This is very interesting. Permit me to make some Roy Model migration points and one general equilibrium point. A "slow moving" local disaster shifts expectations about the future economic opportunity at the origin. The most able and ambitious young people will move away (1/N). https://twitter.com/samh510/status/1314193962505302016

The young, amble and ambitious people will move to cities where they earn $ and can remit some of this back home. Max and I discuss this in our handbook chapter.
https://escholarship.org/content/qt5b55x5w5/qt5b55x5w5.pdf?t=ptngtl (2/3).

The origin location that has experienced the slow moving "environmental disaster" will experience population loss. A simple Malthus model of resource scarcity highlights that the loss of population increases the well being of those who remain (more resources per-capita).

This dynamic adaptation process is facilitated by markets. The key here is to accelerate the pace of the out-migration from the shocked area so that the new equilibrium is reached faster. @mushfiq_econ work is key here; https://onlinelibrary.wiley.com/doi/abs/10.3982/ECTA10489

One final point. Suppose that the cities that grow because of in-migration feature increasing returns to scale in productivity. In this case, the macro-economy can be strengthened by the micro shock to the rural area because the shock accelerates the sticky migration process.

This thread traces out another example of "cross-elasticites" in environmental and urban economics. Climate change economics will make faster progress if more scholars work on this issue. See Kahn 2021.