According to Kinjo Akio and Tokashiki Iken, the kata “Rohai” originated from Monk Fist boxing or Lohan Quan. The pronunciation of “Lohan” then became Okinawanized to “Rohai” (ローハイ). When Rohai kata was transplanted to Okinawa is unknown. That said Gohakukai founder Tokashiki Iken states in “Karate-do & Kobudo: A basic investigative report” (pg. 74 to 84) that the Rohai he learned was taught by Matsumora Kosaku (1829-1898) to Iha Kodatsu (1873-1928) and finally inherited by Nakasone Seiyu (1893-1983). He comments that there are ryu-ha (流派）or styles and their off-shoots which use the kanji “Rohai” (鷺牌; heron – sign), but it is uncertain whether these kanji are either ateji (当て字) (Chinese characters selected to fit the pronunciation in question with little nor no bearing on the meaning of the kata) or have some relation with the originator of this kata.
That said, let’s take a closer look at the Rohai passed down to Tokashiki Iken sensei. This performance of Rohai is by Tokashiki Tadao senei at Kinjo sensei’s 40th Anniversary Demonstration of teaching Gohakukai in Canada in May of 2013. Enjoy.