The AyrMesh Hub is powered over its Ethernet cable, and can accept voltages between 10 and 24 Volts DC. As such, it is pretty easy to power it from a battery recharged from a wind turbine or solar panel.
Tycon Power is producing solar and wind-powered units for just this sort of application, and we recommend them as an excellent and cost-effective solution. The first step is to determine what size system you need. We recommend a system with at least 36 Ah batteries for 24+ hours of backup with no power - go to the 50 Ah battery system for 48 hours of backup.
Tycon sells battery units (their "UPS Pro" series), and we recommend the 36Ah battery and the 50Ah battery module mated with the 30W solar panel or the 60W solar panel kits. You can also use their wind turbine to charge the batteries.
Tycon also sells fully-integrated, ready-to-use systems (their "Remote Pro" series), complete with battery modules and solar panel kits. The RPPL-12-36-30 (for use in the red and dark orange areas of the map) uses a 30W solar panel and 36 Ah batteries, while the RPST-12-100-60 (for use in the yellow and light orange areas of the map) uses a 60W solar panel and 100 Ah batteries (which may be overkill, but the Hub should never run out of battery power).
You can purchase these items from Streakwave. If there's sufficient interest, we may start selling and supporting them ourselves.
Note that these systems are meant to be mounted on a sturdy pole because of the wind loading on the solar panels. If you use a wind turbine, of course, you'll want to use a very sturdy mount.
This is an "Engineering Note" we wrote on this topic, with a lot of information about how to do it. Please feel free to comment on it here or to firstname.lastname@example.org.