<p>You can find gridded topography and bathymetry data, freely accessible, on the website of the NOAA. For instance you have the ETOPO1 dataset <a href="http://www.ngdc.noaa.gov/mgg/global/global.html">here</a>.</p>

<p>Once you downloaded it you can work it out with your favourite GIS software or GIS-supporting programming language.</p>

<p>The equations to calculate the volume based on the gridded cells is given on <a href="http://www.ngdc.noaa.gov/mgg/global/etopo1_ocean_volumes.html">this page</a> from the NGDC website.</p>

<blockquote>
  <p>Volume Calculation </p>
  
  <p>Volumes were calculated for each ocean grid cell in ETOPO1 using
  Equation 1 to determine cell area, and Equation 2 to determine cell
  volume. Cell areas and volumes were then summed over each ocean or
  marginal sea.</p>
  
  <p>Equation 1: $dA = \frac{a^2\cdot cos(ø)\cdot (1-e^2)\cdot dø\cdot dl}{(1-e^2 \cdot sin^2ø)^2}$<br>
  Equation 2: $dV = dA \cdot depth$</p>
  
  <p>where:<br>
  Latitude (ø)  = latitude of cell's center (in radians)<br>
  Unit of Latitude (dø) = 1 arc-minute ($2.908882 \cdot 10^{-4}$ radians)<br>
  Unit of Longitude (dl)    = 1 arc-minute ($2.908882 \cdot 10^{-4}$ radians)  </p>
  
  <p>The WGS84 spheroid was used for values of Earth's radius and
  eccentricity:<br>
  Equatorial radius (a) = 6378.137 km<br>
  Eccentricity (e)  = 0.08181919</p>
</blockquote>

CC BY-SA 3.0
2014-07-07T07:32:35.390Z
2014-07-07T07:32:35.390Z
plannapus
<p>I'm interested in this problem because I'm interested in obtaining a rough estimate of the average temperature increase of the sea given a net radiative forcing of 0.6 W/m^2.</p>

<p>But in order to obtain an estimate, I need to know the volume of the ocean between 0-2000m. I'm also interested in knowing the volume of the ocean between any other two arbitrary layers of the ocean (0-1000m, 1000-2000m, 0-4000m, etc..)</p>

<p><img src="https://i.sstatic.net/wvAA8.png" alt="enter image description here"></p>

CC BY-SA 3.0
2014-07-05T23:32:00.713Z
Are you sure you are looking for volume? Volume = height x width x depth.  If you are curious about a particular ocean... you could look up the surface area of the ocean and multiply it times the depth.
f.thorpe
CC BY-SA 3.0
2014-07-06T04:50:35.243Z
Yes. Thing is, bathymetry matters, making width hard to calculate.
InquilineKea
CC BY-SA 3.0
2014-07-06T05:28:26.497Z
Ah so it sounds like you want a computer program like ArcGIS that can load bathymetry and do 3-D computations.
f.thorpe
<ocean><bathymetry>
How do I find the volume of ocean between any two layers of ocean depth?
InquilineKea
# How do I find the volume of ocean between any two layers of ocean depth?

(Asked by: username_0 on 2014-07-05)

I'm interested in this problem because I'm interested in obtaining a rough estimate of the average temperature increase of the sea given a net radiative forcing of 0.6 W/m^2.

But in order to obtain an estimate, I need to know the volume of the ocean between 0-2000m. I'm also interested in knowing the volume of the ocean between any other two arbitrary layers of the ocean (0-1000m, 1000-2000m, 0-4000m, etc..)

![enter image description here](https://i.sstatic.net/wvAA8.png)

**Tags:** ocean, bathymetry

> **Comments:**
> **username_1**: Are you sure you are looking for volume? Volume = height x width x depth.  If you are curious about a particular ocean... you could look up the surface area of the ocean and multiply it times the depth.  
> **username_0**: Yes. Thing is, bathymetry matters, making width hard to calculate.  
> **username_1**: Ah so it sounds like you want a computer program like ArcGIS that can load bathymetry and do 3-D computations.  

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## 1 answers

### Answer by username_2 on 2014-07-07. Score: 7

You can find gridded topography and bathymetry data, freely accessible, on the website of the NOAA. For instance you have the ETOPO1 dataset [here](http://www.ngdc.noaa.gov/mgg/global/global.html).

Once you downloaded it you can work it out with your favourite GIS software or GIS-supporting programming language.

The equations to calculate the volume based on the gridded cells is given on [this page](http://www.ngdc.noaa.gov/mgg/global/etopo1_ocean_volumes.html) from the NGDC website.

> Volume Calculation
>
> Volumes were calculated for each ocean grid cell in ETOPO1 using
> Equation 1 to determine cell area, and Equation 2 to determine cell
> volume. Cell areas and volumes were then summed over each ocean or
> marginal sea.
>
> Equation 1: $dA = \frac{a^2\cdot cos(ø)\cdot (1-e^2)\cdot dø\cdot dl}{(1-e^2 \cdot sin^2ø)^2}$  
> Equation 2: $dV = dA \cdot depth$
>
> where:  
> Latitude (ø) = latitude of cell's center (in radians)  
> Unit of Latitude (dø) = 1 arc-minute ($2.908882 \cdot 10^{-4}$ radians)  
> Unit of Longitude (dl) = 1 arc-minute ($2.908882 \cdot 10^{-4}$ radians)
>
> The WGS84 spheroid was used for values of Earth's radius and
> eccentricity:  
> Equatorial radius (a) = 6378.137 km  
> Eccentricity (e) = 0.08181919


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