Beautiful Nature Reserve in Israel. Ayun River is a perennial stream and a tributary of the Jordan River. The stream originates from two springs in the Marjayoun valley in southern Lebanon, runs southward for seven kilometers through various irrigation ditches, then flows into Israel near Metulla, where it continues through the Hula Valley in the Galilee Panhandle until emptying in the Hasbani River just before it reaches the Jordan River.