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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..)
You can find gridded topography and bathymetry data, freely accessible, on the website of the NOAA. For instance you have the ETOPO1 dataset here.
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 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
