If you google "global warming and drought" what you will find is that science has found that some droughts have clear global warming fingerprints and some don't. The most famous connection is between the terrible droughts in Syria/Iraq  that preceded the Syrian Civil War and climate change-induced alterations in rainfall patterns. 

https://climateandsecurity.org/2014/03/26/review-two-new-studies-on-syria-drought-climate-change-natural-resource-management-and-the-uprising/

But by focusing solely on drought, though, you're missing the larger picture of impacts, especially those that relate to the different kinds of droughts and the secondary impacts of higher temperatures. Here's an indepth study from the National Climate Assessment of global warming impacts in the PNW that might address some of your concerns.

http://nca2014.globalchange.gov/report/regions/northwest