What and Where is the Kidron Valley?

The Kidron Valley, which separates the Temple Mount from the Mount of Olives is one of those historical places you can just walk past without even knowing you did.

You'll walk along it along the eastern side of the Temple Mount, and have to cross it in order to get to the Garden of Gethsemane and Dominus Flevit, among other things. But the sign explaining it is down in the cemetery.

Back in the day of David, the upper part of this valley was known as the King's Garden, or the King's Valley, and David ran through it when he fled Absolam. 

It's also believed that King Jehoshaphat overthrew Israel's enemies in 2 Chronicles 26 there, and in 2 Chronicles 29-31, as the Levites carried out Hezekiah's instructions to purify the Temple and tossed unclean items into the valley.

Jesus and His disciples would have crossed this valley whenever they entered or left Jerusalem and travelled to Bethany, and of course, when going to/from the Garden of Gethsemane (John 18). 

It's also mentioned one more time in the Old Testament the Valley of Jehoshaphat, the word "Jehoshaphat" means "God has Judged", and according to Joel 3:

“In those days and at that time,

    when I restore the fortunes of Judah and Jerusalem,

2 

I will gather all nations

    and bring them down to the Valley of Jehoshaphat.[b]

There I will put them on trial

    for what they did to my inheritance, my people Israel,

because they scattered my people among the nations

    and divided up my land" (verses 1-2)

In the spring, the Kidron river runs through here, and the grass is green. It's beautiful to see! But this is how it looks in the heat of July:

It also holds Jerusalem's oldest cemetery. You can see Absolam's pillar in the distance. Further down there are caves dating to the 9th and 7th centuries B.C. 

Until it connects with the Hinnom Valley and travels out to the Dead Sea. But that's a post for another day!

Here's my question for now: In Zechariah 14, the prophecy of Jesus' second coming is that His feet will stand on the Mount of Olives, which will split in two. Water will flow towards the east and west, into the Mediterranean and into the Dead Sea, which will come back to life. 

If this is a river valley (though very dry when I took these pictures), and it leads to the Dead Sea, is this the route the eastbound river will take?