Date of Award


Document Type


Degree Name

Master of Science


Department of Engineering Physics

First Advisor

Devin Della-Rose, PhD


This research is an extension to the research conducted by K. Leka and G. Barnes of the Colorado Research Associates Division, Northwest Research Associates, Inc. in Boulder, Colorado (CORA) in which they found no single photospheric solar parameter they considered could sufficiently identify a flare-producing active region (AR). Their research then explored the possibility a linear combination of parameters used in a multivariable discriminant function (DF) could adequately predict solar activity. The purpose of this research is to extend the DF research conducted by Leka and Barnes by refining the method of statistical discriminant analysis (DA) with the goal of selecting those photospheric magnetic parameters most capable of identifying flare-producing active regions in hopes of increasing the reliability of short term flare warnings and the understanding of flare production. The data for this research were photospheric vector magnetograms captured by the Imaging Vector Magnetograph (IVM) at the University of Hawai`i Mees Solar Observatory at Haleakala and provided by CORA. Increasing the data set size was an essential task for this research in order to have a more statistically significant training sample for DA. This research also modified current DF procedures to enable the customization of the costs of flare false alarms and flare misses. Work was also done to expand the binary DF results to produce flare probability forecasts. The selection of the optimum combination of photospheric magnetic parameters to be used as predictors in a linear DF began with the elimination of redundant parameters and those parameters least likely to contribute to flare production. The selection of parameters was governed by maximizing the Mahalanobis distance in a step-up method. The DF results show a pre-flaring active region may be characterized by larger magnetic flux, an active region with a larger area of magnetic shear angle greater than 80°, larger current of heterogeneity, larger spatial vertical magnetic field gradient, and a larger kurtosis of the shear angle. With the optimum combination of parameters, DF flare probability forecasts were compared to the daily forecasts produced by the National Oceanic and Atmospheric Administration, Space Environment Center (NOAA SEC). The Chi-Squared values of each forecast show the objective DF based flare probability forecasting method performs as well as the subjective forecasting method employed by the SEC.

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