Mars ancient ocean volume question

Hi. I have a very specific question and I don’t know how to calculate the answer. If someone can help, then thanks. Please tell me: how do I calculate the volume of water that would be required to fill an ocean in the northern lowlands of Mars such that it would cover the bottom of Valles Marineris and its outflow channels, but otherwise leave the southern hemisphere highlands as dry land?

The key is really the first step of getting the data in a ‘distortionless’ projection for volumetric calculations.

How I’d do it:

  1. Convert MOLA elevation to a sinusoidal projection.
  2. Choose the elevation that you think is “the bottom of Valles Marineris and its outflow channels”.
  3. Create a mask for all elevations below that level. Depending on how you feel about filling craters not connected to the northern lowlands, you could select the largest masked area to avoid spurious additional volume from non-connected craters/basins (e.g. Argyre).
  4. Create a raster with the value equal to the the value in step 2 that is masked out by step 3.
  5. Subtract step 4 result from step 1.
  6. Sum the result from step 5 which would be in m^3.
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Thanks for your help!