River channels and valleys have been observed on several planetary bodies in addition to the Earth. Long sinuous valleys on Venus, our Moon and Jupiter's moon Io are clearly formed by lava, and branching valleys on Saturn's moon Titan may be forming today by rivers of methane. But by far the most dissected body in our Solar System apart from the Earth is Mars. Branching valleys that in plan resemble terrestrial river valleys are common throughout the most ancient landscapes preserved on the planet. Accompanying the valleys are the remains of other indicators of erosion and deposition, such as deltas, alluvial fans and lake beds. There is little reason to doubt that water was the erosive agent and that early in Mars' history, climatic conditions were very different from the present cold conditions and such that, at least episodically, water could flow across the surface. In addition to the branching valley networks, there are large flood features, termed outflow channels. These are similar to, but dwarf, the largest terrestrial flood channels. The consensus is that these channels were also cut by water although there are other possibilities. The outflow channels mostly postdate the valley networks, although most are still very ancient. They appear to have formed at a time when surface conditions were similar to those that prevail today. There is evidence that glacial activity has modified some of the water-worn valleys, particularly in the 30–50° latitude belts, and ice may also be implicated in the formation of geologically recent, seemingly water-worn gullies on steep slopes. Mars also has had a long volcanic history, and long, sinuous lava channels similar to those on the Moon and Venus are common on and around the large volcanoes. These will not, however, be discussed further; the emphasis here is on the effects of running water on the evolution of the surface.
Because there are no rivers flowing on Mars today, our perception of its fluvial history is based almost entirely on remote sensing, and particularly on the morphology of the surface as observed in satellite imagery. Fortunately, we have excellent coverage. Almost the entire planet has been imaged at 100 metre per pixel resolution and substantial fractions at resolutions down to 1 metre per pixel. In addition, we have global altimetry at a few hundred metres per pixel and compositional data from infrared spectroscopy with spatial resolutions of a few tens of metres. These data are supplemented by views from the ground at several locations, particularly at the two sites explored by the rovers Spirit and Opportunity.
To provide some context for discussion of the fluvial features, this study begins with a summary of present conditions on Mars and an outline of the planet's geological history insofar as we know it. There follows detailed discussions of the valley networks, the large flood features and other water-worn or water-deposited forms. Included will be brief discussions of evidence for former oceans and speculation on the nature of the hydrological system that resulted in the water-worn features that we see. Table 1 provides a few useful facts to aid the discussion.
2. Present climatic conditions
Discovery of Mars' branching valley networks during the Mariner-9 mission in 1972 was a complete surprise because, by that time, we already knew that Mars had a very thin CO2 atmosphere and that the surface was much too cold to permit streams of liquid water at the surface. At 1.5 times the Earth's distance from the Sun (table 1), and with almost no greenhouse effect, mean surface temperatures are well below freezing. The mean daily temperature at the equator is close to −60°C (213 K) and drops to −125°C (148 K) at the winter pole. During the day, however, temperatures at the surface may fluctuate widely. At noon, they can reach as high as 30°C (303 K) depending on season, location and surface properties, although this is somewhat deceptive in that temperatures are close to the daily mean of 60° below freezing just a centimetre or two below the surface. The mean surface pressure is close to the triple point pressure for water of 6.1 mbar. Thus, at higher elevations, where the pressure is below the triple point, ice if heated will sublime rather than melt.
Roughly 30 per cent of the CO2 in the atmosphere freezes out in the winter hemisphere to form a seasonal polar cap. Growth and recession of the two seasonal caps cause movement of CO2 back and forth between the two hemispheres. As the seasonal caps recede in summer, they expose semi-permanent water-icecaps around 3 km thick at each pole. Water ice is also pervasive just below the surface at latitudes greater than 60° and may be present locally below the surface at lower latitudes. Despite the widespread presence of water ice, however, liquid water can exist near the surface only temporarily and in very small amounts under present conditions. Widespread presence of seemingly water-worn channels suggests therefore that climatic conditions were very different at times in the past.
The tilt of Mars' rotational axis (25.2°) is similar to the Earth's (23.5°); so Mars, like the Earth, has seasons. Mars' orbit has, however, a significant eccentricity. This causes the seasons to have different lengths. At present, southern summer (158 days) is shorter and hotter than northern summer (183 days), but the length and intensity of the seasons change slowly with time as the various orbital and rotational parameters change. One astronomical parameter that has a significant effect on the water cycle is the tilt of the rotational axis, or obliquity. The Earth's tilt undergoes little change but Mars' obliquity changes significantly. During the last 10 Myr, it has been as low as 15° and as high as 45°. Laskar et al.  estimate that there is a 63 per cent probability that the obliquity reached 60° in the last 1 Gyr. At high obliquities when the summer pole faces the Sun, water ice sublimes from the poles and precipitates out at lower latitudes. Warming of ice on Sun-facing slopes during high obliquities could then provide meltwater to cut small channels.
3. Geological overview
Two-thirds of the Martian surface is heavily cratered like the surface of the highlands on our Moon (figure 1). The surface has clearly survived from the period of heavy bombardment that all the planetary bodies in the inner Solar System experienced prior to around 3.7 Ga. The geological history of Mars has been divided into three periods: the Noachian, Hesperian and Amazonian (for a detailed summary of the geological history, see Carr ). The Noachian refers to the period of heavy bombardment. The rest of the planet's history is divided somewhat arbitrarily into the Hesperian and Amazonian, largely on the basis of numbers of superimposed impact craters. The absolute age of the boundary between the Hesperian and Amazonian is not known but is estimated to be between 2.9 and 3.3 Ga . The heavily cratered Noachian terrain is mostly in the Southern Hemisphere and is at an elevation roughly 6 km higher than the more sparsely cratered lowlands in the north. The contrast between the two hemispheres has been called the global dichotomy and attributed to a giant impact very early in the planet's history. The valley networks are mostly incised into the heavily cratered Noachian uplands. Other than the dichotomy, the largest surviving impact basin on the planet is Hellas, which is 4000 km across, and has a rim that reaches 2 km above the datum and a depth that extends to 8 km below the datum. The Hellas basin dominates drainage in the eastern part of the Southern Hemisphere. Elsewhere, drainage is mostly controlled by the north south regional slope created by the global dichotomy.
Much of the geological activity subsequent to the end of heavy bombardment was related to the volcanic province of Tharsis, a broad elevated area 5000 km across and 10 km high centred on the equator at 265° E (figure 1). The volcanic pile that forms the Tharsis bulge had probably largely accumulated by the end of heavy bombardment, as the drainage pattern of the Noachian valleys is consistent with the present topography around the bulge. The province continued, however, to be a focus of volcanic activity for the rest of the planet's history. Several volcanoes formed within the province and most of intervening plains are characterized by numerous lava flows one upon another. The volcanoes are enormous by terrestrial standards. The present edifice of Olympus Mons is 550 km across, 21 km high and surrounded by a cliff up to 9 km high. Alba Patera, the largest volcano on the planet in areal extent, is 2000 km across but only a few kilometres high. The large size of the volcanoes has been attributed to the lack of plate tectonics, the long life of the magma sources and the buoyancy of the magmas. Although the present surfaces of the volcanoes have few impact craters, which indicate that the surface is young, the volcanoes probably have been active throughout the history of the planet, with large eruptions spaced widely in time. Elysium, another much smaller volcanic province, is the source of several large, seemingly fluvial, channels.
The presence of the Tharsis volcanic pile has deformed the crust and created a vast array of radial fractures around the pile. These may have acted as conduits for groundwater and enabled the release of groundwater to the surface. Rifting along the radial fractures has also resulted in the formation of a vast canyon system, the Valles Marineris. The canyons extend from the summit of the Tharsis bulge eastward for 4000 km where they merge with some large channels. In the central section, where several canyons merge, the depression that they form is 600 km across and several kilometres deep. The alignment of many of the canyon walls radial to Tharsis indicates that faulting played a major role in the formation of the canyons, although branching side canyons and landslides show that other processes were involved. Within the canyons are thick, layered deposits containing hydrated sulphates. The canyons may once have contained lakes that drained catastrophically eastwards to form the large channels with which they merge. The deposits within canyons are mostly Hesperian in age, significantly younger than most of the valley networks.
At each pole is a 3 km thick stack of finely layered, ice-rich deposits that extend out roughly to the 80° latitude circle. The deposits are young. Crater counts suggest 105–107 years, with those in the south being somewhat older than those in the north. The layering is caused by different proportions of dust incorporated into the ice as the caps accumulated, the depositional rates being modulated by variations in the planet's orbital and rotational motions. The young ages are indicative of the earlier-mentioned episodic removal of the caps during periods of high obliquity. Dust storms are common at present during summer months, some occasionally achieving global proportions. Drifts and dunes that are seen in almost every high-resolution image of the surface attest to the efficacy of the wind in moving fragmental material around the surface.
4. Valley networks
The Noachian uplands are highly eroded. Craters, the dominant landform in the uplands, occur in widely ranging states of preservation. Some craters are almost perfectly preserved; others, even some hundreds of kilometres across are so filled and eroded as to be barely discernible. Clearly, the Noachian terrain has undergone extensive erosion, with the younger craters being barely eroded and the oldest visible craters having been almost completely eliminated. In contrast, impact craters on post-Noachian surfaces are almost all perfectly preserved. It appears that there were continuously high or episodically high rates of erosion during the Noachian, and that rates fell precipitously at the end of the period, around 3.7 Ga, then remained low for the rest of the planet's history. Average erosion rates during the Noachian are estimated to be around 10−6 to 10−5 m per year, the low end of continental denudation rates on the Earth . These rates should, however, be viewed with some caution because we do not know how old the oldest features that we can see are. According to the late heavy bombardment model, no topographic features have survived from prior to around 3.9 Ga; in other models, some of the large basins such as Hellas may be as old as 4.4 Gyr. Average post-Noachian erosion rates were two to five orders of magnitude lower than those in the Noachian although there were episodic, local, erosional events, such as the large floods, that accomplished a significant amount of erosion.
Branching valley networks, that in plan resemble terrestrial river systems, are common throughout the Noachian uplands. In view of their branching morphology, the presence of subsidiary features such as deltas, the general availability of water, at least as ice, and the lack of plausible alternatives, there is little reason to doubt that the valleys were cut by water. Most of the valley networks are incised into the degraded Noachian landscape [5–7], and one issue is the extent to which fluvial processes such as those that formed the branching valleys contributed to the general degradation. Although all the heavily cratered terrain is degraded, not all of it is dissected by valley networks. Broad areas in the Southern Hemisphere to the east and southwest of the Hellas impact basin are largely undissected, as is another large area, northwest Arabia, in the Northern Hemisphere (figure 1). Elsewhere, however, the old terrain is mostly dissected, at least at latitudes below 50°. Crater counts and transection relations indicate that most of the valleys formed in the late Noachian or early Hesperian. Dissection of terrains younger than lower Hesperian by branching networks is rare but has occurred locally. Some Hesperian lava plains adjacent to Echus Chasma are, for example, densely dissected by branching valleys  and several late Hesperian to Amazonian volcanoes (Hecates Tholus, Ceraunius Tholus, Alba Patera) have numerous valleys on their flanks.
Most of the Martian valleys illustrated in figure 1 are narrow and inset into an otherwise poorly dissected terrain. They more resemble terrestrial river channels than terrestrial river valleys. The valleys are mostly 1–4 km wide and have U-shaped to rectangular cross sections downstream. Upstream they either become shallower and more V-shaped or they retain their downstream cross section until they terminate in a broad alcove. The more prominent valleys are typically incised into the surface to a depth of 50–300 m  and the depth of incision may remain almost constant for large distances. Typically, the more prominent valleys are outlined by steep walls with an abrupt scarp at the edge of the upland surface. Most of the valleys are less than 200 km long and drain into local depressions, but a few reach lengths of over 2000 km. Drainage densities in the Noachian terrain widely range from undissected to densely dissected local areas, with values in the 0.1–1 km−1 range [7,10]. The average drainage density for the Noachian terrain as a whole is 0.01 km−1, two to three orders of magnitude less than typical terrestrial values.
Details of the valley floors are usually masked by later deposits, particularly dunes. Irwin et al.  and Jaumann  have, however, identified a number of valleys with inner channels from which they were able to estimate stream discharges, which ranged from 300 to 5000 m3 s−1. The rates are comparable to terrestrial rates for similar drainage areas. From the contributing areas, they derived runoff production rates of 0.1–6 cm d−1. Jaumann  estimated that it would take 1800 years to cut a valley with an inner channel in the Libya Montes that they studied, but thought it more likely that the channel was cut over a much more extended period of time during episodic fluvial events. This conclusion is consistent with modelling studies of landscape development under the influence of episodic fluvial and impact events that suggest that the incised valleys were formed over hundreds of thousands to millions of years by multiple, modest-sized fluvial events separated widely in time .
Most of the narrow-incised valleys illustrated in figure 1 appear to have formed in the late Noachian and early Hesperian under environmental conditions that were fundamentally different from the earlier conditions under which crater rims were eroded and local lows filled . The younger valleys are incised into the alluvium that fills the local depressions and, where deltas occur (see later text), the deltas are comparable in volume to the incised valleys. There has been minimal contribution from the areas of the drainage basins that lie between the valleys. The period of late incision appears to have started abruptly, ended abruptly and contributed little to the general degradation of the Noachian landscape.
Low drainage densities, abrupt terminations of many tributaries and the difficulties in envisaging how early Mars could be warm enough for precipitation and surface runoff suggested to many early researchers that the valley networks could have formed by groundwater sapping alone [14–16]. Better imaging now shows that the early measurements of extremely low drainage densities were due in part to the poor resolution of the then available images. We now know that area filling drainage is common (figure 2), although average drainage densities are still lower than typical terrestrial values . Precipitation and surface runoff have clearly been contributors to formation of the valley networks. Nevertheless, groundwater sapping has also likely played a role, particularly in the formation of some prominent younger valleys such as Nirgal Vallis (figure 3) and Nanedi Vallis, which have very open networks and tributaries with abrupt, alcove-like terminations. In the early Hesperian, there may have been a transition from precipitation-dominated to groundwater-controlled valley formation [17,18].
Although dissection of plains younger than lower Hesperian is rare, several volcanoes with surfaces that are much younger are densely dissected. It is not clear whether these volcano flank valleys are similar in origin to the typical Noachian valleys. They could have formed by mechanisms unique to volcanoes such as erosion of pyroclastics by nuées ardentes, hydrothermal circulation of groundwater and melting of ice, or they could be lava channels. They will not be discussed further.
5. Drainage basins
Altimetry shows that, independent of the impact craters, the Noachian terrain is poorly graded, having numerous closed depressions. During fluvial episodes, these depressions presumably contained lakes. Several global-scale basins can be extracted from the altimetry. These are not true drainage basins in the sense that drainage paths are continuous from the divides to the basin exits, as would normally be the case for large basins on the Earth. They do, however, show how global drainage would converge and divide if all local lows were filled. In the Southern Hemisphere, most of the regional drainage is towards either the Argyre or the Hellas basins. In the Northern Hemisphere, drainage is into the northern lowlands that form part of the hemispheric dichotomy. Despite considerable relief along the dichotomy boundary and around Hellas, large drainage basins analogous to the Mississippi and Amazon basins did not develop. Seemingly, the cumulative effects of erosion, alluviation and stream capture were insufficient to result in integration of drainage over large areas and growth of large basins. The elimination of relief by erosion and infilling was not rapid enough to keep pace with the creation of new relief by impacts and volcanism; so large, integrated drainage basins did not form.
The lack of regional drainage is well demonstrated by Hellas. Despite more than 10 km of relief between the floor of Hellas and its rim crest and despite the area having possibly experienced 100–400 Myr of erosion during the Noachian, there are no significant valleys draining into Hellas from the north and west. Even if Hellas formerly contained a lake to the −3.1 km level , there are still 5 km of relief from the rim crest down to the proposed lake level to enable drainage. If the observed degradation of craters superimposed on the rim was due to fluvial erosion, then most of the drainage must have been local, with the water accumulating in local depressions to be lost by infiltration or evaporation. Such a scenario is also consistent with the apparent failure to transport large amounts of sediment from the Hellas drainage basin into the central depression. Comparing the present topography of Hellas with the models of the original topography suggests that the basin probably contains no more than 2×104 km3 of fill. The Hellas drainage basin covers 1.5×107 km2; so, despite the highly eroded craters on the rim, which imply hundreds of metres of erosion, no more than about 1 m has been eroded from the basin rim and transported into the basin. The sediment eroded from the highs must simply have accumulated locally.
Quantitative measures of stream profiles and basin shapes support the supposition that most Martian drainage basins are less well developed than their terrestrial counterparts [20,21]. In the case of terrestrial basins, over long time scales, relief is slowly reduced over the entire basin. Higher order streams commonly have little relief and form alluviated plains. In most terrestrial basins, the local slope S is approximately A−θ, where A is the area upstream of the given point and θ is called the concavity exponent. The larger the upstream area that drains through a point in a basin, the lower the slope at that point; the higher the value of the exponent, the more concave is the basin. Terrestrial basins typically have values that range from 0.3 to 0.7, with the smallest exponents in basins of sporadic runoff or where groundwater sapping dominates or both. Concavity exponents of most Martian basins are in the 0.2–0.3 range, indicating poor concavity. Another indicator of basin shape is how the circularity of the basin shape varies with elevation. The higher the elevation slice through a typical terrestrial basin, the more circular the basin outline. This tendency to higher circularities at higher elevations is significantly less pronounced with Martian basins . The low circularity is most evident in the longest streams, those that extend from the highs on the Hellas rim, northwestward towards Chryse basin. The poor development of basins is also reflected in the basin divides. Because terrestrial basins tend to have significant concavity, the steepest slopes tend to be around the periphery of a basin. In contrast, because of their low concavities, Martian basin divides are difficult to discern in images and most can only be determined from the altimetry .
6. Lakes and deltas
Lakes were probably common throughout the poorly graded Noachian terrain, while it was undergoing fluvial erosion [24,25]. Most valleys terminate in closed depressions such as craters or low areas between craters, where at least transient, closed lakes almost certainly formed. Many of these areas are underlain by seemingly fine-grained, horizontally layered, easily erodible sediments [26,27]. Chlorine-rich deposits  and sulphates  in local depressions within the Noachian uplands may be the result of evaporation from such lakes. Lakes were common in impact craters, as indicated by numerous crater rims breached by ingoing and/or outgoing valleys. A prominent example is the crater Gusev in which the Spirit rover landed. It is breached by a large channel, Ma'adim Vallis, which itself appears to have formed by drainage of a large lake in the uplands to the south of Gusev . Many old impact craters have flat floors underlain by finely layered sediments. A striking characteristic of many of these sediments is their remarkably regular, rhythmic layering. The layering could result from a variety of causes such as successive impacts and volcanic events, or changes in the erosional regime as a result of climate change. While all these processes may have contributed, the extreme regularity of some of the layering argues against impacts and volcanism as primary causes. The rhythmic depositional patterns suggest an astronomical forcing. Erosion and sedimentation may have been modulated by climate changes that resulted from variations in the orbital and rotational motions of the planet.
Almost 300 depressions have been identified within the highlands that have both inlet and outlet valleys, indicating the former presence of an open basin lake, i.e. one that overflowed . In most of these lakes, the lake volume is proportional to the watershed area, which suggests that the lakes were fed mostly by precipitation and runoff rather than by groundwater upwelling. Modelling by Matsubara et al.  suggests that the open basin lakes had rates of evaporative loss over surface runoff comparable to lakes in the Great Basin in the western USA. If climatic conditions were similar to the Great Basin, then the typical lake would have had to persist for several hundred years to maintain the observed lake levels. However, most basins are closed. From the fact that most local basins did not overflow, coupled with estimates of peak discharges from channel dimensions and computer simulations of fluvial erosion of cratered landscapes, Howard  and Barnhart et al.  concluded that the valley network system did not result from a few deluge-type events, such as might be caused by large impacts, but rather from modest, episodic fluvial events spread over extended periods of time.
Most valleys terminate at grade in depressions with little or no indication of deposits at their mouths, which suggests that in most cases the materials eroded to form the valleys were either too fine-grained to form a delta or were distributed across the depressions to form subaerial alluvial fans. Where lakes were present, the lake levels may have fluctuated and so no delta formed. Despite their general absence, a few tens of deltas have been recognized [11,34]. Most are in local depressions such as craters but some that occur over a narrow elevation range along the dichotomy boundary have been interpreted as having formed where valleys debouch into a northern ocean . The deltas typically are fan-shaped, outlined by an outward-facing scarp and have distributary channels on their upper surfaces (figure 4). The channels are either incised into the upper surface or left as positive features after preferential erosion of the interchannel areas. Two particularly striking deltas are in the craters Eberswalde  and Jazero (figure 5). If peak flows, estimated at 102–103 m3 s−1 from input channel dimensions, were continuously sustained, then both these deltas could have formed in a few tens of years. More likely they formed by intermittent flow over much longer periods [36–38]. The lack of deep incision of the deltas as the lake levels declined suggests that the fluvial activity that resulted in delta formation declined abruptly.
In summary, Mars experienced a period of fluvial incision around 3.7 Ga that left much, but not all of the Noachian highlands dissected by branching valley networks. Prior to that time, high erosion rates had produced a highly degraded landscape. The branching valleys added little to that degradation. Little evidence survives of the processes that caused the early degradation. Although water erosion was likely involved, integration of drainage over large areas did not occur either in the early phase or in the subsequent incision phase. During the late incision, lakes were common throughout the Noachian, some with deltas where streams entered. The valley and delta dimensions, coupled with lake volumes and drainage basin areas, suggest that incision involved peak stream discharges comparable to terrestrial rivers. The time over which most of the valleys formed is poorly constrained. Failure to fill most closed basins suggests that the valleys were not formed by a few deluge events but by intermittent modest-sized events, perhaps spread over an extended period of time.
7. Outflow channels
Large flood channels or outflow channels are the characteristic fluvial feature of the late Hesperian era. They are very different from the branching valley networks just described. They have no tributaries. They start full-size from a single source, commonly in rubble-filled depressions or at a graben. They are mostly very large, but vary greatly in size. The largest, Kasei Vallis, is over 400 km across at its mouth and in places over 2.5 km deep (figure 6). Others are only a few kilometres across at their source. They have low sinuosity, smoothly curving walls and most contain teardrop-shaped islands around which flow has diverged and converged. On the channel floors are a range of bedforms, including longitudinal striae, cataracts, plucked zones and inner channels. In toto, they are remarkably similar to large terrestrial flood features, such as the Channeled Scablands of eastern Washington State in the USA [39,40]. The size of the largest channels implies huge discharges. Estimates for Kasei Vallis range as high as 108–109 m3 s−1 [41,42], when compared with 107 m3 s−1 for the Channeled Scablands  and a peak of 3×104 m3 s−1 for the Mississippi. While the resemblance of some of the channels to terrestrial flood features is impressive, a fluvial origin has been questioned. Leverington , for example, argues that the channels were cut during large eruptions of fluid lava. But the consensus is that the channels were cut by water, based on the strong resemblance to terrestrial flood features, on the availability of water as indicated by other indications of hydrological activity such as the valley networks, and on geophysical modelling of channel formation, as discussed later. We will assume in the following discussion that the outflow channels were cut by water though recognizing that there are other possibilities.
Most outflow channels formed in the late Hesperian , or around 3–3.5 Ga , and most occur around the Chryse basin, a low area in the Northern Hemisphere centred on 330° E, between the Noachian uplands of Arabia to the east and the Tharsis rise to the west. The basin is open to the low-lying plains to the north. The channels start in the higher ground around the basin, extend into the basin and then northward into the low-lying, northern plains. Many of the channels emerge full-size from closed, rubble-filled depressions (figure 7). Maja Vallis, for example, emerges from a deep depression with an outlet 4 km above the floor of the depression. If formed by water, then a lake must have been left in the depression after the flood, a conclusion that is supported by the presence stacks of layered sulphates on the depression's floor. Other source depressions also contain sulphate deposits. Some of the Chryse channels merge to the southeast with the floors of the large canyons that form the eastern end of Valles Marineris. A likely possibility is that the canyons once contained lakes that were released catastrophically to the east to cut the channels. Again, thick sulphate deposits and other layered sediments in the canyons support the former presence of lakes. Elsewhere, channels start at graben. A particularly prominent example, Mangala Vallis, several hundred kilometres long and in places over 100 km across starts at a notch cut in a graben wall (figure 8). Another channel, Athabasca Vallis in Elysium, that starts at a graben has an unusually young age of less than 107 years, as indicated by the number of superimposed impact craters. Several outflow channels start adjacent to volcanoes in both of the two largest volcanic provinces Tharsis and Elysium. Thus, outflow channels vary greatly in size, age and geological context. What they have in common is that they start almost full-size, with no indication of convergent surface drainage to provide their discharge.
The full-size start and lack of tributaries indicate that the outflow channels formed not by precipitation and surface runoff but by rapid release of a stored volume of water. In the case of the channels that emerge from the eastern end of the Valles Marineris, the stored volume was probably intra-canyon lakes. But many of channels, particularly those around the Chryse basin, start in rubble-filled hollows, with floors at elevations well below the elevation of the channel floors and with volumes too small to explain the size of the channels. Carr  proposed that the outflow channels that start in rubble-filled hollows were caused by eruptions of groundwater trapped under high pressure below a kilometres thick cryosphere. Thick aquifers, high hydrostatic pressures and high permeabilities are needed to account for the high discharges. A kilometre thick cryosphere is needed to contain the pressurized groundwater until containment is breached, for example, by a large impact or a tectonic event. After the flood, the surface collapses to form a rubble-filled hollow. The necessity of a thick cryosphere implies that in contrast to formation of the valley networks, a cold climate like today's is needed to form the outflow channels. This model has since been elaborated upon in considerable detail by Andrews-Hanna & Phillips  and Hanna & Phillips , who suggest that tectonic forces could have contributed to the pressurizing of the aquifer and that superlithostatic pore pressures could cause opening of fractures within the aquifer, thereby increasing its permeability and enabling high discharges. Hydrofracturing of the cryosphere may also be one cause of release of water from the confined groundwater. Their modelling results are sensitive to the aquifer properties but in a typical result for Ares Vallis, a peak discharge of 8×106 m3 s−1 is reached after 7 h, after which the discharge rate drops quickly. After 23 days, 1000 km3 of water has been released. After the flood, the path through the cryosphere would refreeze and the aquifer, if of large areal extent, could be recharged by diffusion of groundwater from distil sources, and the flood repeated. If this modelling is realistic, then a large channel such as Ares Vallis, which has a volume of roughly 105 km3, may have formed by multiple, short-lived floods, each with a far smaller volume of water than the total volume needed to erode the channel. Another possibility is that the flow around the channel to the surface is not restricted by the intrinsic permeability of the fractured aquifer but instead, the aquifer partly disintegrates and some is carried to the surface by the massive discharge, thereby leading to collapse to form the rubble-filled hollow after the event. In this way, larger floods would be possible and fewer would be needed to form an Ares-like channel.
The start of the outflow channels at graben is simply explained by the pressurized aquifer model: the faulting disrupted both the aquifer and the cryosphere seal, thereby providing pathways for flow through the aquifer and to the surface. Some graben, such as the Cerberus Fossae, appear to have been the source of eruptions of both groundwater and lava, which suggests that, in some cases, floods may not be simply triggered by tectonic activity but also by injection of dikes . Such an origin seems particularly likely for several channels that originate in graben around the periphery of the large volcano Elysium Mons. Eruption of groundwater along the large faults that formed the equatorial canyons may also be the cause of the lakes that are postulated to have been formerly present within the canyons.
The source of the water in the aquifers is uncertain. Much of it may have been inherited from the earlier era, represented by the valley networks, when warm surface conditions permitted precipitation and infiltration. As surface conditions changed, water involved in the earlier hydrological cycle may have become trapped beneath the growing cryosphere. Alternatively, or in addition, water could have been added from primary magma sources beneath the volcanic regions of Tharsis and Elysium. Other possibilities are that aquifers were recharged by basal melting of ice deposits at the poles  or melting of ice deposits that formed in Tharsis during periods of high obliquity .
We saw earlier that abundant evidence of surface runoff during the Noachian suggests that large bodies of water may have been present at that time, at least episodically, both as sources and sinks. A number of linear features around the northern plains  and in Hellas  have been suggested as possible shorelines, as have the presence of deltas at similar elevations . The ages of many of the proposed shorelines are uncertain but some in the uplands could be Noachian. However, the linear features, being discontinuous, at varying elevations, and being open to other interpretations are not compelling evidence of former oceans. Nor are oceans necessary for precipitation. The valley networks may have formed by the melting of ice driven from the poles during periods of high obliquity, or they could result from precipitation of water injected into the atmosphere during large impacts . In addition, we saw earlier that large drainage basins with large streams to carry surface runoff into the major basins did not develop. If large bodies of water were present in low areas such as Hellas, then they were probably fed by groundwater. The evidence for oceans is thus equivocal. While the simplest explanation of the high erosion rates and abundance of valley networks in the Noachian is that conditions were Earth-like and that evaporation from ocean-like bodies of water was in quasi-equilibrium with precipitation, runoff and infiltration, other scenarios are possible.
The evidence for post-Noachian oceans is perhaps somewhat more convincing. Large outflow channels drain into the northern plains. If the channels were each eroded by a single or a few large events, then large volumes of water must once have been present in the northern plains. Linear features on Hesperian surfaces around the northern plains are better preserved than the Noachian ones because of the low Hesperian erosion rates. Ghost craters in low parts of the northern plains suggest the presence of effluent deposited during the floods . Many landforms in the lower areas of the northern plains have been compared with terrestrial features that form by meltwater under a static ice sheet  that could have been a frozen remnant of an ocean. There are thus several lines of evidence suggestive of the former presence of large bodies of water. On the other hand, if Andrews-Hanna & Phillips  are correct and individual flood volumes are much smaller than the channel volumes, then large bodies of water need not have been present. So, we are left with similar ambiguities as with the Noachian.
Gullies are by far the most common fluvial feature that has formed in the last few billion years of Martian history. They are common on steep slopes in the 30–60° latitude belts with a preference for poleward facing slopes (figure 9). They typically consist of an upper theatre-shaped alcove that tapers downslope to converge on a channel that extends further downslope to terminate in a debris fan [26,27]. The channels are mostly several metres wide and hundreds of metres long. Their origin is controversial. Although initially attributed to groundwater seeps, this origin now seems unlikely, given the probable thick cryosphere during the second half of Mars' history and the common presence of gullies at locations where groundwater is unlikely, as on slopes around mesas and central peaks and at crater rim crests. Dry mass-wasting may contribute to their formation, but this also seems to be an unlikely cause because many of the gullies cut through bedrock ledges. Erosion by wind or ice appears ruled out by their morphology, and erosion by liquid or gaseous CO2 appears ruled out by stability relations. All the morphological attributes are consistent with water erosion, and the broad consensus is that that is their cause.
In the southern highlands at mid-latitudes, where most of the gullies occur, average daily summer temperatures are in the 220–230 K range and surface pressures are below the triple point of water. While groundwater seeps might temporarily exist under such conditions, particularly in the presence of salts, accumulation of sufficient liquid to erode gullies is unlikely. One possibility is that the gullies result from the temporary presence of water produced by the melting of snow and ice deposited at mid-latitudes during periods of high obliquity . Such an origin is supported by modelling studies [57,58] and by observations of gullies emerging from beneath what appear to be ice deposits on steep slopes. The age of the gullies cannot be accurately determined, but they probably have been forming episodically, when obliquities were high enough, throughout the last 3 Gyr and possibly longer. They appear fresh because of the extremely low erosion rates, but are unlikely to have been forming continuously because there is little evidence that they have caused significant backwasting of slopes and filling of the craters, despite the long times over which they probably have been forming. Thus, fluvial activity during the last 3 Gyr of Mars' history has been minor, and restricted mainly to rare groundwater eruptions, very rare valley network formation of unknown causes and the gullying of steep slopes, probably from melting of ice during high obliquities.
10. Global implications
The relatively high erosion rates and presence of valley networks imply that during the Noachian, Mars was at least episodically warm and wet. This conclusion is supported by the surface mineralogy. Widespread presence of phyllosilicates in Noachian terrains [29,59] indicates weathering under warm, moist conditions. In contrast, in the Hesperian, erosion rates are extremely low and valley networks are rare. The characteristic erosional feature of the Hesperian is the outflow channel, many of which probably formed by eruptions of groundwater from below a thick cryosphere. Phyllosilicates are not found in the late Hesperian terrains but evaporitic minerals, particularly sulphates, are common. All the evidence points to a period of transition in the late Noachian–early Hesperian time period (figure 10). Temperate conditions prevailed when valley networks were forming in the late Noachian, but a thick cryosphere had developed by the late Hesperian when most of the outflow channels formed.
Andrews-Hanna & Lewis  used global-scale hydrological models to explore what might have happened during this transitional period. They suggest that during the Noachian, water was abundant, warm conditions prevailed and precipitation kept the near-surface close to saturation. However, loss of water as a result of large impacts and solar wind interactions resulted in a lowering of the groundwater table, precipitation became more rare but groundwater upwellings driven by topographic variations occurred locally. Their modelling demonstrates that the preferred locations for upwellings are those places where sulphates are found, such as Meridiani Planum where the rover Opportunity landed. The upwellings presumably created local lakes, which, on evaporation, left behind the sulphate deposits that we observe. Further cooling and additional water losses led to more lowering of the global groundwater table and ultimately trapping of groundwater beneath a thick cryosphere.
A major issue is how Noachian Mars became warm and wet. The geological evidence for an early warm, wet Mars is compelling yet how such conditions were achieved is very unclear. According to stellar evolution models, 3.8 Ga the luminosity of the Sun was 75 per cent of its present value . This would imply a mean surface temperature on Mars of 196 K if there were no greenhouse warming . Achieving the warming necessary to bring the mean surface temperature up to 273 K would require that the atmosphere intercept 85 per cent of the radiation from the surface when compared with 56 per cent for the Earth . A very powerful greenhouse is needed.
Until the 1970s, the early atmospheres of the Earth and Mars were thought to be reducing. If so, then several greenhouse gases (CH4, NH3, H2S, H2O) could have provided the necessary warming. It is now thought, however, that early core formation and massive loss of hydrogen left both the mantle and atmosphere oxidized [63–65], and the atmosphere dominated by CO2 and H2O. With the low early solar luminosity and as a result of cloud formation, it may not be possible to warm the Martian surface higher than about 230 K, with just a CO2/H2O atmosphere, no matter how thick it is . In addition, with Mars' low gravity, it is difficult to retain a thick atmosphere against blow-off by large impacts  and a warm CO2/H2O atmosphere tends to self-destruct by forming carbonates. Carbonates are detected at the Martian surface, although not in the amounts expected from a massive CO2/H2O atmosphere.
There is thus considerable uncertainty. One possibility is that episodic, massive volcanic events introduced large amounts of CO2, SO2 and possibly other greenhouse gases into the atmosphere . This resulted in temporary warmings, melting of water ice and initiated hydrological cycles. The warm conditions ended when the strong greenhouse gases were flushed out. Another possibility is that temporary warm conditions with accompanying rainfall were episodically caused by large impacts . But both these hypotheses have many unresolved issues. How early Mars became warm enough to allow widespread fluvial erosion remains a mystery.
One final mystery concerns life. Conditions on early Mars appear to have been Earth-like. We know that life started early on the Earth, although exactly when is still controversial [69,70]. Even if some form of life did start on early Mars, its unambiguous detection will be difficult, as exemplified by the controversy over the Martian meteorite ALH84001 [71,72]. Nevertheless, as in situ analyses become more sophisticated and return of samples carefully selected for their habitability and preservation potential becomes more feasible, the answer to whether some form of life ever started on Mars may not be that far in the future.
One contribution of 10 to a Theme Issue ‘River history’.
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