More and more earthquake early warning systems (EEWS) are developed or currently being tested in many active seismic regions of the world. A well-known problem with real-time procedures is the parameter saturation, which may lead to magnitude underestimation for large earthquakes. In this paper, the method used to the MW9.0 Tohoku-Oki earthquake is explored with strong-motion records of the MW7.9, 2008 Wenchuan earthquake. We measure two early warning parameters by progressively expanding the P-wave time window (PTW) and distance range, to provide early magnitude estimates and a rapid prediction of the potential damage area. This information would have been available 40 s after the earthquake origin time and could have been refined in the successive 20 s using data from more distant stations. We show the suitability of the existing regression relationships between early warning parameters and magnitude, provided that an appropriate PTW is used for parameter estimation. The reason for the magnitude underestimation is in part a combined effect of high-pass filtering and frequency dependence of the main radiating source during the rupture process. Finally we suggest only using Pd alone for magnitude estimation because of its slight magnitude saturation compared to the τc magnitude.