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On Earth, there is enough Hydrogen and Oxygen to make 13,88 million km$^3$ of water (calculation below). However, oceans contain only a tenth of that.

Clearly, most of the hydrogen must be stored in other chemical compounds different to water. Or, as water deep within Earth's interior: some studies suggest the water on Earth's interior could contain three times as much as the water near the surface.

On the other hand there are many chemical reactions, like the well known photosynthesis and respiration, that can transform water into other compounds and vice versa.

We often think that there is a fixed amount of liquid water on Earth (plus or minus what is being recycled in the atmosphere). But it seems to me that the processes above could change the water amount significantly over geological timescales.

So my question could be stated as follows: over geological timescales, what determines the amount of liquid water on Earth?

Here are two examples of the processes I'm thinking about:

  1. Reservoir transfers: If water from a well is removed, the ground water reservoir around it will slowly re-fill the well. Would the same happen with Earth's oceans if removed? Would water from the deep Earth's interior partially re-fill the oceans through volcanic eruptions?

  2. Chemical balance: For a chemical reaction that can go both ways, if the reactants and products are in equilibrium and I remove the product compounds, more of them will be generated until a new equilibrium is reached. Would the same happen if I remove the water from Earth's surface? Will Hydrogen and Oxygen from rocks and air combine to partially replenish the oceans?

(This question was inspired by How much water is the atmosphere losing to space?)


Calculation of the maximum possible water on Earth

The maximum amount of water you can have on Earth is limited by the available hydrogen. Now, for each gram of bulk Earth there are 260 $\mu\text{g}$ of hydrogen and plenty of Oxygen.

Given that the Earth's mass is $5.972 \times 10^{27}$, and 260 $\mu\text{g/g}$ correspond to Hydrogen, that would total $1.552 \times 10^{24}$ g of Hydrogen, that at a molar mass of 1.007 g/mol, corresponds to $1.540 \times 10^{24}$ mol, enough to make $7.703 \times 10^{23}$ mol of water (as two atoms of hydrogen are required in a molecule of water). And since water has a molecular mass of 18.0152 g/mol, such an amount of water would weigh $1.3877\times 10^{25}$ grams. Finally, assuming a density of 1 $\text{g/cm}^3$ we get a total of $1.3877\times 10^{25}$ $\text{cm}^3$ or $13,877,025,731\, \text{km}^3$; that corresponds to 10.01 times the amount of water near Earth's surface (including oceans, lakes, rivers, ground water, etc.) and that is estimated to add up to 1,386,000,000 $\text{km}^3$.

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  • $\begingroup$ It's going to depend on where you put all the water you removed. This might be better suited for Worldbuilding SE because it involves a scenario resuliting from some unspecified process. $\endgroup$ – Spencer Feb 4 at 21:18
  • $\begingroup$ @Spencer As you can see from the question that inspired this one, I thinking very precisely in water loss to space, as it might have happened to Mars. However, as a thought experiment and to make the discussion easier I'm asking for the case when all the water disappears suddenly, instead of the gradual loss of atmospheric escape. $\endgroup$ – Camilo Rada Feb 4 at 22:01
  • $\begingroup$ Something to remember: There's plenty of water locked up in minerals in the solid earth - crust and mantle. Considering only "groundwater" is missing a lot of it. $\endgroup$ – Gimelist Feb 6 at 22:46
  • $\begingroup$ @Gimelist That's precisely what I meant, not ground water. The well analogy might be confusing, but that's why I specified "trough volcanic eruptions". But I don't know which processes beside volcanism can unlock that water within rocks. $\endgroup$ – Camilo Rada Feb 6 at 23:30
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I'm ignorant of all the organic and inorganic chemical reactions that can destroy or create water, and the factors controlling them. But I can give a shot to the part of the question related to volcanoes and the water stored on Earth's interior:

The most abundant gas in volcanic eruptions is water, corresponding to more than the 80% of emitted gases in volume (source). If we consider on of the largest volcanic eruptions we know about: The toba supervolcano eruption 75,000 years ago. The water volume emitted has been estimated in $540\, \text{km}^3$.

enter image description here

Figure: Comparison of ejected material from notable eruptions (source)

From that perspective, you can see that you would need about 2.5 million Toba eruptions to re-fill the oceans.

In the past, over the history of Earth it could be reasonable to think that the volcanic output could average to the equivalent one Toba eruption every 2000 years, something that would be enough to deliver the volume of water currently in the oceans, but over 4.5 billion years.

However, most volcanic activity on Earth is related to subduction volcanism (including Toba), and such volcanism relies on water input to produce the erupting magmas, and arguably, a large fraction of the erupted water is the same water that was lost in the corresponding subduction zone.

We can then conclude that volcanic water input could eventually help keeping the level on a drying ocean, but at a very slow rate and over very long timescales. But if the oceans ever go dry, volcanism is unlikely to revert the situation.

In the context of the question that motivated this one, the rate at which volcanoes release water dwarf that of water losses to space. However, over long enough times those losses could dry our both the ocean and the Earth interior. But more importantly, I don't know if the net transfer of water from/to the Earth's interior is zero (in balance) or if the mantle is actually sucking water from the oceans, or filling them up. It might be that instead of worrying of planets loosing their water to space, we should worry about them loosing it to their guts.

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    $\begingroup$ I totally appreciate the Rada-oceanography-programme of questions & self-answers that is going on at the moment. I think those Q&A can be interesting for a number of people. Other question: It is often quoted that Earth consists of 50% oxygen, by mass (or was it by number). This should give a much larger number than 10 oceans worth of material stored on Earth. Is then 50%Earth minus 10 Oceans simply not accessible somehow, i.e. because bound in $\rm SiO_2$? $\endgroup$ – AtmosphericPrisonEscape Feb 4 at 16:33
  • $\begingroup$ @AtmosphericPrisonEscape There are lots of Oxygen (although I think about 25%), the limiting factor to make water is the Hydrogen. $\endgroup$ – Camilo Rada Feb 4 at 16:35
  • $\begingroup$ Ok, so the answer to that question is in fact your calculation in your question. Thanks! $\endgroup$ – AtmosphericPrisonEscape Feb 4 at 16:36
  • $\begingroup$ @AtmosphericPrisonEscape I would say so, haha. I hope someone can address the chemistry side of the question, or refute/improve my answer. The key factor I didn't address is what is the actual net transfer of water between the surface and the mantle. $\endgroup$ – Camilo Rada Feb 4 at 16:39
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    $\begingroup$ Yeah I have actually never thought about that, that there could be net transfer of elements into the mantle. The classical story about oxygenation of the oceans, surface and atmosphere is that oxygen could only build up in the atmosphere after all surface rocks were done oxygenating, and those of course cycled from surface to mantle. So the naive conclusion from that is that the mantle should be saturated. Do we have evidence for/against this scenario? $\endgroup$ – AtmosphericPrisonEscape Feb 4 at 16:42
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Reactions that can produce or destroy water:

${\displaystyle {\hbox{H}}_{2}{\hbox{CO}}_{3}\to {\hbox{H}}_{2}{\hbox{O}}+{\hbox{C}}{\hbox{O}}_{2}}$

(and there is plenty of ${\hbox{H}}_{2}{\hbox{CO}}_{3}$ (carbonic acid) in the sea water).

${\displaystyle {\hbox{HCl}}+{\hbox{NaOH}}\to {\hbox{H}}_{2}{\hbox{O}}+{\hbox{NaCl}}}$

Combustion: ${\displaystyle {\hbox{C}}_{3}{\hbox{H}}_{8}+5{\hbox{O}}_{2}\to 3{\hbox{CO}}_{2}+4{\hbox{H}}_{2}{\hbox{O}}}$

Hydrochloric acid and sodium hydroxide: $HCl + NaOH \to H_2O + NaCl$

Calcium + Hydrochloric acid: $CaCO_3 + 2 HCl \to CaCl_2 + H_2O + CO_2$

$CO_2 +H_2 \to CO + H_2O$

$2H_2 + O_2 \to 2H_2O $

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    $\begingroup$ Is this supposed to be a complete list? $\endgroup$ – Camilo Rada Feb 5 at 2:39
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Photosynthesis and respiration only exchange water for organic compounds and vice versa, those reactions can not alter the amount of water in the earth, only convert a small part into organic compounds.

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    $\begingroup$ They can definitely store organic compounds (those are fossil fuels). And what about inorganic reactions? Is there any that can transform rocks into water? $\endgroup$ – Camilo Rada Feb 4 at 16:55
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    $\begingroup$ -1 As this does not answer the question. $\endgroup$ – MrSpudtastic Feb 4 at 20:18

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