AVP: Alien vs. Predator

In 2004, a satellite detects a mysterious heat bloom beneath BouvetÃ¸ya, an island about one thousand miles off the coast of Antarctica. Wealthy industrialist Charles Bishop Weyland (Lance Henriksen) discovers through thermal imaging that there is a pyramid buried 2000 feet beneath the ice. He attempts to claim it for his multinational communications company, Weyland Industries, a subsidiary of the Weyland Corporation, and assembles a team of experts to investigate. The team includes archaeologists, linguistic experts, drillers, mercenaries, and a guide named Alexa Woods (Sanaa Lathan).
As a Predator ship reaches Earth's orbit, it fires a beam that creates a passage through the ice towards the source of the heat bloom. When the team arrives at the abandoned whaling station above the heat source, they find the passage and descend beneath the ice. They locate the mysterious pyramid and begin to explore it, finding evidence of a prehistoric civilization and what appears to be a sacrificial chamber filled with human skeletons with ruptured rib cages.
Meanwhile, three Predators arrive and kill all the humans on the surface. They make their way down to the pyramid and arrive just as the team unwittingly activates the structure. The Alien Queen awakes from cryogenic stasis and begins to produce eggs. When the eggs hatch, several facehuggers attach themselves to humans trapped in the sacrificial chamber. Chestbursters emerge from the humans and quickly grow into adult Aliens. Conflict erupts between the Predators, Aliens, and humans, resulting in several deaths. Two Predators are killed by an Alien, and Weyland is killed by the remaining Predator, while allowing Alexa and archaeologist Sebastian De Rosa (Raoul Bova) enough time to escape. The two witness the Predator kill a facehugger and an Alien with a shuriken before unmasking and marking himself with the blood of the facehugger. After Alexa and Sebastian leave, another facehugger attaches itself to the unmasked Predator.
Through translation of the pyramid's hieroglyphs, Alexa and Sebastian learn that the Predators have been visiting Earth for thousands of years. It was they who taught early human civilizations how to build pyramids, and were worshiped as gods. Every 100 years they would visit Earth to take part in a rite of passage in which several humans would sacrifice themselves as hosts for the Aliens, creating the "ultimate prey" for the Predators to hunt. If overwhelmed, the Predators would activate a self-destruct device to eliminate the Aliens and themselves. The two deduce that this is why the current Predators are at the pyramid, and that the heat bloom was to attract humans for the sole purpose of making new Aliens to hunt.
Alexa and Sebastian decide that the Predators must be allowed to succeed in their hunt so that the Aliens "do not reach the surface". Unfortunately, Sebastian is captured by an Alien, leaving only Alexa and the Predator to fight against the Aliens. The two form an alliance and use a self-destruct device to destroy the pyramid and the remaining Aliens. Alexa and Scar reach the surface, where they battle the Alien Queen. They defeat the Queen by attaching its chain to a water tower and pushing her over a cliff, dragging the Queen to the ocean floor. Scar, however, is impaled through the torso by the Alien Queen's tail and succumbs to his wounds and dies.
A Predator ship uncloaks and several Predators appear. They retrieve their fallen comrade and an elite Predator presents Alexa with one of their spear weapons in recognition of her skill as a warrior. As the Predators retreat into space, a chestburster with a hybrid form of an Alien and a Predator erupts from Scar's chest, beginning the events of Aliens vs. Predator: Requiem.

Question: Where does Alexa and Scar battle the alien queen?
Answer: surface