Abstract In this thesis solar active longitudes of X-ray flares and sunspots are studied. The fact that solar activity does not occur uniformly at all heliographic longitudes was noticed by Carrington as early as in 1843. The longitude ranges where solar activity occurs preferentially are called active longitudes. Active longitudes have been found in various manifestations of solar activity, such as sunspots, flares, radio emission bursts, surface and heliospheric magnetic fields, and coronal emissions. However, the active longitudes found when using different rigidly rotating reference frames differ significantly from each other. One reason is that the whole Sun does not rotate rigidly but differentially at different layers and different latitudes. The other reason is that the rotation of the Sun also varies with time. Earlier studies used a dynamic rotation frame for the differential rotation of the Sun and found two persistent active longitudes of sunspots in 1878-1996. However, the migration of active longitudes with respect to the Carrington rotation was treated there rather coarsely. We improved the accuracy of migration to less than one hour. Accordingly, not only the rotation parameters for each class of solar flares and sunspots are found to agree well with each other, but also the non-axisymmetry of flares and sunspots is systematically increased. We also studied the long-term variation of solar surface rotation. Using the improved analysis, the spatial distribution of sunspots in 1876-2008 is analyzed. The statistical evidence for different rotation in the northern and southern hemispheres is greatly improved by the revised treatment. Moreover, we have given consistent evidence for the periodicity of about one century in the north-south difference.

No / A crucial challenge to successful flare prediction is forecasting periods that transition between "flare-quiet" and "flare-active." Building on earlier studies in this series in which we describe the methodology, details, and results of flare forecasting comparison efforts, we focus here on patterns of forecast outcomes (success and failure) over multiday periods. A novel analysis is developed to evaluate forecasting success in the context of catching the first event of flare-active periods and, conversely, correctly predicting declining flare activity. We demonstrate these evaluation methods graphically and quantitatively as they provide both quick comparative evaluations and options for detailed analysis. For the testing interval 2016-2017, we determine the relative frequency distribution of two-day dichotomous forecast outcomes for three different event histories (i.e., event/event, no-event/event, and event/no-event) and use it to highlight performance differences between forecasting methods. A trend is identified across all forecasting methods that a high/low forecast probability on day 1 remains high/low on day 2, even though flaring activity is transitioning. For M-class and larger flares, we find that explicitly including persistence or prior flare history in computing forecasts helps to improve overall forecast performance. It is also found that using magnetic/modern data leads to improvement in catching the first-event/first-no-event transitions. Finally, 15% of major (i.e., M-class or above) flare days over the testing interval were effectively missed due to a lack of observations from instruments away from the Earth-Sun line.