The Rome "Allegory of Water" is part of a series of the elements which Jan Brueghel painted between 1606-1611. The series currently resides in the Galleria Doria Pamphilj. See also:

• Allegory of Earth (Rome)
• Allegory of Air (Rome)
• Allegory of Fire: Venus in the Forge of Vulcan (Rome)

Many copies all over the place, again; Ertz lists only "better" ones but there are also ones in Burghley House, Slot Neues Palais in Potsdam, one recently art market in Paris, Saltram House... These include a number of pretty distant variants.
Autograph variant sold Sotheby's London 8.vii.99 #53 with pendant Air; this is now Ertz #498.
Apparently independent copies (not in series) are about evenly balanced between Doria Pamphilj and Lyons versions, at least, there are a lot of each. What there are not are independent copies of the Ambrosiana version.
NB that doing elements as pendants rather than series--"Earth and Water" as one and then "Fire and Air" as another--seems to have been Jan the Younger's idea. there are lots of these, again in lots of versions--but not by Jan the Elder. There is however one version that is so much better than all the others that it seems to represent a genuine link to Jan the Elder's ideas. It isn't anywhere in Ertz. It's in the Uffizi, Photo RKD.
Ertz now accepts 2 "double element" paintings in Potsdam as Jan the Elder; I would not agree with this.
Many copies and variants in the RKD and Witt Library that are listed under the other Allegory of Water paintings.