A new approach, based on an extensible model for the field of equatorial currents and the use of large sets of spacecraft data that became available in recent years, has been shown to dramatically improve the resolution of the empirical picture of the magnetospheric magnetic field. However, accumulation of data, necessary for high resolution in space, may be too long and smear out important dynamical effects. We show that the problem can be resolved using the nearest-neighbor approach, in which the spatial structure of each state of the magnetosphere is described by fitting the empirical model to a local subset of data. It includes both the actual data obtained for the given state and data from other time intervals (e.g., similar phases of other storms), neighboring the present state in the space of global parameters, solar wind electric field, Sym-H index, and its time derivative. New findings in the picture of magnetic storms emerging from the new model include a consistent description of the ring current density peak in the postmidnight sector during the main phase and the premidnight depression of the equatorial magnetic field. The model also shows a strong erosion of the ring current on the dayside during the early main phase and its enhancement in a broad area in the evening sector extending from the geosynchronous orbit to the magnetopause near the Sym-H minimum. Another interesting effect is a double partial ring current during the main phase, consistent with the energy density profiles derived from energetic neutral atom images.