Forestry management was a big thing back in the day, mostly in the form of pollarding and coppicing (not so much wholesale replantation).
What I meant by "rings" though might not have been clear – not an actual contiguous ring encircling, but rather woodlands that are a particular distance from the city. Forestry, like other agricultural efforts, naturally settled into areas a particular distance according to (mostly) consequences of travel and transport time: soft delicate vegetables & fuit nearest, forestry (frequent firewood needs mean closer), easily transported agriculture (grains, infrequent transport), and finally agricultural product that come equipped with their own 4 legs furthest away.
https://en.wikipedia.org/wiki/Coppicing
I don't actually recall just how far these distances were, so quite possibly further away than what MFCG maps. All good.