  The magnetic field permeating the solar atmosphere is generally thought to
provide the energy for much of the activity seen in the solar corona, such as
flares, coronal mass ejections (CMEs), etc. To overcome the unavailability of
coronal magnetic field measurements, photospheric magnetic field vector data
can be used to reconstruct the coronal field. Currently there are several
modelling techniques being used to calculate three-dimension of the field lines
into the solar atmosphere. For the first time, synoptic maps of photospheric
vector magnetic field synthesized from Vector Spectromagnetograph (VSM) on
Synoptic Optical Long-term Investigations of the Sun (SOLIS) are used to model
the coronal magnetic field and estimate free magnetic energy in the global
scale. The free energy (i.e., the energy in excess of the potential field
energy) is one of the main indicators used in space weather forecasts to
predict the eruptivity of active regions. We solve the nonlinear force-free
field equations using optimization principle in spherical geometry. The
resulting three-dimensional magnetic fields are used to estimate the magnetic
free energy content E_{free}=E_{nlfff}-E_{pot}, i.e., the difference of the
magnetic energies between the nonpotential field and the potential field in the
global solar corona. For comparison, we overlay the extrapolated magnetic field
lines with the extreme ultraviolet (EUV) observations by the Atmospheric
Imaging Assembly on board SDO. For a single Carrington rotation 2121, we find
that the global NLFFF magnetic energy density is 10.3% higher than the
potential one. Most of this free energy is located in active regions.
