The phrase "approaches the surface" is correct and usable in written English.
It can be used in contexts where something is moving closer to or nearing the surface of a medium, such as water or a physical object.
Example: "As the submarine approaches the surface, the crew prepares for their ascent."
Alternatives: "nears the surface" or "draws near to the surface".
The pressure drops as the boiling water approaches the surface, causing it to flash into steam.
"But as the diver approaches the surface, the decreasing water pressure causes a drop in pressure of the oxygen in the brain.
As a submarine approaches the surface, the officers can sweep the horizon through the submarine's periscope, and in favorable conditions can see a ship six to eight miles away.
All arteries have a pulse, but it is most easily felt at points where the vessel approaches the surface of the body.
Even a big school such as this behaves as if it were one organism, with a roughly spherical shape that is flattened when the school comes into shallow waters or approaches the surface.
This change is enough to threaten cold-water coral communities, and some scientists fear that additional communities will be placed at risk if the boundary approaches the surface of the ocean.
Others live deeper and do not approach the surface.
Gravity anomalies are low over thick sedimentary layers and high when denser rocks approach the surface.
Their energy is spent in crossing that great submerged highland east of Cape Cod known as Georges Bank, the crests of whose highest hills approach the surface at the Cultivator Shoals.
Images taken by the spacecraft as it approached the surface showed one large crater, 500 feet wide, and a smattering of small ones.
As diapirs first rise through the planet's interior and approach the surface, they can lift the rocks above them, fracturing the surface in a radial pattern.
