William Scarborough points out that this plane used to be 13-P-12. In another photo on that page, he implies that 13-P-15 is "an unusually high aircraft number". Indeed, a squadron was typically assigned 12 PBYs.
The Navy decided in mid-1938(?) that, by increasing squadron strength to 15 planes, patrol coverage could be extended using the existing Patrol Squadrons, rather than adding the overhead of new squadrons.
VP-13 (formerly VP-18) was based at Pearl Harbor, having arrived in mid-September, 1939 - about the same time VP-21 (formerly VP-1) flew its PBY-4s to their new base at Cavite, Luzon, Philippines. VP-13 became VP-26 on 1939-Dec-11 and, six months later, flew its freshly-overhauled PBY-4s to the Philippines to trade planes with VP-21, then flew the other's tired planes back to Pearl Harbor for overhaul. By 1940-Dec-16, VP-26 had returned to Cavite with the overhauled planes, joining VP-21 to form a new Patrol Wing - PatWing-10. Accordingly, VP-21 was redesignated VP-101, and VP-26 became VP-102.
Since the squadron insignia dates this photo after VP-13's TransPac to Hawaii, a remote possibility is that this plane used to be 21-P-12.
PBY Catalina In Action p20
(Photo from the R.L.Lawson collection, courtesy of the Nat'l Museum of Naval Aviation)