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The magnetic field permeating the solar atmosphere is generally thought toprovide the energy for much of the activity seen in the solar corona, such asflares, coronal mass ejections (CMEs), etc. To overcome the unavailability ofcoronal magnetic field measurements, photospheric magnetic field vector datacan be used to reconstruct the coronal field. Currently there are severalmodelling techniques being used to calculate three-dimension of the field linesinto the solar atmosphere. For the first time, synoptic maps of photosphericvector magnetic field synthesized from Vector Spectromagnetograph (VSM) onSynoptic Optical Long-term Investigations of the Sun (SOLIS) are used to modelthe coronal magnetic field and estimate free magnetic energy in the globalscale. The free energy (i.e., the energy in excess of the potential fieldenergy) is one of the main indicators used in space weather forecasts topredict the eruptivity of active regions. We solve the nonlinear force-freefield equations using optimization principle in spherical geometry. Theresulting three-dimensional magnetic fields are used to estimate the magneticfree energy content E_{free}=E_{nlfff}-E_{pot}, i.e., the difference of themagnetic energies between the nonpotential field and the potential field in theglobal solar corona. For comparison, we overlay the extrapolated magnetic fieldlines with the extreme ultraviolet (EUV) observations by the AtmosphericImaging Assembly on board SDO. For a single Carrington rotation 2121, we findthat the global NLFFF magnetic energy density is 10.3% higher than thepotential one. Most of this free energy is located in active regions.

First use of synoptic vector magnetograms for global nonlinear force free coronal magnetic field models