Storage of fresh vegetables

In the past I tried laying carrots in between layers of sawdust. In a lidded bucket then kept in the shed. It didn’t go well for me. I think because my shed had a tin roof so temperature fluctuated to much. Personally I’d just leave them in your cupboard or where ever you normally store them. They all last quite well. I also find if they start going a bit soft. Stick them in a glass or jug of water to rehydrate. I’d be tempted to dehydrate some of the carrots & parsnips as you have so many.