How would missile defense systems work against North Korea?

(CNN)If North Korea fires a missile at a US target or ally, there are a number of defense systems that could shoot it down.

The first piece of the controversial THAAD missile defense system arrived in South Korea Monday night, hours after North Korea test-fired four ballistic missiles into the Sea of Japan, also known as the East Sea.
The Patriot and Aegis systems are already deployed in the Pacific region.
    THAAD, the Terminal High Altitude Area Defense system, can shoot down short- and medium-range ballistic missiles in the latter stages of their flight as they plunge toward their targets.
    But its presence in South Korea might be just as important for its sophisticated radar -- the AN/TPY-2 X-Band radar -- which could provide the first warning of any missile launched from North Korea.

    Why does that matter?

    The missiles that North Korea fired Monday were thought to be of longer range, designed for targets beyond South Korea. That would put THAAD interceptors out of range.
    But by being closer to North Korea, THAAD's radar could provide critical early tracking data to missile interception systems farther afield, such as those protecting Japan or US bases in Guam, according to data from the Pentagon's Missile Defense Agency.
    Those other protection systems, including the Aegis and Patriot missile defense systems, are linked to THAAD by the US military's Command and Control, Battle Management and Communications system, known as C2BMC, according to contractor Lockheed Martin.

    Could it have detected the most recent missiles?

    The THAAD battery's radar in South Korea would have detected the launch of the North Korean missiles launched on Monday. Determining the missiles were not targeting South Korea, the THAAD battery would send radar tracking data to US Navy warships equipped with the Aegis missile defense system sailing between South Korea and Japan.
    The Aegis ships would combine data from THAAD's radar with information from their own AN/SPY-1 radar to track and fire interceptors at the enemy missiles midflight, US military documents show.
    USS Monterey launches an interceptor missile during a live-fire test of the Aegis weapons systems.
    If Aegis interceptors were unable to make the intercept, data from both the Aegis radar and the THAAD radar could be transmitted via the C2BMC system to Patriot missile batteries, which a