Comparison of coronal extrapolation methods for cycle 24 using HMI data

Two extrapolation models of the solar coronal magnetic field are compared using magnetogram data from the SDO/HMI instrument. The two models, a horizontal current-current sheet-source surface (HCCSSS) model and a potential field-source surface (PFSS) model differ in their treatment of coronal currents. Each model has its own critical variable, respectively the radius of a cusp surface and a source surface, and it is found that adjusting these heights over the period studied allows better fit between the models and the solar open flux at 1 AU as calculated from the Interplanetary Magnetic Field (IMF). The HCCSSS model provides the better fit for the overall period from 2010 November to 2015 May as well as for two subsets of the period - the minimum/rising part of the solar cycle, and the recently-identified peak in the IMF from mid-2014 to mid-2015 just after solar maximum. It is found that a HCCSSS cusp surface height of 1.7 Rs provides the best fit to the IMF for the overall period, while 1.7 & 1.9 Rs give the best fits for the two subsets. The corresponding values for the PFSS source surface height are 2.1, 2.2 and 2.0 Rs respectively. This means that the HCCSSS cusp surface rises as the solar cycle progresses while the PFSS source surface falls