We report here on the present state-of-the-art in algorithms used for resolving the 180 • ambiguity in solar vector magnetic field measurements. With present observations and techniques, 268 T.R. METCALF ET AL. some assumption must be made about the solar magnetic field in order to resolve this ambiguity. Our focus is the application of numerous existing algorithms to test data for which the correct answer is known. In this context, we compare the algorithms quantitatively and seek to understand where each succeeds, where it fails, and why. We have considered five basic approaches: comparing the observed field to a reference field or direction, minimizing the vertical gradient of the magnetic pressure, minimizing the vertical current density, minimizing some approximation to the total current density, and minimizing some approximation to the field's divergence. Of the automated methods requiring no human intervention, those which minimize the square of the vertical current density in conjunction with an approximation for the vanishing divergence of the magnetic field show the most promise.
[1] Magnetic field data at 1/3 s resolution are used from the ACE spacecraft for days 7 to 33 in 2001 (Bartels rotation 2286) to characterize the statistical properties of discontinuities during this period. A method is developed for finding discontinuities independent of spread angle between magnetic fields across the discontinuity. This was viewed as necessary since larger spread angle discontinuities can occur in close proximity with smaller ones, and the smaller ones are numerous. Discontinuities are found to occur in groupings, and the separation between successive discontinuities has a distribution which is lognormal. With the expectation that most discontinuities have normals across or nearly across the magnetic field, the cross-product method is used to find the normal. Combining normal direction and plasma data from the ACE spacecraft, we find that the most probable width for discontinuities is 4 to 8 proton inertial lengths or gyroradii. For small b(ratio of proton gas and magnetic pressure), the widths scale better with proton inertial length while for large b with proton gyroradius. Most discontinuities have small changes in the total magnetic intensity and are ramp-like. The statistical properties of the discontinuities appear to come from a single population. To identify this population, rotational and tangential discontinuities and also discontinuities associated with Alfvénic turbulence are considered. The population is most consistent with turbulence.
On the basis of observations of solar granulation obtained with the New Solar Telescope (NST) of Big Bear Solar Observatory, we explored proper motion of bright points (BPs) in a quiet sun area, a coronal hole, and an active region plage. We automatically detected and traced bright points (BPs) and derived their mean-squared displacements as a function of time (starting from the appearance of each BP) for all available time intervals. In all three magnetic environments, we found the presence of a super-diffusion regime, which is the most pronounced inside the time interval of 10-300 seconds. Super-diffusion, measured via the spectral index, γ, which is the slope of the mean-squared displacement spectrum, increases from the plage area (γ = 1.48) to the quiet sun area (γ = 1.53) to the coronal hole (γ = 1.67). We also found that the coefficient of turbulent diffusion changes in direct proportion to both temporal and spatial scales. For the minimum spatial scale (22 km) and minimum time scale (10 sec), it is 22 and 19 km 2 s −1 for the coronal hole and the quiet sun area, respectively, whereas for the plage area it is about 12 km 2 s −1 for the minimum time scale of 15 seconds. We applied our BP tracking code to 3D MHD model data of solar convection (Stein et al. 2007) and found the super-diffusion with γ = 1.45. An expression for the turbulent diffusion coefficient as a function of scales and γ is obtained.
Power spectra of the line-of-sight magnetograms were calculated for 16 active regions of different flare activity. Data obtained by the Michelson Doppler Imager instrument on board the Solar and Heliospheric Observatory in high-resolution mode were used in this study. For each active region, the daily soft X-ray flare index, A, was calculated. This index characterizes the flare productivity of an active region per day, being equal to 1 when the specific flare productivity is one C1.0 flare per day. The power index, , of the magnetic power spectrum, E(k) $ k À , averaged over all analyzed magnetograms for a given active region, was compared with the flare index. It was found that active regions, which produced X-class flares, possessed a steep power spectrum with > 2:0, while flare-quiet active regions with low magnitude of A displayed a Kolmogorov-type spectrum of % 5/3. Observational data suggest that the flare index A may be determined from the power index by A( ) ¼ 409:5( À 5/3) 2:49 . The magnitude of the power index at the stage of emergence of an active region seems not to be related to the current flaring level of this active region, but rather reflects its future flare productivity, when the magnetic configuration becomes well evolved. This finding shows the way to distinguish at the very early stage those solar active regions that are ''born bad'' and have a potential to produce significant disturbances in the Earth magnetosphere.
In this study we use the ordinal logistic regression method to establish a prediction model, which estimates the probability for each solar active region to produce X-, M-, or Cclass flares during the next 1-day time period. The three predictive parameters are (1) the total unsigned magnetic flux T flux , which is a measure of an active region's size, (2) the length of the strong-gradient neutral line L gnl , which describes the global nonpotentiality of an active region, and (3) the total magnetic dissipation E diss , which is another proxy of an active region's nonpotentiality. These parameters are all derived from SOHO MDI magnetograms. The ordinal response variable is the different level of solar flare magnitude. By analyzing 174 active regions, L gnl is proven to be the most powerful predictor, if only one predictor is chosen. Compared with the current prediction methods used by the Solar Monitor at the Solar Data Analysis Center (SDAC) and NOAA's Space Weather Prediction Center (SWPC), the ordinal logistic model using L gnl , T flux , and E diss as predictors demonstrated its automatic functionality, simplicity, and fairly high prediction accuracy. To our knowledge, this is the first time the ordinal logistic regression model has been used in solar physics to predict solar flares.
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