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The paraboloid model of Saturn's magnetosphere describes the\udmagnetic field as being due to the sum of contributions from the internal\udfield of the planet, the ring current, and the tail current, all contained\udby surface currents inside a magnetopause boundary which is taken to be a\udparaboloid of revolution about the planet-Sun line. The parameters of the\udmodel have previously been determined by comparison with data from a few\udpasses through Saturn's magnetosphere in compressed and expanded states,\uddepending on the prevailing dynamic pressure of the solar wind. Here we\udsignificantly expand such comparisons through examination of Cassini\udmagnetic field data from 18 near-equatorial passes that span wide ranges of\udlocal time, focusing on modelling the co-latitudinal field component that\uddefines the magnetic flux passing through the equatorial plane. For 12 of\udthese passes, spanning pre-dawn, via noon, to post-midnight, the spacecraft\udcrossed the magnetopause during the pass, thus allowing an estimate of the\udconcurrent subsolar radial distance of the magnetopause R1 to be made,\udconsidered to be the primary parameter defining the scale size of the\udsystem. The best-fit model parameters from these passes are then employed to\uddetermine how the parameters vary with R1, using least-squares linear\udfits, thus providing predictive model parameters for any value of R1 within the range. We show that the fits obtained using the linear\udapproximation parameters are of the same order as those for the individually\udselected parameters. We also show that the magnetic flux mapping to the tail\udlobes in these models is generally in good accord with observations of the\udlocation of the open-closed field line boundary in Saturn's ionosphere, and\udthe related position of the auroral oval. We then investigate the field data\udon six passes through the nightside magnetosphere, for which the spacecraft\uddid not cross the magnetopause, such that in this case we compare the\udobservations with three linear approximation models representative of\udcompressed, intermediate, and expanded states. Reasonable agreement is found\udin these cases for models representing intermediate or expanded states

Optimization of Saturn paraboloid magnetospheric field model parameters using Cassini equatorial magnetic field data