We model the open magnetic field region in Saturn's southern polar ionosphere during two compression regions observed by the Cassini spacecraft upstream of Saturn in January 2004, and compare these with the auroral ovals observed simultaneously in ultraviolet images obtained by the Hubble Space Telescope. The modelling employs the paraboloid model of Saturn's magnetospheric magnetic field, whose parameters are varied according to the observed values of both the solar wind dynamic pressure and the interplanetary magnetic field (IMF) vector. It is shown that the open field area responds strongly to the IMF vector for both expanded and compressed magnetic models, corresponding to low and high dynamic pressure, respectively. It is also shown that the computed open field region agrees with the poleward boundary of the auroras as well as or better than those derived previously from a model in which only the variation of the IMF vector was taken into account. The results again support the hypothesis that the auroral oval at Saturn is associated with the open-closed field line boundary and hence with the solar wind interaction.