There were two types of willow.
(Leviticus 23:40; Job 40:22; Isaiah 15:7; 44:3-4; Psalm 137:1-2). This was supposed to be the weeping willow, called by Linnaeus Salix Babylonica, from the reference in Psalm 137. This tree is frequently found “on the coast, overhanging wells and pools. There is a conspicuous tree of this species over a pond in the plain of Acre, and others on the Phoenician plain.” There are several species of the salix in Israel, but it is not indigenous to Babylonia, nor was it cultivated there. Some are of opinion that the tree intended is the tamarisk or poplar.
(Ezek. 17:5), called by the Arabs the safsaf, the general name for the willow. This may be the Salix Aegyptica of naturalists.
Tristram thinks that by the “willow by the water-courses,” the Nerium oleander, the rose-bay oleander, is meant. He says,
“It fringes the Upper Jordan, dipping its wavy crown of red into the spray in the rapids under Hermon, and is nutured by the oozy marshes in the Lower Jordan nearly as far as to Jericho… On the Arnon, on the Jabbok, and the Yarmuk it forms a continuous fringe. In many of the streams of Moab it forms a complete screen, which the sun's rays can never penetrate to evaporate the precious moisture. The wild boar lies safely ensconced under its impervious cover.” —Henry Baker Tristram, The Natural History of the Bible