Double Dipping: The two mikva'os used by the Kohen Gadol on Yom Kippur

During the service of Yom Kippur the Kohen Gadol immersed in two different mikva'os a total of five times. The first of these was done in a mikveh located above the Water Gate on the southern side of the Temple. The remaining four immersions were done in a mikveh built on the roof of the Chamber of Parvah in the southeast corner of the Courtyard.

The Ma'ayan Mikveh
Both mikva'os were fed from the Eitam Spring, apparently for the purpose of granting them the halachic status of a ma'ayan [flowing spring], as opposed to a mikveh of collected rainwater.

Not being an expert on the laws of mikveh, I consulted with my rav about this question. I was told that, while the laws are somewhat complex, the basic idea is that whenever a mikveh is directly connected to a spring (even through a system of pipes) it assumes the status of a ma'ayan. In the case of the mikva'os used by the Kohen Gadol, this would mean that as soon as the system of pipes bringing the water from the Eitam Spring was closed, which was necessary for the inverted siphon principle to work (as discussed in the last post), a direct connection between spring and mikveh was formed, granting them the status of a ma'ayan. After Yom Kippur the system was opened and the direct connection was broken, so although spring water remained within each mikveh, this water no longer possessed ma'ayan status. The following year the system would be closed once again and the mikva'os would regain their status of a ma'ayan.

Two Levels of Sanctity
These two mikva'os had different levels of sanctity. As a general rule, one is required to immerse prior to entering the Courtyard, and the Kohen Gadol would therefore perform his first immersion of Yom Kippur in a mikveh located just outside the Courtyard. For this reason, the mikveh above the Water Gate was not imbued with the higher sanctity of the Courtyard but rather the lesser sanctity of the Temple Mount. The four immersions performed during the course of the Yom Kippur service were required to be done within the Courtyard and for this reason the mikveh above the Chamber of Parvah possessed the sanctity of the Courtyard.

According to Tosafos
At issue is how this latter mikveh could have possessed Courtyard sanctity since the Gemara (Pesachim 85b) writes that "upper levels and roofs [of Courtyard chambers] do not possess sanctity." Tosafos (Yoma 31a) provide one solution: The Chamber of Parvah was an underground room and the floor of the Courtyard formed its roof, thus the mikveh was now in the Courtyard proper. Now, we know that the only way to access the mikveh above the Chamber of Parvah was via a stairwell in the adjacent Chamber of Rinsers, and Tosafos are forced to conclude that it, too, was underground. The arrangement would look something like this:

Cross-section of the southeast corner of the Courtyard (looking south).
Arrangement of the three chambers according to Tosafos.

Tosafos go on to cite the Gemara (ibid.) that underground chambers, like upper levels and roofs, also do not possess Courtyard sanctity. However, this is only true when the underground area opens to the Temple Mount, but when it can be accessed directly from the Courtyard then it does possess Courtyard sanctity. This is an important point here because otherwise, the mikveh above Parvah – while physically located in the Courtyard – would have been considered "outside" the Courtyard since the only access to it is via the underground Chamber of Rinsers. However, since this chamber is accessed via the Courtyard it, too, is considered part of the Courtyard even though it is underground. As a result, the mikveh above Parvah is also granted Courtyard sanctity since it is accessed via a room which (we now know) has Courtyard sanctity as well.

According to Tiferes Yisrael
The Mishnah (Middos 5:3) states that the three chambers under discussion here were [physically] "in the Courtyard" yet according to Tosafos only one of these chambers was actually "in" the Courtyard – the other two were underground! To put that Mishnah back to rights, Tiferes Yisrael (ad loc.) brings Parvah and Rinsers above the ground.

Arrangement of the three southern chambers according to Tiferes Yisrael

As for the original question of how the mikveh can have Courtyard sanctity if it is built on the roof, Tosafos' same logic can be applied: since the only way to access the mikveh is via Rinsers, and Rinsers opens to the Courtyard, then the mikveh assumes Courtyard sanctity even though it is on the roof.