Madai Stayed Behind
Madai was a son of Japheth, who was one of the three sons of Noah. Madai is linked to the Medes whose capital was Ecbatana (moderm Hamadan), at the base of Alvand mountain.
The original land allotments after the flood were generally Japheth got the north (Turkey), Shem the middle, and Ham the south (Egypt). It should be noted that Media and the mountains of Ararat were considered apart of Shem's middle allotment. This supports Alvand or other mountain in the Iranian Zagros Mountains. Mt. Ararat in Turkey would have been considered apart of Japheth's northern allotment, so should not be considered the mountains of Ararat location mentioned in the Bible. Noah's Ark landed in what would become Shem's middle region.
In Jubilees 10:35, Madai, one of Japheth’s sons, declines his original land inheritance in the north (west of his brothers Gomer and Magog, which would be west of Turkey and the Black Sea) and chooses to stay behind in the land of Shem. This clue is so important regarding the location of the mountain where Noah’s Ark landed, it is worth repeating... Madai stayed behind with Shem’s family.
See map above, where it seems that Madai and Lud must have swapped land allotments. Why else would you have most of Japheth's sons located in modern Turkey except for Lud (son of Shem) stuck in the middle of them? Madai stayed near Noah and Shem, in particular Shem's son Arpachshad, near the mountain where Noah's Ark landed.
This negotiated arrangement eventually became the Medes and Persians or Medo-Persians. It was the combining of the families of Shem and Japheth, in particular Arpachshad’s sister marrying Madai.
Jubilees 7:14-17 describes how Shem built a city close to Noah on the mountain. Noah and Shem stayed on or near Lubar, one of the mountains of Ararat, where the Ark landed.
So, if Madai stayed behind with Shem’s family, and Shem stayed on the mountain close to Noah... it would stand to reason that Madai lived near the mountain where the Ark landed.
It is interesting that there is a claim of Shem's tomb near the summit of Alvand. There are pieces of red clay bricks inside the tomb area. The size is around 8 wide feet by 18 feet long, which seems rather large.
According to the Book of Jubilees:
5:28 “And the ark went and rested on the top of Lubar, one of the mountains of Ararat”
7:16 ”And Shem dwelt with his father Noah, and he built a city close to his father on the mountain”
10:15 “And Noah slept with his fathers, and was buried on Mount Lubar in the land of Ararat”
More clues that support Alvand mountain as the location where Noah's Ark landed.