Calculating rafter size with purlin bracing
I like your drawing/sketch. Even I understand how you propose to add the "steeper" roof pitch. I even see how you plan to lap the joists at the interior "support" and fasten to the existing roof structure...nice touch. 

Unless you plan on using one of those super heavy "concrete" roof tiles that weighs more than 8 lbs. per square foot, 2x8's at 24" oc or 2x6's at 16" oc. (Grade: standard and better) will support a Dead Load of 15 psf plus a Live Load of 15 psf.