Comparison of NLFFF Extrapolations for Chromospheric and Photospheric Magnetograms of AR J. McTiernan SSL/UCB SHINE 2005 Workhsop

Fig 1: Photospheric magnetogram, AR 10486, 29-OCT UT (from K.D. Leka) Chromospheric magnetogram, AR 10486, 29-OCT UT (from T.R. Metcalf) BxBy Bz BxByBz

Fig 2: Field extrapolations, via optimization method (Wheatland, Sturrock, Roumelotis 2000) Top: Photospheric Bottom: Chromospheric

Quantitative Comparison Metrics for Field Vectors Cauchy-Schwarz: Good = 1.0 Field direction Mean Vector Error: Good = 0.0 Field Magnitude

Fig 3:Comparison for the chromospheric B field and the extrapolation from photospheric field 3200 km from the photosphere.

Fig 4: Comparison of the mean values of the metrics, with photospheric extrapolation shifted up by 1 grid point (approx km):

Fig 5: Average fractional uncertainty in the extrapolated field, assuming uncertainty of 100/50G in chromospheric Bxy/Bz and 50/25 G in photospheric Bxy/Bz, from a monte carlo calculation:

Fig 6: Average (median) variation of metrics from ideal values normalized by uncertainty:

Discussion: Figure 1: the two magnetic fields differ slightly in Bz, more in Bx and By. The chromospheric one is more noisy. Figure 2: the field lines look relatively similar close to the surface, including some long, filament-like lines, but not so similar farther away. Figure 3: we use the Cauchy and mean error metrics for quantitative comparison. (Only for relatively strong fields, to avoid having the result overwhelmed by noise). For the Cauchy metric, there is good agreement except for a few points. For the mean error, the agreement is less good. Figure 4: The agreement seems to decrease with height. Figure 5: The idea here is to determine how well the field extrapolations match given the uncertainties in the measured fields. These are the error bars in the extrapolated field. Figure 6: Given uncertainties in B, you can get uncertainties in the two metrics. This shows the deviation of each metric divided by its uncertainty. For a good fit, this number should be of order 1.

Conclusions: The agreement between the extrapolations from the photospheric and chromospheric magnetograms is good for the Cauchy metric close to the surface, but not good at larger heights. But if all you need is the direction of the B field, or pictures of B field lines in the low corona, then the photospheric magnetogram can be used, even though the field in the photosphere is not force-free. This is helpful since photospheric magnetograms are more readily available. The agreement between the extrapolations for the mean error metric, which is sensitive to the difference in the magnitude of each magnetic field component, is not very good at all. This work was supported by a NASA SEC theory grant. The processing of the magnetogram data, by T. Metcalf & K.D. Leka was supported by by NASA grant NAG and by AFOSR contract F C-0019.