The dayside magnetopause moves closer to the Earth with increasing southward IMF Bz. Is the response of magnetopause to solar wind parameters, southward IMF Bz, and dynamic pressure Dp linear or nonlinear? GOES observations on 6 April 2000 shows that the magnetopause is still outside of geosynchronous orbit even though the southward IMF Bz is greater than 25 nT and Dp is near 8 nPa. We suggest that the earthward motion of the dayside magnetopause saturates for large southward IMF Bz. Magnetosheath encounters observed by GOES satellites during 1999--2000 are used as a database for selecting a functional form of the saturation effect based on the calculations of the modified magnetopause model of Chao et al. <2002>. To obtain a relationship of the threshold of southward IMF Bz for saturation occurring as a function of Dp, an iteration procedure is used to minimize the false alarm rate (FAR) and maximize the probability of prediction (PoP). The relationship B'z = -8.1 - 12.0 ¿ log (Dp + 1) is obtained where B'z is the threshold of IMF Bz for saturation. This relationship is applied to a modified Chao et al. <2002> model and the new model is compared against magnetosheath encounters observed by the LANL MPA instruments on 31 March 2001.