In this paper, we fit the time series, which likely has abrupt change processes (ACP), with piecewise function deducing for describing the mean abrupt change from the logistic model. Thus combined with the theory of probability distribution formed the basis for considering the process in which abrupt change amplitude is maximum, as is the ACP. The parameters reflecting the beginning moment of the abrupt change, abrupt change amplitude, abrupt change rate, persistence time, and instability are determined and analyzed. By testing the time series in a 500 hPa temperature field during the period 1948-2012, we determine the following results: (1) Abrupt changes started in 1956-1959, 1970-1979, 1986-1994, and 1994-2004. We considered more probabilities by testing the start moment of the ACP. In these changes,the temperatures of all changes in the means show increases except for that in 1986-1994, and the rate increases if the abrupt change amplitude is large. (2) In spatial distribution of the abrupt change moment, the moment of the grid points in which the abrupt change occurred in 1956-1959 and 1970-1979 above the sea occurred earlier than that in the grid points above Eurasia, whereas the abrupt changes in 1986-1994 and in 1994-2004 show opposite behavior. (3) The abrupt change amplitude of temperature occurring in low latitudes is lower than that occurring in high latitudes. (4) Under the context of global warming, the statistics distribution of the persistence time shows that an increasing number of grid points require shore time to complete an abrupt change. (5) During the abrupt change process, the instability of the system was enhanced significantly.