Coarse mulch will let water and oxygen through easier than fine mulch. It won't hold back as much rainfall or dew as fine mulch would (on the theory that fine mulch can act like a sponge, but coarse mulch acts more like coarse gravel).
I never read that coarse mulch might allow more evaporation than fine mulch, but it seems reasonable that a thin layer of coarse mulch must let humidity escape faster than the same thickness of fine mulch.
>> We normally have 35 to 45 inches of rain from November through March or April. In a dry year, we get about 25 inches. This year, so far, we have only gotten 1.25 inches. Doesn't look good.
Good luck! Maybe 5 years ago I drove through Tulare County, and it was worse than desert. It looked like land that had been irrigated ten years previously, but had not had a drop since then.