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We improve the description of the evolution of the Sun's open and totalmagnetic flux on time scales of years to millenia. In the model employed herethe evolution of the solar total and open magnetic flux is computed from theflux emerging at the solar surface in the form of bipolar magnetic features,which is related to the sunspot number cycle parameters and can be estimatedfrom historical records. Compared to earlier versions of the model in additionto the long-lived open flux, now also a more rapidly decaying component of theopen flux is considered. The model parameters are constrained by comparing itsoutput with observations of the total surface magnetic flux and with areconstruction of the open magnetic flux based on the geomagnetic indexes. Amethod to compute the Sun's total magnetic flux and the sunspot number duringthe Holocene, starting from the open flux obtained from cosmogenic isotopesrecords, is also presented. By considering separately a rapdly evolving and aslowly evolving component of the open flux the model reproduces the Sun's openflux, as reconstructed based on the aa-index, much better and a reasonabledescription of the radial component of interplanetary magnetic field data areobtained. The greatest improvement is in the reproduction of the cyclicvariation of the open flux, including the amplitudes of individual cycles.Furthermore, we found that approximately 25% of the modeled open flux valuessince the end of the Maunder Minimum are lower than the averaged value duringthe current low minimum. The same proportion is observed in reconstructions ofthe open flux during the Holocene based on cosmogenic isotopes, which suggeststhat the present solar minimum conditions are below average, but notexceptional in terms of the magnetic flux.

Evolution of the solar magnetic flux on time scales of years to millenia