1. A method of detecting a tsunami by using a global positioning system (GPS), comprising the steps of: (a) distributing a plurality of GPS receivers over a sea surface in a target area; (b) transmitting a plurality of first signals from GPS satellites through an ionosphere above the target area to each of the plurality of GPS receivers such that each of the plurality of GPS receivers has a coordinate generated respectively by each of the plurality of GPS receivers, and transmitting a plurality of second signals and the coordinates of the plurality of GPS receivers to a computer; (c) processing the second signals to acquire a real-time monitoring data indicating a distribution of electrons in a portion of the ionosphere disposed above the target area; and (d) determining an occurrence of the tsunami by identifying a perturbation of electron density caused by the tsunami based on the distribution of the electrons provided by the real-time monitoring data.