# How long would it take oceans to evaporate if they stopped gaining water?

How long would it take for the oceans to evaporate if the following were true?

1. They suddenly stopped gaining water through rain/rivers/etc., and

2. External patterns (e.g. atmospheric humidity) were actively maintained as they currently are
(water in excess of this is diverted to some other heavenly body)

(Let's consider "almost all" the water, since evaporating every last drop might take absurdly long.)

As a starting point I've posted my own answer, but I'm not sure how accurate it is at all.

(I'm not sure if this should be on EarthScience, or Physics, or Chemistry... please migrate if needed.)

• @Mehrdad I suggest you do not put this question to EarthScience or Physics in that case because your suggestion is thoroughly unphysical. You can make it physical by just removing the atmosphere altogether so that your oceans will evaporate to the vacuum of space. – GretchenV Aug 10 at 10:04
• @GretchenV: I mean I haven't put it on those sites, so it seems like a pointless argument to have, but frankly so much useful physics has developed from unrealizable thought-experiments that the idea that that prevents a physically meaningful answer is frankly absurd. All you need to do is to find enough matter & energy to collect precipitation & water flowing into the ocean and then divert it off the planet. It might be beyond foreseeable technology, but that doesn't imply it violates the laws of physics. And how you do it or which planet you move it to is hardly relevant. – Mehrdad Aug 10 at 13:06
• This is not an issue with your question, but just something i find super interesting as a world builder: what are you doing with that idea? The 2 restrictions are so unrealistic that i suspect something really creative and interesting. I would love it if you could hint at what this could be useful for – Raditz_35 Aug 11 at 12:26

I could assume that salt only goes into the ocean, and not out, giving me 9 million years. Oceans have on average 35 parts of salt per thousand, while fresh water has less than 500 per million, and the average is about 50 ppm 0.035/0.00005= 500. Rivers have delivered enough water to refill the oceans 500 times in the last 4.5 billion years. 4,500,000,000/500 = 9 million years.

However, that is wrong, as the salinity of the has been constant for a while. Because the rate of evaporation is inversely proportional to the salinity of the water (page 43), I get this equation: $\frac{dDepth}{dt} = 1.2*Depth^3$ This can be solved to get $\frac{1}{Depth^2}=1.2*10^{-11}t+7*10^{-8}$. To get the water level less than 1 centimeter, it takes $10^{14}$ years. To get the water level less than 1 meter, it takes $10^{11}$ years. To make the water the depth of the salt on the ocean floor, which is 54 meters, it takes 28 million years. To get it to twice that depth, it takes 8 million years. For the oceans to be evaporated in less than 5000 years, there would still be over 2 an a half kilometers of water remaining.

All these times are overestimated because the salty water would fall to the bottom, and only a certain amount of salt can dissolve into water.

My own estimate is as follows: The ocean is on average 3.7km deep. If we assume the ocean evaporates at at 3mm/day (Earth's average?) ÷ 70% (how much of the surface is ocean water), this gives a timeframe of around $\frac{3700}{0.003 ÷ 70\%} ÷365 \approx 2365 \textbf{ years}$.

However, this completely neglects atmospheric features that change with depth, such as air pressure, or pretty much any other effect. So I really have no idea how accurate this is.

• Where did the 3mm a day figure come from? – Tim B Aug 10 at 9:41
• @TimB: Here, but I really have no idea how accurate it is. It wasn't the easiest thing to Google. (Edit: I edited it in.) – Mehrdad Aug 10 at 9:47
• There are a number of other complicating factors too - such as the ocean surface area reducing as the water dries up. – Tim B Aug 10 at 10:04
• @TimB: I thought about that too, but imagining the underwater topology I didn't think it would matter much (maybe a factor of 50% if I really push it). I'm just trying to get a ballpark estimate, like figuring out if it's in the thousands or millions. But admittedly I don't really know, which is why I asked the question and said that my answer neglects a lot... – Mehrdad Aug 10 at 10:09
• The real number will be higher, because as oceans will evaporate, their salinity will increase, and evaporation will slow down. Also, the ice caps, which see almost no evaporation, will be able to feed oceans for millions of years. – Alexander Aug 10 at 19:09