4.4 Summary of automatic methods

The potential-field acute angle method is easy to implement and fast, but its performance of 0.64 – 0.75 is relatively poor. The method is, however, very important as an initial step for more sophisticated methods. Using more sophisticated reference fields (linear force-free fields, constant shear, non-potential fields) in the acute angle method improves the performance to about 0.83 – 0.90. Linear force-free or similar fields are a better approximation to a suitable reference field, but the corresponding assumptions are not fulfilled in a strict sense, which prevents a higher performance. The magnetic pressure gradient and pseudo-current methods are more difficult to implement as simple acute angle methods, but do not perform significantly better. A higher performance is prevented, because the basic assumptions are usually not fulfilled in the entire region. For example, the assumption that the magnetic pressure always decreases with height is not fulfilled over bald patches (Titov et al., 1993). The multi-step U. Hawai’i iterative method and the minimum energy methods showed the highest performance of > 0.97. The pseudo-current method is in principle similar to the better performing minimum energy methods, but due to several local minima it is not guaranteed that the method will always find the global minimum. Let us remark that Metcalf et al. (2006Jump To The Next Citation Point) introduced more comparison metrics, which, however, do not influence the relative rating of the discussed ambiguity algorithms. They also carried out another test case using the Chiu and Hilton (1977) linear force-free model, for which most of the codes showed an absolutely better performance, but again this does hardly influence the relative performance of the different methods. One exception was the improved non-potential magnetic field algorithm, which performed with similar excellence as the minimum energy and U. Hawai’i iterative methods. Consequently these three methods are all suitable candidates for application to data. It is, however, not entirely clear to what extent these methods can be applied to full-disk vector magnetograms and what kind of computer resources are required.

4.4.1 Effects of noise and spatial resolution

The comparison of ambiguity removal methods started in Metcalf et al. (2006) has been continued in Leka et al. (2009Jump To The Next Citation Point). The authors investigated the effects of Poisson photon noise and a limited spatial resolution. It was found that most codes can deal well with random noise and the ambiguity resolution results are mainly affected locally, but bad solutions (which are locally wrong due to noise) do not propagate within the magnetogram. A limited spatial resolution leads to a loss of information about the fine structure of the magnetic field and erroneous ambiguity solutions. Both photon noise and binning to a lower spatial resolution can lead to artificial vertical currents. The combined effect of noise and binning affect the computation of a reference magnetic field used in acute angle methods as well as quantities in minimization approaches like the electric current density and ∇ ⋅ B. Sophisticated methods based on minimization schemes performed again best in the comparison of methods and are more suitable to deal with the additional challenges of noise and limited resolution. As a consequence of these results Leka et al. (2009) suggested that one should use the highest possible resolution for the ambiguity resolution task and if binning of the data is necessary, this should be done only after removing the ambiguity. Recently Georgoulis (2012Jump To The Next Citation Point) challenged their conclusion that the limited spatial resolution was the cause of the failure of ambiguity removal techniques using potential or non-potential reference fields. Georgoulis (2012) pointed out that the failure was caused by a non-realistic test-data set and not by the limited spatial resolution. This debate has been continued in a reply by Leka et al. (2012). We aim to follow the ongoing debate and provide an update on this issue in due time.

4.4.2 HAO AZAM method

This is an interactive tool, which needs human intervention for the ambiguity removal. In the test case, which has been implemented and applied by Bruce Lites, all pixels have been identified correctly. It is of course difficult to tell about the performance of the method, but only about a human and software combination. For some individual or a few active regions the method might be appropriate, but not for a large amount of data.

4.4.3 Ambiguity removal methods using additional observations

The methods described so far use as input the photospheric magnetic field vector measured at a single height in the photosphere. If additional observations/measurements are available they can be used for the ambiguity removal. Measurements at different heights in order to solve the ambiguity problem have been proposed by Li et al. (1993) and revisited by Li et al. (2007Jump To The Next Citation Point). Knowledge of the magnetic field vector at two heights allows us to compute the divergence of the magnetic field and the method was dubbed divergence-free method. The method is non-iterative and thus fast. Li et al. (2007) applied the method to the same flux-rope simulation by Fan and Gibson (2004) as discussed in the examples above, and the method recovered about a fraction of 0.98 pixels correctly. The main shortcoming of this method is certainly that it can be applied only if vector magnetic field measurements at two heights are available, which is unfortunately not the case for most current data sets.

Martin et al. (2008Jump To The Next Citation Point) developed the so-called chirality method for the ambiguity removal, which takes additional observations into account, e.g., Hα, EUV, or X-ray images. Such images are used to identify the chirality in solar features like filaments, fibrils, filament channels, or coronal loops. Martin et al. (2008) applied the method to different solar features, but to our knowledge the method has not been tested with synthetic data, where the true solution of the ambiguity is known. Therefore, unfortunately one cannot compare the performance of this method with the algorithms described above. It is also now obvious that fully automatic feature recognition techniques to identify the chirality from observed images need to be developed.

After the launch of Solar Orbiter additional vector magnetograms will become available from above the ecliptic. Taking these observations from two vantage positions combined is expected to be helpful for the ambiguity resolution. If separated by a certain angle, the definition of line-of-sight field and transverse field will be very different from both viewpoints. Removing the ambiguity should be a straightforward process by applying the transformation to vertical and horizontal fields on the photosphere from both viewpoints separately. If the wrong azimuth is chosen, then both solutions will be very different and the ambiguity can be removed by simply checking the consistency between vertical and horizontal fields from both observations.

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