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Why does ATC use data coming from an aircraft itself instead of using the readings from the airport radar?

Also could Aeroperú 603 have been saved if the pilots had ignored the pitot static altitude and instead listened to the "Altitude Too Low" warning that came directly from the Radar Altitude system (i.e. one that works by using radio waves to determine the altitude)?

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    $\begingroup$ You seem to have two different questions here: why does ATC rely on data transmitted by aircraft rather than on data from ground-based radar; and could the crew have used their onboard radar altimeter as a substitute for their pitot-static system? Please try to ask one question at a time, as far as possible, it helps to get better answers. $\endgroup$ – Pondlife Nov 12 '17 at 15:23
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The altitude data on ATC screens comes from the static system of the aircraft, because that is the only sufficiently precise source. The area primary radar is, at long range, only accurate to maybe a mile and that applies to vertical position too. For horizontal position when the separation is 5 nautical miles this is good enough. But the vertical separation is 1,000 ft and the radar simply can't distinguish that. So the aircraft transmit their altitude in the Mode C and Mode S (ADS-B) and that is used for altitude display.

Also, the on-board instruments measure barometric altitude and that is what aircraft are instructed to fly. But a precise radar can only measure geometric altitude, which due to changing atmospheric condition is different, so it wouldn't help anyway.

In future, the position data will more and more be also obtained from the aircraft. The ADS-B broadcasts GPS position and this is more precise than the primary radar and is available even over open sea where primary radar coverage is not possible. Therefore newer systems depend on what the aircraft itself reports more, not less.

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