This tradition is much older than a modern liturgy, however:
Chronicon Paschale (PG 92, column 545): Ἐγεννήθη Χοιὰχ κη' ὥρᾳ ζ' τῆς νυκτός. ἐβαπτίσθη Τυβὶ ια' ὥρᾳ ι' τῆς ἡμέρας ὑπὸ Ἰωάννου ἐν τῷ Ἰορδάνῃ ποταμῷ, καὶ ὁ Ἰορδάνης ἀνεπόδισεν εἰς τὰ ὀπίσω. εἴπεν δὲ ὁ κύριος τῷ Ἰωάννῃ· «Εἴπον τῷ Ἰορδάνῃ· ‹Στῆθι· ὁ κύριος ἦλθεν πρὸς ἡμᾶς.›» καὶ εὐθέως ἔστησαν τὰ ὕδατα. / He was born on the twenty-eighth of Choiac at the seventh hour of the night. He was baptized on the eleventh of Tubi at the tenth hour of the day by John in the Jordan river, and the Jordan stepped backward. And the Lord said to John, "Say to the Jordan, 'Stand; the Lord has come toward us.'" And immediately the waters stood.
Itinerary of the Piacenza Pilgrim 11: 11 I observed Epiphany at the Jordan, where so many miracles occur on that night, in that place where the Lord was baptized [ubi baptizatus est dominus]. An obelisk was erected there, hidden by a screen; in that place, where the water turned back in its channel [ubi aqua rediit in alueo suo], a wooden cross is set in the water and steps go down into the water on both sides, made of marble. Great vigils are held on the eve of Epiphany, with a great many people. At the fourth or fifth cock crow morning services are held. When the morning services have been completed, at dawn the ministers come forth; with the deacons standing by, the bishop goes down into the river and at the very moment that he begins to bless the water, right away the Jordan turns back on itself with a roar and the water stands still until the baptisms are accomplished. And all the Alexandrian shipwrights have their staff there on that day, with jars full of spices and balms, and at the very moment when he has blessed the spring, before they have begun to baptize, they pour out all those jars into the river and take from there blessed water and use it to sprinkle water onto their ships before they are put to sea. When the baptisms are completed they all go down into the river for a blessing, dressed in linen and many other types of fabric which they will keep to be buried in. When the baptisms are done, the water returns to its natural place. And the Jordan flows from the Sea of Tiberias to the Dead Sea, where it ends, 130 miles more or less. [Link: http://andrewjacobs.org/translations/pi ... lgrim.html.]
Isho'dad of Merv and Dionysius bar Salibi both apparently reflect this same tradition:
Isho‛dad: „And immediately, as the Diatessaron attests, there shone a mighty light, and over the Jordan hung bright clouds… and the Jordan stopped its course during which time its waters did not move.” (nach Winkler, Appearance [s. Anm. 47], 311).
Dionysius bar Salibi: „And immediately, as the Gospel of Diatessaron testifies, a mighty light flashed upon the Jordan and the river was girdled with white clouds… and the Jordan stood still from its flowing, though its waters were not troubled.” (nach Winkler, Appearance [s. Anm. 47], 312).
[Link: https://www.academia.edu/35530729/_Der_ ... esdienstes.]
Some of the exact imagery seems to derive from one of the psalms:
1 When Israel went forth from Egypt,
The house of Jacob from a people of strange language,
2 Judah became His sanctuary,
Israel, His dominion.
3 The sea looked and fled [ἡ θάλασσα εἶδεν καὶ ἔφυγεν];
The Jordan turned backward [ὁ Ιορδάνης ἐστράφη εἰς τὰ ὀπίσω].
4 The mountains skipped like rams,
The hills, like lambs.
5 What ails you, O sea, that you flee?
O Jordan, that you turn back?
6 O mountains, that you skip like rams?
O hills, like lambs?
7 Tremble, O earth, before the Lord,
Before the God of Jacob,
8 Who turned the rock into a pool of water,
The flint into a fountain of water.
Besides just the general interest that this tradition offers (as sort of a sister tradition to the light or fire which supposedly shone at the baptism in some traditions), it also betokens yet another conscious connection between the figures of Jesus and Joshua.
Ben.