<p>It is not hard to do this calculation if you have global topography. Using a version with <span class="math-container">$\frac{1}{6}$</span>- degree resolution and a sea level rise of 1027 m, the result is @Erik's value of 445 million cubic km. Here's the bit of MATLAB code:</p>
<pre><code>H = 1027;   % sea level rise (m)
topo(topo&lt;0) = 0;   % change all ocean depths to zero
topo(topo&gt;H) = H;   % level off all land at a height of H
topo = topo.*(cosd(lat')*ones(1,2160)); % land volume per grid cell
land = sum(topo(:))*18.5^2/1000; % total land volume in km^3
water = sum(cosd(lat))*2160*18.5^2*H/1000 - land; % added water volume
</code></pre>
<p>Greenland and Antarctica fare ok, but Europe and Australia are basically gone:
<a href="https://i.sstatic.net/iuKle.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/iuKle.png" alt="world map with 1027m sea level rise" /></a></p>

CC BY-SA 4.0
2021-02-07T09:35:57.583Z
Greenland and Antarctica are mostly ice which would float away and melt, the rock topography is hardly above sea level. So they would not fare ok and we all have to huddle in the Himalayas, Rockies and Andes.
uUnwY
CC BY-SA 4.0
2021-02-07T17:39:36.223Z
I guess this explains why all humans originated fro Addis Ababa. LOL it's at 7770 feet elevation haha.
CommaToast
CC BY-SA 4.0
2021-02-07T17:42:49.440Z
@Stephan Matthiesen if the ice would all melt then wouldn't the sea level up even higher?
CommaToast
CC BY-SA 4.0
2021-02-07T22:25:49.210Z
@CommaToast Yes, but the Antarctic ice would only contribute about 60m and Greenland 10m or something like that; that would be disastrous if it happened in real life; but in our scenario with more than 1km sea level rise an additional few ten metres won't make much difference.
uUnwY
CC BY-SA 4.0
2021-02-07T23:04:41.707Z
If all the Antarctic ice melted, it would apparently raise current sea level by 60m.  However, the total volume of Antarctica above an elevation of 1027m is 15.3M cubic km.  If it were all ice that melted, that would raise the sea level by an additional 27 m for a total of 1054 m (some small fraction of it is actually land).  However, all the ice below an elevation of 1027 would lower the total a bit when it melted, because water is denser than ice.  So assuming all Antarctic ice melts would change the result to about 1050 m.  Greenland ice could up this by a few m.
Ben51
CC BY-SA 4.0
2021-02-07T04:10:19.950Z
2021-02-07T04:10:19.950Z
Ben51
<p>What amount of average sea level rise (in meters above 2020 levels) would be associated with a 25% increase in total ocean volume?</p>
<p>The reason I ask is because of <a href="https://sciencenordic.com/chemistry-climate-denmark/the-earth-has-lost-a-quarter-of-its-water/1462713" rel="noreferrer">this study</a> that indicates Earth has lost appx. 25% of its water to space via methanogenesis process splitting the hydrogen molecules off of H2O, then the hydrogen escaping into space.</p>
<p>Regardless of whether this study is accurate, it has made me wonder what the Earth would have looked like with 25% more water. How much of a sea-level rise would that represent?</p>
<p>Obviously this would be a fairly complex equation since terrain is not uniform in contour. Less land is displacing every new layer of water you ade, compared to a lower layer of water. So (in addition to any changes from the radius of the sphere increasing) there should be a decreasing amount of average sea level increase per unit of water volume, until all land is covered.</p>
<p>I've looked to <a href="https://www.floodmap.net/" rel="noreferrer">FloodMap.net</a> for an answer, but they don't seem to provide the amount of water volume, at least, not to free users.</p>
<p>Curious if there is an open source code library that can handle this kind of calculation, or if there is a simple formula that would get us within a reasonable margin of error (i.e. it would provide a sea level that could be plugged into FloodMap to show what shorelines would look like under 25% more water, given today's continents).</p>

CC BY-SA 4.0
2020-11-18T09:09:36.957Z
You'll want to know about one third additional current ocean volume, not a quarter. According to the article "the oceans have lost about a quarter of their water since the Earth’s early days". This leaves us with three quarters of original ocean volume, thus the "missing" quarter makes up a third of todays oceans. Which is about 445 million cubic kilometer (https://www.ngdc.noaa.gov/mgg/global/etopo1_ocean_volumes.html).
Erik
<climate-change><oceanography><earth-history><sea-level>
How far would average sea level rise from a 25% increase in total ocean volume?
CommaToast
# How far would average sea level rise from a 25% increase in total ocean volume?

(Asked by: username_0 on 2020-11-17)

What amount of average sea level rise (in meters above 2020 levels) would be associated with a 25% increase in total ocean volume?

The reason I ask is because of [this study](https://sciencenordic.com/chemistry-climate-denmark/the-earth-has-lost-a-quarter-of-its-water/1462713) that indicates Earth has lost appx. 25% of its water to space via methanogenesis process splitting the hydrogen molecules off of H2O, then the hydrogen escaping into space.

Regardless of whether this study is accurate, it has made me wonder what the Earth would have looked like with 25% more water. How much of a sea-level rise would that represent?

Obviously this would be a fairly complex equation since terrain is not uniform in contour. Less land is displacing every new layer of water you ade, compared to a lower layer of water. So (in addition to any changes from the radius of the sphere increasing) there should be a decreasing amount of average sea level increase per unit of water volume, until all land is covered.

I've looked to [FloodMap.net](https://www.floodmap.net/) for an answer, but they don't seem to provide the amount of water volume, at least, not to free users.

Curious if there is an open source code library that can handle this kind of calculation, or if there is a simple formula that would get us within a reasonable margin of error (i.e. it would provide a sea level that could be plugged into FloodMap to show what shorelines would look like under 25% more water, given today's continents).

**Tags:** climate-change, oceanography, earth-history, sea-level

> **Comments:**
> **username_1**: You'll want to know about one third additional current ocean volume, not a quarter. According to the article "the oceans have lost about a quarter of their water since the Earth’s early days". This leaves us with three quarters of original ocean volume, thus the "missing" quarter makes up a third of todays oceans. Which is about 445 million cubic kilometer (https://www.ngdc.noaa.gov/mgg/global/etopo1_ocean_volumes.html).  

---

## 1 answers

### Answer by username_2 on 2021-02-07. Score: 3 | Accepted answer

It is not hard to do this calculation if you have global topography. Using a version with $\frac{1}{6}$- degree resolution and a sea level rise of 1027 m, the result is @username_1's value of 445 million cubic km. Here's the bit of MATLAB code:

```
H = 1027;   % sea level rise (m)
topo(topo<0) = 0;   % change all ocean depths to zero
topo(topo>H) = H;   % level off all land at a height of H
topo = topo.*(cosd(lat')*ones(1,2160)); % land volume per grid cell
land = sum(topo(:))*18.5^2/1000; % total land volume in km^3
water = sum(cosd(lat))*2160*18.5^2*H/1000 - land; % added water volume

```

Greenland and Antarctica fare ok, but Europe and Australia are basically gone:
[![world map with 1027m sea level rise](https://i.sstatic.net/iuKle.png)](https://i.sstatic.net/iuKle.png)

> **Comments:**
> **username_3**: Greenland and Antarctica are mostly ice which would float away and melt, the rock topography is hardly above sea level. So they would not fare ok and we all have to huddle in the Himalayas, Rockies and Andes.  
> **username_0**: I guess this explains why all humans originated fro Addis Ababa. LOL it's at 7770 feet elevation haha.  
> **username_0**: @Stephan Matthiesen if the ice would all melt then wouldn't the sea level up even higher?  
> **username_3**: @username_0 Yes, but the Antarctic ice would only contribute about 60m and Greenland 10m or something like that; that would be disastrous if it happened in real life; but in our scenario with more than 1km sea level rise an additional few ten metres won't make much difference.  
> **username_2**: If all the Antarctic ice melted, it would apparently raise current sea level by 60m.  However, the total volume of Antarctica above an elevation of 1027m is 15.3M cubic km.  If it were all ice that melted, that would raise the sea level by an additional 27 m for a total of 1054 m (some small fraction of it is actually land).  However, all the ice below an elevation of 1027 would lower the total a bit when it melted, because water is denser than ice.  So assuming all Antarctic ice melts would change the result to about 1050 m.  Greenland ice could up this by a few m.  

---

