Solar flares produce radiation which can have an almost immediate effect on the near-Earth environment, making it crucial to forecast flares in order to mitigate their negative effects. The number of published approaches to flare forecasting using photospheric magnetic field observations has proliferated, with varying claims about how well each works. Because of the different analysis techniques and data sets used, it is essentially impossible to compare the results from the literature. This problem is exacerbated by the low event rates of large solar flares. The challenges of forecasting rare events have long been recognized in the meteorology community, but have yet to be fully acknowledged by the space weather community. During the interagency workshop on "all clear" forecasts held in Boulder, CO in 2009, the performance of a number of existing algorithms was compared on common data sets, specifically line-of-sight magnetic field and continuum intensity images from MDI, with consistent definitions of what constitutes an event. We demonstrate the importance of making such systematic comparisons, and of using standard verification statistics to determine what constitutes a good prediction scheme. When a comparison was made in this fashion, no one method clearly outperformed all others, which may in part be due to the strong correlations among the parameters used by different methods to characterize an active region. For M-class flares and above, the set of methods tends towards a weakly positive skill score (as measured with several distinct metrics), with no participating method proving substantially better than climatological forecasts.

A classification infrastructure built upon Discriminant Analysis has been developed at NorthWest Research Associates for examining the statistical differences between samples of two known populations. Originating to examine the physical differences between flarequiet and flare-imminent solar active regions, we describe herein some details of the infrastructure including: parametrization of large datasets, schemes for handling "null" and "bad" data in multi-parameter analysis, application of non-parametric multi-dimensional Discriminant Analysis, an extension through Bayes' theorem to probabilistic classification, and methods invoked for evaluating classifier success. The classifier infrastructure is applicable to a wide range of scientific questions in solar physics. We demonstrate its application to the question of distinguishing flare-imminent from flare-quiet solar active regions, updating results from the original publications that were based on different data and much smaller sample sizes. Finally, as a demonstration of "Research to Operations" efforts in the space-weather forecasting context, we present the Discriminant Analysis Flare Forecasting System (DAFFS), a near-real-time operationally-running solar flare forecasting tool that was developed from the research-directed infrastructure.

Although for many solar physics problems the desirable or meaningful boundary is the radial component of the magnetic field B r , the most readily available measurement is the component of the magnetic field along the line-of-sight to the observer, B los . As this component is only equal to the radial component where the viewing angle is exactly zero, some approximation is required to estimate B r at all other observed locations. In this study, a common approximation known as the "µ-correction", which assumes all photospheric field to be radial, is compared to a method which invokes computing a potential field that matches the observed B los , from which the potential field radial component, B pot r is recovered. We demonstrate that in regions that are truly dominated by radially-oriented field at the resolution of the data employed, the µ-correction performs acceptably if not better than the potential-field approach. However, it is also shown that for any solar structure which includes horizontal fields, i.e. active regions, the potential-field method better recovers both the strength of the radial field and the location of magnetic neutral line.

The problem of bias, meaning over- or under-estimation, of the component perpendicular to the line-of-sight [$B_{\perp }$ B ⊥ ] in vector magnetic-field maps is discussed. Previous works on this topic have illustrated that the problem exists; here we perform novel investigations to quantify the bias, fully understand its source(s), and provide mitigation strategies. First, we develop quantitative metrics to measure the $B_{\perp }$ B ⊥ bias and quantify the effect in both local (physical) and native image-plane components. Second, we test and evaluate different options available to inversions and different data sources, to systematically characterize the impacts of these choices, including explicitly accounting for the magnetic fill fraction [$f\!\!f$ f f ]. Third, we deploy a simple model to test how noise and different models of the bias may manifest. From these three investigations we find that while the bias is dominantly present in under-resolved structures, it is also present in strong-field, pixel-filling structures. Noise in the spectropolarimetric data can exacerbate the problem, but it is not the primary cause of the bias. We show that fitting $f\!\!f$ f f explicitly provides significant mitigation, but that other considerations such as the choice of $\chi ^{2}$ χ 2 -weights and optimization algorithms can impact the results as well. Finally, we demonstrate a straightforward “quick fix” that can be applied post facto but prior to solving the $180^{\circ}$ 180 ∘ ambiguity in $B_{\perp }$ B ⊥ , and which may be useful when global-scale structures are, e.g., used for model boundary input. The conclusions of this work support the deployment of inversion codes that explicitly fit $f\!\!f$ f f or, as with the new neural-net, that are trained on data that did so.

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