Calculate ocean area using ETOPO

Hi,

I am wanting to calculate the area of a section of ocean (which also contains land) between two (lat,lon) points. I know I can import the ocean coverage and bathmetry in to Matlab from ETOPO, but unsure how to then get an area from this. Area would need to account for depth and bathymetry (i.e not just surface area). Is this even possible? If so I'd appreciate any pointers.

Thanks

[KSSV]

How is your domain shape? If it is a perfect rectangle, simply use lengthxbreadth.

Answer 1

[Anurag]

Hi Ben,

I understand that you need to calculate the surface area of a section of the ocean between two (lat, lon) points also accounting for the depth and bathymetry. Considering both the surface area and the bathymetry, involves integrating over the three-dimensional space.

Follow the following steps to compute this:

• Load Bathymetric data. Please refer to the below documentation to know more about the “geotiffread” function: https://www.mathworks.com/matlabcentral/fileexchange/29425-geotiff-reader

[Z, R] = geotiffread('path_to_etopo_file.tif');

• Define region of interest

latRange = [startLat, endLat];
lonRange = [startLon, endLon];

• Extract Relevant Bathymetric Data. Use the coordinates to extract relevant portion of the data. Please refer to the below documentation to know more about the “find” function: https://www.mathworks.com/help/matlab/ref/find.html

latIndices = find(R.LatitudeLimits(1) <= R.LatitudeLimits(2) & R.LatitudeLimits(1) <= latRange & latRange <= R.LatitudeLimits(2));

lonIndices = find(R.LongitudeLimits(1) <= R.LongitudeLimits(2) & R.LongitudeLimits(1) <= lonRange & lonRange <= R.LongitudeLimits(2));

subZ = Z(latIndices, lonIndices);

• Calculate Volume or Area. Please refer to the below documentation to know more about the “trapz” function: https://www.mathworks.com/help/matlab/ref/trapz.html

volume = trapz(trapz(subZ, 1), 2);

Please note that the above calculations have been done with the assumption that the region of interest is small enough to ignore the curvature of earth, else you may need to convert the latitudes and longitudes to Cartesian coordinates and accounting for the earth’s radius.

Hope this helps!

Regards,

Anurag