Modeling the Global Water Cycle—The Effect of Mg‐Sursassite and Phase A on Deep Slab Dehydration and the Global Subduction Zone Water Budget

We study the interplay of the thermal structure within subducted oceanic slabs together with the stability fields of hydrous phases that control slab dehydration and the amount of water transported into the deeper mantle. We implement different published thermodynamic data for phase A and Mg‐sursassite into a model of 56 subduction zones and evaluate the effect of these phases on the global water budget. We modeled vertical fluid fluxes within the slab such that dehydration‐derived fluid was allowed to react with fluid‐undersaturated rocks in other parts of the slab. The effect of Mg‐sursassite on the global water budget is limited, because the Clapeyron slope of this dehydration reaction is steeper than most pressure‐temperature trajectories in subduction zones. Two sets of published thermodynamic data for phase A yield significantly different values for the amount of deeply subducted water, ranging between 8 × 108 Tg/Ma and 1.4 × 109 Tg/Ma. In some subduction zones, the differences span several orders of magnitude. The absolute modeled amount of deeply subducted water strongly depends on the depth and intensity of slab mantle hydration, but a comparison of modeled and experimental data indicates that the thermodynamic dataset that yielded higher values is more reliable and should be implemented in future thermodynamic models. Our results show that the stable phases around the choke point as well as the slope and position of the phase A‐out reaction influence the deep water release from the slab, but the slope and position of the phase A dehydration reaction mainly control the recycling of water into the deep mantle.


Introduction
Subduction zones are the major tectonic features on our planet where water is distributed between the hydrosphere, atmosphere, lithosphere, and the Earth's deep interior (e.g., Hacker, 2008;Konrad-Schmolke et al., 2016;Rüpke et al., 2004;Schmidt & Poli, 2003;van Keken et al., 2011).The subduction of the hydrated oceanic lithosphere induces two large-scale element cycles.Dehydration of the subducting slab leads to fluid liberation and an upward directed fluid flow toward the overlying crust and mantle.This fluid flux has major implications for subduction zone dynamics (e.g., Hattori & Guillot, 2003;Wada et al., 2008), earthquake intensity and frequency (e.g., Omori et al., 2004;Peacock, 2001), melt production in the overlying mantle wedge (e.g., Pearce & Peate, 1995), the formation of continental crust (e.g., Tatsumi, 2005) and the recycling of volatile components into the hydrosphere and atmosphere via volcanic activity (e.g., Johnston et al., 2011;Smye et al., 2017).In turn, hydrous minerals stable within the slab at high and ultra-high-pressure conditions can transport water into the deeper mantle, which feeds the global water cycle within the solid Earth (e.g., Hacker, 2008;Karlsen et al., 2019;Poli & Schmidt, 2002;Rüpke et al., 2004;Shaw et al., 2008).This deeper water cycle is important for mantle rheology (e.g., Hirth & Kohlstedf, 2003) and plate tectonic speeds (e.g., Bercovici, 2003) as water in nominally anhydrous mantle minerals, such as olivine and pyroxene, significantly reduces their shear strength and thus facilitates viscous flow.Furthermore, quantification of the water budget in subduction zones is pivotal for the determination of the global amount of water present on our planet through time as well as for the global cycling of fluid-mobile elements and their isotopic compositions (e.g., Elliott et al., 2006).
As most processes controlling the water budget in subduction zones occur at depths inaccessible for direct observations, thermomechanical (e.g., Gerya, 2011), thermodynamic (e.g., Duesterhoeft et al., 2014), and geochemical models (e.g., Kimura, 2017) are of fundamental importance as they constrain and quantify potential hydration and dehydration reactions as well as fluid-rock interactions in the subducted lithosphere.Combinations of these model approaches have been shown to yield important insights into subduction zone processes (e.g., Konrad-Schmolke & Halama, 2014;Konrad-Schmolke et al., 2016).However, the deep water cycle beyond subarc depths as well as the global water budget are not well constrained (e.g., Hacker, 2008;Van Keken et al., 2011).Three parameters pivotal to the deep water cycle, that is, the hydration state of the incoming oceanic plate, the thermal structure of subduction zones, and the stabilities of hydrous phases at high and ultra-high pressure conditions are still debated.In the last decade, substantial work has been done to better quantify these parameters (e.g., Grevemeyer et al., 2018;Ranero & Sallarès, 2004) and nowadays global data on the thermal structures of subduction zones, derived from numerical simulations, exist (e.g., Syracuse et al., 2010).Furthermore, laboratory experiments continuously deliver new thermodynamic data on hydrous high-and ultra-high pressure minerals (e.g., Hermann & Lakey, 2021;Komabayashi, Hirose, et al., 2005).As a consequence, several detailed numerical simulations of deep water budgets in subduction zones have been published based on these thermodynamic and thermomechanical datasets (Hacker, 2008;Konrad-Schmolke et al., 2016;Van Keken et al., 2011).All models show that the lithospheric mantle of the subducting plate plays a major role in deeply subducted water, as it is most capable of transferring water into the deep Earth.This is because temperatures in the mantle rocks of the slab stay sufficiently low during subduction and a potentially hydrated slab mantle can contain significant amounts of water.
The interplay of the stabilities of hydrous mantle minerals at greater depth, the thermal structure of the subducting slab and the possibility of deep water subduction is best visualized by a schematic phase diagram based on thermodynamic calculations (Figure 1).The strongly curved and negatively sloped chlorite-out and antigorite-out reactions together with the positively sloped phase A-out reaction lead to an anhydrous nose in a pressuretemperature (P-T) diagram where only nominally anhydrous minerals such as olivine, pyroxene and garnet are stable.The stability fields of the hydrous phases antigorite, chlorite and phase A form a thermal minimum, the socalled "choke point" (Kawamoto et al., 1996), in P-T space between about 5 and 7 GPa, corresponding to depths of approximately 150-200 km.In this "choke point region", the antigorite-out, chlorite-out and phase A-out reactions separate hydrous from anhydrous rocks in the P-T diagram.Hence, slab geotherms that trend at lower temperatures than the choke point and have a steeper slope than the phase A-out reaction will be able to transport water into the deeper mantle where it can be incorporated into phase E above 10 GPa (Ohtani, 2005) and finally be stored in wadsleyite, ringwoodite and bridgmanite in the mantle transition zone (e.g., Fu et al., 2019;Iwamori, 2004;Pearson et al., 2014).In turn, along hotter slab geotherms, hydrous phases will break down and the resulting fluid phase is able to return in relatively short timescales to the Earth's surface.Hence, the position of the "choke point" and the slope of the phase A-out reaction are forming the bottle neck for water subduction to the Earth's deeper mantle.
However, experiments have shown that a number of dense hydrous magnesium silicates (DHMS) as well as several aluminum-bearing high pressure phases are potentially stable just in that "choke point region" (Figure 1).Among them are Mg-sursassite (Fockenberg, 1998;Hermann & Lakey, 2021), the 10 Å-phase (Fumagalli & Poli, 2005;Pawley & Wood, 1995) and the 11.5 Å-phase (Fumagalli et al., 2014;Gemmi et al., 2016;Hermann & Lakey, 2021), hydrous aluminum pyroxene (HAPY, Gemmi et al., 2011), chondrodite as well as by OHclinohumite (e.g., McGetchin et al., 1970;Stalder and Ulmer, 2001).Consequently, the stability fields of those phases might bridge the hydrous regions between the antigorite, chlorite and phase A stability field and therefore might allow for a deep water transfer in slabs whose geotherms would otherwise trend into the anhydrous part of the phase diagram, as shown for the example of Mg-sursassite in Figure 1.
In this study, we use the latest published global data on subduction zone thermal patterns in 2-dimensional numerical thermodynamic forward models to simulate dehydration and deep water cycling in subduction zones.We Writing -original draft: Nils Benjamin Gies, Matthias Konrad-Schmolke Writing -review & editing: Jörg Hermann Geochemistry, Geophysics, Geosystems 10.1029/2024GC011507 incorporate available thermodynamic data for Mg-sursassite, representative for those phases potentially bridging the "choke point," and test different published thermodynamic datasets for phase A as these are the only comprehensive thermodynamic data on phases stable around and above the choke point.We pay special attention to the Clausius-Clapeyron slope of the phase A dehydration reaction on the water budget in subduction zones.Our models consider fluid-rock interaction to account for intra-slab rehydration that might facilitate deep water transport and can lead to pronounced fluid liberation at slab depths exceeding 150 km (e.g., Konrad-Schmolke et al., 2016).
The focus of our models is an evaluation of the effect of the stability of Mg-sursassite, representative for high pressure phases stable around the so-called "choke point," and the Clausius-Clapeyron slope of the phase A dehydration reaction on the water budget in subduction zones.This would help to evaluate and improve our current ability to quantify water cycling in subduction zones as part of the deep global water cycle.

The Slab Dehydration Model
Thermodynamic forward modeling, water fractionation, and mineral and element transport within the modeled subducting oceanic lithosphere is based on the numerical model described in Smye et al. (2017).The model uses discretized pressure (P), temperature (T), trench distance (X) and depth (Y) data for 56 individual subduction zones derived from thermomechanical models (Syracuse et al., 2010) as input for a Gibbs energy minimization algorithm (Perple_X version 6.6.9,Connolly, 1990) to calculate modes and compositions of stable phases at every P-T-X increment.The P-T-X dataset is organized in 29 slab-parallel incremented P-T-X paths, simulating a fivelayer structure of oceanic lithosphere and the overlying mantle wedge.We consider the subducting slab mantle overlain by two mafic layers consisting of gabbros and the simplified volcanic complex representing the sheeted dykes and pillow lavas, followed by a thin layer of sediments and parts of the overlying wedge mantle.The increments of the different paths are arranged such that the same Xincrement of an overlying path plots vertically above the increment of the path beneath it, thus allowing the simulation of vertical fluid fluxes within a slab-perpendicular rock column.The initial chemical rock compositions of every path that represent the lithological structure of the subducted slab are given in Table 1.
Thermodynamic calculations start at the lowermost path with the increment closest to the trench.The stable phase assemblage is calculated at this node and the chemical composition resulting from the phase assembly including water bound in hydrous minerals is passed on to the next node along the slabparallel path in the direction of the subduction.Free H 2 O liberated by the dehydration reactions is added to the composition of the vertically overlying node, simulating the buoyancy driven vertical upward fluid flow.Free water in the uppermost path is considered as water that left the subducting slab and intruded in the overlying mantle wedge.Thermal buoyancy in the wedge was ignored and the force for the convection of the mantle wedge is due to the coupling of the subducting slab.Water fluxes into the deep mantle were calculated based on the speed and length given by van Keken et al. (2011) for each representative subduction zone.Density and water content are constrained by the thermodynamic calculations in the last calculation node.
For the P-T-X-Y relations in the various subduction zones, we used the dataset described by van Keken et al. (2011), based on the "D80" data by Syracuse et al. (2010).It contains 56 2D cross sections perpendicular to the trench (van Keken et al., 2011) after the global geometry of subduction zones compilation of Syracuse and Abers (2006).The spacing of the cross sections along the different subduction zones is approximately 700 km.Based on the geometry of each segment, the 2D section is chosen to represent the trench average of the segment.The Syracuse models have been challenged recently (e.g., England & Smye, 2023;Holt & Condit, 2021;Penniston-Dorland et al., 2015) to show significantly lower temperatures compared to the exhumed rock records.For example, Qu et al. (2023) have shown that different estimates based on the rock record as well as various models converge at pressures above 2.5 GPa, which is still shallower than the stability of the phases investigated in this paper.But, to date, the Syracuse model is the only available dataset that provides a full grid of steady state P-T-X-Y points, reaching to 7 GPa through the subducted slab to conduct the presented modeling approach on a global scale.
In order to demonstrate the complex relations between the thermal structure of the subducted slab, the thermodynamic phase relations at depth and the water budget during subduction, four subduction zones are chosen to serve as representative examples for different dip angles and temperature patterns (Figure 2).The Cascadia subduction zone is representing shallow dipping and "hot" subduction zones, New Britain and Nicaragua are representing steeply dipping and "moderately hot" subduction zones and Kamchatka is chosen to represent "cold" subduction zones.Although, all 56 subduction zones are considered in the calculations of the global water cycle, the model results of these four will be shown in the following paragraphs.The Syracuse models cover a wide range of P-T conditions and slab geometries.Cascadia, New Britain, Nicaragua, and Kamchatka are representative of the observations encountered and can be used as a general guide for water recycling in subduction zones, even if other thermal models are preferred.

Initial Bulk Rock Compositions of the Slab
The nodes in each path contain pressure, temperature, trench distance and depth derived from the "D80" dataset from Syracuse et al. (2010).Bulk rock chemical data were assigned to each node corresponding to the representing rock unit within the slab.The model consists of a dry wedge mantle layer (8 km, primitive upper mantle (PUM) of Workman and Hart (2005)), a sediment pile with 7 wt% H 2 O (variable thickness for each subduction zone- Plank & Langmuir, 1998), igneous basaltic crust (2 km volcanics and sheeted dykes with 3 wt% H 2 O, 5 km Gabbro with 1 wt% H 2 O, N-MORB- Workman & Hart, 2005) a hydrated slab mantle with 2 wt% H 2 O (12 km, depleted MORB mantle (DMM)- Workman & Hart, 2005).The degree and depth of hydration is likely an upper  Workman and Hart (2005).
boundary for hydration of the lower plate mantle rocks and was chosen to be able to compare the results with previous estimates of the globally subducted water (e.g., Hacker, 2008;Van Keken et al., 2011).

Equation of State (EoS) and Thermodynamic Standard State Data for DHMS
Equations of state (EoS) are general mathematical formulations that aim to predict the relations of volume, pressure and temperature of phases at any arbitrary physical conditions based on a least-squares fit to experimental data.All EoS commonly applied to geoscientific problems are based on several assumptions and therefore involve certain simplifications regarding the precision of their predictions (Duesterhoeft, 2016).Consequently, the formulations of different EoS are often debated and, depending on the envisaged problem, different EoS are used to predict the P-V-T behavior of the phases of interest.In this study, we use the Murnaghan EoS (Murnaghan, 1937) expanded with a fourth-order thermal expansion coefficient term and a linear temperature dependence of the bulk modulus.

The Extended Murnaghan EoS
The Murnaghan EoS relates the molar volume (V) of a substance at a certain isotropic confining pressure (P) to the standard state molar volume (V 0 ) by: With K 0 being the bulk modulus at ambient temperature and zero pressure and K I being its pressure derivative.
The thermal expansivity coefficient alpha is fitted to experimental data with a fourth-order term of the form: where T is the temperature of interest and P r is the reference pressure.
The molar volume at a certain temperature is calculated as follows: To additionally account for a temperature dependence of the compressibility of a substance the isothermal bulk modulus is calculated as follows: Where T is the temperature of interest and T r is the standard state temperature (298.15K).The extended Murnaghan EoS as programmed in Perple_X is then in the form of ] The temperature dependence at reference pressure of the (constant pressure) heat capacity was calculated with The different parameters used in Perple_X for Phase A and Mg-Sursassite are given in Table 2.

Phase A
Since the first synthesis and description of phase A by Ringwood and Major (1967), it has been obvious that phase A plays a fundamental role in the water budget in subduction zones and in the global water cycle.Based on different types of high and ultra-high pressure experiments, it has been proposed that significant amounts of water might be recycled into the deeper mantle via subduction of the hydrated slab mantle (e.g., Luth, 1995;Wunder, 1998;Yamamoto & Akimoto, 1974, 1977).Nevertheless, there is a lack of clarity regarding the thermodynamic properties of phase A and other hydrous phases stable at higher temperatures, such as the 11.5 Å-phase, clinohumite and chondrodite.To date, none of the published works presents a comprehensive set of newly determined thermodynamic properties of phase A and the majority of studies concentrate on the determination of the unit cell volume as well as its pressure sensitivity (e.g., Crichton & Ross, 2002;Holl et al., 2006;Komabayashi, Omori, & Maruyama et al., 2005;Komabayashi, Hirose, et al., 2005;Kuribayashi et al., 2003;Pawley et al., 1995).Only a few works combine the published or newly determined datasets to develop an equation of state for phase A and calculate P-T phase diagrams in order to quantify the water budget of subduction zones (e.g., Komabayashi, Omori, & Maruyama et al., 2005;Komabayashi, Hirose, et al., 2005;Pawley et al., 1996;Yang et al., 2021).
Here, we use two sets of published thermodynamic data that are predominantly contrasting regarding the incompressibility, that is, the bulk modulus and its pressure and temperature derivatives, of phase A. Dataset 1 (Table 2) uses the data from Komabayashi, Hirose, et al., 2005, who calculated the enthalpy and entropy of formation from the reaction brucite + enstatite = phase A based on the experiments of Pawley and Wood (1995) and determined the heat capacity parameters as well as the thermal expansion parameters experimentally.The latter P-V-T data were fitted to the Murnaghan EoS.Standard state volume and bulk modulus data were taken from Crichton and Ross (2002) and the thermal expansivities are based on the data of Holland and Powell (1998).
Dataset 2 is chosen as it is commonly used with the thermodynamic datasets of Holland and Powell (1998) as well as Holland and Powell (2011).The standard state thermodynamic data and equation of state of this dataset (Table 2) are compiled using the experiments of Pawley et al. (1995) as well as a number of estimated values for the heat capacity function and for entropy.This dataset is characterized by a significantly higher bulk modulus of 145 GPa (Pawley et al., 1995) compared to 95 GPa (Crichton & Ross, 2002) used in dataset 1.The full record of thermodynamic parameters is given in Table 2.

Mg-Sursassite
For Mg-sursassite, only the thermodynamic data given in Grevel et al. (2001) and Bromiley and Pawley (2002) exist.Grevel et al. (2001) reported calorimetric and P-V-T data for Mg-sursassite using three different Mgsursassite samples, which were synthesized in piston cylinder experiments at 5 GPa and 600-700°C, following the Experiments described in Fockenberg (1998).The standard state enthalpy of formation (∆H 0 ) was calculated from drop solution values obtained from high-temperature oxide melt calorimetry experiments at 700°C .Differential scanning calorimetry in the step-scanning mode in a temperature range from 50 to 500°C was used to measure the heat capacity (C P ) of Mg-sursassite.The P-V-T data of Mg-sursassite is reported as the bulk modulus obtained by fitting the data of cubic anvil high-pressure experiments up to 8 GPa and 800°C to a Birch-Murnaghan EoS.The standard state Gibbs energy of formation (∆G 0 ) was calculated from the reaction of periclase, corundum, quartz and water taken from Holland and Powell (1998).In order to be consistent with the Perple_X programming we fitted ∆G 0 such that the Mg-sursassite-out reaction intersects with the chlorite-out reaction at 948 K, as in the experiments of Bromiley and Pawley (2002).

Other Phases
Recent experiments have shown that the hydrous field can be significantly extended toward higher temperatures even at pressures above 12 GPa by the stability of the 23Å-phase (potentially the same as the 11.5Å-phase; Cai & Inoue, 2019) and chondrodite as well as by OH-clinohumite (e.g., McGetchin et al., 1970;Stalder & Ulmer, 2001).
As the stability of these phases shows positive slopes, they are probably relevant for the deep water cycle and might significantly enlarge the stability fields of hydrous phases around the choke point.However, reliable thermodynamic data of these phases are lacking so far.Hence, quantification of their effects on the global water cycle is not yet possible in this work.Therefore, more experimental data, especially on the P-V-T relations of these phases, will certainly improve the reliability of the thermodynamic models such as the ones presented here and hence set better constraints on the global water cycle.Water in Nominally anhydrous minerals is beyond the scope of this paper, but will be investigated and discussed in a follow-up study.

Crustal Rocks
Phase relations, water contents and P-T trajectories of the crustal rocks in our models, that is, sediments as well as volcanics, dykes and gabbros, are shown in Figure 3.The diagrams are color coded for whole rock water content and show that most of the water is lost at temperatures between 500 and 700°C by chlorite, talc and lawsonite breakdown.Figure 3a shows the phase relations for the mafic crust, whereas Figure 3b displays the modeled phase relations for the sediment composition.Phase assemblages containing melt were not considered in the models, but the wet basalt as well as the wet pelite solidus are shown in the mafic and felsic rock compositions, respectively.The white and red colored paths in Figure 3a display the coldest and hottest paths in the various slabs, respectively.The sediment layers in our model follow a single path representing the top of the slab temperature for each subduction zone.
All the hotter and most of the cooler paths in the mafic crust trend beyond the talc stability, many even exceed lawsonite stability and therefore indicate that large parts of the mafic oceanic crust are almost entirely dehydrated at pressures above 6 GPa (Figure 3a).
In the sedimentary layer, all the P-T trajectories trend beyond the stability field of lawsonite, with phengite being the only hydrous phase left (Figure 3b).Phengite, whose stability field might be overestimated due to the limited accuracy of the thermodynamic data, is stable even at slab depths exceeding the decoupling at 80 km.Therefore, the K 2 O content of the two lithologies (mafic and felsic crust) controls the water content that can be transferred to greater depth in crustal rocks, apart from water in nominally anhydrous minerals.However, both diagrams also show that the water content of the deeply subducted crustal rocks is below 2 and 0.5 wt% for the sediments and the mafic crust, respectively.Regarding the volumetric relations in the slab, both sediments and mafic rocks play a minor role during deep subduction if nominally anhydrous phases are ignored as is the case in this study.Hence, the focus of this work will be on the mantle part of the subducted slab in the following paragraphs.

Mantle Rocks
The set of four contoured P-T pseudosections shown in Figure 4 is calculated for a water saturated depleted mantle composition (DMM of Workman and Hart (2005)) and compares the two different thermodynamic datasets for phase A without and with the Mg-sursassite stability field.Water saturation is chosen to demonstrate the potential hydration capacity of the ultramafic mineral assemblages but is not intended to reflect the real water content of the slab mantle.
The major dehydration occurs by brucite-, antigorite-and chlorite-out reactions at pressures below 6 GPa and phase A breakdown above the choke point that is in all calculations around 6 GPa and 600°C.Brucite stability enables water contents of up to 12 wt% and in the presence of antigorite the rocks can hold as much as about 10 wt% of water.In contrast, beyond antigorite stability the water content of the mantle rocks in the presence of chlorite or at pressures above 6 GPa where phase A is stable is only up to about 4 wt%.Hence, the amount of water subducted to pressures beyond 8 GPa is restricted by the phase A abundance and is limited to about 4 wt%, considering the thermodynamically constrained abundance of phase A in a DMM composition (Figure 4).Furthermore, slab mantle dehydration during subduction is a one-or two-stage process, depending on whether the initial hydration of the slab mantle is below or above 4 wt% water.In those slabs with higher initial water contents, the antigorite-out reaction will be followed by the chlorite-or phase A-out reaction, whereas in slabs with a mantle hydration below this value only the chlorite-and phase A-out reactions will release significant amounts of water that potentially migrate upward and influence the processes in the slab-mantle interface, the mantle wedge and the overlying crust (cf.Figures 4 and 5).
The topological differences between the two different thermodynamic datasets (cf.Figures 4a and 4b as well as Figures 4c and 4d) are significant.The volume function data published in Komabayashi, Hirose, et al. (2005) (as part of dataset 1) yields a slightly shallower and straighter Clausius-Clapeyron slope of the phase A-out reactions toward higher temperatures compared to dataset 2, which uses the bulk modulus from Pawley et al. (1996).The shallower slope of the phase A-out reaction significantly enlarges the stability field of phase A at pressures above 8 GPa.Furthermore, phase A stability is also slightly enlarged toward lower pressures around the choke point, using dataset 1.We will see in our later calculations that the slope of the phase A-out reaction and thus also phases potentially stable at higher temperatures than phase A play a major role in the dehydration behavior of certain subduction zones.
Mg-sursassite occurs from 4 to between 7 and 9 GPa (depending on the presence of phase A) with a slightly curved and sub-vertical zero-mode line located at about 700°C.Hence, it bridges the choke point by intersecting the chlorite-and antigorite-as well as the phase A-out lines and shifts the maximum temperature for hydrous phases at around 6.5 GPa by some 125°C toward higher temperatures.It is notable, however, that the Al content of the mantle rocks has an influence on the stability and abundance of the Al-bearing phase Mg-sursassite, as shown in Figure 4c.For a DMM composition, the thermodynamically constrained modal abundance of Mg-sursassite is up to 13%, which can retain only about 1 wt% of water.In the choke-point region, however, the presence of Mgsursassite influences the dehydration pattern of slabs that would otherwise completely dehydrate when crossing the antigorite-and chlorite-out reactions, which will be demonstrated in the following paragraphs.

The Dehydration Behavior of Different Subduction Zones
In order to simulate a more realistic dehydration scenario of the various subduction zones, we limited the amount of water in the mantle rocks to 2 wt%.Although, this value is arbitrary, we would like to account for the fact that water saturation is unlikely in the slab mantle lithologies.
In the following diagram, contours for the water content are skipped as all assemblages are water-undersaturated until the stippled line marked with "H 2 O"..Only beyond this water-saturation line water coexists as a free fluid phase.Instead, the slab paths are color coded for their water content.Decreasing water contents with increasing depth denote dehydration reactions, increasing values indicate intra-slab re-hydration through fluid liberation and upward migration from deeper parts of the slab.The hourglass topology of the hydrous assemblages is unchanged compared to the water saturated calculations, but the water saturation line is close to the breakdown reactions of all hydrous phases, whose slopes and positions are unchanged compared to the calculations assuming water saturation.Water contents hosted in NAMs are not considered and will be discussed elsewhere.

Hot Subduction Zones as Exemplified by the Cascadia Subduction Zone
The diagrams in Figure 5 show the calculated pressure-temperature (P-T) paths for the slab mantle part of the Cascadia subduction zone color coded for the water content of the 12 different layers.As none of the slab paths crosses the Mg-sursassite stability field, the dehydration scenario is the same in Figures 5a and 5b.In all scenarios, intra-slab re-hydration plays a role, as water contents of most slab paths increase from 2 to about 2.5 wt.% at pressures above 2 GPa.However, the thermal structure of the slab leads to a complete dehydration when all paths leave the chlorite stability field between 700 and 800°C at pressures between 2 and 3 GPa.One single slab mantle dehydration event caused by the chlorite-out reaction will be the consequence in such hot subduction zones.

Cold Subduction as Exemplified by the Kamchatka Subduction Zone
The slab paths for the Kamchatka subduction zone are shown in Figure 6.As the dataset from Syracuse et al. (2010) contains data only up to 7 GPa, we linearly extrapolated the slab paths to 10 GPa to predict the P-T trajectories and potential dehydration at depth beyond 220 km.
As in the case of the Cascadia subduction zone, neither the phase A-out reaction nor the Mg-sursassite stability field is crossed by the majority of the slab paths in the different models.Almost the entire mantle part of the slab is within the stability fields of hydrous minerals and apart from two extrapolated paths in the calculations using dataset 2, none of the mantle paths enters the anhydrous field.Consequently, all of the initial 2 wt% water stored in the ultramafic part of the slab is subducted beyond 300 km depth.Geochemistry, Geophysics, Geosystems 10.1029/2024GC011507

Intermediate Subduction Zones Exemplified by the Nicaragua and New Britain Subduction Zones
In contrast to the afore examples, where either all slab paths fully dehydrate in all scenarios (Cascadia) or almost no dehydration occurs in each model (Kamchatka), the results for the intermediate subduction zones, exemplified by the Nicaraguan and New Britain subduction zones, are very much different for the various model approaches.
Figures 7a and 7b show the slab path dehydration for the Nicaraguan subduction zone modeled without Mgsursassite.Irrespective of the thermodynamic dataset for phase A, all slab paths trend into the field of anhydrous mineral assemblages; hence, no water can be transferred into the deeper mantle in these scenarios.After a short period of intra-slab re-hydration at around 5 GPa, complete dehydration of the slab occurs during the chlorite and antigorite breakdown at about 5.5 GPa and around 600°C.As these conditions are within the stability field of Mg-sursassite, the dehydration of the Nicaraguan slab is significantly different if Mg-sursassite is considered (Figures 7b and 7c).
Using the thermodynamic dataset 1, all slab paths trend into the stability field of Mg-sursassite, where the thermodynamically constrained modal abundance of Mg-sursassite of up to 13% results in about 1 wt% of water stored in the subducted mantle lithosphere.This water can be almost entirely transferred into Phase A as the slopes of the slab paths are sufficiently steep to enter the Phase A stability field (Figure 7c).
In contrast, all slab paths leave the fields of hydrous minerals if dataset 2 is used for phase A, and complete dehydration of the slab occurs when the slabs leave the Mg-sursassite stability field.Due to the smaller stability field of Phase A calculated using dataset 2, no water can be transferred into Phase A (Figure 7d).Nevertheless, it is noteworthy that in this model the final dehydration of the slab occurs about 100 km deeper caused by the stability of Mg-sursassite between 5 and 7 GPa.
Even more drastic are the differences among the models in case of the New Britain subduction zone (Figure 8).In the models excluding Mg-sursassite, almost the entire slab dehydrates between 5 and 6 GPa (Figures 8a and 8b), similar to the former Nicaraguan example.If Mg-sursassite is considered in the models, the dehydration scenarios differ between a complete transfer of water into the deep mantle, when calculated with dataset 1 (Figure 7c) and an almost complete dehydration in case of dataset 2 (Figure 7d).In the former case, the bridging effect of Mgsursassite on the subduction zone water budget is the largest of all models.We will show in the following paragraphs how these phase topologies translate into 2D subduction zone models.

Slab Dehydration Patterns
Slab dehydration patterns yield a more detailed insight into the slab-internal fluid-rock interaction, the resulting fluid fluxes into the mantle wedge as well as the subducted water amount.Due to the discretized model setup and the limited spatial resolution of the thermal input dataset, mineral reactions and the resulting water fluxes appear segmented.This is, of course, an artifact of the model setup and must be considered in the interpretations.All slab dehydration models are run with an initial water content of 2 wt% throughout the entire 12 km of the slab mantle, as outlined in the model set up.

Cascadia
The results shown in Figure 9 are from the model run using the thermodynamic dataset 1.Only one set of calculations is shown, as Mg-sursassite does not affect the model results, because none of the slab P-T trajectories crosses the Mg-sursassite stability field (Figure 5).In the upper panel (Figure 9a), the water flux from the different layers and at the top of the model is shown.The lower panel (Figure 9b) shows the amount of free water percolating through the slab (the upper slab figure) and the water content of the solid phases within the subducted slab (the lower slab figure).
In Cascadia, slab dehydration starts early by minor water liberation from the sediment pile already at a Moho depth of approximately 30 km (Figures 9a and 9b).In our model, the liberated fluids are resorbed by the overlying mantle wedge and do not reach the top of the mantle wedge (Figure 9b).However, the thermomechanical model used here (Syracuse et al., 2010) for the temperature-depth-trench distance relations assumes different states of coupling between the upper and the lower plates (see Figure 9b).In a steady state, the mechanically decoupled forearc mantle would likely be water saturated and crustal fluids might migrate further upward and reach the upper plate Moho.
At a depth of about 60 km, dehydration of the mafic crust starts by chlorite breakdown in the uppermost MORB layer (Figure 9b).Fluids liberated at this stage migrate into the overlying mantle wedge and cause further hydration of the ultramafic rocks, which is associated with the formation of chlorite and amphibole in the hydrous forearc mantle (lower panel in Figure 9b).Slab mantle dehydration begins at about 72 km depth at the base of the slab mantle induced by the breakdown of chlorite.The liberated and rising fluid immediately hydrates the overlying lithologies.This causes the formation of amphiboles and the consumption of all fluid until 80 km depth (Figure 9b).Also, at about 75 km depth, dehydration of the base of the oceanic crust starts with the decomposition of chlorite.Fluids released by this reaction contribute to further hydration of the forearc mantle, which continues until the breakdown of the amphibole at about 80 km depth, which marks the end of major crustal dehydration.
Significant water liberation into the overlying mantle wedge does not occur until the hanging wall mantle reaches 70 km depth.Here, the breakdown of chlorite in the hanging wall mantle as well as antigorite dehydration at the base of the slab mantle deliver the majority of the water flux into the mantle wedge.At this stage, phengite is the only stable hydrous mineral in the oceanic crust accounting for about 0.03 wt% water (lower panel in Figure 9b).This amount is the entire water that is subducted to depths beyond 100 km in the Cascadia subduction zone.Water liberated from the crust is transferred to the base of the mantle wedge and is released by chlorite breakdown in the ultramafic rocks.Fluids liberated from the slab mantle pass through the oceanic crust and mix with the slab mantle fluids before entering the overlying mantle wedge.

Kamchatka
The three models in Figure 10 are calculated with the different thermodynamic datasets (a-d: dataset 2, e and f: dataset 1) and with Mg-sursassite absent (a and b) and present (c-f) in order to demonstrate the (slightly) different dehydration patterns.In contrast to the Cascadia subduction zone, dehydration of the Kamchatkan slab is entirely controlled by the dehydration of the oceanic crust, irrespective of which thermodynamic dataset is used or whether Mg-sursassite is present or absent.In all model setups, crustal dehydration starts at the top of the oceanic crust (at about 75 km slab depth) by lawsonite breakdown and leads to a hydration of the overlying ultramafic rocks of the wedge mantle associated with the formation of amphibole.The fluid influx from the crust leads to a fast water saturation of the overlying ultramafic rocks and the liberated fluids are more or less directly transferred into the mantle wedge.After a first fluid pulse between 80 and 100 km slab depth (Figures 10a-10c, and 10e), the dehydration of the crust proceeds more or less continuously by lawsonite breakdown and liberates small amounts Geochemistry, Geophysics, Geosystems 10.1029/2024GC011507 of fluids until a depth of about 275 km.Phengite is the only remaining hydrous phase in the oceanic crust, which carries about 0.03 wt% water into the deeper mantle.Apart from a minor water release by phase A and/or Mgsursassite dehydration in the uppermost part of the slab mantle, significant dehydration of the subducted mantle rocks does not occur as water is directly transferred from chlorite into antigorite and from antigorite into phase A. This enables subduction of almost the entire 2 wt% water from the initial hydration in the slab into the deeper mantle.As Mg-sursassite is stable in the slab mantle together with phase A (Figures 10b, 10d, and 10f), it does not significantly influence the total amount of subducted water.
The position of the initial crustal dehydration in all models is controlled by the transition from partially to fully coupled plates (see Figure 10b), which is constrained by the thermomechanical model.At this transition the Geochemistry, Geophysics, Geosystems 10.1029/2024GC011507 isotherms are very closely spaced, and the temperature rises quickly in the upper part of the subducted plate (Figure 2).Hence, the depth of the onset of water liberation from the slab should not be overinterpreted as it is directly related to the boundary conditions of the thermomechanical model.The evidence from the Kamchatka model, however, is that Mg-sursassite always coexists with another hydrous phase (antigorite and/or phase A, Figures 10d and 10f) and thus plays a minor role in the water budget of the Kamchatkan slab.

Nicaragua
In contrast to the hot and cold subduction zones, as exemplified by the Cascadian and Kamchatkan subduction zones, the dehydration patterns of intermediately warm subduction zones are more complex and dependent on the presence of Mg-sursassite, or other phases stable around the choke point, as well as on the extent of the phase A stability field.
Figures 11a and 11b show the dehydration pattern of the Nicaraguan slab using the thermodynamic dataset 2 without considering Mg-sursassite.Similar to the Kamchatkan example, slab dehydration starts at about 80 km depth at the top of the oceanic crust by lawsonite breakdown.The rising fluids cause wedge mantle hydration in a small region and subsequently migrate to the overlying wedge (Figure 11a).After a significant pulse between 80 and 110 km depth, lawsonite dehydration in the crust leads to a low but continuous fluid flux from the crust into the overlying mantle wedge (Figure 11b).Geochemistry, Geophysics, Geosystems 10.1029/2024GC011507 At a depth of 160 km, slab mantle dehydration starts at the base of the slab mantle layer.Fluids liberated first by antigorite and later by chlorite breakdown do not reach the slab Moho but are resorbed by continuous hydration reactions in the slab mantle (Figure 11b).At 170 km depth slab mantle dehydration occurs also at the top of the mantle and together with fluids liberated at the base of the slab mantle leads to a drastic release of water between 170 and 180 km depth (Figure 11b), which enters the overlying mantle wedge (Figure 11a).After this dehydration event, the slab mantle is entirely dry as there is no overlap of the stability fields of antigorite and phase A (cf. Figure 7d).Water flux at the top of our model beyond slab mantle dehydration is limited and caused by ongoing crustal dehydration by lawsonite breakdown (Figure 11b).
The same model approach, but considering Mg-sursassite (Figures 11c and 11d), leads to a similar dehydration scenario of the slab, but has important implications for deep water recycling.The models with and without Mg- Geochemistry, Geophysics, Geosystems 10.1029/2024GC011507 sursassite show the same dehydration pattern to a depth of about 170 km (cf.Figures 11b and 11d).Crustal dehydration causes a limited hydration of the base of the mantle wedge, leads to an initial water pulse from amphibole decomposition in the ultramafic rocks and continuously delivers water into the overlying mantle wedge.Mantle dehydration starts at the base of the slab mantle and leads to a drastic water release at the tip of the antigorite-out reaction at about 170-180 km depth.This strong dehydration pulse is less intense in the model considering Mg-sursassite (Figures 11c and 11d), as in the model shown in Figures 11a and 11b.This is because the formation of Mg-sursassite in the slab mantle at about 130 km depth allows for the storage of about 1 wt% water in the ultramafic rocks of the slab mantle.The water stored in Mg-sursassite is transported into the deeper mantle to depths of about 280 km (Figure 11d).Mg-sursassite dehydration occurs between 230 and 280 km depth and leads to a significant water input into the mantle wedge at these depths (Figure 11c).Dehydration of Mgsursassite at the base of the slab mantle at 230 km starts to release water, which continues until a complete dehydration of the slab mantle is reached at 280 km (lower panel in Figure 11d).
The latter is not the case if the thermodynamic dataset 1 is used (Figures 11e and 11f).Figure 11f shows the same slab dehydration pattern as Figure 11d, but the water released by Mg-sursassite dehydration starting at 230 km depth leads to a slab mantle dehydration and the formation of phase A whose stability field is larger in case of dataset 1. Comparing Figures 7c and 11f shows that although the uppermost parts of the slab mantle dehydrate during further subduction, phase A is stable in large parts and transfers about 1 wt% water into the deeper mantle.

New Britain
The dehydration patterns of the New Britain subduction zone are also influenced by the size of the stability field of phase A and the presence of Mg-sursassite.These phases dictate the total amount of water subducted to depths between 150 and 270 km depth.The models using the thermodynamic dataset 2 (Figure 12a-12d) show a clear two stage dehydration.Crustal dehydration caused by lawsonite breakdown starts at 80 km depth, causes hydration of the base of the mantle wedge and leads to a pronounced water flux between 80 and 100 km depth by amphibole dehydration in the mantle wedge.After this first pulse lawsonite dehydration delivers continuous water to the mantle wedge until a slab depth of 150 km is reached.Slab mantle dehydration starts at the base of the slab mantle layer, but the liberated fluids are consumed by hydration of the overlying mantle rocks (lower panels in Figures 12b and 12d) and the formation of antigorite and phase A at depths greater than 175 km (Figures 12b  and 12d).The breakdown of antigorite at about 190 km depth leads to a strong water pulse at the tip of the antigorite-out reaction (Figures 12b and 12d) and a complete dehydration of the lower portions of the slab mantle if Mg-sursassite is not considered in the model (Figure 12b).The liberated fluids slightly re-hydrate the oceanic crust, but most rise directly into the overlying mantle wedge, leading to a second pronounced water peak at the top of the model (Figures 12a and 12c).
The small overlap of the antigorite and phase A stability fields lead to water transfer into phase A, but as most of the slab P-T trajectories trend beyond phase A stability only a small region in the center of the slab mantle remains hydrated (Figure 12b).
Whereas in the model without Mg-sursassite the mantle is almost entirely dry, significant amounts of water can be transferred to greater depth if Mg-sursassite becomes stable between 120 and 140 km depth (Figure 12d).
In the models using the dataset 1 (Figures 12e and 12f), the enlarged stability field of phase A overlaps with the antigorite stability field, which allows for a complete water transfer to the deeper mantle.As a result of the overlapping stability fields of phase A and antigorite, the second water pulse caused by antigorite dehydration in the slab mantle is entirely missing (Figure 12e).

Effect on the Global Subducted Water
In order to quantify the amount of water subducted into the deeper mantle (beyond 300 km depth), we summarized the water contents of the rocks in the last modeled column from each subduction zone.Values were converted from wt% H 2 O in solid rock to Tg/Ma depending on the subduction speed and subsequently normalized to 1 km subduction zone length.Figure 13a shows the results for the chosen representative subduction zones Cascadia, Nicaragua, New Britain and Kamchatka and Figure 13b shows the results for all 56 modeled subduction zones.In both Figures, the thermodynamic datasets and calculations with and without Mg-sursassite are compared.
In case of Cascadia, only water stored in phengite present in the sediment and basaltic layers gets deeply subducted (Figure 13a).Consequently, the amounts of subducted water are low compared to the other subduction zones and differences between the modeling approaches are minor.
In case of the Nicaraguan subduction zone, large differences in the total amount of deeply subducted water exist when dataset 1 is used.Here, the calculations including Mg-sursassite yielded much higher values than those not considering Mg-sursassite.This difference does not exist using the thermodynamic dataset 2. The reason for that is the larger stability field of phase A in dataset 1 and the resulting lower intersection of the phase A dehydration reaction with the stability field of Mg-sursassite (see Figures 7 and 11).A number of slab paths that are crossing the Mg-sursassite stability field reach the phase A stability and are able to transfer water into phase A. In case of the smaller phase A stability field when dataset 2 is used, fewer slab paths cross the Mg-sursassite stability and reach the phase A stability field.A similar effect can be seen in the data from New Britain.Due to the lower pressure intersection of the phase A and Mg-sursassite out reactions (Figures 8 and 12), most slab paths reach the phase A stability field without crossing the Mg-sursassite field.In contrast, in case of the smaller phase A stability field using dataset 2, Mgsursassite is needed to transfer significant amounts of water from the antigorite to the phase A stability field.As expected from the calculations above, the differences between the various modeling approaches are very limited for the Kamchatkan subduction zone.
Figure 13b shows the sum of water subducted in all subduction zones and a summary of the published data on the deeply subducted water.Subduction speed and subduction zone lengths were considered to calculate the amount of deeply subducted water.Regarding the global water budget, Mg-sursassite does not significantly affect the (a) Irrespective of the model approach, the amount of subducted water is negligible for Cascadia and there are no significant differences between the models for the cold Kamchatkan subduction zone.For the intermediately worm Nicaraguan and New Britain subduction zones, the choice of the model setup significantly influences the result.(b) Mg-sursassite has a negligible impact on the amount of globally subducted water.In contrast, the thermodynamic dataset used in the models is critical for the results.
Geochemistry, Geophysics, Geosystems 10.1029/2024GC011507 amount of deeply subducted water.It is rather the slope and position of the phase A dehydration reaction, which is the main difference between the thermodynamic datasets 1 and 2, that makes a significant difference in the globally subducted water.

Reliability of the Slab Path Data
Criticism on the thermomechanical subduction zone models and the resulting thermal datasets led to intense discussions on the reliability of such models (e.g., Penniston-Dorland et al., 2015).It is evident that the ground proof for these models, that is, the surficial heat flow and seismic data, is very scarce and often ambiguous.The dataset of Syracuse et al. (2010) that is used in this work has the advantage that the most critical parameter, that is, the position of the coupling between the lower and the upper plate, is varied and the effect on the different P-T trajectories is evaluated.In their different approaches, coupling of the upper and the lower plates is assumed to occur (a) at 80 km depth (D80 model), (b) at a constant trench distance (X25 model) and (c) at a certain temperature (T550 model).Furthermore, one model setup defines the maximum subarc mantle wedge temperature (W1300 model).However, slab surface and slab interior temperatures are similar at 30 and 240 km depth in all model approaches, which is also supported by the comparison of models and exhumed rocks of Qu et al. (2023).
To demonstrate the limited variability in P-T trajectories for the different models, the absolute range of Moho temperatures for all modeled slabs is shown in Figure 14d.Apart from a few slab paths at very low temperatures, the majority of the modeled trajectories lies within a certain range.An evaluation of whether all of these slab paths are too cold, as suggested by Penniston-Dorland et al. (2015), is beyond the scope of this paper.It is noteworthy here that if the thermomechanical models yielded too low thermal gradients, the globally subducted amount of water would likely be lower, but the effect of Mg-sursassite and other phases stable around the choke-point on the slab dehydration would then predominantly affect the cold subduction zones.Additionally, it is necessary to have a full grid of steady state P-T-X-Y points through the subducted slab to conduct this type of model, which, on a global scale to this date, is only available from the Syracuse models.Once additional thermal models are available as P-T-X-Y data, they can also be utilized.Furthermore, with P-T-X-Y-Z matrices, the presented model can also be applied in steady state 3D models.

"Circum-Choke Point" Phases
Provided that the mantle part of subducted slabs is hydrated to a certain extent, the above models demonstrate that the deep water cycle and thus the potential water transfer to the mantle transition zone is dependent predominantly on two factors: First, the position and extent of the stability fields of phases bridging the choke point, like Mgsursassite, the 10Å-phase, 11.5Å-phase or OH-clinohumite, and second, the Clausius-Clapeyron slopes of phases stable above the choke point, like for example, phase A. Due to their steep Clapeyron slopes, Mg-sursassite and the 10Å-phase are only relevant in subduction zones with very steep P-T trajectories, whereas the stability of phase A is crucial for the water budget of most subduction zones.Furthermore, it is evident that the slab mantle chemistry plays a role as several hydrous high pressure phases incorporate aluminum, such as Mg-sursassite, the 11.5Å-phase or the hydrous aluminum pyroxene (HAPY), hence most circum-choke point phases.In this work, we used the chemistry of a depleted MORB mantle (DMM, Workman & Hart, 2005) that contains 3.98 wt% Al, thus allows for the formation of Al-bearing phases.
Our model results show that several subduction zone slab paths are crossing the stability field of Mg-sursassite and for a few subduction zones, Mg-sursassite enables water transfer of up to 1 wt% into phase A (Figures 7  and 8).Given the small number of works that experimentally determined thermodynamic parameters, the reliability of our calculations can only be validated by comparison with experimentally determined stability fields of the phases of interest.Figure 14a shows a comparison of our calculated phase topologies and the experimentally determined stability fields of Mg-sursassite (Bromiley & Pawley, 2002;Fockenberg, 1998) and the 10Å-phase (Fumagalli & Poli, 2005;Pawley et al., 2011;Pawley and Wood, 1995).Apart from the experiments of Fockenberg (1998), all experimentally determined stability fields for Mg-sursassite and the 10Åphase have a similar position and slope than the Mg-sursassite stability modeled with our dataset (bold lines in Figure 14a).This agreement between modeled and experimental results has two important implications.First, it implies that the thermodynamic parameters from Grevel et al. (2001) obviously reflect the physico-chemical behavior of Mg-sursassite in complex mantle rocks very well.Second, as the position and Clapeyron slope Geochemistry, Geophysics, Geosystems 10.1029/2024GC011507 of the 10Å-phase coincides with that of Mg-sursassite, the Grevel et al. (2001) dataset could be used to estimate the stability of the 10Å-phase in Al-bearing mantle rocks.As there is no reliable thermodynamic dataset for the 10Å-phase currently available (Pawley & Wood, 1995) one could hence argue that our models are representative for the effect of both Mg-sursassite and the 10Å-phase on the global water cycle.However, it has to be considered that the 10Å-phase would additionally account for a certain amount of water potentially stored in the slab mantle and that the amount of water subducted to depth beyond 7 GPa could be significantly higher if the 10Å-phase was stable.In order to calculate approximate phase relations in rocks with coexisting Mg-sursassite and the 10Å-phase, reliable thermodynamic data on the 10Å-phase are needed.It has to be noted, however, that the steep slope of the 10Å-phase dehydration reaction also limits, similar as in case of Mg-sursassite, its potential of transferring water into phase A and beyond.Geochemistry, Geophysics, Geosystems 10.1029/2024GC011507 Depending on mantle rock chemistry, two other phases that might significantly influence the phase relations around the choke point are the 11.5Å-phase (Hermann & Lakey, 2021) and high aluminum pyroxene (HAPY, Gemmi et al., 2011).Unfortunately, only a few experimental data points are available on the stability field for these phases (Figure 14b).The stability field of the 11.5Å-phase is only relevant for metasomatic rock types with an increased Al content (Hermann & Lakey, 2021).As the stability of the 11.5Å-phase has a positive slope, it is likely relevant for the deep water cycle.Indeed, recent experiments have shown that the hydrous field can be significantly extended toward higher temperatures even at pressures above 12 GPa by the stability of the 23Åphase (potentially the same as the 11.5Å-phase; Cai & Inoue, 2019) and chondrodite as well as by OHclinohumite (e.g., McGetchin et al., 1970;Stalder & Ulmer, 2001); however, reliable thermodynamic data of these phases are lacking so far.Hence, quantification of their effects on the global water cycle is not yet possible.

Clausius-Clapeyron Slope of Phase A and Its Intersection With the Mg-Sursassite Stability Field
The main differences between the two sets of thermodynamic standard state data used in our models are the bulk modulus (K) of phase A and its pressure derivative (K I ), the standard state entropy (S 0 ) and enthalpy (H 0 ) as well as the formulation of the heat capacity function f(C p ).In dataset 1 K, S 0 and f(C p ) are determined by Komabayashi, Hirose, et al., 2005, whereas K I is taken from Crichton and Ross (2002).Dataset 2 predominantly uses the standard state data published in Holland andPowell (1998, 2011), which are primarily based on the experiments of Pawley et al. (1995).Both datasets rely on the standard state volume data from Pawley et al. (1995).Regarding the EoS used to connect these data, there are several other approaches of predicting the P-V-T relations of minerals than the Murnaghan EoS used in this study, particularly at high and very high pressures (e.g., Duesterhoeft, 2016;Poirier & Tarantola, 1998;Stacey, 2005), but it is beyond this work to determine the reliability or precision of a certain EoS.
The critical parameter controlling the slope and position of the phase A dehydration reaction in our calculations is the bulk modulus K, which differs by about 50% between the two datasets (97,5 vs. 145 GPa for set 1 and 2, respectively).Figure 14c shows the two superimposed phase diagrams from Figures 6c and 6d as well as the stability field of Mg-sursassite to demonstrate the different slopes and positions of the phase A-out reaction calculated with the different datasets and the resulting intersection with the Mg-sursassite dehydration.Also shown are the experimental results on the phase A stability field from six different publications.All experimental data indicate a larger phase A stability field than that calculated using dataset 2. Four experiments lie between the two calculated phase A-out reactions and two indicate a phase A stability toward higher temperatures than modeled with dataset 1.In four published experiments the slope of the phase A-out reaction is (sub-) parallel to the one calculated with dataset 1 and only one has a similar (steep) slope as that calculated with dataset 2. The resulting intersections, hence the positions of the various choke points, differ by almost 2.5 GPa (i.e., about 100 km depth!) between the experiments of Luth (1995) and dataset 2. However, based on the comparisons of the calculated and experimentally determined stability fields of phase A, we assume that the stability field calculated with dataset 2 is too small and its slope is too steep.This is further supported by an unrealistic value of K of 145 GPa, which is larger than that of olivine (forsterite 125 GPa and fayalite 133 GPa).Therefore, we prefer the models obtained using dataset 1.
Our results show that slab paths of many subduction zones have a slope similar to that of the phase A dehydration reaction above the choke point.Hence, only those hydrous phases that are stable at higher temperatures than phase A and that have a Clausius-Clapeyron slope similar to or shallower than phase A are potentially capable of contributing to the transport of water to the mantle transition zone.Phases stable beyond phase A but with a steeper slope, such as balangeroite and Al-bearing phase E (Maurice et al., 2018), might enlarge the hydrous field, but most slab paths will trend beyond their stabilities before they enter the stability fields of wadsleyite and ringwoodite.

Deep Dehydration of the Subducted Slab
The dehydration of subducted slabs has several geodynamic implications.At shallower depth fluid liberation influences the pore fluid pressure at the slab interface and thus the earthquake cycle (e.g., Dal Zilio & Gerya, 2022;Muñoz-Montecinos et al., 2020), it causes hydration of the forearc mantle wedge (e.g., Bostock et al., 2002;Hyndman & Peacock, 2003) and at intermediate depths it triggers mantle melting in the sub-arc region (Pearce & Peate, 1995).Today, improved seismic instrumentation further reveals the importance of Geochemistry, Geophysics, Geosystems 10.1029/2024GC011507 deep dehydration of the subducted slab (Omori et al., 2004).Slab dehydration at depths exceeding 200 km might cause asthenospheric upwelling associated with rifting processes and intracontinental volcanism (e.g., Zhao & Ohtani, 2009).It is likely responsible for deep earthquakes between 200 and 600 km depth (e.g., Omori et al., 2004).However, our models show that apart from hot subduction zones, deep slab mantle dehydration might occur in most other subduction zones.Our models further show that the prediction of such deep dehydration processes differs between the chosen sets of thermodynamic parameters for phase A and the stabilities of phases around the choke point, such as Mg-sursassite, 11 Å phase and the 10 Å phase (Figures 10-12).This circumstance points out the importance of improved experimentally determined thermodynamic data for these phases.
Nevertheless, in the following section, we give an example of an interesting correlation of our modeled dehydration pattern with seismic data from the Chilean subduction zone.Figure 15 shows a correlation of earthquake hypocenters from between 18 and 24°S (Sippl et al., 2018) along the West coast of South America (a) and our model results for the Northern Chilean subduction zone (about 21°S; b and c).The modeled slab shape and position fits very well with the observed seismicity, as indicated by the red stippled lines in (a) that mark the upper and lower boundaries of our model.
The intra-slab seismicity pattern shows a double seismic zone down to about 80-100 km depth that grades into a 25-30 km thick zone with a very high seismicity density and a more homogeneous distribution of hypocenters.Within this zone of high seismic activity the slab is slightly bent downward and further downdip at a depth between 200 and 250 km is another earthquake cluster from which a trail of hypocenters emerges (arrow in Figure 15).This hypocenter trail can be traced upward to almost close to the surface.It is yet unclear inasmuch as dehydration reactions account for the intense seismicity down to 150 km depth (e.g., Fang & van der Hilst, 2019;Sippl et al., 2018).Hence, the major crustal (lawsonite) and mantle (antigorite) dehydration predicted by our model that correlates well with the dense cluster between 80 and 150 km depth might only weaken the slab and trigger buoyancy-related fracturing and seismicity (Sippl et al., 2018) in that region.Nevertheless, we would like to focus on the trail of earthquakes that emerges from the slab at about 200 km slab depth and reaches almost until the surface.The Mgsursassite dehydration reaction coincides spatially almost perfectly with the observed seismicity and the earthquake trail.Although it is questionable, whether the earthquake trail is caused by fluid migration, it is generally possible that dehydration and fluid percolation cause seismicity (Davies, 1999;Ferrand et al., 2017) and that the deep earthquake cluster as well as the upward directed hypocenter trail is caused by deep dehydration of Mg-sursassite, the 10 Å-phase and/or phase A. Another model showing similar patterns could be dynamic slab segmentation and grain size reduction in the subducting slab (Gerya et al., 2021).Such a process could be coupled with dehydration reactions and fluid liberation.
In any case, this example shows the need of better and more reliable thermodynamic data for ultra high-pressure phases as models, such as the one presented here, together with the integration of petrogeochemistry into geophysical models as well as high-resolution seismic data can shed light on the fate of deeply subducted slabs.

Summary of the Effect on the Global Water Cycle
Only a few studies have attempted to quantify the global water cycling between the hydrosphere and geosphere.The published data (Figure 13b) can be separated into those that concentrate on the thermodynamic constraints of phase assemblages in the subducting slab (e.g., Hacker, 2008;Rüpke et al., 2004;Schmidt & Poli, 2003;van  with a dominant antigorite dehydration between 300 and 350 km trench distance and Mg-sursassite dehydration between 400 and 450 km trench distance.The Mg-sursassite dehydration occurs between 200 and 250 km slab depth (c) and can be nicely correlated with a trail of hypocenters that emerges at this depth from the slab and that can be traced to a depth of about 50 km (a).Keken et al., 2011; this study) and those that tie the water cycling to Phanerozoic hydrosphere constraints, such as sea level changes (e.g., Karlsen et al., 2019;Parai & Mukhopadhyay, 2012) or sea water isotopic composition (e.g., Wallmann, 2001).With the present-day knowledge, the global water cycle is significantly under-determined and quantifications can only be seen as estimates that constrain the order of magnitude of water cycling.Unknowns comprise the total amount of water on Earth, the container volume of the ocean basins including its change over Earth's history, the mantle outgassing rate and the hydration state of the subducted lithosphere, just to name a few.However, looking at the different datasets published so far shows that the differences among them are less than one order of magnitude, indicating that our present knowledge might not be far from reality, especially regarding the fact that two different approaches to the problem lead to quite similar results (Figure 13b).
The total amount of recycled water beyond 10 GPa in our calculated models is in the range from 8.5 × 10 8 Tg/Ma, in case the thermodynamic dataset 2 is used and Mg-sursassite is not considered, to a maximum of about 1.4 × 10 9 Tg/Ma, using the thermodynamic dataset 1 and considering Mg-sursassite (Figure 13).These values are calculated for 2 wt% of water initially contained in the slab mantle to a depth of 12 km.This value, although observed in some offshore regions of subduction zones (e.g., Ranero et al., 2005), is arbitrary, as detailed data about the extent of slab mantle hydration is still missing.The values of assumed mantle hydration in other models of similar kind (Hacker, 2008;Rüpke et al., 2004;Schmidt & Poli, 2003;van Keken et al., 2011) range from 2 km hydration depth with 2 wt% H 2 O (van Keken et al., 2011) to 10 km hydration depth with 1 wt% H 2 O (Rüpke et al., 2004) and 12 km hydration depth with 2 wt% H 2 O (this study), which likely explains the ca.6-fold span in the model results (Figure 13b).Hence, our results are quantitatively at the upper end of the published values for deeply subducted water.By extending the hydration depth and intensity, the amount of water recycled into the deeper mantle can be significantly enlarged.Thus, more data on global hydration depth and intensity for the individual subduction zones is needed to better constrain water transport into the deeper mantle.
More important than the absolute values is the fact that our results clearly demonstrate that the presence of Mgsursassite and/or the 10Å-phase has an influence on the deep water cycle only in intermediately hot subduction zones, such as Nicaragua and New Britain, but is negligible in hot (e.g., Cascadia) or cold (e.g., Kamchatka) subduction zones (Figure 13a).Predictions of the amount of globally subducted water are only marginally influenced by the presence of Mg-sursassite and/or the 10Å-phase in the subducted mantle (Figure 13b).In contrast, the choice of the thermodynamic dataset regarding phase A has a substantial influence on the outcome of the results for specific subduction zones as well as for the global results.This circumstance is also reflected in the literature data.The thermodynamic data used in dataset 2 is implemented in the frequently used Holland and Powell (1998) internally consistent thermodynamic dataset and its later updates.Indeed, publications that use this dataset (e.g., Hacker, 2008;Van Keken et al., 2011) yield consistently lower values comparable to our results utilizing dataset 1 (Figure 13b).Following our comparison with experimental data (Figure 14c), it is likely that the data from Komabayashi, Hirose, et al. (2005) represents the stability field of phase A much better and should be used in future models.Furthermore, it is notable that the data from those publications that are based on observations of the Phanerozoic hydrosphere changes yield significantly lower values than those based on thermodynamic calculations.This circumstance might point to the fact that the slab mantle hydration in most thermodynamic models is overestimated.However, these models are difficult to compare because of several parameters with large uncertainties, for example, subduction geometry, speed, thermal patterns as well as degree and intensity of hydration of the subducting slab.

Concluding Remarks
We have used the thermal data from 56 subduction zones (Syracuse et al., 2010) to determine the global water budget in subduction zones.In our thermodynamic models, we implemented different published thermodynamic datasets for phase A and Mg-sursassite to study the effect on the global water budget.The stability of Mgsursassite has a significant influence on the water budget of intermediately hot subduction zones, such as Nicaragua and New Britain.Hot subduction zones, such as Cascadia, and cold subduction zones, such as Kamchatka, are negligibly influenced by the presence of these "circum-choke point" phases.Neither is the amount of globally subducted water beyond 300 km depth, which is dominated by the abundance of phase A in cold subduction zones.
The choice of the thermodynamic data of phase A has a significant influence on the water budget in many subduction zones.This is because many P-T trajectories of the slab Moho in most subduction zones have a slope Geochemistry, Geophysics, Geosystems 10.1029/2024GC011507 similar to the Clapeyron slope of the phase A-out reaction.Slight changes in the position and shape of the phase A stability field have drastic effects on the transport of water into the deeper mantle.The thermodynamic data implemented in the commonly used Holland & Powell (1998) database and its updates yield a consistently smaller phase A stability field, which is, compared to experimental data at the lower end of all published results.In contrast, datasets using the experimental results from Komabayashi, Hirose, et al. (2005) match much better the experimentally determined phase A stability and are preferred in our study.
Both, Mg-sursassite stability as well as the choice of the phase A thermodynamic dataset have an influence on the dehydration behavior of subducted slabs, such that water release at greater depth occurs at varying trench distances, different depths and might even be completely hindered, if the entire water can be stored in stable dense hydrous magnesium silicates.In general, the stability of "circum-choke point" phases can lead to deep volatile release down to about 300 km depth.

Figure 1 .
Figure 1.Simplified pressure-temperature (P-T) phase diagram for ultramafic rock compositions color-coded for the maximum water content.Important for the deep water cycle is the position of the "choke point" and the P-T trajectories of the subducted slabs.Two Moho P-T paths of a hot (Cascadia) and cold (Kamchatka) subduction zone are shown to demonstrate the relation of choke-point position and slab temperature.

Figure 2 .
Figure 2. Depth-trench distance-temperature relations of the four exemplary subduction zones Cascadia, Nicaragua, New Britain and Kamchatka.Stippled lines outline the top and bottom of the models, and solid lines within the slab are from top to bottom: top of sediments, top of mafic crust and Moho.Note that the strong temperature increase at 80 km depth in all models is the result of the transition of coupling and partial coupling of the slab and mantle wedge that is set to this depth.See text for further discussion.

Figure 3 .
Figure 3. P-T pseudosections calculated for the water saturated composition of the mafic crust (a, NMORB) and the sedimentary layer (b, GLOSS) color coded for the water content of the solids.The P-T trajectories in (a) mark the hottest (red) and coldest (white) paths of the respective lithological units for all 56 modeled subduction zones.The stability fields of the minerals are labeled such that the label is on the "present" side of the zero-mode line.Both mafic and sediment units transport only negligible amounts of water into the deeper mantle.Lws = lawsonite, Grt = garnet, Tc = talc, Chl = chlorite, Zo = zoisite, Amph = amphibole, Phng = phengite.

Figure 4 .
Figure 4. P-T pseudosections calculated for the water saturated depleted MORB mantle (DMM) composition and color coded for the water content in solids.The stability fields of the minerals are indicated by the labels on the "present" side on the zero-mode lines.Diagrams in (a) and (b) are calculated without considering Mgsursassite (Mg-sur), diagrams in c and d are calculated including Mg-sursassite.The diagrams in the left column (a and c) are calculated utilizing thermodynamic dataset 1 (see Table 2), and those on the right side (b and d) are calculated using the thermodynamic dataset 2. Water saturation is chosen to demonstrate the maximum water content of the mantle rocks.The dotted lines in (c) indicate the stability fields of amphibole and Mg-sursassite in the more fertile primitive upper mantle (PUM) composition representing the overlying mantle wedge.

Figure 5 .
Figure 5. Simplified P-T pseudosections calculated for depleted MORB mantle (DMM) composition containing initially 2wt% water.Shown are only phase fields for hydrous phases (solid lines) and the water saturation curve in solids (stippled line).The P-T trajectories show the modeled slab paths for the slab mantle in the Cascadia subduction zone and are color coded for the water content in solids.Upper diagrams (a) and (b) are calculated without considering Mg-sursassite, the lower diagrams (c) and (d) are calculated with Mg-sursassite.Left and right column diagrams are calculated using the different thermodynamic datasets.In hot subduction zones, all slab mantle P-T trajectories trend into the anhydrous phase field already below antigorite, phase A, or Mg-sursassite stability.

Figure 6 .
Figure 6.Same diagrams as in Figure 5 but the P-T trajectories showing the modeled slab paths for the slab mantle in the Kamchatkan subduction zone (color coded for the water content in solids).Narrow stippled P-T trajectories are extrapolated paths (see text).In the Kamchatkan subduction zone, all slab mantle P-T trajectories trend into the phase A stability field without crossing the Mg-sursassite stability field.Only above 9 GPa and only when using the thermodynamic dataset 2 the uppermost slab mantle P-T path trends into the anhydrous field (b and d).All other paths transport the initial 2wt% water into the deeper mantle.

Figure 7 .
Figure7.Same diagrams as in Figure5but the P-T trajectories showing the modeled slab paths for the slab mantle in the Nicaraguan subduction zone (color coded for the water content in solids).Narrow stippled P-T trajectories are extrapolated paths (see text).In intermediately warm subduction zones, Mg-sursassite and the choice of the thermodynamic dataset play an enormous role in calculating the deeply subducted water.In the models not considering Mg-sursassite (a) and (b), all slab paths trend into the anhydrous field and dehydrate between 5 and 6 GPa.Mg-sursassite allows the transfer of water into phase A in the lower part of the slab mantle if the thermodynamic dataset 1 is used (c).Calculations utilizing thermodynamic dataset 2 predict complete slab dehydration between 7 and 8 GPa (d).

Figure 8 .
Figure8.Same diagrams as in Figure5but the P-T trajectories showing the modeled slab paths for the slab mantle in the New Britain subduction zone (color coded for the water content in solids).Narrow stippled P-T trajectories are extrapolated paths (see text).Similar as in the Nicaraguan case, Mg-sursassite and the thermodynamic dataset have a strong influence on the deeply subducted water.Without Mg-sursassite large parts of the slab mantle dehydrate between 5 and 6 GPa and only a limited amount of water can be subducted beyond 10 GPa (a) and (b).Mg-sursassite allows for the transfer of about 1 wt% of water into phase A, where it is subducted to the deeper mantle in case of thermodynamic dataset 1 (c) or released from the slab between 8 and 9 GPa when thermodynamic dataset 2 is used (d).

Figure 9 .
Figure 9. Results of the 2D thermodynamic model for the Cascadia subduction zone.(a) Free water flux on top of the different lithological layers and on top of the model (wedge mantle).(b) Calculated amount of free water (upper slab figure) and water in solids (lower slab figure).Additionally shown are the zero-mode lines of the dehydrating phases and the regions where the thermomechanical model assumes a coupled, partly coupled and decoupled slab-mantle interface.See text for further discussion.

Figure 10 .
Figure10.Results of the 2D thermodynamic model for the Kamchatkan subduction zone.The diagrams in (a) and (b) are calculated using thermodynamic dataset 2 without Mg-sursassite.The major dehydration peaks result from an initial crustal dehydration that liberates water into the overlying mantle wedge that subsequently dehydrates and is responsible for the large peak at 200 km trench distance.After continuous lawsonite dehydration phase A breakdown in the uppermost slab mantle layers (b) results in two prominent peaks at 350 km trench distance (a).(c) and (d) A similar dehydration scenario occurs if Mg-sursassite is implemented into the thermodynamic dataset 2. (e) and (f) In case of thermodynamic dataset 1, slab mantle dehydration is entirely missing.

Figure 11 .
Figure 11.Same diagrams as in Figure 10, but calculated for the Nicaraguan subduction zone.The slab mantle dehydration is strongly influenced by the thermodynamic dataset and by the implementation of Mg-sursassite.Thermodynamic dataset 2 without Mg-sursassite results in a single prominent peak of water liberation from the slab mantle at about 190 km trench distance (a).The peak is the result of slab dehydration at the tip of the curved antigorite-out reaction (b) that completely dehydrates the slab mantle.Mg-sursassite leads to the transfer of water to greater depth (d) and a significant dehydration between 200 and 250 km trench distance (c).In case of thermodynamic dataset 1, water is transferred into phase A (f) and the slab mantle dehydration at depths exceeding 200 km is limited (e).

Figure 12 .
Figure 12.Same diagrams as in Figure 10, but calculated for the New Britain subduction zone.The slab mantle dehydration in the model without Mg-sursassite starts at about 175 km trench distance (a) continues by dehydration of phase A at the top of the slab mantle (b).Mg-sursassite incorporation leads to a gap in the dehydration (c) and incomplete mantle dehydration (d).In the model using the thermodynamic dataset 2, mantle dehydration is completely absent (e) and (f).

Figure 13 .
Figure13.Calculated amounts of water subducted beyond 300 km for the selected exemplary subduction zones (a) and for all 56 modeled subduction zones (b).(a) Irrespective of the model approach, the amount of subducted water is negligible for Cascadia and there are no significant differences between the models for the cold Kamchatkan subduction zone.For the intermediately worm Nicaraguan and New Britain subduction zones, the choice of the model setup significantly influences the result.(b) Mg-sursassite has a negligible impact on the amount of globally subducted water.In contrast, the thermodynamic dataset used in the models is critical for the results.

Figure 14 .
Figure 14.Comparison of the model results with experimentally determined stabilities of Mg-sursassite and the 10Å-phase (a), phase A (b), chondrodite, 23Å-and 11.5Å-phase as well as high-Al pyroxene (HAPY) and OH-clinohumite (c), and the P-T trajectories of the different thermomechanical model approaches (d), Colored lines indicate full range of slab Moho temperatures.See text for discussion.

Figure 15 .
Figure 15.Comparison of the model results and the position of earthquake hypocenters in the central Chilean subduction zone between 20°and 22°N.(a) Correlation of hypocenters taken from Sippl et al. (2018) and the assumed slab boundaries used in our model.Triangles on top of the diagram are volcanic centers projected into the plane at 21°N.(b) Modeled slab mantle dehydration in the North Chilean subduction zone is clearly bimodal with a dominant antigorite dehydration between 300 and 350 km trench distance and Mg-sursassite dehydration between 400 and 450 km trench distance.The Mg-sursassite dehydration occurs between 200 and 250 km slab depth (c) and can be nicely correlated with a trail of hypocenters that emerges at this depth from the slab and that can be traced to a depth of about 50 km (a).

Table 1
Chemical Bulk Composition and Size of the Different Layers in the Slab Model