On the evolution of the water ocean in the plate-mantle system

Mantle convection simulations

Another important influence of hydrated mantle rocks is the variation in density caused by hydrated mantle minerals, as noted by Nakagawa et al. (2015):

$$ \rho \left({T}_{ad},p,C,{C}_w\right)=\rho \left({T}_{ad},C,p\right)\left(1-\alpha \left({T}_{ad},C,p\right)\left(T-{T}_{ad}\right)\right)-{\Delta \rho}_w{C}_w $$

(6)

where ρ(T_ad, C, z) is the combined reference density between harzburgite and mid-ocean ridge basalt (MORB) compositions, with a 2.7% density difference, as shown in Fig. 1 (and a 3.6% density difference between olivine- and pyroxene-related phases); T_ad is the adiabatic temperature in the mantle; ∆ρ_w is the density variation due to the water content; and C_w is the water content. Generally, the densities of hydrous minerals are less than those of dry minerals, but the value of ∆ρ_w is less constrained by high-pressure/high-temperature (high P-T) experiments; the densities of hydrous minerals are generally 0.1 to 1.0% less than those of dry mantle minerals (Richard and Iwamori 2010).

The numerical setup used in this study is described as follows: 1024 (azimuthal) × 128 (radial) grid points with four million tracers are used to track the chemical composition, melt fraction, and mantle water content. The boundary conditions for temperature are fixed temperatures at the surface (300 K) and the core-mantle boundary (CMB; 4000 K). The initial conditions include an adiabatic temperature of 2000 K at the surface plus a thin thermal boundary layer (to explain the thermal boundary conditions at the surface and CMB), a basaltic composition of 20%, and a dry mantle (zero water content). The composition of the mantle is assumed to be uniform so that partial melting can create heterogeneous features in the mantle. The mantle can become hydrated up to the boundary conditions of the mantle water content (described in the “Computing the water ocean mass”) via surface plate motion.

Water solubility maps

Figure 1 shows the maximum H₂O content of the mantle peridotite system based on the work of Iwamori (2004, 2007) and Nakagawa et al. (2015) (Fig. 1a) and includes the stability fields of hydrous phases that are stable at lower mantle conditions (Fig. 1b). These data are used to compute the excess water migration in the convecting mantle. At the lower mantle condition, without DHMS solubility, the water solubility of the lower mantle minerals is set as 100 wt. ppm. With DHMS solubility, in addition to the existing DHMS (phases A to D), because a new hydrous mineral phase has recently been discovered to exist at lower mantle pressures, i.e., “phase H” (Komabayashi and Omori 2006; Nishi et al. 2014; Ohira et al. 2014; Walter et al. 2015; Ohtani 2015), we have added the stability field of DHMS including phase H to the water solubility map of the mantle peridotite system (Fig. 1c). Compared to the water solubility map for pressures of less than 28 GPa (Iwamori 2004, 2007), few experimental results are available for pressures of greater than 28 GPa to constrain the exact phase boundaries and the maximum amount of H₂O in the peridotite system. The effect of aluminum on the stability of DHMS including phase H depends on the partitioning of Al among mantle minerals, including DHMS, phase H, and δ-AlOOH, which is currently poorly constrained. For instance, we assume that the stability of phase H in the natural peridotite system is similar to that of the pure MgSiO₄H₂ phase H (Ohira et al. 2016), which can be used to establish a minimum P-T stability range. Considering the bulk peridotite composition and the maximum modal amount of phase H in the peridotite system, we estimate that the maximum H₂O content in the phase H-bearing P-T range is 8 wt.%. At pressures and temperatures higher than the stability field of DHMS with phase H, we set a maximum H₂O content of 100 ppm below the solidus (e.g., Panero et al. 2015) and 0 ppm above the solidus, as in Nakagawa et al. (2015).

Computing the water ocean mass

Chemical-hydrous structure with effects of DHMS

Figure 2 shows the chemical-hydrous structure of the mantle with and without the water solubility effects of DHMS at t = 4.6 billion years and for μ₀ = 0.2, with an assumed total water volume of 12 ocean masses in the planetary system (exosphere plus interior). In both cases, extremely high-viscosity structures are found in the lower mantle due to the high efficiency of heat transfer of hydrous mantle convection (Nakagawa et al. 2015). Without DHMS, we assume that the water solubility of the lower mantle minerals is set as 100 wt. ppm. Without DHMS solubility, the dry mantle transition zone corresponds to upwelling plumes, which can have a temperature that is hotter than 2000 K. As shown in Fig. 6c of Nakagawa and Iwamori (2017), the high temperatures associated with mantle plumes correspond to water contents of zero. Incorporating the DHMS stability field into the water solubility maps (see Fig. 1a, b) reveals that the high-temperature mantle plumes may have a certain water content, unlike in the case without DHMS solubility limits. Another major difference between the cases with and without DHMS solubility is that the hydrated region at a depth of 660 km expands to the uppermost lower mantle in cold downwelling regions because of the high water content of DHMS (see arrows at the bottom of Fig. 2). Since we also assume that a density reduction occurs due to the hydration of the mantle minerals (Nakagawa et al. 2015), smaller-scale basaltic piles are found in the deep mantle compared to those generated by dry mantle convection (e.g., Nakagawa and Tackley 2011).

To confirm how DHMS affects the mantle water content, Fig. 3 shows the 1D horizontally averaged mantle water content corresponding to the hydrous structure in Fig. 2. Without the effects of DHMS, the mantle transition zone is the main water absorber; however, with the effects of DHMS, an additional region of high water content can be found at depths of up to ~ 1500 km. The water content in the mantle transition zone in these cases ranges from 0.1 to 1.0 wt.%. This range is similar to those inferred from the electrical conductivity structure of the mantle transition zone (e.g., Kelbert et al. 2009) and from seismic imaging (Houser 2016; Schmandt et al. 2014). Moreover, these results also seem to be consistent with the measurements of the water content of diamond inclusions in wadsleyite (Pearson et al. 2014). To confirm the cause of the water enhancement in DHMS found in Fig. 3, Fig. 1a, b shows the water solubility maps on which the 1D vertical structures of temperature have been plotted. Comparing a cold temperature profile with the water solubility map in Fig. 1b appears to indicate that phase H appears in the temperature profile at a depth of ~ 1500 km (corresponding to a pressure of approximately 60 GPa).

Water mass evolution and plate-like behavior: with and without DHMS

Figure 4 shows the temporal variations in the surface water mass and surface mobility that can be computed using the ratio of the surface velocity to the root mean square velocity in the entire mantle with and without DHMS, as shown in Fig. 2. Over 4.6 billion years, the surface seawater comprises 2.2 ocean masses without DHMS and 1.2 ocean masses with DHMS. Both cases are started with 12 ocean masses in total amount of water. This means that, for the mantle water mass, 9.8 ocean masses without DHMS and 10.8 ocean masses with DHMS are absorbed in the mantle. Therefore, when the DHMS effect is included, this water is more likely to be partitioned into the deep mantle to match the constraint on the present-day Earth’s ocean mass. In Figs. 1b and 3, with DHMS, more water can be absorbed in the upper lower mantle compared to a case without DHMS, which is caused by phase D and/or phase H. However, as shown in Table 3 of Iwamori (2007), the maximum amount of water that can be stored is 9 to 11 ocean masses, assuming that the maximum H₂O content in the lower mantle is 100 ppm and assuming an average geotherm corresponding to that beneath 60 Ma oceanic lithosphere with a mantle potential temperature of 1300 °C (Iwamori 2007). This may suggest that the DHMS plays a minor role in the mantle water mass, which contributes at most to ~ 1 ocean mass of water mass in the whole mantle because the effects of DHMS only appeared in the cold subducting regions.

Figure 5 shows the mantle water fluxes (ingassing, dehydration, and degassing) as a function of time with and without DHMS. The procedures for computing these water fluxes can be found in Nakagawa and Iwamori (2017) and Nakagawa and Spiegelman (2017). They are given as follows:

$$ {F}_R=\left\{\begin{array}{c}\underset{S}{\int }{\rho}_m{u}_z{C}_w dS\ \left(\mathrm{if}\ {u}_z<0\right)\\ {}0\ \left(\mathrm{if}\ {u}_z\ge 0\right)\end{array}\right. $$

(10)

$$ {F}_G={\dot{M}}_{\mathrm{erupt}}{C}_{w,\mathrm{erupt}} $$

(11)

$$ {F}_E=\underset{S}{\int }{\rho}_m{C}_{w,\mathrm{ex}}{u}_f dS $$

(12)

where ρ_m is the mantle density; \( {\dot{M}}_{\mathrm{erupt}} \) is the total mass of erupted material; C_w is the water content; u_z is the radial velocity; C_w,erupt is the water content of the erupted material, which is equivalent to the water content of the molten material; C_{w, ex} is the excess water content relative to the water solubility; and u_f is the conventional form of fluid migration velocity expressed numerically, which is computed as the ratio of the radial grid spacing to the time step size but is not very sensitive to the grid spacing shown in the Appendix of Nakagawa and Iwamori (2017), and the subscripts of those fluxes are R = ingassing, G = degassing, and E = dehydration. Basically, the uptake of water from the surface reservoir by plate subduction is the dominant flux process, with a magnitude on the order of 10¹³ kg/year, with the two other fluxes involving the release of water at the surface of approximately an order of magnitude lower than that involved in the uptake process. Thus, the surface seawater is gradually reduced by the ingassing process with surface plate motion. These profiles of water fluxes without DHMS are not very different from those in a case with the DHMS solubility field because the effective depth of the mantle water cycle associated with those fluxes is approximately 150 to 200 km (Nakagawa and Spiegelman 2017). This means that the DHMS solubility field is less sensitive to the physical processes of the mantle water cycle.

To assess the model sensitivities to the total amount of water in the planetary system, Fig. 6 shows the temporal variations in the surface seawater, mantle mass, and surface mobility with DHMS, which indicate that the surface seawater completely dries up before reaching the age of the Earth for a total amount of water of less than nine ocean masses. This implies that the total amount of water in the planetary system should be preferably in about 12 ocean masses, for the surface seawater to be consistent with the surface seawater on the present-day Earth. This preferred amount of water coincides with the storage capacity of the silicate mantle, as mentioned above (Iwamori 2007), although the mantle temperature reproduced in this study (e.g., Fig. 1) is lower than the 60 Ma geotherm assumed by Iwamori (2007). This indicates that (1) DHMS in the lower mantle, which was ignored in Iwamori (2007), plays a minor role, and (2) the present-day mantle could contain a maximum amount of water due to continuous hydration (Fig. 6). As discussed in the the “Introduction,” the total amount of water in the Earth system has been estimated to be 1.2 to 3.3 ocean masses, which is based on the water contents of oceanic basalts (mid-ocean ridge basalts (MORB) and ocean island basalts (OIB)) and assumes that the entire mantle is sampled by MORB and OIB (Hirschmann 2006). While the upper mantle comprises the MORB source, OIB likely represents only a part of the crust-mantle cycling system (e.g., White and Hofmann 1982; Christensen and Hofmann 1994). The apparent difference in the estimated amount of water (i.e., 10–12 vs. 1.2–3.3 ocean masses) could be due to the regions that are not sampled by either MORB or OIB.

Regarding the surface mobility, which is one diagnostic for assessing the occurrence of plate-like behavior and is computed as the ratio of surface velocity to the root mean square of the convective velocity of the entire mantle (bottom of Fig. 6), it appears to not change very much after all the surface seawater is absorbed into the deep mantle. This suggests that the surface seawater found on the Earth’s surface is not strongly correlated with the occurrence of surface plate motion. To confirm this hypothesis, Fig. 7 shows the sensitivity of the total amount of water to water fluxes, which indicates that the degassing flux is still active when the surface seawater is exhausted. This suggests that the surface seawater could be regenerated with mantle degassing, and the water-weakening effect is still valid but that it is immediately returned to the deep mantle via plate subduction. Therefore, surface plate motion will still be very active even if all surface seawater is exhausted.

Water mass evolution: model sensitivity to the strength of the oceanic lithosphere

Figure 8 shows the temporal variations in both the surface and mantle water masses over 4.6 billion years for different friction coefficients (0.1, 0.2, 0.3, and 0.6) corresponding to different strengths of oceanic lithosphere. All of the cases shown here include the solubility effects of DHMS. For weaker oceanic lithosphere (μ₀ = 0.1 and 0.2), the surface seawater can be partitioned with a similar value as the present-day Earth’s ocean mass over 4 billion years. On the other hand, for stronger oceanic lithosphere (μ₀ = 0.3 and 0.6), the amount of surface seawater still remains at approximately five ocean masses. This mechanism can be explained by the mass-averaged temperature profile as a function of time as shown in Fig. 7b, c. In weaker oceanic lithosphere, heat transport is more efficient due to the vigorous surface plate motion and large number of plate boundaries (Nakagawa and Iwamori 2017). The mantle temperature is cold enough to pass into the water solubility field of DHMS with phase H. However, stronger oceanic lithosphere cases indicate higher mantle temperatures, so that the mantle temperature does not pass into the water solubility field of DHMS. To confirm this implication, Fig. 9 shows the 1D horizontally averaged mantle water content as a function of pressure. For weaker oceanic lithosphere, a high water content region can be found at both the mantle transition zone and upper lower mantle corresponding to DHMS solubility. In contrast, for stronger oceanic lithosphere, water enhancement is only found in the mantle transition zone. This is caused by the difference in mantle temperatures shown in Fig. 7b and the heat transfer efficiency of plate-mantle dynamics.

Findings

DHMS and other potential mechanisms of water transport into the deep mantle

First, the stability fields of DHMS including phase H that are stable under lower mantle pressure conditions are poorly constrained, as was described earlier in the “Water solubility map” section. In this study, our stability field of phase H corresponds to that of Ohira et al. (2016) and features a minimum stability field of 70 to 80 GPa. If the stability field is raised to more than 100 GPa and higher temperatures, more water can be transported via plate subduction, which may shorten the lifetime of surface seawater; to achieve an Earth-like planet, more water is required in the system.

Second, other potential host minerals of water exist in the deep mantle, such as δ-AlOOH (Ohira et al. 2014) or pyrite-type FeOOH (Nishi et al. 2017). These minerals appear to be stable at typical lower mantle temperatures and pressures. However, the amount of water that these minerals can retain in the deep mantle remains unclear. The possible water solubilities of the lower mantle minerals, including phase H, δ-AlOOH, and pyrite-type FeOOH, which could potentially be accurately determined via experiments, could greatly influence the survival time of surface seawater. The inclusion of additional lower mantle minerals could result in a much shorter seawater survival time than that observed in the cases examined in this study. Note that the volume-averaged water content of the lower mantle is be expected to be ~ 100 ppm or less (Karato 2011; Panero et al. 2015), but these estimates remain highly controversial and are dependent on identifying the possible host minerals of water in the deep lower mantle. Therefore, these estimates should be determined more quantitatively to resolve this issue.

Third, a hydrogen diffusion mechanism is also a significant process in the mantle water cycle (Richard et al. 2002, 2006) and is still unresolved in this study. Numerical modeling results suggest that hydrogen diffusion seems to saturate the mantle with water on a much shorter timescale than that without incorporating hydrogen diffusion (Nakagawa 2017). The incorporation of a water-saturated mantle leads to a steady state in the evolution of surface seawater induced by the mantle water cycle. As a result, the lifetime of surface seawater can be expected to be longer in this study.

Moreover, the rheological properties of the hydrous lower mantle are highly uncertain because of the difficulty of experimental determination, even for dry mantle conditions (e.g., Girard et al. 2016). Under dry mantle conditions, the lower mantle minerals are expected to exhibit the shear localization mechanism with diffusion creep deformation (Girard et al. 2016). However, it is unclear whether this type of deformation mechanism occurs under hydrous lower mantle conditions. If the rheological properties of the lower mantle are similar to those of the upper mantle, more water could be transported into the deep mantle, and the lifetime of surface seawater may be shorter due to the more vigorous convective dynamics in the lower mantle.

Strength of the oceanic lithosphere

As indicated in Fig. 7, the friction coefficient has a great influence on the partitioning of water between the surface and deep mantle reservoir; more surface seawater is absorbed in conjunction with smaller friction coefficients (weaker oceanic lithosphere) because the mantle temperature is sufficiently cold so that both the mantle transition zone and upper lower mantle may be worked as large water reservoirs (see Fig. 8). Hence, a large amount of water should be required when the strength of oceanic lithosphere is very weak; however, using the range of friction coefficients suggested by observational data analysis (up to 0.7; Zhong and Watts 2013), the total amount of water in the entire system could be reduced but still be larger than those of the suggested by simple parameterized convection models (e.g., Sandu et al. 2011). However, it should be noted that a weaker oceanic lithosphere is preferable for understanding the plate-like behavior in a dry mantle convection system (μ₀ < 0.1; Moresi and Solomatov 1998; Crameri and Tackley 2015). Moreover, in this study, we incorporate the effect of “water weakening” to reduce the yield strength of the oceanic lithosphere under a water-saturated situation.

Total amount of water in the planetary system

In most geodynamic models with water circulation, the partitioning of water between surface seawater and the deep mantle at the present is assumed to range from 1:1 to 1:2 (Franck and Bounama 2001; Rüpke et al. 2004; Sandu et al. 2011; Korenaga 2011), which is consistent with the results of the mineral physics experiments (Hirschmann 2006). In particular, Franck and Bounama (2001) also suggested that the lifetime of surface seawater may be dependent on the efficiency of regassing caused by plate subduction. However, in this study, the regassing flux is automatically regulated by the water solubility map, including the “choke point” observed at a depth of 150 to 200 km, which is reduced by up to a few orders of magnitude for the regassing flux at this depth. The most important issue in those geodynamic models is that it is difficult to account for the water solubility of mantle minerals, and the water cycle is assumed to involve only degassing for the water release from the deep interior to the exosphere and water uptake by the regassing process from the surface to the deep mantle. In addition, degassing is assumed to occur only along mid-ocean ridges but should also occur along island arcs. Furthermore, the scaling relationship is based only on heat transfer in steady-state mantle convection, which is only applicable for cases with less vigorous mantle convection. Therefore, simplified mantle dynamics models with water circulation underestimate both the regassing flux and the degassing flux and therefore require a smaller amount of total water in the entire planetary system (~ 3 ocean masses) than the amount inferred from early planetary formation estimates (5 to 15 ocean masses). To avoid these underestimates caused by the assumption of scaling relationships in plate-mantle dynamics, we conducted a series of full mantle convection simulations with water migration, including actual water solubility maps for deep mantle minerals. The results indicate that a large amount of water is needed in the planetary system to achieve a consistent lifetime of surface seawater in the plate-mantle system. This finding is consistent with the estimates of the total amount of water in the entire planetary system inferred from early planetary formation processes.

However, this argument leads to issues related to the sources of the volatile components in the early Earth and their initial amounts (e.g., Albarede 2009). In Nakagawa and Spiegelman (2017), these issues did not affect the initial amount of water in the deep mantle, but the deep mantle should contain a certain amount of water, as illustrated in the water solubility maps of the mantle minerals. These issues remain in models of the early thermal and chemical state of the planetary mantle that do not start from a full magma ocean condition (a fully molten mantle is expected to have been present in the early Earth). To further resolve these issues, the initial state of mantle convection should be seriously examined in a future study that assumes initially fully molten mantle conditions (Lourenço et al. 2016) and then checks the consistency of these conditions with the theoretical estimates of the size of the water reservoir at the surface (Hamano et al. 2013).

Finally, the following evolution of surface seawater associated with a plate-mantle system is proposed; a certain amount of water (volatiles) is delivered to the planet before or after the magma ocean forms (potentially by a giant impact or late veneer accretion, see review by Genda (2016)). After the magma ocean solidifies, surface seawater forms. The partition ratio of water between the surface and the deep mantle is dependent on the water solubility of the deep mantle, which is in turn dependent on the temperature and composition of the early Earth’s mantle. Vigorous surface plate motion can transport surface water into the deep mantle; however, because of the high temperatures in the deep mantle, relatively little water stays in the deep mantle. When the mantle is sufficiently cooled by mantle convection, the water transported via plate subduction can be stored in the mantle transition zone and the uppermost lower mantle, thereby gradually reducing the volume of surface water to the present-day amount. Although this conceptual model would be slightly modified by a better understanding of the global-scale mantle water circulation and more accurate water solubility limits of lower mantle mineral assemblage, it is overall a robust model.