Hydrated peridotites control the scarcity of water subduction to mid-upper mantle depths

The presence of liquid water makes our planet unique. Its budget over geological timescales, i.e., the long-term global sea level, depends on the balance of water exchanges between the Earth's mantle and the surface through both volcanism (mantle degassing) and subduction of hydrous minerals (mantle regassing). Current estimates of subduction water fluxes predict that regassing exceeds degassing by 50%, thereby suggesting a sealevel drop of several hundred meters in the last 540 Ma. The models further suggest that the subducting crust is the main supplier of water to the deep mantle. In contrast, various observations advocate for a near-steady state long term sea level and report voluminous water subduction via the hydrated lithospheric mantle. We have revised the subduction water flux calculations using constraints from recent experimental data on natural peridotites under high-pressure and high-temperature conditions. Our novel thermopetrological models show that the present-day global water retention in subducting plates beyond mid-upper mantle depths barely exceeds the estimations of mantle degassing, and thus quantitatively support the steady-state sea level scenario over geological times. Furthermore, the limited mantle regassing is solely driven by the lithospheric mantle of the coldest subduction zones.

The water exchange between the Earth's surface and the deep interior is a key process for the evolution of our planet. Water affects the mantle rheology [1] and allows Earth-like plate tectonics [2], while liquid-surface water is essential for planet habitability [3]. The degassing of water from the mantle takes place through volcanism. Mantle regassing occurs via the subduction of water chemically bound to hydrous minerals. Metamorphic reactions with increasing temperature (T) and pressure (P) liberate part of the water from the subducting plates.
A fraction of the subducted water is nonetheless retained and returns to the deep mantle. Its proportion remains debated, as does the global cycle of water.
The most comprehensive study on water fluxes at present-day subduction zones estimated a water retention of 3.4´10 8 Tg/Myr in oceanic plates beyond a 230-km depth [4]. These thermopetrological models suggested that half of the retention occurred within the oceanic crust, and a third within the hydrated lithospheric mantle, which was assumed to be 2 km thick worldwide at the trench. Because mantle degassing is approximately 2´10 8 Tg/Myr [5,6], the predicted Global Water Retention (GWR) would have induced a drop in the global mean sea level by more than 300 m over the Phanerozoic (last 540 Myr) [5], assuming a constant GWR over time. This is, however, close to the upper bound of retention proposed to ensure a modest sea-level decrease during this Eon, thought to be less than 350 m and more likely approximately 100 m, as inferred from continental-freeboard constraints [7,8].
Furthermore, based on reconstructions of time-dependent subduction rates, it was proposed that GWR was either relatively stable in the past or higher during specific events, e.g., during the rift pulse at approximately 150 Ma [9]. A GWR at present-day of 3.0´10 8 Tg/Myr or higher, as predicted by thermopetrological models [10,4,11,12], seems thus inconsistent with a timeintegrated low imbalance between mantle degassing and regassing. Only studies neglecting water subduction via the hydrated mantle were able to reach such a limited mantle regassing [13]. The growing evidence of hydration of the subducted lithospheric mantle exceeding a thickness of 2 km [14,15,16] urges the need to address this paradox.
The mineralogical changes, with increasing T and P, during subduction of the mafic crust and of the hydrated ultramafic mantle, control the deep-water fluxes. Hence, quantitative studies of GWR rely on state-of-the-art petrological modeling of hydrated subducted lithologies.
Lawsonite is the main water carrier in crustal layers beyond subarc depths (Fig. 1a). Its stability field is relatively well known from experimental studies [17,18]. In contrast, the main hydrous phases in peridotitic systems under postarc PT conditions are far less constrained [19]. The large uncertainties partly arise from the difficulty in handling laboratory water-rich experiments with natural samples at mid-upper mantle depth conditions. Hence, experimental data on peridotite are lacking in the 6-8 GPa range (see Supp. Info). Furthermore, the poorly constrained effect of some minor elements (Al, Fe) and the unknown prevailing oxidation state of ultramafic rocks under high-PT conditions [20,21] preclude proper petrological modeling of subducted ultramafic rocks. Consequently, experimental and modeled phase diagrams often differ at pressures above 6 GPa ( Fig. 1b and 1c).
Here, we update the estimation of present-day GWR by building upon recent experimental results on the stability of hydrous phases in natural hydrated peridotites. By considering the new experimental findings in chemically realistic systems at high PT conditions, the current view of relatively large amounts of water reinjected into the deep upper mantle is challenged.

Thermopetrological modeling of present-day subduction zones
We model the thermal state of 56 subduction transects [22], representing all present-day subduction zones (see Methods). The thermodynamic database ref. [23] and code Perple_X [24] are used to build phase diagrams, assuming bulk compositions relevant for the crustal and mantle layers at the subduction trenches ("basalt", Fig S3a, "gabbro" and "simple peridotite model" Fig. 1a,b). However, to enhance the accuracy of the modeled mineralogical evolution of hydrated peridotites up to mid-mantle depths, we build a hybrid phase diagram that combines experimentally derived assemblages from naturally complex systems and thermodynamic modeling ("complex peridotite model" Fig. 1c, see Methods).
At shallow depths, water subduction in the basaltic and the gabbroic layers occurs via amphibole, and at subarc and postarc depths via lawsonite [25]. At the depth where the slab surface starts dragging the overlying mantle [26,27], 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 to remain stable for most present-day subduction transects up to ~8 GPa. At pressures higher than 8 GPa, the stability of lawsonite becomes slightly dependent on temperature. Thus, in all but the hottest subduction transects (e.g., Cascadia), the oceanic crust crosses its "water line" [28], i.e. the last phase transition beyond which hydrous minerals are unstable, between depths of 250 km and 310 km.

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 models [17,20]. Chlorite is stable at T and P higher than 600°C and lower than 6 GPa, respectively. The geotherms at the Moho of selected subduction transects are represented by thick colored lines.
Our two petrological models for peridotite display substantial differences. Below 7 GPa, the main difference resides in the formation of the 10-Å phase [29,30,31], which enlarges the temperature range of the stability of hydrous minerals in the complex model. The striking differences impacting water 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 [20] but within a narrower temperature range compared to that of brucite in the simplified system. These differences in 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" [32], controls the water retention in this system. The Moho-geotherms (Tonga, S. Kurile and Java) passing above or near the choke point are quasi-parallel 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 water up to mantle-transition depths, where very high-P hydrous phases (E,D) may be stable over a wide range of temperatures [19,4,33].
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 beyond 6-7 GPa.
However, since the phase transition from aluminous-phase E to anhydrous olivine is quasiisothermal beyond 8 GPa(ref.), many moderately cold Moho geotherms pass above the choke point but cross the water line between 9 and 12 GPa (see Supp. Info). The combined absence of brucite and the quasi-isothermal water line above 8 GPa become thus potential inhibitors for deep-water subduction.

Near-complete dehydration depths
To further evaluate the impact of the petrological assumptions, we calculate the depth at which the hydrated lithologic layers nearly become dry (95% dehydration, see Methods) for all subduction transects, focusing on the lowermost-basaltic, gabbroic and hydrated peridotitic layers (Fig 2). The latter is assumed to be 4-km thick (15% hydration), which is a reasonable average consistent with geophysical observations [34].
The top basaltic layers mainly dry near the depth at which the slab and mantle are kinematically coupled (80-110 km). The dehydration of the gabbros occurs within the depth range of 245-295 km in all but the hottest subduction transects (Fig. 1a). The dehydration pattern of the lithospheric mantle is more dependent on the thermal state of the transects. Most importantly, it strongly depends on the petrological model. We thus define three groups based on the way the petrological assumptions impact the mantle-dehydration mode (Fig. 2).

Global water retention
We now estimate the global water fluxes using the complex peridotite model (Fig. 3). First, our predicted global water input at the trenches is 12. that the GWR has been roughly stable through time [4,9], our results quantitively support a very weak imbalance between mantle degassing and regassing, ensuring less than approximately 100 m of sea level change through the Phanerozoic [5].
Our new thermopetrological model for peridotite suggests that a large amount (4.1´10 8 Tg/Myr) of water is released between depths of 230 and 350 km, the fate of which would be controlled by the subsequent fluid migration paths. In fact, an underlying assumption for our estimation of GWR is that the released water at these depths ends in the outgassing budget. This is reasonable since recent fluid-flow modeling studies suggest multiple mechanisms for redirecting deep-released water towards the arc [36,37]. A small amount of those fluids may nonetheless be conveyed to the mantle transition zone through hydration of nominally hydrous minerals in the slab (~0.1 wt%, [38]) but in moderate proportions compared to our estimated GWR. In addition to addressing the past inconsistency between previous calculations of GWR by thermopetrological modeling and indirect estimations of mantle regassing, our work further reconciles the former with a range of geophysical observations. Seismic reflection and tomography show that the oceanic mantle is hydrated up to depths of 10-30 km below the Moho at various present-day subduction trenches [39,16,40], but extensional earthquakes at the outer rise suggest that hydration mostly occurs within the first 5 km of the oceanic mantle [15].
Noticeably, we predict that an average serpentinization thickness of 4-6 km below the Moho is consistent with observed long-term mean sea-level variations. Additional calculations with a 6km and an 8-km thick hydrated mantle at subduction trenches lead to GWRs of 2.6´10 8 Tg/Myr and 4.1´10 8 Tg/Myr, respectively, at a depth of 350 km (see Supp. Info). Thus, only an 8-kmthick serpentinized mantle may appear excessive regarding the long-term sea level changes.
Conversely, a 2-km thick hydrated mantle drops GWR to 0.5´10 8 Tg/Myr, which would produce an unrealistic sea-level rise over geological times. Too small of an amount of water carried beyond the mid-upper mantle would further be inconsistent with the evidence of hydration of the mantle transition zone [41,42].
The scarcity of volume-change-induced earthquakes in oceanic plates beyond a depth of 300 km suggests that, on average, few dehydration reactions occur in the deep upper mantle [43,44].
In fact, only very cold-slab subduction zones such as Tonga and Kurile display frequent earthquakes between depths of 300 and 500 km [43]. This observation is consistent with our predictions that the coldest slabs (such as Tonga, Kuriles or Hokkaido) are the sole water carriers beyond mid-upper mantle depths. This latter outcome of our study concurs with the heterogeneous hydration of the mantle transition zone inferred from shear-wave velocity anomalies [45].

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 [37]. We consider a composite rheology (diffusion and dislocation) for the wedge where the shear viscosity is written as where &'( is the maximum viscosity (10 )* Pa s), and !"## and !"$% are the viscosities of diffusion and dislocation creep, respectively. They are given by: where the subscript i denotes either diffusion or dislocation creep, b is the grain size, and 22 is the second invariant of the strain rate. , -. , , and are the preexponential factor, water content, activation energy, and gas constant, respectively. , , and are the grain-size, watercontent, and stress exponents, respectively. The rheological parameters are set to experimentally determined values for wet olivine [1] (see the values in the supporting information).
The discretized problem with finite elements is solved with the software TerraFERMA [46].
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 [22,4]. 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 [26] (Fig. S1). We adopt a realistic geometry for the top of the subducting slab based on the model Slab 2.0 [47].

Complex (natural) peridotite modeling
We first compile available experimental data on phase assemblages in natural [20] and modeled peridotite systems containing Fe 3+ , Al, Ca and Na [30,31] at temperatures higher than 600°C and pressures higher than 4 GPa (see Fig. S2a).
These reported phase relations serve as a basis for modifying the pseudosections modeled by using Perple_X under these conditions. 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 two approximations at these P-T conditions: a conservative and a high estimate of the extent of the stability field of the hydrous phases (Fig. S2b). Note that our calculations of GWR in the main text rely on the high estimate, but we also provide the values obtained with the low estimate in the Supp. Info (Section S3.3). Mass balances are performed to infer the water contents in the modified phase assemblages (Fig. S2b).

Calculation of the water fluxes
We adopt the approach of ref W12 to calculate the water 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 water contained in each column (or a lithologic layer) is given by a summation of the water content of the cells and converted into a mass flux (in Tg/Myr) by using the horizontal projection of the subduction velocity at the top of the column. Note that, in our approach, the water mass flux (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 [49]. Our calculation of the water content suffers from minor numerical artifacts that lead to artificial small amounts of water retained in the computing cells, although the PT conditions of dehydration are reached. As a consequence, we choose to compute the 95% dehydration depth to analyze the dehydration pattern of the hydrated lithologic layers (Fig. 2). Finally, to calculate the GWR, we multiply the retention modeled for each transect by the corresponding length given by ref S10. Note that the 4% of water retained in the basaltic crust at a 230-km depth is due to both minor numerical artifacts and small amounts of actual water retention during progressive dehydration (Fig. S3a).