***** NOT A TEACHER *****
Hello, Bokkie:
Thanks for the thought-provoking question that prevented me from getting much sleep last night.
1. To me, there seems to be a definite difference between "a" and "b." But I am unable to articulate (explain) that difference.
a. "The coastal mountain ranges partly control California's weather." -- ENCYCLOPEDIA OF CALIFORNIA (1999).
b. "The television spots [commercials] emphasize the paradise-like qualities of California weather immortalized by the Beach Boys." -- CRITICAL PEDAGOGIES (2009)
*****
2. I found three quotations that may interest you.
c. "The show closed early because Jolson didn't like New York's weather anymore and wanted to return to Los Angeles." -- NO LEGS, NO JOKES (2008).
d. "I left Southern California without giving any thought to what New York weather might be like." -- TELL ME NO (2010).
e. "Hating the New York weather, Grove decided to move to California." -- ICONS OF BUSINESS (2007).
(All of these books were accessed through the "books" section of Google, where thousands of books have been digitalized for our use. It's a good way to see how professional writers use the language. Simply type in "New York's weather" (use the quotation marks!), and you'll be given many example sentences. Then do the same for "New York weather.")