Resolving the 180° Ambiguity in Solar Vector Magnetic Field Data: Evaluating the Effects of Noise, Spatial Resolution, and Method Assumptions

Abstract

The objective testing of algorithms for performing ambiguity resolution in vector magnetic field data is continued, with an examination of the effects of noise in the data. Through the use of analytic magnetic field models, two types of noise are "added" prior to resolving: noise to simulate Poisson photon noise in the observed polarization spectra, and a spatial binning to simulate the effects of unresolved structure. The results are compared through the use of quantitative metrics and performance maps. We find that while no algorithm severely propagates the effects of Poisson noise beyond very local influences, some algorithms are more robust against high photon-noise levels than others. In the case of limited spatial resolution, loss of information regarding fine-scale structure can easily result in erroneous solutions. Our tests imply that photon noise and limited spatial resolution can act so as to make assumptions used in some ambiguity resolution algorithms no longer consistent with the observed magnetogram. We confirm a finding of the earlier comparison study T.R. Metcalf deceased, July 2007. that results can be very sensitive to the details of the treatment of the observed boundary and the assumptions governing that treatment. We discuss the implications of these findings, given the relative sensitivities of the algorithms to the two sources of noise tested here. We also touch on further implications for interpreting observational vector magnetic field data for general solar physics research.

Nonlinear force-free field extrapolation of the coronal magnetic field using the data obtained by the Hinode satellite

“…To do the physical analyses for the solar eruptive events, a higher-resolution grid should be used in the NLFFF extrapolation calculations (e.g., 1″/pixel, the same resolution as the XRT images). For the magnetograms that are not at the central area of the Sun's disk, the projection effect and the 180°ambiguity in the SP magnetic field data also need to be resolved more carefully and accurately [Georgoulis, 2005;Metcalf et al, 2006;Wiegelmann et al, 2008;Martin et al, 2008;Leka et al, 2009]. Besides the comparison between the extrapolated field lines and the coronal loop images, and the preliminary physical analyses used in this paper, topological techniques and more physical measures should be introduced to quantitatively analyze the topological and physical properties of the extrapolated fields [Longcope, 2005;Zhao et al, 2005;DeVore and Antiochos, 2000;Bleybel et al, 2002;Zhang and Low, 2005;Régnier and Canfield, 2006;Démoulin, 2007;Thalmann et al, 2008;Schrijver et al, 2008;DeRosa et al, 2009] and their relationships to the solar eruptive events.…”

The Helioseismic and Magnetic Imager (HMI) Vector Magnetic Field Pipeline: Overview and Performance

“…This method has been shown to be among the best performing on a wide range of tests on synthetic data for which the answer is known (Metcalf et al, 2006;Leka et al, 2009). However, Leka et al (2009) showed that the minimum energy state is not always the correct ambiguity resolution in the presence of noise.…”

“…However, Leka et al (2009) showed that the minimum energy state is not always the correct ambiguity resolution in the presence of noise. Furthermore, convergence of the optimization Figure 4 The radial component of the field for HARP 1795 (NOAA AR #11512) on 1 July 2012 at 00:00 TAI, saturated at ±500 G. Axes are in pixels.…”

“…In areas close to pixels with well-determined fields, the method performs well, as it quickly produces a smooth transition to noisy pixels. While the result is always a smooth solution, the algorithm can become trapped in a smooth but incorrect result, which tends to be propagated outwards from the well-measured field (Leka et al, 2009). Therefore this method is currently used for SHARPs, and in small intermediate areas around well-determined fields for the full-disk.…”

Rapid Penumbra and Lorentz Force Changes in an X1.0 Solar Flare

“…; logT=5.0) images, with a pixel size of 0 6 and a cadence of 24 s, to determine the flare location and morphology. We use vector magnetic-field data from the version of Space weather HMI Active Region Patches (SHARP; Turmon et al 2010), which were obtained by using the Very Fast Inversion of the Stokes Vector algorithm (Borrero et al 2011) and the remaining 180°a zimuth ambiguity was resolved with the Minimum Energy code (Metcalf 1994;Leka et al 2009). The vector field data, with a 12 minute cadence and an accuracy of 100 G for the horizontal field, was remapped to the Lambert cylindrical equal-area projection and transformed into the standard heliographic spherical coordinates.…”