For context, the following images show the HARP on 2011 February 17 at 04:36. The first shows the helioplanar components of the field over an image of the vertical component of the field. The second shows the same components over an image of the chi-squared value returned by the inversion. For most of what follows, the focus will be on a subarea at roughly 380:439,290:339.

The next four images show the subarea at consecutive times from 2011 February 17: 04:36 to 05:12. One small patch shows large changes in the disambiguation from one time to the next, including one instance of "checkerboard". (Images are intentionally shown upside down for comparison with later results which have not been corrected for upside down perspective of HMI, but fullsize links are right side up.) All of these solutions can also be obtained at a single time by using different random number seeds in the disambiguation. Thus, the solution has not yet converged to a global minimum.

Can areas such as these be identified?

One way which works: use multiple random number seeds and see where the same solution is obtained. In the following plot, 10 seeds were used, and black areas are where all 10 obtained the same result; colours indicate the fraction of seeds which agreed when not all 10 were the same (blue: 9/10, green: 8/10, yellow: 7/10, red: 6/10, purple: 5/10). The first image shows the full HARP, with the area highlighted above at approximately (200,120); the second image shows just the subarea.

Another approach one might hope to work is to look at the change in the energy of the solution when flipping each pixel individually. The following plot shows the log of the change in energy. The blue contour encloses the pixels in the previous plot for which all random number seeds obtained the same solution. The red contour is of the change in energy, indicating that one cannot simply separate out the challenging area without also exclusing many pixels which converged. For the most part, the change in energy does a good job of identifying which pixels have converged, with a few small areas where it fails.

Another approach is to look at the value of the divergence as approximated in the disambiguation code. If the assumptions of the code are correct, the magnitude of the divergence should be small. The following plot shows the magnitude of the divergence, with the same blue contour enclosing pixels which converged based on the different random number seeds. In the challenging area, the magnitude of the divergence is large, so this area can be identified.... but at the cost of various other areas which converged also being flagged as having a large divergence.

Is there a combination of these which would help to distinguish this area? Maybe, but a few quick experiments did not result in anything noticably better.

One final possibility is to use the quality of the inversion to try to identify where the disambiguation is likely to fail. The following image of chi-squared (with helioplanar components of the field) shows a slightly enlarged subarea. Indeed chi-squared is large in the area previously considered where the disambiguation fails, but it is also large in the sunspot penumbra at approximately 125,90 where the disambiguation has converged, so this also does not provide a way to determine where the disambiguation is likely to fail.