Space weather is the response of our space environment to the constantly changing Sun. As the new technology advances, mankind has become more and more dependent on space system, satellite-based services. A geomagnetic storm, a disturbance in Earth's magnetosphere, may produce many harmful effects on Earth. Solar flares and Coronal Mass Ejections (CMEs) are believed to be the major causes of geomagnetic storms. Thus, establishing a real time forecasting method for them is very important in space weather study.

The topics covered in this dissertation are: the relationship between magnetic gradient and magnetic shear of solar active regions; the relationship between solar flare index and magnetic features of solar active regions; based on these relationships a statistical ordinal logistic regression model is developed to predict the probability of solar flare occurrences in the next 24 hours; and finally the relationship between magnetic structures of CME source regions and geomagnetic storms, in particular, the super storms when the index decreases below -200 nT is studied and proved to be able to predict those super storms.

The results are briefly summarized as follows: (1) There is a significant correlation between magnetic gradient and magnetic shear of active region. Furthermore, compared with magnetic shear, magnetic gradient might be a better proxy to locate where a large flare occurs. It appears to be more accurate in identification of sources of X-class flares than M-class flares; (2) Flare index, defined by weighting the SXR flares, is proved to have positive correlation with three magnetic features of active region; (3) A statistical ordinal logistic regression model is proposed for solar flare prediction. The results are much better than those data published in the NASA/SDAC service, and comparable to the data provided by the NOAA/SEC complicated expert system. To our knowledge, this is the first time that logistic regression model has been applied in solar physics to predict flare occurrences; (4) The magnetic orientation angle θ, determined from a potential field model, is proved to be able to predict the probability of super geomagnetic storms (Dst ≤ -200nT). The results show that those active regions associated with |θ| < 90° are more likely to cause a super geomagnetic storm.