Climate of Mars

Climate of Mars
Mosaic image of Mars as seen by Viking 1, 22 February 1980

The climate of Mars has been an issue of scientific curiosity for centuries, not least because Mars is the only terrestrial planet whose surface can be directly observed in detail from the Earth.

Although Mars is smaller at 11% of Earth's mass and 50% farther from the Sun than the Earth, its climate has important similarities, such as the polar ice caps, seasonal changes and the observable presence of weather patterns. It has attracted sustained study from planetologists and climatologists. Although Mars's climate has similarities to Earth's, including seasons and periodic ice ages, there are also important differences such as the absence of liquid water (though frozen water exists) and much lower thermal inertia. Mars' atmosphere has a scale height of approximately 11 km (36,000 ft), 60% greater than that on Earth. The climate is of considerable relevance to the question of whether life is or was present on the planet, and briefly received more interest in the news due to NASA measurements indicating increased sublimation of the south polar icecap leading to some popular press speculation that Mars was undergoing a parallel bout of global warming.[1]

Mars has been studied by Earth-based instruments since as early as the 17th century but it is only since the exploration of Mars began in the mid-1960s that close-range observation has been possible. Flyby and orbital spacecraft have provided data from above, while direct measurements of atmospheric conditions have been provided by a number of landers and rovers. Advanced Earth orbital instruments today continue to provide some useful "big picture" observations of relatively large weather phenomena.

The first Martian flyby mission was Mariner 4 which arrived in 1965. That quick two day pass (July 14–15, 1965) was limited and crude in terms of its contribution to the state of knowledge of Martian climate. Later Mariner missions (Mariner 6, and Mariner 7) filled in some of the gaps in basic climate information. Data based climate studies started in earnest with the Viking program in 1975 and continuing with such probes as the highly successful Mars Global Surveyor.

This observational work has been complemented by a type of scientific computer simulation called the Mars General Circulation Model.[2] Several different iterations of MGCM have led to an increased understanding of Mars as well as the limits of such models. Models are limited in their ability to represent atmospheric physics that occurs at a smaller scale than their resolution. They also may be based on inaccurate or unrealistic assumptions about how Mars works and certainly suffer from the quality and limited density in time and space of climate data from Mars.

Contents

Historical climate observations

Giancomo Miraldi determined in 1704 that the southern cap is not centered on the rotational pole of Mars.[3] During the opposition of 1719, Miraldi observed both polar caps and temporal variability in their extent.

William Herschel was the first to deduce the low density of the Martian atmosphere in his 1784 paper entitled On the remarkable appearances at the polar regions on the planet Mars, the inclination of its axis, the position of its poles, and its spheroidal figure; with a few hints relating to its real diameter and atmosphere. When two faint stars passed close to Mars with no effect on their brightness, Herschel correctly concluded that this meant that there was little atmosphere around Mars to interfere with their light.[3]

Honore Flaugergues 1809 discovery of "yellow clouds" on the surface of Mars is the first known observation of Martian dust storms.[4] Flaugergues also observed in 1813 significant polar ice waning during Martian springtime. His speculation that this meant that Mars was warmer than earth was inaccurate.

Martian paleoclimatology

Prior to any serious examination of Martian Paleoclimatology one has to agree on terms, especially broad terms of planetary ages. There are two extant age systems for Mars. The first is based on crater density and has three ages, Noachian, Hesperian, and Amazonian. An alternate mineralogical timeline has been proposed, also with three ages, Phyllocian, Theikian, and Siderikian.

Recent observations and modeling is producing information not only about the present climate and atmospheric conditions on Mars but also about its past. The Noachian-era Martian atmosphere had long been theorized to be carbon dioxide rich. Recent spectral observations of deposits of clay minerals on Mars and modeling of clay mineral formation conditions [5] have found that there is little to no carbonate present in clay of that era. Clay formation in a carbon dioxide rich environment is always accompanied by carbonate formation, though once formed they are susceptible to destruction by volcanic acidity.

The discovery of water-formed minerals on Mars including Hematite and jarosite by the Opportunity rover, and goethite by the Spirit rover has led to the conclusion that climatic conditions in the distant past allowed for free flowing water on Mars. The morphology of some crater impacts on Mars indicate that the ground was wet at the time of impact.[6] Geomorphic observations of both landscape erosion rates[7] and martian valley networks[8] also strongly imply warmer, wetter conditions on Noachian-era Mars (approximately greater than 4 billion years ago). However, chemical analysis of martian meteorite samples suggests that the ambient near-surface temperature of Mars has most likely been below 0 C° for the last four billion years.[9]

Some scientists maintain that the great mass of the Tharsis volcanoes has had a major influence on the climate of Mars. Erupting volcanoes give off great amounts of gas. The gases are usually water vapor and carbon dioxide. Estimates put the amount of gas released to the atmosphere from Martian volcanoes as enough to make the atmosphere thicker than the Earth's. In addition, the water vapor from the volcanoes could have made enough water to place all of Mars under 120 meters of water. Carbon dioxide is a greenhouse gas that raises the temperature of a planet by trapping heat in the form of infrared radiation. So Tharsis volcanoes, by giving off carbon dioxide, could have made Mars more Earth-like in the past. Mars may have once had a much thicker and warmer atmosphere, and oceans and/or lakes may have been present.[10] It has however proven extremely difficult to construct convincing global climate models for Mars which produce conditions above freezing at any point in its history,[11] though this may simply reflect problems in accurately calibrating such models.

Weather

Mars temperature and circulation vary from year to year (as expected for any planet with an atmosphere). Mars lacks an ocean, a source of much inter-annual variation on earth. Mars Orbital Camera data beginning in March 1999 and covering 2.5 Martian years[12] shows that Martian weather tends to be more repeatable and hence more predictable than that of Earth. If an event occurs at a particular time of year in one year, the available data (sparse as it is) indicates that it is fairly likely to repeat the next year at nearly the same location give or take a week.

On September 29, 2008, the Phoenix lander took pictures of snow falling from clouds 4.5 km above its landing site near Heimdall crater. The precipitation vaporized before reaching the ground, a phenomenon called virga.[13]

Clouds

Animation of ice clouds moving above the Phoenix landing site over a period of ten minutes.

Mars' dust storms can kick up fine particles in the atmosphere around which clouds can form. These clouds can form very high up, up to 62 miles above the planet.[14] The clouds are very faint and can only be seen reflecting sunlight against the darkness of the night sky. In that respect, they look similar to the mesospheric clouds, also known as noctilucent clouds on Earth, which occur about 50 miles (80 km) above our planet.

Temperature

Differing values have been reported for the average temperature on Mars,[15] with a common value being −55 °C (−67 °F).[16] Surface temperatures have been estimated from the Viking Orbiter Infrared Thermal Mapper data; this gives extremes from a warmest of 27 °C (81 °F) to −143 °C (−225 °F) at the winter polar caps.[17] Actual temperature measurements from the Viking landers range from −17.2 °C (1.0 °F) to −107 °C (−161 °F).

It has been reported that "On the basis of the nighttime air temperature data, every northern spring and early northern summer yet observed were identical to within the level of experimental error (to within ±1 K)" but that the "daytime data, however, suggest a somewhat different story, with temperatures varying from year-to-year by up to 6 K in this season.[18] This day-night discrepancy is unexpected and not understood". In southern spring and summer variance is dominated by dust storms, which increase the value of the night low temperature and decrease the daytime peak temperature,[19] resulting in a small (20C) decrease in average surface temperature, and a moderate (30C) increase in upper atmosphere temperature.[20]

Atmospheric properties and processes

Low atmospheric pressure

The Martian atmosphere is composed mainly of carbon dioxide and has a mean surface pressure of about 600 pascals, much lower than the Earth's 101,000 Pa. One effect of this is that Mars' atmosphere can react much more quickly to a given energy input than can our atmosphere.[21] As a consequence, Mars is subject to strong thermal tides produced by solar heating rather than a gravitational influence. These tides can be significant, being up to 10% of the total atmospheric pressure (typically about 50 Pa). Earth's atmosphere experiences similar diurnal and semidiurnal tides but their effect is less noticeable because of Earth's much greater atmospheric mass.

Although the temperature on Mars can reach above freezing (0 °C), liquid water is unstable over much of the planet, as the atmospheric pressure is below water's triple point and water ice simply sublimes into water vapor. Exceptions to this are the low-lying areas of the planet, most notably in the Hellas Planitia impact basin, the largest such crater on Mars. It is so deep that the atmospheric pressure at the bottom reaches 1155 Pa, which is above the triple point, so if the temperature exceeded 0 °C liquid water could exist there.

Wind

The surface of Mars has a very low thermal inertia, which means it heats quickly when the sun shines on it. Typical daily temperature swings, away from the polar regions, are around 100 K. On Earth, winds often develop in areas where thermal inertia changes suddenly, such as from sea to land. There are no seas on Mars, but there are areas where the thermal inertia of the soil changes, leading to morning and evening winds akin to the sea breezes on Earth.[22] The Antares project "Mars Small-Scale Weather" (MSW) has recently identified some minor weaknesses in current global climate models (GCMs) due to the GCMs' more primitive soil modeling "heat admission to the ground and back is quite important in Mars, so soil schemes have to be quite accurate. "[23] Those weaknesses are being corrected and should lead to more accurate assessments going forward but make continued reliance on older predictions of modeled Martian climate somewhat problematic.

At low latitudes the Hadley circulation dominates, and is essentially the same as the process which on Earth generates the trade winds. At higher latitudes a series of high and low pressure areas, called baroclinic pressure waves, dominate the weather. Mars is dryer and colder than Earth, and in consequence dust raised by these winds tends to remain in the atmosphere longer than on Earth as there is no precipitation to wash it out (excepting CO2 snowfall).[24] One such cyclonic storm was recently captured by the Hubble space telescope (pictured below).

One of the major differences between Mars' and Earth's Hadley circulations is their speed[25] which is measured on an overturning timescale. The overturning timescale on Mars is about 100 Martian days while on Earth, it is over a year.

Effect of dust storms

2001 Hellas Basin dust storm
Time-lapse composite of the Martian horizon during Sols 1205 (0.94), 1220 (2.9), 1225 (4.1), 1233 (3.8), 1235 (4.7) shows how much sunlight the July 2007 dust storms blocked; Tau of 4.7 indicates 99% blocked. credit:NASA/JPL-Caltech/Cornell

When the Mariner 9 probe arrived at Mars in 1971, the world expected to see crisp new pictures of surface detail. Instead they saw a near planet-wide dust storm[26] with only the giant volcano Olympus Mons showing above the haze. The storm lasted for a month, an occurrence scientists have since learned is quite common on Mars. As observed by the Viking spacecraft from the surface,[19] "during a global dust storm the diurnal temperature range narrowed sharply, from fifty degrees to only about ten degrees, and the wind speeds picked up considerably---indeed, within only an hour of the storm's arrival they had increased to 17 meters per second, with gusts up to 26 meters per second. Nevertheless, no actual transport of material was observed at either site, only a gradual brightening and loss of contrast of the surface material as dust settled onto it." On June 26, 2001, the Hubble Space Telescope spotted a dust storm brewing in Hellas Basin on Mars (pictured right). A day later the storm "exploded" and became a global event. Orbital measurements showed that this dust storm reduced the average temperature of the surface and raised the temperature of the atmosphere of Mars by 30 °C.[20] The low density of the Martian atmosphere means that winds of 40 to 50 mph (18 to 22 m/s) are needed to lift dust from the surface, but since Mars is so dry, the dust can stay in the atmosphere far longer than on Earth, where it is soon washed out by rain. The season following that dust storm had daytime temperatures 4 °C below average. This was attributed to the global covering of light-colored dust that settled out of the dust storm, temporarily increasing Mars' albedo.[27]

In mid-2007 a planet-wide dust storm posed a serious threat to the solar-powered Spirit and Opportunity Mars Exploration Rovers by reducing the amount of energy provided by the solar panels and necessitating the shut-down of most science experiments while waiting for the storms to clear.[28] Following the dust storms, the rovers had significantly reduced power due to settling of dust on the arrays.

Dust storms are most common during perihelion, when the planet receives 40 percent more sunlight than during aphelion. During aphelion water ice clouds form in the atmosphere, interacting with the dust particles and affecting the temperature of the planet.[29]

It has been suggested that dust storms on Mars could play a role in storm formation similar to that of water clouds on Earth.[citation needed] Observation since the 1950s has shown that the chances of a planet-wide dust storm in a particular Martian year are approximately one in three.[30]

Saltation

The process of geological saltation is quite important on Mars as a mechanism for adding particulates to the atmosphere. Saltating sand particles have been observed on the MER Spirit rover.[31] Theory and real world observations have not agreed with each other, classical theory missing up to half of real-world saltating particles.[32] A new model more closely in accord with real world observations demonstrates that saltating particles create an electrical field that increases the saltation effect. Mars grains saltate in 100 times higher and longer trajectories and reach 5-10 times higher velocities than Earth grains do.[33]

Cyclonic storms

Hubble, colossal Polar Cyclone on Mars

First detected during the Viking orbital mapping program, cyclonic storms similar to hurricanes have been detected by various probes and telescopes. Images show them as being white in color, quite unlike the much more common dust storms. These storms tend to appear during the northern summer and only at high latitudes. Speculation is that this is due to unique climate conditions near the northern pole.[34]

Methane presence

Methane has been detected in the atmosphere of Mars by ESA's Mars Express probe at a level of 10 nL/L.[35][36][37] Since breakup of that much methane by ultraviolet light would only take 350 years under current Martian conditions, some sort of active source must be replenishing the gas.[38] Mars' current climate conditions may be destabilizing underground clathrate hydrates but there is at present no consensus on the source of Martian methane.

Carbon dioxide carving

Mars Reconnaissance Orbiter images suggest an unusual erosion effect occurs based on Mars' unique climate. Spring warming in certain areas leads to CO2 ice subliming and flowing upwards, creating highly unusual erosion patterns called "spider gullies".[39] Translucent CO2 ice forms over winter and as the spring sunlight warms the surface, it vaporizes the CO2 to gas which flows uphill under the translucent CO2 ice. Weak points in that ice lead to CO2 geysers.[39]

Mountains

Martian storms are significantly affected by Mars' large mountain ranges.[40] Individual mountains like record holding Olympus Mons (27 km) can affect local weather but larger weather effects are due to the larger collection of volcanoes in the Tharsis region.

One unique repeated weather phenomena involving Mountains is a spiral dust cloud that forms over Arsia Mons. The spiral dust cloud over Arsia Mons can tower 15 to 30 kilometers (9 to 19 miles) above the volcano.[41] Clouds are present around Arsia Mons throughout the Martian year, peaking in late summer.[42]

Clouds surrounding mountains display a seasonal variability. Clouds at Olympus Mons and Ascreaus Mons appear in northern hemisphere spring and summer, reaching a total maximum area of approximately 900,000 km2 and 1,000,000 km2 respectively in late spring. Clouds around Alba Patera and Pavonis Mons show an additional, smaller peak in late summer. Very few clouds were observed in winter. Predictions from the Mars General Circulation Model are consistent with these observations.[42]

Polar caps

An illustration of what Mars might have looked like during an ice age between 2.1 million and 400,000 years ago, when Mars's axial tilt is believed to have been much larger than today.
HiRISE image of "dark dune spots" and fans formed by eruptions of CO2 gas geysers on Mars' south polar ice sheet.

Mars possesses ice caps at both poles, which mainly consist of water ice; however, there is frozen carbon dioxide (dry ice) present on their surfaces. Dry ice accumulates in the northern polar region (Planum Boreum) in winter only, subliming completely in summer, while the south polar region additionally has a permanent dry ice cover up to eight metres (25 feet) thick.[43] This difference is due to the higher elevation of the south pole.

So much of the atmosphere can condense at the winter pole that the atmospheric pressure can vary by up to a third of its mean value. This condensation and evaporation will cause the proportion of the noncondensable gases in the atmosphere to change inversely.[24] The eccentricity of Mars's orbit affects this cycle, as well as other factors. In the spring and autumn wind due to the carbon dioxide sublimation process is so strong that it can be a cause of the global dust storms mentioned above.[44]

The northern polar cap has a diameter of approximately 1,000 km during the northern Mars summer,[45] and contains about 1.6 million cubic kilometres of ice, which if spread evenly on the cap would be 2 km thick.[46] (This compares to a volume of 2.85 million cubic kilometres for the Greenland ice sheet.) The southern polar cap has a diameter of 350 km and a maximum thickness of 3 km.[47] Both polar caps show spiral troughs, which were formerly believed to form as a result of differential solar heating, coupled with the sublimation of ice and condensation of water vapor.[48][49] Recent analysis of ice penetrating radar data from SHARAD has demonstrated that the spiral troughs are formed from a unique situation in which high density katabatic winds descend from the polar high to transport ice and create large wavelength bedforms.[50][51] The spiral shape comes from Coriolis effect forcing of the winds, much like winds on earth spiral to form a hurricane. The troughs did not form with either ice cap, instead they began to form between 2.4 million and 500,000 years ago, after three fourths of the ice cap was in place. This suggests that a climatic shift allowed for their onset. Both polar caps shrink and regrow following the temperature fluctuation of the Martian seasons; there are also longer-term trends that are not fully understood.

During the southern hemisphere spring, solar heating of south polar dry ice deposits leads in places to accumulation of pressurized CO2 gas below the surface of the semitransparent ice, warmed by absorption of radiation by the darker substrate. After attaining the pressure needed to burst through, the gas erupts in geyser-like plumes. While the eruptions have not been directly observed, they leave evidence in the form of "dark dune spots" and lighter fans atop the ice, representing sand and dust carried aloft by the eruptions, and a spider-like pattern of grooves created below the ice by the outrushing gas.[52][53] (see Geysers on Mars.) Eruptions of nitrogen gas observed by Voyager 2 on Triton are thought to occur by a similar mechanism.

Solar wind

Mars lost most of its magnetic field about four billion years ago. As a result, solar wind and cosmic radiation interacts directly with the Martian ionosphere. This keeps the atmosphere thinner than it would otherwise be by solar wind action constantly stripping away atoms from the outer atmospheric layer.[54] Most of the historical atmospheric loss on Mars can be traced back to this solar wind effect. Current theory posits a weakening solar wind and thus today's atmosphere stripping effects are much less than those in the past when the solar wind was stronger.[citation needed]

Seasons

In spring, sublimation of ice causes sand from below the ice layer to form fan-shaped deposits on top of the seasonal ice.

Mars has an axial tilt of 25.2°. This means that there are seasons on Mars, just as on Earth. The eccentricity of Mars' orbit is 0.1, much greater than the Earth's present orbital eccentricity of about 0.02. The large eccentricity causes the insolation on Mars to vary as the planet passes round the Sun (the Martian year lasts 687 days, roughly 2 Earth years). As on Earth, Mars' obliquity dominates the seasons but, because of the large eccentricity, winters in the southern hemisphere are long and cold while those in the North are short and warm.

The seasons present unequal lengths are as follows:

Season Sols
(on Mars)
Days
(on Earth)
Northern Spring, Southern Autumn: 193.30 92.764
Northern Summer, Southern Winter: 178.64 93.647
Northern Autumn, Southern Spring: 142.70 89.836
Northern Winter, Southern Summer: 153.95 88.997

Precession in the alignment of the obliquity and eccentricity lead to global warming and cooling ('great' summers and winters) with a period of 170,000 years.[55]

Like Earth, the obliquity of Mars undergoes periodic changes which can lead to long-lasting changes in climate. Once again, the effect is more pronounced on Mars because it lacks the stabilizing influence of a large moon. As a result the obliquity can alter by as much as 45°. Jacques Laskar, of France's National Centre for Scientific Research, argues that the effects of these periodic climate changes can be seen in the layered nature of the ice cap on the planets north pole.[56] Current research suggests that Mars is in a warm interglacial period which has lasted more than 100,000 years.[57]

Because the Mars Global Surveyor was able to observe Mars for 4 Mars years, it was found that Martian weather was similar from year to year. Any differences were directly related to changes in the solar energy that reached Mars. Scientists were even able to accurately predict dust storms that would occur during the landing of Beagle 2. Regional dust storms were discovered to be closely related to where dust was available.[58]

Evidence for recent climatic change

Pits in south polar ice cap, MGS 1999, NASA

There have been changes around the south pole (Planum Australe) over the past few Martian years. In 1999 the Mars Global Surveyor photographed pits in the layer of frozen carbon dioxide at the Martian south pole. Because of their striking shape and orientation these pits have become known as swiss cheese features. In 2001 the craft photographed the same pits again and found that they had grown larger, retreating about 3 meters in one Martian year.[59]

These features are caused by the dry ice layer sublimating exposing the inert water ice layer.

More recent observations indicate that Mars' south pole is continuing to sublime. "It's evaporating right now at a prodigious rate," says Michael Malin, principal investigator for the Mars Orbiter Camera (MOC).[60] The pits in the ice continue to grow by about 3 meters per Martian year. Malin states that conditions on Mars are not currently conductive to the formation of new ice. A NASA press release has suggested that this indicates a "climate change in progress"[61] on Mars. In a summary of observations with the Mars Orbiter Camera, researchers speculated that some dry ice may have been deposited between the Mariner 9 and the Mars Global Surveyor mission. Based on the current rate of loss, the deposits of today may be gone in a hundred years.[58]

Elsewhere on the planet, low latitude areas have more water ice than they should have given current climatic conditions.[62] Mars Odyssey "is giving us indications of recent global climate change in Mars," said Jeffrey Plaut, project scientist for the mission at NASA's Jet Propulsion Laboratory, in non-peer reviewed published work in 2003.

Attribution theories

Causes of the polar changes

Colaprete et al. conducted simulations with the Mars General Circulation Model which show that the local climate around the Martian south pole may currently be in an unstable period. The simulated instability is rooted in the geography of the region, leading the authors to speculate that the subliming of the polar ice is a local phenomenon rather than a global one.[63] The researchers showed that even with a constant solar luminosity the poles were capable of jumping between states of depositing or losing ice. The trigger for a change of states could be either increased dust loading in the atmosphere or an albedo change due to deposition of water ice on the polar cap.[64] This theory is somewhat problematic due to the lack of ice depositation after the 2001 global dust storm[65] Another issue is that the accuracy of the Mars General Circulation Model decreases as the scale of the phenomenon becomes more local.

It has been argued that "observed regional changes in south polar ice cover are almost certainly due to a regional climate transition, not a global phenomenon, and are demonstrably unrelated to external forcing."[55] Writing in a Nature news story, Chief News and Features Editor Oliver Morton said "The warming of other solar bodies has been seized upon by climate sceptics.On Mars, the warming seems to be down to dust blowing around and uncovering big patches of black basaltic rock that heat up in the day"[66][67]

Assertion that solar irradiance is causing global warming on Mars

Despite the absence of a time series for Martian global temperatures, K. I. Abdusamatov has proposed that "parallel global warmings" observed simultaneously on Mars and on Earth can only be a consequence of the same factor: a long-time change in solar irradiance."[68] While some climate change skeptics take this as proof that humans are not causing climate change, Abdusamatov's hypothesis has not been accepted by the scientific community. His assertions have not been published in the peer-reviewed literature, and have been dismissed by other scientists, who have stated that "the idea just isn't supported by the theory or by the observations" and that it "doesn't make physical sense."[69] Other scientists have proposed that the observed variations are caused by irregularities in the orbit of Mars or a possible combination of solar and orbital effects.[70]

Mars Global Climate Zones, based on temperature, modified by topography, albedo, actual solar radiation.

Climate Zones of Mars

Terrestrial Climate zones first have been defined by Wladimir Köppen based on the distribution of vegetation groups. Climate classification is furthermore based on temperature, rainfall, and subdivided based upon differences in the seasonal distribution of temperature and precipitation; and a separate group exists for extrazonal climates like in high altitudes. Mars has no vegetation, nor rainfall, so any climate classification could be only based upon temperature; a further refinement of the system may be based on dust distribution, water vapor content, occurrence of snow. Solar Climate Zones can also be easily defined for Mars.[71]

Current missions

The 2001 Mars Odyssey is currently orbiting Mars and taking global atmospheric temperature measurements with the TES instrument. The Mars Reconnaissance Orbiter is currently taking daily weather and climate related observations from orbit. One of its instruments, the Mars climate sounder is specialized for climate observation work.

Future missions

MSL is scheduled for 2011, followed by the Mars Scout mission in 2013. Both candidates (MAVEN and Great Escape) for the 2013 mission were to have climate study implications as they are upper atmosphere scientific packages with the MAVEN spacecraft being the final choice.

The People's Republic of China is launching a Mars orbiter called Yinghuo-1 in 2011. Its mission is not entirely clear but will focus mainly on the study of the external environment of Mars and should thus gain some data of interest to Mars climatologists. Russia will simultaneously launch Phobos-Grunt on the same rocket. Its destination and main focus will be Phobos but certain Mars climate related data are scheduled to be coming back from this probe as well.

See also

Notes

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