This is assuming a pot with straight sides, at least above the lowest water level during cooking.
This would be accurate at room temperature, but under stovetop conditions wouldn't evaporation rate be determined mostly by the amount of heat energy added to the water?
In my experience, the surface area where evaporation occurs has the most impact. If I know (and obviously I do every time, just measure it) the evaporation area size, that's what I use to dial in how much pre-boil wort I need the first few times I use a set of equipment.
But heat energy is the second most important factor. Sea level, salt/mineral levels, and other factors are - in my experience - not worth considering. But I've not tried to brew beer on the top of a mountain.
I've brewed over 300 batches of beer in vessels of various dimensions (including surface area and evaporation area), and with various amounts of heat energy, applied in various places in the vessel. Ranging from 2kW to 18kW, sometimes heat applied under the pot, sometimes distributed throughout for example 3 heating elements at various heights. 2kW for all from 15L to 60L vessels, 6-18kW from 25L to 120L, and 18kW (IIRC) for 500-800L.
When brewing beer, the boil usually lasts for 60-90 minutes, and the boil off rate is extremely important for hitting your target gravity and volume, and getting a consistent result if you're brewing the same recipe again.
What you do as a brewer is you test the equipment on the first 2-3 batches and then after that you can hit your target boil-off with 99% accuracy every time, or 100% in an enterprise-grade professional setup.
I've never been more than 5-10% off my estimated boil-off rate for the first batch, and I only account for surface area in that estimate. Even with 6kW for 25L.
The evaporation rate from the pot as a whole at any given time will then be that rate per unit area, which depends on that host of factors, times the surface area.
So once you know how deep a layer of extra water you need to add to cover evaporation in one pot, that will be the same depth of water you need to add to a different size pot if you are cooking in that different sized pot at the same temperature, pressure, etc. as the first pot.
Think of it this way: Imagine you have a rectangular pot, with a removable divider in the middle that effectively turns it into two smaller pots side by side.
If you put the divider in and cook some rice in the left side, you need a certain depth of extra water. If instead you cooked that rice in the right side, you'd need the same depth of water there.
Now imagine cooking in both sides simultaneously. You'd still need the same depth in each side as when you were cooking in that side solo.
OK, now imagine cooking in both sides, but without the divider installed. That's not really any different than with the divider installed. Each side is still going to need the same depth of water as before.
(Well, there will be some difference. Not all heat gets into what you are cooking through the bottom of the pan. The sides get hot too, and some heat comes in that way. Remember that the evaporation rate at any given point on the surface depends on conditions at that point. A spot in the center will take longer to reach a given temperature than a spot near a side, and so we'll have a non-uniform evaporation rate across the surface. I don't think this will make much difference as far as rice cooking goes, but figuring out for sure would require knowing a lot more about how heat moves within a batch of cooking rice than I do).