I lived in a somewhat more moderate part of CA, but we still had super hot summers and sometimes pretty cold winters, so while I don't have a lot of specifics on the root cellar/crawl space per se, I know the climate enough to make a couple points to consider.
1. Humidity: we had stuff dehydrate effortlessly and quickly, just sitting on tables indoors. For produce storage in a ventilated crawl space, you will have to somehow manage the humidity to keep everything from drying out (unless that is what you want). This might be something that can be managed with an enclosure and some evaporative set up, but it is something you will want to keep an eye on.
2. Pests: this is probably already being considered, but cool sheltered places were very attractive to small pests. This is true everywhere, but I remember that while other parts of the country were a free for all of insect and rodent life, the tough survived in CA and I didn't want to mess with them
especially unexpectedly in a dark place.
This might be something a metal locker can address, or a repurposed file cabinet or something like that, and there will be other better info on that (construction) aspect, but I thought I'd just mention those things from my lived experience in the climate.
On a positive note, you can really take advantage of the dry climate to preserve a lot of things with dehydration! Strings of peppers and fruits and tomatoes etc can hold well in a small place and just naturally desiccate with a little attention and air circulation!
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