Dtyjlui

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 $mutext{g}$ of hydrogen and plenty of Oxygen.

Given that the Earth's mass is $5.972 times 10^{27}$, and 260 $mutext{g/g}$ 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 $1.3877times 10^{25}$ grams. Finally, assuming a density of 1 $text{g/cm}^3$ we get a total of $1.3877times 10^{25}$ $text{cm}^3$ 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 $text{km}^3$.

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 $540, text{km}^3$.

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.

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 $

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.