But the appreciation of the land doesn't affect your adjusted basis or your sale price. Regardless of what it was that produced the rise in value, the calculation is going to be the same. Cost basis, adjusted for depreciation, will always be less than sale price even at net zero, unless you spent more on new improvements than you claimed in depreciaton (let's ignore that for the sake of discussion).
In this case, transactional costs aside, sale price is $200k and adjusted basis is $100K, fully attributable to prior depreciation.
BTW, I didn't mean to say that the value of the improvements never changed. I meant that each year's depreciation should be based on the same original value. We're not recalculating value, we're just claiming depreciation and reducing the basis accordingly. And yes, if the value of the structure drops and the property sells for the same price, that implies the land is a higher percentage of the value at sale.
However, I still see the question of ratios as a red herring. Buy the property, calculate the basis, subtract land value, depreciate improvements, adjust basis by equal amount, sell and calculate gains. End. I don't ever have to calculate a ratio to do this correctly. It's like adding a variable to the equation that doesn't affect the end result, and I was never good enough at math to suffer needless complexity.