glacial landscapes to about 3.6 Ga, which corresponds to the late Noachian/early

Hesperian. This study supports a glacial erosive agent for the origin of these valleys and brings the rst morphometric evidence of an ancient glacial landscape composed of glacial valleys associated with glacial cirques in the southern highlands. Finding similar glacial landscapes in other impact craters or in the intercrater plains in the southern highlands would allow better constraint on the distribution of the ice for early Mars.

Fig. 1 .

 1 Fig. 1. Terra Sabaea and Noachis Terra in the southern highlands. (a) Study area and areas used for comparison. The red line represents the valley networks mapped by Hynek et al. (2010). Mars orbiter laser altimeter (MOLA) digital elevation background. (b) USGC geological map of the area (Tanaka, 2014). Images credit NASA/JPL/University of Arizona.

Fig. 2 .

 2 Fig. 2. Location of the three study areas. (a) Context camera (CTX) mosaic of the study area with MOLA digital elevation map. The red lines are the valley networks identied by Hynek et al. (2010) (b) Mountain 1 CTX images with MOLA background . (c) Crater 1 CTX images with MOLA background . (d) Dawes crater CTX images with MOLA background. All the images and data used are sum up in the supplementary (Table3). Images credit NASA/JPL/University of Arizona.

Fig. 3 .

 3 Fig. 3. Example of studied valleys. The west rim of Dawes crater visualised using (a) CTX images P11_005461_1706_XI_09S323W; P17_007742_1708_XN_09S323W (b) MOLA colorised data overlain on CTX images. The black arrows indicate the location of the valleys. Images credit NASA/JPL/University of Arizona.

Fig. 4 .

 4 Fig. 4. Valley and valley head morphometric measurement. (a) A valley in Dawes crater and its associated valley head, where 0% correspond to the furthest point downstream and 100% the furthest point upstream. Background is CTX images (P17_007742_1708_XN_09S323W; P11_005461_1706_XI_09S323W ) and MOLA elevation data. (b) Slope map of the valley in (a) (calculated from HRSC DTMRDR: h1950_0000_bl3 ) where the dashed line shows the position of the cross-sectional prole shown in (e). (c) Detailed view of the valley head shown in (a). (d) Slope map of the valley head, where the dashed line shows the position of the longitudinal prole shown in (f ). Images credit NASA/JPL/University of Arizona.

  Fig. 5. Bakhuysen crater (a) Background using CTX images (G05_020309_1568_XN_23S343W; G12_022933_1578_XI_22S344W; B18_016551_1566_XN_23S344W; B20_017263_1573_XI_22S343W; B18_016617_1562_XI_23S345W; B17_016195_1563_XN_23S345W; P11_005475_1569_XN_23S343W ) and MOLA elevation data. (b) Detailed view of the uvial valleys shown in (a) (G12_022933_1578_XI_22S344W). Images credit NASA/JPL/University of Arizona.

Fig. 7 .

 7 Fig. 7. Study area of Chamonix in the French Alps on Earth. Colorized elevation data from 25m/pixel DEM BDALTIr_2-0_ASC_25M_LAMB93_IGN69_D073. Images credit IGN-F

  Fig.

Fig. 10 .

 10 Fig. 10. Box and whisker plot of valley head: (a) width, (b) length, (c) altitudinal range, (d) amplitude, (e) axial gradient and (f ) size.

Fig. 11 .

 11 Fig.

Fig. 12 .

 12 Fig. 12. Box and whisker plot of length to width ratio for valleys in each study areas. 140 valleys have been plotted, 36 from Bakhuysen crater, 23 from GLF-crater, 42 from Dawes crater 33 from crater 1 and 6 from mountain 1 . The median values are respectively: 20.8; 3.6; 2.3; 2.8 and 2.7.

Fig. 13 .

 13 Fig. 13. (a) Box and whisker plot of cross-sectional area/ drainage area for the studied valleys. We can observe two groups, one composed of the valley from Bakhuysen crater with a mean cross sectional area/drainage area of 0.001 and the second composed of GLF-crater, Dawes crater, Crater 1, and mountain 1 with a mean cross sectional area/drainage area of 0.004. (b) Box and whisker plot of cross-section area at 0%, 25%, 50%, 75% and 100% of the valley length for Dawes crater, Crater 1 and Mountain 1.

Fig. 14 .

 14 Fig. 14. Box and whisker plot of elevation of the identied valleys from MOLA elevation data.

Fig. 15 .

 15 Fig. 15. Longitudinal prole of valley heads from HRSC DTMRDR. (a) In Dawes crater (h5184_0000_da4), (b) In Crater 1 (h1961_0000_bl3 ), (c) Longitudinal prole of a typical terrestrial glacial cirque. Modify

Fig. 17 .

 17 Fig. 17. Box and whisker plot of (a) valley head width to length ratio, (b) valley head length to height ratio.

Fig. 18 .

 18 Fig. 18. Geomorphological map of the proposed glacial landscape. (a) Dawes crater distribution of the glacial valleys and cirques on the inner wall of the crater overlain on CTX images. (b) Detail of glacial assemblage, the main glacial valley is surrounded by three glacial cirques. (c) Crater 1 distribution of the glacial valleys and cirques on the inner wall of the crater overlain on CTX images. (d) Detail of glacial assemblage, the main glacial valley is surrounded by two glacial cirques. (e) Mountain 1 distribution of the glacial valleys on the wall of the moutain overlain on CTX images. (f ) Detail of glacial valleys, we can not found glacial cirque on that mountain. Images credit NASA/JPL/University of Arizona.

Fig. 19 .

 19 Fig. 19. Timing of formation of the glacial landscape in Dawes crater. (a) Results are for crater with diameter > 1 km with Hartmann and Neukum (2001) chronology function. The red triangles represent the counts performed on the inner wall (3.66 Ga) and the black squares the counts performed on the crater oor (3.52 Ga). (b) Results are for crater with diameter > 1 km with Hartmann (2005) chronology function. The red triangles represent the counts performed on the inner wall (3.57 Ga) and the black squares the counts performed on the crater oor (3.34 Ga). A detail map of the count area is in the supplementary (Fig. 21).

Fig. 20 .

 20 Fig. 20. Valley head morphometry. (a) Allometric (double log (4)) plot of valley heads from Dawes crater (N=77). the allometric coecients are 0.98 (length), 0.91 (width) and 1.1 (altitudinal range). (b) Allometric (double log (4)) plot of valley heads from Crater 1 (N=25) the allometric coecients are 0.82 (length), 0.86 (width) and 1.3 (altitudinal range). The size is calculated from 3 √ LW H and the magnitude is the dierents

Fig. 21 .

 21 Fig. 21. Map of the count-areas of craters > 1km in Dawes crater. (a) Dawes crater oor. (b) Dawes crater inner walls.

Table 2 .

 2 Parameters measured for the valleys and valley heads used in this study. Selected from several terrestrial studies

Table 10 .

 10 Average values for each measured parameter for valleys in each studied zone.

	Bakhuysen crater GLF-crater Dawes crater Mountain 1 Crater 1 Chamonix
	Number of valleys identied	36	23	42	6	33	13
	Average length (km)	10	4.2	4.4	5	3.8	4.7
	Average width (km)	0.5	1.2	2	1.8	1.3	1.5
	Average aspect ratio length:width	21.5	3.7	2.4	2.7	2.9	3.2
	Average elevation (m)	170	1280	1600	2200	2150	2500
	Average depth (m)	15	20	56	143	25	308
	Average cross-sectional area (m²)	6537	12647	24568	45591	13631	480793
	Average V-index	0.07	0.15	0.20	0.21	0.23	0.21
		Dawes crater	Crater 1	Evans and Cox (2017)	Barr and Spagnolo (2015)
	Number of valley heads identied	75	25	1593		10362
	Average width (m)	2398	2177	656		749
	Average length (m)	2317	2120	625		744
	Average amplitude (m)	388	493	260
	Average altitudinal range (m)	519	452	310		309
	Average size (m)	1377	1242
	Average width to length ratio	1.05	1.02	1.05		1.03
	Lip average height (m)	75	35
	Average axgrad (°)	9.97	13.18	23.1		24.2
	Average length to height ratio	4.94	3.87	2.03		2.58
	Number of valley head linked with the valley	41	13

Table 11 .

 11 Average values for each of the measured parameters for valley heads in each of studied areas and average values from terrestrial cirque from[START_REF] Barr | Glacial cirques as palaeoenvironmental indicators: Their potential and limitations[END_REF];[START_REF] Evans | Comparability of cirque size and shape measures between regions and between researchers[END_REF]

Table 12 .

 12 Mann-Whitney table for a bilateral test.

Acknowledgments

The authors acknowledge the CTX Team for the availability of the data on the web site http://ode.rsl. wustl.edu/mars/ and the HRSC Team of the German Aerospace Center (DLR) Berlin, who provided map projected HRSC DEM data. We acknowledge the Orsay Planetary Picture Library for the data provided and images processing (http://fototek.geol.u-psud.fr). Authors are funded by the Programme National de Planétologie (PNP) of Centre National de la Recherche Scientique/Institut National des Sciences de l'Univers, and the Centre National d'Etudes Spatiales (CNES). The authors also acknowledge Pierre Lahitte for the terrestrial DEM of Chamonix valley. The authors are very grateful to the two reviewers, Susan Conway and Ian S. Evans, for their very constructive comments and suggestions that have improved the work presented here. References Amerson, B. E., Montgomery, D. R., Meyer, G., 2008. Relative size of uvial and glaciated valleys in central idaho. Geomorphology 93 (3-4), 537547, doi: 10.1016/j.geomorph.2007.04.001.

Supplementary material CTX/ HRSC