6.6 Comparison of methods and the NLFFF consortium
Since 2004, a group of scientists chaired by Karel Schrijver compare, evaluate, and improve methods for
the nonlinear force-free computation of coronal magnetic fields and related topics. The test cases are
available at http://www.lmsal.com/~derosa/for_nlfff/. So far, six workshops have been organized and
the consortium published four joint publications:
- Schrijver et al. (2006) performed blind tests on analytical force-free field models with various
boundary conditions to show that in general the NLFFF algorithms perform best where the
magnetic field and the electrical currents are strongest, but they are also very sensitive to
the specified boundary conditions. Nevertheless, it was shown that the optimization method
as proposed by Wheatland et al. (2000) and as implemented by Wiegelmann (2004) was the
fastest-converging and best-performing one for this analytical test case.
- Metcalf et al. (2008) tested the performance of the NLFFF algorithms applied to a solar-like
reference model including realistic photospheric Lorentz forces and a complex magnetic field
structure. All the codes were able to recover the presence of a weakly twisted, helical flux
rope. Due to the sensitivity to the numerical details, however, they were less accurate in
reproducing the field connectivity and magnetic energy when applied to the preprocessed,
more force-free, chromospheric-like boundary conditions. When applied to the forced, not
preprocessed photospheric data the codes did not perform successfully, indicating that the
consistency of the used boundary conditions is crucial for the success of the magnetic field
extrapolations. It also showed that the magnetic field connection between the photosphere,
chromosphere, and lower corona needs to be additionally precisely modeled.
- Schrijver et al. (2008) used four different codes and a variety of boundary conditions to compute
14 NLFFF models based on Hinode/SOT-SP
data of an active region around the time of a powerful flare. When applied to this real
solar data, the models produced a wide variety of magnetic field geometries, energy contents,
and force-freeness. Force-free consistency criteria, like the alignment of electric currents with
magnetic field lines, have been best fulfilled for computations with the Grad–Rubin approach.
It was concluded that strong electrical currents in the form of an ensemble of thin strands
emerge together with magnetic flux preceding the flare. The global patterns of magnetic fields
are compatible with a large-scale twisted flux rope topology, and they carry energy which is
large enough to power the flare and its associated CME.
- DeRosa et al. (2009) found that various NLFFF models differ remarkably in the field line
configuration and produce different estimates of the free magnetic energy when applied to
Hinode/SOT-SP data. This problem was recognized already in the first application to Hinode
data in Schrijver et al. (2008) and it has been worked out that a small field-of-view vector
magnetogram, which does not contain an entire active region and its surroundings, does not
provide the necessary magnetic connectivity for successful NLFFF extrapolations. As visible
in Figure 10 the stereoscopically-reconstructed loops by Aschwanden et al. (2008b) do not
agree well with the NLFFF models. Unfortunately, the FOV of Hinode covered only a small
fraction (about 10%) of area spanned by loops reconstructed from STEREO/SECCHI images.
The quantitative comparison was unsatisfactory and NLFFF models have not been better as
potential fields here. In other studies NLFFF methods have shown to be superior to potential
and linear force-free extrapolations (Wiegelmann et al., 2005). NLFF field lines showed in
particular excellent agreement with the observed loops, when both footpoints are within the
FOV of the vector magnetogram and sufficiently far away from the boundaries.
Figure 10: A series of coaligned images of AR 10953. Blue lines are stereoscopically-reconstructed
loops (Aschwanden et al., 2008b). Red lines are extrapolated nonlinear force-free field lines from
Hinode/SOT with MDI data outside the Hinode FOV (the dotted line). Image reproduced by
permission from Figure 1 of DeRosa et al. (2009), copyright by AAS.
When presented with complete and consistent boundary conditions, NLFFF algorithms generally
succeed in reproducing the test fields. However, for a well-observed dataset (a Hinode/SOT-SP
vector-magnetogram embedded in MDI data) the NLFFF algorithms did not yield consistent solutions.
From this study we conclude that one should not rely on a model-field geometry or energy estimates unless
they match coronal observations. It was concluded that successful application to real solar data likely
requires at least:
- Large model volumes with high resolution that accommodate most of the field-line connectivity
within a region and to its surroundings.
- Accommodation of measurement uncertainties (in particular in the transverse field component)
in the lower boundary condition.
- ‘Preprocessing’ of the lower-boundary vector field that approximates the physics of the
photosphere-to-chromosphere interface as it transforms the observed, forced, photospheric field
to a realistic approximation of the chromospheric, nearly-force-free, field.
- The extrapolated coronal magnetic field lines should be compared and verified by coronal
In the meantime, some work has been done in reply to these conclusions. New implementations of the
Grad–Rubin and optimization methods do accommodate the measurement errors; see Sections 6.2 and 6.4
for an overview and Wheatland and Régnier (2009), Wiegelmann and Inhester (2010), and Amari and Aly
(2010) for the corresponding original publications. On the instrumentation side SDO/HMI provides us with
full-disk measurements of the photospheric magnetic field vector, which should allow us to
find suitable large model volumes. The first vector magnetograms from SDO/HMI have been
released at the end of 2011 and currently research on using them for force-free extrapolations is