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By coupling a solar surface flux transport model with an extrapolation of theheliospheric field, we simulate the evolution of the Sun's open magnetic fluxand the heliospheric current sheet (HCS) based on observational data of sunspotgroups since 1976. The results are consistent with measurements of theinterplanetary magnetic field near Earth and with the tilt angle of the HCS asderived from extrapolation of the observed solar surface field. This opens thepossibility for an improved reconstruction of the Sun's open flux and the HCSinto the past on the basis of empirical sunspot data.

Modeling the Sun's open magnetic flux and the heliospheric current sheet