Carport using unusual construction method

I looked that pitch up.
If I'm correct in understanding the charts, that may be less than the minimum suggested for shingles. Or at least, right on the edge.
That was my concern when I asked.
IF that is the case and you change, I would suggest modified bitumen.
Also if the new roof abuts the house siding, consider the effects of splashing rain on the siding.
Thanks, adriver! You are right about the pitch. It's only about half the pitch that shingle manufacturers recommend. I really appreciate that you pointed this out. I am going to have to add a Grace Ice and Water Shield underlayment (or the equivalent) on the roof sheathing, before laying down the tarpaper.

My shop next to the carport has Hardiboard lapped siding, which is a masonry product and quite resistant to rot. I have caulked all the Hardiboard overlaps thoroughly with DAP "Custom Flexible Patch" elastomeric patching compound, which is the caulk that Hardiboard recommends. I really like the Hardiboard, even though it is a bit difficult to work with, and it has been really waterproof after painting and caulking with the elastomeric patching compound. No leaks whatsoever inside the barn from driving rain.