The first thing I did in the Flickr Commons was to search for "Japan".
Besides the Waseda University baseballers, this one jumped out at me from the Library of Congress:
Now, I've been through a few bad typhoons in Tokyo, but that's ridiculous. I thought it would be easy to identify a devastating typhoon within the Bain photo range, and maybe even figure out where the Meiji was tied up.
It was easy to figure out where Meiji's homeport was. She was built in 1874, and by the 1910s served as a training vessel, tied up at the (predecessor to) the Tokyo University of Marine Science and Technology at the mouth of the Sumida River. With a storm coming, it's probably safe to assume they had her there.
Dating the photo has been more difficult. I suppose not all research leads to a tidy ending. My best guess was October, 1917, based on descriptions of other damage to the Meiji and the magnitude of damage in Tokyo Bay. A history of the ship on the marine science university's site mentions that the bowsprit was broken in 1917 during the typhoon.
Unfortunately the Library of Congress photo is of is the aft, so that's not helpful.
This also contradicted the 1912 date given in another typhoon photo by a commenter, and was outside of LC's stated range of 1910-1915. So I went back to the search engines.
It seems that the 1910s were a bad decade for typhoons in Japan, despite Wikipedia's lonely mention of 1917. 1910, 1911, and 1914 were each mentioned by different sources as having bad typhoons. The 1912 typhoon that hit Osaka apparently did not affect Tokyo much, so I've dismissed that date.
I'm left wondering if LC has the right date range for this photo - there are occasional mistakes in the Bain caption cards. 1917 still seems like the most likely candidate, with a storm surge that was so huge that it is referred to as a tsunami (that's a tidal wave, caused by an earthquake not a storm). It would take something significant to lift all of the ships up onto land - Meiji Maru's is one of several in the Bain collection.
Sources strongly supporting 1917:
The Great Tsunami of Taisho Year 6, part of the series "Fighting Disaster". Includes an excerpt from a paper describing a ship up against JR Tsudanuma station in the 1917 typhoon, which like the maritime academy is on the north shore of Tokyo Bay.
Missionary Review of the World, which discusses the damage to St. Luke's Hospital in the 1917 typhoon. St. Luke's is on the other side of Tsukishima at the mouth of the Sumida River from the maritime academy where the Meiji Maru was docked.
List of major natural disasters in history mentions the 1917 typhoon but no other for the 1910s in the Tokyo area.
Sources listing 1917 as well as other years:
Review of photo collection held by Tokyo Fire Department. Singles out 1917 but also mentions August 1910 and July 1911 as particularly bad storms.
History of Tama River.
Another list of major natural disasters includes 1911 and 1914 as well as 1917 for the Tokyo area.