Scientific Speculation - Desert Planet Realism - Minimum possible hydrosphere

My question is fairly straightforward, but answering it is proving rather difficult.

The scenario is on a planet with some water. The surface is dominated by deserts, both hot and cold depending on latitude. However, the atmosphere must be breathable by humans.

So the question is: What is the minimum amount of surface water that a planet could have that would sustain sufficient photosynthesis to render the atmosphere breathable?

For reference - The planet has a mass and size similar to the Earth, and is also similar in geological composition. The major difference is that it received a smaller compliment of water, or has lost water somehow.

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Desert Planet Realism - Minimum possible hydrosphere

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