THE BIRTH Jules Janssen

J.-M Malherbe
email: jean-marie.malherbe@obspm.fr

THE FOUNDATION OF MEUDON OBSERVATORY AND THE MONT BLANC ADVENTURE (1875-1895)

Keywords: Janssen, Sun, physical astronomy, imagery, spectroscopy, solar spectrum, observatories, Meudon, Mont Blanc

Jules Janssen is a well known astronomer. He introduced in 1868 the spectroscopic technique to observe permanently solar prominences. He also invented innovative methods in imagery and photography. This paper focuses on the period going from the foundation of Meudon Observatory, associated to the birth of astrophysics and solar physics in France, to the Mont Blanc saga, with the creation of the observatory and the three scientific ascents of Janssen to the top of the mountain. As most documents are written in French, this fantastic and unbelievable adventure for the end of the XIX th century, deserves to be related in English, and reveals the long term vision of Janssen's astronomy. It involved specialized instruments, located in well chosen places where atmospheric troubles are minimized. High altitude observations, at Mont Blanc (or from balloons also experienced by Janssen), prefigure space astronomy which will develop much later. Hence, Janssen appears as a precursor of modern astronomy, well ahead of his time.

INTRODUCTION

Jules Janssen was born in 1824 (Figure 1). He was attracted late by scientific studies (mathematics, physics) and became "docteur ès sciences" in 1860. His thesis did not concern astronomy, but optical properties of the eye's medium. The works of Gustav Kirchhoff (1824Kirchhoff ( -1887) ) and Robert Bunsen (1811Bunsen ( -1899) ) in the field of spectroscopy, explaining the existence of lines discovered by Joseph von Fraunhofer (1787-1826) in the solar spectrum, had a strong influence on Janssen. He soon understood that spectroscopy will permit the determination of the chemical composition of the Sun and stars. Janssen started spectroscopic observations in 1862, designed direct vision spectroscopes based on Giovanni Amici (1786-1863) prisms, and became an incredible and tireless globe-trotter [START_REF] Launay | The Astronomer Jules Janssen: A Globetrotter of Celestial Physics[END_REF] to catch solar eclipses. He observed the solar spectrum in many high altitude stations, in order to separate the solar and telluric lines (atmospheric lines, such as dioxygen O2 or water vapor H2O, weaken with altitude). The most fruitful expedition was probably the long eclipse of 18 August 1868 in India (6 min 47 s duration according to NASA) reported by [START_REF] Launay | Observations of the total solar eclipse of 18 August 1868 carried out by Jules Janssen at Guntoor, India[END_REF]. Janssen observed solar prominences around the solar disk masked by the Moon. These features are cold hydrogen condensations in the hot solar corona, revealed by the red light of the Hα line emission (656.3 nm wavelength). Prominences are not directly visible outside eclipses due to the brightness of the disk. After the phenomenon, Janssen positioned his spectroscope on the prominence region and saw that Hα emission was present in the spectrum ! This major discovery, which was also made independently at the same time by Norman Lockyer , permitted hereafter observations of solar prominences at any time in Hα or other chromospheric lines. In 1869, Janssen formulated the principle of the spectro-helioscope to form monochromatic images of solar structures. With a spectroscope rotating at high speed around its optical axis, the entrance slit scans a 2D field of view, and a second slit selects, on exit, a broad line in the solar spectrum. Hence, the retinal persistence provides monochromatic images of the Sun in the selected waveband. This discovery is at the base of the photographic spectro-heliograph invented independently in 1892 by Henri Deslandres (1853Deslandres ( -1848) ) at Paris andGeorge Hale (1868-1938) at Chicago. Modern spectro-heliographs are still in use today (in Meudon or Coïmbra). During the 1868 eclipse in India, Janssen also noticed a yellow line in the spectrum of prominences, but he was not interested in. Norman Pogson (1829Pogson ( -1891) ) distinguished a new line just besides the well known chromospheric D1/D2 sodium doublet [START_REF] Nath | Norman Robert Pogson and observations of the total solar eclipse of 1868 from Masulipatam, India[END_REF], and Lockyer concluded that it was a new chemical element, helium, revealed by the yellow D3 line (587.6 nm wavelength). Helium will be found in minerals three decades later. In 1870, Paris was besieged by the Prussian army, and Janssen used a balloon flight to escape the enemy and attend another eclipse in Algeria; this uncommon event developed his fondness for aeronautics. In 1871, back in India for a new eclipse, Janssen observed the green line at 530.3 nm (later called coronium), previously discovered by Pogson in 1868 [START_REF] Nath | Norman Robert Pogson and observations of the total solar eclipse of 1868 from Masulipatam, India[END_REF], although usually ascribed to Charles Young during the 1869 eclipse in America. At that time, the atomic structure was unknown, so that coronium will only be identified 60 years later (in the 1930s by W. Gotrian and B. Edlén) as a forbidden line of the highly ionised FeXIV (13 lost electrons), indicating that the corona is 200 times hotter than the solar surface, a great advance in solar physics ! Janssen was elected in 1873 at the French Academy of Sciences. He was the inventor of the photographic revolver [START_REF] Launay | Jules Janssen's "Revolver photographique" and its British derivative, "The Janssen slide[END_REF] to record the Venus transit observed in Japan in 1874, and more generally to produce motion pictures of dynamic events. The revolver may be considered as a remote ancestor of the cinematograph. Let us now come to the foundation of Meudon in 1875 and to the birth of physical astronomy in France.

Figure 1: Famous astronomer Jules Janssen (1824Janssen ( -1907) ) founded Meudon Observatory in 1875 and started the Mont Blanc adventure in 1888 to study di-oxygen lines of the solar spectrum (courtesy Paris Observatory).

MEUDON AND THE BIRTH OF PHYSICAL ASTRONOMY AND SOLAR PHYSICS

Meudon is an old royal domain. The first chateau (XVI th century) was burnt down in 1795 and demolished in 1806. The new chateau, built under King Louis XIV in 1706 for his son, the "Grand Dauphin", was occupied by the Prussian army in 1870, which installed gun batteries there in order to shoot over Paris; this chateau was also partly burnt during the war (Figure 2). At this moment, Janssen was convinced that the alliance between emerging techniques, such as photography and spectroscopy, was going to launch a new research field. For that purpose, he was looking for a place to create a large observatory, including spectroscopic laboratories, in a good and large site outside Paris city, in order to develop this new field named "physical astronomy". This science was dedicated to the study of the physical and chemical nature of celestial objects (contrarily to Paris observatory traditionally involved in celestial mechanics and astrometry). The word "astrophysics" was introduced later. This movement occurred also in many countries, and was symbolized by the creation of the Astrophysical Journal (1890) by G. Hale in the USA, and Nature (1869) by N. Lockyer in Great Britain. In France, several scientists, such as Alfred Cornu (1841-1902), Georges Rayet (1839-1906) and others (Le [START_REF] Gars | Cornu : trois parcours exemplaires dans la construction de l'astronomie physique en France (1860-1890)[END_REF][START_REF] Gars | L'émergence de l'astronomie physique en France[END_REF] were implied. In England, previous works of Carl Gauss, Michael Faraday, Jean-Baptiste Biot, André-Marie Ampère were unified by James Maxwell (1831-1879), who produced the theory of electric and magnetic fields, including electromagnetic waves, which had a crucial importance in the development of astrophysics.

Janssen's personal activities, in solar imagery and spectroscopy, are in France at the origin of solar physics. For the new observatory, the government proposed two domains, and Janssen chose Meudon. This place was proposed in 1875 by Mac Mahon and Meudon was definitely affected in 1879 by Jules Grévy, both successive presidents of the French Republic. However, Janssen was authorized to install his instruments as early as 1876. The domain was ruined and occupied by soldiers, so that Janssen began observations of the Sun with temporary huts and instruments used for the Venus transit previously observed in Japan (next section). Meanwhile, an architect was appointed to transform the chateau and prepare the construction of the large 18.5 m diameter dome (Figure 2). The financial support of the government arrived after 1880, so that it took 10-15 years to complete this major project. The transformations and repairs of the chateau were completed in 1893 [START_REF] Janssen | Annales de l'Observatoire d'astronomie physique de Paris sis Parc de Meudon[END_REF][START_REF] Janssen | Mémoires et observations. Note sur les instruments de l'observatoire de Meudon[END_REF]. The 18.5 m iron dome (replaced by copper in 1924) was manufactured by the Cail company (Figure 3). It covers a double refractor, of 16 m focal length, well adapted to observations of small angular diameter objects, such as planets, nebulae, double stars or stellar clusters. The large size of lenses provided excellent resolving power. The optics was made by the Henry brothers of Paris observatory (Paul Henry, 1848-1905, and Prosper Henry, 1849[START_REF] Janssen | Atlas de photographies solaires[END_REF]. The cross section is rectangular (90 cm x 170 cm), because two refractors are superimposed, one of 83 cm diameter (f = 16.10 m) for visual observations and the second of 62 cm (f = 15.90 m) for photographic plates (it was optimized for the blue part of the spectrum). The mechanical mount was a masterpiece of Paul Gautier (1842Gautier ( -1909)). This beautiful instrument was renovated in the sixties [START_REF] Muller | La rénovation de la grande coupole de Meudon[END_REF].

Figure 3: The Meudon chateau is unusual in that it is built across a change in ground level, which explains why Figure 2 shows the telescope part beginning one storey up, whereas the above view shows it beginning at ground level. The large 18.5 m dome was built in 1893 by the Cail company. The mass of the dome is about 100 tons. The double refractor has a visual objective (83 cm diameter) and a photographic objective (62 cm), 16 m focal length, polished by brothers Henry of Paris observatory. The equatorial mount is of German type and was manufactured by the Gautier enterprise. This is the largest refractor in Europe (after [START_REF] Janssen | Annales de l'Observatoire d'astronomie physique de Paris sis Parc de Meudon[END_REF].

The second innovative instrument (Figure 4) was a large 100 cm diameter Newtonian telescope, with short focal length (3 m), so that it was highly luminous (F/3). It was located in a small dome (7.5 m diameter), also built by the Cail company, not far from the large dome of the double refractor. Here again, the mirror was polished by the Henry brothers, and the mechanics was manufactured by P. Gautier. At this time, Meudon instruments were among the most modern in the world. The double refractor is still the largest in Europe, but it is no more in activity. The 100 cm telescope is still used for teaching purposes but the optical combination was changed into a Cassegrain one in 1970, which increased the equivalent focal length to 22 m. This powerful first astronomical equipment was accompanied a variety of laboratories, arranged in the old horse stables, allowing the production of spectra of known gases under various pressures, in order to compare them to celestial ones. A second 7.5 m dome was also constructed by Cail for the refractor dedicated to solar photography (next section).

THE SOLAR PHOTOGRAPHIC ATLAS (1876-1903)

Janssen founded Meudon to develop celestial photography and spectroscopy. The scientific activities, before the construction of the large instruments which required nearly two decades, started with regular observations of the solar surface continuing until the publication of the "Atlas de photographies solaires" by [START_REF] Janssen | Atlas de photographies solaires[END_REF]. This atlas is a selection of what Janssen thought to be the best pictures of the photosphere. Thirty images were chosen among of the 6000 photographic plates obtained from 1876 to 1903. Most correspond to a solar diameter of 30 cm. This big collection was equivalent, in volume (but not in quality), to the lunar atlas of Henri Puiseux and Maurice Loewy, performed between 1893 and 1910 with the "grand équatorial coudé" at Paris observatory (6000 plates also). Unfortunately, all the solar plates but seven were destroyed in the seventies [START_REF] Launay | Jules Janssen et la photographie[END_REF][START_REF] Launay | The Astronomer Jules Janssen: A Globetrotter of Celestial Physics[END_REF]. The photographs of the solar surface were obtained with an excellent refractor (Figure 5, left, and Figure 6) built by several experts [START_REF] Le Cocguen | La lunette de photographie solaire Janssen[END_REF]. The 13.5 cm diameter objective (2.2 m focal length) is due to Adam Prazmowski (1821-1885) and was optimized for the blue-violet part of the spectrum. The mechanical assembly was built by Wilhelm Eichens (1818-1884). The Prazmowski refractor was initially installed on a rolling support made of wood (Figure 6), which complicated the precise orientation of solar images. An equatorial mount was designed later by Eichens for the second 7.5 m dome of the observatory. Photographic plates were produced by the Meudon laboratory with the maximum sensitivity around the G Fraunhofer line (430 nm wavelength). It was a long process to prepare the wet-collodion with iodide and bromide of ammonium, cadmium, or potassium (about 25 g dissolved in a mixture of one litre of alcohol and sulfuric ether). We know today that the contrast of the solar granulation increases towards short wavelengths and is best in the G band. It is composed of many lines of the CH molecule, unresolved in Janssen's epoch, and bright points appear as magnetic proxies of thin concentrated flux tubes. Observations in the G band were revisited in the seventies with large telescopes and narrow interference bandpass filters (0.8 nm); this waveband has become a universal standard in imagery of the solar surface.

Figure 6: The solar refractor used by Janssen in Meudon park. The 135 mm objective was built by A. Prazmowski, the mechanics by W. Eichens and the wood enclosure by Bigot. Special shutters, first made by Prazmowski, and later by Gautier, were designed for exposure times as short as 0.2 milliseconds. The primary image (2 cm) was magnified to 30 cm and formed on wet-collodion plates sensitive to blue light (courtesy Paris Observatory).

Images with the Prazmowski doublet (solar disk of 2 cm diameter) were excellent and optically magnified by an ocular to have a final diameter of 30 cm, and occasionally 50 cm or more according to the seeing. The exposure time was critical to freeze the atmospheric turbulence, which evolves fast (1000 Hz), in order to get high resolution pictures. For that purpose, Janssen imagined a specific shutter design, the "photographic trap" (this is the ancestor of curtain shutters; however, Hippolyte Fizeau and Léon Foucault used similar mechanisms for their 1840s daguerreotypes of the Sun). It is made of a high speed translating slit of adjustable width, which allows exposure times as short as 1/6000 second ! The first traps were made by Prazmowski, but they generated some vibrations. Improved traps were later produced by Gautier. Figure 7 shows an outstanding image of the solar granulation (1877), published in the solar atlas, obtained with the Prazmowski refractor, and highly magnified. It would be impossible today to reach such a quality, because of the seeing and environmental degradation caused by the growth of Paris city. An exceptional picture of a sunspot (1885), with moderate magnification and also published in the atlas, is displayed in Figure 8. Finally, an example of the full Sun ( 1893), obtained at the primary focus of the refractor (without any magnification), is presented in Figure 9 together with the "photographic trap" located in the image plane.

Figure 7: The solar granulation observed by Janssen on 10 October 1877 with special photographic emulsions, prepared in the laboratory and sensitive to the blue part of the solar spectrum, around the Fraunhofer G line at 430 nm wavelength. Granules are small convective cells of 1000 km (1.5 arc second) covering the solar photosphere. The picture quality is not homogeneous, even in the case of short exposure times. Indeed, the atmospheric turbulence (tip-tilt component) is frozen, but local defocusing and distortions still exist. Today, they could be corrected by adaptive optics. The field of view is about 75 x 100 arc seconds (after Janssen's "Atlas de photographies solaires", 1903).

THE SOLAR SPECTRUM AND THE MONT BLANC ADVENTURE (1888-1895)

Janssen, besides three decades of solar imagery, studied in parallel the solar spectrum. In 1862, he observed details of the Brewster bands of di-oxygen O2, in the red and near infrared part of the spectrum, namely the A band (760 nm wavelength) and the B band (680 nm). An important question arose: is there a contribution of the Sun to the O2 spectral lines, or are they strictly of telluric origin ? We know today that oxygen is present in the solar atmosphere, but not in the di-atomic form (O2). It appears in some molecules such as CO, SO, OH, metallic oxides such as SiO or TiO, and is among the most abundant elements in the solar atmosphere, together with carbon, nitrogen, neon and many metals. The abundance is of course far from hydrogen and helium (the main elements). Oxygen also exists in the mono-atomic form (O) and is revealed by the ultraviolet spectrum of the million degrees solar corona (the external envelope), as neutral (OI) or in various states of ionization, from OII (1 lost electron) to OVIII (7 lost electrons), depending on temperature conditions. Of course, these properties were unknown in Janssen's epoch. He first found evidence of the B band of O2 in the Meudon spectroscopic laboratory. In 1889, the Eiffel tower in Paris was completed. Janssen observed from Meudon the light beam of this giant light-house, at a distance of 7700 m, equivalent to the thickness of the Earth's atmosphere, and saw the absorption lines of atmospheric O2. An experiment, made at Meudon with a 60 m pipe filled with pure di-oxygen at the pressure of 28 bars, equivalent to the atmospheric thickness, showed clearly the A and B bands. Even with a 120 m pipe of pure O2 at the pressure of 1 bar and equivalent to only 1/10 of the atmospheric thickness, the B band appeared. However, if there was no doubt that O2 lines of the solar spectrum mainly originate in the air-mass above the observer, a contribution of the Sun might exist and stay hidden. The only way to resolve this question consisted of observing the solar spectrum at the highest possible altitude: this was the starting point of the Mont Blanc adventure [START_REF] Malherbe | Les observatoires du Mont Blanc en 1900[END_REF][START_REF] Grévoz | Le pari fou de Jules Janssen, le savant épris du Mont Blanc[END_REF].

Figure 10: The north face of Mont Blanc and the route to the summit across the glaciers. R1 is the "Grands Mulets" refuge (3050 m) where first spectroscopic observations were done by Janssen in 1888. R2 is the "Grand Rocher Rouge" hut (4500 m) especially built in 1893 as a relay for the construction of the observatory (the "Corridor" is the historical route of the first ascent of 1786, but never used today). R3 is the refuge and geophysical observatory of J. Vallot (4360 m), erected on the "Rochers foudroyés". Janssen visited R1 and R3 in 1890, and R1 and R2 during his ascents of 1893 and 1895 (courtesy Paris Observatory).

In 1887, Janssen went to the Pic du Midi de Bigorre (2870 m), where an observatory was founded in 1875 by Charles Champion de Nansouty (1815-1895) and Xavier Vaussenat (1831-1891) for meteorological purposes (astronomy came later under the auspices of Benjamin Baillaud, 1848Baillaud, -1934)). Janssen always travelled with a standard spectroscope manufactured by Jules Duboscq (1817-1886), in order to facilitate the comparison of results obtained in different places and elevations. He sometimes used, in addition, more dispersive instruments. One year after observations at Pic du Midi, he decided to approach Mont Blanc and first went to the "Grands Mulets" refuge (R1 in Figure 10).

4.1

The first approach of high altitude: the ascent of the "Grands Mulets" (1888) For Janssen, going to the "Grands Mulets" (3050 m), the main step along the Mont Blanc route from Chamonix, was much more complicated than going to Pic du Midi (a region of medium mountains accessible in summer by trails), because the refuge is located among chaotic glaciers, particularly rugged in autumn. Large and deep crevasses are open, and finding a path, even for mountain guides, is a complicated task [START_REF] Janssen | Sur le spectre tellurique dans les hautes stations et en particulier sur le spectre de l'oxygène[END_REF]. Moreover, Janssen was handicapped physically by his claudication since childhood (consecutive to an injury) and had to be carried during the ascent. It took two days from Chamonix, instead of one day for experienced alpinists. Janssen chose October in order to benefit from very cold and dry air conditions, which reduce the intensity of atmospheric lines (water vapor) in the solar spectrum. The first day, Janssen travelled on the back of a mule, which followed the trail from Chamonix to the "Pierre pointue" chalet (2300 m). The second day was much more difficult. There is never a permanent trail across glaciers and the guides have to find a complicated path among huge crevasses. Janssen imagined an appropriate means of transport: the ladder-chair (Figure 11). The astronomer was carried by four or six guides and the ascent was so long that it was not until night that the caravan arrived at the refuge (Figure 12). Janssen used the Duboscq spectroscope, which was composed of three arms and two prisms. The first arm contained the adjustable slit and the collimator. The second was a chamber, with a focusing lens and an eyepiece to observe the spectrum. The third arm projected a measurement scale onto the prisms. The spectrograph was fed by a Prazmowski heliostat (Figure 12). Janssen observed at the "Grands Mulets" a marked decrease in intensity of O2 lines (the B group), but it was not sufficient to conclude that O2 does not exist in the Sun's atmosphere. It was necessary to reach higher altitudes and install a new station with permanent and powerful scientific equipment, in good observing conditions: this was the birth of the observatory project.

Figure 11: In order to cross the crevassed glaciers, Janssen designed a 4 m ladder-chair with four carriers for his ascents to the "Grands Mulets" refuge (3050 m). The crevasses are so numerous and so large along this route that it is impossible to use a sleigh (drawing after a photography of E. Whymper, Janssen, 1895).

The first ascent of Mont Blanc (1890)

Jospeh Vallot (1854Vallot ( -1925) ) erected in 1890 a laboratory on Mont Blanc slopes [START_REF] Vallot | Construction de l'Observatoire du Mont Blanc[END_REF], at 4360 m elevation (R3 in Figure 10). It was a multi-purpose station to study meteorology, geophysics, medicine, cartography and glaciology, but astronomy was not concerned. In order to observe the solar spectrum at the summit of the mountain, Janssen decided to follow the R1-R3 route of Figure 10. It took several days to reach the summit (Janssen, 1890a). Mules were used between Chamonix and the glaciers. Then, Janssen was carried up to R1 (the "Grands Mulets") with the ladder-chair, as in 1888. Above R1, the glaciers are smoother and Janssen imagined another means of transport, a special sleigh adapted to the constraints of high altitude (Figures 13 and14). Many guides were necessary to pull up the astronomer from R1 to the Vallot laboratory at R3. Janssen stayed there three days with Vallot, because of bad weather. The summit of Mont Blanc was reached successfully with the sleigh and twelve guides ("my twelve apostles", as Janssen said). The ascent was particularly difficult along the narrow ice ridge leading to the summit. Janssen observed rapidly the solar spectrum with the Duboscq spectroscope, still revealing the B group of di-oxygen, but with strongly reduced intensity.

Figure 13: Left: the mountain guides of Chamonix. The special sleigh was used above the "Grands Mulets" refuge where the glacier is easier, with few crevasses. Janssen was accompanied during this expedition by 22 persons, twelve of whom were guides. Right: Janssen's sleigh above the refuge on the way to the Mont Blanc. The guides used a rope ladder to pull up the sleigh. For the ascents of 1893 and 1895, they sometimes used winches, especially designed by Janssen, which were anchored in the snow or ice by picks (drawings after photographs, Janssen, 1890b).

The observatory and second ascent of Mont Blanc (1893)

The laboratory of J. Vallot, erected in 1890 on rocks located 450 m below the summit (the "Rochers foudroyés", R3), was a nice structure for the study of earth sciences, such as glaciology, but astronomy was outside its scope. For celestial observations, a clear horizon is required, and the flanks of mountains are not convenient. Moreover, they generate atmospheric turbulence. At the summit, one can expect laminar air flows, in favour of good images and seeing. For these reasons, astronomers prefer the top of high mountains. Janssen naturally targeted the Mont Blanc summit. This logical choice, not well understood in the valley, was interpreted as a competition between both characters.

The success of the previous ascent (1890) was reported to the French Academy of Sciences, which encouraged the project of a high altitude astronomical observatory. Several sponsors, friends of the sciences, such as Raphaël Bischoffsheim (1823-1906), Prince Roland Bonaparte (1858-1924), Baron Alphonse de Rothschild (1827Rothschild ( -1905) ) brought more than 250 000 francs and a society was founded with former minister of finance Léon Say (1826-1896) acting as the president. He was charged with negotiating an annual grant from the government.

However, the summit of Mont Blanc is not an hospitable place ! It is covered by ice and snow and is subject to terrible storms and winds. There is no rock to establish the foundation of a sustainable construction. The famous engineer Gustave Eiffel (1832Eiffel ( -1923)), one of Janssen's friends, promised to erect a metallic laboratory, but only if rocks could be found 12 m below the iced summit. The Swiss engineer Xavier Imfeld (1853-1909), a topographer, was charged in 1891 with ice soundings. Two horizontal tunnels of 23 m length were excavated to search for rocks, without any success [START_REF] Durier | Les travaux de M. Eiffel au Mont Blanc[END_REF]. Eiffel withdrew from the project, and Janssen reconsidered it on a new basis.

The idea was now to put the observatory directly on ice. But it was necessary to test whether the resistance of the snow was sufficient to support the weight of the construction. An experiment was undertaken at Meudon in 1892 during the winter. A pile of snow was packed in order to reach the density measured at the summit of Mont Blanc. Then, a column of 360 kg of lead was elevated above, corresponding to a pressure of 4000 kg/m². The settling was evaluated at 8 mm only, so that a construction of 5 m x 10 m size, weighing a few tens of tons, made of wood, appeared quite reasonable. The shape was a truncated pyramid [START_REF] Tissandier | L'Observatoire du Mont Blanc[END_REF], with the lower part buried into the snow in order to resist the violent storms which occur at high altitude. In order to deal with horizontality fluctuations, in particular under the pressure and motion of ice, several actuators were incorporated at the base of the wooden structure (Figure 15). The observatory was built in Meudon under the supervision of the architect Emile Vaudremer . It was transported to Chamonix by train in several parts and divided into 800 man loads. The route to Mont Blanc was divided into four sections and a new hut (R2 in Figure 10) was built during the 1892 summer at the "Grand Rocher Rouge". The first section was Chamonix-glacier (with the help of mules), and the three other sections (glacier-R1 refuge, R1-R2 hut, R2summit) were only man-portable. The R2 hut (4500 m) was strategic, because it was used by the carpenters during the erection of the observatory, both for lodging and storage of materials and tools. The 1892 summer was used for carriage and the beginning of the construction, which was finished in 1893. Winches were useful to raise the heaviest charges, and Janssen, in September 1893, planed his second ascent to inaugurate the observatory (Figures 16 and17). He chose the itinerary R1-R2 (Figure 10) followed during the construction, and the winches, still in place, helped the guides to lift the traveller's sleigh [START_REF] Janssen | L'observatoire du Mont Blanc[END_REF].

Janssen brought the Duboscq spectroscope and a second spectrograph with better dispersion, able to resolve the doublets of the B group of O2. It was composed of a 5 cm x 8 cm, 568 groves/mm Rowland grating and longer focal length lenses. The focal length of the collimator and the photographic chamber were respectively 1.10 m and 1.50 m, and their diameter was 10.8 cm. A 0.85 m focal length objective formed a 7.6 mm diameter solar image on the 20 micrometre spectrograph slit. A spectrum of the B band of O2 obtained with this spectrograph is shown in Figure 18.

In 1894, a long-running meteorograph (Figure 19) was manufactured by Jules Richard (1848-1930) and mounted at the observatory in 1895 [START_REF] Janssen | Météorographe à longue marche de l'Observatoire du Mont Blanc[END_REF]. It had, in principle, 8 months of autonomy in order to pass the winter, a period where ascents are impossible. It was driven by a clock mechanism with a 90 kg counterweight descending several meters. This high precision instrument was able to record, on paper rolls, temperature, pressure, hygrometry, wind speed and direction. However, the climatic conditions were extremely severe for the meteorograph, so that this high performance, but very delicate machine, never worked for very long.

Figure 15: Mont Blanc Observatory (5 m x 10 m base) was designed, mounted and tested in Meudon, then dismounted and transported to Chamonix by train. The 15 tons of wood were conveyed to the summit of Mont Blanc by many carriers. Eight hundred loads were necessary, and the heaviest parts of the framework were hauled with winches. At the summit of Mont Blanc, the first floor was buried into the snow in order to resist the winds and storms, which can be extremely violent at this altitude. The structure was supported by several actuators in order to keep it horizontal and compensate for ice movements. A central spiral staircase (not represented) provided access to the floors and the meteorology tower. The Observatory was covered by double walls (After Tissandier, 1893, left, and courtesy Paris Observatory, right). The main astronomical equipment was a large refractor designed in Meudon, transported to the summit in 1895 and assembled there in 1896. This ambitious instrument 1906) was composed of a static external tube of 70 cm diameter enclosing the rotating internal tube (35 cm diameter) of the refractor, supporting a 30 cm objective (two lenses of 5.40 m focal length) made by the Henry brothers of Paris Observatory. The axis of the metallic tubes was parallel to the Earth's polar axis. The internal tube was mounted on rollers and there was a clock-type mechanical motor. The diameter of the solar image at the focus was 49.4 mm. The refractor was fed by a polar siderostat, with a flat mirror of 60 cm diameter. This mirror was removable, so that when the refractor was not used, it was protected by a metallic cover. The refractor was built and tested in Meudon (Figure 20). It was then dismounted, segmented into several parts and transported to the summit of Mont Blanc under the form of many carrier charges, not exceeding 30 kg. The heaviest charge was the mirror of the siderostat (62 kg). At the focus, micrometric eyepieces and photographic plates were available. It was possible to catch a celestial object using coordinates, with two graduated circles. The first one was attached to the refractor (right ascension), while the second one was fixed to the flat mirror (declination). There was a cranked mechanical transmission to adjust the inclination of the flat mirror from the observing room. A small telescope (8 cm diameter) was attached to the 30 cm main refractor to facilitate the pointing of celestial objects, and a second auxiliary telescope, with larger field of view, was also present.

A small removable spectrograph was mounted later, in 1904 (Figure 20), with the following characteristics: 60 cm focal length collimator and two chamber objectives of either 30 cm or 60 cm focal length. The dispersive element was a flint prism. The height of the slit was 9 mm. The polished nickel of the slit reflected light towards a small control telescope focused on the slit jaw. Photographic plates were available. The spectrograph permitted, for instance, the measurement of the width of the solar chromosphere (2900 km) which is not visible in white light, but only in some Fraunhofer lines such as Hα or CaII H and K.

The observer stood inside the observatory, on the lower level. As the refractor was long (6 m), the northern wall of the upper level was open (Figures 21 and22) and the 30 cm objective was permanently outside. A platform was constructed to access the cover of the tube and install or remove the polar siderostat. Such a powerful and outstanding astronomical instrument was really unexpected at 4810 m, among glaciers, ice and cold ! Apart the major difficulties of ascents (the summit is 3800 m above Chamonix), the most important obstacles were meteorological conditions: strong winds, thunderstorms and atmospheric electricity, powdery snow and frost, and condensation of water vapor on optical pieces forming frost. But no rust was observed, because it never rains at this altitude and the air remains always dry.

Janssen saw the refractor at the summit in disassembled parts during his last ascent (Janssen, 1895a and1895b). For a 71 year-old person, constrained to be carried by guides or pulled up with a sleigh, it was an exploit. Janssen did not himself use this incredible instrument, because it only became operational one year later, in 1896. He examined the lines of the solar spectrum with a two-prism arrangement of the Duboscq spectroscope fed by a heliostat. He concluded that "the presence of oxygen and water in the solar envelope, and their respective physical state, seem to be answered questions, but this problem is so crucial that observations need to be repeated". Janssen also noticed an almost imperceptible displacement of the observatory, which was expected.

Activities of the observatory after 1895

About 25 researchers visited the observatory (Figures 23 and24), either for solar or night observations with the 30 cm refractor, and an associated spectrograph installed in 1904 by Gaston Millochau (1866-1922), a Meudon astronomer. During ten years, between 1896 and 1906, about five scientific expeditions per year were undertaken. A famous visitor, Milan Stefanik (1880Stefanik ( -1919)), one of the co-founders of the Czechoslovakian Republic, was an astronomer and collaborated with Janssen at Meudon. He organized during seven years observations at Mont Blanc, and beat the record of length for a stay at the summit, together with Millochau, with 13 consecutive days. Aleksey Hansky (1870Hansky ( -1908)), who became an astronomer at the Poulkovo Observatory, also worked with Janssen, and made many successful ascents over eight years. He stayed up to 12 consecutive days at the summit.

Most research and results were summarized by [START_REF] Radau | L'astronomie au Mont Blanc[END_REF]. Many astronomical observations were undertaken, besides the studies of the visible solar spectrum by Janssen, which were continued in 1898 by Aymar de La Baume-Pluvinel (1860-1938). We can cite the investigations of the zodiacal light, the imaging of Venus and Mercury, the study of the near infrared and ultraviolet solar spectrum and some attempts at observations of the hot solar corona outside eclipses (which will not be successful before the Lyot's coronagraph, see Dollfus, 1983). Measurements of the total solar irradiance (TSI) were performed with the actinometers of André Crova . The TSI was at that epoch called the "solar constant" (this is the solar flux entering the atmosphere, about 1360 W/m², we know today that it fluctuates during the eleven-year solar cycle). Hansky tried to improve the precision of the pyrrheliometer of Claude Pouillet (1790-1868), with the new pyrometer telescope of Charles Féry (1865Féry ( -1935)). He conducted several observations between 1898 and 1904 which led to a more precise value for the effective temperature of the Sun.

In meteorology, although this was far from the main goal, some observations concerning atmospheric electricity and ozone can be mentioned. The observatory, without any satisfying ground conductor, was not protected against lightning strikes, in contrast to the Vallot laboratory which was almost a Faraday cage, so that atmospheric phenomena were impressive. The thermometer recorded temperatures as low as -45°C in winter 1901, but the long-running meteorograph never worked properly in these difficult conditions. Miscellaneous research in physics, such as gravimetry with astronomer Guillaume Bigourdan (1851Bigourdan ( -1932)), electrical conductivity of the snow, telegraphy with wires put on the glaciers between the "Grands Mulets" refuge and Mont Blanc, medicine and biology, were also undertaken at the observatory, and were reported by Janssen in the second volume of "Annales de l'Observatoire d'astronomie physique de Paris, sis parc de Meudon" in 1906.

The decline of the observatory (1907-1909)

After his last ascent (1895), Janssen went to Chamonix in 1897 to organize an expedition, and later collaborated from Meudon in scientific missions until his death in 1907. However, the observatory began to sink slowly into the snow (Figure 25). The manoeuvre of actuators (1904,1906) was efficient until the formation of a crevasse below the observatory; it soon became displaced, uninhabitable and dangerous. In 1909 (Figure

Figure 2 :

 2 Figure 2: The ruins of Meudon chateau in 1871 (left) and the restored and transformed chateau in 1893 (right) with the new 18.5 m dome. The red boxes (left) indicate the parts which were completely destroyed by fire and suppressed (after Janssen, 1896).

Figure 4 :

 4 Figure 4: The dome of the 100 cm diameter Newtonian telescope at F/3 (3 m focal length), in 1893. It was changed into a Cassegrain telescope in 1970 to increase the focal length to 22 m (after Janssen, 1896).

Figure 5 :

 5 Figure 5: The temporary installation of solar refractors at Meudon Observatory in 1878. At left, the Adam Prazmowski refractor, at right the Carl Steinhel refractor used for The Venus transit of 1874 and a small temporary 5 m diameter dome (courtesy Paris Observatory).

Figure 8 :

 8 Figure 8: A large sunspot group observed by Janssen on 22 June 1885 with photographic emulsions sensitive to the blue part of the solar spectrum. Sunspots have a size comparable to the Earth, are related to solar activity and cyclicity, and exhibit strong magnetic fields (0.2 tesla). The granulation is also well visible in the upper part. The field of view is about 150 x 180 arc seconds (courtesy Paris Observatory).

Figure 9 :

 9 Figure 9: The full Sun observed by Janssen on 2 June 1893 showing sunspot groups and the shutter located at the primary focus of the refractor (at right), allowing extremely short exposure times to freeze the turbulence (courtesy Paris Observatory).

Figure 12 :

 12 Figure 12: Left: the refuge "Les Grands Mulets", 3050 m, the main station on the route to Mont Blanc at Janssen's time. It is located on a rocky spur surrounded by steep glaciers with large and deep crevasses. The refuge was visited four times by Janssen, in 1888, for spectroscopic observations, and in 1890, 1893 and 1895 for his three ascents of the summit (author's collection). Right: the Prazmowski heliostat to catch the solar light and a portable Duboscq spectroscope (courtesy CNUM/CNAM).

Figure 14 :

 14 Figure 14: Janssen's sleigh (top of the photography) waiting to cross a large crevasse on a ladder. Deep crevasses similar to this one are numerous and dangerous on the route to the Mont Blanc (author's collection).

Figure 16 :

 16 Figure 16: Janssen's Observatory in 1893 at the summit of Mont Blanc (author's collection).

Figure 17 :

 17 Figure 17: Janssen's Observatory at the summit of Mont Blanc, a few years after the inauguration of 1893 (courtesy Paris Observatory).

Figure 18 :

 18 Figure 18: Lower panel: the solar spectrum obtained at Mont Blanc with the Rowland grating spectrograph. The B band of oxygen spectral lines (O2 molecule) appears at the wavelength of 680 nm, in the red. Upper panel: the spectrum of the Jungfraujoch (3600 m) for comparison, degraded to almost the same resolution and observed by Delbouille et al (1973) with wavelength indicated in Angström (courtesy Paris Observatory).

Figure 19 :

 19 Figure 19: The long-running meteorograph manufactured by J. Richard for the Mont Blanc observatory in 1894. A = clock able to work during 8 months. B = barometer and graph. C = mercury column. D = anemometer and graph. E = thermometer and graph. F = hygrometer and graph. G = the counterweights of the paper rolls. H = clock pendulum. I = clock transmission axis to the instruments (drawing, after Janssen, 1894).

4. 4

 4 The 30 cm refractor and the third ascent of Mont Blanc (1895)

Figure 20 :

 20 Figure 20: The 30 cm diameter, 5.40 m focal length refractor (left) mounted and tested at Meudon in 1895. The two-lens objective was made by the Henry brothers of Paris observatory. The direction of the tube was parallel to the earth rotation axis. The refractor was fed by a 60 cm polar siderostat (flat mirror on top, left).This mirror was manually removed and replaced by a cover outside observing sessions. The refractor was installed at Mont Blanc during the summers of 1895 and 1896. A 0.60 m focal length spectrograph (centre) was available at the focus of the telescope in 1904. At right, the refractor in imagery mode with the eyepiece holder (after[START_REF] Millochau | La grande lunette de l'observatoire du Mont Blanc[END_REF][START_REF] De Fonvielle | A l'Observatoire du Mont Blanc[END_REF].

Figure 21 :

 21 Figure 21: The 30 cm fixed-direction refractor at Mont Blanc Observatory was operational in 1896. An opening was created for the tube in the northern wall. The telescope just rotated around its axis (right ascension) to compensate for diurnal motion. The platform was used to install and remove the flat mirror of the 60 cm polar siderostat to catch the light and adjust the declination (courtesy Paris Observatory).

Figure 22 :

 22 Figure 22: Janssen's Observatory at the summit of Mont Blanc, with the meteorological turret. The 30 cm diameter, 5.40 m focal length refractor was only available in 1896 (compare to Figures 16 and 23). The platform giving access to the cover of the refractor is located north of the construction and is visible at left. The refractor is parallel to the Earth's rotation axis and fed by a 60 cm polar siderostat. It was necessary to install the flat mirror before observations (courtesy Paris Observatory).

Figure 23 :

 23 Figure23: The Mont Blanc Observatory, west side. In both pictures, the 60 cm polar siderostat is mounted in front of the 30 cm objective, at left. The cover of the refractor lies on the platform (courtesy Paris Observatory).

Figure 24 :

 24 Figure 24: Observations, measurements, experiments and life at the Mont Blanc Observatory (courtesy Paris Observatory and La Nature).

CONCLUSION: JANSSEN'S HERITAGE

During two centuries, from 1667, Paris Observatory was mainly devoted to celestial mechanics and astrometry. Janssen introduced physical astronomy in France, following similar movements in Europe and in the USA. Meudon Observatory was initially named "Observatoire d'astronomie physique", which indicates clearly the aim of the founder in 1875. Janssen combined two major techniques, photography and spectroscopy, applied to the study of the physical and chemical nature of celestial objects, in particular the Sun. Meudon and Paris observatories amalgamated in 1926 and belong today to the oldest and biggest astronomical institutions in the world. The Mont Blanc adventure was motivated by the question of the nature (solar or terrestrial) of di-oxygen lines in the solar spectrum, at an epoch when stratospheric balloons, rockets or satellites did not exist (although some balloons already reached higher elevations than Mont Blanc). Indeed, 50% of the atmosphere is below the summit of the mountain. Janssen could not look for durability when he decided to put the observatory directly on ice, in contrast to average altitude observatories created at the same moment. This audacious project consisted also of exploring the potential of high altitude for other astronomical questions. In that sense, Janssen can be considered as a precursor of modern astronomy, involving, on one hand large urban and multi-purpose institutes, and on the other hand many dedicated instruments in much better sites or space missions which eliminate atmospheric absorption, and rarely exceed 20 years of lifetime. Hence, the heritage of Janssen is not only the development of physical astronomy and associated techniques, but also a new vision of astronomical projects based on specific and short duration instruments. Janssen was a specialist of the Sun: space solar missions, such as SOHO and Solar Orbiter, are the continuation of this strategy at the European scale. The Mont Blanc summit was not suitable for permanent stations, but recent and similar high altitude observatories located in drier sites, such as Hawaii (4200 m, optical-telescopes) or Atacama (5100 m, radio-telescopes), with easier access, form a continuity. Janssen concluded in 1900: "Progress in science needs to specialize instruments, increase their size, and locate them in places where atmospheric troubles are minimized, leading inevitably to well chosen and high altitude stations".

ACKNOWLEGMENTS

The author wishes to kindly thank the three referees, among them Dr James Lequeux and Dr William Tobin, and the Editor, Pr Wayne Orchiston, for extremely helpful corrections, comments and suggestions.

ON-LINE SUPPLEMENT MATERIAL (MPEG 4 VIDEO MOVIE, JPEG IMAGES)

This short MPEG 4 video movie (2 min 30 s) shows a scientific ascent of Mont Blanc in 1900 at the epoch of Janssen's Observatory. This expedition follows the R1-R3 route (Figure 10) across glaciers. The movie starts at the entry of the glaciers (2400 m) and ends at Janssen's Observatory (after an old 9.5 mm black and white movie, author's collection). It is available here (low quality only): https://drive.google.com/file/d/1mnpz_fFKQuYwaDcmeSNr1nSwa0rp-y2r/view?usp=sharing The figures of this paper are available in JPEG here: https://drive.google.com/drive/folders/1OCg2sz7J9THyz-ShyS1AaFLSKD5kPpAo?usp=sharing A remark: today, the French normal way of ascent starts à the "Nid d'aigle", a station (2370 m) at the end of a rack-railway coming from Saint Gervais. This is the "Aiguille du Goûter" route, open later than the historical route from Chamonix (used by Janssen), but faster and avoiding the falling and dangerous seracs of the "Dôme du Goûter". The Italian normal way was open by the pope Achille Ratti in 1890 (the "Aiguilles Grises" route) and merges with the French one at "Col du Dôme" (4250 m), just below Vallot's Observatory which still exists.

Most papers published at the end of the XIX th century or at the beginning of the XX th century were written in French language. Janssen's monumental work was compiled by H. Dehérain in two volumes (1929, 1930). Dehérain, H., 1929Dehérain, H., , 1930. . Oeuvres scientifiques de Jules Janssen (two volumes). Société d'éditions géographiques, maritimes et coloniales, Paris. On-line at CNUM/CNAM. http://cnum.cnam.fr/redir?8RA35.1 (volume 1, 1929) and http://cnum.cnam.fr/redir?8RA35.2 (volume 2, 1930).


D Arcay
email: nestor.cerpa@umontpellier.fr

Sea-level stability over geological time owing to limited deep subduction of hydrated mantle

Liquid surface oceans are a seemingly unique feature of Earth. Long-term, global sea level depends on the balance of water fluxes between Earth's mantle and surface: between mantle degassing through volcanism and mantle regassing via the subduction of hydrous minerals. However, the overall balance of these fluxes at geological timescales remains uncertain. Geological observations suggest the stability of the long-term sea level and thus a near-steady-state regassing-degassing balance. In contrast, according to current thermopetrological modelling, the global input of H2O inferred from geophysical observations leads to an unequivocal excess of regassing relative to degassing. Here we use recent experimental high-pressure data on natural hydrated peridotites to update the thermopetrological models and to reassess the calculations of H2O fluxes into the mantle via subduction. Our models of 56 subduction transects show that a global input of 15-20 × 10 8 Tg H2O every million years yields a limited global mantle regassing of 2.0-3.5 × 10 8 Tg H2O every million years. The regassing occurs exclusively via the hydrated lithospheric mantle of the coldest subducting plates. Our requantification of the H2O budget associated with subduction matches the estimations of mantle degassing and suggests that global sea levels have been relatively stable over geological timescales.

The water exchange between the Earth's surface and the deep interior is crucial for the evolution of our planet. Hydrous components affect mantle rheology [START_REF] Hirth | Rheology of the upper mantle and the mantle wedge: A view from the experimentalists[END_REF] and allow Earth-like plate tectonics [START_REF] Regenauer-Lieb | The initiation of subduction: criticality by addition of water?[END_REF] , while liquid-surface water is essential for planet habitability [START_REF] Kasting | Evolution of a habitable planet[END_REF] . The mantle degasses H2O through volcanism. Mantle regassing occurs via the subduction of H2O chemically bound to hydrous minerals. However, metamorphic reactions with increasing temperature (T) and pressure (P) partly liberate this H2O from the subducting oceanic plates. The fraction of the H2O that is retained in the slab returns to the deep mantle but its proportion remains debated. At first order, the imbalance between mantle degassing and regassing exerts a first-order control on the long-term eustatic sea-level [START_REF] Conrad | The solid Earth's influence on sea level[END_REF] . Hence, a precise quantification of the subducted H2O fluxes is required to decipher the global water cycle.

The most comprehensive study on H2O fluxes at present-day subduction zones 5 estimated a Global H2O/Water Retention (GWR) of 3.410 [START_REF] Vail | Seismic stratigraphy and global changes of sea level: Part 4. Global cycles of relative changes of sea level[END_REF] Tg/Myr beyond a 230-km depth. Their thermopetrological models predicted that half of the retention was controlled by the mafic crust, and a third by the hydrated lithospheric mantle, assumed to be only 2 km thick worldwide at subduction zone trenches. Because mantle degassing is approximately 210 [START_REF] Vail | Seismic stratigraphy and global changes of sea level: Part 4. Global cycles of relative changes of sea level[END_REF] Tg/Myr 6,7 , the predicted GWR would have decreased the global mean sea level by approximately 100 m over the Phanerozoic 6 (last 540 Ma, if constant over time). This is, however, close to the upper bound of retention ensuring a modest sea-level decrease (<100 m) during this Eon, as inferred from stratigraphic constraints [START_REF] Parai | How large is the subducted water flux? New constraints on mantle regassing rates[END_REF][START_REF] Vail | Seismic stratigraphy and global changes of sea level: Part 4. Global cycles of relative changes of sea level[END_REF][START_REF] Hallam | Phanerozoic sea-level changes[END_REF][START_REF] Haq | A chronology of Paleozoic sea-level changes[END_REF] (Extended Data Fig. 1). Furthermore, reconstructions of time-dependent subduction rates in the Phanerozoic suggest that GWR was higher during specific events, e.g., during the rift pulse at approximately 150 Ma [START_REF] Haq | A chronology of Paleozoic sea-level changes[END_REF] . A GWR at present-day of 3.410 8 Tg/Myr or higher, as predicted by current thermopetrological models 5,[START_REF] Rüpke | Serpentine and the subduction zone water cycle[END_REF][START_REF] Faccenda | Deep slab hydration induced by bending-related variations in tectonic pressure[END_REF][START_REF] Magni | Deep water recycling through time[END_REF] , seems thus inconsistent with a time-integrated low imbalance between mantle degassing and regassing. Only studies neglecting H2O transfer via the hydrated mantle were able to reach such a criterion 15 . The growing evidence of an hydrated lithospheric mantle thicker than 2 km [START_REF] Ranero | Bending-related faulting and mantle serpentinization at the Middle America trench[END_REF][START_REF] Contreras-Reyes | Upper lithospheric structure of the subduction zone offshore of southern Arauco peninsula, Chile, at ∼38˚S[END_REF][START_REF] Emry | Incoming plate faulting in the Northern and Western Pacific and implications for subduction zone water budgets[END_REF][START_REF] Cai | Water input into the Mariana subduction zone estimated from ocean-bottom seismic data[END_REF] (see also Supplementary Information S3), as well as the potential ability of metasomatized ultramafic rocks at the slab-mantle interface to convey H2O to the mid-mantle [START_REF] Hermann | Water transfer to the deep mantle through hydrous, Al-rich silicates in subduction zones[END_REF] , urge the need to address this paradox.

The mineralogical changes in the subducting mafic crust and ultramafic mantle, control the deep-H2O fluxes. Hence, quantitative studies of GWR rely on state-of-the-art petrological modeling of subducted hydrated lithologies.

Lawsonite is the main H2O carrier in the crust beyond subarc depths (Fig. 1a). Its stability field is relatively well known from experimental studies 21,[START_REF] Okamoto | The high-pressure synthesis of lawsonite in the MORB+ H2O system[END_REF] . In contrast, the postarc main hydrous phases for ultramafic systems are far less constrained [START_REF] Iwamori | Phase relations of peridotites under H2O-saturated conditions and ability of subducting plates for transportation of H2O. Earth and Planet[END_REF][START_REF] Maurice | The stability of hydrous phases beyond antigorite breakdown for a magnetite-bearing natural serpentinite between 6.5 and 11 GPa[END_REF] . The large uncertainties partly arise from the difficulty in handling laboratory H2O-rich experiments with natural samples at mid-upper mantle depth conditions. This is evidenced by the lack of experimental data on hydrous peridotite in the 6-8 GPa range (Supp. Info. Fig. S2b). Moreover, the poorly constrained effect of some minor elements (such as Al) and the unknown prevailing oxidation state of ultramafic rocks under high-PT conditions [START_REF] Maurice | The stability of hydrous phases beyond antigorite breakdown for a magnetite-bearing natural serpentinite between 6.5 and 11 GPa[END_REF][START_REF] Maurice | The intrinsic nature of antigorite breakdown at 3 GPa: Experimental constraints on redox conditions of serpentinite dehydration in subduction zones[END_REF] preclude a proper petrological thermodynamic modeling of subducted ultramafic rocks. Consequently, experimental and modeled phase diagrams differ at pressures above 6 GPa (Fig. 1b,c and Fig. S2a,b).

Here, we improve the estimation of present-day GWR using recent experimental results on the stability of hydrous phases in natural hydrated peridotites. By considering the new experimental findings in naturally complex systems at high PT conditions [START_REF] Maurice | The stability of hydrous phases beyond antigorite breakdown for a magnetite-bearing natural serpentinite between 6.5 and 11 GPa[END_REF] , the current view of relatively large amounts of H2O reinjected into the deep upper mantle is challenged.

Thermopetrological modeling of present-day subduction zones

We model the thermal state of all present-day subduction zones (56 subduction transects [START_REF] Syracuse | The global range of subduction zone thermal models[END_REF] , see Methods). We use the thermodynamic database ref. 27 and code Perple_X [START_REF] Connolly | The geodynamic equation of state: what and how[END_REF] to build phase diagrams, assuming bulk compositions relevant for the crustal and mantle layers at the subduction trenches ("basalt", Fig S5a,"gabbro" and "simplified peridotite model" Fig. 1a,b). To enhance the accuracy of the modeled mineralogical evolution of hydrated peridotites up to mid-mantle depths, we combine thermodynamic modeling to experimentally-derived assemblages from naturally complex systems [START_REF] Maurice | The stability of hydrous phases beyond antigorite breakdown for a magnetite-bearing natural serpentinite between 6.5 and 11 GPa[END_REF] and we build a hybrid-phase diagram ("complex peridotite model" Fig. 1c, see Methods).

At shallow depths, H2O subduction in the crustal layers occurs via amphibole, and at subarc to postarc depths via lawsonite [START_REF] Schmidt | Devolatilization during subduction[END_REF] . At the depth where the slab surface starts dragging the overlying mantle [START_REF] Wada | Common depth of slab-mantle decoupling: Reconciling diversity and uniformity of subduction zones[END_REF][START_REF] Arcay | Dynamics of interplate domain in subduction zones: influence of rheological parameters and subducting plate age[END_REF] , lawsonite is destabilized (700 to 900°C at 8 GPa, Fig. 1a) within the basaltic uppermost layers of the subducting plates. Below, the slower heating of the gabbroic layer enables lawsonite stability for most subduction transects up to ~8 GPa. At higher pressures, the stability of lawsonite little depends on temperature. Thus, in all but the hottest subduction transects (e.g., Cascadia), the oceanic crust crosses its "water line" [START_REF] Liu | Effects of H2O on the phase behaviour of the forsterite-enstatite system at high pressures and temperatures and implications for the Earth[END_REF] , i.e. the last phase transition beyond which hydrous minerals are unstable, between depths of 250 km and 310 km.

The two petrological models for peridotite display important differences. Below 7 GPa, the formation of the 10-Å phase [START_REF] Ulmer | Serpentine stability to mantle depths and subduction-related magmatism[END_REF][START_REF] Fumagalli | Experimentally determined phase relations in hydrous peridotites to 6• 5 GPa and their consequences on the dynamics of subduction zones[END_REF][START_REF] Dvir | Fluids in the peridotite-water system up to 6 GPa and 800 C: new experimental constrains on dehydration reactions[END_REF] enlarges the temperature range of the stability of hydrous minerals at ~5-6 GPa in the complex model. However, the striking differences impacting H2O subduction occur in the mineral assemblages above 8 GPa. In the simplified model, phase A breaks down at approximately 650°C to form brucite, the stability of which increases with pressure. In contrast, in the complex model, brucite is absent. Balangeroite and aluminous phase E form instead [START_REF] Maurice | The stability of hydrous phases beyond antigorite breakdown for a magnetite-bearing natural serpentinite between 6.5 and 11 GPa[END_REF] but within a narrower temperature range compared to that of brucite. These phase assemblages lead to significantly different water lines.

In the thermodynamically (simplified) modeled system, the slope of the water line is negative below 6 GPa and positive above (Fig. 1b). The point of inflection (6 GPa and 580°C), referred to as the "choke point" [START_REF] Kawamoto | Experimental evidence for a hydrous transition zone in the early Earth's mantle[END_REF] , controls the H2O retention in this system. The Moho-geotherms (Tonga, S. Kurile and Java) passing above or near the choke point are quasiparallel to the water line at higher P, stabilizing hydrous minerals in the lithospheric mantle within a few kilometers below the Moho. The ability of a subducted-mantle geotherm to pass the choke point has thus been related to its capacity to carry H2O down to mantle-transition depths, where very high-P hydrous phases (E and D) may be stable over a wide range of temperatures 5, [START_REF] Iwamori | Phase relations of peridotites under H2O-saturated conditions and ability of subducting plates for transportation of H2O. Earth and Planet[END_REF][START_REF] Komabayashi | Internally consistent thermodynamic data set for dense hydrous magnesium silicates up to 35 GPa, 1600 C: implications for water circulation in the Earth's deep mantle[END_REF] .

In the complex peridotite model, the choke point shifts to higher T and P (680°C -7 GPa, Fig. 1c). This enlarges the range of Moho geotherms stabilizing hydrous minerals up to 6-7 GPa. However, since the phase transition from aluminous-phase E to nominally anhydrous peridotite is quasi-isothermal beyond 8 GPa 24 , many moderately cold Moho geotherms pass above the choke point but cross the water line between 9 and 12 GPa (e.g. Java). The combined absence of brucite and the quasi-isothermal water line above 8 GPa become thus potential inhibitors to H2O transport to great depths.

Near-complete dehydration depths

To illustrate the impact of the petrological assumptions, we calculate the depth at which the lowermost-basaltic, the gabbroic and the hydrated peridotitic layers become nearly dry (95% dehydration, see Methods). The latter is assumed to be 4-km thick (~15% serpentinization) in our reference case, following previous studies on GWR [START_REF] Hacker | H2O subduction beyond arcs[END_REF] .

The top basaltic layers mainly dry near the depth at which the slab and mantle are kinematically coupled (i.e. at 80-110 km). The dehydration of the gabbros occurs within the depth range of 200-300 km in all but the hottest subduction transects (Fig. 1a). The dehydration pattern of the lithospheric mantle is partly controlled by the thermal state of the transects, but primarily depends on the petrological model. We define three groups of transects based on the way the petrological assumptions impact the mantle-dehydration pattern (Fig. 2).

Most transects belong to group 1, in which the lithospheric mantle dries within the depth range of 120-190 km, assuming the simplified peridotite model. Considering a complex peridotite model, the formation of the 10-Å phase in hot and moderately hot transects (subgroup 1.1) deepens the lithospheric mantle drying by 10 km (Cascadia) to 45 km (NCChile). Apart from the hottest transects, the H2O transport is limited by the breakdown of lawsonite in subgroup 1.1. If the 10-Å phase breaks down to balangeroite and aluminousphase E (moderately cold geotherms, subgroup 1.2), dehydration occurs deeper than in the simplified system and up to 310 km (Ryukyu) when the aluminous-phase E destabilizes. The transects in group 2 (moderately cold to cold geotherms) never dry when assuming a simplified peridotite model, owing to the formation of phase A and brucite. In contrast, the complex peridotite model induces the drying of the lithospheric mantle between 300 and 350km depths, following the breakdown of the aluminous-phase E. The hydrated mantle in the coldest-slab transects, forming group 3, never dries before reaching the mid-upper mantle regardless of the peridotite model. These coldest transects are the sole able to convey H2O to the mantle transition zone according to our preferred complex peridotite model.

Global Water Retention

We compare the global H2O flux predictions to the bounds allowing a relatively stable sea level during the Phanerozoic. The upper limit of 3.6±0.6 ×10 8 Tg/Myr ensures less than 100 m of sea-level decrease [START_REF] Parai | How large is the subducted water flux? New constraints on mantle regassing rates[END_REF] (Extended data Fig. 1). The lower limit for GWR is derived from the total degassing of H2O at mid-ocean ridges and ocean islands (2.1±0.8 ×10 8 Tg/Myr 6 ), which would prevent an increase in sea-level, consistently with the majority of reconstructions of eustatic sea-level for the current eon [START_REF] Vail | Seismic stratigraphy and global changes of sea level: Part 4. Global cycles of relative changes of sea level[END_REF][START_REF] Hallam | Phanerozoic sea-level changes[END_REF] (although see ref . 10). Hence, we define the admissible GWR range as 2.1-3.610 8 Tg/Myr.

We first estimate the H2O fluxes using the complex peridotite model and our reference case assuming a globally uniform 4-km thick hydrated mantle (Fig. 3a). The predicted Global Input of H2O at the trenches is 12.410 8 Tg/Myr, which is consistent with previous estimations considering the additional 10 8 Tg/Myr of H2O input by sediments 5 .

At a 230-km depth, that is after mantle dehydration in subgroup1.1, the GWR is 5.7 ×10 8 Tg/Myr (Fig. 3), driven by both the lithospheric mantle (61%) and by the gabbroic layer (35%). Adding the potential H2O flux subducted within sediments 5 (0.310 8 Tg/Myr), the resulting GWR at a depth of 230 km clearly overreaches the admissible GWR.

Gabbros (but also basalts and sediments) are all dry by a 300-km depth. Hence, the GWR at a 350-km depth is solely controlled by the lithospheric mantle of the coldest subduction zones (group 3) and equals 1.210 [START_REF] Vail | Seismic stratigraphy and global changes of sea level: Part 4. Global cycles of relative changes of sea level[END_REF] Tg/Myr (65% of which result from retention in Tonga and South Vanuatu; Extended Data Fig. 2). Our modeled GWR is lesser than the admissible GWR. Note that a slightly modified petrological assumptions (decreasing serpentinization with distance to the Moho and a reduced stability field of hydrous phases near the choke point, Supplementary Information S4.4.3 and S4.4.5) little affect the latter results. Assuming that the GWR was roughly stable through the Phanerozoic 5,6 , a complexperidotite model would predict that mantle degassing slightly dominated. For comparison, the GWR computed at a 350-km depth is nearly doubled with the simplified peridotite model (Fig. 4) and thus falls within the range of admissible GWR. As shown below, this observation does not hold anymore when considering a more prominent hydration of the lithospheric mantle, as proposed by multiple observations for natural subduction zones.

Consequences of a high mantle hydration at the subduction trenches on GWR

Extensional earthquakes at the outer rise suggest that hydration mostly occurs within the first 5 km of the oceanic mantle [START_REF] Emry | Incoming plate faulting in the Northern and Western Pacific and implications for subduction zone water budgets[END_REF] . The GWR computed by assuming a globally uniform 6-km thick hydrated mantle lies within the admissible GWR range only when considering the complex peridotite model (Fig. 3b and4). Our prediction of GWR using a globally-uniform 8km thick hydrated mantle exceeds this bound (Fig. 4 and see S4.4.1).

We nonetheless acknowledge that a globally uniform thickness of hydrated mantle might be a strong, and perhaps limiting, assumption. A compilation of the available data on the extent of mantle serpentinization at present-day subduction zones (thickness and serpentinization degree), shows indeed a worldwide disparity (Supplementary Information S3.1). We find that the serpentine content of the incoming plate correlates relatively well with a plastic-radius of slab curvature [START_REF] Buffett | Curvature of subducted lithosphere from earthquake locations in the Wadati-Benioff zone[END_REF] . This result is used to derive a parameterization of the mantle-hydrated thickness for each modeled transect (SI S3.2).

The parameterized thickness of hydrated mantle spans the range 0.8-8.8 km, with a global average of 5.6 km. The corresponding Global Input is similar to that computed with a globally-uniform thickness of 6 km. Because some of the cold subduction zones promoting deep-H2O retention are also predicted to host a thicker serpentinized mantle (Tonga, Kermadec), the GWR at a 350-km depth is higher (3.110 8 Tg/Myr) than in the uniform case with 6 km (Figure 4). The GWR assuming a more realistic variable-thickness of hydrated mantle nonetheless remains consistent with a modest sea-level decrease. We emphasize that both a worldwide variability in the extent of mantle hydration and the reduced stability field of hydrous phases predicted by the complex petrology around mid-upper mantle PT conditions ensures a modest return of H2O to the deep-upper mantle via only a few cold subduction zones.

Sensitivity of predicted GWR to warmer conditions of subduction

The mantle temperature near the choke point of the simplified peridotite model (P ≃ 6 GPa) is crucial for the predictions of deep-H2O retention, since higher temperatures would lead to the mantle dehydration in the transects of groups 2 and 3. One could then hypothesize that an enhanced dehydration predicted with the simplified peridotite would reduce (or eliminate) the discrepancy between the modeled and the admissible GWR. To test it, we perform additional models with warmer conditions of subduction: a high mantle potential temperature, a shallow coupling depth between the slab and the mantle, and shear heating along the subduction interface (see SI-S5). Deeper than 150 km, this yields an increase in Moho temperatures of 35-70°C at the choke point pressure (6-7 GPa) depending on the transect, if the effective friction coefficient μ is equal to 0.03, and of 45 to 90°C when it is 0.05. Considering a global-uniform serpentinized mantle thickness of 4 km, we find that warmer conditions with μ>0.03 and a simplified peridotite model leads to a total amount of H2O retained at a 350-km depth equivalent to the reference thermal conditions and the complex peridotite model (Fig. S14c). However, we note that to reach such an estimate the models need to be tuned to quite extreme warm conditions. We argue that these could hardly be reached in all subduction zones. Moreover, the warmer-condition assumption results in the release of the bound-H2O in the lithospheric mantle above depths of 200-250 km. It follows that such conditions would imply the quasi-absence of aqueous-fluids available to assist the triggering of intermediate-to-deep seismicity observed beyond 200 km depth in many presentday subduction zones (see SI-S6), which therefore also advocates for the relevance of the complex peridotite model.

The fate of deep-subducted H 2 O

We estimate that GWR at mid-upper mantle depths is 10 to 20% of the Global Input and that mantle regassing exceeds mantle degassing only in moderate proportions, including in our preferred model where the local thicknesses of the hydrated mantle in the coldest subduction zones are as high as ~9 km. Hence, our novel thermo-petrological models lessen the discrepancies between thermo-petrological modelling of subductions zones, the geophysical evidence of large amounts of H2O entering the trenches and the geological constraints on a long-term steady sea level.

An underlying assumption of our study is that all the H2O release above a 350-km depth returns to the surface (i.e. that mantle regassing is entirely controlled by GWR). Other studies assumed instead that part of the released H2O was conveyed by the downgoing mantle and contributed to mantle regassing [START_REF] Parai | How large is the subducted water flux? New constraints on mantle regassing rates[END_REF] . We argue that compaction-driven porous flow may redirect most of the deep-released H2O towards the arc [START_REF] Wilson | Fluid flow in subduction zones: The role of solid rheology and compaction pressure[END_REF][START_REF] Cerpa | Fluid migration in the mantle wedge: Influence of mineral grain size and mantle compaction[END_REF] , whether under the form of aqueous or supercritical fluids [START_REF] Mibe | Second critical endpoint in the peridotite-H2O system[END_REF] . Some deep-released fluids may nonetheless be conveyed to the mantle transition zone through partitioning into nominally anhydrous minerals (~0.1 wt% [START_REF] Padrón-Navarta | A subsolidus olivine water solubility equation for the Earth's upper mantle[END_REF] ) but in moderate proportions compared to our estimated GWR.

Finally, our models may help explain other geophysical observations such as the triggering of intermediate-to-deep seismicity. At the global scale, a drop in the number of volume-change-induced earthquakes in oceanic plates beyond mid-upper mantle depths has been suggested to highlight that only a few dehydration reactions occur in the deep upper mantle [START_REF] Omori | Dehydration and earthquakes in the subducting slab: empirical link in intermediate and deep seismic zones[END_REF][START_REF] Green | Seismic evidence of negligible water carried below 400-km depth in subducting lithosphere[END_REF][START_REF] Ferrand | Seismicity and mineral destabilizations in the subducting mantle up to 6 GPa, 200 km depth[END_REF] . Our first-order analysis of global seismicity reveals in fact that the subduction zones of groups 2 and 3 may host a moderate seismic activity within the depth range of 200-350 km, and a weak activity beyond (see SI-S6 -Fig. S15). If the triggering of these earthquakes is favored by dehydrating-slab fluids, we stress that only the dehydration profiles from the complex peridotite model could explain the vertical distribution of seismicity, specially at depths greater than 250 km. Our study also shows that the lithospheric mantle of the coldest slabs (e.g. Tonga, Kermadec or Vanuatu) are the sole H2O carriers beyond midupper mantle depths. This may explain why despite the potential ability of the mantle transition zone to be an important H2O reservoir [START_REF] Smyth | Structural systematics of hydrous ringwoodite and water in Earth's interior[END_REF][START_REF] Fei | High water solubility of ringwoodite at mantle transition zone temperature[END_REF] , global-seismic surveys only show a heterogeneous hydration of the transition zone [START_REF] Houser | Global seismic data reveal little water in the mantle transition zone[END_REF] .

Figure 1 Diagrams of bound-H2O content for a gabbro (a), a simplified peridotite model (b) and a complex peridotite model (c). The stability fields of the main hydrous phases are depicted by white lines. These are lawsonite (law), antigorite (atg), chlorite (chl), phase A (phA), brucite (br), 10-Å phase (10-Å), balangeroite (bal), and aluminous-phase E (Al-phE).

For T lower than 600°C, antigorite and phase A form at pressures lower and higher than 6 GPa, respectively, in both peridotite model 21,[START_REF] Wilson | Fluid flow in subduction zones: The role of solid rheology and compaction pressure[END_REF] . Chlorite is stable at T and P higher than 600°C and lower than 6 GPa. The geotherms at the Moho of the 56 modeled subduction transects are represented by the colored lines, among which five of them have been highlighted using thicker lines. The geotherms are color-coded following their thermal state, given by the product of the normal convergence rate and the square root of the incoming plate age at trench [START_REF] Maunder | Modeling slab temperature: A reevaluation of the thermal parameter[END_REF] .

Figure 2: Depth of near-complete (95%) dehydration of the hydrated lithologic layers for each subduction transect. Both the simplified and the complex models are reported for the peridotite. The depth is that of the bottom of the layer when near-complete dehydration occurs. Note that the absence of a symbol means that the layer has not reached a 95% of dehydration. Three groups are defined based on the dehydration mode of the hydrated mantle. Group 1: 95%-dehydration of the mantle regardless peridotite model considered. Group 2: dehydration before 350 km depth only in models with the complex peridotite. Group 3: dehydration of the hydrated mantle does not occur before 350 km depth for any of the models.

Methods

Thermal modeling. We consider two-dimensional thermomechanical models in which the kinematics of the subducting slab and of the overriding crust are prescribed while the creeping mantle wedge is dynamic. The mass, momentum and energy conservation equations are solved assuming that mantle flow has reached a steady state [START_REF] Cerpa | Fluid migration in the mantle wedge: Influence of mineral grain size and mantle compaction[END_REF] (i.e., solving a steady-state heat equation). We do not include shear heating in the equation of energy, unless specified (see section S5). We consider a composite rheology (diffusion and dislocation) for the wedge where the shear viscosity η is written as

1 η = ( 1 η diff + 1 η disl + 1 η max )
where η max is the maximum viscosity ( 1024 Pa s), and η diff and η disl are the viscosities of diffusion and dislocation creep, respectively. They are given by:

η i = ( A i b -α i C OH β i exp ( E i RT )) -1 γ έII ( 1 -γ γ )
where the subscript i denotes either diffusion or dislocation creep, b is the grain size, and έII is the second invariant of the strain rate. A , C OH , E , and R are the preexponential factor, water content, activation energy, and gas constant, respectively. The parameters α , β , and γ are the grain-size, water-content, and stress exponents, respectively. The rheological parameters are set to experimentally determined values for wet olivine (Supplementary Information Table S2). The discretized problem with finite elements is solved with the software TerraFERMA [START_REF] Wilson | Terra FERMA: The Transparent Finite Element Rapid Model Assembler for multiphysics problems in Earth sciences[END_REF] . We use an unstructured mesh with element sizes ranging from approximately 1 km near the tip of the corner flow to 10 km sufficiently far from the tip where the gradients are smoother.

Thermal-model setup. We perform tests for the 56 transects of major subduction zones defined in previous studies 5, [START_REF] Syracuse | The global range of subduction zone thermal models[END_REF] . Our models consist of a fixed rigid upper crust, a subducting slab with a prescribed velocity, and a dynamic viscous mantle wedge that is coupled with the slab below a 75-km depth (Fig. S1), except in the warmer-condition models where we set this depth at 65 km (see section S5). We adopt a realistic geometry for the top of the subducting slab based on the model Slab 2.0 [START_REF] Hayes | Slab2, a comprehensive subduction zone geometry model[END_REF] . For consistency, we consider realistic geometries above a 150-km depth. At higher depths, we extrapolate the slab surface with a constant dip to the bottom of the model domain. The imposed subducting slab velocity v ❑ and upper crust thickness of each modeled transect are as in refs. 5 and 26. The nature (continental vs. oceanic), which defines the boundary condition on the back-arc side as discussed below, and the thickness of the upper plate, as well as the subduction velocity (trench-normal component) and slab age, are taken from ref. 26. The slab thermal structure at the trench is computed following the GDH1 plate cooling model [START_REF] Stein | A model for the global variation in oceanic depth and heat flow with lithospheric age[END_REF] . At the bottom of the slab, we impose the mantle potential temperature T m =1421.5 ºC , as in previous estimations of GWR 5 . Note that we also run some models with T m =1450 ºC (see Section S5). The surface temperature is set to 0 °C. On the back-arc side, up to the mantle inflow-outflow transition depth, we impose either the GDH1 model when the upper plate is oceanic or a one-dimensional conductive model if the upper plate is continental. The latter temperature boundary condition is capped to the mantle potential temperature. A free-stress boundary condition is imposed on the back-arc side.

Petrological modeling. We adopt a generic lithologic model for the hydrated top of the oceanic plates entering the trench [START_REF] Hacker | H2O subduction beyond arcs[END_REF] , which consists of a 2-km thick basaltic layer, a 5-km thick gabbroic layer, and a globally-uniform thickness ( h serp ) of the hydrated mantle equals to 4 km in our reference case. We further consider cases with globally-uniform thicknesses of the hydrated mantle equal to 2, 6, and 8 km, as well as a case where h serp varies as a function of the equivalent radius of curvature of the subduction transect (see Supplementary Information S3). The basaltic layer is subdivided into a 0.3-km thick upper volcanic layer, a 0.3-km thick lower volcanic layer, and a 1.4 km thick dike layer, which differ by their initial H2O contents of 3.1, 2.6, and 1.8 wt. %, respectively. The gabbroic layer has an initial H2O content of 0.8 wt. %, and the hydrated lithospheric mantle an initial H2O contents of 2 wt. %, unless otherwise stated. Note that a H2O content in the lithospheric mantle of 2 wt. % corresponds to approximately 18% serpentinization, which is consistent with serpentinization degrees inferred from geophysical observations [START_REF] Hacker | H2O subduction beyond arcs[END_REF] . The phase relations are computed with the thermodynamic code Perple_X 28 using the thermodynamic database of ref 27. More details on the thermodynamic calculations are given in Supplementary Information. For the complex peridotite model, we combine the phase assemblages predicted by thermodynamic calculations to experimental data on phase relations at high PT obtained from natural serpentinites containing magnetite [START_REF] Maurice | The stability of hydrous phases beyond antigorite breakdown for a magnetite-bearing natural serpentinite between 6.5 and 11 GPa[END_REF] (see below).

Complex (natural) peridotite modeling. We first compile available experimental data on phase assemblages in natural [START_REF] Maurice | The stability of hydrous phases beyond antigorite breakdown for a magnetite-bearing natural serpentinite between 6.5 and 11 GPa[END_REF] and modeled peridotite systems containing Fe 3+ , Al, Ca and Na [START_REF] Fumagalli | Experimentally determined phase relations in hydrous peridotites to 6• 5 GPa and their consequences on the dynamics of subduction zones[END_REF][START_REF] Dvir | Fluids in the peridotite-water system up to 6 GPa and 800 C: new experimental constrains on dehydration reactions[END_REF] at temperatures higher than 600 °C and pressures higher than 4 GPa (see Fig. S2b). These reported phase relations serve as a basis for modifying the pseudosections modeled using Perple_X under these conditions (Fig. S2a). Given the lack of experimental data in the range of 6.5 to 8 GPa, we derive two approximate phase transitions (10-Å phase to olivine and Al-bearing phase E to olivine) by implementing at these P-T conditions: a high (HMmax) and a conservative (HMmin) estimate of the extent of the stability field of the hydrous phases (Fig. S2c). Note that our calculations of GWR in the main text are mostly based on the highestimate case HMmax, but we also performed calculations with the low estimate. Mass balances are performed to infer the H2O contents in the modified phase assemblages (Fig. S2c).

Calculation of the H2O fluxes. We adopt the approach of ref. 55 to calculate the H2O distribution in the two-dimensional subduction models. The hydrated portion of the subducting slab is divided into 500-m wide vertical columns. The columns are further subdivided into cells with a height of 100 m. We then calculate the mass of H2O retained by each cell given the PT conditions at its center. The total mass of the H2O retained in each column (or a lithologic layer) is given by a summation of the H2O content of the cells and converted into a mass flux (in Tg/Myr/m) by using the horizontal projection of the subduction velocity at the top of the column. Note that, in our approach, the H2O mass flux (H2O/water retention) at a given depth is that of the vertical column for which the top lies at this depth. We do not consider the rehydration of previously dehydrated cells [START_REF] Fei | High water solubility of ringwoodite at mantle transition zone temperature[END_REF] . We choose to compute the 95% dehydration depth instead of full dehydration to analyze the dehydration pattern of the hydrated lithologic layers (Fig. 2) for two reasons. First, in the mafic lithologies, phengite is stable up to 9.5 GPa and can retain residual amounts of H2O (<0.2 wt.%) after lawsonite breaks down. Thus, the depth of total dehydration would not illustrate the condition at which most of the H2O is released from the mafic lithologies. Second, our calculation of the H2O content may also suffer from minor numerical artifacts which may lead to artificial residual amounts of H2O retained in the computing cells, although the PT conditions of dehydration are reached. Finally, to calculate the GWR, we multiply the retention modeled for each transect by the corresponding length given by ref 26. Note that the 4 wt.% of GWR within the basaltic crust at a 230-km depth is due to both small amounts of actual H2O retention by phengite and minor numerical artifacts.

Extended Data Fig. 0: The first row displays the average change in sea level over the Phanerozoic derived from geological constraints. The second and third row provide bounds on the GWR (admissible GWR) compatible with a 0 to 100-m of change in sea-level. Note that the asterisk (2 nd row) denotes an indirect bound where we have assumed that a 0-m change of sea level over the Phanerozoic will be achieved if the GWR is equal to the total H2O degassing both at mid-ocean ridges and at ocean islands. The fourth row shows the estimated GWR by the thermo-petrological models of ref. 5.

Figure 3 :

 3 Figure 3: Global input of H2O at the trenches of present-day subduction zones and global H2O retention (GWR) computed using a complex peridotite model for the hydrated lithospheric mantle. We display our reference model with a globally uniform thickness of hydrated mantle of 4 km (a) and of 6 km (b).

Figure 4 :

 4 Figure 4: GWR as function of the Global Input at the subduction trenches, depending on the petrological assumptions and the thickness of hydrated mantle at the trenches (see legend).

Acknowledgments. The authors would like to thank Andrea Tommasi and Serge Lallemand for their very useful suggestions, and Stéphane Arnal and Fabien Rétif for their assistance in installing the code on the clusters. This study was publicly funded by through ANR under the "Investissements d'avenir,

Code availability. The code TerraFERMA used to compute the thermal models is open-source and available here http://terraferma.github.io/ . The thermodynamic code Perple_X is freely available here http://www.perplex.ethz.ch/ and information to reproduce the results are provided in the Methods section and in the Supplementary Information. Data availability. The numerical data generated for the 56 subduction transects (geotherms and water retention within the subducting slabs) will be made available at a public repository upon acceptance of publication.

Author contributions. N. C. conceived the study, designed and performed the numerical models, analyzed the results, and wrote the first draft of the paper. D. A. provided funding for the project, participated to conceive the study and analyzed the results. J. A. P.-N. contributed to the petrological modeling and to the analysis of the results. All authors discussed the implications of the study and participated to the writing of the paper.