That is a very good question, Shlomo. The pictures of the Mikdash that Acharonim of previous generations drew (Tosfos Yom Tov, Tiferes Yisrael etc.) do not include conjectures as the location of the Amas ha'Mayim. Here is what I could put together.

(a) The Amah ran through the Azarah, according to Rashi here and many other Rishonim. This is evidenced by the fact that runoff of blood from the Mizbe'ach would drain into the Amah (Midos 3:2).

The Amah exited the Azarah and fell into the surrounding Kidron valley (ibid.). It may have left the Azarah through the Sha'ar ha'Mayim on the Southern side of the Azarah, according to the reading of the Vilna Gaon (Midos 2:6). The Gaon sees in that Mishnah that this gate was called "Water Gate" (n.p.i.) in part because water trickled under it out of or into the Azarah (see also Tiferes Yisrael there).

It is not clear from the sources where the Amah entered the Azarah. Current experts claim that the water must have flowed to the Azarah through aqueducts beginning in an area some 40 km. away from Yerushalayim known as Solomon's Pools. They even point to a hole in the wall of the Old City (not far from Dung Gate) through which the flow entered the city in raised lead pipes. (Tosfos Rid in Eruvin 104a writes, based on a Yerushalmi, that the source of the Amas ha'Mayim was Ein Einim.)

It is also not clear through how much of the Amah flowed.

(b) Drainage channels was generally underground, beneath (and outside of) the Har Habayis complex. It is certainly possible that the Amah too was below ground and only parts of it were exposed so that birds that were disqualified from Korbanos (Zevachim 8:8, Temurah 7:6), or spilt embers (Tamid 5:5), could be shoveled into it.

We do find that the Kiyor was lowered into an underground "pit" (Yoma 37a) of water, but that seems to have been a pit of runoff water from the Azarah (as the Tosfos Rid writes in Eruvin 104a) and not the Amas ha'Mayim. Some archeaological research has been done regarding underground tunnels or cisterns in the Har ha'Bayis complex (which take up a large area to the south of where we would expect the Azarah to be), but nothing conclusive has been found yet.

(c) An "Amah" is given that name because the dimensions of man-made water channels were normally an Amah wide and an Amah deep (Rashi Bava Kama 50b).

However, that does not mean that these were the dimensions of the Amah in the Azarah. Any water channel was called "Amah", even if it was larger or smaller than an Amah, since the standard size for water channels was an Amah (Rashba Bava Basra 99b; see Tosfos there). As mentioned above, the Amas ha'Mayim of the Azarah may have been underground altogether, and so it was much deeper than an Amah.

Best regards,

Mordecai Kornfeld

Kollel Iyun Hadaf