Was watching this old movie from 1957 staring Alan Ladd and Sophia Loren (her American film debut) and was surprised when I saw the SUP in the background!
Here is a link to surf reasearch www.surfresearch.com.au/0000h_SurfSki.html
About half way down there Is a photo from 1937 and an an explanation I pasted the text
below, sorry I can't post the photo, damn iPad
Interestingly, the nose leash, now affixed to the paddle, continued to be used into the 1940s before disappearing with the construction of longer and narrower skis more suitable for SLSC competition.
Initially paddled and ridden sitting on the board, in the hands of skilled riders the skis enjoyed a short period of popularity ridden standing up, possibly at the time rivalling surfboards in populatity.
The riding of surf skis while standing probably faded as skis established a rescue and a racing role for the SLSC and as surfboard builders moved over to a similar hollow construction that was vastly more bouyant than the solid timber surfboard designs.