Authors: Guanglu Shi (Purple Mountain Observatory), Li Feng (Purple Mountain Observatory), Beili Ying (Purple Mountain Observatory), Shuting Li (Purple Mountain Observatory), Weiqun Gan (Purple Mountain Observatory)

Solar magnetic fields are closely related to various physical phenomena on the sun, which can be extrapolated with different models from photospheric magnetograms. However, the open flux problem (OFP), the underestimation of the magnetic field derived from the extrapolated model, is still unsolved. To minimize the impact of the OFP, we propose three evaluation parameters to quantitatively evaluate magnetic field models and determine the optimal free parameters in the models by constraining the coronal magnetic fields and the interplanetary magnetic fields (IMFs) with real observations. Although the OFP still exists, we find that magnetic field lines traced from the coronal models effectively capture the intricate topological configurations observed in the corona, including streamers and plumes. The OFP is lessened by using the Helioseismic and Magnetic Imager synoptic map instead of the Global Oscillation Network Group daily synoptic maps, and the potential field source surface + potential field current sheet (PFSS+PFCS) model instead of the current sheet source surface (CSSS) model. For Carrington Rotation 2231 at the solar minimum, we suggest that the optimal parameters for the PFSS+PFCS model are Rss = 2.2-2.5 Rsun and Rscs = 10.5-14.0 Rsun, as well as for the CSSS model are Rcs = 2.0 – 2.4 Rsun, Rss = 11.0 – 14.7 Rsun and a = 1.0 Rsun. Despite the IMFs at 1 au being consistent with the measurements by artificially increasing the polar magnetic fields, the IMFs near the sun are still underestimated. The OFP might be advanced by improving the accuracy of both the weak magnetic fields and polar magnetic fields, especially considering magnetic activities arising from interplanetary physical processes.