D. A. Falconer (UAH/MSFC/NSSTC), R. L. Moore, G. A. Gary, (NASA/MSFC/NSSTC) Development of Empirical Tools for Forecasting Safe or Dangerous Space Weather from Magnetograms

Results of Work in Progress 1.Measures of active-region total nonpotentiality are strong predictors of CME productivity (success rate ~75%) (Figure 1). 2.Measures of magnetic twist (size-normalized nonpotentiality) and our active-region size measure (total magnetic flux Φ) are equally weaker predictors of CME productivity (each has success rate ~65%) (Figure 1 & Canfield, Hudson, & McKenzie 1999). 3.CME productivity is determined mainly by the active region’s total nonpotentiality. 4.Weighted neutral-line-length measures of magnetic shear and magnetic gradient (the total-nonpotentiality measures WL SS and WL SG ) are both strong predictors of CME productivity for active region of any degree of magnetic complexity (success rate ~75%) (Figure 3). 5.For forecasting CMEs from active regions within 30 o of disk center, measures of total nonpotentiality from non-deprojected magnetograms work as well as those from deprojected magnetograms (Figure 5). 6.For forecasting CMEs from active regions within 30 o of disk center, WL SG measured from MDI line-of-sight magnetograms works as well as WL SG measured from deprojected vector magnetograms (Figure 5). I

Figure 1: Correlation of magnetic measures with CME productivity and with each other for bipolar active regions. Each panel shows one magnetic measure (measures defined in Figure 2) plotted against another for 36 magnetograms marked with +’s or +’s. The span of the + shows the measurement uncertainty. The +’s represent active regions that produced CMEs, within 0-2 days of the day of the magnetogram; the +’s represent active regions that did not. For total nonpotentiality measures (WL SS, WL SG, and I N ), the +’s tend to fall beyond the threshold lines and the +’s tend to fall short. The CME-prediction success rate of each correlation is the percentage shown and the corresponding confidence levels of the correlations are the percentages in the parentheses below the success rates. The minimum step size in success rate for this sample is 6% (2/36*100%). A difference of one step size between the success rates of two measures is not significant (corresponds to roughly 1σ). Performance of CME Predictors for Bipolar Active Regions

Ф=  B V da (B V >100G) WL SS =  dx where  is the shear angle I N =  B H  dl, of green contour Definition of Active-Region Magnetic Measures Figure 2 The Magnetic Measures. Upper Left: Part of a deprojected MSFC vector magnetogram showing a nonpotential predominately bipolar active region, with contours of the vertical magnetic field component (solid contours: positive). The potential (green arrows) and observed (red arrows) horizontal fields are shown with only 1 in 25 pixels plotted. Upper Right: The neutral lines on which the observed horizontal field is greater than 150G are the shaded red curves. The degree of shear along the neutral line is indicated by the shading. Lower-Right The red arrows are the observed horizontal field. I N is found from applying Ampere's law to the green integration contour, and  IN =  I N / .  BC is the alpha that minimizes the quantity  (B H sin(θ o -θ ff )) 2 da. Lower- Left: The neutral line on which the potential horizontal field is greater than 150G is the shaded red curve. The magnitude of the gradient of the vertical field is indicated by the shading. Another version of this measure, N WL SG, is obtained by using the non- deprojected line-of-sight field instead of the deprojected vertical field. WL SG =  Gdx where G is the gradient of B V

Performance of WL SS and WL SG as CME Predictors for Bipolar or Multibipolar Active Regions Figure 3 Weighted neutral line length measures applied to bipolar, multibipolar and combined samples. Each panel is similar to those in Figure 1. For each sample, the weighted neutral line measures have ~75% success rate in predicting whether an active region will or will not be CME productive in the 0-2 day window. Note how the confidence level varies in the three cases even though the success rate is the same. This is due to the different sample sizes (36, 12, and 48 respectively for the bipolar, multi-bipolar, and combined samples). The step size in the success rates for the bipolar, multibipolar, and combined samples are respectively 6%, 16%, and 4%.

Earth-Moon Space CME All Clear Figure 4. Elements of our approach to forecasting All Clear for CMEs dangerous to Earth-Moon Space. Center: MDI magnetogram with blue boxes enclosing magnetic regions that might produce Earthward CMEs and red circle with extension to the west limb outlining the area from which CMEs that can by dangerous to Earth-Moon space usually originate. To obtain the probability of an Earthward CME, we must assess the CME-production probability of each active region in the red circle. For forecasting SEP events in Earth-Moon space we would have to also include any active region in the area westward of the circle. Left: MDI photospheric image showing strong magnetic regions have sunspots and weaker ones do not. Right: SEP storm from strong Earthward CME emerging from behind occulting disk in LASCO/C2 coronagraph image centered on EIT coronal image showing bright flare in large sunspot region from which the CME exploded. II

Development of Tools for All Clear Forecasting Overall Plan Use active-region total nonpotentiality measures from MDI full-disk magnetograms to categorize the total nonpotentiality of all sunspot (Figure 5) and spotless active regions (Figure 7). Determine empirically the probability an active region will be CME productive given the active region’s type (sunspot or spotless) and its degree of nonpotentiality (Figure 6). From full-disk magnetograms, produce All Clear for CMEs Dangerous to Earth-Moon Space Forecasts (Initially Earthward CME All Clear, for which the MDI magnetograms are better suited.). Proposed Initial Steps Expand our present 12 multibipolar sample to 25 active regions, and combine this with the 25 bipolar active regions for which there is MDI coverage. For each active region, compile its CME history, and determine the total nonpotentiality on each day the active region is within 30 o of disk center (4 days/active region), producing a 200 magnetogram sample. Divide the active-region magnetograms into 4 nonpotentiality categories and empirically determine for each category the probability of a CME occurring (Figure 6). Perform similar analysis for spotless active regions (Figure 7).

Performance of MDI Magnetograms for CME Forecasting Figure 5 Evaluation of total nonpotentiality from MDI magnetograms for prediction of CME productivity. Each panel is similar to those in Figure 1. Left Panel: Here we compare gradient-weighted neutral line length measured from deprojected and non-deprojected vector magnetograms of active regions within 30 o of disk center to show that they are strongily correlated with each other and that each is as strongily correlated with CME productivity as the other. This shows that we can use non-deprojected magnetograms to measure active-region total nonpotentiality and predict CME productivity. Right Panel: Here we compare WL SG evaluated from MDI magnetograms with that from MSFC deprojected magnetograms for the 25 days of the bipolar active-region sample for which there is both MSFC and MDI coverage.

Probability of CME Occurrence as a Function of Total Nonpotentiality Figure 6: The chance of CME production by a sunspot active region as a function of total nonpotentiality for 3 forecast windows. We have divided the present 48 magnetogram sample into 4 categories of sequentially greater nonpotentiality. The * estimates the percentage of the time that an active region in the category will produce a CME during the forecast window. The error bars indicate the 1-sigma uncertainty of this estimates. The error bars will be roughly half as large for our 200 magnetogram sample.

Figure 7. Example CME-productive spotless active region. Above Panels: Running-difference LASCO/C2 image centered on running- difference EIT Fe XII coronal image showing flare brightening and coronal dimming as the CME exploded from the active region and the resulting halo CME in LASCO/C2. Upper-Right Panel: Full-disk MDI magnetogram (12:51) with box enclosing active region from which the CME originated. Right panel: Expanded view of the active region. Lower-Right Panel: The magnetogram has been processed to define the neutral line, with color shading for the magnitude of the gradient of the line-of-sight field. Integrating the gradient along the neutral line gives N WL SG for this spotless active region. Forecasting CMEs from Spotless Active Regions

Future Work 1.Test CME predictive ability of N WL SG for spotless active regions (Figure 7). 2.Evaluate whether inclusion of other measures (for example total magnetic flux) can significantly improve prediction success rate over just using total nonpotentiality (Figure 8). 3.Determine whether there is a significant correlation between CME productivity and the time derivative of either total nonpotentiality or total flux (Figure 9). III

Bivariant Analysis Figure 8. Test of whether active-region CME productivity depends on active-region size in addition to total nonpotentiality using bivariant analysis. Left Panel: Here, we are plotting the normalized flux and weighted length of strong gradient (as in Figure 1) and plot three curves with different weighting κ of the total flux. The κ used and the predictive 0-2 day success rate of that κ is shown next to each curve. None of three values of κ’s is significantly better than the others for CME prediction. Middle panel: The CME prediction success rate is shown for a range of values of κ. The error bars are the 1-sigma error bars for our present sample of 48 magnetograms. The horizontal lines indicate the range of the values of κ for which the success rates are within 1 or 2 sigma of the maximum success rate. The results illustrate that our present sample size is too small to show whether there is some additional dependence on Φ. Right Panel: The size of the error bars for our planned 200 magnetogram sample. κκ

Dependence of CME Productivity on Magnetic Evolution Figure 9 Does the time rate of change of total nonpotentiality or total magnetic flux have CME predictive ability? The two panels above show two different active regions with WL SG and Φ plotted in arbitrary units. Each vertical tick mark shows the uncertainty for that measure, the curve is a three-point running average. Left: AR8100 was growing in size and total nonpotentiality and produced the first of several CMEs on November 3. Right: AR 9502 decreased in total nonpotentiality and size over the four days of observation and produced CMEs on the 15 th and 22 nd. By evaluating rates of magnetic evolution of each active region of our 200-magnetogram sample we will determine whether the time rate of change of either total nonpotentiality or total flux has a CME predictive ability comparable to that of the magnitude of total nonpotentiality or total flux.