HMI, Photospheric Flows and ILCT Brian Welsch, George Fisher, Yan Li, & the UCB/SSL MURI & CISM Teams

HMI Team Mtg., 2006 M3: Mag Data Products

Correlation Tracking

Image Deprojection

Output Pipeline

Velocity inversions generate a 2D map v(x1,x2)from one 2D image, f1(x1,x2), to another, f2(x1,x2).

The map depends upon:

1. the difference f(x1,x2) = f2(x1,x2) – f1(x1,x2)

2. assumption(s) relating v(x1,x2) to f/t, e.g.: – continuity equation, f/t + t(vtf) = 0, or – advection equation, f/t + (vtt)f = 0, etc.

Based on the assumption chosen, v(x1,x2) is not necessarily velocity – e.g., group velocity of interference patterns.

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Local correlation tracking (LCT) finds v(x1,x2) by correlating subregions; it assumes advection.

1) for ea. (xi, yi) above |B|threshold…

2) apply Gaussian mask at (xi, yi) …

3) truncate and cross-correlate…

*

4) v(xi, yi) is inter-polated max. of correlation funct

=

==

Demoulin & Berger (2003) argued that LCT applied to magnetograms does not necessarily give plasma velocities.

uf vnBh-vhBn is the flux transport velocity• uf is the apparent velocity (2 components)

• v is the actual plasma velocity (3 comps)

The apparent motion of flux on the photosphere, uf, is a combination of horizontal flows and vertical flows acting on non-vertical fields.

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The magnetic induction equation’s normal component relates velocities to dBn/dt.

Bn/t = h(vnBh-vhBn) = -h(ufBn)

• In fact, -h(uLCTBn) only approximates Bn/t, so

uLCT uf

• Inductive LCT (ILCT) finds uf that matches Bn/t exactly and closely matches uLCT.

• Writing ufBn = -h + h x( n), we find via Bn/t = h

2

by assuming uf = uLCT, so h2 = - h x( uLCTBn)

Doppler shifts ( vn) can’t distinguish between flows paral-lel to B, perpendicular to B, or in an intermediate direction.

• Since Bn/t = x (v x B), flows v|| along B do not affect Bn/t, so “inductive flow” methods only determine v.

• Once v is known, the measured Doppler shift allows determination of v||.

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Aside: fundamentally, two components of uf(x1,x2) cannot determine three components of plasma velocity, v(x1,x2).

• Hence, other velocity fields v(x1,x2) consistent with Bn/t can be found.

• Other techniques available include:– Minimum Energy Fit (MEF, Longcope, 2004)– Differential LCT (DLCT) & Differential Affine

Velocity Estimator (DAVE) (Schuck, 2006)

The FLCT code’s current version combines pro- grams written in IDL & C, and open source code.

1. IDL2. C3. Standard C library routines: stdio.h, stdlib.h, math.h4. Fastest Fourier Transform in the West (FFTW), v. 3.0 The executable has been compiled & tested on several architectures.1. Linux2. Solaris3. Windows4. Macintosh

• HMI has Npix ~ 107 pixels within 60o of disk center. - MDI’s 10242 HMI’s 40962 x 16

- MDI, w/in ~30o HMI, w/in ~60o x 2.5

• We track pixels with |Bn| > |B|thresh = 20G

~ 25% of Npix at solar max.

~ 5% of Npix at solar min. • FLCT speed is ~linear in Npix correlated.

- t ~ (1 sec/100 pix) x (2.5 x 106 pix) ~ 2.5 x 104 sec ~ 7 hr!- at solar min., w/ |B|thresh = 100G (~1% of Npix), t ~ 20 min.

Matching HMI’s 10-minute vector magnetogram cadence will be challenging.

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IVM difference images of BLOS in AR 9026, with a ~4 min. cadence, show large-scale, alternating field fluctuations that inhibit accurate tracking.

Velocity estimates work from difference images, so temporal artifacts must be removed.

Accurate velocity estimates also require deprojection of full-disk magnetograms.

• Away from disk center, flows with a component along LOS are foreshortened by curvature of the solar surface.

• Conformal deprojections, e.g., Mercator, locally preserve angles; scales are distorted, but easily fixed.

• This is optimal for tracking, since neither flow

component is biased by the deprojection.

• (Apparent changes in lengths perpendicular to the LOS from center-to-limb are negligible.)

FLCT was initially tested using a known image.

We found FLCT could accurately reconstruct the imposed flow.

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FLCT was also tested on magnetograms with imposed differential rotation – again, recovering the input flow.

White dots are imposed differential rotation profile; red dots are raw velocities from Mercator projection; green are properly rescaled; white diamonds are latitudinally binned averages of green dots.

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We have implemented a preliminary, automated “Magnetic Evolution Pipeline” (MEP).

http://solarmuri.ssl.berkeley.edu/~welsch/public/data/Pipeline/

• cron checks for new magnetograms with wget

• New magnetograms are downloaded, deprojected, and tracked using FLCT.

• The output stream includes deprojected m-grams, FLCT flows (.png graphics files & ASCII data files), and tracking parameters.

• Full documentation & all codes are on line.

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• Sub-pixel interpolation was made more efficient.

• Correlation is now accomplished by spawning a C subroutine that employs FFTW.

• FLCT is readily parallelizable; we envision this “soon.”

• Computing velocities in neighborhoods, as opposed to each pixel, is another way to increase speed.

Several performance-enhancing modifications to FLCT were implemented and more are planned.

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Conclusions• Accurate flow estimates will require

– deprojection of full-disk magnetograms, and– careful temporal filtering.

• Matching planned data cadences will be challenging. Solutions:– parallelization– find v(x1,x2) on tiles, not every pixel

– more restricitve |Bn| thresholding

• Essential tools for an LCT pipeline are in place.

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References• Démoulin & Berger, 2003: Magnetic Energy and Helicity Fluxes at the Photospheric

Level, Démoulin, P., and Berger, M. A. Sol. Phys., v. 215, # 2, p. 203-215. • Longcope, 2004: Inferring a Photospheric Velocity Field from a Sequence of Vector

Magnetograms: The Minimum Energy Fit, ApJ, v. 612, # 2, p. 1181-1192.• Schuck, 2005: Tracking Magnetic Footpoints with the Magnetic Induction Equation, ApJ

(submitted, 2006) • Welsch et al., 2004: ILCT: Recovering Photospheric Velocities from Magnetograms by

Combining the Induction Equation with Local Correlation Tracking, Welsch, B. T., Fisher, G. H., Abbett, W.P., and Regnier, S., ApJ, v. 610, #2, p. 1148-1156.

Yang’s e-mail.

“It would be great if you can talk about your ILCT method/ code

during the session. Because this session is ‘data products’ session,

… briefly summarize your algorithm first, and then focus onaddressing following issues:

1. Nature of the codes (Language, etc); 2. Additional supporting software (IDL, MATHLIB, ...); 3. Computational requirements (run time estimate,

system requirements, etc); 4. Requirements for the input data & format of the output

products; 5. Potential challenges, test procedures, target date for

completion of codes, etc... Time is 15 minutes, but … leave 5 minutes for further

discussion.”