A semi-submersible drilling vessel has a deckbox structure, one or more pontoons, and multiple support columns extending upward from the one or more pontoons and supporting thereon the deckbox structure. An annular riser joints storage caisson extends downwardly from the deckbox structure, wherein the storage caisson delimits an annular storage space configured for storage therein of an annular array of riser joints in vertical orientation thereof. A riser joints carousel device is provided in the annular storage space, which riser joints carousel device is configured to carry an annular array of riser joints in vertical orientation thereof in a mobile manner relative to the annular storage caisson so that the array of riser joints is movable along an annular path through the storage spaced between the inner and outer wall of the storage caisson. The deckbox structure is provided with a riser joint transfer passage at a riser joint transfer location above the annular path of the riser joints carried by the riser joints carousel device through the storage space. The vessel is provided with a riser joint vertical transfer device configured to lift and lower a riser joint out of and into the riser joints carousel device, passing therein vertically through the riser joint transfer passage of the deckbox structure.